1. No category

Estimating global radiation at ground level
from satellite images
Knut-Frode Dagestad
DOCTOR SCIENTIARUM THESIS IN METEOROLOGY
AT
UNIVERSITY OF BERGEN
MAY 2005
Preface
This synthesis and collection of papers constitute a thesis presented in partial fulfillment of the
requirement for the degree of Doctor Scientiarum in meteorology at the Geophysical Institute,
University of Bergen, Norway.
This thesis discusses the Heliosat algorithm which estimates solar radiation at ground level from
satellite images. The performance of various versions of the algorithm has been analysed, and
modifications are suggested.
Acknowledgments
First of all I want to thank my two supervisors, Arvid Skartveit and Jan Asle Olseth for excellent
support and invaluable feedback.
This work is a part of the project "Heliosat-3", which has been funded by the European Commision.
It has been a pleasure to work in the Heliosat-3 team, and the mood has always been humoristic and
positive, despite that we were missing our satellite for a long time. A special thanks goes to the
German colleagues Richard Müller, Rolf Kuhlemann and Hermann Mannstein who invited me to
stay in their private homes during three of my stays in Germany.
I also want to thank all the staff and students at the Geophysical Institute for a very good working
environment. In particular I want to mention Børge and Gard with whom I have shared my
refrigerator and many enjoyable moments. I also want to mention Yngvar Gjessing for sharing
some of his wisdom in many fields. Many thanks to Christiane and Frode for proofreading the
thesis.
I am also very grateful to the Nansen Center for financially supporting this work the last nine
months, and also for the very interesting new job which I am looking forward to do wholeheartedly
from now on.
Finally, thanks to my family and friends for helping me having a somewhat normal social life (at
least until recent months).
Bergen, May 2005
Knut-Frode Dagestad
Table of Contents
1 Introduction...................................................................................................................................... .1
2 History of the Heliosat algorithm..................................................................................................... .2
2.1 The original version.................................................................................................................. .2
2.2 Heliosat-1...................................................................................................................................3
2.3 Heliosat-2...................................................................................................................................4
2.4 Heliosat-3 (objectives of this thesis)..........................................................................................5
3 The concepts of the Heliosat algorithm.............................................................................................6
3.1 An empirical approach...............................................................................................................6
3.2 A physical approach...................................................................................................................6
3.3 A sensitivity analysis................................................................................................................ .8
4 Summary of results..........................................................................................................................12
4.1 Paper I...................................................................................................................................... 12
4.2 Paper II.....................................................................................................................................13
4.3 Paper III................................................................................................................................... 14
4.4 Paper IV................................................................................................................................... 14
4.5 Paper V.................................................................................................................................... 15
5 Concluding remarks.........................................................................................................................15
6 Bibliography.................................................................................................................................... 16
7 Part II - The papers I-V................................................................................................................... 17
List of Papers
Paper I
Dagestad, K-F. (2004). Mean bias deviation of the
Heliosat algorithm for varying cloud properties and sunground-satellite geometry. Theoretical and Applied
Climatology, 79, 215–224.
Paper II
Müller, R. W., Dagestad, K-F., Ineichen, P., Schroedter,
M., Cros, S., Dumortier, D., Kuhlemann, R., Olseth, J. A.,
Piernavieja, C., Reise, C., Wald, L. and Heinemann, D.
(2004). Rethinking satellite based solar irradiance
modelling - The SOLIS clear sky module. Remote Sensing
of the Environment, 91, 160-174.
Paper III
Dagestad, K-F. and Olseth, J.A. (2005). An alternative
algorithm for calculating the cloud index. Manuscript.
Paper IV
Dagestad, K-F. and Wald, L. (2005). Assessment of the
database HelioClim-2 of hourly irradiance derived from
satellite observations. Draft.
Paper V
Dagestad, K-F. (2005). Simulations of bidirectional
reflectance of clouds with a 3D radiative transfer model.
Manuscript.
1 Introduction
Every second the sun radiates more energy than people have used since the beginning of time. The
amount of solar energy reaching earth is 1.76 x 1017 joules per second; more than 10000 times the
global energy consumption today. Still this enormous source of energy accounts for only 0.1% of
the total consumption, whereas 77% comes from fossil fuels (Worldwatch Institute 2003). The
reasons for the low exploitation rate of solar energy are that it is difficult to collect since it is spread
over the whole earth, and difficult to predict since it is fluctuating in time and space. To increase the
efficiency of solar thermal power plants a detailed knowledge of the spatial and temporal variation
of solar irradiance is needed. Such a climatology can be made by interpolating between
measurement stations, as has been done in e.g. the European Solar Radiation Atlas, ESRA
(Scharmer 1994). However, low spatial and temporal resolution of such data has led to nonoptimal
site selection and incorrect system sizing, and thus unnecessary use of conventional energy sources.
Over the last two decades satellite-based retrieval of solar radiation at ground level has proven to be
highly valuable for the solar energy community. With satellite pixel sizes of typically 2.5
kilometres, the spatial resolution of the estimates is much better than the data interpolated from
ground measurements. It has also been found that for hourly values of global irradiance satellite
retrievals are more accurate than interpolating ground measurements from stations which are more
than 30 kilometres apart (Zelenka et al. 1999). However, the global markets for renewable energy
sources such as solar and wind power are expected to see a dramatic expansion in the near future
(Worldwatch Institute 2003), and there is a demand for solar radiation data of even higher quality.
This can be made possible with more sophisticated satellite technologies and by improvement of the
algorithms for conversion of satellite data into solar radiation data.
Heliosat is an algorithm which has been developed to estimate global horizontal irradiance at
ground level from images taken in the visible range by the European meterological satellite series
Meteosat. Starting with the launch of Meteosat-8 in August 2002 these satellites have now
increased capabilities; the size of a pixel is now 1 kilometre, compared to 2.5 kilometres earlier, and
the temporal resolution is increased from 2 to 4 images per hour. In addition, the number of spectral
channels is increased from 3 to 12, making it possible to get a more accurate description of the
atmospheric state. The work of this thesis deals with the improvement of the Heliosat algorithm,
partly by taking advantage of the enhanced capabilities of the new generation of the Meteosat
satellites.
The thesis is composed of two parts:
Part I provides an overview of the thesis. This introduction is the first chapter of this part. Chapter 2
gives an overview of the history of the Heliosat algorithm, and describes the various versions of the
algorithm which are referred to later in the thesis. Section 2.4 discusses the prospects of Heliosat-3,
the latest version which has been developed within the EU-project of the same name, based partly
on the work of this thesis. Therefore this section also gives the objectives of the thesis. Chapter 3
discusses the concepts behind the Heliosat algorithm, and also gives an analysis of how sensitive
the output of the algorithm is to some of its components. A summary of the five papers of the thesis
is given in chapter 4 and concluding remarks are given in chapter 5.
Part II encompasses the five papers which constitute the main scientific work of the thesis.
1
2 History of the Heliosat algorithm
The first experimental weather satellite, TIROS-I, was launched by the USA in 1960. After several
years of experiments the satellites were gradually improved and better adapted to their specific uses.
17 years later, in 1977, the European Space Agency launched Meteosat-1, the first satellite of the
European meteorological satellite system. The main purpose of the Meteosat-satellites was to
improve weather forecasts by giving the meteorologists a visual overview of the cloud cover on a
global scale. In addition, several other applications of the satellite images quickly emerged; among
them were methods to estimate the solar irradiance at ground level. However, the satellite data were
very simple; each pixel of the images consisted of a digital count between 0 and 255, and these
pixel counts could not even be reliably calibrated into radiances. Despite the input being simple, the
output of these algorithms was surprisingly accurate when compared to ground measurements. The
Heliosat algorithm, originally proposed by Cano et al. (1986), was one of the most popular
algorithms because it was accurate and easy to implement (Grüter et al. 1986).
Heliosat was widely used in operational schemes around the world (Wald et al. 1992), and over the
years it was modified several times. The naming of the different versions can be confusing, as a lot
of versions exist with only minor differences from others. The following sections describe the
versions which are referred to later in the papers of this thesis, and at the same time they give an
overview of the major steps of the evolution of the Heliosat algorithm.
2.1 The original version
The first journal paper about the Heliosat algorithm was published in 1986 (Cano et al. 1986). This
original version used uncalibrated counts of the Meteosat High Resolution Visible (HRV) sensor to
calculate a reflectivity of the pixels:
=
C
G clear
(1)
Here C is the digital counts of a pixel, an 8-bit number between 0 and 255, and Gclear is the clear sky
global irradiance at ground level from an empirical model. The clear sky model in the first Heliosat
scheme was very simple as it used only the solar elevation as input, and no information about the
atmospheric turbidity at the given site. As a second step a cloud index n was calculated from a time
series of reflectivities:
n=
−clear
cloud −clear
(2)
Here ρclear and ρcloud are the reflectivities corresponding to clear and overcast conditions,
respectively. ρclear was decided by a histogram technique so that it is the "most frequent low
reflectivity" of a given pixel for a given month. Similarly ρcloud was chosen as the "most frequent
high reflectivity". A simple linear relation was then assumed between the cloud index and the
clearness index kc:
k c≡
G
=anb
G TOA
(3)
The clearness index is the ratio of the actual global irradiance, G, to the irradiance at the top of the
atmosphere, GTOA. The parameters a and b were tuned to ground measurements at a number of sites
to minimise the deviation. Different values of the parameters were found for different sites and
2
times of day, reflecting diurnal and spatial variation of atmospheric turbidity.
Although this scheme was very simple in its principle, implementation was relatively complex: the
parameters a and b varied between the sites, and interpolation and extrapolation was done to
provide global application. In some operational versions different values of these parameters were
also used for morning, noon and afternoon. Consequently the accuracy was good at sites and times
for which the constants a and b were tuned, and less good at sites where they were interpolated.
2.2 Heliosat-1
"Heliosat-1" refers in this thesis to the modified version of the algorithm which was developed
within the EU-project "Satel-Light" (Fontoynont et al., 1998). This was the first operational large
scale implementation of the algorithm, and global irradiance and derived products for the period
1996-2000 are disseminated for most of Europe on the web server www.satel-light.com. The main
differences from the original version are described in Beyer et al. (1996), Fontoynont et al. (1998)
and Hammer (2000):

The reflectivity (ρ) is now calculated with:
=
C −C atm
G TOA
(4)
The radiation scattered back to the satellite from atmospheric molecules, Catm, is subtracted
from the satellite measurements so that ρ is a reflectivity of the ground and clouds only. An
empirical expression for Catm was developed by Beyer et al. (1996) and later modified by
Hammer (2000). The expression was tuned to digital counts of cloud free pixels over sea,
assuming that the reflected radiance from the sea surface is negligible compared to the
scattered radiance from air molecules.
Instead of normalising with a modelled clear sky irradiance, the irradiance at the top of the
atmosphere, GTOA, is now used in the normalisation.

The clearness index kc (Equation 3) is replaced by the clear sky index k, the actual global
irradiance, G, divided by the output of a clear sky model, Gclear:
k≡

G
G clear
(5)
In contrast to the relation between the cloud index and the clearness index (Equation 3)
which had to be tuned to ground data at all sites, the relation between the cloud index and
the clear sky index is now the same for any site. This new empirical relation is given by:
1.2
1−n
k=
2
2.0667−3.6667 n1.6667 n
0.05
for n −0.2
for n ∈[−0.2, 0.8]
for n ∈[ 0.8,1.1]
for n1.1
(6)
The cloud index is still calculated with Equation 2.
In the original version the spatial and temporal variation of atmospheric turbidity was accounted for
indirectly by tuning the parameters of the relation between the cloud index and the clearness index
(Equation 3). In the Heliosat-1 version the atmospheric turbidity is a directly input parameter to the
clear sky model. This is more convenient because such turbidity parameters are already available
3
for other purposes, and they are also easier to interpret physically, in contrast to the parameters a
and b of Equation 3.
The clear sky model used in the Satel-Light project consists of a model for the direct irradiance
from Page (1996) and a model for the diffuse irradiance from Dumortier (1995). As input they used
monthly values of Linke turbidities from a database developed by Dumortier (1998), height above
sea level and solar elevation. The Linke turbidity coefficients are commonly used in meteorology,
and account for the combined attenuation of broadband solar irradiance by aerosols and water
vapour.
For the operational scheme an average of 3 pixels in the north-south direction and 5 pixels in the
east-west direction was used, corresponding to a roughly square area in Europe where pixels are
longer in the north-south direction due to the oblique viewing angle. The averaging led to better
results, probably because the scale of this larger pixel-cluster better correlates the interval between
subsequent images (30 minutes) with typical movement of clouds which are obstructing the path
between the ground and the satellite sensor. Besides, this averaging is smoothing out the variability
related to non-lambertian reflectivity, an issue which is discussed in Paper V of this thesis.
In Heliosat-1 the ground albedo was calculated separately for each slot (images acquired at the
same time (UTC) of day belong to the same slot) for each month. This gave a better correlation with
ground measurements, probably because the sun-ground-satellite configuration was kept fairly
constant, thus minimising the effect of non-lambertian reflectivity.
2.3 Heliosat-2
Heliosat-2 uses the same principles as Heliosat-1, but a major difference is that calibrated radiances
instead of raw digital counts are used as input (Rigollier et al. 2004). The HRV sensor of Meteosat
is not calibrated routinely by Eumetsat, but a method for operational calibration was developed and
used at Ecole de Mines in France (Lefevre et al. 2000, Rigollier et al. 2002). Heliosat-2 was also
developed at Ecole des Mines, mainly during the EU-project SoDa from 2000-2001 (www.sodais.com).
With calibrated radiances as input, Heliosat-2 uses the opportunity to replace some of the empirical
parameters in the scheme with known physical/empirical models from external sources:

The correction for the backscattered radiation from the atmosphere (Equation 4) is based on
the ESRA clear sky model (Rigollier et al. 2000, Geiger et al. 2002). Here the clear sky
diffuse irradiance is multiplied with a factor (empirical though) to convert the diffuse
downwards irradiance to radiance upwards in the direction of the satellite.

For calculation of the reflectivity, the ESRA clear sky model is used to calculate the
transmissivity downwards to the ground and clouds and upwards to the satellite.

An expression for the reflectivity of the thickest clouds is based on measurements from the
Nimbus-7 satellite (Taylor & Stowe 1984).
No external physical model is used for the ground reflectivity, but rather second lowest value of the
reflectivity of a time series for a given pixel. The extreme minimum is avoided because it can be
due to artefacts in the processing of the satellite image. The relation between the cloud index and
the clear sky index is the same as in the Heliosat-1 version (Equation 6). Thus, despite a physical
calculation of the reflectivity, an empirical relation is still used to calculate the global irradiance
from the cloud index.
4
2.4 Heliosat-3 (objectives of this thesis)
This thesis is a part of the EU-project "Heliosat-3", with the objective of further development of the
Heliosat-algorithm to take advantage of the new generation of the Meteosat satellites. While the
first seven Meteosat satellites (1977 until present) had only three spectral channels, the next
generation (Meteosat Second Generation, MSG) has 12 spectral channels. When the project started
in May 2001 the objective was to create an algorithm which in principle consisted of two steps:
1. The new spectral channels of the MSG-satellites should be used to acquire a thorough
description of the atmospheric state for any pixel of any image:
- clouds (optical depth, coverage, height, phase (water/rain), effective droplet size)
- aerosols (type, single scattering albedo, optical depth)
- water vapour amount
- ozone amount
2. Given a description of the atmospheric state and the solar elevation, the global irradiance
and other spectral and angular components should be calculated, preferentially with an
advanced Radiative Transfer Model.
For the retrieval of the cloud properties, the scheme APOLLO (Saunders et al. 1988, Saunders
1988, Gesell 1989, Kriebel et al. 1989 and Kriebel et al. 2003) is adapted to the MSG satellites.
APOLLO was originally developed for the AVHRR sensor of the NOAA satellites, but adaptation
to MSG was performed within the project by the German Remote Sensing Data Center (Deutsche
Zentrum für Luft und Raumfahrt, DLR), one of partners of the Heliosat-3 consortium.
However, the launch of the first of the MSG-satellites was delayed from October 2000 until 28
August 2002. Furthermore, a power supply switched off unexpectedly in October 2002, resulting in
even more delay of the operation. Following was a period of commissioning and validation by
Eumetsat, and subsequently implementation of the APOLLO algorithm by DLR. Consequently the
APOLLO derived cloud parameters were not available for development of a new scheme until after
the official end of the project in May 2004. However, the EU extended the project until February
2005, but within the remaining time no improvement of the Heliosat algorithm was achieved by
integrating the cloud products in the scheme.
Anticipating the delay of data from MSG, the objective within the project was modified to improve
the Heliosat-1 scheme based on the calculation of a cloud index. The Heliosat-3 project also deals
with the calculation of other solar radiance component like splitting into direct and diffuse
radiation, and splitting into spectral components like Ultraviolet, Photosynthetically Active
Radiation, Solar Cell Response and Luminance/Illuminance, but this thesis is focusing mainly on
the calculation of the horizontal global irradiance.
The main objectives of this thesis are then:

To develop a clear sky model which can use the operationally retrieved values of aerosols,
water vapour and ozone as input. By replacing the simple empirical models used earlier with
a numerical Radiative Transfer Model it will also be possible to have spectral output which
will ease the subsequent calculation of spectral radiative parameters.

To improve the calculation of the cloud index with respect to the following points:

-
It should be based more on general physical principles and less on tuned empirical
parameters. This will ensure that the scheme will also work well for conditions different
from those where the tuning has taken place.
-
It should be as fast and easy to implement as possible for use in an operational scheme.
To assess the uncertainty related to sub-pixel variability of the cloud properties. A 3D
5
Radiative Transfer Model will be used to give advice on the ideal size of a pixel and
possibly also to suggest modifications to the scheme.

In general to improve the accuracy of the calculation of global irradiance, both on a short
term but also on longer terms by building the algorithm on physical principles. The
algorithm will then be easier to interpret/understand for further development.
3 The concepts of the Heliosat algorithm
Like radiation itself, the Heliosat algorithm has a dualistic nature. It can be interpreted as a physcal
algorithm, based on the equation for conservation of energy. However, it can also be interpreted as
a very simple empirical algorithm, which seems to work well mainly due to statistical cancelling of
errors. A very simple - perhaps naive - interpretation of the Heliosat algorithm is given in section
3.1, and in section 3.2 a more strict physical interpretation follows. Section 3.3 is an analysis of
how sensitive the output of Heliosat is to the choice of the parameters ρclear and ρcloud (Equation 2).
3.1 An empirical approach
A simple interpretation of the Heliosat algorithm is the following:
1. The reflectivity of a Meteosat pixel is calculated by normalising the raw digital counts with
incoming radiation at the top of the atmosphere.
2. From a time series the "typical lowest and highest reflectivities" are identified.
3. When the reflectivity is equal to the lowest value the irradiance at ground equals the output
of an empirical clear sky model.
4. When the reflectivity is equal to the highest value the irradiance at ground is estimated to be
zero.
5. For intermediate reflectivity the irradiance is linearly interpolated between zero and the clear
sky value.
Some corrections are then added to these simple principles:

The scattered radiation from air molecules is subtracted from the normalised digital counts
with an empirical formula. This makes the reflectivity more lambertian, at least for the clear
sky case, and hence it is easier to compare reflectivities measured under different sunground-satellite geometries.

Empirical experience tells us that even under the thickest cloud cover it is never completely
dark. When the reflectivity is close to the "typical highest reflectivity" the global irradiance
is therefore increased to ca 5-10% of the clear sky value.

It is found that by averaging the reflectivity over 3x5 pixels the accuracy of the algorithm is
higher when compared to ground measurements.
3.2 A physical approach
Conservation of energy implies that solar radiation reaching the top of the atmosphere can be either:
1. reflected to space,
2. absorbed in the atmosphere or
3. absorbed in the ground.
6
In the general case this can be expressed as:
I =RG 1− A
(7)
where

I is the incoming irradiance at the top of the atmosphere

R is the irradiance reflected to space

G is the irradiance reaching the ground (global irradiance)

α is the ground albedo

A is the radiation absorbed in the atmosphere
In the case of no clouds or overcast we have, respectively:
I = R clear G clear 1− Aclear
(8)
I =R cloud G cloud 1− A cloud
(9)
and
For these cases 'clear' and 'cloudy' atmospheres have to be defined for a reference.
By neglecting the atmospheric backscatter correction used in Heliosat-1 and Heliosat-2 (Equation
4), and assuming isotropic reflection in all cases, the calculation of the cloud index (Equation 2) is
equivalent with:
n=
R− Rclear
R cloud −R clear
(10)
where radiances have been replaced by irradiances. Solving for these irradiances in Equations 7-9
and inserting into Equation 10 gives:
n=
1− Gclear −G  Aclear− A
1−G clear −G cloud  Aclear− Acloud
(11)
Solving again for the global radiation G in the general case and introducing the clear sky index k
gives:
k≡
G cloud
n  A cloud− A clear Aclear− A
G
=1−n
n
G clear
G clear
1− G clear
(12)
By neglecting the variation of atmospheric absorptance (A=Aclear=Acloud) this reduces to:
k =1−n
G cloud
n
G clear
(13)
A typical value for the ratio Gcloud/Gclear is 0.1, but it depends on the solar elevation and the choice of
the reference cloud. Equation 13 is not identical to the empirical relation which has been tuned for
best performance of the actual Heliosat algorithm (Equation 6), but there are also several
differences between the "real world" and this idealised version:

Reflectivities are not generally lambertian.
7






A correction for the backscattered radiation from air molecules is used in Heliosat.
The absorptance in the atmosphere varies with solar elevation, cloudiness and turbidity.
The Meteosat HRV sensor does not measure broadband radiances but is limited to 0.45-1.0
micrometres.
Heliosat is tuned to give best correlation between estimated global irradiance averaged over
an area (satellite pixel) at a single point in time, and measured global irradiance at ground at
a single spot but averaged in time.
The theoretical model considers an atmosphere which is homogeneous in the horizontal
direction. In reality there are large variations, especially of cloud properties. Thus the
empirical relations implicitly account for effects like reduced irradiance due to shadows
from nearby clouds, and enhanced radiation due to scattered radiation from broken clouds.
The broadband ground albedo α will change slightly when the spectral variation of the
incoming irradiance is changing due to varying atmospheric conditions and solar elevation.
3.3 A sensitivity analysis
Whether Heliosat is interpreted physically or empirically, the definitions of the reference
reflectivities for clear and overcast conditions (ρclear and ρcloud, respectively) are vital. In the various
versions of the Heliosat algorithm these parameters are calculated in different ways:

In the original version of the Heliosat algorithm (Cano et al. 1986) ρclear and ρcloud were
defined as the "most typical values of the reflectivity for clear and overcast conditions".
These values were calculated from a time series of the reflectivities with a histogram
technique to find the most frequent high and low values from the typical bi-modal
distribution.

In Heliosat-1 the parameter ρcloud was set to the constant of 160 normalised digital counts for
all pixels (Hammer 2000). This value was chosen as the 96 percentile of a time series of all
the reflectivity values for the whole field of view of Meteosat.

In Heliosat-2 an external empirical model was used for ρcloud since calibrated radiances were
used as input instead of uncalibrated digital counts, whereas the parameter ρclear was taken as
the second lowest value of a time series.
For consistency with Equation 6, a stringent definition of ρclear should be "the reflectivity for which
the global irradiance at ground is equal to the clear sky model". Similarly the definition of ρcloud
should be "the reflectivity for which the global irradiance at ground is equal to 6.7% of the clear sky
model (Equation 6 evaluated at n=1)"
The global irradiance calculated with Heliosat is given by Equation 5, which can be written as:
G=Gclear k  n
(14)
It is obvious from this equation that the error of the estimated global irradiance is proportional to
the error of the clear sky model. Thus an accurate clear sky model is vital. The sensitivity of the
estimated global irradiance to the parameter ρclear can be found by differentiating Equation 14:
dG
dk ∂ n
=G clear
dn ∂ clear
d  clear
The relative sensitivity is given by:
8
(15)
1 dG
1 dk ∂n
=
G d  clear k n dn ∂ clear
(16)
Assuming first a simple relationship k = 1 - n, Equations 15 and 16 become, respectively:
cloud −
dG
=G clear
d  clear
cloud −clear 2
(17)
1 dG
1
=
G d  clear cloud −clear
(18)
and
For the parameter ρcloud the corresponding absolute and relative sensitivities are, respectively:
−clear
dG
=G clear
2
d  cloud
cloud − clear 
(19)
−clear
1 dG
=
G d cloud  cloud −clear cloud −
(20)
and
Figure 1 shows the sensitivities from Equations 17, 18, 19 and 20 plotted versus the cloud index for
typical values of ρclear and ρcloud of 0.2 and 0.8 respectively. On the upper part of the figure one can
see that the estimated global irradiance is most sensitive to ρclear for clear cases and to ρcloud for
cloudy cases. The magnitude is, however, equal: a 0.01 too high value of ρclear will give an
overestimation of global irradiance by almost 2 percent of the clear sky values for clear cases, and a
0.01 too high value of ρcloud will give the same overestimation of global irradiance for the cloudy
cases. Hence if one assumes equally many clear and cloudy cases, the average bias of the Heliosat
algorithm is equally sensitive to both parameters. However, since the irradiance is lower for the
cloudy cases, the relative bias for the cloudy cases is much higher, as seen on the lower part of
Figure 1.
9
Figure 1: Sensitivity to the parameters ρclear and ρcloud of the global irradiance estimated with the Heliosat-algorithm.
Values of 0.2 and 0.8 are used for ρclear and ρcloud respectively. The upper figure shows the change, in units of the clear
sky irradiance Gclear, resulting from a unit change of the parameters ρclear and ρcloud. This is calculated with equations 17
and 19, respectively. The lower figure shows the same, but the unit of change is the fraction of the actual estimated
irradiance. This is calculated with equations 18 and 20.
Figure 2 shows the sensitivities using the relation between the clear sky index and the cloud index
which is used in Heliosat-1 and Heliosat-2 (Equation 6). The relative sensitivity to the parameter
ρcloud is now not singular for a cloud index of one, as it is for the simple relation k=1-n. However,
the lower part of the figure shows that a value of ρcloud which is too large by only 0.01 will lead to an
overestimation of the global irradiance by almost 10 percent for the cloudy cases.
10
Figure 2: Same as Figure 1, but the relationship between the clear sky index and the cloud index is given by equation 6
from Fontoynont et al. (1998). The new equations corresponding to equations 17, 18, 19 and 20 are not shown in the
text.
11
4 Summary of results
4.1 Paper I
The first paper is mainly a validation of the Satel-Light version of the Heliosat-algorithm (section
2.2). The objective of this work was to identify how well the algorithm is working for various
situations and from that find out how it can be improved. To investigate the influence of the sunground-satellite geometry, the performance of the algorithm was analysed for variations of the three
angles shown on Figure 3.
For overcast situations Heliosat gave too high solar irradiance for low sun and too low irradiance
for high sun. For clear situations there were no such biases. In Heliosat there is an implicit
assumption that the variation of solar irradiance with solar elevation is similar for clear and cloudy
cases. However, numerical simulations with a radiative transfer model showed that irradiance at
ground is decreasing faster with solar zenith angle for overcast conditions than for clear conditions.
A semi-empirical correction for this was suggested.
The deviation between satellite estimates and ground measurements also depends on the solar
azimuth angle (or time of day), but much of this variation can be explained by the correlation
between the azimuth angle and the solar zenith angle. However, for Bergen it was found that while
the modelled global irradiances were symmetric around noon, the measurements were higher in
afternoon than in the morning. This asymmetry was only found for intermediate cloudiness, thus
suggesting an explanation: even though the average cloudiness did not change with time of day, the
scattered clouds were more likely to be positioned over land (to the east) than over sea (to the west).
Thus there is greater chance that a given cloud fraction will make shadows at the pyranometer in the
morning than in the afternoon. Heliosat relies on the hypothesis that clouds are randomly placed
within a pixel, but this "frozen turbulence hypothesis" seems to be violated for Bergen. Empirical
corrections for this phenomenon can easily be implemented for a particular site like Bergen, but a
general correction is impossible without knowledge of the local conditions for each pixel.
The bias is also seen to depend strongly on the co-scattering angle ψ (Figure 3), but again most of
this is seen to be due to the correlation with solar zenith angle. When this correlation is corrected
for, the opposition effect is seen: when the sun and the satellite are in the same direction (ψ is close
to zero) less shadow is seen, and hence the reflectivity is higher. This gives a higher cloud index,
and thus the global irradiance is underestimated.
The performance of Heliosat was also analysed in light of the total cloud cover and the height of the
base of the lowest clouds, as estimated from human observers at ground. For Bergen it was seen
that for overcast situations the observed irradiance was smaller than the modelled irradiance. A
possible explanation for this is that the clouds in Bergen are very thick, something which also is
found by Leontieva et al. (1994). A correction for this can be possible with the second generation of
Meteosat satellites (MSG), from which cloud optical thickness can be retrieved by use of more
spectral channels. It was also found that Heliosat overestimated global irradiance when the observed
height of the cloud bases was very low. Numerical simulations with a radiative transfer model
suggest an explanation: by increasing the height of the clouds, the irradiance reaching ground is
constant, while the increased reflection is perfectly matched by a decrease of radiation absorbed in
the atmosphere. With the MSG satellites cloud (top) height will also become available, and hence a
correction for the influence of the cloud height can be implemented.
12
Figure 3: The three angles which are used in this thesis to describe the sun-ground-satellite configuration: solar zenith
angle (θ), satellite zenith angle (φ) and co-scattering angle (ψ).
4.2 Paper II
One of the objectives of the Heliosat-3 project was to include a Radiative Transfer Model (RTM)
directly into the scheme. The advantage of using an RTM is that it can take more detailed input data
than the simple models used earlier, and that it can produce spectral output in addition to integrated
broadband irradiances. However, it will be unrealistic to run an RTM for each pixel in each image.
With approximately 2.5 million pixels to be processed for each image, and an RTM runtime of
typically 5 seconds, it would take approximately 3500 hours to process one image. Since MSG
produces one image every 15 minutes this approach can not be used in an operational scheme, even
with the fastest computers available. Paper II introduces a workaround solution to this problem: an
RTM will be used for the clear sky calculations only, and with a spatial resolution of 100 times 100
kilometres. This reduces the runtime to a manageable length, while keeping adequate resolution to
describe the spatial variation of atmospheric turbidity. The full resolution will only be used for
calculating cloud parameters, which will then be combined with the clear sky calculations with a
simple empirical relationship to estimate the radiation at ground. The cloud parameters can then be
the traditional cloud index, but also the more physical cloud parameters retrieved with the APOLLO
scheme. The paper demonstrates that it is sufficient with two model runs per pixel per day, and that
the diurnal variation of the clear sky irradiance can be parameterised with the output from the two
model runs. Paper II was mainly written by the first author, Richard Müller. My contribution was
discussion and development of the concept of how to reduce the necessary number of runs with an
RTM, during a stay in Oldenburg, during project meetings and by email. I also wrote section 4.3 of
the paper, a validation of the scheme using daily values of ozone and water vapour and
13
climatological values of aerosol type and optical depth.
4.3 Paper III
This paper presents two modifications to the algorithm which is used to calculate the cloud index.
The first modification concerns the backscatter correction in the Heliosat scheme (Equation 4). In
the calculation of the cloud index the part of the satellite signal that is scattered from the
atmospheric molecules is subtracted. This correction was introduced by Beyer et al. (1996), and an
empirical expression was developed. By assuming that the reflected radiance from the sea surface is
negligible to the contribution scattered from the air molecules, Beyer et al. fitted an expression to
the count values of Meteosat HRV images for a number of cloud free pixels over sea in Western
Europe for August 1993. In Hammer (2000) this expression was modified by fitting to a larger
database. Paper III of this thesis replaces these empirical expressions with an analytical expression.
This is possible by assuming a plane-parallel atmosphere and that multiple scattering is negligible
for the wavelengths of the satellite sensor. The expression is derived for monochromatic radiation,
but it is demonstrated that by use of an "equivalent wavelength" it is not necessary to perform
integration over the spectral region of the sensor. While the empirical expressions used earlier are
tuned for a particular satellite sensor, the new analytical expression can easily be adapted to other
sensors. Furthermore, while the empirical equations are fitted to certain sun-ground-satellite
configurations (Figure 3), the new expression is valid for all angles for which the plane-parallel
approximation is reasonable.
The second modification concerns the calculation of the reflectivity of the ground for each pixel. In
earlier versions of Heliosat this parameter (ρclear) was determined for each month and each slot. This
assures that the sun-ground-satellite geometry is fairly constant, and therefore avoids partly the
problem of non-lambertian reflection. However, this is a time consuming part of the algorithm, and
besides it can be difficult to determine ρclear for months and slots with few clear situations. In Paper
III it is demonstrated that the lower bound of reflectivity can be parameterised with the coscattering angle (ψ on Figure 3). Thus the ground albedo for each pixel can be calculated once and
for all, and the algorithm will then be significantly faster and simpler to implement.
Global irradiances are calculated using both the modified cloud index from this paper and the
traditional cloud index from the Heliosat-1 version (Section 2.2). Two different clear sky models
are also used for the calculations: the model from Heliosat-1 and the new SOLIS model developed
in Paper II, both using climatological input of turbidity data. When compared to ground
measurements at five European stations, it is found that the accuracy is quite similar for all of the
four combinations of the two cloud indices and the two clear sky models. However, it is found that
the new cloud index is on the average higher than the traditional one, particularly for low values as
it is less frequently negative, and that the SOLIS model gives generally lower clear sky values than
the traditional clear sky model. Consequently the new cloud index gives best results when
combined with the old clear sky model, and vice versa. It is therefore important to be aware of this
when combining a cloud index with a clear sky model in the Heliosat scheme.
4.4 Paper IV
Paper IV gives a validation of the database HelioClim-2, which provides global irradiance for the
solar energy and daylight community on the internet. The HelioClim-2 data is calculated with the
Heliosat-2 algorithm (section 2.3) using Meteosat images which are sampled in both time and space
as input. The sampling is done to be able to efficiently process long time series of data for the whole
field of view of Meteosat for climatological purposes. In this paper five European ground stations
are used for the comparison.
14
For daily values of global irradiance HelioClim-2 performs much better than the previous version of
the database (HelioClim-1) which used a lower sampling frequency in both time and space.
However, HelioClim-2 gives a larger Root Mean Square Deviation than Heliosat-1 (section 2.2).
Most of this difference is probably due to the sampling of the satellite data, but some of it can also
be due to differences between the Heliosat-1 and Heliosat-2 algorithms.
HelioClim-2 overestimates the global irradiance for all five ground stations, and for the station
Bergen the bias is as large as 21%. Since there are also more cloudy cases in Bergen than for the
other sites, it is suggested that Heliosat-2 overestimates the global irradiance for the cloudy cases. It
is shown that this overestimation can be due to a too high value for the cloud reflectivity.
This paper is a draft only. The second author, Lucien Wald, will later conclude the paper with a
discussion of the effects of interpolating and sampling the satellite data which are input to
HelioClim-2. Besides, HelioClim-2 will be reprocessed with a lower value of the cloud reflectivity,
as suggested in the draft, to see if the bias will be smaller.
4.5 Paper V
The greatest challenge of the Heliosat algorithm is that cloud properties are varying on a scale
which is often smaller than the size of the satellite pixels. This sub-pixel variability cannot be
accounted for directly, since detailed information is missing. Nevertheless it is of interest to have an
estimate of the variability of the reflected radiance for different sizes of the pixels. In this paper a 3dimensional radiative transfer model, SHDOM, is used to simulate the reflectance towards a
satellite from two different cloud fields. One is a rather homogeneous stratocumulus field, but with
typical 'bumps' on the top, and the second is a broken cumulus field with only scattered clouds.
With the sun and 'satellite' in fixed positions, the cloud fields are rotated in the azimuth direction. It
is found that by observing the full stratocumulus field of 3520 metres, there is no variation of the
reflectance. For the cumulus cloud field the variability is approximately 10-20 percent, even though
the size of this field is larger; 6700 metres. Looking at smaller subsets of the cumulus cloud field,
the variability is extreme, while for the stratocumulus field it is more moderate.
In Paper V the distribution of reflected radiance from the stratocumulus field in different directions
is also compared with reflectances measured with Meteosat. When plotted versus the co-scattering
angle (ψ on Figure 3) it is found that the reflectance of the thickest clouds measured with Meteosat
is rather homogeneous, but with a minimum around ψ = 60 degrees. The simulated reflectances
depend on ψ in a qualitatively similar way, but the variation is much larger: the reflectivity for ψ =
60 degrees is only 50 percent of the reflectivity for ψ close to zero (i.e. when the sun and the
satellite are in the same direction, as seen from the cloud field). One of the objectives of this study
was to find a parameterization of ρcloud, the albedo of the thickest cloud used in Heliosat. However,
it was found from the Meteosat reflectivities that the thickest clouds were close to lambertian
reflectors while the angular distribution of radiances was more variable for low and intermediate
cloudiness. Hence, it should make more sense to parameterise the cloud index - clear sky index
relationship with ψ than parameterising the reflectivity of the thickest clouds.
5 Concluding remarks
Heliosat is an algorithm for estimating solar radiation at ground from images taken in the visible
range by geostationary satellites. This algorithm consists in principle of two parts: 1) a model to
describe the radiation at ground level when there are no clouds, and 2) a method to combine the
output of this clear sky model with a measure of the cloud cover to estimate the solar radiation in
the general case when there are clouds.
Paper II of this thesis shows a new clear sky model scheme, SOLIS, which is based on a numerical
15
Radiative Transfer Model, replacing the simple empirical models used earlier. Firstly, this permits
the use of more detailed information about aerosols (dust), water vapour and ozone as input,
parameters that in the near future will be retrieved operationally using the new generation of the
Meteosat satellites. Secondly, the model also provides spectral output which will be useful for
deriving specific solar radiation parameters like Ultraviolet radiation, Photosynthetically Active
Radiation, Illuminance (visible light) and Solar Cell response. The SOLIS model is seen (in papers
II, III and IV) to give reasonable results using climatological input parameters. However, the
potential of the scheme can only be released in the near future when operationally retrieved
atmospheric parameters are used as input.
Paper III suggests two modifications to the traditional algorithm for calculation of the 'cloud index'.
First, a parmeterisation of the effect of non-lambertian reflection from ground makes the algorithm
significantly faster and easier to implement. Second, an analytical correction for the radiation
scattered from the atmospheric molecules towards the satellite is derived, replacing an empirical
expression in the original algorithm. This makes the algorithm more general, and also easier to
interpret and develop further. A validation versus ground measurements shows that the accuracy
using the new cloud index is similar to using the old one. However, it is also demonstrated how
biases which are due to the cloud index and the clear sky model can cancel or add up, and thus it is
important that these two separate components of the algorithm are "kept in balance" with each
other.
Papers I and IV are validations of several different versions of the Heliosat algorithm. This has
given a basis for understanding the algorithm and several corrections and modifications are
suggested. Paper V is an assessment of the influence of sub-pixel variability of cloud properties on
the reflectance.
6 Bibliography
Beyer H.G.; Costanzo C.; Heinemann D;, 1996: Modifications of the heliosat procedure for
irradiance estimates from satellite images, Solar Energy, 56, 207-212.
Cano D; Monget JM;, Albuisson M; Guillard H; Regas N; Wald L;, 1986: A method for the
determination of the global solar radiation from meteorological satellite data, Solar Energy, 37, 3139.
Dumortier, D, 1998: The Satel-Light model of turbidity variations in Europe. Report for the 6th
Satel-Light meeting in Freiburg, Germany, September 1998
Dumortier, D, 1995: Modelling global and diffuse horizontal irradiances under cloudless skies
with different turbidities. Technical report for the Daylight II project, JOU2-CT92-0144
Fontoynont, M; Dumortier, D; Heinemann, D; Hammer, A; Olseth, J A; Skartveit; Ineichen,
P; Reise, C; Page, J; Roche, J; Beyer, H; Wald, L, 1998: Satel-Light: A www server which
provides high quality daylight and solar radiation data for western and central Europe. Proc. 9th
conference on satellite meteorology and oceanography in Paris, 25-28 May 1998, pp. 434-437
Geiger M.; Diabaté L.; Ménard L.; Wald L., 2002: A Web service for controlling the quality of
global solar irradiation, Solar Energy, 73 (6), 475-480.
Gesell, G., 1989: An Algorithm for Snow and Ice Detection Using AVHRR Data: An Extension to
the APOLLO Software Package, International Journal of Remote Sensing, 10 (4-5), 897-905.
Grüter, W.; Guillard, H.; Möser, W.; Monget, J-M.; Palz, W.; Raschke, E.; Reinhardt, R.E.;
Schwarzmann, P. and Wald, L., 1986: Solar Radiation Data from Satellite Images. Solar Energy
R&D in the European Community, Series F, Volume 4, D. Reidel Publishing Company, p. 100
Hammer, A, 2000: Anwendungsspezifische Solarstrahlungsinformationen aus Meteosat-daten,
PhD thesis, University of Oldenburg.
16
Kriebel K. T., Gesell G., Kästner M., Mannstein H, 2003: The cloud analysis tool APOLLO:
Improvements and Validation, Int. J. Rem. Sens, 24, 2389-2408.
Kriebel, K.T.; Saunders, R.W.; Gesell, G., 1989: Properties of Clouds Derived from Fully
Cloudy AVHRR Pixels, Beiträge zur Physik der Atmosphäre, 62 (3), 165-171.
Lefèvre M.; Bauer, O.; Iehle, A.; Wald, L., 2000: An automatic method for the calibration of
time-series of Meteosat images, International Journal of Remote Sensing, 21 (5), 1025-1045.
Leontieva, E; Stamnes, K; Olseth, J A;, 1994: Cloud optical properties at Bergen (Norway) based
on the analysis of long-term solar irradiance records, Theoretical and Applied Climatology, 50, 7382.
Page, J, 1996: Algorithms for the Satel-Light programme. Technical report for the Satel-Light
programme
Rigollier C; Bauer O; Wald L;, 2000: On the clear sky model of the 4th European Solar Radiation
Atlas with respect to the Heliosat method, Solar Energy, 68(1), 33-48.
Rigollier C.; Lefèvre M.; Blanc Ph.; Wald L., 2002: The operational calibration of images taken
in the visible channel of the Meteosat-series of satellites., Journal of Atmospheric and Oceanic
Technology, 19 (9), 1285-1293.
Rigollier, C; Lefèvre, M; Wald, L, 2004: The method Heliosat-2 for deriving shortwave solar
radiation from satellite images, Solar Energy, 77, 159-169.
Saunders, R.W, 1988: Cloud top temperature/height: A high resolution imagery product from
AVHRR data, Meteorological Magazine, 117, 211-221.
Saunders, R.W. and K.T. Kriebel, 1988: An improved method for detecting clear sky and cloudy
radiances from AVHRR data, International Journal of Remote Sensing, 9, 123-150.
Scharmer, K;, 1994: Towards a new atlas of solar radiation in Europe, Solar Energy, 15, 81-87.
Taylor, V.R.; Stowe, L.L., 1984: Atlas of reflectance patterns for uniform Earth and cloud surfaces
(Nimbus 7 ERB - 61 days). NOAA Technical report NESDIS
Wald, L.; Wald, J-L. and Moussu, G., 1992: A technical note on a low-cost high-quality system
for the axquisition and digital processing of images of WEFAX type provided by meteorological
geostationary satellites, International Journal of Remote Sensing, 13, 911-916.
Worldwatch Institute, 2003: State of the World 2003, New York: W.W. Norton & Company.
Zelenka A.; Perez R.; Seals R.; Renne D., 1999: Effective accuracy of satellite-derived hourly
irradiances, Theor. Appl. Climatol., 62, 199-207.
7 Part II - The papers I-V
17
Paper I
Dagestad, K-F. (2004)
Mean bias deviation of the Heliosat algorithm
for varying cloud properties and
sun-ground-satellite geometry
Theoretical and Applied Climatology, 79
215–224
Theor. Appl. Climatol. 79, 215–224 (2004)
DOI 10.1007/s00704-004-0072-5
Department of Geophysics, University of Bergen, Bergen, Norway
Mean bias deviation of the Heliosat algorithm for varying
cloud properties and sun-ground-satellite geometry
K.-F. Dagestad
With 10 Figures
Received October 26, 2003; revised April 5, 2004; accepted May 20, 2004
Published online September 29, 2004 # Springer-Verlag 2004
Summary
Reflectances measured by the ‘visible’ channel of Meteosat
are converted to global radiation at the ground by the
Heliosat-algorithm. This algorithm is based on the inverse
relationship between reflectance and transmittance. This
relationship is, however, complicated by two factors: 1) the
absorptance of the atmosphere is varying, and 2) the reflectivity is different in different directions. These two
factors are again depending on the state of the atmosphere
(mainly clouds) and the sun-ground-satellite geometry. The
performance of the Heliosat-method is here tested against
ground data from Bergen (Norway), Geneva (Switzerland)
and Lyon (France), and analysed in light of cloud properties
as observed from ground, and different sun-ground-satellite
geometries. Situations where modelled and measured
radiation differ are identified, and possible causes are suggested. Some of the suggestions are supported by calculations with a radiative transfer model.
1. Introduction
Geostationary satellites have become a valuable
tool for estimation of global radiation at ground
level. Although ground measurements often will
be the most accurate for a fixed position, the
network of measuring sites is sparse, especially
over sea. The spatial coverage is substantially
improved by a geostationary satellite, which covers almost half of the earth, with typical pixel
sizes of 5 5 km2. The satellite vs. ground truth
Root Mean Square Deviation (RMSD) for hourly
global irradiance is typically 20–25%, which is
comparable to the accuracy obtained by interpolation from ground stations some 20–30 km apart
(Zelenka et al., 1999).
Still there is some potential for improvement;
through newer satellites (more channels, smaller
pixels, higher time resolution) and refinement of
the conversion algorithms (e.g. Heliosat). With
the Meteosat Second Generation (MSG) satellites, more information about the atmospheric
state (including clouds) will be available. This
information can improve the scheme, if the effect
of the various parameters can be properly accounted for.
For this paper the performance of the Heliosat
method is analysed with respect to variations of
the Mean Bias Deviation (MBD) due to different
cloud properties or sun-ground-satellite geometries. Heliosat-derived hourly global irradiances
are compared to ground measurements in Bergen,
Norway (60.4 N, 5.3 E), Geneva, Switzerland
(46.2 N, 6.1 E) and Lyon, France (45.8 N,
4.9 E) for the years 1996 and 1997. The performance of the Heliosat method was tested against
seven Norwegian and five other European stations by Olseth and Skartveit (2001). Tests of
satellite based estimates against ground truth data
have also been done by Ineichen and Perez
(1999). These papers did not, however, use infor-
216
K.-F. Dagestad
*
Fig. 1. Three of the angles used in this paper: solar zenith
angle , satellite zenith angle and co-scattering angle .
Not shown on this figure is the solar azimuth angle, which
relates the solar position to the north-direction
mation about observed ground truth cloud properties and the sun-ground-satellite angles, except
for the solar elevation.
Three angles affect the signal received by
Meteosat: 1) the solar zenith angle , 2) the satellite zenith angle , and 3) the ‘co-scattering
angle’ , between the direction towards Meteosat
and the sun as seen from ground. These angles
are shown on Fig. 1. Of these, only the solar
zenith angle affects the global radiation measured at ground.
The signal received by the Meteosat VISsensor (0.5–0.9 mm) is scattered=reflected from
four different scattering agents:
*
*
*
Clouds are the main reflectors of solar radiation in the earth-atmosphere system. They
absorb moderately, but the scattering is very
strong. Angular distribution of scattering from
individual cloud droplets is well known from
theory (Mie), but ice crystals, multiple scatter
and macroscopic cloud structure make the picture more complex.
Aerosols, like cloud droplets, are also scattering strongly forward. They are, however, more
evenly distributed, and exist in smaller
amounts. The collective scattering from an
aerosol layer is therefore closer to the angular
distribution given for individual particles by
the Mie-theory.
The third scattering agent is the air molecules.
Because of their smaller sizes they scatter
solar radiation according to the theory of
Rayleigh; symmetric in the forward- and backward directions, with smaller amounts to the
sides.
The satellite signal also contains radiation reflected from the ground. For terrestrial surfaces
the reflection is nearly isotropic (Lambertian).
However, for rough surfaces, there will be
strong backward reflection, since an observer
(satellite) in this position will see less shadows
(opposition effect). For ocean the reflection
can be strong in the forward direction if the
sun is low (specular reflection).
Since each of these four scattering agents has
different angular distributions, it is difficult to
find a general relationship between the radiance
towards a satellite and the top of atmosphere
reflection. However, some semi-empirical corrections exist in the Heliosat-scheme (next
section).
Some of the solar radiation is also absorbed in
the atmosphere, typically 10–15% for high sun
and up to 20–30% for low sun. The main absorbers are water vapour, aerosols, and ozone.
Quantitatively water vapour is most important,
but since the most intense water vapour absorption bands are quickly saturated, the absorptivity
due to water vapour is normally not very variable. Aerosols are more variable, however, both
in amount and type, and therefore changing aerosol conditions may have large impacts on the
global radiation. Absorption by ozone is generally small for global solar irradiances, but may be
important for a satellite received signal in case of
dense cloud cover and low sun, when the radiation makes a long path through the ozone layer,
both downwards and upwards. The total absorptivity is sensitive to the solar zenith angle, which
determines the path length of the photons. A
change of the atmospherical absorptivity disturbs
the inverse relationship between reflectance
and transmittance. Since it is not directly measured it has to be estimated by an empirical
formula.
2. The Heliosat method
The Heliosat method was first proposed by Cano
et al. (1986). It has been modified several times,
and is still under development. The version
Mean bias deviation of the Heliosat algorithm
presented here is the version used by the SatelLight project (www.satel-light.com; Iehle et al.,
1997; Hammer et al., 1998, 2003). The method
consists of two clearly separated steps:
1. First a ‘cloud index’ is determined from time
series of pixel counts from the VIS-channel of
Meteosat (0.5–0.9 mm). The cloud index is a
measure of the relative reflectivity of the
clouds (in the direction of Meteosat).
2. The cloud index is combined with an empirical clear sky model to give the global irradiance at ground.
The details are as follows:
2.1 Finding the cloud index
The relative reflectivity of a pixel is defined by:
C C0 Catm
ð1Þ
" cos where " is the correction for the sun-earth distance, C is the raw pixel count of Meteosat (an
integer between 0 and 255), and C0 is an instrument offset used to adjust the null point of the
sensor. Catm is the contribution scattered from the
cloud free atmosphere. This part is subtracted
because of its highly anisotropic character. Catm
has been estimated with semi-empirical formulas, depending only on the three angles shown
on Fig. 1. For the Satel-Light project the following formula was used:
Catm ¼
ð1 þ cos 2
217
and no correction are made for e.g. the opposition effect. The cloud index is 1 when ¼ c and
zero when ¼ g. Due to the anisotropy of the
reflected radiation, n can thus be smaller than 0
or greater than 1.
2.2 Determining the global radiation
from the cloud index
The Heliosat method is based on an empirical
relationship between the cloud index and the
clear sky index k defined by:
G
ð4Þ
k
Gclear
where G is the actual global radiation and Gclear
is global solar irradiance estimated by a clear sky
model. Input data to this model are the solar
zenith angle and climatologial monthly values
of the Linke turbidity factor at the relative optical
air mass of 2. The direct part of the clear sky
model is given by Page (1996), and the diffuse
part by Dumortier (1995). For the direct part also
the height above sea level is used as an input
parameter.
The relation between n and k used by the
Satel-Light project is:
k ¼ 1:2
for n 0:2
k ¼1n
for 0:2n0:8
2
ð5Þ
for
0:8n1:1
k ¼ 3155nþ25n
15
k ¼ 0:05
for n 1:1
————————————————————
2
Þð0:55 þ 25:2 cos 38:3 cos þ 17:7 cos 3 Þ
ð2Þ
cos 0:78 ————————————————————
The cloud index is then defined by:
g
n
c g
ð3Þ
where is the relative reflectivity of the actual
pixel, and g and c is the relative reflectivity of
the same pixel with no clouds and overcast conditions, respectively. g is taken as the most frequent value for each pixel, and different values
are used for each month. c is the relative reflectivity of a very dense cloud cover; a constant
value (of 160) was chosen for all pixels, taken
as the 96 percentile point for all pixels from a
time series. This means that both clouds and
ground are treated as Lambertian in Heliosat,
This formulation ensures that G ¼ Gclear when
n ¼ 0 and not less than 5% of Gclear even under
the thickest clouds. The role of the clear sky
model is actually to estimate the absorption in
the atmosphere, which is not measured directly.
A k ¼ 1 n relation is equivalent to assuming
that the absorptivity does not change with
cloudiness.
3. Description of data
3.1 Observed global irradiances
For all three sites global radiation is measured with
Kipp & Zonen pyranometers; CM6 in Lyon and
218
K.-F. Dagestad
CM10=CM11 in Geneva (http:==idmp.entpe.fr)
and Bergen (Radiation Yearbooks 1996–1997).
For Bergen the measurements are given as hourly
values in solar time, where e.g. the values at 12
means measurements between 11:30 and 12:30.
For Geneva and Lyon the timing of the measurements was different, but the data were summed
and weighted to yield the same time format as for
Bergen. To ensure high quality of the data, only
hours with the sun entirely above the horizon are
used, with the second criteria that the mean solar
elevation for the hour is also at least 10 . Data
from November to April were not used for any of
the sites due to potential snow cover.
3.2 Global irradiances from Heliosat
From the Satel-Light webpage (www.satel-light.
com), estimates of global irradiances were downloaded for the three sites for the years 1996 and
1997. Data are given each 30 minutes (repetition
cycle of Meteosat). Hourly values of the Heliosatestimates were created by weighting with the
number of minutes they overlap a given hour.
Each satellite measurement was assumed to have
a ‘radius of coverage’ of 15 minutes, which
means that e.g. the hour 12 (11:30–12:30) is covered by satellite measurements within the interval 11:15–12:45.
The pixel size for the ‘visible’ Meteosatchannel is 2.5 2.5 km2 at nadir, with increasing
size away from the sub-satellite point. In Central
Europe (like Geneva and Lyon) a pixel covers
approximately 2.5 km in longitude and 4 km in
latitude. For Bergen the corresponding numbers
are 2.5 km in longitude and 7 km in latitude.
Tests within the Satel-Light project showed that
best results were obtained by averaging 5 pixels
in longitude and 3 pixels in latitude. So for the
data used here Heliosat was applied to pixels of
approximately 12 12 km2 for Geneva and Lyon
and approximately 12 21 km2 for Bergen. The
averaging of pixels makes the covered area more
equal to the area of the sky ‘‘seen’’ by an instrument on ground, which is typically 50 50 km2.
3.3 Observed cloud properties
The third independent data source is the cloud
observations from ground. Every three hours (9,
12. . .UTC) many parameters are observed, of
which two are used here; the fractional cloud
cover (given in octa) and the height of the base
of the lowest clouds. Note that these are only
rough estimates by a human observer. For Bergen
the cloud observations are taken on the same site
as the radiation measurements. In Geneva the
station is 5.5 kilometres away and in Lyon it is
less than 5 kilometres away. Data are provided by
the Norwegian Meteorological Institute, Meteo
Suisse and Meteo France respectively.
4. Comparison between Heliosat
and ground measurements
The hourly global irradiances are normalized
with the clear sky model of Satel-Light (Section
3.2), and the resulting clear sky indices are
denoted by ksat for the Heliosat derived values
and kobs for the ground measured values. The
term ‘deviation’ is in this section defined by
ksat kobs . In the following sections the Mean
Bias Deviation (MBD) is analysed in light of
the solar zenith-, solar azimuth- and co-scattering
angles and the observed cloud amount and height
of the cloud bases.
4.1 Solar zenith angle
Figure 2 shows the MBD plotted against solar
zenith angle for observed cloud amount of 0
Fig. 2. Mean Bias Deviation (MBD) of the satel-light derived clear sky indices versus the ground observed counterparts ðksat kobs Þ for Bergen, Geneva and Lyon plotted
versus the solar zenith angle. Upper part is for ‘clear’ cases,
with observed cloud amount of 0 or 1 octa. Lower part is
for ‘cloudy’ cases with observed cloud amounts of 4–8 octa
Mean bias deviation of the Heliosat algorithm
or 1 octa (‘clear’) and 4 octa (‘cloudy’). For
Geneva and Lyon the bias is small for the clear
cases, except a positive bias for low sun. For the
cloudy cases Heliosat gives too small values for
high sun (<50 ) and too high values for low
sun. The reason for this could be that either the
reflectance (and hence cloud index) or the global
irradiance at ground (and hence clear sky index)
varies differently with with and without clouds.
To test these hypotheses, a small case study was
performed with the radiative transfer model
SBDART (Richiazzi et al., 1998).
Reflected top of atmosphere irradiance and
global irradiance at ground was simulated for
different solar zenith angles for a clear sky case
and for a cloudy case with various cloud optical
depths. The simulations showed that the dependence of reflected irradiance on is almost completely similar with and without clouds (figure
not shown). The global irradiance at ground,
however, varies differently with for the clear
and cloudy case, as seen on Fig. 3. The values
are normalized so that the areas under the curves
are equal, so that only the relative variation with
is shown. The global irradiance at overcast
is higher for high sun and lower for low sun, relatively to the clear case. The ‘crossing’ appears
around a solar zenith angle of 35 . This might
be the most likely explanation for the variation of the bias shown on Fig. 2. Furthermore,
Fig. 3. Global irradiance at ground versus solar zenith angle simulated with SBDART with and without clouds. The
values are normalized so that the area under the curves are
equal. The clouds used were water clouds with an optical
depth of 20 for the wavelength of 0.55 mm
219
it was found that already at an optical depth of
4 the variation of global irradiance with theta did
not change with further increase in cloud thickness. One must remember two things, however:
the clouds in SBDART are plane-parallel and
reflected irradiance was used instead of radiances
in a certain direction.
A physical explanation for the different solar
zenith angle dependence of global irradiance
for clear and cloudy skies can be found from
Skartveit and Olseth (1996); Their model of diffuse sky irradiance on an inclined plane assumes
that at overcast conditions 30% of the horizontal
diffuse irradiance is due to collimated radiation
from zenith. This ‘zenith brightening’ for overcast conditions appears at all solar zenith angles.
Therefore, when the sun is located close to
zenith, where the cloud transmissivity is largest,
the global irradiance is relatively high. Accordingly the transmissivity decreases more rapidly
as the sun is moving away from zenith for overcast than for clear conditions.
A simple empirical correction for this bias
can be made based on Fig. 2, by replacing ksat
by ksat þ F1 ðÞ for overcast situations. However,
based on Fig. 3 a more physical correction can
be deduced, by multiplying the clear sky index
for overcast conditions with a correction describing the effect of the zenith brightening:
replacing ksat by ksat F2 ðÞ No attempt will be
made to determine such functions here, based on
a sparse data set and a simple case study with
SBDART.
For Bergen the cloudy cases are qualitatively
similar to the cloudy cases in Geneva and Lyon,
except that the variation of the MBD with is not
as strong in Bergen as it is in Geneva and Lyon.
For the clear cases in Bergen Heliosat gives too
low global irradiance for low sun. Bergen differs
from the other two sites by higher latitude and
higher satellite zenith angle. The radiance scattered from a long atmospheric column can be comparable to reflection from clouds when the satellite
zenith angle and solar zenith angle are very large,
and Heliosat may overestimate the cloud amount
for these cases. In other words: the correction for
backscatter from the atmosphere (Eq. 2) may give
too low values when both the sun and satellite are
close to the horizon. As a consequence, the cloud
index will be too high, and the estimated irradiance too low, as is the case on Fig. 2.
220
K.-F. Dagestad
Fig. 4. Mean Bias Deviation (MBD) of the satel-light derived clear sky indices versus the ground observed counterparts ðksat kobs Þ for Bergen, Geneva and Lyon plotted
versus the solar azimuth angle
4.2 Solar azimuth angle
Figure 4 shows the MBD plotted against solar
azimuth angle. This angle is here defined as 0
when the sun is to the north, and increases during
the day with a value of 180 when the sun is to the
south. For Geneva and Lyon we see a similar
shape; Heliosat gives too high values in the morning and afternoon, and too low values around noon
( ¼ 180 ). Most probably this is due to the relationship between the solar azimuth angle and the
solar zenith angle; the solar zenith angle is lower
when the sun is in the south (mid of the day).
For Bergen, however, there is a ‘strange’
diurnal trend of the bias, with Heliosat giving
too high estimates in the morning and too low
values in the afternoon. It is found, furthermore,
that Heliosat-estimates (ksat) are symmetrical
about noon (azimuth ¼ 180 ), while observed
clear sky indices (kobs) have the asymmetry
reflected in Fig. 4. Looking more closely, this
asymmetry is not present for small cloud
amounts or for fully overcast, but only for intermediate cloud amounts. For observed cloud
amount in the range 4–7 Fig. 5 shows that
the mean observed clear sky index in Bergen
ranges from 0.53 in the morning to 0.68 in
the afternoon. Since a similar asymmetry does
not exist for totally overcast, the reason is probably the cloud position on the sky, rather than
different cloud thickness. Since Bergen is situated on the west coast, most probably at this
time of the year (summer=autumn) there are
more frequently clouds to the east (over land)
than to the west (over sea). Observers at the
Meteorological Institute in Bergen confirm that
this is also their experience (personal communication), although no quantitative measurements of this phenomena exists. Heliosat
relies on the assumption that clouds are randomly placed in space, probably a good
assumption, except for orographic clouds or
for clouds along land=sea boundaries. To correct for such phenomena, Heliosat needs very
small pixels. This again introduces other problems, such as the need to correct for the shadows made by the clouds, and thus generally
gives higher RMSD.
Some of the variations in Fig. 5 are also due to
the simple fact that the mean cloud amount is
somewhat higher in the morning than in the afternoon. The mean cloud amount for the dataset on
Fig. 5 is ranging from 5.8 to 6.3 with the higher
values in the morning. Based on numbers from
Olseth and Skartveit (1993) this alone cannot
account for the large variation in the clear sky
index.
4.3 Co-scattering angle
Fig. 5. Mean observed cloud index in Bergen for each hour
with observed cloud amounts in the range of 4–7 octa
The angle between the direction towards the satellite and the sun, as seen from ground, is here called
the ‘co-scattering’ angle. ( on Fig. 1). It is physically meaningful to investigate this angle since
the phase functions for scattering by molecules,
aerosols and cloud droplets depend on it. Also
the amount of shadows seen on ground and clouds
varies mainly with . When is zero, no shadows
are seen from the satellite, and the reflectivity
should reach a peak value (opposition effect).
Figure 6 shows the MBD plotted against the
co-scattering angle. Here the clear (observed
Mean bias deviation of the Heliosat algorithm
Fig. 6. Mean Bias Deviation (MBD) of the satel-light derived clear sky indices versus the ground observed counterparts ðksat kobs Þ for Bergen, Geneva and Lyon plotted
versus the co-scattering angle. Upper part is for ‘clear’
cases, with observed cloud amount of 0 or 1 octa. Lower
part is for ‘cloudy’ cases with observed cloud amounts of
4–8 octa
cloud amount 1=8) and cloudy (observed cloud
amount 4=8) cases are separated. For Geneva
and Lyon the bias is close to zero for the clear
cases, except for slightly negative values for
<5 and positive values as increases above
70 .
For the cloudy cases the picture is similar,
except for a ‘strange dip’ at around 30 . This
can be explained through the relationship
221
between
and , as shown on Fig. 7: For
around 30 , the mean value of the solar zenith
angle is at a minimum. So the bias shown for
the cloudy cases on Fig. 2 also shows up on
Fig. 6 via the dependence. When an empirical correction based on Fig. 2 is made; ksat ¼
ksat =400 þ 0:105 for cloud amount larger
than 2, the bias for the cloudy cases on Fig. 6
is similar to the clear cases (figure not shown).
The only remaining ‘feature’, the negative MBD
for <5 , can be explained by the opposition
effect: No shadows are seen from Meteosat when
the sun is in the same direction, the reflectivity is
larger, and hence the cloud index is too high and
the estimated global irradiance too low. However,
less than 2% of the hours have less than 5 , so
the influence on the overall performance of
Heliosat is small. Since the ‘dip’ in the MBD
at low values of appears both with and without
clouds, the opposition effect occurs both on
clouds and on the ground.
For Bergen most of the variation of the MBD
with
is also due to the relation between the
co-scattering angle and the solar zenith angle
(Fig. 7). However, since the MBD varies differently with in Bergen compared to Geneva and
Lyon (Fig. 2), it also looks different on Fig. 6.
But also in Bergen a clear sign of the opposition
effect is seen for less than 5 .
4.4 Cloud cover
Figure 8 shows MBD versus total cloud amount
observed from ground. For all three sites the
MBD is fairly constant, but rises when the cloud
amount is 8=8 (Heliosat gives too high global
irradiance). For Bergen the increase is larger,
and also starts at cloud amount 7=8. Two theories
Fig. 7. Correlation between the solar zenith angle and the
co-scattering angle. The ordinate is the mean of the solar
zenith angle within each ‘bin’ of the co-scattering angle
(abscissa). The borders of the bins equal the x-grid
Fig. 8. Mean Bias Deviation (MBD) of the satel-light derived clear sky indices versus the ground observed counterparts ðksat kobs Þ for Bergen, Geneva and Lyon plotted
versus the total cloud amount given in octa
222
K.-F. Dagestad
to explain the overestimation by Heliosat for
fully overcast are proposed here:
1. For cloud amount less than 8=8, at least some
direct radiation reaches ground. Some of
this is then reflected, and some is even reflected back to ground again. Such multiple
scattering=reflection might in some cases
even augment the global irradiance above
the incoming irradiance on the top of the
atmosphere (for short-term values). A full
cloud cover caps off the direct source, and
it becomes darker at ground without the
reflectivity increasing proportionally.
2. The thickest clouds most probably also have
cloud amounts of 8=8. After ‘the hole is
filled’, the clouds might thicken to make it
very dark at ground, without the reflectivity
rising enough to compensate. Simulations
with SBDART (not shown) support this
hypothesis: The decrease of radiation reaching ground when cloud thickness increases
very much are mainly ‘lost’ due to absorption
within the clouds rather than due to reflection
to space. It is reasonable that Bergen has the
highest increase of MBD for totally overcast,
since it is a coastal city placed in the westerlies at 60 N. Leontieva et al. (1994) showed
that the clouds in Bergen have high optical
thickness. MSG data will make it possible to
retrieve estimates of the cloud optical depth.
This parameter might be a valuable replacement or addition to the cloud index.
For broken clouds, the MBD has a rather constant level for all sites. This level is mainly set by
the clear sky model with its climatologically
input of the Linke turbidity coefficient. Equation
4 shows the sensitivity of the clear sky model on
the performance of Heliosat: any error in the
clear sky model gives the same error on the modelled global irradiance. Apparently the Linke turbidity coefficient fits well for Lyon, while it is too
low for Geneva and too high for Bergen. In the
future, with the use of the new MSG satellites,
hopefully more accurate real time input to the
clear sky models will be available.
4.5 Height of cloud base of lowest clouds
Figure 9 shows the MBD plotted against the
height of the base of the lowest clouds as estimated by an observer at ground. The bias is not
Fig. 9. The upper part shows the Mean Bias Deviation
(MBD) of the satel-light derived clear sky indices versus
the ground observed counterparts (ksat kobs) for Bergen,
Geneva and Lyon plotted versus the observed (estimated)
height of the base of the lowest clouds. The lower part
shows the histogram of the number of hours within each
‘bin’, where the borders of the bins equal the x-grid
very large for medium and high clouds, but
increases substantially for height of the cloud
base lower than 600 metres. However, as Fig. 9
also shows, there are few cases with the cloud
base below 600 metres; between 12% and 18%
for the three sites. Consequently the effect on the
overall bias is not very large, but it is still interesting to examine the physics behind it. With
Fig. 10. Reflection, absorption and global irradiance simulated with SBDART versus the height of the cloud base.
The solar zenith angle is 0 and the clouds have an optical
depth of 20 for the wavelength 0.55 mm. For all heights of
the cloud base the clouds have a geometrical thickness of
1 km (one layer in the model). All values are normalized
with the incoming irradiance at the top of atmosphere for
the corresponding solar zenith angle
Mean bias deviation of the Heliosat algorithm
SBDART the height of the clouds can be changed
keeping everything else constant. Figure 10
shows the changes of reflectivity, global irradiance and absorptivity in the atmosphere with
changing height of the clouds. The fraction of
the incoming irradiance that reaches the ground
is more or less unaffected by the cloud height.
The reflectivity, however, increases with cloud
height, and this is matched by a decrease in the
absorptivity. This means that higher clouds ‘shelter’ the solar radiation from the absorbing species
in the lower atmosphere. The height of the clouds
affect the reflectivity (cloud index) without
affecting the global irradiance (clear sky index),
hence the relationship given by Eq. 5 is disturbed.
Figure 9 shows that the effect is only obvious
for cloud heights below 600 metres. This makes
sense, since both aerosols and water vapour normally decrease exponentionally with height. The
SBDART simulations, however, indicate that
there should be an effect also by raising the
clouds all the way to the tropopause. While the
cloud properties (optical- and geometrical thickness, effective radii and water phase) are kept
constant in the model, these properties most
likely change with height in the ‘real world’. This
is probably more important than merely lifting
the clouds, and therefore it is not surprising that
the modelled effect of raising the clouds is not
clearly observed for the highest clouds on Fig. 9.
*
*
*
*
223
and the solar zenith angle. Some effects seem,
however, to be due to other reasons.
For Bergen, Heliosat provided too high estimates in the morning and too low estimates
in the afternoon. The reason seems to be that
Bergen is situated on the west coast, and hence
clouds in the summer are more frequent to the
east (over land) than to the west (over sea).
For the co-scattering angle less than 5 we see
that Heliosat does not account for the opposition
effect; higher reflectivity due to less shadows
leads to 5% too low global irradiances. However, this is the case for less than 2% of the hours,
so the overall effect due to this is very small.
Observed cloud amounts showed influence on
the MBD, except for fully overcast, where
Heliosat gave too high values for all three
sites; 5% for Geneva and Lyon and 10%
for Bergen. Two possible explanations are proposed; 1) less multiple reflection between
ground and the atmosphere when there are
no ‘holes’ in the cloud cover, and 2) clouds
with full coverage may also be very thick.
For all three sites, the height of the base of the
lowest clouds showed a clear influence on the
bias. This is also reproduced with a radiative
transfer model, and a physical explanation is
given. However, the effect is only seen for
cloud bases below 600 metres, which includes
only 12–18% of the hours, so the effect on the
total bias is again small.
5. Conclusions
Acknowledgements
Global irradiances estimated with the Heliosat
method using Meteosat-data from 1996=97 as
input are compared to ground observed counterparts in Bergen, Geneva and Lyon. The biases are
analysed with respect to variations of the sunground-satellite geometry and ground observed
cloud amounts and height of cloud base.
This work is a part of the project Heliosat-3 funded by the
European Commission (NNK5-CT-200-00322). I thank project colleagues for valuable advice. Solar radiation and cloud
data from Geneva was provided by Pierre Ineichen at
CUEPE, University of Geneva and similar data from Lyon
were provided by Dominique Dumortier at ENTPE, Lyon.
Cloud observations from Bergen was provided by Magnar
Reistad at the Norwegian Meteorological Institute.
*
Variations of MBD with solar zenith angle
are small for clear cases. For cloudy cases
Heliosat gives too low estimates for high sun
and too high estimates for low sun. A possible
explanation, which is supported by radiative
transfer calculations, is that global irradiance
varies differently with respect to solar zenith
angle for clear and cloudy cases. Some variations of MBD with respect to the solar azimuth- and co-scattering angle are shown to
be due to the relationship between these angles
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Author’s address: Knut-Frode Dagestad (e-mail: Knutfrode.Dagestad@gfi.uib.no), University of Bergen, Department of Geophysics, Allegaten 70, 5007 Bergen, Norway.
Paper II
Müller, R.W., Dagestad, K-F.,
Ineichen, P., Schroedter, M., Cros, S., Dumortier, D., Kuhlemann, R.,
Olseth, J. A., Piernavieja, C., Reise, C., Wald, L. and Heinemann, D. (2004)
Rethinking satellite based solar irradiance modelling - The SOLIS clear sky module
Remote Sensing of the Environment, 91
160-174
Remote Sensing of Environment 91 (2004) 160 – 174
www.elsevier.com/locate/rse
Rethinking satellite-based solar irradiance modelling
The SOLIS clear-sky module
R.W. Mueller a,*, K.F. Dagestad b, P. Ineichen c, M. Schroedter-Homscheidt d, S. Cros e,
D. Dumortier f, R. Kuhlemann g, J.A. Olseth b, G. Piernavieja h,
C. Reise i, L. Wald e, D. Heinemann g
a
University of Oldenburg, now at Deutscher Wetterdienst, Frankfurter Street 135, 63067 Offenbach, Germany
b
University of Bergen, Bergen, Norway
c
University of Geneva, Geneva, Switzerland
d
German Aerospace Center—German Remote Sensing Data Center (DLR-DFD), Germany
e
Ecole des Mines de Paris, France
f
Ecole Nationale des Travaux Publics de l’Etat, France
g
University of Oldenburg, Oldenburg, Germany
h
Instituto Tecnologico de Canarias, Spain
i
Fraunhofer Institute for Solar Energy Systems, Germany
Received 23 July 2003; received in revised form 26 February 2004; accepted 28 February 2004
Abstract
Accurate solar irradiance data are not only of particular importance for the assessment of the radiative forcing of the climate system, but
also absolutely necessary for efficient planning and operation of solar energy systems. Within the European project Heliosat-3, a new type of
solar irradiance scheme is developed. This new type will be based on radiative transfer models (RTM) using atmospheric parameter
information retrieved from the Meteosat Second Generation (MSG) satellite (clouds, ozone, water vapour) and the ERS-2/ENVISAT satellites
(aerosols, ozone).
This paper focuses on the description of the clear-sky module of the new scheme, especially on the integrated use of a radiative transfer
model. The linkage of the clear-sky module with the cloud module is also briefly described in order to point out the benefits of the integrated
RTM use for the all-sky situations. The integrated use of an RTM within the new Solar Irradiance Scheme SOLIS is applied by introducing a
new fitting function called the modified Lambert – Beer (MLB) relation. Consequently, the modified Lambert – Beer relation and its role for
an integrated RTM use are discussed. Comparisons of the calculated clear-sky irradiances with ground-based measurements and the current
clear-sky module demonstrate the advantages and benefits of SOLIS. Since SOLIS can provide spectrally resolved irradiance data, it can be
used for different applications. Beside improved information for the planning of solar energy systems, the calculation of photosynthetic active
radiation, UV index, and illuminance is possible.
D 2004 Elsevier Inc. All rights reserved.
Keywords: Solar irradiance modelling; Remote sensing
1. Introduction
Satellite-based remote sensing is a central issue in
monitoring and forecasting the state of the Earth’s atmosphere. Geostationary satellites such as METEOSAT or
GOES provide cloud information in a high spatial and
temporal resolution. These satellites are, therefore, not only
* Corresponding author.
E-mail address: richard.mueller@dwd.de (R.W. Mueller).
0034-4257/$ - see front matter D 2004 Elsevier Inc. All rights reserved.
doi:10.1016/j.rse.2004.02.009
useful for weather forecasting, but also for the estimation of
solar irradiance, since the knowledge of the radiance
reflected by clouds is the basis for the calculation of the
transmitted irradiance. Additionally, a detailed knowledge
about atmospheric parameters involved in scattering and
absorption of sunlight is a further necessity. An accurate
estimation of the downward solar irradiance is not only of
particular importance for assessing the radiative forcing of
the climate system, but also absolutely necessary for an
efficient planning and operation of solar energy systems and
the estimation of the energy load. Solar resource assessment
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
161
from geostationary satellites constitutes a powerful alternative to a meteorological ground network for both climatological and operational data (Perez et al., 1998).
Solar irradiance schemes provide accurate solar irradiance data with a high spatial and temporal resolution using
weather satellites such as METEOSAT and Meteosat Second
Generation (MSG). Currently, most of the operational
calculation schemes for solar irradiance are semiempirical
and based on statistical methods. They use cloud information from the current METEOSAT or GOES satellite and
climatologies of atmospheric parameters, e.g., turbidity
(characterising the combined effect of aerosols and water
vapour; see Perez et al., 2001 and references therein). The
Heliosat method (Cano et al., 1986; Beyer et al., 2003) is
certainly one of the best known. It converts METEOSAT
satellite data into irradiance with a better accuracy than
interpolated ground measurements could provide (Zelenka
et al., 1999; Perez et al., 1998). It is applied routinely in real
time at the University of Oldenburg since 1995. It has
permitted the establishment of the server Satel-Light, which
delivers valuable information on daylight in buildings to
architects and other stakeholders (Fontoynont et al., 1997).
It has also been used within the SoDa project1 (Wald et al.,
2002) for the calculation of the solar irradiance. Furthermore
there exists derivates of Heliosat, e.g., Heliosat-2 (Lefèvre et
al., 2002), which is optimised as an operational processing
chain for climatological data. With the launch of the
Meteosat Second Generation (MSG) satellite, the possibilities for monitoring the Earth’s atmosphere have improved
enormously. The MSG satellite will not only provide higher
spatial (1 km) and temporal (15 min) resolution, but also
offers with its 11 channels from 0.6 to 13 Am, the potential
for the retrieval of atmospheric parameters such as additional cloud parameters, ozone, water vapour column, and
with restrictions aerosols. These capabilities plus the synergy with other sensors, such as those aboard ERS-2 and
ENVISAT (GOME/ATSR-2 and SCIAMACHY/AATSR),
permit us to attain a refinement in the solar irradiance
modelling. These refinements necessitate a rethinking of
satellite-based solar irradiance modelling and going ahead
with a drastic revision of the current Heliosat processing
scheme. The current Heliosat scheme cannot exploit enhanced information about the atmosphere provided by
improved satellite capabilities. Thus, it was necessary to
develop a new scheme, which will be able to exhaust the
enhanced capabilities of MSG (SEVIRI) and ENVISAT
(SCIAMACHY). The accuracy of the calculated irradiance
is expected to increase significantly with a scheme that can
exhaust the capabilities of the new satellites. The new
calculation scheme has to be fast, accurate, and should
provide—in contrast to Heliosat and Heliosat-2—spectrally
resolved solar irradiance data.
As a consequence of the things mentioned above, the
new scheme is based on the integrated use of a radiative
transfer model (RTM), whereas the information of the
atmospheric parameters retrieved from the MSG satellite
(clouds, ozone, water vapour) and from the GOME/ATSR-2
instruments aboard the ERS-2 satellites (aerosols, ozone)
will be used as input to the RTM-based scheme.2 The direct
integration of an RTM into the calculation schemes—
instead of using precalculated look-up tables—is only
possible if the necessary computing time can be kept small.
For this purpose, a functional treatment of the diurnal solar
irradiance variation is applied, allowing an appropriate
operational use of an RTM within the calculation scheme.
This paper focuses on the description of the new clear-sky
module, especially on the integrated use of the radiative
transfer model (Section 2). The linkage of the clear-sky
module with the cloud module is briefly described in order
to point out the benefits of the integrated RTM use for allsky situations as well.
1
Integration and Exploitation of Networked Solar Radiation Databases
for Environment Monitoring Project.
2
In the near future, the information from GOME/ATSR-2 will be
replaced by SCIAMACHY/AATSR on ENVISAT.
2. SOLIS—the new scheme
2.1. Overview
The integrated usage of the RTM within the scheme is
related to the clear-sky scheme using the well-established
n –k relation of the Heliosat method (Cano et al., 1986;
Beyer et al., 1996) or the Cloud Optical Depth (COD)
option to consider cloud effects. It is important to note that
the integrated use of the RTM within the clear-sky module is
linked with an enormous improvement for all-sky situations
as well. It is not a restriction of the model. This issue will be
discussed in more detail in Section 8.1. On the other hand,
the benefits and needs of the described clear-sky module can
only be understood if it is seen in the context of its main
purpose—the operational satellite-based solar irradiance
modelling with a large geographical coverage. Keeping this
in mind, it is also necessary to describe briefly the treatment
of the clouds and the basics of the linkage between the clearsky module—described in detail in this paper— and the
cloud modules, which are partly still under development.
The cloud modules will be discussed in more detail in a
forthcoming paper after reliable MSG data will be available.
2.1.1. Using n – k relation
The Heliosat method was originally proposed by Cano et
al. (1986) and later modified by Beyer et al. (1996) and
Hammer (2000). The basic idea of the Heliosat method is a
two-step approach. In the first step, a relative normalised
cloud reflectivity—the cloud index—is derived from
METEOSAT images. The derived cloud index is correlated
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R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
to the clear-sky index k, which relates the actual ground
irradiance G to the irradiance of the cloud-free case Gclear
sky. Consequently, in addition to the cloud index derived
from the satellite signal, a clear-sky model, providing Gclear
sky, is necessary for the estimation of the actual ground
irradiance. The n – k relation is powerful, validated, and
leads to small root mean square deviation (RMSD) between
measured and calculated solar irradiance for almost homogenous cloud situations (RRMSD of 13 – 15% for hourly
values; Hammer, 2000). With MSG data, it can be expected
that the treatment of clouds using the current n– k will be
improved only due to the higher spatial and temporal
resolution.
applied, making an appropriate explicit operational use of
an RTM within the calculation schemes possible.
Starting point of the integrated use is the assumption that
daily values of the atmospheric clear-sky parameters in a
spatial resolution of 100 100 or 50 50 km are sufficient.
This assumption is reasonable for solar energy applications
in consideration of accuracy and operational practicality,
because of the following.
2.2. Basic considerations
Daily values of water vapour and aerosols are linked with
a great improvement compared to the current implicit use
of a monthly turbidity climatology or aerosol and watervapor climatologies.
Current restrictions in the art of retrieval limit the
available input with respect to the temporal and spatial
resolution of the atmospheric clear-sky parameters. For
example, the retrieval of aerosols from satellites is
handicapped by the small aerosol reflectance and the
perturbation of the weak signal by clouds and surface
reflection. In addition, the retrieval of water vapor is not
possible for cloudy pixels. For these reasons, retrieval of
daily values in 50 50-km resolution with a ‘‘global’’
coverage in an appropriate accuracy would be a great
improvement. The effect of ozone is small compared to
that of aerosols and water vapour; therefore, daily ozone
values are sufficient.
The temporal daily fluctuations of solar irradiance are
generally dominated by cloud fluctuations. The cloud
information is used in MSG pixel resolution (see Table
1), hence in a high temporal and spatial resolution.
The usage of the modified Lambert – Beer function,
described in Section 2.5, should enable the correction of
derivations from the daily values of the clear-sky
irradiance in an easy and fast manner (see Section 2.5).
MSG will scan the atmosphere with a very high spatial
resolution (see Table 1, e.g., approximately 2.5 million
pixels have to be processed every 15 min for Europe). Thus,
the computing time necessary to calculate the solar irradiance for each pixel has to be very small to make an
operational usage of the solar irradiance scheme possible.
Instead of using look-up tables, a new, more powerful
and flexible method, the integrated use of RTM within the
scheme based on a modified Lambert –Beer (MLB) relation,
will be applied. The integration of an RTM into the
calculation schemes, instead of using precalculated lookup tables, is only possible if the necessary computing time
can be decreased enormously. For this purpose, a functional
treatment of the diurnal solar irradiance variation was
Using daily values of the atmospheric parameters (O3,
H2O(g), aerosols) within a region of 100 100 km
(50 50 km) and the modified Lambert – Beer function,
only two RTM calculations are necessary to define the
complete diurnal variation of the clear-sky irradiance for
a given atmospheric state (see Fig. 1). The effect of
clouds on the clear-sky irradiance is considered by using
the n– k relation or the COD option (Section 2.1). By this
way, the cloud effect is considered in MSG pixel resolution, whereby no additional explicit RTM runs are
needed. Fig. 1 illustrates the new scheme and the
integrated use of the RTM within the clear-sky scheme.
The modified Lambert – Beer (MLB) function is discussed
in detail in the next section.
2.1.2. Using COD-based code
Within this option, the information of the cloud optical
depth (COD) is used to consider the cloud effect. The COD
will be retrieved operationally from MSG with software
from the German Aerospace Center (DLR), based on the
Apollo (Kriebel & Gesell, 1989; Saunders & Kriebel, 1988)
or Nakajima (Nakajima & King, 1990) method. The RTM
model SBDART (Ricchiazzi et al., 1998) has been used to
find a parameterisation in order to relate the all-sky irradiance to the clear-sky irradiance. Within this parameterisation, the effective cloud-particle radii, derivable with the
Nakajima and King (1990)-based scheme, can also be used.
The derived parametrisation needs some fine-tuning and has
to be tested with MSG data. It will be discussed in more
detail in a forthcoming paper.
Regardless of the treatment of clouds, the basis for the
calculation of the all-sky radiation is the clear-sky module,
which is described in detail in the next section.
2.3. The modified Lambert –Beer function
Table 1
Improvements in METEOSAT resolution
MSGDMETEOSAT
The Lambert –Beer relation is given by
Spatial
resolution
Temporal
resolution
Spectral
channels
1/3 kmD2.5/5 km
15 minD30 min
12D3
I ¼ I0 expðsÞ
ð1Þ
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
163
In a second step, a correction of s0, or the equivalent to this,
of the parameter (s0)/(cos(hz)) is performed, leading to the
so-called modified Lambert – Beer relation (MLB).
s0
ð5Þ
Iðhz Þ ¼ I0 exp
cosðhz Þ
cosa ðhz Þ
The correction parameter a is calculated at a SZA of 60j.
The modified Lambert – Beer relation (Eq. (5)) cannot
only be applied to wavelength bands for direct irradiance,
but also to wavelength bands of global and diffuse irradiance. However, in order to apply the modified Lambert –
Beer relation to global and diffuse irradiance, the following
things have to be considered. At low visibilities (high
optical depth, high aerosol load), I0 in Eqs. (4) and (5)
has to be enhanced for global and diffuse radiation. A
general equation has been developed which is applied to
I0 to get I0,enh.
Idiffuse
ð6Þ
I0
I0;enh ¼ ð1 þ I0 Idirect Iglobal
Fig. 1. Diagram of the spatial and temporal linkage between clear-sky and
cloud information.
where s is the optical depth and within the scope of
atmospheric radiation, I is the direct radiation at ground
with sun in zenith, I0 is the extraterrestrial irradiance.
Consideration of path prolongation and projection to the
Earth’s surface leads to Eq. (2), where hz is the solar zenith
angle (SZA) and I(hz) is the irradiance at hz.
s
Iðhz Þ ¼ I0 exp
cosðhz Þ
cosðhz Þ
ð2Þ
This formula describes the behaviour of the direct monochromatic radiation in the atmosphere. Transformation of
Eq. (2) leads to the optical depth s
s ¼ ln
Iðhz Þ
I0 cosðhz Þ
cosðhz Þ
ð3Þ
In order to apply the Lambert – Beer relation to wavelength
bands of direct irradiance, the above Lambert – Beer relation
(Eq. (2)) has to be applied in a modified manner, using a
two-step approach.
In a first step, the ‘vertical’ optical depth s0 is calculated
at a SZA of zero degree (hz = 0), using Eq. (4), which is a
special case of Eq. (3).
Iðhz ¼ 0Þ
s0 ¼ ln
I0
ð4Þ
In order to avoid switching between I0 and I0,enh, I0,enh is
always used instead of I0 in Eqs. (4) and (5) for diffuse and
global irradiance.
Additionally, for diffuse irradiance, the multiplication
with cos(hz) in Eq. (3) has to be skipped for diffuse
irradiance, since consideration of the projection to the
Earth’s surface is no longer feasible.
It is important to notice that
I(hz) in Eqs. (4) and (5) stands either for global, direct, or
diffuse irradiance at the given SZA;
the fitting parameter a has different values for direct,
global, and diffuse irradiance;
s0 is always calculated at a SZA of zero and the
correction parameter a at a SZA of 60j, independent
whether the MLB relation (Eq. (5)) is applied to global,
direct, or diffuse irradiance.
Using the Modified Lambert –Beer (MLB) relation, the
calculated direct and global radiation can be reproduced
very well (see Fig. 2).
2.3.1. General remarks
The usage of the modified Lambert –Beer function is
physically motivated, but it is actually a fitting function.
This is especially obvious for the case of diffuse radiation.
In principle, it is possible to fit the RTM calculations with
any appropriate function, for example, a modified polynomial of third or higher degree (ecos3(x) + fcos2(x) + g).
Hence, the big advantage of the modified Lambert –Beer
function is not the feasibility to fit the RTM calculations, but
that it is possible to yield a very good match between fitted
and calculated values by using only two SZA calculations
(e.g., better match than obtained with a polynomial of third
degree). This is possible since the change of the irradiance
164
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
with SZA is related to the Lamber –Beer law; hence, using
the modified Lambert –Beer relation, ‘‘the degrees of freedom can be reduced.’’ Moreover, the parameter a can be
calculated without the need for a numerical fit, respectively.
The function was tested for many different atmospheric
states, e.g., four different aerosol types, five different
visibilities (5, 10, 23, 50, 100), different water-vapour
amounts, different standard atmospheres, and surface models. No atmospheric clear-sky state is expected for which the
MLB fit will not work. For our purpose, the sense of an
appropriate fitting function is to save calculation time
without losing ‘‘significant’’ accuracy. The question if a
fitting function is usable for that purpose depends on the
difference between the fitted values and the RTM calculated
values. The differences in the broadband irradiance (306.8 –
3001.9 nm) are usually less than 8 W/m2 for high SZA and
less than 5 W/m2 for SZA below 75j (8 and 4 W/m2 for
direct irradiance, respectively). For the wavelength bands,
the differences are typically less than 1 W/m2 below a SZA
of 75j.
2.3.2. Discussion
For monochromatic radiation, s is constant and consequently equals s0 for all SZA. In the case of wavelength
bands, s is not constant, but changes smoothly with increas-
Fig. 3. For monochromatic radiation, the Lambert – Beer relation is still a
good approximation if the ‘vertical’ optical depth s0 is used. In order to
yield a better match, a correction of formula (2) (MLB relation) is
necessary.
ing SZA. s0 is just the optical depth at hz = 0 and no longer
equal to s for all SZA. The reason for that is the nonlinear
nature of the exponential function; the monochromatic
optical depths are, in contrast to the irradiance, not additive.
I ¼ Iðk1 Þ þ Iðk2 Þ; but s psðk1 Þ þ sðk2 Þ
ð7Þ
That is the reason why a correction of the optical depth, or
an equivalent to this, of the parameter (s)/(cos(hz)) is
necessary.
With respect to global irradiance, it has to be mentioned
that the Lambert –Beer law (Eq. (2)) is still a good approximation for ‘monochromatic’ global radiation and moderate
aerosol load, using s0 (see Fig. 3). For high aerosol load, the
modified Lambert – Beer relation has to be used in order to
get a good match with explicit RTM results. Moreover, for
wavelength bands, the use of the modified Lambert – Beer
relation is absolutely necessary. The Lambert – Beer relation
describes the attenuation of incoming radiation. The incoming diffuse radiation at the top of the atmosphere is
negligible. The source of diffuse radiation is the attenuation
of the direct radiation due to scattering processes. Hence, the
Lambert – Beer law is related to the amount of diffuse
radiation, but does not describe the magnitude of the diffuse
radiation. However, fitting with the modified Lambert – Beer
relation works very well (see Fig. 2).
2.4. Radiative transfer model
The radiative transfer model (RTM) used within the
clear-sky module, LibRadtran,3 is a collection of C and
Fortran functions and programs for calculation of solar and
thermal radiation in the Earth’s atmosphere. It has been
validated by comparison with other models (Koepke et al.,
1998; Van Weele et al., 2000) and radiation measurements
(Mayer et al., 1997). It is very flexible with respect to the
Fig. 2. Comparison between RTM calculations and fit using the modified
Lambert – Beer relation for different atmospheric states.
3
available at http://www.libradtran.org.
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
atmospheric input, e.g., different possibilities for the input
of the aerosol information can be chosen by the user.
LibRadtran offers the possibility of using the correlated-k
approach of Kato et al. (1999). The correlated-k method is
developed to compute the spectral transmittance (hence the
spectral fluxes) based on grouping of gaseous absorption
coefficients. The main idea is to benefit from the fact that
the same value of the absorption coefficient k is encountered
many times over a given spectral interval. Thus, the computing time can be decreased by eliminating the redundancy,
grouping the values of k, and performing the transmittance
calculation only once for a given value of k.
Using the correlated-k option, the spectral resolved data
can be calculated operationally in MSG pixel resolution, a
new feature, so far not implemented in the Heliosat or
Heliosat-2 method. Consequently, solar irradiance scheme
(SOLIS) calculates the global, direct, and diffuse irradiance,
not only for the broadband wavelength region (300 –300
nm), but for each of the Kato correlated-k (Kato et al., 1999)
wavelength bands. The spectral output is provided for 27
bands between 306.8 and 3001.9 nm, which is sufficient for
solar energy applications. Also, additional wavelength
bands below 306.8 or above 3001.9 nm can be used. The
MLB relation works very well for the spectrally resolved
data (see Fig. 4 as an example).
2.5. Further benefits of the MLB function with respect to the
use of water vapour, aerosol and ozone input information
The modified Lambert –Beer relation is defined with the
parameters ‘‘vertical’’ optical depth and the correction
parameters ai. These parameters are calculated for a given
atmospheric state (O3, H2O(g), AOD). A useful feature of the
MLB is that different water vapour or ozone content affect
the ‘‘vertical’’ optical depth s0 and not the correction
parameter a (Fig. 5). Since s0 is calculated at a SZA of
zero degree, the calculation and usage of look-up tables is
165
Fig. 5. Correction of H2O deviations. The values derived with the MLB
relation are compared for different H2O(g) amounts. H2O is specified in ppm
(parts per million). Recalculation of the vertical optical depth leads to a
good agreement between MLB values and the explicit RTM runs for the
same ai.
straightforward, because calculations at zero degree SZA
deal with vertical columns and not with slant columns. For
aerosols, both quantities—s0 and ai—change for different
values of the aerosol optical depth (AOD). In contrast to O3
and H2O(g), which are pure absorbers, aerosols are strong
scattering particles, affecting not only s0 but also the
correction parameter ai. If the changes in ai are neglected
and only s0 is corrected, deviations occur increasing with
increasing SZA. Consequently, another correction has to
applied. In the case of aerosols, deviations from the assumed
value can be approximately corrected by applying the
following equations. To correct for increase of AOD from
sA1 to sA2
sA1
Icor ¼ 2 IMLB
I 0;sA2
I 0;sA2 cosðhz Þ
I 0;sA1
ð8Þ
To correct for decrease in AOD from sA2 to sA1
I 0;sA1
sA2
Icor ¼ 0:5 IMLB
0;s þ I 0;sA1 cosðhz Þ
I A2
ð9Þ
sA1
is the diurnal variation of the irradiance for the
Here IMLB
AOD A1 or A2, as given by the modified Lambert – Beer fit,
I0,sA2 and I0,sA2 are the irradiances at a SZA of zero for AOD
A1 and A2, respectively. Based on these equations (Eqs. (8)
and (9)), the correction and use of look-up tables is
Table 2
Ground stations used for the model – measurements comparison
Fig. 4. Comparison between RTM calculations and fit using the modified
Lambert – Beer relation. Example for a fit within a small wavelength band.
Station
Latitude
(j)
Altitude
(m)
Albany (NY)
42.7
100
Burns (OR)
Eugene (OR)
FSEC – Cocoa (FL)
Geneva (CH)
43.6
44.1
28.3
46.2
1265
150
8
410
Climate
Time
base (min)
humid
continental
semiarid
temperate
subtropical
semicontinental
1
5
5
6
1
166
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
Table 3
Aerosol load, water-vapor column, and Linke turbidity for the 13
considered days
Station
Day, year
Tau 550
w (cm)
TL
Albany
June 25,
September 16, 2001
January 15,
June 15,
August 12, 2002
February 14,
October 17, 2002
March 29,
November 28, 1999
July 21,
March 31, 1996, 1998
April 7, July 19,
2003, 2002
0.089,
0.048
0.027,
0.093,
0.053
0.073,
0.032
0.142,
0.081
0.093,
0.384
0.083,
0.087
3.0, 1.0
3.2,
2.5
2.0,
3.1,
2.5
2.7,
2.5
3.5,
3.0
3.0,
5.3
2.6,
3.0
Burns
Eugene
FSEC
Geneva
Fig. 6. Correction of Aerosol deviations, here for urban aerosols. The
correction leads to an good agreement below SZA of 75j. The correction
works also if marine aerosol with a AOD is corrected to urban aerosols with
an AOD of 0.5.
Geneva
0.4, 2.0,
1.0
1.1, 1.5
2.0, 2.0
1.5, 1.1
0.6, 1.7
3.1. Comparison of model results against ground
measurements
straightforward. Look-up tables, providing the irradiance for
different AOD, has only to be calculated for a SZA of zero.
All other information needed to apply the above correction
equations are provided by the MLB fit, using daily values as
input. By this way, the effect of deviation from the daily
value can be corrected in an easy and fast manner. However,
before the correction methods would be included in the
operational SOLIS version, further validations and optimisation of the correction procedures have to be performed.
3. Intrinsic precision of the SOLIS irradiance
In this section, the atmospheric data input is retrieved
from the ground-based measurements used also for the
model – solar irradiance data comparison. The main focus
of this comparison is therefore to investigate the intrinsic
precision of the direct-beam model.
3.1.1. Measurements
The direct-beam and global irradiance produced with the
SOLIS scheme is compared with ground measurements
taken at five stations with different latitudes, altitudes, and
climates as given in Table 2. The comparison is done against
measurements for clear and stable meteorological conditions
and for different water vapour and aerosol atmospheric
loads (Fig. 6). From each of the five databases, 2– 4 clear
days are extracted for winter and summer season. The
stability of the atmospheric conditions is manually verified
for each day: during the considered period of time, the water
vapour content, the aerosol optical depth, and the Linke
turbidity coefficient as defined by Ineichen and Perez (2002)
are relatively stable as illustrated for February 14, 2002 in
Eugene (OR) in Fig. 7.4 The days used in this comparison
are listed in Table 3.
Quality control has been done to eliminate specific
measurements for which the direct-beam sensor is
obstructed, but not the global sensor.
3.1.2. Retrieval of the atmospheric parameters
For all the data, the Linke turbidity TL can be calculated
from the normal direct-beam radiation. In order to ensure
compatibility, even if the turbidity is relatively stable during
the considered periods, the coefficient is evaluated at air
mass 2. The water vapor column w is evaluated from ground
measurements of the ambient temperature and relative
humidity. With the knowledge of TL and w, and with the
help of a model developed by Ineichen (2003), the aerosol
optical depth can be retrieved. These three parameters are
given in Table 3 for the considered data.
An average value of 340 DU for the ozone content is
taken for the comparison. It has been shown (Ineichen,
Fig. 7. February 14, 2002, Eugene (OR). The stability of the atmospheric
parameters is illustrated vs. solar time.
4
When a complete day is extracted, the morning/afternoon symmetry
is respected.
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
167
IDMP station in Freiburg (47j59VN, 7j50VE) and with
measurements of the meteorological station in Bergen,
Norway (60.4jN, 5.3jE). Additionally, SOLIS calculations
are compared with the clear-sky model used in the Heliosat
method (Cano et al., 1986; Beyer et al., 2003).
4.1. Atmospheric data input
The present study deals with the clear-sky case, relevant
input parameter are ozone, water vapor, and aerosols.
Standard climatology profitless are used in order to take
the effect of Rayleigh scattering and the effect of other gas
absorber into account.
Fig. 8. Horizontal direct-beam irradiance evaluated by SOLIS vs. the
correspondent ground measurements.
2003) that the influence of different ozone columns on
broadband irradiance estimated by SOLIS is negligible.
3.1.3. Comparison
The result of the comparison is given in Fig. 8. The graph
illustrates the modelled horizontal direct-beam irradiance vs.
the ground measurements. The mean bias difference between model and measurements (MBD) and the root mean
square difference (RMSD) for the 4320 values are the
following:
horizontal direct-beam irradiance: MBD = 1 W/m2 or
0.2% and the RMSD = 11 W/m2, or 2.3%
horizontal global irradiance: MBD = 0 W/m2 and the
RMSD = 22 W/m2, or 4.0%
The result for the global irradiance is remarkably good,
taking into account that the same aerosol type was used for
all the simulations. It is important to note that for the purpose
of this comparison, the atmospheric clear-sky parameters are
retrieved from the direct-beam measurements against which
the model is compared. Within this scope, the result of the
direct-beam comparison can be considered as the intrinsic
precision of the SOLIS model, if accurate daily values of the
atmospheric clear-sky parameter are used as input.5
4. Application of the model: comparison with
measurements using autonomous atmospheric input
The purpose of the comparison is to discuss the advantages and benefits of the SOLIS clear-sky module especially
with respect to the use of aerosol and water-vapor information instead of turbidity. The benefits and limitations of the
currently available atmospheric input date is discussed
briefly as well. Therefore, calculation using the described
SOLIS scheme are compared with measurements from the
5
Daily values are not daily means.
4.1.1. Ozone
To derive actual distributions of total column ozone,
backscatter measurements from the Global Ozone Monitoring Experiment (GOME) onboard the ERS-2 satellite
are used (Burrows et al., 1998). The core element of the
retrieval is a DOAS (Differential Optical Absorption
Spectroscopy) fitting technique. Due to the scanning
geometry, the level-2 total column ozone data are distributed heterogeneously in time and space. To gain
synoptic distributions of total column ozone and to
consider atmospheric variability the data assimilation
technique Kalman-Filtering is used (Daley, 1991). It is
applied in conjunction with a spectral statistical planetary
wave approach (Bittner et al., 1997; Bittner & Erbertseder, 2000) For this study, GOME GDP level 2 data
version 3.0 from ESA/DLR are used, this data are also
available at http://wdc.dlr.de. The data assimilation approach delivers global ozone column maps for a certain
point in time with a horizontal resolution of 0.36j.
4.1.2. Water vapour
Total water-vapour column data (TWC) were prepared
using the TOVS (TIROS Operational Vertical Sounder)
instrument on the NOAA-14 satellite. TOVS raw data are
analysed with the International TOVS Processing Package
(ITPP; Jun et al., 1994; Jun, 1994), a physical retrieval
scheme to derive atmospheric temperature and water vapour
profitless for both cloudy and cloud-free situations. The
average distance between retrievals is approximately 80
km, but the data are distributed irregularly in space (polar
orbiting satellite). Therefore, a distance-weighting interpolation scheme is applied which delivers twice daily an
European TWC data set with a spatial resolution of 0.5j
(Schroedter et al., 2003). This data product is available at the
World Data Center for Remote Sensing of the Atmosphere
http://wdc.dlr.de). The quality of TWC in comparison with
the ECMWF (European Center of Middle Range Weather
Forecasting) model has been monitored for the whole year
2000. The comparison delivers differences from 0.19 F 4.41
mm6 for December 2000 to 4.56 F 5.75 mm for August
6
Bias F standard deviation.
168
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
2000. This fits the required data accuracy of less than 10 mm
very well.
In the future, it is planned to use water vapour column
information derived from MSG itself. This will provide an
improved spatial resolution and a better coverage for both
Europe and Africa. It can be expected that the accuracy of
the retrieved H2O(g) amounts will be in the same range.
4.1.3. Aerosols
The new surface irradiance scheme allows the use of
further aerosol data sets with aerosol optical depth (AOD)
and aerosol type as parameters. It has recently been shown
that aerosol parameters can be retrieved over land from the
MISR and MODIS instruments onboard the EOS-TERRA1
(launched December 1999) and EOS-AQUA (launched May
2002) satellites (Tanre et al., 2001; Kahn et al., 1997) and
from a synergetic retrieval (Holzer-Popp et al., in press a,b) of
SCIAMACHY and AATSR onboard the ENVISAT satellite
(launched March 2002). Therefore, the proposed new scheme
holds the potential to use this upcoming operational satellite
data sets in order to include up-to-date aerosol information.
In order to get the information about the aerosols for the
comparison presented in this paper, Linke turbidity values
based on Kasten (1996) together with the GADS/OPAC
aerosol climatology are used. The GADS/OPAC climatology (Hess et al., 1998; Koepke et al., 1997) provides
information of the AOD and the aerosol type, whereby
the AOD is dependent on the relative humidity. However,
the spatial and temporal resolution of the GADS/OPAC
climatology is coarse, as only summer and winter season
and a 5j spatial resolution is available. The Linke turbidity
climatology provides Linke turbidities in a monthly and 5
min of arc angle resolution worldwide (available at http://
www.helioclim.net/-linke/index.html). It has to be noted
that this small spatial resolution is just possible, using
improved interpolation routines such as data fusion. The
underlying measurement data have a much higher spatial
resolution.
averaging window. The input values for ozone and water
vapor were 275 DU and 15 mm, respectively. Note that
ozone has no big effect on the broadband irradiance, but
does on the UV.
The turbidity map provides a turbidity of 4 for the
respective months. That corresponds to a visibility of 34
km and an aerosol optical depth (AOD) of 0.23, respectively. The conversion of turbidity to visibility has been performed with the radiative transfer model MODTRAN
(Abreu & Anderson, 1996). GADS/OPAC provides an
AOD of 0.18 –0.25 for relative humidities between 50%
and 80% and urban as an aerosol type. The range of the
AOD is in consistency with the visibility derived from the
Linke turbidity climatology. The average relative humidity
for the clear-sky days was approximately 50%, leading to an
AOD of 0.18.
In Figs. 9 and 10, the comparison between SOLIS
calculated and measured direct and global irradiance is
diagrammed. It has to be noted that whether urban or rural
aerosols are used, no significant differences in the calculated
direct solar irradiance occur. Hence, just the results for the
urban aerosols are diagrammed. In the case of global
irradiance, the chosen aerosol type has a significant effect
on the global irradiance. In both figures, the results of the
Heliosat clear-sky model, described in Beyer et al. (2003),
are also diagrammed.
Using the aerosol information provided by the OPAC/
GADS climatology (AOD of 0.18, urban aerosol type) as
input, the calculated global and direct irradiance matches the
measurements very well, as shown in Figs. 9 and 10. The
relative root mean square error is 1.9% for global and 4.2%
for direct irradiance with a relative bias of 0.6%and 0.5%,
respectively. In addition, the SZA dependency is reproduced
very well by the SOLIS model.
In contrast to the results of the SOLIS calculations, the
Heliosat model results in a good match for the global
irradiance, but with a significant underestimation of the direct
4.2. Comparison of measurements and model, Freiburg,
August 2000
Cloud-free situations were selected according to the
cloud index derived with the Heliosat method from
METEOSAT images. A situation was assumed to be
cloud-free if the cloud index n of the respective pixel was
within the interval from 0.03 to 0.03 and the spatial
variation of the cloud index was less than 0.02. It is likely
that some situations with partial cloud cover are still
included, which especially affects the direct irradiance,
leading to an increasing statistical uncertainty.
The ground measurements have originally a temporal
resolution of 10 s. They are averaged to 30-min means in
accordance with the temporal resolution of the satellite. The
point in time when the pixel above the measurement station
is scanned from the satellite lies in the middle of the 30-min
Fig. 9. Comparison between SOLIS and measurements using the GADS/
OPAC information for the aerosols. The calculated Heliosat clear-sky
irradiance is also diagrammed. The differences between the models are
mainly due to the different atmospheric input information.
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
169
Fig. 10. Comparison between SOLIS and measurements using the GADS/OPAC information for the aerosols. The calculated Heliosat clear-sky irradiance is
also diagrammed.
irradiance for the given turbidity of 4. Since the turbidity
defines the attenuation of the direct irradiance, this indicates
that the chosen turbidity is too low. However, decreasing the
turbidity to values around 3 leads to a better match between
the measurements and the Heliosat modelled direct irradiance, on the one hand, but it leads to an overestimation of the
global irradiance on the other. The reason is the redundant
information of the turbidity in comparison with a separated
treatment of aerosol type, aerosol optical depth, and water
vapour. The effect of the aerosol type on the global irradiance
cannot be considered by using turbidity.
Consequently, a consistent match between measurements
and calculated direct and global irradiance is only possible
using information about the aerosol optical depth, the aerosol
type and the water content ‘‘separately.’’ Using the Heliosat
clear-sky model or any other model that is just based on
turbidity, the effect of different aerosol types on the global
irradiance cannot be considered, because the information
about the atmospheric state is redundant. This effect is even
significant for the measurement site, but is higher for sites
with higher aerosol load, or for sites characterised by special
types of aerosols events, like desert storms or biomass
burning. That is a drawback of Heliosat-1 and -2, but
demonstrates the advantages of the SOLIS model. Moreover,
reliable information of the spectral distribution of the irradiance cannot be derived by using only turbidity, without any
additional information about the atmospheric state. Additionally, changes in stratospheric aerosols, e.g., an increase of the
load after a volcanic eruption, cannot be treated with the
current Heliosat method without a refitting of the empirical
equation. Using SOLIS, just the enhanced aerosol load has to
be changed in the input file and the effect is considered.
In a comparison with measurements at Mannheim (Germany), it was possible to verify that urban aerosols with a
AOD of 0.18 is a reliable input for Freiburg. The station
Mannheim is nearby the station Freiburg and is characterised by a similar micro-climate—cities within the Rhine
valley climate. The bias between SOLIS results and measurements was below 1x
.
4.2.1. Spectral resolved irradiance data
Using the same atmospheric input (urban aerosol,
AOD = 0.18), the measured and calculated illuminance has
been compared for August 2000, Freiburg. The illuminance
is a measurement of a quantity of light as perceived by the
human eye. In order to calculate the illuminance, the
spectrally resolved irradiance output of SOLIS is weighted
with the light sensitivity of the human eye. The derived
value is then multiplied with 0.683 in order to convert W/m2
to klux. The measurements and the calculation matches very
well, demonstrating that the spectral output of the model is
reliable (see Fig. 11). In addition, the model results for rural
aerosols are also diagrammed.
Fig. 11. Measured and modelled illuminance, clear-sky situations, Freiburg,
August 2000.
170
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
Table 4
The clear days (all in May) used in this comparison
Station
Day
Year
Water column (mm)
Ozone (DU)
Bergen
(60.4N, 5.3E)
7, 19
6, 8
12, 13, 14
1999
2000
2000
7.5, 10.6
8.1, 11.6
13.6, 11.0, 8.1
368, 316
347, 342
309, 306, 319
4.2.2. General remarks
It has to be mentioned that a good match between
measured and calculated irradiances cannot be expected
for every month within one season. Similar comparisons
for September 2000 and 1999 lead to an acceptable but
inferior match between measurements and SOLIS calculated irradiance. This is most probably due to the fact that a
seasonal aerosol climatology is to coarse, see also Section
4.3. Changes in the aerosol content within a season due to
transport processes are not considered, but they affect the
measurements. Using climatological atmospheric data instead of daily values as input to SOLIS increases the
RMSE significantly. This effect has been investigated
within a study for Geneva (P. Ineichen, personal communication).
4.3. Comparison in Scandinavia
SOLIS calculations are compared against ground-measured hourly global and direct irradiance of the Nordic site:
Bergen, Norway (60.4jN 5.3jE). Cloud-free days were
selected according to the following criteria: (1) The
ground-observed cloud cover should not exceed 1 octa
during the day; (2) the curve of direct-beam normal radiation should be smooth and symmetric around noon solar
time. To allow the comparison with the clear-sky model of
Heliosat, which uses monthly Linke turbidity coefficients as
input, days were selected from the same month (here May).
The selected days are shown in Table 4. The value of the
Linke turbidity for May is 3.6 for Bergen. Daily values of
total water column (TWC) and ozone were used as input to
SOLIS, see 4.1. The GADS/OPAC aerosol climatology
suggests ‘maritime tropical’ and ‘summer maritime tropical’
as aerosol types for Bergen. In SOLIS, ‘maritime’ aerosols
were used, in addition to ‘rural’ and ‘urban’ ones. For
Bergen, the aerosol optical depth at 0.55 Am is given as
0.06 and 0.15 for a relative humidity of 10% and 90%,
respectively. The actual relative humidity varies between
10% and 90% for the clear days, with the lowest humidities
around and after noon.
4.3.1. Results
4.3.1.1. Direct irradiance. Fig. 12 shows the observed
direct irradiance for the clear days in Bergen plotted against
the SOLIS and Heliosat modelled values. Most observations
fit well the SOLIS data for low and high aerosol optical
depth (0.06 and 0.15). However, for 1 day in Bergen, the
measured values are clearly lower and fit well with a higher
aerosol optical depth of 0.28. This value is not unreasonable; Olseth and Skartveit (1989) found the range of aerosol
optical depth in Bergen to be 0.07 to 0.28 with a mean value
of 0.13. The effect of water vapour is seen to be smaller than
the effect of aerosols. The effect of ozone is negligible (for
broadband irradiance as here). However, for spectral output,
also accurate values of water vapour and ozone are of great
importance.
It is clear that the Heliosat model with monthly input
cannot be expected to be very accurate on day to day
variations, but may give good mean values. It appears,
however, that SOLIS is capable of reproducing hourly
radiation, given that the daily input (in particular aerosols)
is accurate.
4.3.1.2. Global irradiance. Observed global irradiances
for Bergen are plotted against SOLIS and Heliosat modelled
values in Fig. 13 (top). Here, the SOLIS values are too high,
while the Heliosat clear-sky model is closer to the observed
values. However, if the aerosol type is changed from ‘maritime’ to ‘urban’, SOLIS match the observed values much
better (Fig. 13, bottom). For the calculated direct irradiance,
the aerosol type was of little or no importance, but for global
irradiance, the aerosol type (single scattering albedo) largely
Fig. 12. Observed direct irradiances vs. modelled values by SOLIS and Heliosat. The aerosol optical depths are shown in the legend. Aerosol type is
‘‘maritime.’’
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
171
Fig. 13. Same as Fig. 12, but for global irradiance. Aerosol type is ‘‘maritime’’ on upper figure, and ‘‘urban’’ on lower figure.
affects the diffuse part. Since Bergen is a city with 235,000
citizens, urban aerosols are not unreasonable. The GADS/
OPAC climatology has quite coarse resolution (5j), so it
cannot account for microclimatic conditions represented by
cities, especially if they are surrounded by a rural region.
5. Discussion
5.1. Treatment of clouds
The integrated use of the RTM is performed within the
clear-sky module. For the treatment of clouds the n – k
relation or the COD option is used. With respect to the
COD option, an RTM is used to find the parameterisation,
but not directly integrated. The question arises why an
integrated use of an RTM within the cloud module is not
needed on the one hand or not possible on the other. The n – k
or COD option works well for almost homogenous cloud
situations. Consequently, the difficulties or limitations of
both options arises from heterogenous cloud effects.
With respect to 3-D cloud effects, an operational usage of
an RTM for the treatment of heterogenous clouds (whether
directly or using precalculated look-up tables) is not feasible
today. The limitations of 3-D cloud modelling do not enable
realistic RTM calculations of 3-D cloud problems in an
operational manner. Just case studies are feasible. With
respect to the operational use of an RTM, the problem is
the nonavailability of realistic specification of heterogenous
clouds from measurements. MSG will not provide sufficient
information about 3-D cloud characteristics. No other satellite or measurement setup provides this information for the
needed temporal resolution and spatial coverage nowadays.
Besides, an explicit or integrated use of RTM is not practicable since the needed calculation time of 3-D RTM models is
too large for an operational adaptation.
5.2. Spectral resolved irradiance for cloudy situations
Within previous studies, it has been shown that the cloud
index is independent on the wavelength in the range of the
MSG visible channels. However, the shape of the spectral
clear-sky irradiance changes due to the scattering effects in
consequence of the cloud particles. In order to correct the
change in the spectral shape, the RTM model LibRadtran
has been used to calculate look-up tables. First comparisons
between measured and simulated illuminance indicate that
the spectrally resolved output is now serviceable for ‘‘allsky’’ situations as well. However, further validations should
be done.
Using the COD option for the treatment of clouds, the
effect of clouds on the spectral distribution of clear-sky
irradiance is already considered. Consequently, the integrated use of the RTM is the basis for spectral resolved solar
irradiance data for all-sky situations as well.
6. Summary and conclusion
Within this paper, the power and advantages of the new
SOLIS model have been discussed. The main scope has
been the SOLIS clear-sky module, but also the treatment of
the clouds, even though this is still under development,7 has
been briefly discussed in order to explain the expected
7
However, a SOLIS all-sky working version is available on request.
172
R.W. Mueller et al. / Remote Sensing of Environment 91 (2004) 160–174
benefits of the integrated RTM use for the all-sky situations
as well.
The integration of the RTM into the calculation schemes
is associated with a high flexibility with respect to changes
of the atmospheric state and the different user requirements
on the solar irradiance data. SOLIS provides the possibility
to use enhanced information of the atmospheric state and,
hence, the potential to improve the accuracy of the calculated direct, global, and diffuse irradiance. Additionally,
spectrally resolved data can be calculated operationally in
MSG pixel resolution.
The Modified Lambert – Beer relation enables the integrated use of RTM within the clear-sky scheme. The
integrated use of RTM is linked with high flexibility relating
to the input of the atmospheric state, changes in theory (e.g.,
new aerosol models), and the desirable output parameters.
The integrated use of the RTM is linked with the
following benefits:
Spectral information is automatically provided using the
correlated-k option included in the RTM LibRadtran
package (http://www.libradtran.org/).
Consistent calculations of global, direct, and diffuse
radiation for clear-sky cases within one single scheme
considering different aerosol types and not only turbidity.
Hence, an improved estimation of the relation between
global and direct radiation is possible, especially for
clear-sky situations. The separated use of H2O and
aerosol information is a requirement for accurate
information of the spectral distribution of irradiance.
Deviations of the atmospheric state from the average (O3,
H2O(g), aerosols) can be easily corrected using the results
of the modified Lambert –Beer fit.
Clear and easy linkage with cloudy sky scheme, whereby
the treatment of heterogenous cloud effects is not
restricted.
The usage of the modified Lambert –Beer law enables
not only the direct integration of an RTM into the
irradiance scheme, but also the potential for the calculation
and use of easy handling look-up tables. The advantages of
the modified Lambert – Beer relation, and hence, the integrated RTM use, can be adapted to other solar irradiance
models as well and is therefore a new milestone in solar
irradiance modelling.
The SOLIS model has been validated in three steps.
In Section 2.3, it has been demonstrated that the MLB
function matches the RTM results very well. The
differences in the broadband irradiance (306.8 – 3001.9
nm) are usually less than 8 W/m2 for high SZA and less
than 5 W/m2 for SZA below 75j (8 and 4 W/m2 for
direct irradiance, respectively).
In Section 3, it has been demonstrated that SOLIS is able
to reproduce very accurately (hourly) values of direct and
global broadband irradiance if accurate daily atmospheric
input parameters are used. The estimated RMSD is 2.3%
for direct irradiance and 4% for global irradiance.
In Section 4, SOLIS has been compared with measurements and with the Heliosat method, whereby H2O(g) and
O3 retrieved from satellite data and the GADS/OPAC
aerosol climatology (Hess et al., 1998; Koepke et al.,
1997) have been used as input to SOLIS. It has been
demonstrated that SOLIS is able to reproduce the
measurements very well within the scope of the
uncertainties introduced by the rough spatial and
temporal resolution of the aerosol climatology. For
broadband clear-sky irradiance aerosols are by far the
most important parameter. Since a model depends on
accurate atmospheric input data, there is an urgent need
to improve the information about aerosols. Additionally,
it has been shown that the aerosol type has a significant
effect on the global irradiance. A consistent match
between model and measurements for both global and
direct irradiance was only possible by consideration of
the aerosol type. In contrast to the Heliosat method
(Beyer et al., 2003), which is dedicated to use turbidity
information, the full information about the clear sky
atmosphere, including aerosol type, can be used by
SOLIS.
The improvements in the art of retrieval during the last
years are impressive and still going on. Together with new
remote sensing instruments such as SCIAMACHY or SEVIRI (aboard ENVISAT, MSG), it can be expected that the
information about the atmospheric state, especially with
respect to clouds and aerosols, will be further improved.
In order to benefit from the enhanced information about the
atmospheric state, a model such as SOLIS is necessary.
Keeping this in mind, the final conclusion can be drawn
that the enhanced capabilities of the new MSG and ENVISAT satellites, together with the new type of solar irradiance
scheme, SOLIS, will provide solar irradiance data with high
accuracy, high spatial and temporal resolution, and large
geographical coverage, all within the European Heliosat-3
project.
Acknowledgements
The Heliosat-3 project is funded by the EC (NNK5-CT200-00322).We thank Arve Kylling (NILU) and Bernhard
Mayer (DLR) for providing the LibRadtran RTM package.
The DWD is acknowledged for the data of the Mannheim
station. Thanks to A. Drews for the grammatical
corrections.
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Paper III
Dagestad, K-F. and Olseth, J.A. (2005)
An alternative algorithm for calculating the cloud index
Manuscript
An alternative algorithm for calculating the cloud index
Knut-Frode Dagestad and Jan Asle Olseth
Geophysical institute
University of Bergen
Allegaten 70
5009 Bergen
Norway
April 2005
Abstract
The cloud index is an important component of the Heliosat algorithm, which estimates solar
radiation components from Meteosat High Resolution Visible images. The cloud index quantifies
the reflective properties of the atmosphere, and varies from 0 at clear conditions to 1 at overcast.
The algorithm is semi-empirical in the way that it includes several constants that need to be tuned.
Some of these were removed in the Heliosat-II algorithm (Rigollier et al., 2004) which introduced
the Meteosat calibration constant to replace the "pseudo reflectivity" with a "real reflectivity". This
approach is followed here, and two additional changes are made: 1) An analytical expression is
introduced to correct for backscattered radiation from air molecules. 2) A correction is made for
non-lambertian reflectivity, removing the time consuming need for determining the ground
reflectivity for each month and each slot. The new cloud index is used to calculate global
irradiances which are validated against hourly measurements from five European ground stations.
The average root mean square deviation is 15.5% for a six month spring/summer period, of
comparable accuracy as using the more time consuming traditional algorithm of Hammer (2000).
1 Introduction
For more than 20 years global irradiance at ground level has been successfully estimated from
images taken by meteorological satellites. Since the input to the models is extremely simple, a
single digital count per pixel, the methods need also to be very simple. So instead of a physical
approach of using forward calculations and the principle of conservation of energy, the methods
rely on the simple idea of using relative values of the digital counts:

when a pixel is relatively dark, cloud free conditions are assumed, and the output of the
model is simply global irradiance calculated with a clear sky model

when the pixel is relatively bright, overcast conditions are assumed, and the output of the
model is e.g. 5% of the corresponding clear sky value

for intermediate brightness a simple linear transformation is assumed
On top of this scheme empirical corrections have been made with success, e.g. a subtraction of the
scattered radiance from air molecules, which depends strongly on the geometry. Although such
corrections improve the performance, they have some disadvantages:

it is less obvious how to interpret physically the "relative reflectivity" and the cloud index
1

corrections based on tuning to data may have unpredictable effects outside the specific sites
or time periods which they are tuned to

will new corrections describe a real physical phenomenon or just a side effect of earlier
corrections?
Therefore, the number of corrections should be kept to a necessary minimum, and based on physical
reasoning whenever possible. Here an analytical expression for the backscattered radiation from the
atmosphere is derived and applied to the Heliosat-scheme. This removes the uncertainty related to
the empirical expression from Hammer (2000) which could include components from aerosols and
the sea surface, and which was also tuned to measurements for certain pixels for a certain time
period. The analytical expression is also more straightforward to adapt to other sensors.
Another necessary procedure in the Heliosat-scheme is to compensate for the lower bound of the
relative reflectivity (ρground) which varies with time. The current approach in the Heliosat-scheme
uses a histogram technique to determine the ground reflectivity for each slot (images acquired at the
same UTC-time of day belong to the same "slot") and month, thus keeping the sun-ground-satellite
geometry fairly constant. Some problems with this approach are:

The number of data points available to find ρground is maximum 31, which sometimes gives
numerical unstabilities

This procedure is a very time-consuming part of the Heliosat scheme
Besides, even for the same time of day, the geometry can change somewhat during a month. For
Paris, as an example, the angle between the directions towards the sun and Meteosat for the 12 UTC
slot is varying between 4 and 16 degrees during September. To overcome these problems, ρground is
parameterised as a function of the angle between the directions to the sun and satellite as seen from
ground ("co-scattering angle"). In addition to saving computing time, this permits the use of a much
lager data sample to determine ρground , thus eliminating the problems for pixels and slots with few
clear situations during a month.
2 An alternative algorithm for the cloud index
2.1 Calculation of the reflectivity from Meteosat counts
A part of the signal that a "visible" satellite sensor receives when viewing earth is directly scattered
from air molecules. This part depends strongly on the sun-ground-satellite geometry, and as the
radiation at ground is independent of the satellite position, it should be corrected for. The traditional
approach in the Heliosat algorithm is to subtract a quantity from an expression which is tuned to
satellite counts from cloud free pixels over sea (Hammer, 2000). It was however shown by
Dagestad (2001) that most of this signal is first order scattered radiance, and hence an analytical
expression for this component could be used. Under the assumption of a plane-parallel atmosphere
the following expression for radiance scattered towards a satellite is derived (see Appendix):
1
2
1
− 


31cos  
cos 
r atm =I 0
[1−e cos  cos  ]
16 
cos cos 
(1)
where θ is the solar zenith angle, φ is the satellite zenith angle and ψ is the "co-scattering angle". I0
is the solar constant of 1367 W/m2. According to the Appendix an optical depth τ of 0.0426 is
representative for the Meteosat-7 and 8 HRV channels, corresponding to an "equivalent
wavelength" of 680 nanometres.
Equation 1 is singular for θ or φ at 90 degrees, but should have sufficient accuracy up to at least 85º
2
for a spherical atmosphere. The advantage of this expression compared to the one from Hammer
(2000) is that it is not fitted to certain angular configurations, and that it contains no signal from the
surface or other atmospheric components.
The reflectivity is then calculated by:
=
C−C off c f
 r atm
−
 I  cos 
I 0 cos 
(2)
where:
- C is the raw Meteosat HRV counts
•
- Coff is the constant instrument offset (51 for Meteosat-8)
•
- cf = 0.56
W
W
is the calibration constant and Iμ = 1403 2
is the
m ⋅str⋅ m⋅counts
m ⋅m
band
•
2
solar irradiance of the Meteosat-8 HRV channel (Govaerts et al., 2004)
- ε is the correction for varying sun-earth distance
The factor π is included to convert the reflected radiance to irradiance under the assumption of
lambertian reflectance. This assumption is discussed in the next section. For the calculation of the
cloud index ρ could be interpreted as the reflectivity of the ground and clouds, although this is not
strictly physical correct.
2.2 Calculation of the cloud index from the reflectivity
In the Satel-Light version of the Heliosat scheme (Fontoynont et al., 1998) the (pseudo) ground
reflectivity is determined for each pixel and for each month and slot. It is however seen that the
reflectivity depends strongly on the co-scattering angle ψ, and thus a parameterisation will be made
to correct for this. The correction probably includes the effects of:

non-lambertian reflection from the ground surface itself

varying amounts of shadows due to nearby terrain and broken clouds

scattering and absorption due to interaction with air molecules, aerosols and clouds
Figure 1 shows the reflectivity according to Equation 2 plotted versus ψ for six sites in Europe and
the Canary Islands. For each of these sites the 4-percentile value is calculated for ψ within each ten
degree bin. A 3rd order polynomial is then fitted to these points, and plotted as broken curves on the
figure. The mean of the polynomials is taken, and normalised to the value 1 for ψ = 0˚, to be used as
a "shape function":
 g shape =1−0.59 0.11 20.05 3
(3)
where ψ is given in radians. The ground reflectivity can then be estimated by:
 ground = g0  g shape 
(4)
where ρg0 is the reflectivity of the pixel for ψ=0. This constant is determined by taking the 4percentile of a time series of reflectivities divided by the "shape function". To avoid noise ψ should
be kept below 50˚. The advantage of this approach is that the ground reflectivity can be determined
once and for all, saving a lot of computer power. Besides, the difficulty of determining the
reflectivity for months/slots with few clear situations is also avoided. ρground from Equation 4 is
plotted as solid lines on Figure1. Still the ground albedo can be determined more frequently to
account for effects which are truly due to changes of the reflecting properties of the ground surface
(e.g. snow cover and vegetative changes).
3
Figure 1: Reflectivities for the Meteosat-8 pixels of 6 European sites (dots) calculated with Equation 2 for all Meteosat8 images between 16 March and 31 August 2004, plotted as a function of the co-scattering angle ψ. Broken lines: third
order polynomials of ψ fitted to 4 percentiles within each ten degree bin (0-10, 10-20, etc). Solid lines: ground albedo
calculated by Equation 4 by use of the procedure described in section 2.2
The upper boundary of reflectivities (cloud reflectivity) is seen to vary much less with ψ (or solar
zenith angle θ) and a constant value of 0.81 is chosen as ρcloud, taken as the 98 percentile of the
counts. This is assumed to be the reflectivity of the "thickest clouds". The 98 percentile is chosen
instead of the maximum value to avoid any outliers. The cloud index (n) is then finally calculated
from:
n=
− ground
cloud − ground
3 Description of data for validation
3.1 Ground measured global irradiances
In this study the satellite derived irradiances are compared to hourly measurements of global
irradiances at five European stations for the period 16 March to 31 August 2004 (Table 1). All
measurements are done with Kipp & Zonen pyranometers, and the data are manually quality
controlled by the respective data providers (see acknowledgements).
4
(5)
Table 1: Stations with ground based hourly global irradiances.
Station
Elevation Latitude Longitude
[m.a.s.l.]
[ºN]
[ºE]
Instrument
Barcelona
98
41.39
2.12
Kipp & Zonen CM 11
Bergen
45
60.40
5.32
Kipp & Zonen CM 11
Freiburg
275
48.02
7.84
Kipp & Zonen CM 11
Geneva
425
46.20
6.13
Kipp & Zonen CM 10
Lyon
170
45.78
4.93
Kipp & Zonen CM 6
3.2 Satellite derived global irradiances
Global irradiances are calculated by the following empirical relationship (Rigollier et al., 1998)
using the cloud indices of section 2.1 as input:
1.2
1−n
k=
2
2.0667−3.6667 n1.6667 n
0.05
for n −0.2
for n∈[−0.2 , 0 .8]
for n∈[ 0.8 , 1.1]
for n1.1
(6)
The clear sky index k is defined as the ratio between the actual global irradiance, G, and the clear
sky global irradiance, Gclear, which can be modelled with a clear sky model.
k≡
G
G clear
(7)
Two different clear sky models are used in this study:

The model used by the Satel-Light project (Fontoynont et al., 1998) which consists of one
model for the direct irradiance (Page, 1996) and one model for the diffuse irradiance
(Dumortier, 1995). The input used is height above sea level, solar elevation and monthly
values of Linke turbidities from a database developed by Dumortier (1998).

The SOLIS model (Mueller et al., 2004) which uses two simulations with the radiative
transfer model libRadtran (www.libRadtran.org) per day to parameterize the diurnal
variation of global irradiance (and other spectral and angular components). SOLIS uses
climatological values of water vapour (NVAP, www.stcnet.com/projects/nvap.html) and
aerosols (SYNAER, Holzer-Popp et al., 2002a, 2002b) as input. Operational retrieval of
aerosols and water vapour for input to SOLIS is planned for the near future within the EUproject Heliosat-3.
Two different cloud indices are also used:

the cloud index calculated with the algorithm in section 2

the "old" cloud index described in Hammer (2000). Adaptation from Meteosat-7 to
Meteosat-8 was performed by Annette Hammer and Rolf Kuhlemann at the University of
Oldenburg (personal communication) including a change of ρcloud from 160 counts to 650
counts (Meteosat-8 gives 10-bit values, whereas Meteosat-7 gives 8-bit values)
5
4 Validation
4.1 Verification of the algorithm for calculation of ground reflectivity
In section 2.2 a new method to calculate the ground reflectivity in Heliosat was developed. This
method will here be validated against five stations which are independent from the stations used for
development. Figure 2 shows reflectivities calculated with Equation 2 from the hourly means of the
satellite counts for the five stations in table 1. It is seen that the ground albedo calculated with the
algorithm of section 2.2 is nicely fitting the lower bound of reflectivities. The fit is actually better
than for the development stations; the reason for this is that the averaging of four 15 minute values
to create hourly values is removing much of the "noise" seen in the plot of 15-minute values on
Figure 1. The shape function (Equation 3) describes well the non-lambertian variation of reflectivity
for all stations, even though ρg0 varies between 0.165 for Bergen and 0.208 for Barcelona and Lyon.
Figure 2: Calculated reflectivities for the hourly means of the satellite counts for the stations of Table 1 (points).
Ground albedo from the algorithm in section 2.1 is plotted as solid lines.
4.2 Optimal pixel size
In earlier versions of Heliosat, with data from Meteosat First Generation (MFG, Meteosat 1-7), the
best accuracy was obtained by averaging cloud indices over 15 pixels, 5 pixels in the east -west
direction and 3 pixels in the north-south direction (Fontoynont et al., 1998). To find the optimal
pixel size for Meteosat-8, cloud indices are here calculated for the following configurations: single
pixel, 3x3, 5x5, 7x7 and 1x3, 3x5, 5x7 and 7x9. The n times (n+2) configurations gives an
approximately square area in Europe where pixels are longer in the north-south direction due to
6
oblique viewing angle. Figure 3 shows the Root Mean Square Deviation (RMSD) of hourly global
irradiances for all five ground stations. Only results with the Satel-Light clear sky model are shown,
but both the old and the new cloud indices are used. For both cloud indices and for all stations,
averaging over 3x5 pixels gives the lowest RMSD. (The only exception is Lyon where 5x5 pixels
gives slightly lower RMSD). This is the same results as for MFG, even though the MSG pixels have
roughly nine times smaller area. In this study all irradiances are hereafter calculated with cloud
indices averaged over 3x5 pixels.
Figure 3: Root Mean Square Deviation (RMSD) of hourly global irradiances calculated with the Heliosat-method,
using two different cloud indices. For the solid lines the cloud indices are averages over n x n pixels; for the broken
lines the number of pixels in the east-west direction is n+2.
4.3 Validation of hourly global irradiances
Table 2 shows RMSD and Mean Bias Deviation (MBD, model-observation) for all stations and for
both cloud indices and both clear sky models (chapter 3). Only hours for which the solar elevation
is always above 5 degrees are compared. For the average over all stations the new cloud index with
the Satel-Light clear sky model gives the lowest RMSD (15.5%) and also the smallest MBD
(-0.9%). However, when the SOLIS clear sky model is used the old cloud index performs better,
and the global irradiances calculated with the new index are then on average 3% too low.
7
Table 2: Root Mean Square Deviation (RMSD) and Mean Bias Deviation (MBD, model-observation) for two different
clear sky models (SOLIS, Satel-Light) and two different cloud indices ("New" and "Old", see chapter 3). The values are
given in percent of mean observed global irradiance. Bold numbers show the lowest RMSD for the given station.
New cloud index
SOLIS
Observed
Station
[W/m2]
Old cloud index
Satel-Light
SOLIS
Satel-Light
Number of
RMSD MBD RMSD MBD RMSD MBD RMSD MBD
hours
Barcelona
531
1475
14.7
-6.4
12.9
1.1
13.7
-3.9
13.6
3.8
Bergen
280
2073
23.4
0.2
23.5
0.4
23.1
0.0
23.3
0.2
Freiburg
389
1753
17.1
-6.0
16.3
-2.2
16.5
-3.3
16.5
0.6
Geneva
459
1656
14.0
-3.1
13.9
-2.3
13.8
-0.6
13.9
0.2
Lyon
432
2003
13.1
0.4
13.3
-1.3
13.6
2.5
13.4
0.8
All stations
410
8960
16.1
-3.0
15.5
-0.9
15.7
-1.0
15.7
1.2
Table 2 gives no unique answer to which is the best cloud index and which is the best clear sky
model. According to Table 3 the Satel-Light clear sky model generally gives higher clear sky
irradiances than the SOLIS model, and Figure 4 shows that the new cloud index is generally higher
than the old one. Hence a too high cloud index can compensate for a too high clear sky value and
vice versa. The frequency distributions of Figure 4 show that the new cloud index has a clear peak
close to zero, while the old one has more frequently negative values. Negative cloud indices give
clear sky indices higher than 1, which could compensate for a clear sky model giving too low
values. For the clear sky models it should be stressed that the input to the models is probably more
important than the models themselves, so an interesting prospect for the near future is the inclusion
of daily retrieved atmospheric parameters into the SOLIS model within the Heliosat-3 project. The
new cloud index has however the advantage of being fast and easy to calculate routinely, and as it is
based on physical quantities it should be easier to do possible physical and/or empirical corrections
in the future.
Table 3: Mean clear sky global irradiances of all hours for all stations and both clear sky models. See chapter 3 for
description of the models.
SOLIS
Satel-Light
Barcelona
613.1
662.2
Bergen
484.2
484.6
Freiburg
576.9
600.5
Geneva
605.9
610.8
Lyon
606.2
595.5
All stations
573.3
584.6
8
Figure 4: Frequency distributions of the two different cloud indices for the five stations of Table 1.
5 Summary and discussion
Two modifications are made to the traditional algorithm for calculation of the cloud index:

An analytical expression for the scattered radiance from air molecules is introduced,
replacing an empirical expression.

The variation of the parameter ρground is parameterised as a function of the angle between the
directions towards the sun and the satellite. This permits to calculate ρground once and for all,
replacing a time consuming histogram technique which has to be applied separately to each
slot and month.
These two corrections are applied in the Heliosat scheme to calculate global irradiances and the
results are compared to hourly measurements from five ground stations in Europe. The RMSD and
the MBD are very similar compared to the results using the traditional cloud index from Hammer
(2000). One cloud index gives however better results with one clear sky model, while the other
cloud index gives better results with another clear sky model. It is seen that the Satel-Light clear sky
model generally gives higher values than SOLIS, and that the new cloud index introduced here is
generally higher than the one from Hammer (2000). Thus it is evident that sometimes errors are
cancelling each other in the Heliosat-scheme, and sometimes they are adding up. Using
climatological values of turbidity as input to the clear sky models, the clear sky model is by now a
large uncertainty in the Heliosat-scheme. This makes it difficult to find the optimal cloud index.
The inclusion of real time atmospheric parameters in the new SOLIS clear sky model in the near
future looks promising. As the clear sky value will then have a stronger physical basis, both the
cloud index and the relationship with the clear sky index should be suitably chosen, and perhaps
9
tuned to ground data to minimise the deviation. The remaining empirical parameters which can be
adjusted for best performance are:

The method to determine ρcloud. Here a 98 percentile of reflectivities is used, but there is no
clear physical reasoning behind such a choice. The bias of the Heliosat-algorithm is highly
sensitive to the choice of ρcloud.

The method to determine ρground. The bias is not as sensitive to this parameter, as it is in both
the nominator and denominator of equation 5, but it should certainly be chosen so that when
the reflectivity equals ρground , the observed clear sky value is matching the clear sky model.

The clear sky - cloud index relationship. For the cloud index approaching 1 the value of the
clear sky index should be in accordance with the value of ρcloud. In other words; the clear sky
value for the cloud index equal to 1 should be similar to what is observed under a cloud
cover giving a reflectivity equal to ρcloud.
It is seen that the new cloud index has a clear peak around zero, while the traditional has more
frequently negative values. The reason is that the old histogram technique gives a higher value for
ρground than the new algorithm presented in section 2.2. There are two ways the cloud index can
become negative; one is when the atmosphere is clearer than the "reference atmosphere" for which
the clear sky model applies. For this case a negative cloud index gives correctly a global irradiance
which is higher than the clear sky model. A second reason can be that the pixel is completely in
shadow from a nearby cloud which is not seen on this pixel. In this case the conditions are taken as
very clear, while the ground measured irradiance is low due to the shadows. Probably both
situations occur, and the effects are cancelling each other. That the 'traditional' cloud index is more
frequently negative needs not be a bad sign, but one should be aware of the difference when it is
combined with a clear sky model.
For both cloud indices and clear sky models averaging the cloud index over 3x5 pixels gives best
results.
Acknowledgements:
This work is a part of the project Heliosat-3 funded by the European Commission (NNK5-CT-20000322). We thank project colleagues for valuable discussions and advices. The following persons
are thanked for providing the ground measurements for the validation: Antonio Ortegón Gallego
(Barcelona), Christian Reise (Freiburg), Pierre Ineichen (Geneva) and Dominique Dumortier
(Lyon). We also thank Jethro Betcke and Rolf Kuhleman at the University of Oldenburg for
providing data from Meteosat-8 for specific sites.
6 References
Rigollier, C; Lefèvre, M; Wald, L (2004) The method Heliosat-2 for deriving shortwave solar
radiation from satellite images, Solar Energy 77, 159-169
Hammer, A (2000) Anwendungsspezifische Solarstrahlungsinformationen aus Meteosat-daten,
PhD thesis, University of Oldenburg
Dagestad, K-F (2001) Ein modellstudie av samanhengen mellom reflektert radians ved toppen av
atmosfæra og globalstråling ved bakken, Master Thesis, University of Bergen
Govaerts, Y; Clerici, M (2004) MSG-1/SEVIRI Solar Channel Calibration, ; Commisioning
Activity Report for Eumetsat. EUM/MSG/TEN/04/0024, Version 1.0, 21 Jan 2004
Fontoynont, M; Dumortier, D; Heinemann, D; Hammer, A; Olseth, J A; Skartveit; Ineichen,
P; Reise, C; Page, J; Roche, J; Beyer, H; Wald, L (1998) Satel-Light: A www server which
provides high quality daylight and solar radiation data for western and central Europe, Proc. 9th
conference on satellite meteorology and oceanography in Paris, 25-28 May 1998, pp. 434-437
10
Rigollier, C.; Wald, L. (1998) Using Meteosat images to map the solar radiation:improvements of
the Heliosat method, Proceedings of the 9th Conference on Satellite Meteorology and
Oceanography. Published by Eumetsat, Darmstadt,Germany, EUM P 22, pp. 432-433
Page, J (1996) Algorithms for the Satel-Light programme, Technical report for the Satel-Light
programme
Dumortier, D (1995) Modelling global and diffuse horizontal irradiances under cloudless skies
with different turbidities, Technical report for the Daylight II project, JOU2-CT92-0144
Dumortier, D (1998) The Satel-Light model of turbidity variations in Europe, Report for the 6th
Satel-Light meeting in Freiburg, Germany, September 1998
Mueller, R; Dagestad, K-F; Ineichen, P; Schroedter, M; Cros, S; Dumortier, D; Kuhlemann,
R; Olseth, J. A; Piernavieja, C; Reise, C; Wald, L; and Heinemann, D (2004) Rethinking
satellite-based solar irradiance modelling, The SOLIS clear sky module, Remote Sensing of the
Environment 91, 160-174
Holzer-Popp, T; Schrodter, M; Gesell, G (2002a) Retrieving aerosol optical depth and type in
the boundary layer over land and ocean from simultaneous GOME spectrometer and ATSR-2
radiometer measurements, 1, Method description, J. Geophys. Res. 107, AAC16-1 – AAC16-17
Holzer-Popp, T; Schrodter, M; Gesell, G (2002b) Retrieving aerosol optical depth and type in
the boundary layer over land and ocean from simultaneous GOME spectrometer and ATSR-2
radiometer measurements, 2, Case study application and validation, J. Geophys. Res.
Paltridge, G; Platt, C (1976) Radiative processes in meteorology and climatology, Elsevier, ISBN
0-444-41444-4
Appendix
A.1 An analytical expression for the backscattered radiation from air
molecules
An analytical expression for the scattered radiance from the air molecules towards a satellite will
here be derived for plane-parallel conditions. It is assumed that there are no other scattering or
absorbing agents in the atmosphere, and that all photons are scattered only once. Figure 5 shows a
situation with a solar zenith angle θ, and a satellite viewing the sunlit area at ground with a zenith
angle φ. The optical depth due to scattering is increasing downwards from 0 at the top of
atmosphere to τ and τ+dτ at two indicated levels.
11
Figure 5: Schematic illustration of the infinitesimal volumes of the
atmosphere between the optical depth τ and τ + δτ from which solar
radiation is scattered towards a satellite. θ and ф are the solar and satellite
zenith angles, respectively.
The amount of radiation scattered per volume unit at level τ is given by:
direct radiation into volume dV −direct radiation out of dV 
dV 
I e
−
cos
−I  e
−d 
cos 
d
cos 
−
−d 
=
(8)
−
cos 
=
I e cos  1−e cos ≈ I  e cos 
d 
where Iλ is the incoming monochromatic irradiance at the top of the atmosphere.
The scattered radiation from the volume dVφ that reaches the satellite is given by:
scattered radiation
× phase function×transmissivity towards satellite×volume=
unit volume
−
−
cos
cos  d 
I  e P  e
cos 
(9)
where P(ψ) is the scattering phase function and ψ is the angle between the directions towards the
sun and satellite as seen from ground. Integration from τ = 0 at the top of the atmosphere to τ gives
the scattered radiance towards the satellite from the whole atmospheric column down to the level τ:
r =
I  P 
cos 

∫e
0
'
− 
1
1


cos  cos 
1
1
−


cos 
d  ' =I  P 
[1−e cos  cos  ]
cos cos 
12
(10)
The Rayleigh scattering function is well known:
P =
3
2
1cos 
16
(11)
Note that in this context ψ is 180 degrees minus the more commonly used scattering angle, and is
therefore referred to as the 'co-scattering angle'. Equation 11, however, remains unchanged. An
expression for the vertical optical depth of the atmosphere due to Rayleigh scattering as a function
of wavelength is found from Paltridge et al. (1976):
=
−4.05


0.311 m
(12)
A.2 Adaptation to the Meteosat-8 HRV response function
Equations 10, 11 and 12 describe monochromatic radiation scattered towards a satellite. To get the
actual radiance observed by Meteosat it should be integrated over all wavelengths, weighted with
the Meteosat-8 HRV response function:
r atm =
∫ r R HRV d 
∫ RHRV d 
(13)
Then the equation would have to be integrated numerically for any actual geometrical
configuration. Figure 6 shows that by using an 'equivalent wavelength' of 680 nanometres radiances
very close to what is obtained by numerical integration over all wavelengths are found. To a good
approximation the following equation can therefore be used for the scattered solar radiation from air
molecules reaching Meteosat-8:
1
2
1
−


31cos 
cos 
r atm =I 0
[1−e cos  cos ]
16 
cos cos 
(14)
where I0 is the solar constant of 1367 W/m2. Equation 12 gives a value for the optical depth τ of
0.0426 for λ = 680 nanometres.
The same equation can be used for Meteosat-7 which has the same spectral response function of the
HRV-channel. For other spectral channels similar 'equivalent wavelengths' could be obtained by the
same integration. It was shown in Dagestad (2001) that for the wavelengths of the Meteosat HRV
function single scattering is dominant. Care should however be taken for wavelengths where
multiple scattering is dominant.
13
Figure 6: Calculation of the radiance scattered from air molecules and observed by the Meteosat-8 HRV channel for
various angular configurations. The x-axis is the result obtained by numerically integrating Equation 13. The y-axis is
the results by using Equation 14 with optical depths for the wavelengths indicated on the figure. The geometrical
configurations used are the actual configurations for all Meteosat-8 images for the period 16 March to 31 August 2004
for the same stations as in Figure 1.
14
Paper IV
Dagestad, K-F. and Wald, L. (2005)
Assessment of the database HelioClim-2 of hourly irradiance
derived from satellite observations
Draft
Assessment of the database HelioClim-2 of hourly
irradiance derived from satellite observations
Knut-Frode Dagestad 1) and Lucien Wald 2)
1)
2)
Geophysical Institute, Univeristy of Bergen, Allegaten 70, Norway
Groupe Télédétection & Modélisation, Ecole des Mines de Paris / Armines,
BP 207, 06904 Sophia Antipolis cedex, France
Draft
May 2005
Abstract
This paper presents a validation of the database HelioClim-2, which provides solar irradiance data
processed from satellite images on a web server (www.helioclim.net). Like HelioClim-1,
HelioClim-2 is using the Heliosat-2 algorithm for the processing, but the input satellite data to
HelioClim-2 are sampled at a higher frequency both in space and time. When compared to daily
sums of global irradiance at five European locations for the period March to August 2004,
HelioClim-2 gives a Root Mean Square Deviation (RMSD) of 16%, compared to 30% for
HelioClim-1. For hourly irradiances HelioClim-2 gives an RMSD of 26%, compared to 18% for the
Heliosat-1 method. It is seen that HelioClim-2 overestimates the global irradiance for all stations. A
likely reason is found to be a too high value of the cloud reflectivity within the Heliosat-2
algorithm.
1 Introduction
The benefit of observations made by geostationary satellite for assessing the solar irradiance –also
called shortwave downwelling irradiance- has been demonstrated by a large number of studies. The
Ecole des Mines de Paris has created a database called HelioClim-1 by applying the method
Heliosat-2 (Rigollier et al. 2004) to images acquired by the series of Meteosat satellites, from
Meteosat-4 to -7. The geographical coverage of HelioClim-1 is the field of view of Meteosat, i.e.,
Europe, Africa and the Atlantic Ocean. The database contains daily irradiation -or daily mean
irradiance- for every day from 1985 up to present. The quality of HelioClim-1 has been assessed by
several comparisons between ground measurements and HelioClim-1 values (Lefèvre et al. 2005;
Cros, 2004). HelioClim-1 data are available by the means of the SoDa web service (www.sodais.com). This database has met an unexpected success: approximately 1000 requests per month in
early 2005.
Building on this success, Ecole des Mines de Paris took the opportunity of the launch of the new
series of Meteosat satellites to create a new database HelioClim-2. This new series Meteosat Second
Generation (MSG) became operational in late January 2004 and the new satellited is called
1
Meteosat-8. HelioClim-2 is also accessible by the means of the SoDa web service. It provides
hourly mean irradiance from February 2004 up to present. The geographical coverage is similar to
that of HelioClim-1.
The present article is the first assessment of the quality of HelioClim-2, of both hourly and daily
mean irradiances, with respect to ground measurements. In addition, other sources of data, e.g.,
HelioClim-1, are used.
2 The HelioClim-2 database
The method Heliosat-2 is operated in real-time on Meteosat-8 data acquired by a receiving station at
Ecole des Mines de Paris. Because Heliosat-2 has been developed to perform on images acquired in
a broadband range, the MSG data acquired in the narrow visible bands VIS-1 (650 nm) and -2 (850
nm) are combined together to simulate the broadband channel of Meteosat-7 (Cros et al. 2005). The
calibration coefficients are read in the header of the Meteosat-8 images on the one hand and on the
Web site of Eumetsat for Meteosat-7 on the other hand (www.eumetsat.de). The radiances are remapped before they are processed by the method Heliosat-2; first they are filtered by a 17x17 filter
(Aiazzi et al. 2002) to remove all fine structures and then re-mapped on a regular grid in latitude
and longitude. The cell is squared and its size is 5' of arc angle, that is approximately 10 km at midlatitude.
The differences between HelioClim-1 and -2 are summarized in Table 1. This table gives also an
overview of other sources of data that will be discussed later.
Table 1: Overview of the input data to the various implementations of the Heliosat algorithm(s) compared in this paper.
An overview of the Heliosat-1 and Heliosat-2 algorithms is shown in Table 3.
Satellite
Sensor
Type of Data
Size of original pixel (nadir)
Original sampling period
Spatial sampling
Temporal sampling
Spatial averaging
Algorithm used
HelioClim-1
HelioClim-2
Heliosat-1, Heliosat-1,
M-7
M-8
Meteosat-7
Meteosat-8
Meteosat-7 Meteosat-8
HRV
HRV simulated from
MSG SEVIRI-VIS-1
and -2
HRV
SEVIRIHRV
Reduced format
IDS-B2
Re-mapped data
Highresolution
image
Highresolution
image
5 km
3 km
2.5 km
1 km
30 minutes
15 minutes
30 minutes
15 minutes
every 6th pixel
5 minutes of arc
~10 km at midlatitude
every pixel
every pixel
one image out of 6 one image out of 4 every image every image
(3 hours)
(one hour)
none
single pixel + 2
different averages
5 x 5 pixels 3 x 5 pixels
Heliosat-2
Heliosat-2
(Heliosat-1) (Heliosat-1)
2
3 Ground measurements and other data for comparison
Ground measurements from five sites located in Europe (Table 2) for the period 16 March to 31
August 2004 are compared to HelioClim-2 values. In addition, we take advantage of the fact that
both Meteosat satellites are observing the same area for this period. Accordingly, for the same sites
also HelioClim-1 values (daily values from Meteosat-7 images) are available. Also available is data
made by the University of Oldenburg using the method Heliosat-1 applied to Meteosat-7 images hereafter called Heliosat-1 M-7 (see Table 1). Finally, a last series of data is available: a modified
version of Heliosat-1 applied to the high spatial resolution data of Meteosat-8 - hereafter called
Heliosat-1 M-8 (see Table 1). The two latter data sets are the courtesy of the University of
Oldenburg. Table 3 shows the difference between Heliosat-1 and Heliosat-2. The modified
Heliosat-1 uses the SOLIS clear-sky model (Mueller et al. 2004) instead of the model of diffuse
irradiance from Dumortier (1995) and direct irradiance from Page (1996). Only days for which data
are available from all stations and all four models for all hours were used, ensuring that all models
are compared with the exact same measurements. This included 155 days with 1475 hourly values.
Table 2: Global irradiances from these five stations are compared to satellite derived data.
Elevation Latitude Longitude
Station
[m]
[ºN]
[ºE]
Instrument
Barcelona
98
41.39
2.12
Kipp & Zonen CM 11
Bergen
45
60.40
5.32
Kipp & Zonen CM 11
Freiburg
275
48.02
7.84
Kipp & Zonen CM 11
Geneva
425
46.20
6.13
Kipp & Zonen CM 10
Lyon
170
45.78
4.93
Kipp & Zonen CM 6
Table 3: Differences between the versions of the Heliosat algorithm used in this paper. Heliosat-1 is the version
described in Fontoynont et al. (1998) and Heliosat-2 is described in Rigollier et al. (2004).
Heliosat-1
Heliosat-2
Input data from satellite
raw counts
calibrated radiances
Backscatter correction
Empirical relationship from
Hammer (2000)
Ground albedo
Histogram technique from
Hammer (2000)
Based on the diffuse ESRA
clear sky model, (Rigollier,
2000)
Second minima of time series
of reflectivites
Cloud albedo
Constant of 150 normalized
satellite counts
Empirical model based on
Taylor & Stowe (1984)
Clear sky model
Model of diffuse irradiance
from Dumortier (1995) and
direct irradiance from Page
(1996). Input is Linke
turbidities from Dumortier
(1998)
ESRA clear sky model,
Rigollier (2000) modified
Geiger et al. Input is Linke
turbidities from Lefevre et al.
2004
cloud index - clear sky index
relationship
Empirical relationship from
Rigollier et al. (1998)
Empirical relationship from
Rigollier et al. (1998)
3
4 Comparison with ground data
4.1 Daily values
Table 4 shows a comparison of daily means of solar irradiance from HelioClim-1 and HelioClim-2
versus observations from the five European stations in Table 2. It is seen that HelioClim-2 gives
much better results than HelioClim-1, except for the station in Bergen. The average Root Mean
Square Deviation (RMSD) for HelioClim-2 is 16%, compared to 30% for HelioClim-1. However,
for HelioClim-2 there is a positive bias for all stations, and for Bergen it is as large as 23%. For
HelioClim-1 there is a large bias of 25% for Barcelona. The reasons for these biases will be
discussed in section 5.
Table 4: Root Mean Square Deviation (RMSD) and Mean Bias Deviation (MBD, model - observation) for daily means
of global irradiance for HelioClim-1 and HelioClim-2. Values are given in W/m2 with percentages of the mean
observed values in parantheses.
Observed
HelioClim-1
HelioClim-2
[Wm-2]
MBD
RMSD
MBD
RMSD
211
53 (25)
78 (37)
20 (10)
30 (14)
Bergen
97
8 ( 6)
36 (27)
31 (23)
41 (31)
Freiburg
172
-4 (-3)
41 (24)
2 ( 1)
22 (13)
Geneva
196
-12 (-6)
52 (27)
7 ( 3)
22 (11)
Lyon
183
2 ( 1)
49 (27)
8 ( 4)
18 (10)
All stations
179
9 ( 5)
52 (30)
13 ( 8)
28 (16)
Station
Barcelona
4.2 Hourly values
As HelioClim-1 does not provide hourly values, HelioClim-2 is compared to Heliosat-1 using
Meteosat-7 data. While Heliosat-1 uses full resolution satellite data as input, the input to
HelioClim-2 are sampled in both time and space; see Table 1 for an overview of the differences.
Table 5 shows a comparison of hourly global irradiances from HelioClim-2 and Heliosat-1 versus
observations. In average, Heliosat-1 is seen to give the smallest RMSD, with 18% compared to 26%
for HelioClim-2. In section 5 it will be assessed how much of this difference is due to the spatial
and temporal samling of satellite data, and how much is due to differences of the Heliosat-1 and
Heliosat-2 algorithms.
4
Table 5: Root Mean Square Deviation (RMSD) and Mean Bias Deviation (MBD, model - observation) for hourly global
irradiance for Heliosat-1 and HelioClim-2. Values are given in W/m2 with percentages of the mean observed values in
parantheses.
Station
Observed
Heliosat-1, M-7
HelioClim-2
-2
[Wm ]
MBD
RMSD
MBD
RMSD
Barcelona
531
2 ( 0)
85 (16)
52 (10)
114 (22)
Bergen
280
26 ( 9)
82 (29)
59 (21)
112 (40)
Freiburg
389
-5 (-1)
72 (19)
2 ( 1)
102 (26)
Geneva
459
2 ( 0)
73 (16)
16 ( 3)
103 (23)
Lyon
431
7 ( 2)
63 (15)
24 ( 6)
91 (21)
All stations
409
7 ( 2)
75 (18)
31 ( 8)
105 (26)
5 Analysis of the results
Section 4 shows that HelioClim-2 overestimated the global irradiance for all the five stations, and
particularly for Bergen with a bias larger than 20%. The frequency distributions of hourly clearness
indices (global irradiance divided by irradiance at the top of the atmosphere) on Figure 1 suggest an
explanation for this: for all stations HelioClim-2 gives too few clearness indices below 0.2. Hence
HelioClim-2 overestimates the global irradiance for cloudy conditions. Since Bergen is the site with
the most frequent cloudy conditions and also the site with the largest bias, it is likely that the reason
for the overall overestimation by HelioClim-2 is that it gives too low cloud index for the cloudy
cases, and thus too high irradiance.
5
Figure 1: Frequency distributions of clearness indices for HelioClim-2 (dashed line) and the observations (solid line)
for the five stations in Table 5.
The cloud index n is given by:
n=
− ground
cloud − ground
(1)
where the parameters ρground and ρcloud are the reflectivities of the ground and the thickest clouds,
respectively. A too low cloud index for the cloudy cases (ρ ≈ ρcloud ) will occur when ρcloud is too
high. The effect of a too high value of ρcloud can be illustrated with a case study:
A simplified version of Heliosat is applied to the Meteosat-8 data from Bergen, where constant
values have been used for the parameters ρground and ρcloud. The solid line on Figure 2 shows the
observed clearness indices for Bergen, and the solid line with circles is a 'best fit' to the
observations with ρground and ρcloud tuned to 0.16 and 0.77, respectively. For this case the RMSD and
MBD is 23% and 0%, respectively. With ρcloud increased to 0.95 (dashed line) the most frequent 'low
clearness index' is increased from approximately 0.15 to 0.30, like for the HelioClim-2 values
(Figure 1, 'Bergen'). The RMSD is now 31% and the MBD is 16%. For this case study the
reflectivities were calculated from 3x5 averages of Meteosat-8 counts with backscatter correction
from Dagestad (2005).
6
Figure 2: Frequency distributions of hourly clearness indices for Bergen. The solid line is the observations and the
solid line with circles is a simplified version of Heliosat with a constant 'cloud albedo' of 0.77. For the dashed line the
cloud albedo is increased to 0.95. See the text for details.
The above example suggests that the 'apparent cloud albedo' in the HelioClim-2 algorithm is too
high by an absolute value of approximately 0.18. From Rigollier et al. (2004) ρcloud is given by:
cloud =
eff −atm
T s T v 
(2)
ρeff is here an effective cloud albedo (cloud + atmosphere) from Nimbus-7 measurements given by
Taylor & Stowe (1984). ρatm is in principle the radiance scattered by the atmospheric layer above
clouds, but is modelled by the path radiance for the whole atmosphere. T(θs) and T(θv) are the
transmissivities downwards from the sun and upwards towards the satellite, respectively, where θS
and θV are the solar and satellite zenith angles, respectively. These two transmissivity factors might
be a cause of a too high apparent cloud albedo: the expression used is from the ESRA model
(Rigollier 2000), and is the transmissivity down to ground level. The transmissivity down to the
level of the cloud tops should however be larger, and hence equation 2 should give too high value,
subsequently giving too low cloud index and then too high clear sky index.
In addition to a too high cloud albedo, the sampling of satellite data may introduce a bias; Tables 4
and 5 show that both HelioClim-1 and HelioClim-2 overestimates irradiance for Barcelona and
Bergen. These two sites are located by the coast, and the spatial sampling and filtering of satellite
7
data may therefore include measurements over sea. Since there are generally less clouds over sea
than over land this can give a cloud index which is lower than what whould have been measured for
the pixel covering the measuring station on land.
<< This paper is a draft, and Lucien Wald will later add a discussion in sections 5.1 and 5.2 about
the effect of sampling and averaging the satellite data. Section 6 gives by now preliminary
conclusions >>
5.1 Influence of the averaging by comparison of ground, HC2 single
pixel, HC2 average and HC2 weighted average
Table 6.Root Mean Square Deviations (RMSD) for hourly and daily irradiances for HelioClim-2 for three different
averges. 'Simple average' means averaging 5 pixels (North, South, East, West and the central pixel), for the 'weighted
average' the central pixel has got a weigth of 2. Units are W/m2 , with percentages of the mean observed irradiances in
parantheses. The observed hourly and daily mean values are given in tables 4 and 5 respectively.
Hourly
Station
Single
pixel
Daily
Simple Weighted
average
average
Single
pixel
Simple Weighted
average
average
Barcelona
114 (22.0) 122 (23.0) 123 (23.2)
721 (14.3) 793 (15.7) 810 (16.0)
Bergen
112 (40.0) 104 (37.2) 107 (38.0)
1005 (31.1) 913 (28.2) 942 (29.1)
Freiburg
102 (26.3)
97 (25.0)
521 (12.7) 472 (11.5) 490 (11.9)
Geneva
103 (22.6) 100 (21.7) 100 (21.7)
534 (11.4) 565 (12.0) 539 (11.5)
Lyon
91 (21.1)
All stations
95 (24.5)
88 (20.3)
87 (20.2)
425 ( 9.7) 418 ( 9.5) 406 ( 9.2)
105 (25.5) 102 (24.8) 103 (25.0)
673 (15.7) 660 (15.4) 669 (15.6)
5.2 Influence of the spatial sampling using Oldenburg MSG (1 km) and
ground data
Table 7: Root Mean Square Deviations (RMSD) of the Heliosat-1 method using Meteosat-7 and Meteosat-8 data as
input. Percentages of the mean observed irradiances are given in parantheses. The last column shows the improvement
in percent by using Meteosat-8 HRV as input to Heliosat-1 instead of Meteosat-7 HRV.
Station
Observed
Heliosat-1, M-7
Heliosat-1, M-8
Improvement
[Wm-2]
Barcelona
531
85 (16)
72 (14)
15
Bergen
280
82 (29)
65 (23)
20
Freiburg
389
72 (19)
64 (17)
11
Geneva
459
73 (16)
64 (14)
13
Lyon
431
63 (15)
58 (13)
9
All stations
409
75 (18)
64 (16)
14
8
6 Conclusions
Global irradiances from the database HelioClim-2 have been compared with ground measurements
for five European stations. The results are compared to HelioClim-1 for daily values and to
Heliosat-1 for hourly values. For the daily values HelioClim-2 is a large improvement with a Root
Mean Square Deviation (RMSD) of 16%, compared to 30% for HelioClim-1. Since both databases
are based on the same algorithm, Heliosat-2, the improvement must be due to the increased spatial
and temporal sampling of the input data to HelioClim-2 (Table 1).
Hourly global irradiances from HelioClim-2 are compared with ground measurements and with
output from the Heliosat-1 algorithm. The mean RMSD for Heliosat-1 is 18%, and for HelioClim-2
it is 26%. HelioClim-2 is seen to overestimate the global irradiance for all stations, and particularly
for Bergen where the bias is 21%. It is pointed out that a likely explanation is a too high value of
the parameter ρcloud, which in the Heliosat algorithm is the reflectivity of the thickest clouds. A
reason for this can be that the reflectivity is normalised with the transmissivity down to ground
level, whereas the transmissivity down to the cloud tops should have been used instead. When ρcloud
is too high the cloud index will be too low, and hence the estimated irradiance will be too large.
Cros S., Albuisson M., Wald L., (2005) Simulating Meteosat-7 broadband radiances at high
temporal resolution using two visible channels of Meteosat-8
Dagestad, Knut-Frode, (2005) A new algorithm for calculating the cloud index.
Dumortier, D,(1998), The Satel-Light model of turbidity variations in Europe,
Dumortier, D,(1995), Modelling global and diffuse horizontal irradiances under cloudless skies
with different turbidities,
Fontoynont, M; Dumortier, D; Heinemann, D; Hammer, A; Olseth, J A; Skartveit; Ineichen,
P; Reise, C; Page, J; Roche, J; Beyer, H; Wald, L, (1998) Satel-Light: A www server which
provides high quality daylight and solar radiation data for western and central Europe, Proc. 9th
conference on satellite meteorology and oceanography in Paris, 25-28 May 1998, pp. 434-437
Hammer, A, (2000) Anwendungsspezifische Solarstrahlungsinformationen aus Meteosat-daten,
PhD thesis, University of Oldenburg
Page, J,(1996), Algorithms for the Satel-Light programme,
Rigollier C; Bauer O; Wald L;, (2000) On the clear sky model of the 4th European Solar
Radiation Atlas with respect to the Heliosat method, Solar Energy, 68(1), 33-48
Rigollier, C; Lefèvre, M; Wald, L, (2004) The method Heliosat-2 for deriving shortwave solar
radiation from satellite images, Solar Energy, 77, 159-169
Rigollier, C.; Wald, L., (1998) Using Meteosat images to map the solar radiation:improvements of
the Heliosat method, Proceedings of the 9th Conference onSatellite Meteorology and
Oceanography. Published by Eumetsat, Darmstadt,Germany, EUM P 22, pp. 432-433
Taylor, V.R.; Stowe, L.L.,(1984), Atlas of reflectance patterns for uniform Earth and cloud
surfaces (Nimbus 7 ERB - 61 days), 10, july 1984, Washington, DC, USA
Aiazzi B., Alparone L., Baronti S., Garzelli A., Context-driven fusion of high spatial and spectral
resolution images based on oversampled multiresolution analysis. IEEE Transactions on
Geosciences and Remote Sensing, 40, 2300-2312, 2002.
Cros S., 2004, Création d’une climatologie du rayonnement solaire incident en ondes courtes à
l’aide d’images satellitales (Design of an incident shortwave solar radiation climatology using
satellite images). Thèse de Doctorat en Energétique, Ecole des Mines de Paris, 13 septembre 2004,
157 pages.
Cros S., Albuisson M., Wald L., Simulating Meteosat-7 broadband radiances at high temporal
resolution using two visible channels of Meteosat-8. To be published by Solar Energy, 2005.
Geiger M., Diabaté L., Ménard L., Wald L., 2002. A web service for controlling the quality of
9
measurements of global solar irradiation. Solar Energy, Vol. 73, No 6, pp. 475-480.
Lefèvre M., Albuisson M., Ranchin T., Wald L., Remund J., 2004. Fusing ground measurements
and satellite-derived products for the construction of climatological maps in atmosphere optics. In
Proceedings of the 23rd EARSeL Annual Symposium "Remote Sensing in Transition", 2-4 June
2003, Ghent, Belgium, Rudi Goossens editor, Milpress, Rotterdam, Netherlands, pp. 85-91.
Lefèvre M., Diabaté L., Wald L., Using reduced satellite data sets ISCCP-B2 to assess surface
surface solar irradiance. Submitted to Solar Energy, 2005.
Mueller R.W, Dagestad K.F, Ineichen P, Schroedter M, Cros S, Dumortier D, Kuhlemann R,
Olseth J.A, Piernavieja G, Reise C, Wald L, Heinnemann D, Rethinking satellite based solar
irradiance modelling - The SOLIS clear sky module. Remote Sensing of Environment, 91, 160-174,
2004.
10
Paper V
Dagestad, K-F. (2005)
Simulations of bidirectional reflectance of clouds with a 3D radiative transfer model
Manuscript
Simulations of bidirectional reflectance of clouds
with a 3D radiative transfer model
Knut-Frode Dagestad
Geophysical institute
University of Bergen, Norway
May 2005
Abstract
To get an impression of the impact of the hetereogeneity of cloud properties on the radiance
observed by a satellite for various pixel sizes, a 3-dimensional radiative transfer model (SHDOM) is
used to simulate radiances reflected to space from two cloud fields. For a given sun-cloud-satellite
geometry and for a typical stratocumulus cloud field the radiance is mainly unaffected by rotating
the cloud in the azimuth direction when the pixel size is 3.5 kilometres. For a pixel size of 550
metres there is some more variability, and for a pixel of 55 metres the variability of the radiance is
larger than 100%. As expected, the variability is much larger for a typical cumulus cloud than for
the stratocumulus field. Even for a field as large as 6.7 kilometres there is some variability in the
radiance by rotating the cloud field. For pixels of 670 metres or smaller the variability is extreme, as
clouds are obstructing the viewing path for some rotations and not for others. The angular
distribution of simulated radiances from the stratocumulus field is also compared to reflectances
measured with the Meteosat High Resolution Visible sensor. The angular distribution of the
simulated radiances is similar to what is observed by Meteosat for thin clouds. For the thicker
clouds the distribution of Meteosat reflectances is closer to lambertian.
1 Introduction
For many purposes it is useful to have a description of the fraction of solar radiation that clouds
reflect in different directions. However, a general function can never be found, as the variable 3dimensional structure of clouds makes the reflectance literally unpredictable.
The Heliosat-algorithm (e.g. Cano et al. 1986, Beyer et al. 1996, Fontoynont et al. 1998, Rigollier et
al. 2004) estimates global irradiance from satellite images by a two step process:

first, the combined reflectance from both ground and clouds, measured by the high
resolution visible sensor, is used to calculate the "cloud index", a single parameter
describing the cloud cover.

second, this cloud index is combined with a clear sky model to estimate the actual global
irradiance at ground.
This study addresses one of the implicit assumptions in this approach: that a cloud field is uniquely
determined by its reflectance in one particular direction. A 3-dimensional radiative transfer model,
SHDOM, will be used to assess the variability related to this assumption. SHDOM is used to
simulate the reflected radiances in different directions from two different cloud fields. One of the
cloud fields is a rather homogenous stratocumulus field, while the second is a broken cumulus field.
Keeping the sun-ground-satellite geometry (and everything else) constant, the cloud fields are
rotated 0, 90, 180, and 270 degrees in the azimuth direction. So, with the cloud properties constant
(except for the rotation) the variability of the reflectance, and hence the cloud index, will be
investigated. Finally the spatial distribution of reflectance will be compared with actual reflectances
(though normalised) from the High Resolution Visible sensor of the Meteosat satellite.
1
2 The 3D radiative transfer model SHDOM
SHDOM is an acronym for "The Spherical Harmonics Discrete Ordinate Method" for threedimensional atmospheric radiative transfer, and it is developed by Frank Evans (Evans 1998). The
code combines both discrete ordinates and spherical harmonics to solve the radiative transfer
equation. Spherical harmonics are used to compute the source functions and the scattering integral.
This method saves a lot of computer memory, since in practice the source function is often zero or
smooth for large parts of the medium, and hence can be represented with few spherical harmonic
terms. Another advantage is that the scattering integral is more efficiently computed in spherical
harmonics than in discrete ordinates. Discrete ordinates are used to compute the radiance field,
which is then used to compute the source function, and the process repeats until a stable solution is
found. To speed up calculations and to save memory an adaptive grid is used; i.e. the model can
start with a rather coarse grid, and fills inn extra grid points for better accuracy whenever gradients
exceed a certain threshold. 3D radiative transfer calculations consume a lot of computer memory
compared to 1D calculations, so the methods used to save memory makes it possible to have cloud
fields with adequate spatial resolution even with 1 GB of memory. The model is not restricted to
only atmospheric calculations; the input medium can be specified completely generally with
extinction, single scattering albedo, scattering phase function and temperature. The simulations are
done for non-polarized and monochromatic radiation, but the correlated k-distribution method can
subsequently be used for integration over a spectral band. The horizontal boundaries of the
input/output field may be specified as open or periodic, and the latter is used for the simulations in
this paper.
3 Input data
Two cloud fields are used as input to SHDOM:

An overcast stratocumulus field obtained from a Large Eddy Simulation from the 1987
FIRE experiment (Moeng et al. 1996)

A broken cumulus cloud field, reconstructed from a Landsat image by Frank Evans, the
author of SHDOM
Both cloud fields were used in the second round of the Intercomparison of 3D Radiation Codes,
I3RC (http://i3rc.gsfc.nasa.gov/cases_new.html). Each grid point of the cloud fields contains a
droplet effective radius in micrometres and a Liquid Water Content (LWC) in grams of liquid water
per cubic metres. For the runs with SHDOM a gamma distribution with a shape parameter of 7.5
was used for the droplet size distribution. The cloud fields were then combined with a Mie
scattering table for the wavelength of 670 nanometres to specify the extinction, single scattering
albedo and phase function at each grid point. Table 1 shows technical data of the two cloud fields,
and Figures 1a and 1b and show the vertical Liquid Water Path (LWP). There were no aerosols in
the atmosphere, and the ground albedo was set to zero.
Table 1: Technical data about the two cloud fields input to SHDOM
Stratocumulus
Cumulus
Horizontal pixel size [m]
55
67
Number of pixels horizontally
64
100
Number of pixels vertically
16
36
3520
6700
Total horizontal size [m]
2
Figure 1a: Vertically integrated liquid water content (g/m2) for the stratocumulus cloud field.
Figure 1b: Vertically integrated liquid water content (g/m2) for the cumulus cloud field.
3
4 Results
Two slightly different experiments are performed:

In section 4.1 the variability of the reflectances from two cloud fields is investigated by
rotating the cloud fields while keeping everything else constant. This will be done for
different sizes of the observed area of the cloud field. Thus, this will show to what extent the
3-dimensional inhomogeneities of the clouds affect radiances observed by a satellite sensor,
and the pixel size needed to minimise the variability.

In section 4.2 the variation of the bidirectional reflectance with the sun-cloud-satellite
geometry is analysed. Here, simulations with an overcast stratocumulus cloud field are
compared with reflectances observed with Meteosat.
4.1 Variability of simulated radiances
4.1.1 Experimental setup
3D simulations consume much more computer power than 1-dimensional models, so only some
case studies were performed with SHDOM. The simulated radiances are monochromatic at the
wavelength 670 nanometres. For each cloud field upward radiances were calculated for the
following configurations:

The cloud field was rotated 0, 90, 180 and 270 degrees in the azimuth direction

Six different solar zenith angles were used: 0, 30, 60, 70, 80 and 85 degrees

For each rotation of the cloud field and each solar zenith angle, radiances were calculated
for three different viewing (satellite) zenith angles: 45, 70 and 80 degrees. The view azimuth
angle was always the same as the solar azimuth angle.

Radiances were averaged over three different subsets of the actual cloud fields:
- The pixel in the middle of the cloud field
- 10x10 pixels in the middle of the cloud field
- The whole cloud field
This corresponds to "satellite pixel sizes" of 55, 550 and 3520 metres, respectively, for the
stratocumulus field and 67, 670 and 6700 metres, respectively, for the cumulus field (Table
1).
The experiment is performed to quantify the variation of the observed radiance for different
"satellite pixels sizes" when the cloud field is rotated. Since the cloud fields remain unchanged the
rotation should then isolate the effect of heterogeneity from other cloud properties.
4.1.2 The stratocumulus cloud field
The upper part of Figure 2 shows the simulated radiances from the stratocumulus cloud field with a
view zenith angle of 45 degrees. It is seen that the radiance integrated over the whole cloud field is
practically independent of the rotation of the cloud field. A noticeable variability of the radiance is
seen for the 10 times 10 pixel subset and for the single pixel the radiance is varying by more than
100 percent. For all subsets a significant decrease of the reflectance is seen when the solar zenith
angle is larger than 60 degrees. An explanation for this could be that the "bumps" on the top of the
cloud field is scattering a large fraction of the radiation close to the forward direction, which is
characteristic of Mie scattering. Thus a large part of this radiance can escape the cloud field with
only a single or few scattering events.
The results for a view zenith angle of 70 degrees are seen on the lower part of Figure 2. The
4
radiance from the whole cloud field is still unaffected by the rotation of the cloud field. For the
smaller subsets there is a somewhat smaller variability than for a view zenith angle of 45 degrees,
both in relative and absolute differences. An exception is for solar zenith angles larger than 60
degrees, where the variability for the subsets is similar for both view zenith angles. For a view
zenith angle of 70 degrees a peak in the reflectance is seen when the solar zenith angle is close to
the view zenith angle. This is the opposition effect: no shadows are seen when the sun and the
observer is in the same direction, and the cloud looks brighter. This effect is not clearly seen for the
view zenith angle of 45 degrees (upper part of Figure 2).
The results from a view zenith angle of 80 degrees are very similar to the case with view zenith
angle of 70 degrees, and the results are therefore not shown.
Figure 2: Simulated radiances from the stratocumulus cloud field for view zenith angles of 45 degrees (upper part) and
70 degrees (lower part) plotted versus the solar zenith angle. The left figures show the mean radiance from a single
pixel in the middle of the cloud fields, the middle figures are for a subset of 10x10 pixels in the middle of the cloud field,
and the rightmost figures show the mean radiance from the whole cloud field (64x64 pixels). The different lines are the
radiances after rotating the cloud field 0, 90, 180 and 270 degrees in the azimuth direction. The incoming irradiance
on a horizontal plane at the top of the atmosphere is one unit. The view azimuth angle is always the same as the solar
azimuth angle. Note different scale on y-axes for upper and lower part.
4.1.3 The cumulus cloud field
Radiances from the cumulus cloud field with a view zenith angle of 45 degrees are shown on the
upper part of Figure 3. As expected, the variability is larger than for the stratocumulus field. Even
the mean radiance from the whole cloud field (6700x6700 metres) shows some, although not
dramatic, variability from the rotation. However, for the smaller subsets, the variability is very
large, with observed radiances close to zero for some of the rotations. Although the same pixels at
5
the top of the cloud field are viewed from above, the path to the ground is obstructed by clouds at a
lower level for to of the rotations, while the path is clear for the others.
For a view zenith angle of 70 degrees the results are similar (lower part of Figure 3). But for the
cumulus cloud field no clear opposition effect like in Figure 2 is observed. The reason is probably
that there are very little shadows on the scattered clouds in the cumulus field.
The large decrease of radiance for solar zenith angle above 60 degrees, which is observed for the
stratocumulus field, is not seen for the cumulus field. Since the cumulus clouds are thicker than the
"bumps" on top of the stratocumulus field, radiation penetrating the clouds probably encounters
multiple scattering events, also when the radiation is coming from a very high solar zenith angle.
Thus, fewer photons escape in the forward direction for low sun with the cumulus field than with
the stratocumulus field. Like for the stratocumulus cloud field the results for a view zenith angle of
80 degrees are similar to those for a view zenith angle of 70 degrees, and hence these results are not
shown.
Figure 3: Simulated radiances from the cumulus cloud field for view zenith angles of 45 degrees (upper part) and 70
degrees (lower part) plotted versus the solar zenith angle. The left figures show the mean radiance from a single pixel
in the middle of the cloud fields, the middle figures are for a subset of 10x10 pixels in the middle of the cloud field, and
the rightmost figures show the mean radiance from the whole cloud field (100x100 pixels). The different lines are the
radiances after rotating the cloud field 0, 90, 180 and 270 degrees in the azimuth direction. The incoming irradiance
on a horizontal plane at the top of the atmosphere is one unit. The view azimuth angle is always the same as the solar
azimuth angle. Note different scale on y-axes for upper and lower part.
6
4.2 Comparison with bidirectional reflectance from Meteosat
In this section the reflected radiances simulated with SHDOM are compared to measurements from
the High Resolution Visible (HRV) sensor of the Meteosat satellite. A description of the full 3dimensional distribution of reflectances is difficult, so a single angular parameter will be used for
this purpose. The angle between the directions towards the sun and the satellite as seen from the
cloud ("co-scattering angle", ψ) is convenient; the scattering phase function of cloud droplets
depend solely on this angle, and besides this is the single parameter best describing the amount of
shadows seen on a rough surface.
4.2.1 Bidirectional reflectance observed with the Meteosat HRV sensor
Pixel counts from Meteosat-5 for all images in 1996 have been extracted for the 61 locations shown
on Figure 4. This amounts in total to 425711 values. The HRV channel of Meteosat has a spectral
response function from 0.45 to 1.0 micrometres and so responds to visible and near infrared
radiation. The raw pixel counts, subtracted the constant offset of 5 digital counts, are normalized
with the incoming irradiance at the top of the atmosphere. Scattered radiation from atmospheric
molecules is then subtracted with an empirical expression from Hammer (2000) and the values are
then put into bins for each 5th degree of the co-scattering angle ψ. Within each bin the 5, 15, 35, 55,
75, 95 and 98 percentiles are calculated. These percentiles are intentionally representing increasing
cloud thickness and/or amounts, provided that the cloud properties are independent of the sunground-satellite geometry. The 5 percentile is probably for cloud free cases, and is therefore
representative of the ground reflectance. Since the Meteosat data are not calibrated, only the relative
variation with geometry will be compared with the corresponding variation of the SHDOM results.
Therefore the reflectances are divided by the value of the bin 0º < ψ < 5º for each percentile. These
normalised reflectances are plotted versus ψ on Figure 5 (solid lines).
Figure 4: A Meteosat image from Europe showing the location of the 61 pixels for which the variation
of bidirectional reflectance has been investigated.
7
4.2.2 Bidirectional reflectance simulated with SHDOM
Only the stratocumulus cloud field (Figure 1a) is used for this section. The setup of the simulations
is identical to the description in section 4.1.1, but more view angles are used: For each of the solar
zenith angles, radiance is calculated for every 5th degree of the view zenith angle from 0 to 85
degrees and every 15th degree of the view azimuth angle from 0 to 360 degrees.
The cloud field was not rotated in the azimuth direction, and only the mean radiance from the whole
cloud field was used. Since the incoming irradiance at the top of the cloud field is one unit on a
horizontal plane, the radiances are equivalent to bidirectional reflectances. The solid line with the
black dots on Figure 5 is the mean radiance calculated within the same bins of the co-scattering
angle as for the Meteosat-data. Like for the Meteosat data, the simulated reflectances have also been
normalised with the mean value for ψ less than 5 degrees, so that only the relative variation of
reflectance with ψ is shown.
4.2.3 Comparison of the bidirectional reflectances
Figure 5 shows that the various percentiles of the normalised bidirectional reflectances from
Meteosat (solid lines) have a local maximum for ψ below 5 degrees. Then they decrease with ψ
until approximately 70 degrees, from where the reflectance is increasing. The variation with ψ is
largest for cases with little or no clouds; for thicker clouds (75 and 95 percentiles) the reflectance is
close to lambertian. The 98 percentiles of the reflectances are, however, increasing very much when
ψ is larger than 30 degrees. Hence in some rare cases the reflectance measured from Meteosat can
deviate strongly from lambertian distribution also for very thick clouds.
The normalised radiances from SHDOM (solid line with black dots on Figure 5) have a variation
with ψ which is similar to the 15-percentile of the Meteosat-reflectances. However, the simulated
radiances increase faster with ψ than the Meteosat-reflectances when ψ is larger than 70 degrees.
One of the purposes of this study was to fit a one-parameter (ψ) function to the SHDOM-radiances
to be used as a Bidirectional Reflectance Distribution Function (BRDF) for the maximum cloud
reflectance in the Heliosat-scheme. However, it appears that the stratocumulus cloud field is too
thin to represent the variation of reflectance with the geometry of a thick cloud cover. From the
percentile-plots of the Meteosat-reflectances shown on Figure 5 it is also seen that the angular
variation of reflectance is larger for low and intermediate cloudiness than for the thickest clouds.
8
Figure 5: Relative variation of the reflectance of clouds versus the co-scattering angle ψ. The line with dots is the
reflectance of a stratocumulus cloud field (Figure 1) calculated with SHDOM (section 4.2.2). The lines without dots are
various percentiles of the reflectances measured with the Meteosat HRV sensor for 1996 (section 4.2.1). Each line is
labelled with the corresponding percentile number. Both the simulated and observed reflectances are normalised with
the corresponding mean value for ψ less than 5 degrees.
5 Summary and conclusions
The variability of bidirectional reflectance of clouds due to 3-dimensional inhomogeneities has been
investigated with the 3-dimensional radiative transfer model SHDOM. For very small subsets (~50
metres) of larger cloud fields, there is significant variability of reflectance when the cloud fields are
rotated in the azimuth direction. For larger pixel sizes there is a smoothing due to bright and shaded
parts cancelling each other. For an overcast stratocumulus cloud field there is almost no variation in
the reflectance due to the rotation for a cloud field of the size of 3520 metres. For a broken cumulus
field there is some variability (~10-20 %) even for a cloud field at the size of 6700 metres. Hence,
for the Heliosat method, averaging reflectances over an area of ~10 kilometres will avoid most
variability due to cloud inhomogeneities.
The angular variation of bidirectional reflectance from clouds has also been investigated using both
simulations with the stratocumulus cloud field and measurements from the High Resolution Visible
channel of the Meteosat satellite. It is found that the simulated reflectances show large variations
with the angle between the directions towards the sun and satellite (ψ). The variation is similar to
the variation for thin clouds observed by Meteosat. For the thicker clouds, the Meteosat-reflectances
are close to lambertian. Hence, the assumption in the Heliosat method of lambertian reflectance
from the thickest clouds is reasonable. However, the reflectance varies more with ψ for intermediate
cloudiness, so if possible a correction should be made for this in the future.
9
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