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Clouds and the Earth s Radiant Energy System (CERES) Algorithm Theoretical Basis Document

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Clouds and the Earth s Radant Energy System (CERES) Algorthm Theoretcal Bass Document Grd Sngle Satellte Fluxes and Clouds and Compute Spatal Averages (Subsystem 6.0) G. Lous Smth 1 Takmeng Wong 1 Nchele
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Clouds and the Earth s Radant Energy System (CERES) Algorthm Theoretcal Bass Document Grd Sngle Satellte Fluxes and Clouds and Compute Spatal Averages (Subsystem 6.0) G. Lous Smth 1 Takmeng Wong 1 Nchele McKoy 2 Kathryn A. Bush 2 Rajeeb Hazra 3 Natvdad Manalo-Smth 4 Davd Rutan 4 Mara V. Mtchum 1 1 Atmospherc Scences Dvson, NASA Langley Research Center, Hampton, Vrgna Scence Applcatons Internatonal Corporaton (SAIC), One Enterprse Parkway, Sute 300, Hampton, Vrgna Oregon State Unversty, Corvalls, Oregon 4 Analytcal Servces & Materals, Inc., Hampton, Vrgna June 2, 1997 CERES Top Level Data Flow Dagram INSTR: CERES Instrument Data INSTR Geolocate and Calbrate Earth Radances 1 BDS BDS: B- Drectonal Scans BDS ERBE-lke Inverson to Instantaneous TOA Fluxes 2 EDDB ERBE-lke Averagng to Monthly TOA Fluxes 3 IES ES8 ES9 ES4 ES4G MODIS CID: VIRS CID: Cloud Imager Data CID Determne Cloud Propertes, TOA and Surface Fluxes 4 CRH CRH CRH: Clear Reflectance, Temperature Hstory ES8: ERBE Instantaneous ES9: ERBE Monthly ES4: ES4G: ERBE SSF SURFMAP SSF: Sngle Satellte CERES Footprnt TOA and Surface Fluxes, Clouds SSF SSF Grd TOA and Surface Fluxes 9 SFC MOA MWH MWH: Mcrowave Humdty SURFMAP: Surface Propertes and Maps SURFMAP Compute Surface and Atmospherc Radatve Fluxes 5 CRS CRS: Sngle Satellte CERES Footprnt, Radatve Fluxes, and Clouds SFC: Hourly Grdded Sngle Satellte TOA and Surface Fluxes SFC Compute Monthly and Regonal TOA and SRB Averages 10 MOA MOA Regrd Humdty and Temperature Felds 12 MOA MOA: Meteorologcal, Ozone, Aerosol Data APD GAP OPD APD: Aerosol Data GAP: Alttude, Temperature, Humdty, Wnds OPD: Ozone Profle Data CRS SRBAVG SURFMAP Grd Sngle Satellte Radatve Fluxes and Clouds 6 FSW SRBAVG: Monthly Regonal TOA and SRB Averages GGEO Grd GEO Narrowband Radances 11 GGEO GEO GEO: Geostatonary Narrowband Radances FSW: Hourly Grdded Sngle Satellte Fluxes and Clouds MOA GGEO: Grdded GEO Narrowband Radances FSW GGEO Merge Satelltes, Tme Interpolate, Compute Fluxes 7 SYN SYN: Synoptc Radatve Fluxes and Clouds SYN Compute Regonal, Zonal and Global Averages 8 AVG, ZAVG AVG, ZAVG Monthly Regonal, Zonal and Global Radatve Fluxes and Clouds June 2, Abstract Ths subsystem, Grd Sngle Satellte Fluxes and Clouds and Compute Spatal Averages, provdes the transformaton from nstrumentreferenced data to Earth-referenced data. In ths subsystem, a CERES footprnt s assgned to the approprate regon of a 1 equal-angle grd. Fluxes and cloud propertes are spatally averaged over each regon on an hourly bass. After passng through ths subsystem, the CERES data lose ther traceablty to specfc CERES measurements. Subsystem 6.0 uses the CRS archval product for nput (see Appendx A). The subsystem outputs the FSW archval data product, whch ncludes radatve fluxes at TOA, surface and atmospherc levels for clear sky and total sky condtons, cloud overlap condtons, cloud category propertes, column-averaged cloud propertes, angular model scene classes, surface-only data, and adjustment parameters (see Appendx B). The grddng and spatal averagng subsystem performs two major functons. The frst s to assgn CERES footprnts to the proper grdded regons. Ths assgnment s based on the colattude and longtude of the CERES footprnt feld of vew at the top of the atmosphere. The second major process s to perform spatal averagng of the varous radatve fluxes and cloud propertes over each regon for the tme of observaton Grd Sngle Satellte Fluxes and Clouds and Compute Spatal Averages 6.1. Introducton In order to make the CERES data more useful to researchers, the measured felds are presented n an Earth-based coordnate system. A equal angle grd s defned consstng of regons that are 1 n lattude and 1 n longtude. Average values of the dfferent parameters are computed over each regon at the tme of observaton. Only CERES data obtaned when the nstrument s operatng n the cross-track scan mode wll be used n computng regonal averages. Means of basc physcal quanttes n a regon are computed as arthmetc averages of the quanttes n those CERES footprnts whose centers are wthn the regon. It s also necessary to compute regonal values for other quanttes whch have been computed for ndvdual CERES footprnts, such as varances and probablty dstrbutons. The CERES footprnts are 25-km n dameter near nadr, so that there are more footprnts on the boundary of a regon than nsde the regon. Moreover, as CERES scans away from nadr, the footprnts grow such that they are not small compared to the sze of the regon, and the dstance between footprnts n the scan drecton ncreases. If the footprnts are large compared to the regon, as llustrated n fgure 1, overlap of the footprnts wth each other and wth the boundares of the regon complcates the problem of computng regonal averages. The selecton of partcular footprnts to use at the boundares of the regon and the correlaton of values of overlappng footprnts needs to be consdered. Because of these problems, mproved technques for computng regonal averages have been developed (Hazra et al., 1992, 1993). At present, error studes are underway to defne the degree of mprovement whch these methods provde. June 2, 6.2. Algorthm Descrpton Two basc functons are performed n the 6.0 and 9.0 subsystems. The frst s the grddng functon, n whch ndvdual CERES footprnts are assgned to the approprate regon or grd box. The second s the averagng functon, n whch spatal averages of tme and geometry data, radatve flux data, cloud overlap condtons, cloud category propertes, column-averaged cloud propertes, and angular model scene classes are computed. The data flow dagram (see fgure 2 n CERES Overvew) llustrates these functons. The algorthms used to perform these functons are descrbed below Grddng Algorthm The grd system s an equal area grd of 1 quas-squares n lattudnal rngs or zones. Each 1 square s known as a regon. There are 180 zones, whch are numbered consecutvely startng wth 1 at the north pole. The regons n each zone are numbered consecutvely startng at the 180 longtude, and progressng eastward. The number of the frst regon of the Mth lattude zone wll be NZONE(M). The Mth zone wll contan NZONE(M + 1) NZONE(M) regons. The regons n zone M wll be DLONG(M) degrees wde. DLONG and NZONE arrays wll defne the grd system. The wdth of each regon n a zone s DLONG( M) = 360/ ( NZONE( M + 1) NZONE( M) ) (6-1) The poston COLAT and ALONG for each CERES footprnt s computed by Subsystem 1 based on the optcal axs poston dsplaced by an angle due to the tme response of the detector and electronc flter. The regon number s then computed by makng dstnctons between the colattude and longtude. Frst we count the number of zones from the south pole to the pont, so that the zone number M s determned by: M = 180 INT( 180 COLAT) (1-2) Next we count the number of regons from the 180 longtude to the pont and add the number of the frst regon of the zone. The regon number NREGION for a CERES footprnt s computed as: NREGION = NZONE( M) + INT(ALONG/DLONG(M)) (1-3) Spatal Averagng Algorthms Tme and geometry data Instead of spatally averagng tme and locaton data over a regon, tme and locaton data are determned usng the concept of a key footprnt. The tme of nterest s the over-flght tme, whch s taken as the tme correspondng to the key footprnt assgned to a regon. The determnaton of the key footprnt depends upon the scan mode n operaton when the CERES data were obtaned. Durng cross-track operaton, the regon s scanned n an orderly manner. The set of all footprnts n regon NREGION s denoted as S(NREGION). The KEY footprnt s that footprnt whose axs s closest to the centrod of the regon. The centrod of the regon s calculated usng an sosceles trapezod approxmaton. Gven the centrod of the regon, the KEY footprnt s determned by fndng the footprnt n S(NREGION) for whch ( ALAT ALATCNR)**2 + (( ALONG ALONGCT)*sn(COLAT) )**2 (1-4) s a mnmum, where ALAT and ALONG are the colattude and longtude of a footprnt, ALATCNR and ALONGCT are the lattude and longtude of the centrod of the regon, and COLAT s the colattude of the footprnt. June 2, The KEY footprnts are used to dentfy the Julan date and tme, Sun longtude and colattude, solar zenth angle, spacecraft vewng zenth angle, spacecraft vewng azmuth angle, spacecraft relatve azmuth vewng angle, and nsolaton for each regon Spatal averagng algorthm Means. The regonal average of a quantty x s computed from ts measurements x as x mean = x N S S where N S s the number of footprnts ncluded n the set S for whch the average s beng computed. Ths technque was used for ERBE and for many other satellte processng systems. Gven one or more observatons n a regon, one can compute a regonal average wth no dffculty. Wthout such measurements, one does not wsh to attempt the computaton. Ths algorthm wll be appled to fluxes at the top of the atmosphere, surface and at ntermedate layers n the atmosphere. For averagng mcrophyscal propertes of clouds, t s necessary to account for the amount of clouds for whch a number apples, e.g. n computng the average optcal depth for clouds over a regon, the average apples only to that part of the regon whch has clouds. A regon may contan no clouds, one cloud or many clouds. It follows that for regonal averages of cloud mcrophyscal propertes, a weghtng by the fracton f of cloud n the footprnt s ncluded: x = f x f The drect/dffuse rato r s computed for each CERES footprnt for the downward shortwave flux at the surface. The regonal average drect/dffuse rato s computed on a flux-weghted bass, so that the regonal average rato apples to the regonal average values of drect, dffuse and total downward shortwave flux. The equaton for the regonal average drect/dffuse rato (see Appendx C.1) s: r = r F F ( 1 + r ) ( 1 + r ) Varances. There are two cases of computng varances. For the frst case, there wll be one measurement of a quantty for each CERES footprnt. The varance of ths quantty over the regon wll be gven by s 2 = ( N 1) N 2 2 x Nx mean = 1 For the second case, varances wll be computed n Subsystem 4 for cloud mcrophyscal propertes from MODIS pxels over each CERES footprnt weghted by the CERES pont spread functon as w ( x xˆ ) 2 s 2 = w June 2, It can be shown (see Appendx C.2) that s 2 s related to the varance of the quantty by The parenthetcal expresson of the rght-hand sde wll be a functon of the vew zenth angle α, whch wll vary slowly over a gven regon. Also, the number of MODIS pxels wthn a CERES footprnt wll be nearly the same for all footprnts wthn a regon. Thus, we can smply average the footprnt varances to produce a regonal average varance. Because the statstc thus computed s a functon of vew zenth angle α, ts values should not be compared across a satellte measurement swath except as a measure of the varaton of the bracket term Optcal Depth and Infrared Emssvty Hstograms. For each CERES footprnt, Subsystem 4 wll form a hstogram of vsble optcal depths durng the day and nfrared emssvtes durng the nght. For compactness, these hstograms wll be defned n terms of arrays of optcal depths and emssvtes correspondng to percentles. In the present subsystem t s necessary to reconstruct the hstograms from the percentles, and from them form regonal mean hstograms for each cloud heght class. A set of percentle values {p k } s defned for k [1, 13]. For a gven cloud alttude class the set of optcal depths {x k } correspondng to these percentles s computed by Subsystem 4 for each CERES footprnt. In order to spatally average the hstograms over a regon, we frst reconstruct the hstogram on a fne optcal depth grd consstng of a set of ponts {z j } for j [1, 50]. For optcal depth computatons, these ponts wll not be evenly dstrbuted. The reconstructed hstograms {p j } are then averaged over all footprnts wthn the regon, weghted by the fractonal cloud area f, to produce the regonal mean hstogram {P j }: From these {z j, P j } pars, the x k values correspondng to the selected percentle values of the regonal average optcal depth can then be computed by nterpolaton. In producng ths regonal mean hstogram, the optcal depth grd {z j } s accepted as suffcent so that there s no loss of accuracy due to nterpolaton errors. Thus, the grd wll be somewhat smaller than the accuracy of the optcal depth computaton. The nfrared emssvty hstograms wll be computed n the same manner. The nterpolaton ponts wll dffer between optcal depth and nfrared emssvty because the range of optcal depths s [0, 50] and the range of nfrared emssvty s [0, 1.] Procedural Consderatons Es [ 2 ] = σ 2 F( α) f p ( z j ) P j = Pz ( j ) = f Routne Operatons Expectatons The grddng and spatal averagng functons are performed on an hourly bass. The nput CRS archval data product s an hourly product. The output FSW archval data product s a monthly product. Intermedate FSW-hour data products need to be stored n a data repostory untl an entre month of data s avalable to produce an FSW product to be passed on to the next processng subsystem. We expect that the logstcs for ths wll be worked out cooperatvely by the CERES Data Management Team, the CERES Scence Team, and EOSDIS Excepton Handlng Strategy: Mssng Data, Invald Data All nvald data are expected to have been elmnated from the nput data products by the tme FSW processng takes place. Routne lmt checks wll be made to make sure that data are wthn reasonable lmts. Data that are outsde these lmts wll be excluded from further processng, and a dagnostc June 2, σ 2 report wll be ssued. These data wll also be noted on the qualty control (QC) reports generated by the subsystem Routne Dagnostcs and Qualty Control Expectatons Routne dagnostcs wll nclude a qualty control report for each hourly FSW-hour data product. These reports wll nclude nformaton such as: The number of nput records processed and the number of output records wrtten The number of regons nto whch data were placed The number of CERES footprnts of data placed nto each regon Per regon, the mnmum, maxmum, mean, and standard devaton of selected parameters Mssng data As the defnton of the FSW data product matures, ths lst wll be expanded Storage Estmate We estmate the sze of each FSW-hour zonal product to be 69.5MB (see Appendx B). As the defnton of the FSW data product matures, ths sze estmate may change. There wll be 24 FSW-hour data products per day, and 744 per month. Ths latter number s based on an average of 31 days per month. Thus, we antcpate a monthly sze of 12.22GB. Snce the next step n the CERES data processng system operates on a month of data, FSW wll requre at least 12.22GB of storage space. Fgure 1. Area coverage by scan modes showng cross-track scan. June 2, Appendx A Input Data Products Grd Sngle Satellte Radatve Fluxes and Clouds (Subsystem 6.0) Ths appendx descrbes the data products whch are produced by the algorthms n ths subsystem. The table below summarzes these products, lstng the CERES and EOSDIS product codes or abbrevatons, a short product name, the product type, the producton frequency, and volume estmates for each ndvdual product as well as a complete data month of producton. The product types are defned as follows: Archval products: Internal products: Assumed to be permanently stored by EOSDIS Temporary storage by EOSDIS (days to years) The followng pages descrbe each product. An ntroductory page provdes an overall descrpton of the product and specfes the temporal and spatal coverage. The table whch follows the ntroductory page brefly descrbes every parameter whch s contaned n the product. Each product may be thought of as metadata followed by data records. The metadata (or header data) s not welldefned yet and s ncluded manly as a placeholder. The descrpton of parameters whch are present n each data record ncludes parameter number (a unque number for each dstnct parameter), unts, dynamc range, the number of elements per record, an estmate of the number of bts requred to represent each parameter, and an element number (a unque number for each nstance of every parameter). A summary at the bottom of each table shows the current estmated szes for metadata, each data record, and the total data product. A more detaled descrpton of each data product wll be contaned n a User s Gude to be publshed before the frst CERES launch. Table A-1. Input Products Summary Product Code Name Type Frequency Sze, MB Monthly CERES EOSDIS Sze, MB CRS CER04 Clouds and Radatve Swath Archval 1/Hour June 2, 1997 A - 8 Clouds and Radatve Swath (CRS) EOSDIS Product Code: CER04 The CERES archval product Clouds and Radatve Swath (CRS) s produced by the CERES Instantaneous Surface and Atmospherc Radaton Budget (SARB) Subsystem 5. Each CRS fle contans longwave and shortwave radatve fluxes for the surface, nternal atmosphere and TOA for each CERES feld-of-vew (FOV). The CRS contans data for an one-hour satellte swath (8-12 percent of the Earth) from one satellte. In addton to beng an archval product, the CRS s used by the CERES subsystem Grd Sngle Satellte Radatve Fluxes and Clouds. For each CERES FOV, the CRS contans: CERES FOV geometry, tme, and scene data CERES FOV satellte alttude radance data CERES FOV estmated TOA flux data CERES FOV surface flux data CERES FOV total-sky area data CERES FOV clear-sky area data Cloud category propertes for two of four cloud heght categores (low (L), lower mddle (LM), upper mddle (UM), and hgh (H)) over the CERES FOV Overlap data for four of eleven cloud overlap condtons (clear, L, LM, UM, H, H/UM, H/LM, H/L, UM/ LM, UM/L, LM/L) over the CERES FOV CERES FOV surface radatve parameters Atmospherc flux profles for both clear-sky and total-sky at the surface, 500hPa, the tropopause, and the TOA over the CERES FOV Flux adjustments (tuned-untuned) for clear-sky and total-sky at the surface and TOA over the CERES FOV Adjustment parameters for clear-sky (note that these are calculated for both clear-sky and total-sky FOV) Adjustment parameters for the two cloud categores over the CERES FOV Level: 2 Type: Archval Frequency: 1/ Hour Porton of Globe Covered Fle: Satellte Swath Record: 1 CERES FOV Tme Interval Covered Fle: 1 Hour Record: Instantaneous Porton of Atmosphere Covered Fle: Surface to TOA June 2, 1997 A - 9 Table A-2. Clouds and Radatve Swath (CRS) Descrpton Parameter Unts Range Elements/ Bts/ Product Number Record Elem Code CRS Header Day and tme at hour start N/A ASCII strng A Character name of satellte N/A ASCII strng 1 64 A Character name of CERES nstrument N/A ASCII strng 1 32 A Character name of hgh resoluton mager nstrument N/A ASCII strng 1 64 A Number of mager channels used N/A A Central wavelengths of mager channels µm A Earth-Sun dstance AU A Day and tme IES processed (SS 1.0) N/A ASCII strng V Day and tme Imager Cloud Propertes processed (SS ) N/A ASCII strng V Day and tme Convoluton of Imager wth CERES processed (SS 4.4) N/A ASCII strng V Day and tme TOA and Surface Estmaton processed (SS ) N/A ASCII strng A Number of footprnts n CRS product N/A A CERES FOV Geometry, Tme, and Scene Tme of observaton 1 day A Radus of satellte from center of Earth at observaton 2 km A Colattude of satellte at observaton 3 deg A Longtude of satellte at observaton 4 deg A Colattude of Sun at observaton 5 deg A Longtude of Sun at observaton 6 deg A Colattude of CERES FOV at TOA 7 deg A Longtude of CERES FOV at TOA 8 deg A Colattude of CERES FOV at surface 9 deg A Longtude of CERES FOV at surface 10 deg A Scan sample number 11 N/A A Packet number 12 N/A A Cone angle of CERES FOV at satellte 13 deg A Clock angle of CERES FOV at satellte wrt nertal velocty 14 deg A Rate of change of cone angle 15 deg sec A Rate of change of clock angle 16 deg sec A Along-track angle of CERES FOV at TOA 17 deg A Cross-track angle of CERES FOV at TOA 18 deg A X component of satellte nertal velocty vector 19 km sec A Y component of satellte nertal velocty vector 20 km sec A Z component of satellte nertal velocty vector 21 km sec A CERES vewng zenth angle at TOA 22 deg A CERES solar zenth angle at TOA 23 deg A CERES relatve azmuth angle at TOA 24 deg A CERES vew
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