DFCEMBER 1993 STOWE ET AL. 809Evaluating the Design of an Earth Radiation Budget Instrument with System Simulations. Part I: Instantaneous Estimates LARRY STOWENOAA/NESDIS, Washington, D.C.PHILIP ARDANUY AND RICHARD HUCEKResea~vh and Data Systems, Greenbell, Maryland PETER ABELNASA /Goddard Space Flight Center, Greenbelt, Maodand HERBERT JACOBOWITZNOAA /NESD1S, ~shinglon, D.C.(Manuscript received 16 June 1992, in final form 4 March 1993) ABSTRACT A set of system simulations has been performed to evaluate candidate scanner designs for an Earth RadiationBudget Instrument (ERBI) for the Earth Observing System (EOS) of the late 1990s. Five different instrumentsare considered: t ) the Active Cavity Array (ACA), 2) the Clouds and Earth's Radiant Energy System-Instrument(CERES-I), 3 ) the Conically Scanning Radiometer (CSR), (4) the Earth Radiation Budget Experiment CrossTrack Scanner (ERBE), and 5) the Nimbu~7 Biaxial Scanner (N7). Errors in instantaneous, top-of-the-atmosphere (TOA) satellite flux estimates are assumed to arise from two measurement problems: the samplingof space over a given geographic domain, and sampling in angle about a given spatial location. In the limitwhere angular sampling errors vanish [due to the application of correct angular dependence models (ADMs)during inversion], the accuracy of each scanner design is determined by the instrument's ability to map theTOA radiance field in a uniform manner. In this regard, the instruments containing a cross-track scanningcomponent (CERES-I and ERBE) do best. As errors in ADMs are encountered, cross-track instruments incurangular sampling errors more rapidly than biaxial instruments (N7, ACA, and CSR) and eventually overtakethe biaxial designs in their total error amounts. A latitude bias ( north-south error gradient) in the ADM errorof cross-track instruments also exists. This would be objectionable when ADM errors arc systematic over largeareas of the globe. For instantaneous errors, however, cross-track scanners outperform biaxial or conical scannerstbr 2.5- latitude x 2.5- longitude target areas, providing that the ADM error is less than or equal to 30%. A key issue is thc amount of systematic ADM error (departures from the mean models) that is present atthe 2.5- resolution of the ERBE target areas, lfthis error is less than 30%, then the CERES-I, ERBE, and CSR,in order of increasing error, provide the most accurate instantaneous flux estimates, within 2-3 W m-2 of eachother in reflected shortwave flux. The magnitude of this error is near the 10 W m-2 accuracy requirement ofthe user community. Longwave flux errors have been found to have the same space and time characteristics aserrors in shortwave radiation, but only about 25% as large.1. Introduction The cxchange of radiative energy between sun, earth,and space affects the earth's climate and also is affectedby the earth's climate. Theoretical models (Ramanathan 1987) indicate that increases in mammade greenhouse gases, such as carbon dioxide, over decadal and CorreaT~onding author address: Dr. Larry L. Stowe, NOAA/NESDIS/ASB (E/RAID, World Weather Building, Room 711, Washington, DC 20233.longer time scales, perturb the equilibrium betweenthe two components of the earth's radiation budget(ERB): 1 ) the heat earth absorbs from the sun and 2)the heat earth emits to space. This leads to changes inglobal and regional climate. Thus, with a long, uninterrupted time record of stable ERB measurements, itmay be possible to detect climate change associatedwith increases in trace gas concentrations. Regional and global measurements of ERB havebeen collected since the advent of satellites. The National Aeronautics and Space Administration (NASA)led the experimental development of instruments spe1993 American Meteorological Society810 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 10cifically designed to measure the total flux of radiationfrom the sun and earth with so-called "broadband"(total spectrum) instruments. The most recent in theseries, the Earth Radiation Budget Experiment(ERBE), will end with the imminent deactivation ofthe NOAA-9 and NOAA-IO operational satellites. Atwo-scanner system, the Clouds and Earth's RadiantEnergy System-Instrument (CERES-I), has beenfunded by NASA for the Earth Observing System(EOS) of the late 1990s. There is also a Franco-Sovietprogram, Scanners for Radiation Budget (ScaRaB), tomeasure broadband ERB components in the mid1990s with a scanning instrument. Currently, the climate community is left with, at best, a 15-yr recordof relatively homogeneous, low spatial resolution(2000 km)2, broadband, wide-field-of-view, nonscanner measurements that started with the ERB experiment on the Nimbus-6 satellite in 1975. The paucity of high spatial resolution (250 km)2,broadband datasets for past years, and the clear needfor such data for future years, are of grave concern tothe international meteorological and climatologicalscientific communities and organizations. The NationalEnvironmental Satellite, Data, and Information Service(NESDIS) of the National Oceanic and AtmosphericAdministration (NOAA) may include an Earth Radiation Budget Instrument (ERBI) in future operational payloads. To initiate planning for ERBI, NOAAorganized an international workshop entitled "TheEarth Radiation Budget Requirements Review-- 1987"($towe 1988). One of the many recommendations tocome from the workshop was that a computer simulation of the total system (earth's radiation, instrument,.data processing) should be developed to guide decisionson system design options and to estimate the overallmeasurement error. In response to this recommendation, NOAA NESDIS has undertaken the development and applicationof computer software to simulate the ERB measurement process for five ERBI scanner designs. The instrument designs are unique and represent radiometersthat have been either flown or considered for spacemissions. They include: 1) the Active Cavity Array(ACA), 2) the CERES-I, 3) the Conically ScanningRadiometer (CSR), 4) the ERBE Cross-Track Scanner(ERBE), and 5 ) the Nimbus- 7 (N7) Biaxial Scanner.Briefly, the simulation process is: scanner fields-of-view(FOV) are located on the earth; ERB fluxes derivedfrom 6-day sets of 3-h Geosynchronous OperationalEnvironmental Satellite (GOES) data [ InternationalSatellite Cloud Climatology Project (ISCCP) B 1 ] areused to generate simulated measurements for each instrument; after reduction to the top of the atmosphere(TOA), the measurements contain errors induced byinstrument angular and spatial sampling patterns, FOVsize, and angular model errors in the retrieval system,all of which are evaluated through comparisons to theGOES reference flux fields. The simulation research has been divided into threeparts. Part I considers the simulation of instantaneoussampling of longwave (LW) and shortwave (SW) fluxesat the TOA. As the accuracy of all space- and timescale ERB products depends upon the accuracy of instantaneous fluxes, we chose this as the basis for ourERBI comparisons. The results of this study identifythe observing accuracies and error characteristics foreach candidate design, aiding the selection of a designbest suited for the mission. More information may befound in Stowe et al. (1991 ), from which this paperwas condensed. Part II begins with a baseline design for the instrument selected from this study, CERES-I. Additionalsimulations are performed to support improvementsin its design. Results of these trade-off studies lead toa design that lowers random and systematic errors andsimultaneously increases expected scanner lifetime. InPart lII, simulations are performed with the optimallydesigned CERES-I from Part II to consider samplingerrors over 24-h (diurnal) periods. The accuracy ofdaily averaged ERB measurements for several differentsatellite orbital configurations are studied, and the importance of multiple observing platforms is confirmed.Parts II and III will be documented in subsequent papers. The CERES instrument has been selected for NASAEOS (Moore et al. 1991 ), based in part on results fromthese simulations. Both morning and afternoon sunsynchronous NASA platforms, as well as an asynchronous, 35- inclination Tropical Rainfall MeasuringMission (TRMM) platform, have been chosen for theCERES instrument. The sun-synchronous orbiters include dual scanners, one dedicated to ERB measurements, the other to building improved ADMs. Theseplatforms will provide 15 years of observations througha series of three overlapping 5-yr flights. The presentlaunch scenario calls for the launch of T~RMM in 1997,followed by the launch of the morning polar-orbitinginstrument cluster in mid-1998, and the PM clusterlaunched some 20 months later (late 2000). TheCERES is considered by NOAA to be an operationalprototype instrument, and plans are underway to gainreal-time access to CERES data for operational production of radiation budget products. Space is beingprovided on NOAA's OPQ series of satellites to allowincorporation of CERES when feasible.2. Technical approacha. Earth simulation Reference fields of instantaneous TOA longwave(LW) and shortwave (SW) fluxes, and their hemispherical radiances, are required on a spatial scale thatis small compared to the minimum scanner footprintsize to be studied. The summary description of the fivecandidate radiometers given in Table I shows that the1993 STOWE ET AL.'FABLE 1. Summary description of five prototype scanners.811Radiometer Scan type Footprint sizeOn earth [equivalent Scansampling rate (s-~)* FOV type circular diameter at nadir (km)] period(s)ACA Fixed array of multiple zenith/azimuth anglesCERES-I Two scanners: one cross track, one azimuth slewCSR Conical scan at multiple zenith anglesERBE Cross trackNimbus-7 Biaxial90 Variable 150 3**50 Fixed 40 335 Fixed 50 1714 Fixed 52 47 Variable 80 224 * Number of samples per scan cycle/time of scan cycle.** Sampling repeat cycle.smallest projected FOV size at the TOA is the 40-kmnadir footprint of the CERES-I and, thus, sub-40-kmtruth fields are required. These are derived fromGOES-5 8-km (FOV at nadir) visible (VIS) and in~frared (IR) narrowband counts, centered about 0.6 umand 11.5 um, respectively, and provided at 3-h synopticintervals by the ISCCP B1 data (Rossow et al. 1985).The GOES FOVs are navigated to the earth's surfaceand, after a series of calibration, classification, andconversion steps, counts are transformed to broadbandradiances and then to TOA reflected (SW) and emitted(LW) flux pairs. An associated bispectral (SW and LW )cloud amount estimate is also obtained through application of the maximum-likelihood estimation(MLE) scene identification method of Wielicki andGreen (1989). Redistribution of the fluxes into upwelling radiances is achieved using the ERBE angulardependence models (ADMs), referred to throughoutthis report as the "reference" models (Suttlcs ct al.1988; Suttles et al. 1989), and normalized variationsof them (section 2a.3). The result is a unique TOAradiation field at each 3Hh synoptic time that, althoughderived from "narrowband" data, is representative ofthe spatial and temporal variability of the earth's radiation budget on a 10-km scale. Comparison scannerdata to be presented in section 3 are given for six daysof orbital simulations in July 1983 (on 15, 17, 18, 19,20, and 21 ) and January 1984 (on 25-30) for localmorning ( 1500 UTC) and afternoon (2 t 00 UTC) image times. 1 ) NAVIGATION, QUALITY CONTROL, AND INTERPOLATION GOES data are navigated to earth locations by meansof an algorithm produced at the University of Wisconsin's Space Science and Engineering Center (Smith andPhillips 1972) and mapped onto a 740 x 640 element0.1 - latitude-longitude resolution grid, hereafter calledthe M1 grid. Only the last data value to fall within agrid element is retained. The collocation of concurrentVIS and IR images is checked by cross-correlationanalysis and, if displaced, a shift in the IR image ismade. Typical displacements are within two grid pointsindicating that the images are well registered. Near theGOES-5 subsatellite point (at the equator), the ISCCPB 1 data have their highest resolution (8 km) and theM1 grid has its lowest resolution (approximately 11km). Toward the boundaries of the M1 domain, especially the northern edge, the grid resolution becomeshigher than the data resolution. In this region, the lackof available B1 data results in a characteristic missingvalue pattern that is most dense in the northwest cornerof the domain, farthest from the GOES-5 subsatellitepoint. This is illustrated in Fig. la, where missing valuesin the 1800 UTC VIS image of 29 January 1984 areseen to extend across the length of the northernboundary and southward from the northwest cornerto a latitude of about 20-N. Additional missing valuesare introduced during quality control checks on thegridded B 1 counts, where data spikes at pixel resolutionand bad scan lines are eliminated from further processing. Missing pixel values are adequately replacedusing linear interpolation in counts squared (proportional to radiance). Figure lb shows the same fieldused in Fig. la but after interpolation across missinggrid values. 2) NARROWBAND-TO-BROADBAND RADIANCE CONVERSION The transformation of VIS counts (8 bits) to broadband radiances is accomplished using a three-step procedure that begins with division by 4 to obtainGOES-5 6-bit counts. These have to be related toGOES-2 data through the calibration equation of theinstruments in the form (Muench 1981 ) r = K-2(C2 - Co2) (1)so that they can be converted into broadband radiancesusing GOES-2 N7, narrow to broadband regressionequations (Minnis and Harrison 1984a). In Eq. (1),r is a reflectance factor, K is a sensitivity constant, Cis measured counts, and Co is offset counts corresponding to a zero level of reflectance. Using Eq. ( 1 )812 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME10(a)(b) FIG. 1. A 512-line x 512-pixel image subset of the 640-line x 740-pixel reference field ofGOES-5 visible counts. The upper left-hand corner of the image is located at the northwest cornerof the study domain (47-N, 122-W). Visible counts are shown both (a) prior to and (b) afterinterpolation in space to fill missing values.DECEMBER 1993 STOWE ET AL. 813for equal values of r, a relationship between GOES-2(C2) and GOES-5 (C5) counts is obtained and givenby /K2\2 2 (2) where subscripts 2 and 5 refer to GOES-2 and GOES-5, respectively. Due to an error that was un covered only late in this study, the approximate expression K2 (7-2 - Co.: = ~ (G - Co.5) (3) was used in place of Eq. (2). Equation (3) gives rise to underestimates in SW radiance of about 20% on average. As a result, scanner sampling errors (to be reported in section 3) are also underestimated by about 20% on average. However, sensitivity tests using the correct calibration of Eq. (2) indicate that the accuracy of the various scanner designs, relative to one another, is probably not impacted by this error (see Appendix ). This calibration error has been removed From Parts II and 11I, studies that are to be reported separately. Thc conversion of GOES-5 IR counts to broadband radiances begins with the application of a counts-to blackbody temperature lookup table (provided by ISCCP). Spectral radiances are derived from temper atures by evaluation of the Planck function at 1 t.5 ttm. They are adjusted from GOES-5 viewing geometry to nadir using the narrowband limb-darkening model of Minnis and Harrison (1984b). Broadband radiances are obtained by regression using the GOES-2 N7 mod els of Minnis and Harrison (1984b), also applicable here because the spectral filters of GOES-2 and GOES-5 are nearly identical. They are readjusted back to GOES-5 geometry using the limb-darkening models of Raschke et al. (1973), 3) SCENE IDENTIFICATION AND THE DERIVATION of A TOA RADIATION FIELD Scenes are classified, according to the ERBE system (Wielicki and Green 1989), as combinations of surface type (ocean, land, and desert) and cloud amount cat egory (clear, partly cloudy, mostly cloudy, and over cast). ERBE snow and coastal surface types are not considered in this study. A high-resolution (0.1 o) land ocean map defines continental boundaries and M 1 grid elements straddling coastlines are taken as land. Snow scenes are usually classified as cloudy because of the strong similarity of broadband radiation fields for clouds and snow. Continental geography type (land and desert) is obtained from the land use dataset pub lished by Matthews (1985), and cloud amount iden tification is performed using MLE. For each M1 grid element, TOA fluxes, Fret, are obtained from GOES derived radiances, Rt3oEs, by rearranging the aniso tropic thctor expression (Taylor and Stowe 1984) ~'RGoES Fref -- , (4) ~Orefwhere Prcf is the ERBE anisotropic factor for thescene and angular geometry (between earth, sun, andGOES-5) at the GOES time of observation. When averaged into 2.5- target areas, the flux of Eq. (4) represents the "true" or "reference" ERB parameter thatour simulated satellite system is trying to measure. To simulate the effects of ADM variability, perturbedmodels, p', are introduced that are related to the reference models by (Green 1980) -- -N. (5) Pref- INotice that the isotropic value of 1 is removed fromboth t/ and t~ref in forming their ratio and that N,therefore, is an anisotropic scale factor that may besystematically and/or randomly greater than, less than,or equal to unity. It is easy to verify that the perturbedmodels satisfy the normalization condition 1 ~ p' cos0dfi I, (6) 3r,12~rsince the reference models, t~er, are already normalized.Here 0 is the local zenith angle at a target on the earthand dft is an element of solid angle of the outgoinghemisphere. The perturbed anisotropic models, together with thetlux of Eq. (4), are used to describe a complete radiancefield at the TOA for selected values of N. These experiments involve a redistribution of the total flux intothe upwelling hemisphere, but because of the normalization condition, do not affect the magnitude of theflux itself. For any given N experiment, reference radiances are determined from the reference flux andperturbed anisotropic models as Rrer = ~r-~p'Fr-f, (7) where p' depends on the N value selected according to Eq. (5).b. Measurement simulation Orbits of a polar platform are generated across theM 1 grid in a series of experiments designed to test thesensitivity of the five scanners to varying conditions ofsolar illumination and ADM variability. Illuminationconditions along the subsatellite track are determined,in part, by the choice of orbital ascending node (AN)equator-crossing times. ADM variability is simulatedthrough random and systematic selection of anisotropicscale factors. Instrument noise has not been incorporated into the results of this study, nor have the effectsof a rotating earth.814 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 10 1 ) SIMULATION OF SPACECRAFT MOTION The sun-synchronous satellite is placed at an altitudeof 824 km above mean sea level, in a retrograde orbitof inclination 98.7-, and with an orbital period of 100.7min. Orbital trajectories through the study domain(50--120-W) and crossing the equator at 63-, 86-,and 109-W were constructed. Results for the centertrajectory (86-W) are reported here. At 1500 UTC,local morning conditions exist for this orbit, and theAN equator-crossing time is 0945; at 2100 UTC, afternoon conditions prevail and the AN equator-crossing time is 1515 LST. 2) SIMULATION OF SCANNER OPERATION Distinguishing characteristics of each of the fivescanners are summarized in Table 1. The samplingpatterns they produce are illustrated in Figs. 2b-f. Allof the instruments, except the cross-track ERBE(Barkstrom 1984), employ some means of effectivelyviewing in two directions about an axis through thespacecraft nadir. The ACA (Hoffman 1989), countingits innermost cap, samples in 12 concentric rings aboutnadir with 271 detectors, each having approximatelythe same projected area on earth. The CSR (Wirth etal. 1986) similarly observes local targets at multiplesatellite zenith angles ahead and behind the satellite,but unlike the ACA, it uses only a single detector rapidly scanning through six angular rings. The biaxial N7scanner [in scan mode 5 (Jacobowitz et al. 1984)]sweeps both ahead and behind the satellite to beyondthe horizon and back; and to the sides, but not to thehorizon. It was designed primarily for the collection ofmultiangular data for the development of scene-dependent ADMs. Finally, the CERES-I (design specifications from CERES Team, February 1988) consistsof two scanners: one is a simple cross-track plane scanner (CTPS) like ERBE but with higher spatial resolution; the other, a rotating azimuth plane scanner(RAPS), is identical to the first, except that the scanplane rotates at 5- s-l. Because of its "biaxial" scanning capability, CERES-I would be used not only formapping the radiation budget, but also for the development of improved ADMs. Additional details of theseinstruments are given in Stowe et al. ( 1991 ). 3) SIMULATION OF A RADIOMETER MEASUREMENT Throughout the orbital simulations, an effort is madeto portray the candidate radiometers in a form thatclosely resembles their conceptual designs. Scanningpatterns and data rates are rigidly adhered to and theprojected earth location of the radiometer optical axisis used to define the position of individual observations.Footprint shapes, while not exactly reproduced in oursimulation, are represented by FOVs that remain fixedor variable, according to the basic prototype design,and match the solid angle of the IFOV. Scanner observations are modeled as an integral overthe radiometer FOV expressed as J*FOV Rref Gd~ R .... = , (8) ~FG d fl ovwhere Rmeas is the measured radiance at the satellite,Rref is radiance at the TOA, G is the instrument pointspread function (incorporating the time and angularresponses of the detector), and dr is an element ofsolid angle at the satellite. As this angle is less than 5 ofor the FOV apertures studied, G is hereafter set tounity for all scanners. Equation (8) is evaluated numerically as a discrete sum over all 10-km M 1 gridelements whose midpoints fall within the boundary ofthe instantaneous radiometer footprint (Fig. 3). Inconvolving radiances over the shaded area in Fig. 3,instead of within the exact footprint boundary, a quantization error in the measurement integral is made.For the ERBE instrument, this error is typically 8-70 fornadir observations. When occurring randomly in the90 or more ERBE observations within 2.5- target areas,it leads to about a 1% error in the computed regionalmean satellite flux.c. Top-of-the-atmosphere measurement inversion The procedures for inversion of observed radiancesto fluxes at the TOA, and subsequent space averaging,closely follow ERBE methods (Smith et al. 1986; Wielicki and Green 1989). Longwave and shortwave satellite radiance pairs are classified into scene types usingMLE. The transformation to TOA fluxes utilizes theexpression ~rRmeas mmeas - --, (9) /)refwhere R .... is the measured satellite radiance and prcfis the ERBE model anisotropic factor for the scene.Note that while Rmeas may be generated using the perturbed anisotropic models of Eq. (5), the radiance-toflux conversion is carried out using the ERBE meanmodels. Thus, although TOA departures from the reference ADMs may exist in the simulated earth scene(N-~ 1 ), the ERBE retrieval does not account for them. Each retrieved satellite flux is sorted into 2.5- targetareas according to the coordinates of the FOV midpoint. It is excluded from further processing if its solarzenith angle is greater than 86-, its satellite zenith angleis greater than 70-, or its SW reference anisotropic factor isgreater than 2, as done during ERBE processing.The flux measurements remaining in the target areasare arithmetically averaged and represent the regional,instantaneous satellite flux estimates.d. Error analysis Discrepancies between satellite-derived and actualvalues of instantaneous regional flux estimates at theDECEMBER 1993 STOWE ET AL. 815 ~1 GRID 2, DEGRE~ R~8OLUTION ~6 iIi~,a,a,~s,e,~,e fi%~t~%, t~ i~ ~I h la liltfililt~ilt~lltFilltF, ili.,'FfiTfoT~iI~-,il . 'al~;raliira];;ral ~ [~ ~0?[ 1~?~ ~ 0 -[ -~0 ~I~.1~ -$1~ o~o -~o ,.a~ .~ -8O -~o LOIGIT~DIatt53525155-5-15 -laOERBE SAMPLING PATTERN (~3 SCANS)~ ' '~~' ~l 7 -108 -97 -85 -73 -6~ -50[t5~525155-5-15 -120CSH SAMPLING PATTERN (5 5CANS) I I ~ T ~,.~-~:~y ~"- I ~ ]_ ,...;j.:~?'...'.~:.:., .:.-~, ..,....~, _., ,.,. - ~'~'~~-~'~~- k, '"~' "~" ' "~" -'~:~~~~" \ ~';~'-,"~~:~-"-?;~ -108 -97 -85 -72: -62 -50 RCR-285LI5:~$2~15B~5-1':; -120 5CANNING PATTERN (5 SCANS) U' ~::~y~-q e.]-108 -97 -85 -73 -82 -50 SIMULATED NIdBUS-7 MODE 5 SCAN b ,, ',,,,,..'~ .~ L\\\ I I ~ ,'///[! I ANN%%~',:','::,,.-120 ~ -~ -85 '~J '~, ~ '-aa -so CERE-I~t5~5a5155-5-15 -120 SCANNING PATTERN I2~ SCRNS) ' ' U~ "/~ ~ ~'-' fF .~','.. '..' .' ~ ' .- './~::'-~":::?::;~ i:~;/i.;.ii;;)..!:: , , i,~ .... ' ..... :""' -108-97 -85 -73 -62-50 FIG. 2. The study domain and representative scan patterns for each of the five study instruments. In panel (a) the study domain is shown,excluding a surrounding 2- buffer zone, with superimposed 2.5- target areas. The scan patterns are (b) ERBE, (c) CSR, (d) Nimbus-7, (e)ACA, and (f) CERES-1.TOA are a result of two fundamentally different operational problems. One is spatial sampling over a givengeographic domain; the other is angular sampling of afixed earth location. During computer simulations,these error sources are considered separately.1 ) SPATIAL SAMPLING AND SIMULATION OF ERRORS Spatial sampling errors result from the nonuniformviewing of a target area by the radiometer design and816 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME I0Field of View Projection and Integration Column Number 56 658 664 666 668 670 I I I I I I I I I I-~.~ f .... .... x.-. ~ ~ i/ ~'~"~'~ - . '.,,,:::.~ '~i~i~iii~i~ '~J:!', ii?~!i:i ~ ~ ~ .[ ;~::~::~::: ;:~::;~z;~ ~:~, ~,~ ~ ~?~,~:~ :~:~ ~:~ ~,~,~ ~:~ ~?;~ :~ ~ ~?;~:~~:~ :~:.;~;;~;~;~ ~?~:::~:: - ~:~:~ ?;~ ?:~::~ ~:x ~:?';. :~;~ ~;~?~ ?~j ,~t~? ~ ':-~ :~::~ ~'~ ~. ~ :-~i~;: ::~<.~ :,r~:~;~ ~ ~f~ ~' ;~:~~ ~ ~::~,:~;~ ~ ..... , .-~$~$ ............ ~ ~ ~:~ v~,~ ~:~; ~ ~-~ :~,~ 7J~ ::;:t~ .....-576 -568 -9.8(~'~ ,-570~ -10.0~ ~~ ~ -572 Z -10.2- o~ rr -5?4 -10.4 -10.6 I I I I I I I I I I I I I I I I I ~ -~,~ -~,~ -~,~ -~,~ -~,~ -~.~ -~,~ -~,~ -~,~ Longitude F~o. 3. illustration o~ the integration over the field o- view o[ a sJn~l~ Nimb~x-7 ~RB scanner WOV atthe top o[the atmosphere. For this observation, about 70 ( 10 km)2 elements pa~Jcipate in the measurementintegral.the contamination of edge observations with radiancesfrom outside the target area. The latter effect is mostimportant at high satellite zenith angles where footprintsizes increase and overlap with target boundaries occurs 10-KM SAMPLING PROBABILITY DISTRIBUTION AT THE EQUATOR FOR ONE ORBITAL PASS3530 ACA0 5 10 15 20 25 30 SAMPLING FREQUENCY-~- CERES4 -+- CSR -~- ERBE -~- NIMBUS-7 lqG. 4. The M l grid element sampling frequency probability curvesfor the five ERBI study designs: ACA (inset), CERES-I (solidsquares), CSR (pluses), ERBE (asterisks), and Nimbus-7 (emptysquares).more frequently. The in-target sampling characteristicsof the five radiometer designs are displayed in Fig. 4where the probability of observing an individual M 1grid element in a 2.5- target area a given number oftimes is shown. Because the probability curve varieswith distance from the suborbital track, an averagecurve for the 12 or so target areas lying east to westacross a scan swath between the equator and 2.5-S isillustrated. Under ideal conditions, the probability distribution would be a single spike (at a nonzero frequency) so that every truth field element was sampledan equal number of times at many different viewingangles. Zero sampling frequency indicates that thereare portions of target areas that are not observed bythe particular radiometer. In the case of N7, much of the domain is not sampled, but when an element is viewed, it can contributeto as many as six measurements. The CSR has a broadsampling distribution because its multiple overlappingrings of observations do not yield an even mappingpattern. As a result, the TOA flux field enters the satellite 2.5- box average nonuniformly, especially nearnadir where numerous multiangular overlapping footprints occur. The ACA covers the greatest and broadestrange of sampling frequencies because the radiometerfootprints are large (Table 1 ) and, like the CSR, theyDECEMBER 1993 STOWE ET AL. 817are arranged in multiple rings about nadir, The largefootprints permit a given radiometer to view the sameearth location over many measurement cycles and themultiple rings of radiometers assure that it is viewedfrom many look angles. The ERBE cross-track scannerhas a tight imaging pattern. Each element is utilizedabout 3 _+ 1 times, and practically all elements areviewed. This approaches the ideal sampling distribution. The CERES-I pattern arises because the observations of the RAPS are grouped with those of theCTPS for mapping TOA fluxes. This disrupts the organized array of half-overlapping footprints from theCTPS by superimposing the irregular, multisized distribution of RAPS footprints. The current design produces a sampling frequency of zero with a 6% probability. Unsampled M 1 elements occur at the edge ofthe scan swath where observations beyond 70- of satellite zenith arc rejected (toward the outer edge of thetargets). This does not happen with ERBE because ofits larger footprint size and lower sampling rate (eftTable 1 ). Regional errors in satellite flux estimates are definedby E = FMEAS -- FREF, (10)where FREF is the regional reference flux given by averaging the flux from all 625 elements of a target area.Here F~m^s is the satellite flux estimate obtained byaveraging over the number n of observations fallingwithin the target. A satellite flux estimate Fmcas.i is obtained from Eq. (9). Using successive substitutions ofEqs. (8) and (7) in Eq. (9) and with G set to unity,Fmcas.i may be written ? J~neas, i r= (-- ~ Fre-,i, (1t) \ Prer/iwhere p' is the flux- and solid angle-weighted mean(ovcr the M 1 elements in the FOV) pcrturbed anisotropic factor and/7~r,i is the solid angle-weighted meanreference flux for the ith FOV. Then Eq. (10) becomes E = - -- ]?refd -- /~EF- (12) rl i=~ \Pref /iIn Eq. (12), angular sampling errors are manifestedthrough the ratio P'/Pref. Regional spatial sampling error is defined as the discrepancy between satellite-derived TOA flux estimates and the underlying truth fieldwhen no uncertainty exists in the application of ADMsto the TOA reduction of the satellite observations, thatis, p'= p~t. Equation (12)becomesESPAT1AL = -- ~]- ffref, i -- FREF. ( 13 ) F/ i=1In Eq. (13), the spatial sampling errors involve theradiometer FOV configuration, through the - ' F~ef, i S, andthe scanning pattern design, through the set of observations i = 1, n; but no perturbed ADMs are involved.This can be simulated by using an isotropic radiancefield at the TOA and isotropic ADMs for inversion ofsatellite measurements, that is, both the ~' and Pref areset to unity (subsequently referred to as an "N = 0"experiment). 2) ANGULAR SAMPLING AND SIMULATION OF ERRORS Angular sampling error is defined as the residual inEq. (12) after removal of the spatial error componentfrom the left-hand side. Subtracting Eq. (13) from (12),EANGULAR is given by EANGULAR = E - ESPATiAL = -- ~3 eft/, (14) n i=1 \Pref ]iwhere Api = P ? -- Pref, i - (15)As indicated by Eq. (14), an error is incurred at evewobservation for which ~p ~ 0. In contrast to spatial sampling e~or, angular sampling error arises only at the n obse~ation positionswithin a target area. This e~or component is simulatedusing reduced radiometer footprint sizes, equal in areato the resolution of the M 1 grid, and re~onal referencefluxes averaged only over this set of observed M 1 gridelements. From Eq. (13), with ff~f,i reducing to Fr~f,i,spatial sampling e~or vanishes when Fa~v is replacedby the obm~ed reference flux. Under these conditions,re~onal measurement e~or contains only an angularcomponent given by 1 Z L~r,~, (16) EaN~ULAR n i=i kP~r /iwher~Apc is similar to the Ap of Eq. ( 15 ) except thatnow p' is replaced by p' at the center of the FOV (atan M 1 ~d element). Comparing Eq. (16) to (14) for a fulI-FOV experiment, we find that they differ~nly in the replacementof the FOV average terms, p' and F~r,/ of Eq. (14),with their FOV values (at the MI grid point) in Eq.(16). Thus, Eq. (16) simulates the angular samplinge~or of the various radiometer measurements, and isused to dete~ine the sensitivity of each scanner designto systematic and/or random ADM errors, and to themagnitude of N, the anisotropic scale factor. 3) COMPUTATION OF SAMPLING ERRORS OVER AN ORBITAL PASS Root-mean-square (~s) e~or r over an orbital pass,is ~ven in terms of regional error E; by r = ~ E~ , (17)818 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 10 TABLE 2. Summary of spatial, angular, and total rms samplingerrors (W m-2) for five prototype instruments. The observed totalerror is compared to a computed total based on the assumption thatthe angular and spatial sampling errors are uncorrelated. Samplingperiod: 1800 UTC 29 January 1984; anisotropic source model: N= 1.3. Spatial Angular Observed ComputedRadiometer sampling~ samplingb totalc totalaSW rms errorsACA ! 4.30 3.05 14.37 14.62CERES-I 9.77 7.34 12.01 12.22CSR 13.09 2.98 13.54 13.42ERBE 9.79 9.48 13.04 13.63Nimbus- 7 26.99 6.87 27.15 27.85LW rms errorsACA 2.89 1.03 3.06 3.07CERES-I 1.80 1.95 2.82 2.65CSR 2.39 1.85 3.00 3.02ERBE 1.88 2.25 3.10 2.93Nimbus-7 5.30 1.77 5.69 6.35 a Obtained from full-FOV isotropic experiments. b Obtained from single-element FOV experiments. - Obtained from full-FOV experiments. a Obtained from the spatial and angular sampling by squaring each,adding, and taking the square root.where M is the number of 2.5- target areas viewed.Expressed in terms of regional spatial and angularsampling components, r becomesr = E~e^z~^L,j + 2EsP^T~^L, jE^NGUL^R,j 2 ~1/2 q- E ANGULAR,j ] . (18)In Table 2, nearly identical estimates of r are derivedin two independent ways that indicate that the covariance term of Eq. (18) is small. In the first, 1800UTC scanner data on 29 January 1984 are taken froma 1300 LST orbiter and analyzed directly using Eq.( 17 ). Results for each instrument are given under thecolumn heading, "Observed total." The second procedure assumes that regional spatial and angular sampling errors are uncorrelated and that r can be expressedin the form 2 ~2 ~/2 (19) r = (rSPATiAL + tANGULAR/ ,where rsp^z~^r and r^NaUL^R are regional spatial andangular rms error components, respectively. Values ofr for this method are given under the column labeled"Computed total" and are based on separate estimatesof/'SPATIAL and/'ANGULAR using "N = 0" and "reducedFOV" experiments. Results of the two methods agreeto within 5% for all designs. Equation (19) is useful because it permits the inference of rms error statistics of a given radiometer andorbit AN equator crossing for many anisotropic conditions using only the results of two experiments: 1 )an isotropic, "N = 0" simulation to determine spatialsampling error; 2) an anisotropic, reduced-FOV experiment to determine angular sampling error. FromEq. ( 13 ), spatial sampling error is independent of Nand, once determined, is valid for all N experiments.Angular sampling error is a function ofNthrough A/~c.Using Eqs. (5) and ( 15 ), Apc is given by A~Oc = (N-- 1)(~Oref- 1) (20)and when substituted into Eq. (16) yields E^NaULARin the form E^~OUL^R -- (N-- 1_~) ~ (Or~,i -- 1)Fret, i (21) l'l i= 1 ~Oref, iEquation (21 ) indicates that regional, as well as rmsangular sampling error over an orbital pass, are proportional to the anisotropy of the source radiationthrough the factor, N- 1. Thus, a relationship betweenrms angular errors for different values of N can be derived and is given by rNGUL^R(N2) _ (N2 -- 1)2 r~ANGULAR(NI) (Nt - 1 )2' (22)Total rms sampling error, derived from Eqs. (19) and(22) for any N2, can be expressed as (N2 - 1 )2 2r(N2) = /'2SPATIAL + (Ni 1)2 /'ANGULAR(NI)/ ' (23)where only the rms angular 'sampling error for one N% 1 experiment (N~) and the radiometer spatial sampling error are required. In addition to systematic perturbations in the ERBEmodels, that is, where a single, fixed value of Nis usedat all M 1 grid elements, random perturbations in anisotropic factor have also been explored at this resolution (Stowe et al. 1991 ). Root-mean-square and biaserror components were nearly the same for the twoexperiments, indicating that the effects of randomvariations in ADM models at the 10-km scale cancelalmost entirely over 2.5- target areas. 4) ESTIMATION OF LIKELY VALUES OF N Although total scanner measurement error is the sumof spatial and angular sampling components, the designof an instrument may be chosen to optimize performance relative to only one of the components. Asshown previously, spatial sampling error is independentof N, and is uniquely determined for each sensor design. Angular sampling error, on the other hand, iscontrolled by the value of N. Because the relative performance and ranking of the five radiometers will depend on the value of N, it is important to estimate areasonable value for it. A reasonable value for N has been derived based oncomparison of instantaneous ERBE SW scanner meaDECEMBER 1993 STOWE ET AL. 819(a)1~535p5155-5-15 -lpo REFERENCE FIELD 21Z 7/17/83'~ r~ v~ ~ ~_j--~-~.~_~c ~ x/'~X o o ~-180 -108 -g7 -85 -73 -88 -50(b)1t53585t55-5-15 -180 SW OIF EBSE 81Z 7/17/83 N=O-~',,'~ (:~,;,-, I U~'~ I~---~-~ ,- F '; 0/', :S ~ 'f:j " , -, , -108 -97 -85 -73 -8~ -50 FIG. 5. (a) Reference field of TOA shortwave flux (contourinterval 60 W m-2 and contours less than 240 W rn 2 dashed),and (b), (c) relative departures in satellite-derived fluxes dueto spatial sampling errors (N = 0) (contour interval 10 W m-2with dashed contours negative). Fields are illustrated for oneorbital pass at 2100 UTC ( 1515 local time) on 17 July 1983for the (b) ERBE and (c) Nimbus-7 instruments.surements of the same 2,5- target region from differentsatellites and simulation results. Root-mean-square differences of 15 W m-2 are reported by Barkstrom et al.(1989) between observations from NOAA-9 and ERBS(including satellite nadir angles up to 40-). If it is assumcd that the observed rms difference, when squared,can be partitioned into equal error contributions fromNOAM-9 and ERBS, the rms error for each ERBE instrument is 10.6 W m-2. In our simulations, errors arepartitioned into spatial and angular sampling components and arc found to be uncorrelated. Thus, therms angular sampling error for the ERBE observationscan be computed given the total and spatial errors.Near nadir, simulated ERBE shortwave spatial erroris on the order of 5 W m-2 (see Fig. 5b). Combiningthis with the experimental total of 10.6 W m2 into Eq.(19) yields an angular modeling error of about 9.4W m-2. Also, ERBE simulation results yield an angularsampling error estimate of approximately 20 W m-2for an N value of 1.69 (See Fig. 6a). Substituting simulated and empirical error estimates into Eq. (22), anestimated reasonable value for N is 1.3 or 0.7. Thissuggests that systematic errors in angular models ofabout +_30% may be expected for 2.5- regions.3. Results of the system simulation study Of the many simulations performed for 6 days inJuly 1983 and January 1984 in Stowe et al. (1991),only results for morning (1500 UTC) and afternoon(2100 UTC) sampling times, and a spacecraft ANequator crossing of 86-W are shown here. Maps oftotal and component regional bias errors and graphsof mean bias and rms errors when computed over thedomain of an orbital pass are given. In July, three anisotropic experiments are analyzed IN values of 0, 0.59( 1 / 1.69), and 1.69] and in January only two (N valuesof 0 and 1.69). The N = 0 experiments (in combinationwith isotropic retrievals) are used to measure spatialsampling error. They also approximate total samplingerrors for N = 1 because systematic errors in the application of ADMs do not occur and random ADMerrors (due to scene variability) tend to cancel. The N= 0.59 and N = 1.69 experiments provide not onlyangular (using reduced-FOV experiments) and totalsampling errors for these choices of N, but also, bymeans of Eqs. (22) and (23), for all other values of N.The value ofN = 1.69 is chosen so that the magnitudeofanisotropic stretching may not be so great as to cause820 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 10(a) (b) SN RBH ERR ERBE 21Z 7/17/8:3 N=1.69 SN RBH ERR N-7 21Z 7/17/83 N=l.69u~5 ~S I" ..... ,:, .... ', ,, I/' , / ~5 _ -120 -108 -97 -85 -73 -62 -50 -180 -108 -97 -85 -73 -62 -50 FIG. 6. Departures in satc]iitc-de~vcd TeA shortwave flux estimates relative to the ~eF~rcncc field For 2100 UTC 17 July 1983 due toangular sampling errors. Error patterns arc given For an N = 1.69 anisotropic pc~u~bation of the ERBE models for the (a) ERBE and (b)~5u~-7 instruments. ~ontour intervals are 10 W m-~ and w~th dashed contours negative.p' in Eq. (5) to become less than zero as this violatesconservation of energy. Setting p' to zero in Eq. (5)and using the minimum bidirectional reflectance factorfound in the ERBE models (0.41 for clear ocean), amaximum N of 1.69 is obtained.a. Spatial sampling errors Figure 5a shows the TOA truth shortwave flux field,and Figs. 5b and 5c illustrate the spatial sampling errors(N = 0) associated with the ERBE and N7 measurements of this field for one day and time in July. TheERBE scan pattern produces a highly regular array ofobservation points within any viewed target area region.The result is efficient spatial sampling, which minimizesredundant overlapping footprints and leads to relativelyuniform weighting of all TOA area elements (cf. Figs.2b and 4). To the contrary, the N7 ERB scanner hasa low data rate and a scanning pattern that is not optimized for spatial sampling but rather for angularsampling. As a consequence, different area elementsof the TOA flux field enter the satellite-derived fluxestimate a nonuniform number of times. More importantly many elements are missed completely (cf.Figs. 2d and 4). As a result, cross-track scanners willgenerally achieve a lower spatial sampling error thanbiaxial scanners.b. Angular sampling errors Figures 6a and 6b illustrate angular sampling errorsfor ERBE and N7 in July with N = 1.69. Negativecontours as large as -45 W m-2 are seen in the ERBEerror map of Fig. 6a near the western coast of SouthAmerica. Here ERBE observations are collected overa highly anisotropic surface (ocean), but in the nearnadir (satellite zenith angle less than 30-) directionwhere P~OA < Pref. This is shown in Fig. 7, a plot ofP-OA (forN = 0.59 and N = 1.69) and Pret (the ERBEmodel) as a function of satellite zenith angle for anocean surface. For N > 1, in regions where the originalERBE model is greater than unity, P-OA > Prer; andwhere it is less than unity, P-OA < Prer- A smaller satellite radiance is measured than would have been obtained with the earth behaving in a manner consistentwith the reference ERBE models. Because the true anisotropic behavior of the atmosphere is not known,however, conversion to flux is carded out using thereference ADMs and a flux underestimate is made [ cf.Eq. (11 )]. The N7 instrument is not as sensitive to SOLAR ZENITH=57, REL. AZIM, UTH=75/2551.75a: 1.5 1.25~O 0.75O O.5Z< 0.2,~ RELATIVE AZIMUTH=255 RELATIVE AZIMUTH=75 9'0 ..... go ..... :/o ..... 6 ..... ~o ..... ~/o ..... 9'0 SATELLITE ZENITH ANGLE (DEGREE)-- N:O (ISOTROPIC) + N=0.59 -- N:I (ERBE) ~ N:1.69 FIG. 7. Bidirectional reflectance models for clear ocean at a solarzenith angle of 57-. Model anisotropic factors p are given as a functionof satellite zenith angle for 255- and 75- relative azimuth directions.Separate curves illustrate the scattering characteristics for isotropic(dotted), and ERBE (solid) models as well as for perturbations tothe ERBE models having anisotropy scale factors of N = 0.59 (solidwith vertical bar) and N = 1.69 (solid with asterisks).DECEMBER 1993 STOWE ET AL. 821(a) (b) $N DIF EF~BE 217 7/17/83 N=1.69 $N DIF NIHBU$-7 21t 7/17/88 N=1o69 ~5 [t5 - -15 -1S -120 -108 -97 -85 -73 -62 -50 -1:~0 -108 -97 -85 -73 -62 -50 F~. 8. Total sampling error (angular plus spatial) in satellite-derived TOA shortwave flux estimates relative to the reference field for2t00 UTC t7 July 1983. Error patterns are for the (a) ERBE and (b) Nimbus-7 instruments for atmospheric reflectance patterns moreanisotropic than the ERBE models (N - 1.69). Contour interval is 10 W m-2 with dashed contours negative.ADM errors as is the ERBE because biaxial scanningpermits cancellation of errors made at different viewingangles (Fig. 6b). Near the limb where target areas areseen from only one viewing direction, however, errorsare still large. It is important to remember in this discussion that, although instrument error characteristicsare highlighted at N = t .69, these error magnitudes arelarger than expected under average atmospheric conditions, where N -~ 1.3 not 1.69.c. Total measurement errors Total regional bias errors for the two scanners (withN -- 1.69) are shown in Figs. 8a and 8b. Readily noticeable in the error contours of both figures is thecharacteristic gradient from negative values near nadirto positive values near the edges of the scan swath.This behavior is due to the systematic variation ofADM error with increasing satellite zenith angle thatis implied by Fig. 7 and is here combined with therather randomly distributed spatial sampling error (seeFigs, 5b and 5c). Away from nadir toward the scanning horizon,ERBE errors are generally positive. This is in keepingwith the normalization condition of Eq. (6) and thegreater-than-isotropic scattering required at large satellite zenith angles to compensate for subisotropicscattering near nadir.d. Six-day ensemble errors Root-mean-square and bias errors in instantaneoussatellite shortwave flux estimates are given in Figs. 9and 10, respectively, for a 6-day ensemble, that is, errorsare computed over observations covering six identicalorbital passes, one for each day in a 6-day sequence.Each day and regional (2.5-) observation is consideredan independent measurement. Because ensemble statistics include the effects of daily variations in cloudproperties and distribution, they provide more appropriate estimates of the rms and bias errors for a givenmonth and orbit trajectory than statistics for any oneday alone. Separate results are given for July and January, and at 1500 and 2100 UTC in each figure. Theerror curves are presented as continuous variations inN, although only three data points in July (N = 0, N= 0.59, and N = 1.69) and two in January (N = 0 andN = 1.69) are derived from simulated data. Intermediate results are obtained using Eq. (23) for rms errorsand linear interpolation between data points for biaserrors. Because spatial sampling error is obtained froma unique simulation experiment in which satellite retrievals are performed using isotropic ADMs, it cannotbe represented by a point on these curves for whichthe data represent ERBE model retrievals. However,results for spatial sampling error (N = 0) yield approximately the same results as N = 1 experimentsand, thus, this data point is plotted at N = 1 (eft Stoweet al. 1991 ). Root-mean-square spatial sampling errors in Fig. 9indicate that shortwave errors are generally larger inJuly than in January. This is because more regions liewithin the Northern than Southern Hemisphere ( 15 -S45-N) of the simulation domain, and greater solar insolation levels occur there during northern summer.The different spatial sampling ability of the five scanners largely determines their total rms errors for valuesof Nin the range 0.9 ~< N~< 1.1. The two instrumentscontaining a cross-track scanner (ERBE and CERES-I)perform best and are the only scanners able to mapthe TOA flux field, in the absence of ADM error, toless than 10 W m-2 rms error (user's requirements fromERBRR-87, 1988). The N7 ERB scanner, with itslower sampling rate, returns the highest spatial sampiing errors.822 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 10(a) (c)6-DAY AVERAGE OF DAILY ERROR SU, 15Z, JA#, SAT EGo CROSSING - 86-WSI4, 21Z~ JAH, SAT EQ. CROSSING o Ac~ + o ~c~ +(b) (d) 6-DAY AVERAGE OF DALLY ERROR 6-DAY AVERAGE OF DAILY ERROR S~, 15Z, JULY, SAT EO. CROSSING = ~"~ $~, Z1Z, JULY~ SAT EO. CROSSI~; = ~o~ I I I I J I O6 O.O 't 1.2 1.4 1.6 A~II~OTI~(]~f SCALE F~CE~E~- I ~ -~q & ERB~ X NI~7 FIG. 9. Six-day ensemble total rms sampling error (W m-2) for TOA shortwave flux estimates as a function of anisotropic scale factorN. Error curves are given for the five ERBI study designs for a satellite equator crossing of 86-W. Separate exhibits are shown for Januaryat 1500 and 2100 UTC [panels (a) and (b), respectively] and July at 1500 and 2100 UTC [panels (c) and (d), respectively]. When systematic departures from the reference anisotropic model radiance fields are introduced, all ofthe instruments perform more poorly. Under theseconditions, the satellite estimates contain errors dueboth to spatial sampling and to bidirectional modeling.While the spatial sampling component is fixed, ADMerror increases with departures of N from unity andthe total rms squared error grows as the sum of thesquares of the two components. The error curves forthe cross-track scanners (ERBE and CERES-I) tend tocross those of the conical scanners (ACA and CSR)near the realistic value of N. This crossover is a consequence of cross-track instruments having greatersensitivity to ADM error as N moves away from 1.The growth of ADM error is largest in the pure crosstrack configuration (ERBE), the hybrid cross-trackCERES-I showing a slightly less rapid growth. Outsideof the range 0.7 ~< N ~< 1.3, the conical scanners overtake the cross-track scanners (in terms of less total errorincurred) due to the partial cancellation of ADM errorat different viewing angles. The biaxial N7 ERB alsodemonstrates a decreased sensitivity to ADM errors,but because of extreme spatial sampling errors, its totalerrors are the greatest. The dependence of shortwave flux bias error on Nfor the five ERBI radiometer designs is shown in Fig.10. Values of spatial sampling error are again plottedat N = 1 on the abscissa and, as N departs from unity,the absolute value of the bias error increases. However,the magnitude of the bias is generally greater for thecross-track (ERBE and CERES) than for the biaxialdesigns. The sign of the bias depends on two factors:1 ) whether N is larger (more anisotropic than the reference model ) or smaller (less anisotropic than the reference model ) than 1.0, and 2) whether it is July (subsolar point well north of the equator) or January (subsolar point well south of the equator). For largedepartures of N from 1, the magnitude of bias errortends to be smaller for biaxial designs (ACA, CSR, andN7) than for cross-track scanner designs, as is the casefor rms error. A bias in radiation budget estimates, particularly ifit varies systematically with latitude, can be a seriousproblem. This would introduce errors in the latitudinalDECEMBER 1993 STOWE ET AL. 823a 6-DAY AVERAGE OF DAILY BIAS SW, 15Z, JAN, SAT EQ. CROSSING = 86W 8-12-16~ CSRo o'.s i ~.5 ANISOTROPY SCALE FACTOR, Ni.c 6-DAY AVERAGE OF DAILY BIAS SW, 15Z, JULY, SAT EQ. CROSSING = 86W 0 Ill',~~ii,ob 6-DAY AVERAGE OF DALLY BIAS SW, 21Z, JAN, SAT EQ. CROSSING = 86W~ERBEANISOTROPY SCALE FACTOR, N~ERSE CERES-I CSR ACA~ NtMBU$-i0.5 - 1.5ANtSOTROPY SCALE FACTOR, Nd 6-DAY AVERAGE OF DAILY BIASSW, 21Z~ JUI. Y~ SAT EQ. CROSSING = 86W~CSR ERBE CEREal0:5 i '~:sANISOTROPY SCALE FACTOR, NFIG. 10. As in Fig. 9, but for bias error (W m-2) in TOA shortwave flux estimates.gradients in ERB, which are a direct measure of themcridional heat imbalance that drives the circulationsof the ocean and atmosphere. To determine whethersuch a gradient in bias error occurs when systematicADM error is present, and to what extent it dependson scanner design, the zonal average bias error of theERBE and CSR instruments is plotted as a functionof latitude in Fig. 11 forN =-1.69 for 6 days in Januaryand July. The cross-track scanner design introduces alatitudinally varying bias, while the biaxial design doesnot (this can also be seen in the ADM error maps, Figs.6a and 6b). The bias error is positive in the summerhemisphere (near the latitude of the sun), and negativein the winter hemisphere. This latitudinal dependence of bias error for crosstrack scanners is caused by the scan plane, which isperpendicular to the orbit, rotating with respect to thesolar principal plane as the satellite orbits. A region onthe earth is viewed from only one combination of solarand satellite zenith, and relative azimuth angles. Typical angular reflectance models exhibit the greatest departure from isotropy in the solar principal plane, andthe least departure for an azimuth angle perpendicularto this plane. Also, in this latter azimuth direction, thesurface is reflecting less energy than an isotropic surfaceover a larger range of satellite zenith angles than occursin the principal plane, as shown in Fig. 12. If the perturbed reflectance of the scene is more anisotropic thanthe mean reference model used to convert radiance toflux (i.e., N > 1 ), then the bias errors will generally bepositive for scans close to the principal plane [ moreobservations with ZXpc > 0 in Eq. (16) ], and negativefor scans away from it (more with Apc < 0). At latitudesnear the solar declination, the scan plane is near theprincipal plane, so the error is positive. As the satellitemoves into the winter hemisphere, the scan plane rotates away from the principal plane, introducing negative errors. The biaxial scanner designs are able to view regionsat multiple azimuth angles within the same latitudezone. This capability causes ADM errors to changesign within the same region, so when averaged, theytend to cancel, and remove the latitudinal bias presentin the cross-track design. This characteristic is a major'824 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 10a 2O~ -~o -20 ~ ZONAL BIAS OF SW FLUX21Z, JAN, SAT EQ. CROSSING=86W, N=1.69-15 (~ 1'5 30 45 LATITUDE (DEGREES) ZONAL BIAS OF SW FLUX21Z, JULY, SAT EQ. CROSSING=86W, N=1.69 CSRb 15 '1-1 -15/ ERBE-is 6 l's ~0 45 LATITUDE (DEGREES) FIG. 11. Latitudinal variation of bias error (W m-2) in TOA shortwave flux estimates for conical (CSR--dashed) and cross-track(ERBE--solid) scanners. Error profiles are given for 2100 UTC in(a) January and (b) July for a satellite equator crossing of 86-W andfor atmospheric reflectance more anisotropic than described by theERBE models (N = 1.69).strength of observations taken by biaxial designs in thepresence of systematic ADM errors.4. Conclusions This study assumes that scanner measurement errorof instantaneous earth radiation budget fluxes at thetop of the atmosphere can be summarized in terms ofonly two fundamental, instrument-dependent characteristics: spatial sampling error and sensitivity to errorin angular dependence models (ADMs). The ideal instrument will minimize both. Cross-track scanners dobest in the absence of ADM error. The two conicalscanner designs (ACA and CSR) yield rms spatialsampling errors somewhat larger than those of thecross-track scanners. The N7 ERB instrument, with itsslower, nonuniform spatial sampling, yields the greatestspatial sampling error. This is expected, however, because the scan design for the N7 scanner was optimizedfor the development of ADMs. As ADM errors areincreased by increasing the departure of the anisotropicscaling factor N from 1, the total rms error increases.The biaxial scanning radiometers (ACA, CSR, and N7 )have been shown to be significantly less sensitive toADM errors than a simple cross-track scanner by providing cancellation of opposing ADM errors made atdifferent viewing angles. Under conditions of largeADM variability, they will yield the least errors in retrieved TOA fluxes. When ADM errors are systematicover large areas of the globe, the latitudinal dependenceof bias error is also important. For cross-track instruments, the viewing-solar illumination geometry is asmoothly varying function of latitude, and relativelylarge gradients in bias error may occur. The biaxialscanners acquire observations from many viewing-solar illumination geometries at all latitudes and, as aresult, gradients in bias error are small. Moreover, themultiangular data obtained by these instruments provide the basis for improvements in ADMs and, thus,a capability of reducing angular sampling errors evenfurther. Our results also show that cross-track scannersare likely to outperform biaxial and conical scanners,providing that anisotropy scale factors lie within therange 0.7-1.3 (error ~ 30%). Even then, shortwavespatial sampling errors are at the limit of user accuracyrequirements ( 10 W m-2). Based on these results, the selection of the optimumscanner design for ERBI involves a compromise between a cross-track scan pattern that uniformly mapsthe earth's surface and uniformly samples the incidentradiances while incurring ADM errors; and a biaxialor conical scan pattern that obtains multiple samplesof a given region at various satellite zenith and relativeazimuth angles to minimize the ADM errors, while SW ANISOTROPY Clear-Sky Ocean 3i 2/ Solar Zenith = 40 Specular Reflectance Peako ~" 180 0 ~'~ 1/ '~.~ ~ ~ ~'~ ~ ~o - ~ ~o~0 ~ , , , , , , , , ~ , , ~ , , , ~ ~ , , , , , , , , , ~ , ~ , , , , , , ~ 90 60 30 0 30 60 90 Satellite Zenith Angle -- 180/0 -- 270/90 FIG. 12. Bidirectional reflectance factor -or clear ocean in tworelative azimuth planes: side scattering at 900/270- (dashed); andforward and backscattering at 0-/]80- (solid). The solar zenith an~leis 40-.DECEMBER 1993 S T O W Eincurring larger spatial sampling errors. Because theCERES instrument is composed of a simple cross-trackscanner and a second component in a rotating azimuthplane, it contains both of these elements. Its rms errorsare reduced below those of ERBE and the biaxial scanners for N < 1.3, but they grow with increasing N at afaster rate than errors for the ACA or CSR. For valuesof N > 1.3, the CERES continues to perform betterthan ERBE, but being a compromise design, it mayno longer be the minimum-error design. However, future improvements in ADMs, a database capabilityprovided by CERES, may further reduce uncertaintiesdue to ADM variability. Identical studies of instantaneous error have beencompleted for many days, two seasons, and several satellite equator-crossing longitudes (Stowe et al. 1991 ).These results are all consistent with the above conclusions. Also, the longwave flux errors have been foundto have the same space and time characteristics as theshortwave flux errors, but are only about 25% as large. Therefore, based on this error analysis, it is concluded that the CERES instrument concept is the bestdesign for continuing earth radiation budget measurements into the future. Acknowledgrnents. The authors wish to acknowledgethe support of several others who contributed to thisinvestigation. Richard Frey was of great help in thenavigation and quality control of the ISCCP B 1 GOESradiances. Peter Cheng was invaluable in the coding,debugging, and submission of the many simulationruns required. Robert Ryan, NOAA NESDIS, assistedwith preparation of the figures. Brenda Vallette typedand edited the many versions of this manuscript. Thesupport of Research and Data Systems was funded undcr NOAA Contract 50-DDNF~6-00217. APPENDIX Relative Effect of GOES Calibration Error The CERES4, composed of a cross-track planescanner (CTPS) and a second radiometer in a scanplane rotating at 5- s-1, contains elements of both asimple cross-track and biaxial scanning design. Whenonly the CTPS operates, CERES is a prototype crosstrack instrument with relatively small spatial samplingerrors and a heightened sensitivity to ADM errors. Inbiaxial mode, sensitivity to ADM errors is reduced,but at the cost of increased spatial errors. In phase IIstudies of the CERES-I scan design, observations wereprocessed separately in CTPS-only and biaxial modes,both before [Eq. (3)] and after [Eq. (2)] recalibrationof GOES counts. Although obtained for a scan designsomewhat different than used in the current study, thesedata can be analyzed to determine the dependence ofcalibration error on scan type. Based on the outcome,the relative effect of calibration error on the instrumentaccuracies of Phase I is inferred.ET AL. 825 TABLE A 1. Spatial, angular, and total CERES sampling errors before and after correction of GOES calibration error.rms error (W m-2) Before After ErrorError component recalibration recalibration ratioCross-track scanner only(CTPS mode)Spatial 7.7 8.5 1.10Angular 8.8 10.7 1.22Total 11.7 13.7 1.17Both scanners (biaxialmode)Spatial 12.6 13.8 1.10Angular 7.2 8.9 1.24Total 14.5 16.4 1.13 Table A 1 provides root-mean-square spatial, angular, and total sampling error components for instantaneous SW flux derived from CERES-I, separately in"CTPS-only" and "biaxial" scanning modes. Ensembleerrors for six identical, 1330 LST ascending node orbitsin January (based on 1800 UTC image data for calendar days 25, 26, 27, 28, 29, 30) are given for anenhanced anisotropic atmosphere ofN = 1.3 (section2a.3). 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