GKSS 2001/23

Derivation of thePhotosyntheti ally Available Radiationfrom METEOSAT dataK. S hiller

Derivation of the Photosyntheti ally AvailableRadiation from METEOSAT dataKathrin S hillerAbstra tTwo di�erent models, a Physi al Model and a Neural Net, are used forthe derivation of the Photosyntheti ally Available Radiation (PAR) from ME-TEOSAT data in the German Bight.Both models are onstru ted for the al ulation of PAR in the German Bightin terms of an easily a essible time series of PAR �elds; advantages and disad-vantages of both models are dis ussed.A software pa kage was generated in IDL for the realisation on the omputer,its stru ture is motivated and physi ba kground informations are given.With slight modi� ations all programs an be applied for the al ulation ofPAR for arbitary regions (but not over land).A zip �le ontaining all programs and lasses used, the te hni al html do u-mentation and this report an be obtained fromhttp://gfesun1.gkss.de/software/meteosat2par.Ableitung der zur Photosynthese zur Verf�ugung stehenden Strahlung ausMETEOSAT Daten Abstra tZur Ableitung der zur Photosynthese zur Verf�ugung stehenden Strahlung(PAR) in der Deuts hen Bu ht aus METEOSAT Daten werden zwei vers hiedeneModelle, ein Physikalis hes Modell und ein Neuronales Netz, benutzt.Beide Modelle sind darauf ausgelegt, PAR in der Deuts hen Bu ht in Formeiner einfa h zug�angli hen Zeitreihe von PAR-Feldern zu bere hnen; Vor- undNa hteile beider Modelle werden diskutiert.Zur Realisierung auf dem Computer wurde ein Programmpaket in IDL erstellt,dessen Struktur motiviert wird und physikalis he Hintergr�unde erl�autert werden.Alle Programme sind so angelegt, da� sie si h dur h geringf�ugige Modi�katio-nen eignen, PAR au h f�ur andere Gebiete (aber ni ht �uber Land) zu bere hnen.Ein zip File aller benutzter Programme, Klassen, der te hnis hen html Doku-mentation und dieses Beri htes kann beihttp://gfesun1.gkss.de/software/meteosat2par bezogen werden.2

Contents1 Introdu tion 72 METEOSAT data Pro essing 72.1 The METEOSAT System . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 The Two Models for Deriving PAR 123.1 Physi al Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 The Physi al Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.1 The Heliosat Method . . . . . . . . . . . . . . . . . . . . . . . . 153.2.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.3 Dis ussion of the Physi al Model . . . . . . . . . . . . . . . . . 233.3 The Neural Net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.1 The Neural Net ffbp1.0 . . . . . . . . . . . . . . . . . . . . . . 253.3.2 Dis ussion of the Neural Net . . . . . . . . . . . . . . . . . . . . 294 Analysis of the results for the German Bight 305 Summary 32

1 Introdu tionThe present work ame into being as a part of the `ENVOC: A New Perspe tive ofthe O ean' proje t. Within this proje t the work pa kage 3:4 is on erned with thedevelopment of a model whi h determines the primary produ tion using a ombinationof remotely sensed data from MERIS, ASAR, AATSR or AVHRR and METEOSAT.An important input variable for ea h Primary Produ tion model is the Photosynthet-i ally Available Radiation (PAR). The derivation of PAR in the `German Bight' fromMETEOSAT data was the goal of the work presented here.Sin e the METEOSAT satellite views about 42% of the earth surfa e the �rst sub-task was to generate a program whi h allows to extra t only a subset of METEOSATdata for a spe i�ed `region of interest' (roi).This program and some related auxillary pro-grams will be des ribed in se tion 2 together with a brief introdu tion to METEOSATand the data format `OpenMTP'.The next step was to onsider how PAR ould be derived from these `roi-�les'. Twodi�erent methods have been implemented, the usage of a so alled 'Physi al Model' aswell as a Neural Net parametrization of PAR. Se tion 3 starts with some physi al foun-dations valid for both models. The Physi al Model, its realization and its limitationswill be introdu ed, followed by the des ription of the Neural Network parametrizationtogether with a brief introdu tion to Neural Nets. For both models a quality estimationof the model used will be in luded.Afterwards the results will be dis ussed with fo us on the `German Bight', the regionof interest in the present work. For this purpose data of the day- and month means ofPAR in the roi will be used.All programs for this work were written in `IDL' (Version 5:4) in obje t-orientedmanner. All programs and their purpose will be illustrated in the respe tive se tion.This will in lude motivations of the lass de�nitions as well as a des ription of someasso iated methods. A te hni al des ription of all programs is provided online[1℄.2 METEOSAT data Pro essingThis se tion is on erned with the extra tion of a subset of METEOSAT data for aspe i�ed `region of interest' (roi). To do so, one �rst of all has to deal with the stru tureof METEOSAT image produ ts i.e. the `OpenMTP format'. This is done in the nextse tion in luding an introdu tion to the METEOSAT servi es. Afterwards the softwareused for the extra tion and some auxiliary programs will be dis ussed in some detail.

7

2.1 The METEOSAT SystemImage produ ts ontain the basi image data a quired by the Meteosat satellites. Thesedata are obtained every 30 minutes in three spe tral wavebands. Sin e the satellitesare in geostationary orbit, the overage is approximately hemispheri al and entered onthe sub-satellite longitude rossing with the equator. The main satellite is lo ated overthe Greenwi h meridian.The imagery itself onsists of re tangular arrays of 8-bit-image pixels. The satelliteis spin-stabilised, and the data are a quired at a rate of one image line per satelliterotation. Ea h time the satellite rotates, the radiation dete tors for the various hannelspan a ross the earth 'horizontally' (i.e. eastwards), a quiring one line of data. Betweenea h rotation, a stepping tilt mirror in the amera opti s adjusts the position so that thenext line is o�set 'verti ally' (i.e. northwards) from the last. A total image is a quiredevery 25 minutes. A �ve minute retra e and stand-by period prepares the satellite forthe start of the next image, so that the image interval is 30 minutes. The interval isknown as `slot', and there are 48 slots in ea h day of operations. Slots are numberedfrom midnight so that slot 1 overs data a quired from midnight to 00:30 UTC.Emissions in the following three spe tral wavebands are dete ted by Meteosat:VIS: wavelengths in the range 0.5 to 0.9 mi rons - showing re e ted light in the visiblepart of the spe trum,IR: wavelengths in the range 10.5 to 12.5 mi rons - showing emitted radiation in thethermal infrared part,WV: wavelengths in the range 5.7 to 7.1 mi rons - showing radiation in the watervapour absorption bands.Data are a quired at two resulutions. In the Water Vapour (WV) and Infrared (IR) hannels a omplete image onsists of 2500 x 2500 pixels. This gives a spatial resolutionof about 5 km at the subsatellite point. In the Visible (VIS) band, data are a quiredat twi e this resolution.Images are available in di�erent data formats. All software des ribed in this do u-ment does apply for data in the `OpenMTP �le format' only. The ma hine level repre-sentation of bits and bytes used in the OpenMTP format follows the standard used byUNIX/open systems ar hite ture ma hines. The open system representation uses theIEEE standard for real number representation and ASCII en oding for hara ter data.All OpenMTP �les onsist of a variable number of logi al re ords of variable length.This stru ture ontains three distin t omponents:Re ord 1, ASCII �le header. This ontains general information about the �le inASCII format.Re ord 2, binary �le header. Contains extensive binary format information on theprodu t and its alibration. 8

Re ords 3-N, image line data. The number of lines N of data depends on the han-nel (see above). Ea h image line is (NP+32) bytes in length, where NP is thenumber of pixels per line.Besides the image line data the produ t informations are of great use as one willsee in the following se tions. All informations presented here were taken from publi a-tions of the `European Organisation for the Exploitation of Meteorologi al Satellites -EUMETSAT' [2℄[3℄.2.2 SoftwareBefore reading the image line data for the region of interest (roi) for a spe i�ed timeintervall one needs to he k whether the METEOSAT data are omplete and ontainfull disk re ti�ed data (due to the fa t that a great amount of METEOSAT �les has tobe pro essed one has to make sure that they are uniform and leading to the same roi).To do so, the auxiliary program `list bad files' is provided. The program he kswhether the list of �les is omplete (i.e. 48 slots per day, 3 types of data (VIS, IR,WV) per slot) by reading all the �le names whi h will give information about the date,slot and type. In order to he k if all �les ontain re ti�ed and full disk data theprogram reads the ASCII-header of all �les, in whi h general informations are stored.The ASCII-header provides the re ord `Des ription' (taking one of the values `Imagesubarea' or `Full disk image') and the re ord `Pro essingPerf' (pro essing performed onthe image `Raw Data' or `Re ti�ed Data') for this task. If one ore more �les are missingor ontaining `bad data' (i.e. `Image subarea' or `Raw data' ) the program will list thedate, slot and type of these �les in a �le named `list bad files.txt'.The main program `OpenMTP2roi' reads the image lines belonging to the roi andwrites their roi parts together with an ASCII header (see below) into `roi-�les'. For thispurpose a lass `OpenMTP file' was de�ned with several methods to all. In order todetermine the image lines of interest the user needs to spe ify a grid (i.e. a (south-west)starting point (latitude and longitude) a step-width (in latitudinal and longitudinaldire tion) and the number of steps in (latitude and longitude). The so spe i�ed grid(interpreted as ellipsoidal oordinates) is then onverted to a artesian grid and thento pixel- oordinates, whi h allow to adress roi.Before produ ing the roi-�les, i.e. running the main program, one should make surethat the spe i�ed grid really leads to an image of the spe i�ed region (it was found thatthe routines onverting geographi al- to pixel oordinates work quite well when areasaround 0 latitude were hoosen and that errors of up to three lines or pixels o uredwhen the spe i�ed region is of latitude � 50 degree). For this purpose the auxiliaryprogram `offset' is provided. With this program one an shift the resulting roi toadjust it to the desired position. The framed subarea will be monitored and so an beeasily ompared (by viewing) with a geographi al map of roi. When it oin ides withroi the so found o�set parameters an be used afterwards in the main-program.9

The obje t oriented manner in whi h the programs where written is espe ially usefulsin e the user has not to deal with large and omplex programs.1Cal ulations whi h are ommon to all �les are done only on e in the main pro-gram (i.e. the �rst time one alls the appropiate method) whi h makes it very fast.Su h methods are the `OpenMTP file::grid' method whi h al ulates the artesiangrid spe i�ed by the users geographi al grid input (see above) and the `OpenMTP file::grid onvert' method whi h al ulates the orresponding pixel- oordinate (this methoda tually runs three times, be ause of the di�erent image sizes of `.VIS' and the othertypes (`.IR' and `.WV') leading to three sets of pixel- oordinates).OpenMTP-files

roi-�les

list bad files.pro

film hen.proOpenMTP2roi.pro offset.pro

Fig. 1: The �gure shows the data types and the programs designed for ea htype in a s hemati way. Data types are har terized with the dis symbol, programs are framed.After alling these methods for the de�ned obje t the main program will then extra tthe pixels asso iated with the roi in a �le (named after date, slot and type of the originalinput OpenMTP �le). These roi-�les also ontain an ASCII-header where information ommon to all roi-�les (spe i�ed grid, size of ASCII-header and size of roi-data) andsome astronomi al values needed in order to al ulate PAR are stored. Besides theseinformations this header should ontain the alibration informations (but later on it wasfound that the alibration informations were not present in the OpenMTP-�les binaryheader as they should, so month mean values of the alibration informations had tobe expli itly in luded in the programs whi h needs them). The bene�t of the ASCIIheader will be ome lear when dis ussing the derivation of PAR from these roi-�les. Alist of ontents of this header is given in the table below.For the astronomi al al ulations a lass `roi al ' was de�ned with methods as-so iated with the region, date and time when data were taken but not with the roidata themselves. Su h methods are: al ulating sunrise- and sunset-time (in UTC)1At this point it is worth mentioning that the above programs a ept '.z' and '.gz' OpenMTP �les,so one should never unzip them. 10

Table 1: Contents of the roi ASCII headerDes ription `Region of Interest'Spe tralCont Spe tral Content of (OpenMTP) image data(`VISS + VISN (visible south +north) data')Re 1Size Size of ASCII header in bytes, always set to `800'Re 2Size Size of image in bytesRe tMethod Name of re ti� ation method used (OpenMTP)NumberOfLines Number of lines in the roi image (i.e. steps in Latitude)NumberOfPixels Number of pixels in the roi image (i.e. steps in Longitude)Longitude Longitude of south-west starting point of roiLatitude Latitude of south-west starting point of roiDelta Lon step width in longitudinally dire tion in roiDelta Lat step width in latitudinally dire tion in roiEarth Sun Dist earth sun distan e (in AU) os sun zenith osine of sun zenith angle in roisun azimut rad sun azimuth angle (in rad) in roidiff angle rad azimuth di�eren e sun-satellite (in rad) in roi os sun sat osine of angle between sun and satellite as seen from roi os sat zenith osine of satellite azimuth angleCalibraCoeff absolute alibration oeÆ ient (W=m2STR)Spa eCounts spa e ount (dimensionless)CopyRight `Copyright ( ) GKSS/GFE All rights reserved'(`roi al ::sunrise sunset') , al ulating the sun position ve tor (`roi al ::sun position') i.e. Earth-Sun distan e, zenith- and azimuth angle, and al ulating theazimuth di�eren e from sun and satellite (`roi al ::azidiff sun sat'). The methodfor al ulating sunrise- and sunset-times is used in the main program for spe ifying thenumber of �les that should be onverted to roi-�les in terms of `slots before (or after)sunrise (sunset)' , e.g. for the onversion to PAR only those �les with sunligth presentare of interest.The so reated roi-�les an now be used to al ulate the PAR for the region ofinterest. To get an idea how a series of su h roi-�les looks like the auxiliary program`film hen' is provided, displaying a sequen e of the spe i�ed �les.A summary of the software dis ussed in this paragraph an be seen in �gure 1.11

3 The Two Models for Deriving PARIn this se tion the two di�erent models -the so alled `Physi al Model' as well as theNeural Net parametrization- for the derivation of PAR from METEOSAT data will beintrodu ed. First the physi al foundations valid for both models will be layed. After-wards the two models themselves and their omputational realization will be des ribed.For ea h of the models a brief dis ussion of its s ope and its error budget will be given.3.1 Physi al FoundationsThe amount of `Photosyntheti ally Available Radiation' (PAR) is de�ned byPAR � Z 700nm400nm �h E0(~x; �)d� [photons s�1m�2℄;where E0(~x; �), the spe tral total irradian e, is the total radiant power per square meterat wavelength � oursing through point ~x owing to photons traveling in all dire tions.The term E0�=h in the above de�nition gives the number of photons generating E0.That means for photosynthesis it is the number of available photons rather than theirtotal energy that is relevant to the hemi al transformation. This is be ause a photonof, say, wavelength 400nm, if absorbed by hlorophyll, indu es the same hemi al hangeas does a less energeti photon of wavelength 600nm.Note that PAR is by de�nition a broadband quantity, there is no `spe tral PAR'.However, over a wide variety of surfa e hara teristi s, the onversion fa tor for energyto photons varies by only �10% about a onstant value (this approximation is validwhen not taking into a ount the spe tral dependan e of the total irradian e). Thissimpli� ation is also made in both models des ribed in this se tion, i.e. the globalirradian e will be derived from METEOSAT data and is onverted via a onstant fa torto PAR.The global irradian e rea hing the earth's surfa e is on one hand depending on the urrent position of the sun relative to the earth in spa etime and on the other handin uen ed by s attering and absorption pro esses in the earth's atmosphere. Beforegoing into details about the a tual applied models these two fa tors should be explainedbrie y.Figure 2 (taken from [4℄) shows a elestial sphere with the earth at the enter andthe sun revolving around the earth. In the elestial sphere, the elestial poles are thepoints at whi h the earth's polar axis uts the elestial sphere (mutatis mutandis forthe equator). The interse tion of the plane of the earth's equator with the plane ofthe sun's revolution, the e lipti , makes a �xed angle of � 23:5Æ. However, the anglebetween a line joining the enters of the sun and the earth's equatorial plane hangesevery instant and is alled the de lination angle.The de lination angle and the knowledge of the geographi al position on earth aresuÆ ient to de�ne the sun zenith and azimuth angles, whi h in uen e the amount of12

North Pole ofCelestial Plane

Celestial PlaneSouth Pole ofNSAngleDe lination EarthSun

Apparent Pathof Sun on theE lipti PlaneSolsti eSummer� 23:5Æ

90Æ

EquinoxAutumnalVernalEquinox

Plane of CelestialEquator

Fig. 2: The �gure shows the elestial sphere with the apparent path of sunand the sun's de lination angle.solar radiation rea hing the top of the atmosphere (toa) of the earth. The zenith angleis the angle between the lo al zenith and the line joining the observer and the sun.The solar azimuth is the angle in the lo al oordinate system between the plane ofthe observer's meridian and the plane of a great ir le passing through the zenith andthe sun. Besides these two angles the amount of radiation rea hing the toa of theearth is inversely proportional to the square of its distan e from the sun. Sin e theearth revolves around the sun in an ellipti al orbit with the sun at one of the fo i theearth-sun distan e is, as the de lination angle, a fun tion of the day in the year only2.When solar radiation enters the earth's atmosphere, a part of the in ident energyis removed by s attering and a part by absorption (see �gure 3, taken from [4℄). Bothin uen e the terrestrial spe trum by onsiderably modifying the spe tral energy passingthrough the atmosphere. The s attered radiation is alled di�use radiation. A portionof this di�use radiation goes ba k to spa e and a portion rea hes the ground. Theradiation arriving on the ground dire tly from the solar disk is alled dire t radiation(and is obviously proportional to the osine of the sun zenith angle).The di�use omponent onsists of several parts. Besides the s attering by airmole ules and aerosols the intera tion of dire t solar radiation with the louds resultsin re e ted di�use radiation. Further, a portion of the dire t and the di�use radiationrea hing the earth after the �rst pass through the atmosphere is re e ted ba k to the2The mean earth-sun distan e is alled one astronomi al unit (AU). The minimum distan e is about0:98 AU, and the maximum about 1:02 AU. The earth is at its losest point to the sun (perihelion) onapproximately January the third and at its farthest point (aphelion) on approximately forth of July.The earth is at its mean distan e from the sun at 4th of April and at 5th of O tober.13

AtmosphereSolar Radiationba k to Spa ere e tedClouds Clouds

Anisotropi Di�useRadiation arrivingon a horizontalSurfa eAirAerosolsThin Dire t

Limit of Earth'sMole ules

Fig. 3: The �gure shows the various pro esses in uen ing the amount of ra-diation arriving on the ground.sky, whi h ontributes to the multiply re e ted irradian e. This multiple re e ted irra-dian e (not shown in �gure 3) will depend srongly on the re e tan e properties of the loud system. When the dire tional intensity of the di�use irradian e is not uniformover the sky hemisphere, it is alled anisotropi di�use radiation.Lo al Verti alSun SatelliteZenithSunAngleDi�eren e ofAzimuth Angles

Fig. 4: The �gure shows the position of the sun and a satellite in the lo al oordinate system of an observer on the earth's surfa eBefore summarizing the minimum of input variables for ea h model for derivingthe global irradian e from METEOSAT data one has to take into a ount the satelliteitself. Sin e the `observer', the satellite, is pla ed in a geostationary orbit it has a �xed`viewing' angle onto the earth, i.e. it is never (or only on e per day) inline with dire t omponent of the irradian e rea hing a spe i� region on the earth. Therefore theamount of irradian e dete ted in the satellites radiometer (i.e. the re e ted irradian e)is a fun tion of the angle between the satellite and the sun as seen from the ground (see14

�gure 4). (For the al ulation of this angle the earth's urvature was not taken intoa ount, sin e our roi is suÆ ient small enough to do so.)The above onsiderations are leading to the following set of input variables (besidesthe satellite data themselves):� date and time when data were taken,� lo ation of the region of interest on earth (longitude and latitude),� earth-sun distan e for the time the data were taken,� zenith angle of the sun in the lo al (roi) oordinate system for the time the datawere taken,� zenith angle of the satellite in the lo al oordinate system,� angle between the satellite and the sun as seen in the lo al oordinate system forthe time the data were taken.The physi al informations in this se tion were taken from[4℄ and [5℄.3.2 The Physi al ModelIn this paragraph the physi al model used for derivation of PAR is introdu ed. Firstthe model itself will be des ribed brie y. Afterwards the realization of this model onthe omputer together with some auxiliary programs will be visualized. At the endthere will be a dis ussion of the results and a quality estimation.3.2.1 The Heliosat MethodThe use of satellite-based methods for the retrieval of surfa e solar irradian e relates theearth radian e at satellite altitude to the radiative properties of the system and to thetop of the atmosphere solar irradian e. The satellite radiometer measures within a givensolid angle the radiation s attered ba k to spa e by the system `earth-atmosphere'. Thisquantity is a measure of the planetary albedo and is reversely related to the atmospheri transmission of solar radiation. Sin e surfa e solar irradian e is strongly determined bythe transmission hara teristi s of the atmosphere, there is a strong omplementaritybetween global irradian e and the satellite signal.The use of remotely sensed radian e data from satellites is well-suited to the taskof surfa e solar irradian e estimation for two reasons. First, most of the solar radiationrea hing the earth's surfa e originates from visible to near-infraread wavelength (�15

0:4 � 1:0�m). Energy at wavelengths longer than 1:0�m is almost totally absorbedby even thinnest louds, and energy at wavelengths shorter than 0:4�m is largely lostdue to mole ular s attering and absorption by ozone. Se ond, the louds are the mainmodulator of the surfa e solar irradian e, and they often an be observed easily fromspa e. A high (low) value of net solar ux at the surfa e is onsistently a ompaniedby a low (high) value of loud opti al thi kness, and therefore a low (high) value ofre e ted solar ux at satellite altitude.

Di�use Fra tion Model

Cloud IndexClear Sky IndexGlobal Irradian eClearness IndexDi�use Fra tionDi�use Irradian e(Skartveit et al.)Clear Sky Model(Dumortier/Page)Ground Re e tivityCloud Re e tivityNormalizationMeteosatVisible CountsRe e tivity

Fig. 5: The �gure shows the basi steps for the estimation of global irradian efrom METEOSAT data. Di�use irradian e is al ulated by applyinga statisti al model.The various methods (e.g. [6℄, [7℄) presented in the literature mainly di�er in thedes ription of the relationship between atmospheri transmission and outgoing radian eas seen by the satellite. Physi al models dire tly des ribe the radiative pro esses inthe atmosphere by means of radiative transfer al ulations while empiri al methods arebased on statisti al relationships between satellite and ground measurements. However,16

most operational methods, in luding the one used here, for the estmation of surfa eirradian e a tually in lude elements of the other respe tive on ept.The algorithms for retrieving global irradian e from satellite data where taken fromthe paper by A. Hammer et al. [8℄ and is referred to as the Heliosat Method. It desr ibeshow to al ulate the global irradian e from METEOSAT ounts in VIS. The method isbasi ally driven by the strong omplementary between the planetary albedo re orded bythe satellite's radiometer and the surfa e radiant ux. The planetary albedo in reaseswith in reasing atmospheri turbidity and loud over.For a orre t estimation of the hange in re e tivity for a given image element thein uen e of the in oming radiation on the re e ted radiation has to be onsidered.Therefore a normalization with respe t to the zenith angle of the sun is apllied. Thisrelative re e tivity % % = (C � C0)dist2Irrext os(#)(where C0 is a registration o�set, dist is the earth-sun distan e in AU, Irrext is theextraterrestrial solar spe tral irradian e at mean earth-sun distan e for the spe tralrange of the visible METEOSAT dete tor and # is the sun zenith angle) thus gives ameasure for the planetary albedo.With the relative re e tivities estimated in this manner a loud index n is derivedfor ea h pixel as a measure of loud over:n = %� %g% � %gwhere %g and % are the relative re e tivities in the lear sky and over ast ase, respe -tively.To establish the before mentioned relationship between atmospheri transmissionand planetary albedo, a quantity hara terizing the transmittan e has to be introdu ed.In the paper [8℄ the lear sky index k� is used, whi h is a fun tion of the loud index onlyand is de�ned by the ratio of surfa e global irradian e Ig to surfa e global irradian eunder lear sky onditions I lear (the latter one has to be inferred from a lear skymodel): k� = IgI lear ;= 8>>><>>>: 1:2 : n � �0:21� n : �0:2 < n � 0:82:0667� 3:6667n+ 1:6667n2 : 0:8 < n � 1:10:05 : 1:1 < n;so the surfa e global irradian e an be al ulated, if I lear is known.The lear sky model for al ulating the global irradian e under loudless skies I learis des ribed as a sum of dire t and di�use irradian e. For the dire t omponent of learsky global irradian e a physi al model is used [9℄, whereas for the di�use omponent17

an empiri al models is used [10℄. For both models the relevant parameters, besides theearlier mentioned sun parameters Irrext; dist; # are:� a side spe i� Turbidity TL (see table in [8℄),� the relative airmass m = ( os(#) + 0:50572(96:07995 ir � #)�1:6364)�1,� the rayleigh opti al thi kness%R(m) = (6:6296 + 1:7513m� 0:1202m2 + 0:0065m3 � 0:00013m4)�1.With these parameters the global irradian e under loudless skies I lear an be al ulatedas follows I lear = Idir os(#) + Idiff ;Idir = Irrextdist�2exp(�0:8662TL%R(m)m);Idiff = Irrextdist�2(0:0065 + os(#)(�0:045 + 0:0646TL)� os2(#)(�0:014 + 0:0327TL)):In summary the global irradian e at the surfa e an then be determined from the lear sky index hareterizing the atmospheri transmittan e and the lear sky irradi-an e. While the latter one is modeled with a site spe i� turbidity [11℄, the lear skyindex is derived via the loud index from the normalized satellite ounts (the relativere e tivities). A s heme of the pro edure is given in �gure 5.The model presented here is limited due to the fa t that METEOSAT ounts rep-resent data integrated over quite a large spe tral range. That means by de�nitionthat the physi al model parametrization an only lead to a mean representation of allpro esses a tually depending on the in oming wavelength. Other fa tors determiningthe method's un ertainty are in uen es of louds, aerosols and surfa e re e tion whi hagain are only hara terized by mean in uen es.3.2.2 SoftwareAfter the des ription of the physi al model used its realization on the omputer will nowbe dis ussed. Most of the underlying input parameters in this model are well-de�nedphysi al values; only the relative re e tivities in the lear sky and over ast ase havedo be determined seperately from VIS ounts.In order to pro ess the roi-�les the lass `roi file' was de�ned. It provides severalmethods in luding reading �les (`roi file::file start', `roi file::header info'and `roi file::read roi') and al ulating the global irradian e. For al ulating theglobal irradian e the physi al model was splitted into two parts, i.e. one method todetermine the relative re e tivities (`roi file::refle t bytewise') and one method(the a tual physi al model) whi h uses the determined relative re e tivities `roi file::phys model bytewise'. This was done be ause one �rst has to determine the minimum18

Fig. 6: The �gure shows an example of the output of the `refle t param'auxiliary program.(the above-quoted lear sky ase) and maximum (over ast ase) value of the relativere e tivities whi h then serve as parameters for the a tual model.In order to determine these two values the `refle t param' program was used. It al ulates the relative re e tivities for all pixels whi h are `above sea' from a number ofroi-�les (one should make sure that the program uses roi-�les from days with louds aswell as from those with lots of sunshine in order to get orre t results) and plots themafterwards. From this plot one an then determine the minimum and maximum valueand enter them in the `roi file::phys model bytewise' method. Figure 6 shows theoutput of this auxiliary program for roi-�les of Mar h and July 1994.time series i . dataHelgoland data

time series dataDW Data linear.m jebo read.m

Norderney, List data

Fig. 7: The �gure shows the onversion of the supplied measured data intodata whi h an be easily a est with `time series( i )' methods.As mentioned above (see `Physi al Foundations') the physi al model is deriving theglobal irradian e only. In order to determine PAR from global irradian e a onversion19

fa tor has to be found. For this purpose one obviously needs a set of data of globalirradian e and PAR measured at the same site and time. These data were taken frommeasurements (every ten minutes) for the year 2000 on Heligoland. The data an alsobe used to test the models used and for the training of the Neural Net (see below). Forthe year 1994 data from the `Deuts her Wetterdienst' of measurements of the globalirradian e (every hour) on Norderney and List were taken for the testing and training.

Fig. 8: The �gure shows an example of the output of the `glob2par' auxiliaryprogram for measurements on Heligoland of the year 2000.

time series i . datatime series dataroi-�les

physmodel testing.promake mask.proglob2par.pro

physmodel testing.pro

Fig. 9: The �gure shows the auxiliary programs dis ussed in this se tion to-gether with the data they work on. Data types are hare terized withthe dis symbol, programs are framed.The measured data were �rst onverted into a time series with the help of twoMATLAB auxiliary programs `DW data linear' and `jebo read'. The �rst one wasused for the `Deuts her Wetterdienst' data. Due to the fa t that these data were nearly20

omplete the missing values were derived by linear interpolation. For the latter one theinterpolation was not always possible (it was only done when not more than �ve sequentmeasurements were missing). Figure 7 shows the onversion of the data s hemati ally.Due to the diversity of the two sets of data two distin t lasses had to be introdu edfor reading out the data of the time series for a spe i�ed time, the lass `time series'for Norderney and List data and the lass `time series i ' (`i ' for in omplete) forthe Heligoland data. For both of these lasses methods were provided for reading data(not only s alar type but also ve tor- or grid-like) from the time series �les (whi hhave to have a ertain stru ture dis ribed in the header of the `time series::read'(or `time series i ::read') method) and for returning the value of `data' for a spe -i�ed time (i.e. the methods `time series::value' and `time series i ::value') byinterpolation.

Fig. 10: The �gure shows an example of the output of the `physmodel testing'auxiliary program for the Mar h and June 1994 data.The determination of the above onversion fa tor was done with the auxiliary pro-gram `glob2par' whi h uses the measured data from Heligoland of PAR and globalirradian e. Within the program a linear orrelation of the two data sets is assumed sothat a onstant onversion fa tor is obtained by simple linear regression (assuming aregression line through the origin). The output of the program are two �les, one for21

the regression line and values for the slope and its standard deviation. The other plotgives the deviation of the values from this �tted line. Figure 8 shows these two output�les, giving a onversion fa tor of 2:197(�0:001)[�molWs ℄.Before the a tual al ulation of PAR one should test whether the relative re e -tivities entered in the `roi file::phys model bytewise' method are well suited forderiving the global irradian e for the region of interest. For this purpose the auxiliaryprogram `physmodel testing' is provided. It ompares the measured data of globalirradian e with the al ulated ones. The program al ulates the global irradin e for�ve points (over sea) near the measuring station, looks up the orresponding measuredvalue and reates three �les, one ontaining a s atterplot of the a ulated values vs themeasured ones; leading to a regression line, one ontaining a plot of the deviations andone of the relative errors.Figure 10 shows the output for the 1994 data (Mar h and June). A summary of allauxiliary programs will be given in �gure 9.If the output of the `physmodel testing' program was satisfa tory (i.e. a meandeviation lose to zero, a slope lose to one and a suÆ ient small standard deviation)one an then run the main program alled `physmodel gridded'. The main program al ulates PAR (from the output of the `roi file::phys model bytewise' method viathe onstant onversion fa tor) for all points of the roi-�les and writes the values into atime series (in omplete, grid like type). Using this program is therefor espe ially usefulfor a series of roi-�les. The so generated gridded time series an be easily a essed withthe `time series i ' methods.

Fig. 11: The �gure shows an example of the output of the `PAR means' programfor the month means of Mar h 1994 (left) and the day means of Mar h4th 1994 (PAR is in �molm2s ). For both the region of interest is the`German Bight' with the land overed by a mask.These methods were used to reate another auxiliary program alled `�lm gridded ts'.It displays a `movie' of the PAR time series for an interval spe i�ed by the user who an also adjust the speed and dire tion of this movie intera tively.The reated time series of PAR was also used for al ulations of day- and monthmean values of PAR in the roi. This is useful if the time series overs a range of a month22

PAR means.pro film gridded ts.proday-, month means pi t

roi-�lestime series roi PARphysmodel gridded.pro

Fig. 12: The �gure shows the data types and the main programs for deviationof PAR with the physi al model in a s hemati ally way. Data typesare har terized with the magneti dis symbol, programs are framed.or so and is done with the `PAR means' program. The program will reate a numberof output �les, one of them ontaining a oloured plot of the deviations of the monthmean values of PAR in roi from the total month mean value (red orresponds to valuesof PAR greater then the total month mean value, blue orresponds to a smaller one)and the other ones (as many as there are days in this month) are the orrespondendplots of the deviations of the day mean values in roi from the total day mean values.(Note that the month mean was al ulated as the mean of the day means, so it is a tualthe mean day value and oin ides with the month mean values if all days have the samenumber of slots with sunshine.) For all of these plots only points in roi `above sea' anbe taken taken into a ount sin e the physi al model used is valid only above sea. Thisis rea hed by using a `land-sea mask' reated with the `make mask' program from a roi�le with nearly no louds present in roi. Figure 11 shows an example of the output ofthe `PAR means' program.A summary of all programs dire tly related to PAR is given in �gure 12.3.2.3 Dis ussion of the Physi al ModelThe Physi al Model presented has the advantage that it is appli able to any region overed by water; when hanging the region of interest the model by onstru tionprodu e results with the same quality. This is due to the fa t that the model is based23

on mean representations of the various variables the global irradian e depends on.On the other hand the Physi al Model has the disadvantage of having large errors(see the s atterplot (regression line) and the plot of the deviations in �gure 10). Theorigin of the errors should now be dis ussed in more detail. In the s atterplot a largeamount of points is lose to the origin. These points are asso iated with sunrise orsunset, i.e. with a small amount of global irradian e. On sunrise and -set the angle of thein oming irradian e is lose to �, the path through the atmosphere is of maximum lengthand the earth's urvature has non-negle tible in uen e on the path length. Within themodel the urvature is not taken into a ount, so it is not surprising that most of thesepoints have overestimated global irradian e. In the plot of the relative errors in �gure10 these points are asso iated with the large positve deviations from 200 to 400 %.Anyway, these points are not orrelated with the asymmetry of the deviations inthe above �gure, i.e. the width of the distribution is bigger for underestimating thenfor overestimating the global irradian e. In order to �nd the origin of that the Physi alModel was tested again, but this time with only one day with sunshine (1.6.1994) andafterwards with only one day with an over ast sky (28.3.1994) (for this purpose anauxiliary program `dis ussion phys' was written whi h is just a modi� ation of the`physmodel testing' program). The testing was done by plotting a s atterplot of themodel returned values vs the ground measured ones (again the data from the `Deuts herWetterdienst where used) together with the regression line from �gure 10. Additionallythe values for the two sites (Norderney and List) are hare tarized with two di�erentsymbols. The output an be seen in �gure 13.

Fig. 13: The �gure shows the testing of the Physi al Model for an over astedday (left) and one with lear sky (right). The `x' symbolises pointsfrom List the `4' points from Norderney.In the plot for the lear sky ase it is remarkable that nearly the same amount of al ulated points is pla ed above as is pla ed below the regression line, i.e. this plotleads to a symmetri distribution of the orresponding derivations.On the other hand the plot for the over ast ase shows an asymmetry: a large24

amount of points is pla ed below the line, i.e. the global irradian e is underestimatedvery often. This might be explained by multiple ba kre e tan e in the thin loud ase:then the dire t omponent of the global irradian e an still pass through these louds, apart of it will be re e ted onto the louds and from there ba k to the surfa e leading tobigger then expe ted value of irradian e on the surfa e. These pro esses are not takeninto a ount in the model and may be the reason for the dis ussed asymmetry. In thesame plot one an also see that most of the points orresponding to overestimated globalirradian e originate from the same measuring site, i.e. above the line there are more` rosses' ( orresponding to List). This might be due to the fa t that in the over astsky the global irradian e is strongly depending on the site: when hanging the positiononly by a few kilometers the value might vary drasti ally. Sin e for ea h measuring site�ve points lose to this site where hoosen for the test of the model this ould explainthe overestimating for only one site in a few ases and again the dis ussed asymmetry.In summary the Physi al Models performan e is, as expe ted, better for the learsky ase than for the over ast one due to the omplexity of the pro esses in this ase.The advantage is the broad appli ability of the model.3.3 The Neural NetAnother way of determining global irradia e from METEOSAT data is the usage ofa Neural Net (NN) parametrization whi h will be illustrated in this se tion. The NN`learns' from a training sample ( ontaining a number of input variables as well as thedesired output, i.e. the global irradian e). The so trained NN an then be used forthe derivation of global irradian e from the input variables. The onversion to PAR isdone via the onstant onversion va tor (see above). First of all the NN used will beintrodu ed.3.3.1 The Neural Net ffbp1.0Before des ribing the Neural Network (NN) and its training brie y, some general infor-mations about NN should be given.A NN is an inter onne ted assembly of simple pro essing elements, neurons, whosefun tionality is loosely based on the animal neurons. The prose ing ability of thenetwork is stored in inter-neuron onne tion strength, or weights, obtained by a pro essof adaption to, or learning from, a set of training patterns. Properties ommon to allNN are:� NN's provide a urate, fast and onvenient mathemati al (statisti al) models.25

� NN's have apabilities for informational modeling of dependen ies on more thanone variable.� NN's retrieve a urate algorithms.� NN's are a natural tool for multi parameter retrievals.� NN's an be fast forward models for dire t assimilation.� NN's are robust in the presen e of noise: small hanges in an input signal will notdrasti ally a�e t a neurons output.� Trained NN's an deal with `unseen' patterns and generalize from the trainingset.The program used in the present work `ffbp1.0' is a C-program by H.S hiller [12℄ fortraining of feedforward ba kpropagation NN, a multiple non-linear regression method,running on UNIX omputers. Feedforward ba kpropagation NN are the most frequentlyused NN in remote sensing. `Feedworward' means that input values in the �rst neuronlayer will be only propagated `forward', there are no ba k onne tions whereas `ba k-propagations' means that during the learning of the NN the desired output is omparedwith the NN output, the errors will be tra ed ba k and the weights will be readjusted.The learning fun tion implemented is a gradient des ent algorithm with momentumterm. The program allows for starting with a small net whi h an be enlarged later ifne essary.In the publi ation `Feedforward-Ba kpropagation Neural Net Program `ffbp1.0'[12℄ the usage of this program is des ribed in detail. Therefore in this do umentionthere will be no des ription of this program but the result of the training pro ess willbe presented.For the training of the NN one needs to reate a training �le in whi h in ea hline a number of input variables is written as well as the desired output. The ouputdata where taken from measurments taken in Norderney and List of the `Deuts herWetterdienst' of 1994 on an hourly basis. Sin e METEOSAT data are taken everyhalf an hour one has to have a program whi h an interpolate from the `Deuts heWetterdienst' data for arbitary times. For this purpose again the lass `time series'was used with one method for reading in the `raw' data (`time series::read') and amethod `time series::value' whi h returns the interpolated value (see above, se tion`Software') for any given time (i.e. the time at whi h the satellite s anned roi).Input variables for the NN are:� the alibrated VIS, IR and WV ounts (i.e. radian e in Watts per square meterand steradian)� the azimuth di�eren e (in rad) between Sun and Satellite� the osine of the sun zenith angle divided by the square of the Sun Earth distan e(in AU) 26

The last two values an be al ulated from the parameters of the roi As ii header.In prin iple the alibration oeÆ ients for the three hannels an be taken from theOpenMTP �les binary header, but for the VIS hannel they are only available sin e1995. Details about where the a tual alibration oeÆ ients were taken from an befound in the te hni al desription [1℄.In di�eren e to the `Physi al Model' all three hannels available from METEOSATdata serve as input variables. This is done be ause some of the meteorologi al prop-erties an be `seen' on the IR and WV images. Su h properties in lude loud motion,temperature, upper tropospheri humidity, lear sky radian e and loud top heights.Due to the fa t that these properties are modelled by their mean in uen e in the `Phys-i al Model' only, it is expe ted that the NN works better and over a wider range ofspreading of the input variables.To reate the training �les (i.e. one �le ontaining the input and ouput variablesas olumns ending with `.patt' and one �le ontaining the names of all these variablesending with `.ds p') the program `NN training' was used. From the roi-�le it hooses�ve points lose to Nordernay and List whi h are for sure `above sea'. A s heme of thetraining pro ess is given in �gure 14.plot nn training.pro

ffbp1.0training-�les

NN training.protime series dataroi-�les

Fig. 14: The �gure shows the data types and the programs needed for thetraining of the NN in a s hemati way. The auxiliary programplot nn training an only be run after the training of the NN. Datatypes are har terized with the dis symbol, programs are framed.From this training sample about 90% were used for training the NN and the remain-ing 10% for testing the NN-output. It was found that the training led to best resultswhen two hidden layers with 15 neurons in the �rst and 3 neurons in the se ond layerfor the NN were hoosen. Figur 15 shows the performan e of the trained NN for thetest sample of the mar h and june 1994 data, in whi h the NN-output was ompared27

with the `Deuts her Wetterdienst' measurements. Sin e the NN program ffbp1.0 onlyprovides these plots for the test sample the auxiliary program plot nn training (see�gure 14) was used to obtain the plots for both, the testing and the training sample,for easier omparing the output of the physmodel testing output (see �gure 10) withNN output. 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= 0.007936test 20.140849/2317/1= 0.008693.

Fig. 15: The �gure shows the performan e of the trained NN. In the upper leftpart the regression line of NN-output vs desired output is shown. Theupper rigth part shows a plot of the orresponding deviations. Belowa plot of the relative errors is given.The so trained NN was used to reate an easily a essable time series of PAR �elds.The NN is used in this ontext to extraploate pointlike measurements to enlarge thearea. 28

3.3.2 Dis ussion of the Neural NetBy omparing the performan e of the Physi al Model (see �gure 10) and of the NN(�gure 15) it is obviously that the NN output has a mu h smaller width in the distri-bution of the deviations from the �tted regression line. Also this distribution does notshow the asymmetry present in the Physi al Model. This is due to the fa t that thevarious pro esses in uen ing the ouput in the over ast ase an be taken mu h betterinto a ount in a pure statisti al model su h as a NN.This statement an be prooven when running the NN for only one day with learsky and for one day with over ast sky (for better omparison the same days as inthe dis ussion of the Physi al Model where used). For this purpose the auxiliary pro-gram `dis ussion nn' was written whi h is a modi� ation of the `plot nn training'program. Again, the NN output was plotted vs the measured values as a s atterplottogether with the regression line from �gure 15. For the NN the output shows no asym-metry (i.e. mu h more point above or below the regression line) neither in the learsky ase nor in the over ast ase (see �gure 16). The better performan e for the learsky ase might be explained due to the strong site dependen y in the over ast ase.In the plot the asymmetry of one site (as for List in the testing of the Physi al Modelperforman e) annot be seen. It is ommom to both models that the over ast ase leadsto higher deviations than the lear sky ase.

Fig. 16: The �gure shows the testing of the Neural Net for an over asted day(left) and one with lear sky (right). The `x' symbolises points formList and the `4' points from Norderney.The disadvatage of the NN is that it an not be applied to any other region overedwith water be ause the NN has only `learned' the opti al properties for this spe ialregion of interest. Anyway, when supplied with ground measurements for any other siteanother NN an be trained easily in the same manner as dis ribed above.In summary one an state that the use of a NN for derivation of PAR should bepreferred to any Physi al Model sin e by onstru tion a NN an take the various pro- esses determining PAR on a surfa e mu h better into a ount then a non-statisti al29

model relying on averaged relations.4 Analysis of the results for the German BightIn the previous se tions two di�erent models for deriving PAR (via a onstant onversionfa tor from the derived global irradian e) from METEOSAT data in a region of interest(roi), here the `German Bight', have been introdu ed. Now the output of these models,the Physi al Model and the Neural Net (NN), will be dis ussed with fo us on the roi.For these purpose pi tures of the month mean of Mar h and June 1994 were al u-lated with both of the models. Figure 17 shows the output for the Physi al Model and�gure 18 for the NN. In the �gures the al ulated mean value is always set to `white',values of greater PAR are `red' and lower PAR is `blue'. Ea h olour s ale is de�ned bythe largest derivation from the mean value, i.e. in most of the ases only the maximum(or minimum) of the olour s ale will be a tually used in the orresponding pi ture.The mask used in the pi tures not only overs the land but also small islands and thetidelands between (this is why the mask does not look like the land on a map, but wasnesessary be ause both of the models only work above sea).

Fig. 17: The �gure shows the output of the `PAR means' program for the monthmeans of Mar h 1994 (left) and of June 1994 (PAR is in �molm2s ) al u-lated with the Physi al Model. For both the region of interest is the`German Bight' with the land overed by a mask.As expe ted the ouput looks similar for both models used. The al ulated PAR val-ues for ea h month are of the same order for both models and are a bit lower for the NNoutput. In all ases the derivation from the mean value is of the same order (or bigger)then the orresponding standard derivation when testing the model. Nevertheless theerror in the above pi tures is mu h less then these values due to orrelations from onepixel to the neighbouring ones (i.e. the possibility of an error in al ulating PAR fora region with similar values of PAR is mu h less ompared with the error on just onesingle pixel in this region). 30

Fig. 18: The �gure shows the same month mean values as �gure 17 but thistime al ulated with the NN.

Fig. 19: The �gure shows the day means ( al ulated with the NN) for an over- asted day (left, 28.3.1994) and one day with (nearly) lear sky (right,1.6.1994). Again PAR is in �molm2s .Another noteworthy fa t is the stru ture present in all of the above pi tures: loseto the oast the month mean values of PAR are less then above sea, i.e. in the monthmean it is brighter above sea. At a �rst glan e this may look like an artifa t. Toproof that this is not the ase �gure 19 shows the day means of one day with nearlyno louds present and one day with an over ast sky (for this purpose the same days asin the dis ussions of the models were used). One an see that in both of the pi turesthe above mentioned stru ture is not visible but that the value of PAR is nearly thesame in the whole region. The stru ture might be explained due to blushing on the oast when old and humid airmasses from above the sea and warmer, dryer ones fromabove the land `meet' in oastal regions. Anyway, it is obvious that for deriving anyparameters in roi whi h depend on PAR (as the primary produ tion in roi) one shouldnot use a mean value of PAR for the whole region.31

5 SummaryThe derivation of the Photosyntheti ally Available Radiation (PAR) in the `GermanBight' from METEOSAT data su eeded. From the data a subset orresponding to thisregion of interest (roi) was extra ted. For the a tual derivation of PAR from ountsin the roi-�les two di�erent models have been used, a so alled Physi al Model anda Neural Net (NN) implementation. Both the models al ulate the global irradian ewhi h is afterwards onverted via a onstant fa tor to PAR.To test the quality of the models their output was ompared with ground measure-ments of the global irradian e (Norderney, List). From this it turned out that the NN isbetter suited for the task for several reasons. It �rst of all has a good performan e inde-pendent of the weather onditions, whereas the Physi al Model underestimates PAR foran over ast sky. Se ond the Physi al Model uses only the VIS ounts and des ribes thein uen e of louds and other properties modifying the di�use omponent in an over ast ase only via their mean in uen e whereas the NN extra ts these informations from theIR and WV ounts whi h also serve as input values for the NN. The major advantageof the Physi al Model is the fa t that it is appli able to any region overed by water,by onstru tion it will produ e results of the same quality. If one wants to use the NNin other regions it has to be `taught' for this region to a ount for possible other opti alproperties in this region.The work presented here is a part of the workpa kage 3.4. of the `ENVOC' proje t.This workpa kage is on erned with the determination of the Primary Produ tion in the`German Bight', where PAR serves as an important imput variable. With respe t to thisproje t the most important results are: the value of PAR within this region u tuateso that the use of a mean value for PAR is not re ommended. Therefore the valuesof PAR for all points in the region are written into a time series whi h an be easilya essed for arbitary times in the range overed by the time series. Se ond a robustmethod for the derivation of PAR has been found: the use of the NN is re ommended.

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Referen es[1℄ K. S hiller http://gfesun1.gkss.de/software/meteosat2parTe hni al Des ription available[2℄ The Meteosat System - Satellites, Ground Segment, Missions, Global CoordinationEUM TD 05 Revision 4 (2000)[3℄ The Meteosat Ar hive - Format Guide No.1 - Basi Imagery, OpenMTP FormatEUM FG 1 Revision 2.1 (2000)[4℄ M.Iqbal An Introdu tion to Solar RadiationA ademi Press, 1983[5℄ C.D.Mobley Ligth and Water - Radiative Transfer in Natural WatersA ademi Press, 1994[6℄ R.Frouin et al. A Simple Analyti al Formula to Compute Clear Sky Total andPhotosyntheti ally Available Solar Irradian e at the O ean Surfa eJournal of Geophysi al Resear h, Vol.94, No.C7, 1989, 9731{9742[7℄ W.B.Rossow, R.A.S hi�er Advan es in Understanding Clouds from ISCCPBulletin of the Ameri an Meterologi al So iety, Vol.80, No.11, 1999, 2261{2287[8℄ A.Hammer, D.Heinemann, A.Westerhellweg et al. Daylight and Solar Irradian eData Derived from Satellite Observations - the Satellight Proje tDept. of Energy and Semi ondu tor Resear h, Fa ulty of Physi s, University ofOldenburg, D-26111 Oldenburg, Germany[9℄ J.Page Algorithms for the Satellight programmeTe hni al Report, 1996[10℄ A.Skartveit, J.A.Olseth, M.E.Tuft An Hourly Di�use Fra tion Model with Corre -tion for Variability and Surfa e AlbedoSolar Energy 63, 173{183[11℄ M.Fontoynont et al. Satellight: A WWW Server whi h provides high quality day-light and solar radiation data for Western and Central EuropePro . 9th Conferen e on Satellite Meteorology and O eanography, Paris, 25{29May 1998, 747{750[12℄ H.S hiller Feedforward-Ba kpropagation Neural Net Program ffbp1.0GKSS 2000/37 ISSN 0344-962933