307 
L - Imi 
Tab. 2.1: 
list of variables to select mean standard 
atmosphere pro-files (input data -for radiative 
transfer model) 
(-max — L m i n 
temperature profile: 
subarctic summer 
midlatitude summer 
midlatitude winter 
subtropic 
tropic 
aerosol; 
surface: 
ocean 
wood 
vegetation (low) 
sand 
snow 
bare soil 
visibi1itv: 
Errors, which might occur because of this 
assumption are discussed in Chapter 3. 
L n involves the influence of the actual cloud cover 
N and the optical depth of the clouds within the 
image field of view of the radiometer. 
In our model we assume that any cloud increases the 
reflectance of the earth-atmosphere-system; that 
means: 
L c1 ou d >> L min 
mari time 
rural 
urban 
10 km 
23 km 
50 km 
Tab. 2.2. : 
(a) System and data characteristics of the 
geostationary satellites Meteosat (ESA) and GMS 
(Japan) 
Meteosat 
GMS 
orbit (longitude) 
0° E 
140° E 
scan direction 
stepping S > 
N 
N > S 
scan E > 
W 
W > E 
no. of steps 
2500 
2500 
spin rate (rpm) 
100 
100 
wavelength (>im) IR 
10 
.5 - 12 
.5 
10.5 - 12.5 
VIS 
0 
.4 - 1. 
1 
0.55 - 0.75 
subsatel1ite 
resolution (km) 
IR 
5 
5 
VIS 
2.5 
1.25 
number of lines 
IR 
2500 
2500 
VIS 
5000 
10000 
samples per line 
IR 
2500 
6688 
VIS 
5000 
13376 
image-taking 
duration (min) 
25 
25 
(b) ISCCP averaging and sampling scheme for data 
volume reduction 
Meteosat GMS 
Averaging of visible pixels to match IR resolution 
(2*1) -> (5km) 2 (6*4) -> (5kra) 2 
Sampling of matched resolution pixels to obtain B1 
1 out of (2*2) -> (10km) spacing 
Sampling of B1 to obtain B2 (B3) 
1 out of (3*3) -> (30km) spacing 
The link between these theoretical calculations and 
the satellite measurements is the normalized 
reflected solar radiation M*„. 
Mr “ Mr m , n 
(2.5) Mr„ = 
^Rm«K — Mrmin 
This might not be true in the case of the water 
surfaces (sunglint) or snow. 
Global maps of minimum radiances L ml „ are created 
by storing the lowest radiance value for each pixel 
location measured at a fixed local time over a 
period of one month. Some of them are shown in Fig. 
(2.3). 
is the upward radiance as it would be measured 
above a solid optically thick cloud deck. These 
values are obtained from statistical analysis of 
maps of maximum radiances for the period of one 
month, which we prepare in a similiar way as the 
minimum radiance maps. 
With the knowledge of L«m and L m «x and that of 
those functions M 00 and M 0n we are able to compute 
for the actul value of reflected radiation L of 
each pixel the global radiation using the equations 
(2.6), (2.3), (2.4) and (2.1) successively. The 
daily sums of global radiation are then estimated 
by use of Eq. (2.7). 
In Mo 
(2.7) Moc — Mood — 
In Moo 
Mod : 
daily sum 
of global radiation 
Mood : 
daily sum 
of global 
radiation. 
, cloudfree case 
N: 
number of 
measurements, 
which are 
available per day 
3. Error considerations 
To estimate the accuracy of the model results 
(mainly: daily sum of global radiation), we have to 
distinguish between two species of error sources: 
(1) the model input parameters (e.g. L„ ln , L m .„, 
In, Moo) 
- After the procedure to find the minimum radiances 
Lmin during the period of one month there may be 
still some pixel left with cloud effects. 
Those pixels have to be detected. 
- The normalized reflected solar radiation or the 
'effective cloud cover' L n may be over - or 
underestimated because of the isotropic 
assumption (Eq.2.6) of the radiation field. 
- The visibility, which influences the clear sky 
values Moo and Mood, cannot be adapted to 
special local conditions, if groundbased 
measurements are missing. 
The model is applied to data sets of two different 
geostationary satellite, Meteosat and GMS. (For 
some satellite data and system charcteristics see 
Tab. 2.2) 
Because these satellite instruments measure 
radiances L (Wm -2 sr _1 ) instead of exitances M 
( Wm“ 3 ) it is assumed that the anisotropic 
characteristics of the normalized radiances L n is 
negligible. 
Supposed that most of these uncertainties occur 
statistically and not systematically, we can 
calculate their influence on the computed daily 
sums of global radiation. The result of such a 
sensitive study is shown in Fig. 3.1. The solid 
line in Fig. 3.1 represents the case, which only 
accounts uncertainties in L ml „, L m .* and L. They 
effect the accuracy of the final result mainly 
during cloudy conditions. The uncertainties in the