Remote Sens. 2014,6, 8165-8189; doi:10.3390/rs6098165
A New Database of Global and Direct Solar Radiation Using the
Eastern Meteosat Satellite, Models and Validation
Ana Gracia Amillo 1, Thomas Huld 1,* and Richard Müller 2
1European Commission, Joint Research Centre, Via Fermi 2749, 21020 Ispra, Italy;
2Deutscher Wetterdienst, Frankfurter Straße 135, 63067 Offenbach, Germany;
*Author to whom correspondence should be addressed; E-Mail: firstname.lastname@example.org;
Tel.: +39-332-785-273; Fax: +39-332-789-268.
Received: 26 May 2014; in revised form: 6 August 2014/ Accepted: 8 August 2014 /
Published: 28 August 2014
Abstract: We present a new database of solar radiation at ground level for Eastern Europe
and Africa, the Middle East and Asia, estimated using satellite images from the Meteosat
East geostationary satellites. The method presented calculates global horizontal (G) and
direct normal irradiance (DNI) at hourly intervals, using the full Meteosat archive from
1998 to present. Validation of the estimated global horizontal and direct normal irradiance
values has been performed by comparison with high-quality ground station measurements.
Due to the low number of ground measurements in the viewing area of the Meteosat Eastern
satellites, the validation of the calculation method has been extended by a comparison
of the estimated values derived from the same class of satellites but positioned at 0◦E,
where more ground stations are available. Results show a low overall mean bias deviation
(MBD) of +1.63 Wm−2or +0.73% for global horizontal irradiance. The mean absolute
bias of the individual station MBD is 2.36%, while the root mean square deviation of the
individual MBD values is 3.18%. For direct normal irradiance the corresponding values are
overall MBD of +0.61 Wm−2or +0.62%, while the mean absolute bias of the individual
station MBD is 5.03% and the root mean square deviation of the individual MBD values is
6.30%. The resulting database of hourly solar radiation values will be made freely available.
These data will also be integrated into the PVGIS web application to allow users to estimate
the energy output of photovoltaic (PV) systems not only in Europe and Africa, but now also
Remote Sens. 2014,68166
Keywords: solar radiation; satellite-based retrieval; global horizontal irradiance;
direct normal irradiance
BSRN Baseline Surface Radiation Network
CM SAF Climate Monitoring Satellite Application Facility
DNI Direct Normal Irradiance
ECMWF European Centre for Medium-range Weather forecast
GAW Global Atmosphere Watch
MACC Monitoring Atmospheric Composition and Climate
MFG Meteosat First Generation satellites
MSG Meteosat Second Generation satellites
NWP Numerical Weather Prediction
PVGIS PhotoVoltaic Geographical Information System
RTM Radiative Transfer Model
SAL Surface ALbedo
USGS United States Geological Survey
AM Air Mass (-)
B,Bclear,Ball Direct (beam) radiation, clear-sky & all-sky beam radiation (Wm−2)
CAL Effective Cloud Albedo, also called Cloud Index (-)
DDigital count of the satellite instrument
DN I,DN Iavg Direct normal irradiance & average DNI of all stations (Wm−2)
GGlobal horizontal irradiance (Wm−2)
Gavg Average measured irradiance of all the stations (Wm−2)
Gmeas Measured Global horizontal irradiance (Wm−2)
Gclear Global horizontal clear-sky irradiance (Wm−2)
HGlobal horizontal irradiation (kWh m−2)
HDNI Direct normal irradiation (kWh m−2)
∆HRelative difference in Hbetween the two satellites (%)
kcClear-sky index (-)
ktClearness index (-)
tModiﬁed clearness index (-)
MAB, rMAB Mean Absolute Bias, relative Mean Absolute Bias
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gMAB, rgMAB global Mean Absolute Bias, relative global Mean Absolute Bias
MBD, rMBD Mean Bias Deviation, relative Mean Bias Deviation
gMBD, rgMBD global Mean Bias Deviation, relative global Mean Bias Deviation
NNumber of data points used for the validation (-)
NsNumber of ground stations used for the validation (-)
ρIntensity of reﬂected light measured by satellite (-)
ρthres Threshold value of ρ, for calibration of satellite measurements (-)
ρcs,ρmax Clear-sky and monthly maximum values of ρ(-)
ρmax,corr Value of ρmax corrected as a function of θ(-)
RMSD, rRMSD Root Mean Square Deviation, relative Root Mean Square Deviation
gRMSD, rgRMSD global Root Mean Square Deviation, relative global Root Mean Square Deviation
θSolar zenith angle (-)
Subscript i i’th time series value
Superscript mmeasured value
Superscript rretrieved (estimated) value
Retrieval of ground-level solar radiation retrieved from satellite has been performed by many groups
going back at least to Möser and Raschke, 1984  and Cano et al., 1986 . Another early work is
that of Pinker and Laszlo, 1992 . Since then, both geostationary and polar-orbiting satellites have
been used to estimate solar radiation at ground level, and existing data sets cover nearly the whole earth,
though with widely varying spatial and temporal resolution [4–8].
A number of solar radiation data sets have been retrieved using data from the Meteosat family of
European geostationary satellites situated at 0◦longitude. Examples include SOLEMI [4,9], the different
versions of HelioClim [6,10], CM SAF [9,11], LSA SAF [12,13]. Some of these data are available free of
charge, while others license the data on a commercial basis. The commercial/free status of the individual
data sets may change with time. However, at the time of writing, to our knowledge there are no freely
available high-resolution data for solar radiation retrieved from the eastern Meteosat satellites situated
over the Indian Ocean (These satellites are ofﬁcially named Meteosat Indian Ocean Data Coverage
(IODC). We ﬁnd this rather uninformative and will refer to the satellites as “Meteosat East”).
Here we describe the results of a procedure to retrieve ground-level solar radiation components using
data from the Eastern Meteosat satellites. The resulting database consists of hourly values of global
horizontal (G) and direct normal irradiance (DNI ) at the earth surface with a spatial resolution similar
to the native pixel resolution of the satellite images.
The organization of the paper is as follows: Section 2will give an overview of the methods used for
the calculation of solar irradiance from satellite data and the properties of the resulting solar radiation
database. Section 3 presents the results of the validation of hourly global horizontal and direct normal
irradiance using ground station data. Section 4 discusses the results and presents some applications of
the data. Section 5 contains the conclusions.
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2. Methods and Input Data for the Retrieval of Solar Radiation From Geostationary
2.1. Algorithms for Calculating Surface Solar Radiation Components
The cloudy part of the applied method is based on the well established and widely used Heliosat
method (please see  for an overview of applications). For the calculation of the all sky solar irradiance
the SPECMAGIC algorithm is used . This combination is a standard method for the calculation of
solar surface radiation of the CM SAF, the Climate Monitoring Satellite Application Facility. The method
is described in more detail in the following paragraphs.
The retrieval of the solar surface irradiance is performed in a two step approach. In a ﬁrst step the
effective cloud albedo (CAL) is retreived from the visible broadband channel of the Meteosat satellite.
The observed reﬂection is corrected for different luminance conditions due to variations in the Sun-Earth
distance and the solar zenith angle θ. Furthermore, the dark offset of the instrument has to be subtracted
from the satellite image counts D. The observed reﬂections are therefore normalised by application of
Here, Dis the observed digital count which includes the dark offset D0of the satellite instrument.
f(distance) accounts for the variation in the Earth sun distance. The effective cloud albedo is then
derived from the observed normalised reﬂections by Equation (2):
Here, ρis the observed reﬂection for each pixel and time.
ρmax is the “maximum” reﬂection. It is determined by the 95 percentile of all reﬂection values at
local noon in a target region (latitude 45.8◦S to 52.7◦S and longitude 40◦E to 56◦E) (This region is
for Meteosat East. For the Meteosat satellites at 0◦longitude the target region is correspondingly further
west). This region is characterised by high frequency of cloud occurrence for each month. In this manner
changes in the satellite brightness sensitivity are accounted for. ρmax depends slightly on the scattering
angle, which is the angle between the sun and satellite.
In order to account for this effect the following empirical relation is applied:
ρmax,corr =(ρmax (1 + 0.0017 ∗(45 −θ)) ,0< θ < 80
ρmax, θ > 80 (3)
For the ﬁxed target region the satellite angles are constant and no systematic dependency on the sun
azimuth has been found. This explains why the correction depends only on the solar zenith angle. Details
on evaluation of the self-calibration approach are given in .
ρcs is the clear sky reﬂection, which is a statistical value derived for every pixel and time slot
separately. This is essentially done by estimation of the minimal reﬂection of the satellite images during
a certain time span (e.g., a month) for each time slot. In detail this is done by iteration as follows. At the
start all reﬂection values ρ(within the time span) are used to calculate an average reﬂection. This average
Remote Sens. 2014,68169
reﬂection serves as initial threshold value ρthres . A new average is then calculated with all reﬂections that
are smaller than the initial threshold value plus a small value ǫ, given as ǫ= 0.035ρmax. This average
is then the threshold for the next iteration, where again all reﬂection values below ρthres +ǫare used to
calculate a new value for ρthres. The iteration is proceeded until no reﬂection value is available that is
higher than ρthres +ǫ, hence until the threshold ρthres does not change any more. ρcs is then deﬁned as
being equal to ρthres. It is assumed that at this point all cloudy pixels are ﬁltered out.
As a consequence of the law of energy conservation, radiation which is not reﬂected or absorbed
by clouds passes through the clouds. The effective cloud albedo provides therefore a measure for the
cloud transmission, i.e., the amount of clear sky (=cloudless) radiation that passes through the clouds.
The irradiance can therefore be calculated by Equation (4).
G= (1 −C AL)Gclear (4)
Here, Gis the solar surface irradiance, often referred as global irradiance and Gclear is the radiation
for clear (=cloudless) skies.
This relation is valid for a C AL range between 0 to 0.8, and has to be slightly modiﬁed outside of this
range, please see  or  for further details.
In the second step of the calculation, the clear-sky irradiance Gclear is calculated using the
SPECMAGIC model for clear-sky solar irradiance . Gclear is then used to calculate the global
irradiance using Equation (4).
SPECMAGIC is described in detail in ; here, only a brief outline is given. The clear sky model
is based on radiative transfer modelling (RTM). It is a hybrid Look-Up-Table approach. The RTM is
used to calculate look-up tables. These consider the effect of absorption and scattering of aerosols as
well as rayleigh scattering on the irradiance. The effect of the absorbers water vapour and ozone is
considered by parameterisation developed and validated by radiative transfer modelling. SPECMAGIC
enables the use of enhanced information about the atmosphere: aerosol optical depth, aerosol type, water
vapour and ozone.
In addition to the global irradiance, SPECMAGIC performs also the calculation of the direct
irradiance. The same method (hybrid Look-Up-Table approach) is used to derive Bclear. The beam
irradiance for all sky conditions, Ball is then calculated by the use of Equation (5).
Ball =Bclear (kc−0.38(1 −kc))2.5(5)
where kcis the clear-sky index, which equals 1−CAL in this case. This formula is an adaptation of the
Skartveit diffuse model .
2.2. Sources of Input Data
The accuracy of the estimated Gclear and Bclear depends on the accuracy of the information about
aerosols and water vapour, the dominant variables for cloudless sky irradiance.
The water vapour information results from the analysis of the global Numerical Weather Prediction
model (NWP) of the European Center for Medium Weather Forecast (ECMWF). The weather predictions
system is described in , and the data are available online .
Remote Sens. 2014,68170
For the aerosol information, 8 years (2003–2010) of reanalysis data from the project “Monitoring
Atmospheric Composition and Climate” (MACC) [21–24] have been used to calculate long term monthly
means of aerosol optical depth. These data are in turn used to consider the effect of aerosols on
the solar surface irradiance. The MACC reanalysis data is generated on a Gaussian T159 grid which
corresponds to 120 km resolution. For the use in SPECMAGIC the aerosol data have been re-gridded to
a 0.5 ×0.5 degree regular latitude-longitude grid. Further, high AOD values has been smoothed in order
to account for the sensitivity of CAL on high aerosol loads.
Though it would be possible to use the monthly aerosol data we have chosen to use the long-term
average monthly values. This choice has been made mainly because the time period of the aerosol data
is shorter than that of the satellite data. Using the monthly data for the shorter period would introduce
an inconsistency in the time series. It would also make these data inconsistent with the longer time series
of solar radiation data produced by the CM SAF collaboration, and reduce their usefulness for climate
change studies which are the main motivation for the efforts of CM SAF.
For the surface albedo (SAL) values based on the United States Geographical Survey (USGS)
land-cover map  are used. A formula given in  is applied in order to consider the solar zenith
angle dependency of SAL. For ozone concentration a climatological value is used.
The METEOSAT images used for the calculation of C AL are available from the EUMETSAT web
2.3. Meteosat Satellites Relevant to the Meteosat East Data Retrieval
The solar radiation database presented here is derived from images obtained by a number of
different geostationary meteorological satellites operated by EUMETSAT. These satellites belong the
the Meteosat First Generation (MFG) class, and the images are obtained using the MVIRI on-board
instrument. The relevant satellites are listed in Table 1, with their positions and periods of operation.
The Meteosat satellites are generally placed in one of two geostationary locations: the Meteosat Prime
location at 0◦longitude, and the Meteosat East locations over the Indian Ocean, at around 60◦E.
In this paper we will use these designations (Prime and East) to distinguish the satellite locations.
Table 1. List of relevant Meteosat meteorological satellites, with their active periods.
Satellite Class Start Date End Date Longitude
Meteosat-5 MFG 2 May 1991 13 February 1997 0◦
Meteosat-5 MFG 1 July 1998 16 April 2007 63◦E
Meteosat-7 MFG 6 March 1998 19 July 2006 0◦
Meteosat-7 MFG 1 November 2006 ongoing 57◦E
As can be seen from Table 1, the satellites Meteosat-5 and Meteosat-7 have both been active over
the Meteosat Prime location (0◦longitude) and in different positions over the Indian Ocean. During the
period July 1998 to July 2006 there were two satellites with similar instruments in different positions.
This period allows a direct comparison between the solar radiation estimates from the two satellites.
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2.4. Solar Radiation Retrieval
The computer codes described in Section 2.1 have been applied to produce solar radiation data for
a number of years for the area covered by Meteosat Prime and Meteosat East. The Meteosat First
Generation (MFG) satellites record an image every half hour, but for the present study, only the full-hour
slots have been used.
The calculation of CAL is performed on the satellite image in the native resolution and projection.
However, for the calculation of the solar radiation, the CAL data are projected onto a regular
latitude/longitude grid with spatial resolution 0.05◦(3 arc-minutes). The accuracy of the calculation
of CAL decreases towards the edge of the image where the satellite views the ground and clouds at
a very shallow angle. For this reason the area in which calculations are performed is restricted to a
region 65◦from the satellite nadir point (for instance, for Meteosat 5, when located at 63◦E, the limits
are 65◦N, 65◦S, 2◦W and 128◦E). In the ﬁnal output the data are given on a latitude-longitude grid
(spatial resolution 0.05◦).
3. Validation of Global Horizontal and Direct Normal Irradiance Retrieval from MVIRI Data
The validation of the satellite-based retrieval has been performed by comparison with solar radiation
measurements performed at ground level. A number of statistical measures have been used in this
validation exercise. The deﬁnition of these measures can be found in Appendix.
This section will present the main results of the validation exercise. The data used for the validation
as well as more detailed analysis is available at a dedicated web page .
3.1. Ground Station Measurement Data Used for the Validation
The main source of ground station measurements used in this study is the Baseline Surface Radiation
Network, BSRN . The data from these stations are regarded as being of high quality and have been
used extensively for validation of satellite-derived solar radiation products.
The geographical distribution of these stations is very uneven. While there are several stations in
Western Europe, North America and Japan, Africa and Asia are only covered in a very sparse fashion.
For this reason, a few other stations have been added to the validation exercise, especially for Eastern
Europe. These station data are available from the Global Atmosphere Watch (GAW)  and distributed
by the World Radiation Data Centre . Finally, ground station measurements from the Joint Research
Centre, Ispra, Italy have been added to the list.
The stations used in the validation are listed in Table 2.
The BSRN stations typically supply global horizontal (G) and direct normal irradiance (DN I) values
at an interval of 1 min. This is also the case for the Ispra station. However, the data for Kishinev and
Thessaloniki are available only as hourly values.
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3.2. Data Selection and Quality Control
There are two datasets per station. On the one hand, the estimated values at the station’s location
derived from the satellite images and on the other hand, the measured irradiance data at the station.
As previously mentioned, only one satellite image per hour will be considered and processed for
Since the satellite image has a ﬁnite resolution (about 3–5 km) each pixel effectively is an average
over the corresponding area. This means that it is not possible to capture changes in the solar radiation on
timescales less than a few minutes. For this reason, the ground station measurements have been averaged
over a 10-min window centered around the time the satellite measures the radiance of the image pixel
corresponding to the location of the station. This does not apply to the stations for which only hourly
data are available. This difference should be kept in mind when inspecting the results. The longer
time averaging for the hourly data may lead to smaller values for the mean absolute deviation and the
root-mean-square deviation values, while the mean bias deviation should be relatively unaffected by the
choice of averaging period.
Table 2. List of radiation measurement stations used in the validation of the satellite-based
radiation estimates. The “Prime” and “East” columns indicate whether they were used
to validate data from the Prime and East satellite positions, respectively. Kishinev and
Thessaloniki have only hourly average data available, for the other stations the 1-min data
have been averaged over a 10-min interval.
Station Lat Lon Climate type Prime East Years Used
Cabauw (NL) 51.97N 4.93E Temperate maritime X 2005
Camborne (UK) 50.22N 5.32W Temperate maritime X 2005
Carpentras (FR) 44.05N 5.03E Mediterranean X 2005
Cocos Island (AU) 12.19S 96.84E Tropical wet X 2009
De Aar (ZA) 30.67S 23.99E Arid X X 2002
Florianopolis (BR) 27.53S 48.52W Humid subtropical X 2005
Lindenberg (DE) 52.22N 14.12E Moderate maritime X 2005
Payerne (CH) 46.81N 6.94E Semi continental X 2005
Sde Boqer (IL) 30.87N 34.77E Dry steppe X X 2005, 2009
Solar Village (SA) 24.91N 46.78E Arid X X 2002
Tamanrasset (DZ) 22.79N 5.53E Hot, desert X 2005
Toravere (EE) 58.27N 26.47E Cold humid X 2005
Xianghe (CN) 39.75N 116.96E Continental humid X 2005
Ispra (IT) 45.81N 8.63E Mediterranean moist X 2005
Kishinev (MD) 47.00N 28.82E Cool temperature, moist X X 2005
Thessaloniki (GR) 40.63N 22.96E Mediterranean temperate X X 2005
As a result, both estimated and measured irradiance datasets present one value per hour. Therefore the
ﬁrst step is the selection of the closest moments in time from both of them. Only if the time difference
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between the estimated value and the nearest time-stamped measured value is below 30 min, these values
will be selected; otherwise both values are discarded. So mainly the ground data availability restricts the
number of points in the comparison.
Once the closest moments in time have been selected from both datasets, a simple quality control
procedure is applied to all pairs of data:
•All missing values are removed. BSRN irradiance data usually present “−999” or “−999.9” values
to highlight missing data. In these cases, both measured and the corresponding estimated value
•Negative measured or estimated irradiance values when the sun’s elevation angle is below 0◦are
substituted by zero values and kept in the datasets.
•However, negative measured or estimated irradiance values when the sun’s elevation angle is
above 0◦are removed from both datasets. If one of the values in the pair is wrong, the whole
pair is discarded.
For the analysis of the validation results, apart from the general comparison between estimated
and measured irradiance values of both datasets as a whole, the validation has been performed, also
distributing the data according to different criteria, like months, solar coordinates, angular distance
between the sun and the satellite or sky type. In order to distribute data into different sky types, the sky
classiﬁcation deﬁned by Ineichen et al. , has been used. This one is based on a modiﬁed clearness
t, (Equation (6)), deﬁned by Perez et al. , which has the advantage of being relatively less
dependent on the solar elevation angle than the normal clearness index, kt.
1.031 ·exp −1.4
Here AM is the optical air mass as deﬁned by Kasten . Sky conditions are delineated into three
intervals according to the k′
tvalue as follows:
•Clear sky conditions: 0.65 < k′
•Intermediate conditions: 0.3< k′
•Overcast conditions: 0< k′
For all stations, the validation period is one year. Some of the stations have been compared against
both the Meteosat Prime and Meteosat East estimates, if the station lies within the ﬁeld of view of
Using the measurements from the stations listed in Table 2the validation metrics in
Equations (A2)–(A5) can be calculated from the hourly measured and estimated values. In the following
sections, the MBD values are calculated considering both day and night values, as is common in the
climatological community. This should be borne in mind when comparing these results with those
reported by others. The relative statistics (rMBD, rMAB and rRMSD) will not be affected by this choice.
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3.3. Validation Results, Global Horizontal Irradiance
The results of the validation of the global irradiance estimates are shown in Table 3.
Table 3. Validation of the satellite-based retrieval of global horizontal irradiance, G.
The validation metrics have been calculated according to Equations (A2)–(A5). The values
for average irradiance include also night hours.
Station Year (Gmeas )MBD rMBD MAB rMAB RMSD rRMSD
Wm−2(Wm−2) (%) (Wm−2) (%) (Wm−2) (%)
De Aar 2002 257 1.54 0.60 27.42 10.67 66.13 25.73
Solar Village 2002 280 −7.16 −2.55 22.22 7.93 48.11 17.17
Cabauw 2005 137 −0.50 −0.37 28.31 20.68 62.19 45.44
Camborne 2005 130 −2.40 −1.85 26.85 20.71 58.26 44.93
Carpentras 2005 185 10.10 5.47 22.85 12.38 52.75 28.57
Florianopolis 2005 188 0.54 0.29 39.63 21.13 89.54 47.73
Ispra 2005 154 13.85 9.02 27.41 17.85 58.65 38.20
Kishinev 2005 149 2.05 1.37 30.78 20.59 61.89 41.40
Lindenberg 2005 133 −4.29 −3.22 27.26 20.49 62.59 47.04
Payerne 2005 151 0.89 0.58 29.69 19.61 64.49 42.60
Sde Boqer 2005 250 8.53 3.41 23.76 9.94 53.00 21.18
Tamanrasset 2005 266 6.98 2.63 26.56 10.00 64.96 24.45
Thessaloniki 2005 194 6.90 3.55 31.55 16.22 61.23 31.49
Toravere 2005 119 −4.94 −4.14 27.43 23.00 60.90 51.07
De Aar 2002 250 −3.02 −1.21 28.91 11.55 71.32 28.50
Solar Village 2002 273 −0.62 −0.23 20.50 7.51 48.92 17.91
Kishinev 2005 151 0.75 0.50 32.62 21.64 64.76 42.97
Sde Boqer 2005 251 9.89 3.94 27.25 10.84 60.07 23.90
Thessaloniki 2005 194 −7.05 −3.64 40.14 20.70 79.40 40.95
Xianghe 2005 174 1.46 0.84 44.35 25.48 96.90 55.68
Cocos Island 2009 242 1.38 0.57 39.25 16.25 82.25 34.05
Sde Boqer 2009 252 8.41 3.34 24.34 9.66 53.62 21.27
The MBD remains within ±10 Wm−2for all stations except two (Ispra and Carpentras). These
two stations are also the only ones where rMBD is higher than 5%. rRMSD is much higher, ranging
from 17% to more than 50% in Toravere and Xianghe. This result is common for satellite-based solar
radiation estimates and reﬂects the difﬁculty of correctly estimating the precise position and timing of
clouds. RMSD is generally higher in cloudy climates and at locations near the edge of the satellite
images, such as Toravere and Xianghe.
From the values in Table 3we can calculate the global statistical quantities in Equations (A7)–(A9).
The average measured irradiance of all the stations is Gavg = 196.59 Wm−2, and the global bias deviation
is gMBD = 1.63 Wm−2. The relative global bias is rgMBD = 0.73%, while rgMAB = 2.36% and
rgRMSD = 3.18%. For the calculation of these values, a station used to validate data from both satellites
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is included with the results for both satellites, as if it were two different stations. This is the case of
De Aar, Solar Village, Kishinev, Sde Boqer and Thessaloniki. However, the results for Sde Boqer for
2005 and 2009 considering Meteosat East have been averaged before calculating the aggregate statistics
for all stations.
The mean bias deviation has also been calculated according to the type of sky, as described in
Section 3.2. The results are shown in Table 4. For clear-sky conditions the method tends to underestimate
the irradiance: at most of the stations, there is a negative bias. This bias tends to be larger near the edge
of the satellite images (Toravere and Xianghe have the largest negative bias values), while the bias tends
to be relatively low in desert areas (Sde Boqer, Solar Village and Tamanrasset). At the same time the
irradiance under intermediate sky conditions tends to be overestimated, sometimes by as much as 25%.
In overcast situations the overestimation of the irradiance is even more evident, with the extreme example
of Xianghe where the estimate is 100% higher than the average measured value. This may be due to the
fact that the station is close to the edge of the satellite ﬁeld of view.
Table 4. Relative mean bias deviation of the global horizontal irradiance retrieval, according
to sky type. In this table the average irradiance values (given in Wm−2) are calculated
considering only daytime values.
Station Year Clear Intermediate Overcast
Gmeas rMBD (%) Gmeas rMBD (%) Gmeas rMBD (%)
De Aar 2002 604 1.82 293 −3.04 123 −41.27
Solar Village 2002 657 −0.64 240 −11.75 96 -57.38
Cabauw 2005 423 −6.76 243 2.33 86 34.28
Camborne 2005 448 −9.45 235 1.97 85 30.01
Carpentras 2005 476 1.28 231 20.38 83 56.40
Florianopolis 2005 611 −8.38 316 10.77 109 37.80
Ispra 2005 510 2.26 233 17.23 72 57.37
Kishinev 2005 535 −3.64 287 8.00 68 31.41
Lindenberg 2005 428 −7.90 225 0.33 80 28.47
Payerne 2005 492 −5.84 226 8.29 86 40.64
Sde Boqer 2005 637 1.17 212 18.70 81 32.24
Tamanrasset 2005 654 −1.03 273 23.50 95 63.07
Thessaloniki 2005 608 −1.43 310 17.34 72 34.43
Toravere 2005 382 −10.80 199 1.57 74 33.27
De Aar 2002 580 −3.94 322 15.98 101 61.84
Solar Village 2002 645 −2.18 193 21.87 90 56.92
Kishinev 2005 537 −4.60 288 8.61 68 27.54
Sde Boqer 2005 637 0.55 212 25.03 82 65.63
Thessaloniki 2005 609 −8.42 312 9.47 73 29.07
Xianghe 2005 503 −9.12 305 3.92 94 100.11
Cocos Island 2009 651 −7.16 353 14.14 130 55.53
Sde Boqer 2009 631 −0.17 216 25.80 89 73.82
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These results indicate that SPECMAGIC, while representing well the average irradiance, tends to
make estimates that give intermediate values rather than the extreme values that are measured under
clear-sky or overcast situations.
A graphical comparison of the measured and estimated values is shown in Figure 1, for two stations:
Solar Village in a desert climate and Ispra, Italy which is a humid temperate climate. The overall
MBD for Solar Village is very low, while the Ispra location has the highest MBD of all stations.
The pattern of results is rather different for the two stations. For Solar Village, the majority of points are
below the diagonal (estimated is lower than measured), with a number of scattered points far above the
diagonal. This is consistent with the ﬁnding that the estimates tend to be too low for clear-sky conditions
and too high for more cloudy conditions. For Ispra, the estimated values are generally higher than
measurements at all irradiance levels. This could be due to an underestimate of the effects of aerosols. It
might also indicate a problem in the measurements.
As mentioned in the beginning of this section, all the validation data are available online.
The interested reader may use these data to produce similar plots for any of the stations used in the
Figure 1. Two examples of scatterplots comparing measured and estimated values of G.
(a) Station in Ispra, Italy; (b) Station at Solar Village, Saudi Arabia. The solid line represents
the diagonal y=x.
0 200 400 600 800 1000 1200
Estimated values (Wm-2)
Measured values (Wm-2)
Comparison estimate vs. measurements, Ispra
0 200 400 600 800 1000 1200
Estimated values (Wm-2)
Measured values (Wm-2)
Comparison estimate vs. measurements, Solar Village
3.4. Validation Results, Direct Normal Irradiance
The algorithm described in Section 2.1 can also estimate the direct component of the solar radiation,
either as direct horizontal or direct normal irradiance. DNI is also measured at nearly all BSRN stations
as well as at some of the non-BSRN stations used for the validation in the previous section.
Table 5shows the results of the validation of DN I estimates from the SPECMAGIC model, using
the stations that have DNI data available.
The relative global mean absolute bias (rgMAB) and relative global root mean square deviation
(rgRMSD) have values rgMAB = 5.03% and rgRMSD = 6.30%. These values are signiﬁcantly higher
than the corresponding values for the global horizontal irradiance.
Remote Sens. 2014,68177
For most stations, the mean bias deviation value is higher than the one observed in the validation of
the global irradiance. Also, the rMAB and rRMSD values are approximately twice as high as those of
the global irradiance. However, when global statistics are analyzed we can see that the global MBD
for all the stations and the relative global MBD are lower in the validation of the beam component than
for the global irradiance. The higher deviations of the estimated beam irradiance, in some cases as
overestimation and in other as underestimation, tend to compensate better than in the case of the global
irradiance. The very low overall MBD for DNI should therefore be regarded as fortuitous.
As for the global irradiance estimates, we can calculate the global statistical quantities in
Equations (A7)–(A9). The average measured DNI of all the stations is DN Iavg = 214.62 Wm−2, and
the global mean bias deviation is gMBD = 0.61 Wm−2. The relative global bias is rgMBD = 0.62%.
Table 5. Validation of the satellite-based retrieval of direct normal irradiance, DNI .
The validation metrics have been calculated according to Equations (A2)–(A5). The values
for average irradiance include also night hours.
Station Year (DN Imeas )MBD rMBD MAB rMAB RMSD rRMSD
(Wm−2)(Wm−2) (%) (Wm−2) (%) (Wm−2) (%)
De Aar 2002 330 −13.32 −4.03 72.43 21.93 146.64 44.40
Solar Village 2002 280 −10.18 −3.64 64.15 22.93 123.17 44.02
Cabauw 2005 116 10.32 8.89 52.51 45.24 120.28 103.63
Camborne 2005 112 0.92 0.82 49.75 44.56 117.75 105.48
Carpentras 2005 234 10.93 4.67 56.96 24.35 121.13 51.78
Florianopolis 2005 153 5.94 3.89 59.50 38.96 141.33 92.54
Kishinev 2005 152 −4.29 −2.83 53.90 35.01 124.75 82.27
Lindenberg 2005 143 0.02 0.01 52.06 36.30 120.52 84.02
Payerne 2005 165 3.03 1.87 63.90 39.50 147.06 90.90
Sde Boqer 2005 288 −11.23 −3.90 68.06 23.64 134.53 46.73
Tamanrasset 2005 269 30.58 11.35 75.32 27.96 144.47 53.62
Toravere 2005 133 −17.27 −12.94 60.16 45.09 142.49 106.80
De Aar 2002 321 −25.41 −7.91 71.97 22.40 143.74 44.74
Solar Village 2002 272 8.14 2.99 63.99 23.51 125.37 46.07
Kishinev 2005 152 −4.45 −2.94 56.37 37.16 128.01 84.40
Sde Boqer 2005 288 −8.67 −3.01 74.70 25.91 150.98 52.36
Xianghe 2005 112 4.36 3.87 65.96 58.64 141.14 125.46
Cocos Island 2009 191 22.94 12.02 71.60 37.51 148.28 77.68
Sde Boqer 2009 294 3.09 1.05 71.21 24.21 140.29 47.70
3.5. Comparison of Irradiance Probability Density
Besides the statistical measures (MBD, MAB, RMSD, etc.) used for the validation of the estimation
model, it is interesting to analyze the probability distribution of the irradiance values, to see if the
occurrence of the different irradiance levels are properly represented by the model.
Remote Sens. 2014,68178
For this analysis, the data when the sun’s elevation angle is below 5 degrees are not considered.
The remaining data are distributed into bins of width 50 Wm−2from 0 to 1200 Wm−2. For the direct
irradiance the 0 Wm−2value will not be displayed, in order to avoid the high peak in the probability
distribution at that level of irradiance.
As an example of the probability distribution graphs, those of the global and direct normal irradiances
for Cocos Island and Sde Boqer are shown in Figure 2. These two stations have been chosen as they
represent quite different climates.
For the global irradiance, in general, the model does not provide the very low and high irradiance
values measured at the stations. For intermediate irradiance levels, there is no clear pattern. For the
two stations shown in Figure 2, the overestimation derived from the model for Sde Boqer (+8.41 Wm−2)
is reﬂected in the graph where it is seen that the model has too many occurrences at high irradiance
(800–900 Wm−2) and too few at low irradiance (<100 Wm−2). For Cocos Island there are no consistent
differences in the intermediate irradiance range.
Figure 2. Comparison of irradiance probability density functions for two stations
(Cocos Island and Sde Boqer). (a) Global horizontal irradiance; (b) Direct normal irradiance.
0 200 400 600 800 1000 1200
Hourly G (Wm−2)
Frequency of ocurrence G Cocos Island
0 200 400 600 800 1000 1200
Hourly G (Wm−2)
Frequency of ocurrence G Sde Boquer
0 200 400 600 800 1000 1200
Hourly DNI (Wm−2)
Frequency of ocurrence DNI Cocos Island
0 200 400 600 800 1000 1200
Hourly DNI (Wm−2)
Frequency of ocurrence DNI Sde Boquer
Remote Sens. 2014,68179
Regarding the frequency distribution of the beam normal irradiance values, the general trend for the
various stations is the one observed in Sde Boqer. There is a higher number of observations of very high
irradiance values that are not reached by the estimation model, while for the intermediate irradiance
levels, the estimated values show a higher occurrence. However, it is the opposite case in Cocos Island,
especially in the range of high beam irradiance values. This is reﬂected in the overall high positive
bias (+22.94 Wm−2). This is likely to be due to an underestimation of the aerosol content in the area,
leading to an overestimate of DNI under clear-sky conditions.
The lack of very high DNI values in the satellite estimates may be due to the fact that we are using
long-term averages of AOD data. Periods with exceptionally low aerosol load will tend to have very high
DNI values, which will be seen in the measurements but not captured by the satellite-based estimates.
The hourly estimated and measured data are available in the online supplementary material.
This allows interested readers to construct these graphs for any station in the validation data set.
4. Results and Discussion
The methods described in Section 2have been used to calculate solar radiation parameters for every
full-hour time slot in the period 1999–2013, with a hiatus in 2006 due to uncertainty about the quality
of data from Meteosat-5 towards the end of the operational life of that satellite. Thus, a total of
14 years are available, which makes it possible to calculate long-term averages with low uncertainty
from interannual variation.
4.1. Sample Results
An example of a map of solar irradiance (global horizontal and direct normal) is shown in Figure 3.
The time slot is 09:00GMT on 14 March 2005, showing the maximum irradiance, corresponding to
cloudless conditions, just west of the center of the image (which is at 63◦E), and illustrating the overall
extent of valid data.
4.2. Comparison of Meteosat Prime and East Estimates
From 1998 to 2006 two very similar satellites were both in orbit at the same time at widely different
positions (Meteosat 7 at 0◦and Meteosat 5 at 63◦E). This makes it possible to do a direct comparison of
the solar radiation retrieval from the two satellites in the area where they overlap.
Figure 5shows a map of the relative difference between Hfor the year 2005 calculated from the two
satellites, deﬁned as:
The result shows a signiﬁcant gradient in the east-west direction, with estimates from Meteosat Prime
higher than those of Meteosat East in the western part and vice versa in the eastern part. This means that
the retrieval algorithm tends to give lower values near the edge of the satellite image.
The effects of aerosols and water vapour are calculated by the clear-sky radiation model and are
therefore independent of the viewing angle of the satellite, so the differences shown in Figure 5must in
some way be due to the effect of clouds, either in the calculation of CAL or in the treatment of clouds by
Remote Sens. 2014,68180
the SPECMAGIC algorithm. A possible explanation is that due to the ﬁnite thickness of clouds, broken
cloud ﬁelds can be identiﬁed when viewed directly from above (close to the satellite nadir) but will
appear as continuous cloud cover when viewed from a shallow angle (as is the case near the edge of the
image). This would lead to an overestimation of cloudiness and hence an underestimation of radiation.
Figure 3. Example of solar irradiance from the calculations. The slot shown is 14 March
2005 at 09:00GMT. (a) Global horizontal irradiance G; (b) Direct normal irradiance DNI .
The values are in Wm−2.
The individual hourly slots can be summed to produce maps of the global horizontal and direct normal
irradiation for longer time periods. Figure 4shows Hand HDNI for the year 2002.
Figure 4. Yearly solar irradiation for the year 2002. (a) Global horizontal irradiation H;
(b) Direct normal irradiation, HDNI. The values are in kWh m−2.
Remote Sens. 2014,68181
Figure 5. Relative difference ∆Hin yearly global horizontal irradiation, calculated from the
two satellites for the year 2005 using Equation (7).
In the validation results shown in Table 3some of the stations were visible from both satellites at
the same time. For these stations the same trend is seen. De Aar and Thessaloniki are both closer in
longitude to the Meteosat Prime nadir, and their MBD is more positive for Meteosat Prime (at De Aar,
rMBD is 0.60% for Meteosat Prime vs. −1.21% for Meteoast East, while for Thessaloniki the values are
+3.55% vs. −3.64%). Solar Village is closer to Meteosat East and has rMBD of −2.55% for Meteosat
Prime and −0.23% for Meteosat East. Sde Boqer and Kishinev are close being at equal distance to the
two satellites, and here we see rather little difference in rMBD (3.41% vs. 3.94% for Sde Boqer, 1.37%
vs. 0.50% for Kishinev).
An analogous case is evident in mountain areas which often have very localized gradients in the
available solar radiation. In some cases the local patterns are shifted relative to each other in the data
sets obtained from the two different satellites. This may be due to the effect of parallax when the two
satellites are observing persistent cloud systems over mountains from different angles. This effect will
lead to an increased uncertainty in mountainous regions.
4.3. Comparing the Results with Existing Databases
In the scientiﬁc bibliography there are several publications in which solar radiation estimates retrieved
from satellite images are validated by comparison with ground measurements. The validation is
Remote Sens. 2014,68182
commonly performed on daily or monthly average irradiance values, although in some cases hourly
irradiance values are analyzed, like in this paper.
Two examples of hourly validation data were performed by Ineichen (2011 and 2013) [35,36]. The
author compared the irradiance values derived from various satellite products with the measurements
registered in several stations. It should be noted that these data sets are derived from the Meteosat MSG
class of satellites, so the methods employed are somewhat different. Nevertheless it is possible to get an
idea of how the accuracy of the present data set compares with other recent efforts.
A detailed description of the method we used to compare these results is found in the supplementary
Data of global horizontal and beam normal irradiance are validated in hourly values. The magnitude
of the errors is similar of those reported in this paper.
In the ﬁrst report , ﬁve different satellite products are validated: SolarGis, Helioclim 3 data bank,
3Tier algorithm, EnMetSol considering two different clearsky models (denoted Solis and Dumortier) and
IrSolAv estimates. The estimates are validated with irradiance measurements registered at 20 stations
in the case of the global horizontal irradiance and 12 stations for the beam component. The validation
results for Gand DN I are shown in Table 6.
Table 6. General statistics for the validation of global horizontal and direct normal irradiance
estimation, Ineichen, 2011 . The results for the present work are given as the last column
for comparison. Nsis the number of stations used for the comparison for each product.
SolarGis Heliosat 3 3Tier EnMetSol (solis) EnMetSol (dumor) IrSolAv SPECMAGIC
Global horizontal irradiance
Ns20 20 20 20 20 15 16
rgMBD (%) 0.75 1.90 1.20 0.95 0.95 0.33 0.73
rgMAB (%) 2.15 4.30 3.00 3.05 3.25 2.87 2.36
rgRMSD (%) 2.69 5.54 3.59 3.57 3.75 3.75 3.18
Direct normal irradiance
Ns12 12 12 12 12 7 14
rgMBD (%) −2.50 10.83 8.08 −1.75 6.25 −0.29 0.62
rgMAB (%) 5.33 13.00 10.92 5.58 9.75 2.86 5.03
rgRMSD (%) 6.18 18.67 14.13 6.84 10.97 3.96 6.30
The magnitude of the general statistics are similar to those obtained in the present paper.
The validation of the SPECMAGIC estimates reports rgMBD, rgMAB and rgRMSD values as low as the
best satellite product analyzed in , for both Gand DN I.
If the validation of the global irradiance on the horizontal plane is performed distributing the data
according to sky type, we obtain the results shown in Table 7. Again, the results are similar to those
derived from the SPECMAGIC method.
For all satellite products considered, including SPECMAGIC estimates, the global horizontal
irradiance is underestimated in clear sky situations, while for intermediate and more signiﬁcantly
overcast situations, the solar resource is overestimated.
Remote Sens. 2014,68183
It should be noted that although the number of stations used in  is similar to that used in the present
study, there is not a great overlap in the actual list of stations. In fact, only 8 stations used in  are
the same as those we have used. This may skew the results because some station locations may be more
“challenging” than others for the algorithms. We have therefore repeated the comparison using these
8 stations: Cabauw, Camborne, Carpentras, Payerne, Sde Boqer, Thessaloniki, Toravere (Thessaloniki
is used for the DNI comparison). IrSolAv was not validated for all these stations and therefore has been
excluded from this comparison. These results are given in Table 8.
Table 7. General statistics for the validation of global horizontal irradiance estimation for
clear, intermediate and overcast sky situations’ . The results for the present work are
given as the last column for comparison.
Clear Sky Conditions
SolarGis Heliosat 3 3Tier EnMetSol (solis) EnMetSol (dumor) IrSolAv SPECMAGIC
rgMBD (%) −2.75 −5.25 −4.35 −3.70 −3.70 −5.40 −4.03
rgMAB (%) 2.95 5.35 4.55 4.10 4.00 5.67 4.68
rgRMSD (%) 3.88 6.11 5.37 4.80 4.86 6.16 5.75
Intermediate Sky Conditions
rgMBD (%) 5.05 10.85 4.65 8.00 7.90 7.87 10.24
rgMAB (%) 6.05 11.15 4.85 8.40 8.40 7.87 11.65
rgRMSD (%) 7.37 15.12 6.91 10.44 10.40 10.39 13.94
Overcast Sky Conditions
rgMBD (%) 24.80 62.05 55.85 35.55 34.55 49.33 37.21
rgMAB (%) 24.80 62.05 55.85 35.55 34.55 49.33 46.61
rgRMSD (%) 28.19 77.47 59.36 39.96 39.49 55.21 49.94
Table 8. General statistics for the validation of global horizontal and direct normal irradiance
estimation, Ineichen, 2011 , using only the 8 stations that all validations have in common.
SolarGis Heliosat 3 3Tier EnMetSol (solis) EnMetSol (dumor) SPECMAGIC
Global horizontal irradiance
rgMBD (%) −0.38 −0.75 −0.25 −0.13 −0.13 0.93
rgMAB (%) 1.13 3.50 1.75 2.13 2.63 2.93
rgRMSD (%) 1.46 3.97 2.12 2.26 2.98 3.30
Direct normal irradiance
rgMBD (%) −3.43 8.57 5.29 −2.00 6.57 1.22
rgMAB (%) 6.00 12.29 8.14 6.86 10.00 5.81
rgRMSD (%) 6.46 15.02 9.85 8.26 11.56 7.26
Given the low number of stations, it is difﬁcult to clearly distinguish between the values for the
different products. It is possible to do a test for statistical signiﬁcance of the differences in the
global variances (the square of rgRMSD). A two-tailed f-test statistic (7times7degrees of freedom)
Remote Sens. 2014,68184
on the values for Gin Table 8shows that only SolarGIS is signiﬁcantly better than the results from
SPECMAGIC (p< 0.04). For the DN I comparison (7 stations), none of the rgRMSD results from 
are signiﬁcantly different from the SPECMAGIC result.
Similarly, for the results in Table 6, few of the differences in rgRMSD between SPECMAGIC and
the other products are statistically signiﬁcant: only the differences with Heliosat 3 (Gand DN I) and
3Tier (DNI) are statistically signiﬁcant at p< 0.05. As noted previously, this may be in part due to the
difference in choice of stations.
In the second report , six different satellite products are validated: SolarGis, Helioclim 3, Solemi,
Heliomont (Meteoswiss), EnMetSol, IrSolAv. Estimates are compared with global horizontal and beam
normal irradiance experimental data registered at 17 stations. Results are shown in Table 9. Again, the
range of the statistics is similar to that observed in the present work. In this case, the number of stations
in common is even smaller, and a comparison for these few stations does not make statistical sense.
Table 9. General statistics for the validation of global horizontal and direct normal irradiance
estimation, Ineichen, 2013 . The results for the present work are given as the last column
SolarGis HelioClim 3 Solemi Heliomont EnMetSol IrSolAv SPECMAGIC
Global horizontal irradiance
Ns17 17 17 17 17 15 16
rgMBD (%) 0.00 1.06 2.29 0.71 −0.59 0.47 0.73
rgMAB (%) 1.65 3.41 3.47 2.94 2.71 3.27 2.36
rgRMSD (%) 2.14 4.38 3.84 3.45 3.22 5.39 3.18
Direct normal irradiance
Ns17 17 17 17 17 15 16
rgMBD (%) −2.00 7.94 −12.94 0.18 1.35 4.47 0.62
rgMAB (%) 5.53 10.53 13.53 8.76 7.71 8.60 5.03
rgRMSD (%) 7.43 16.30 16.19 10.40 8.69 12.02 6.30
We have presented the results of applying the Heliosat and SPECMAGIC algorithms to images from
the Meteosat Eastern geostationary satellites in order to produce hourly maps of surface solar irradiance
(global and direct). For validation purposes, estimates from the Meteosat Prime satellites were also
produced. Validation from 16 ground stations show a low overall yearly bias (gMBD) in the estimation
of the global horizontal irradiance of +1.63 Wm−2or +0.73%. The mean absolute bias of the individual
station bias values (rgMAB) is 2.36% while the root-mean-square of the station bias values (rgRMSD) is
3.18%. For the annual average DNI estimation, the corresponding values are: gMBD = +0.61 Wm−2or
+0.62%, rgMAB = 5.03%, and rgRMSD = 6.30%. The very low gMBD value is a fortuitous cancelling of
individual deviations. The two latter values give a better idea of the uncertainty in estimates at individual
locations. A comparison with validation results given by Ineichen [35,36] shows that the accuracy of the
present results is similar to that of other recent works on satellite-based solar radiation databases.
Remote Sens. 2014,68185
The overall deviations from measured data are quite low. However, there are still areas where
improvements could be made. A direct comparison between solar radiation estimates from the Meteosat
Prime and East over the same time period shows that the radiation estimates tend to be higher near the
center of the satellite image than near the edge. This is probably due to the fact that the ﬁnite thickness
of clouds will make the cloud cover seem more extensive when viewed at a shallow angle as is the case
near the edge of the satellite image. To resolve this issue would require more information about cloud
type than is currently available in the method.
For the time being, there is no particular treatment of snow cover in the method, so areas affected by
snow may have larger uncertainties. Since none of the validation stations are in high mountain or arctic
areas, this problem is not seen in the validation results but should be acknowledged anyway. Methods to
account for snow cover are being studied at present and will be applied to future versions of the solar
For the present study, long-term monthly averages of aerosol data have been employed, as described in
Section 2.2. This choice may have an inﬂuence on the year-to-year variability of the total solar radiation,
which is of interest to investors and operators of solar energy power plants. We plan to investigate the
inﬂuence of using monthly aerosol data on the resulting solar radiation time series.
Once processing has been completed, the hourly maps of solar radiation will be made freely available
to the public. To our knowledge, this new data set is the ﬁrst freely available high-resolution solar
radiation data set covering Asia (there exist several for Europe and Africa, and free data are to some
extent also available for the Americas). The new data set should be useful for researchers, planners and
installers of solar energy systems, as well as for studies of climate and biological processes.
The SPECMAGIC method can also calculate spectrally resolved solar irradiance. We plan to use
this feature to produce maps of spectrally resolved irradiance to study the effects of spectral changes on
PV system productivity for the area covered by the data. Maps of photosynthetically active radiation
may also be produced.
Solar radiation data are essential for the estimation of solar energy system performance. An important
application of the data presented in this study will be to perform estimates of solar energy system
performance. In particular, it is planned that these data will be incorporated into the web-based
PV estimation tool PVGIS [37,38].
We would like to thank EUMETSAT for the access to satellite image data and the CM SAF Project
for the possibility to use the algorithms developed within that project.
The contributions of each author to the work described in this paper are as follows:
Ana Gracia Amillo did most of the work on validation of satellite data against ground station data
and the comparison with other recent work and wrote the section on validation and parts of the
results & discussion.
Remote Sens. 2014,68186
Thomas Huld performed the data processing for Meteosat East and some of the Meteosat
Prime data, as well as postprocessing to produce annual means and differences between satellites
(Figures 3–5). He wrote most of the introduction and conclusions and part of the discussion.
Richard Müller produced an updated version of the SPECMAGIC code and processed the
climatological data needed as input. He wrote most of the section on methods.
Statistical Measures Used for the Validation
A number of different statistical measures have been used to estimate the uncertainty in the irradiance
retrieved from satellite data. These are deﬁned brieﬂy here.
For a given set of data (station or satellite-based estimate), the annual average is calculated from the
The Mean Bias Deviation (MBD) is calculated as shown in Equation (A2):
MBD = 1
iis the measured irradiance at the ith time point while Gr
iis the estimated irradiance at the
same time point. In this calculation both day and night time slots are considered. Nis the total number
of time points for which both measured and estimated data are available.
The relative MBD (rMBD) is deﬁned in Equation (A3) as:
rMBD = PN
The Mean Absolute Bias (MAB) is calculated as (Equation (A4)):
MAB = 1
The Root Mean Square Deviation (RMSD) is given as:
RMSD = sPN
Relative values of MAB and RMSD are calculated like Equation (A3): rMAB = MAB/hGiand
rRMSD = RMSD/hGi
Remote Sens. 2014,68187
To get an overall estimate of the bias in yearly average solar irradiation, we can calculate the avarage
of the MBD values at all the station locations. This is termed the global MBD (and respectively, relative
gMBD = 1
rgMBD = 1
Here, MBDsis the MBD of station number s.Nsis the number of stations.
A measure of the uncertainty of the yearly average irradiation in a given point can be given as the
relative global MAB and RMSD:
rgMAB = 1
rgRMSD = sPNs
Conﬂicts of Interest
The authors declare no conﬂict of interest.
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