Ocean Dynamics (2006) 56: 79–85
DOI 10.1007/s10236-006-0058-1
Kathrin Schiller
Derivation of Photosynthetically Available Radiation
from METEOSAT data in the German Bight with Neural Nets
Received: 15 April 2005 / Accepted: 3 January 2006 / Published online: 27 April 2006
# Springer-Verlag 2006
Abstract Two different models, a Physical Model and a
Neural Net (NN), are used for the derivation of the
Photosynthetically Available Radiation (PAR) from
METEOSAT data in the German Bight; advantages and
disadvantages of both models are discussed. The use of a
NN for derivation of PAR should be preferred to the
Physical Model because by construction, a NN can take the
various processes determining PAR on a surface much
better into account than a non-statistical model relying on
averaged relations.
Keywords Photosynthetically Available Radiation .
Neural Nets . German Bight . METEOSAT
1 Introduction
The Photosynthetically Available Radiation (PAR) serves
as an important input variable to any Primary Production
Model. Algorithms for the derivation of PAR (or global
irradiance) from satellite data usually use a combination of
remotely sensed data and empirical models or radiative
transfer calculations. An example of the former (Olseth and
Skartveit 2001) uses a physical model in combination with
METEOSAT data to derive global irradiance over land
with an accuracy of typically 20–25%. (van Laake and
Sanchez-Azofeifa 2004) use MODIS data in conjunction
with radiative transfer calculations, modelling the atmosphere in a few layers and taking into account Rayleigh and
Responsible editor: Jörg-Olaf Wolff
K. Schiller (*)
GKSS Research Centre, Institute for Coastal Research,
Max-Planck-Str. 1,
21502 Geesthacht, Germany
e-mail: kathrin.schiller@gkss.de
aerosol scattering and absorption due to ozone and water
vapour, leading to an absolute error in the order of a few
percent.
An algorithm using feed-forward Neural Networks is
described by (Lòpez et al. 2001). It derives PAR from
ground measurements of temperature, relative humidity,
dew point temperature and global and diffuse irradiance.
Though this algorithm does not use remotely sensed data, it
is mentioned in this study because it uses Neural Net (NN)
approach.
The use of remotely sensed radiance data from satellites
is well suited to the task of surface solar irradiance
estimation (or PAR) for two reasons. First, most of the solar
radiation reaching the Earth’s surface originates from
visible to near-infrared wavelength ( 0:4 1:0μm).
Energy at wavelengths longer than 1:0μm is almost
totally absorbed by even thinnest clouds, and energy at
wavelengths shorter than 0:4μm is largely lost due to
molecular scattering and absorption by ozone (Lacis and
Hansen 1974). Second, the clouds are the main modulator
of the surface solar irradiance reaching the ocean, and they
often can be observed easily from space. A high (low)
value of net solar flux at the surface is consistently
accompanied by a low (high) value of cloud optical
thickness, and therefore a low (high) value of reflected
solar flux at satellite altitude (Hammer et al. 1998). This
statement would not be true over land: the surface albedo of
land may change drastically with site and season; note that
the algorithms presented in this study only work over the
ocean.
Images of the geostationary satellite METEOSAT were
used as input data to the algorithms because of its high
acquisition rate (image data are taken every 30 min) and
because three spectral wavebands: 500–900 nm (visible,
VIS), 1050–1250 nm (infrared, IR) and 5700–7100 nm
(water vapour, WV) are well suited for the task of
derivation of PAR (Schiller 2001).
In the next section, the physical foundations are laid.
Afterwards, each of the two different models for the
derivation of the PAR will be introduced. The Physical
Model is described and discussed first. The NN parame-
80
trization follows. For each of the models a brief discussion
of its scope and its error budget will be given.
2 Physical foundations
For photosynthesis, it is the number of available photons
rather than their total energy that is relevant to the chemical
transformation. Because any absorbed photon with a
wavelength in the range 350–700 nm is equally effective,
it is convenient to express the amount of radiant energy that
fuels photosynthesis in terms of the number of photons.
Originally, the ‘PAR’ has been defined with respect to the
350–700 nm wavelength interval (Tyler 1966). For reasons
related to the technical difficulty of measuring light in the
near-ultraviolet (UV) region, this interval was reduced to
400–700 nm. Neglecting the near-UV domain usually does
not entail a significant error because the contribution of this
radiation range to the total is small, roughly 5–7% for the
radiation incident at the ocean surface (JGOFS Report
2002). In the following, the definition of PAR by Mobley is
availed
Z
λ
E0 ðx! ; λÞdλ
hc
400nm
½photons s1 m2 ;
PAR 700nm
where E0 ðx! ; λÞ, the scalar irradiance, is the total radiant
power per square meter at wavelength λ coursing through
point x! owing to photons traveling in all directions. The
term E0 λ=hc in the above definition gives the number of
photons generating E0 (Mobley 1994).
R 2800nm
The global irradiance Egl 300nm Eðx! ; λÞdλ received
on a horizontal surface from the entire hemisphere
comprises the direct solar irradiance and the diffuse sky
irradiance. This quantity is derived from the METEOSAT
data and is then converted via a constant factor to PAR. In
order to determine this factor, measured data from Heligoland of PAR1 and of global irradiance2Egl were used.
The global irradiance Egl reaching the Earth’s surface is
on one hand depending on the current position of the sun
relative to the Earth in space and on the other hand
influenced by scattering and absorption processes in the
Earth’s atmosphere. The amount of spectral irradiance
reaching the top of the atmosphere is proportional to the
cosine of the sun zenith angle and inversely proportional to
the square of its distance d from the sun.
The amount of radiance detected in the satellite’s
radiometer (i.e. the reflected radiance) is in addition a
1 Kipp
2 Kipp
& Zonen ‘PAR Lite’ Photosynthetic Active Radiometer
& Zonen ‘CM11’ Pyranometer
function of the angle between the satellite and the sun as
seen from the ground.
The above considerations are leading to the following set
of input variables (besides the satellite data themselves,
inducting information about atmospheric effects):
–
–
–
–
–
location (longitude and latitude) of the region of
interest on Earth (defining the local coordinate
system),
Earth–sun distance divided by mean Earth–sun distance d,
zenith angle of the sun θsun in the local coordinate
system,
zenith angle of the satellite θsat in the local coordinate
system,
azimuth angle between the satellite and the sun Φdiff ¼
Φsun Φsat as seen in the local coordinate system.
3 The physical model
The various methods for deriving the global irradiance (e.g.
Frouin et al. 1989; Rossow and Schiffer 1999) presented in
the literature mainly differ in the description of the
relationship between atmospheric transmission and outgoing radiance as seen by a satellite. Physical methods
directly describe the radiative processes in the atmosphere
by means of radiative transfer calculations while empirical
methods are based on statistical relationships between
satellite and ground measurements. However, most operational models, including the one used in this study, for the
estimation of surface irradiance actually include elements
of the other respective concept (Hammer et al. 1998).
The algorithm for retrieving global irradiance from
satellite data was taken from (Hammer et al. 1998) and is
referred to as the Heliosat Method. It describes how to
calculate the global irradiance from METEOSAT counts C
in VIS. The algorithm is basically driven by the strong
correlation between the planetary albedo recorded by the
satellite’s radiometer and the surface radiant flux. The
planetary albedo increases with increasing atmospheric
turbidity and cloud cover.
A measure for the planetary albedo is the relative
reflectivity ϱ,
ϱ¼
ðC C0 Þ d 2
;
Eext cos ðθsun Þ
where C0 is a registration offset, C is the METEOSAT
counts in VIS and Eext cos ðθsun Þ= d 2 is the extraterrestrial
solar spectral irradiance (rate of energy) on a given (by d )
day on a horizontal surface (Iqbal 1983), with Eext ¼
R 900nm
is the extraterrestrial solar spectral
500nm Eext ðλÞdλ
irradiance at mean Earth–sun distance integrated over the
81
spectral range of the visible METEOSAT detector. With the
relative reflectivities estimated in this manner, a cloud
index n is derived for each pixel as a measure of cloud
cover:
n¼
ϱ ϱg
ϱc ϱg
where ϱ g and ϱ c are the relative reflectivities in the clear
sky and overcast sky case, respectively. The two
reflectivities ϱ g and ϱ c have to be estimated separately
from METEOSAT scenes of the region of interest matching
the two sky conditions.
To establish a relationship between atmospheric transmission and planetary albedo, the clear sky index k is
introduced. It is a function of the cloud index n only and is
defined by the ratio of surface global irradiance E gl to
cl
:
surface global irradiance under clear sky conditions E gl
k ¼ E glcl ;
8 gl
1:2 : n 0:2
>
>
<
1 n : 0:2 < n 0:8
¼
2:06673:6667nþ1:6667n2 : 0:8 < n 1:1
>
>
:
E
0:05 : 1:1 < n;
cl
is
so the surface global irradiance can be calculated if Egl
known. This empirical relationship was derived from data
before 1996 by the Satellight team (Fontoynont et al.
1998).
The clear sky model for calculating the global irradiance
cl
under cloudless skies E gl
is described as a sum of direct
and diffuse irradiance. For the direct component Edir of
clear sky global irradiance, a physical model is used
(Page 1996), whereas for the diffuse component Ediff , an
empirical models is used (Dumortier 1995). For both
models, the relevant parameters, besides the earlier
mentioned sun parameters Eext ; d; θsun , are:
–
–
–
In summary, the global irradiance at the surface can then
be determined from the clear sky index characterizing the
atmospheric transmittance and the clear sky irradiance.
While the latter one is modelled with a site-specific
turbidity, the clear sky index is derived via the cloud index
from the normalised satellite counts (the relative reflectivities). The conversion to PAR is done via a constant
conversion factor as indicated in the physical foundations
section. A linear correlation of the two data sets of PAR and
global irradiance was assumed so that a constant conversion factor was obtained by simple linear regression
(assuming a regression line through the origin) giving a
conversion factor of 2:197ð0:001Þ½μmol
Ws .
Figure 1 illustrates the result of the Physical Model. It
shows the month mean values of PAR in the German Bight
for June 1994. Noteworthy is the fact that the deviations
from the mean value for PAR in the German Bight (given
by the number in the middle of the scale) are significant.
3.1 Discussion of the Physical Model
The Physical Model was tested by applying it to data from
March and June 1994 and comparing it to global irradiance
data measured at Norderney and List provided by the
‘Deutscher Wetterdienst’. The testing was done by plotting
the model output vs the ground measured ones. The results
are shown in Fig. 2. Points in the scatterplot Fig. 2a close to
the origin are associated with sunrise or sunset, i.e. with a
small amount of global irradiance. On sunrise and sunset,
the angle of the incoming radiance is close to π, the path
through the atmosphere is of maximum length and the
Earth’s curvature has non-neglectible influence on the path
length. Within the model, the curvature is not taken into
account, so it is not surprising that most of these points
have overestimated global irradiance. In the plot of the
relative errors, Fig. 2c, these points are associated with the
large positive deviations from 200 to 400%. They are not
correlated with the asymmetry of the deviations in Fig. 2b,
a site-specific turbidity TL (Fontoynont et al. 1998),
the relative airmass (Kasten and Young 1989) m ¼
ðcosðθsun Þ þ 0:50572ð96:07995 θsun Þ1:6364 Þ1 ,
the Rayleigh optical thickness (Kasten 1996) ρ R ðmÞ
¼ ð6:6296 þ 1:7513m 0:1202m2 þ 0:0065m3
0:00013m4 Þ1 .
With these parameters, the global irradiance under
cl
cloudless skies E gl
are calculated following (Page 1996)
and (Dumortier 1995) as:
cl
E gl
¼ Edir cos ðθsun Þ þ Ediff ;
Edir ¼ Eext d 2 expð 0:8662TL ρ R ðmÞmÞ;
Ediff ¼ Eext d 2 ð0:0065 þ cos ðθsun Þð0:045 þ 0:0646TL Þ
cos2 ðθsun Þð0:014 þ 0:0327 TL ÞÞ:
Fig. 1 The month mean values of PAR in the German Bight for
June 1994 as calculated by the Physical Model
82
i.e. the width of the distribution is bigger for underestimating then for overestimating the global irradiance. In
order to find the origin of this asymmetry, the Physical
Model was tested again, but this time with a day with
sunshine (1/6/1994) and afterwards with a day with an
overcast sky (28/3/1994). In addition, the values for the
two sites (Norderney and List) are characterised with two
different symbols. The output can be seen in Fig. 3. The
regression line additionally shown was taken from Fig. 2a.
It should be noted that for the clear sky case, the points
are distributed symmetrically about the regression line
leading to a symmetric distribution of the corresponding
derivations.
a
b
a
b
c
Fig. 3 Testing of the Physical Model for an overcast day (a) and
one with clear sky (b). The ‘x’ symbolises points from List the ‘4’
points from Norderney
On the other hand, the plot for the overcast case shows
an asymmetry: a large amount of points is placed below the
line, i.e. the global irradiance is underestimated very often.
This might be explained by multiple backscatter in the thin
cloud case: then the direct component of the global
irradiance can still pass through these clouds, a part of it
will be reflected onto the clouds and from there back to the
surface leading to larger than expected value of irradiance
on the surface. These processes are not taken into account
in the model and may be the reason for the mentioned
asymmetry
In summary, the Physical Model’s performance is, as
expected, better for the clear sky case than for the overcast
one due to the complexity of the processes in this case.
4 The Neural Net
Fig. 2 Performance of the Physical Model when tested vs ground
truth (a) The fitted regression line has a slope of 0:94 and intersects
the ordinate at 33:33 W=m2 : (b) The corresponding deviations
giving a mean value of 16:94 W=m2 and a standard deviation of
117:84 W=m2 . (c) The relative errors
Another way of determining the global irradiance from
METEOSAT data is the usage of a NN parametrization. A
feed-forward (error backpropagation) network was chosen
for its simplicity (Schiller 2000). In the following, its
essentials are briefly summarised. The NN is organised by
layers. There is an input and an output layer and one or
more hidden layer(s) between them. Each layer consists of
neurons: the number of neurons in the input and the output
layer is given by the dimensionality of the given problem
whereas the choice of the number of neurons in the hidden
layer(s) is problem-dependent. All neurons of one layer are
83
linked with all neurons of the next (neighbouring) layer
(there are no back connections, therefore ‘feed-forward’).
Each link has a weight w, the inter-neuron connection
strength.
The ouput signal ok of the k -th neuron in the i -th layer
is given by
X ði1;iÞ ði1Þ
ðiÞ
ok ¼ sð bk þ
wjk
xj Þ
j
ðiÞ
where bk , the bias of the k -th neuron in the i -th layer, is a
value specific for each neuron (being 0 for those in
ði1;iÞ
the input layer), wjk
is the weight of the link between
the k -th neuron in the i -th layer and the j -th neuron in the
ði1Þ
ði 1Þ -th layer, xj
is the output signal of the j -th neuron
in the preceding (i 1 )-th layer (being the input values for
the input layer). The function s is a nonlinear, strictly
monotonic increasing one, mapping the argument domain
ð1; 1Þ onto the codomain ð0; 1Þ . The most popular
choice (also used here) is the logistic function s ðxÞ ¼
ð1 þ exp ð xÞÞ1.
The biases and weights are obtained by a process of
adaption to, or learning from, a set of corresponding input–
output vectors.
P ! During! the learning phase, the error
function
ð odesired oNN Þ (the sum is over all points
in the learning set) is minimised. The errors will be traced
back (therefore ‘error backpropagation’), and the biases
and weights are readjusted accordingly. The learning
function implemented is a gradient descent algorithm
with momentum term (Bishop 1995).
The desired output, i.e. the global irradiance data were
taken from measurements taken in Norderney and List of
the ‘Deutscher Wetterdienst’ of 1994 on an hourly basis.
There are five input variables xi ; i ¼ 1; . . . 5 for the NN:
–
–
–
the calibrated VIS, IR and WV counts (i.e. radiance in
watts per square meter and steradian)
the azimuth difference (in rad) between sun and
satellite
the cosine of the sun zenith angle divided by the square
of the sun–Earth distance (in AU).
the NN output was compared with the ‘Deutscher
Wetterdienst’ measurements. The values of errors of the
so trained NN are:
–
–
–
Trainings’ sample has a total sum of squares of errors:
106.758442,
ratio avg.train/avg.test = 0.864312,
average of residues:
training 106.758442/13453/5 = 0.007936
test 20.140849/2317/1 = 0.008693.
The NN can then be used for the derivation of global
irradiance from the input variables. The conversion to PAR
is again done via the constant conversion factor.
In contrast to the Physical Model, all three channels
available from METEOSAT data serve as input variables.
The IR and WV channels comprise information about
cloud amount, cloud top heigh, etc. Because clouds
strongly influence the diffuse radiation reaching the Earth’s
surface, the inclusion of these channels is advantageous for
deriving the current global irradiance.
Figure 4 shows an example of the performance of the
NN. It shows the month mean values of PAR for June 1994
in the German Bight. The result looks similar to the one
obtained by the Physical Model (see Fig. 1).
4.1 Discussion of the Neural Net
The comparison of the performance of the Physical Model
(Fig. 2) and of the NN (Fig. 5) shows that the NN output
has a much smaller width in the distribution of the
deviations from the fitted regression line (see Fig. 5b). This
distribution does not show the asymmetry present in the
Physical Model due to the fact that the various processes
influencing the output in the overcast case can be taken
much better into account in a pure statistical model
supplied with additional information (i.e. IR and WV
channels).
This statement can be proven when running the NN for a
day with clear sky and for a day with overcast sky (for
better comparison, the same days as in the discussion of the
From a training sample of 15; 770 points, about 85%
were used for training the NN and the remaining 15% for
testing the NN output. It was found that the training led to
best results when two hidden layers with 15 neurons in the
first and three neurons in the second layer for the NN were
chosen, leading to the Ansatz:
3
15
X
X
ð3;4Þ ð3Þ
ð2;3Þ
E gl ¼ s bð4Þ þ
wk s bk þ
wlk
k¼1
ð2Þ
s ðbl þ
5
X
ð1;2Þ
wml xm Þ :
l¼1
m¼1
Figure 5 shows the performance of the trained NN for
the test sample of the March and June 1994 data, in which
Fig. 4 The month mean values of PAR in the German Bight for
June 1994 as calculated by the Neural Net
84
a
a
b
b
c
Fig. 6 Testing of the Neural Net for an overcast day (a) and one
with clear sky (b). The ‘x’ symbolises points form List and the ‘4’
points from Norderney
determining PAR on a surface much better into account
than a non-statistical model relying on averaged relations.
5 Conclusions
Fig. 5 Performance of the trained NN: (a) The regression line of
NN-output vs the desired output is shown giving a slope of 0:89 and
intersecting the ordinate at 27:2 W=m2 : (b) Plot of the corresponding deviations with a mean value of 4:02 W=m2 and the standard
deviation 81:25 W=m2 . (c) The relative errors
Physical Model were used). Again, the NN output was
plotted vs the measured values together with the regression
line from Fig. 5a. For the NN, the output shows no
asymmetry (i.e. much more points above or below the regression line) neither in the clear sky case nor in the
overcast case (see Fig. 6). The better performance for the
clear sky case might be due to the strong site dependency in
the overcast case.
It is common to both models that the overcast case leads
to higher deviations than the clear sky case.
In summary, we state that the use of a NN for derivation
of PAR should be preferred to the Physical Model since by
construction, a NN can take the various processes
The derivation of the PAR in the ‘German Bight’ from
METEOSAT data succeeded. For the derivation of PAR,
two different models have been used, a so-called Physical
Model and a NN implementation. Both the models
calculate the global irradiance which is afterwards
converted via a constant factor to PAR.
To test the quality of the models, their output was
compared with ground measurements of the global
irradiance (Norderney and List). From this, it turned out
that the NN is better suited for the task for several reasons.
It first of all has a good performance independent of the
weather conditions, whereas the Physical Model underestimates PAR for an overcast sky. Second, the Physical
Model only uses the VIS counts and describes the influence
of clouds and other properties modifying the diffuse
component in an overcast case only via their mean
influence whereas the NN extracts these information
from the IR and WV counts which additionally serve as
input values for the NN. The major advantage of the
Physical Model is the fact that it is applicable to any region
covered by water; by construction, it will produce results of
the same quality. If one wants to use the NN in other
regions, it has to be ‘taught’ for this region to account for
85
possible other optical properties in this region. Anyway,
when supplied with ground measurements from other sites,
a NN can be trained easily in the same manner as described
in the Neural Net section.
The accuracy of the NN approach is less than that
operationally used for MODIS data (van Laake and
Sanchez-Azofeifa 2004). However, the method presented
in this study is advantageous with respect to time resolution
(every half an hour) and with the need of only three broad
spectral bands. Whereas the use of NN’s for the derivation
of PAR (Lòpez et al. 2001) is not novel, the combination of
remotely sensed data and NN is. With respect to
applications, the most important results are: The value of
PAR within the German Bight fluctuates so that the use of a
mean value of PAR for the German Bight would introduce
a not justifiable error into the Primary Production
modelling. Then, a robust method for the derivation of
PAR has been found: the use of the NN is recommended.
Successors are welcome to use the software described in
detail in (Schiller 2001).
Acknowledgements This research was supported by the HGF
strategy fund as part of the ENVOC project. The authoress likes to
thank Dr. R. Hollmann for helping me getting started, Dr. R.
Doerffer, Dr. H. Schiller and Dr. R. Röttgers for the helpful
discussions and the EUMETSAT team for the supply of METEOSAT
data.
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