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8/3/2019 Radiometric Calibration of GOE S - 7

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R a d i o m e t r ic C a l ib r a tio n o f G O E S - 7 V I S S RS o l a r C h a n n e l s d u r i n g t h e G O E S P a t h f i n d e rB e n c h m a r k P e r i o dR ob ert J. Frouin* an d James J . Sim pson*

T e G O E S-7 VISSR so l ar c hannel s a re rad i om e tr i ca l lyc a l ib ra t ed f o r t he pe r iod f rom J une 1987 t hrough Nov e m -ber 19 88. Space , Whi te Sands , and the Sonora Deser t areuse d as calibration targets. T hree differe nt calibrationswer e performed: 1) using the stretched data (i .e . , retrans-mi t ted data operat ional ly des t r iped us ing NOAA's nor-mal i zat ion procedure) and cons ider ing indiv idual VISSRdetectors separately; 2) using the stretched da ta averagedover the eight VISSR detectors; and 3) using the stretcheddata fur the r d es t r iped according to S impson e t a l. (1995)and th en averaged o ver the eight VIS SR detectors. Thethird approach provides the best results (i .e . , best equal-ization o f the detectors). Because o f uncertain t ies in themod eling of the V ISSR radiance, usin g separate calibra-t ion coeff ic ients for each detector (f irst approach) maynot redu ce the striping signif icantly . The calibration co-ef fic ients exhibit low freq ue ncy changes th at are no t corre-lated with seasonal variat ions in the extraterrestrial solarirradiance. High freq ue ncy f luctu atio ns are large, andt he y are due i n par t t o NO AA ' s norm al iza t ion proc edurean d to calibration un certainties. Differences betw een thecalibration coeffic ients o f individu al d etectors also arelarge, as well as changes between consecutive VISSRacquisi tion t imes. Com parison o f unta mp ered (retransmit-t e d da t a bu t n o t operationally destrip ed using NO AA 'snormal i zat ion procedure) "Wednesday" 1848 GM T datawi th s t re tched 1831 and 1901 G M T data indicates thatNOAA's normalization procedure, though imperfect , re-duces subs tant ia l ly the s t r ipes present in the uns tre tched

*California Space Institute, S cripps Institution of Oc eanography,University of California, San Diego, La Jolla*Digital Image Analysis Laboratory, Scripps Institution of Ocean-ography, University of California, San D iego, La JollaAddress correspondence to Ja mes J. S impson, Scripps Inst. ofOceanography, Digital Image Analysis Lab ., UCSD , La Jolla, CA92093-0237.Received 3 Augu st 1994; revised 30 January 1995.REM OTE SENS. ENVIRON. 52:95-115 (1995)Elsevier Science Inc,, 1995655 Ave nue of the A mericas, New York, NY 10010

data. There is evidence, however, th at NO AA 's normaliza-tion procedure introduced artificial variations in the countsquared o f the targets th at in one ins tance resul ted in 30%low er calibration coefficients. Th e average calibrationcoeff icients are generally higher by 1 5% than the valuesof Rossow e t a l. (1992); they are in be t ter agreement w i ththe values o f Ab el e t al. (1992) an d Wh it lock et al . (1994).I t i s recomm ended that th e radiometr ic calibrat ion of theVISSR solar channe ls should be per formed as f reque nt lyas possible (every day). Though the stripes in the VISS Rdata t ransmi t ted to Wal lops Is land should be reducedfo r operational, real-t ime purposes (e .g. , we ath er analysisand forecas t) , the or iginal unno rmal i zed data should bearchived fo r sub sequen t use in quanti tat ive, scientif icapplications.

I N T R O D U C T I O NV i s i b l e a n d i n f r a r e d d a t a f r o m t h e V i s i b l e I n f r a r e d S p i nS c a n R a d i o m e t e r ( V I S S R ) a b o a r d t h e G e o s t a t i o n a r y E a r t hO b s e r v i n g S a t e l l i t e s ( G O E S ) m e t e o r o l o g i c a l s a t e l l i t e sh a v e b e e n u s e d i n c r e a s i n g l y i n q u a n t i t a t i v e , e n v i r o n -m e n t a l a p p l i c a t i o n s ( e . g . , r a d i a t i o n b u d g e t m a p p i n g , c l o u dv a r i a b i l i t y a n a l y s e s , a n d s u r f a c e a l b e d o s t u d i e s ). F o rt h e s e a n d o t h e r a p p l i c a t i o n s , a c c u r a t e r a d i o m e t r i c c a l i -b r a t i o n o f t h e s e n s o r s i s e s s e n t i a l. A 1 - 5 % a b s o l u t ea c c u r a c y i s d e si r a b l e d e p e n d i n g o n t h e t y p e o f a p p l ic a -t i o n ( S l a t e r e t a l . , 1 9 8 7 ) . F o r i n s t a n c e , a 1 0 % l o s s i ns e n s i t iv i t y o f t h e V I S S R s o l a r s e n s o r s m a y t r a n s l a t e i n t oa 1 5 W m - 2 ( 7 % ) u n d e r e s t i m a t i o n o f t h e m o n t h l y n e ts u r f a c e s o l a r i r r a d i a n c e i n e q u a t o r i a l r e g i o n s ( G a u t i e ra n d F r o u i n , 1 9 9 2) . T h i s i s j u s t s u f f i c i e n t fo r c h a r a c t e r i z a -t i o n o f i n t e r a n n u a l v a r i a b i l i t y a s s o c i a t e d w i t h l a r g e - s c a l ep h e n o m e n a s u c h a s E 1 N i f io / S o u t h e r n O s c i l l a t i o n e v e n t s .T h e s a m e l o s s i n s e n s i t iv i t y t y p i c a l l y w o u l d i n c r e a s el a n d s u r f a c e r e f l e c t a n c e e s t i m a t e s b y 0 . 0 4, a f ig u r e t h a t

0034-4257 / 95 ! $9.50SSD I 0034-4257(95)00037-2


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b a re l y mee t s t h e ab s o l u t e e r ro r t o l e r an ce o f + 0 . 01 t o0 . 0 5 s u g g es t ed b y H en d e r s o n -Se l l e r s an d W i l s o n (1 9 8 3 )fo r u s e i n c l i ma t e mo d e l s .Ca re fu l p r e f l i g h t l ab o ra t o ry ca l i b r a ti o n o f t h e V ISSRs o l a r s en s o r s w as p e r fo rmed b y t h e San t a Ba rb a ra Re -s ea r ch Cen t e r ( 1 9 8 0 ) u s i n g s t an d a rd ca l i b r a t i o n l amp s .T ran s f e r f u n c t i o n s w e re e s t ab l i s h ed t o ca l cu l a t e s a t e l -l i te - l ev e l rad i an ces f ro m t e l em e t e r e d d i g it a l s en s o r s ig -n a l s . T h es e fu n c t i o n s , h o w ev e r , may n o t b e v a l i d fo rthe da ta acqu i red in o rb i t . Severa l ca l ib ra t ion s tud ies ,f o r ex amp l e , h av e s h o w n h i g h f r eq u en cy v a r i ab i l i t y i ns en s o r s en s i t i v i t y (F ra s e r an d K au fman , 1 9 8 6 ; F ro u i nand Gaut ier , 1987; Par i s and Jus tus , 1988; Whi t lock e ta l. , 1988 ; Ga ut ier a nd F rou in , 1992; Ros sow e t a l. ,1992 ; Whi t lock e t a l . , 1994) . The var ia t ions in sensors en s it iv i ty , a s r ep o r t ed b y t h e a fo r em en t i o n e d i n v es ti g a -t o r s , a r e co mp l ex an d n o t w e l l u n d e r s t o o d . Su p e r i m-p o s ed o n t h e s e h i g h f r eq u en cy f l u c t u a t i o n s , s o me t i mesb u t n o t a l w ay s a t t h e l imi t o f t h e u n ce r t a i n t y l ev e l , a r el o w f r eq u en cy ch an g es . So me p e r i o d i c i t y ch a rac t e r i ze st h e s e l o w f r e q u e n c y c h a n ge s , b u t t h e m i n im a a n d m a x -i ma d o n o t o ccu r a t t h e s ame t i me f ro m o n e y ea r t o t h en ex t . Fu r t h e rmo re , t h e r e i s s u b s t an t i a l d i s ag reemen tb e t w e en t h e r e s u l t s o f t h e v a r io u s s t u d i es , i n p a r t icu l a rb e t w een t h e In t e rn a t i o n a l Sa t e l l i t e C l o u d C l i ma t o l o g ypro jec t ( ISCCP) re la t ive f i t (Rossow e t a l . , 1992) andt h e L an g l ey Res ea rch Cen t e r v a l u e s (W h i t l o ck e t a l . ,1994). This lat ter resul t , however, is consis tent with thato f K l e i n an d H ar t m an (1 9 93 ) , w h o fo u n d t h a t ISCC Pd er i v ed o p t i ca l t h i ck n es s e s w e re an o ma l o u s l y h i g h ( s eea l so Whi t lock e t a l . , 1994) .GOES i s a sp inn ing sa te l l i t e ; i t observes the Ear thd u r i n g 5 % o f each s p i n, an d s p ace fo r 9 5 % . U n s t r e t ch eddata are t ransmi t t ed to Ear th in rea l t ime (e .g . , in a da tab u r s t t h a t o ccu p i e s o n l y 5 % o f t h e t i me fo r a s in g l es p i n o f t h e s a t e l li te ) . S t r e t ch ed d a t a h av e b een r e fo rma t -t ed o n t h e g ro u n d t o o cc u p y 1 0 0 % o f t h e t i me fo r s in g l es p i n , d e s t r i p ed , an d r e t r an s mi t t ed t o t h e s p acec ra f t f o rt ransmiss ion to users .The VISSR, un l ike o the r sa te l li t e ins t ruments such asthe Advanced Very High Resolut ion Radiometer (AVHRR),h as e i g h t ad j acen t d e t ec t o r s p l aced a l o n g a n o r t h - s o u t hl ine (e .g ., Clark , 1983) . Eac h de tec to r senses an approx i -ma t e 0 . 8 0 . 8 k m 2 a r ea o n t h e E a r t h a t n adi r. A mech an -i ca l l y - s t ep p ed mi r ro r p ro v i d es n o r t h t o s o u t h v i ew i n gw h i l e t h e ro t a t i o n o f t h e G O E S s a t e ll i te p ro v i d es w es tto eas t scann ing . The e igh t de tec to rs have a s imi lars p ec t r a l r e s p o n s e , b u t t h e i mag es ap p ea r s t r i p ed , t h a ti s , t h e r e a r e ab ru p t d i s co n t i n u i t i e s i n t h e v a l u es o fr a d i an c e m e a s u r e d b y a d j a c e n t d e t e c t o rs a n d t h e p a t-t e rn r ep ea t s i t s e lf ev e ry e i g h t l in e s . T h e u n s t r e t ch eds a t e l l i t e d a t a a r e r e c e i v e d a t t h e N E S D I S C o m m a n dand Data Acquis i t ion Faci l i ty (CDA) s ta t ion a t Wal lopsI s l an d w h e re t h ey a r e p ro ces s ed ( r e fo rma t t ed , b r i g h t -n e s s - en h an ced , an n o t a t ed , s t r e t ch ed , e t c . ) b e fo r e b e i n gt r an s mi t t ed b ack t o a t r an s p o n d e r o n t h e G O E S s a t e ll i te

fo r b roadcas t to user s t a t ions . A par t i cu lar aspect o ft h is p ro ces s i n g i s t h e n o rma l i za t io n o f t h e d a t a t o o n ed e t ec t o r t o r ed u c e s t r i p e s i n th e i mag es . T h e n o rma l i za -t io n p ro c ed u re i s n o t f ul ly d o cu me n t ed , mak i n g i t imp o s -s i b le t o r eco n s t ru c t t h e r aw d a t a s e t r e ce i v ed a t W a l l o p sI s l an d f ro m t h e p ro ces s ed d a t a s e t a r ch i v ed a t t h e u s e rs t at io n s . D e s p i t e t h e ex i s t en ce o f e i g h t d e t ec t o r s an dt h e i mp e r f ec t n o rma l i za t i o n p ro ced u re , t h e ca l i b r a t i o ns t u d i e s d i s cu s s ed ab o v e h av e i g n o red t h e i n d i v i d u a l i t yo f each d e t ec t o r a s ev i d en c ed b y s t r i p e s in t h e d a ta .Average ca l ib ra t ion coef f i c ien t s in these s tud ies haveb een co mp u t ed fo r a l l t h e d e t ec t o r s , ev en t h o u g h t h ed e t ec t o r s h av e n o t b een eq u a l i zed b e fo re t h e ap p li ca t io no f ca l i b r a ti o n p ro ced u re s . T h i s m ay ex p l a in p a r t o f t h ed i s ag reemen t amo n g t h e v a r i o u s s t u d i e s .Fo r a qu an t i t a t ive u t i l iza t ion o f VISSR v i s ib le da ta ,i t i s important to assess previous cal ibrat ion work, under-s t an d w h e t h e r o b s e rv ed ca l i b r a t i o n ch an g es a r e l i n k edto ins t rument behav ior o r have o ther o r ig ins (e .g . , nor -ma l i za t i o n p ro ced u re , d i f f e r en ce amo n g d e t ec t o r s ) , an ddev i se a s t ra tegy fo r opera t ional rad iomet r i c ca l ib ra t ionof VISS R v i s ib le ima gery . T h i s ac t iv i ty is key to bu i ld ingGO ES P athf inde r da ta se t s which a re sc ien t i f ica l ly va li -da ted , ca ta logued , and read i ly avai l ab le dur ing the p re-E a r t h O b s e rv i n g Sy s t em (E O S) e r a . T h e ma i n g o a l o ft h e Pa t h f i n d e r P ro g ram i s mak e r e s ea r ch -q u a l i t y g l o b a lchange da ta se t s more eas i ly avai l ab le to the sc iencean d en v i ro n men t a l co mmu n i t i e s i n r e s ea r ch an d a s s e s s -men t s .In th i s a r t i c l e , we develop and t es t opera t ionala lgor i thms fo r the in - fl igh t ca l ib ra t ion o f the VISS Rv i s i b l e s en s o r . T h o u g h o u r l o n g - t e rm o b j ec t i v e i s t h ep ro d u c t i o n o f ab s o l u t e ca l i b r a ti o n co e f f ic i en ts f o r t h een t i r e N a t i o n a l O cean i c an d A t mo s p h e r i c A d mi n i s t r a -t ion (NOA A) arch ive o f the G OE S-se r ies sa te l l it es , ( fromFeb ru a ry 1 9 7 8 u n t il t h e f a i l u r e o f G O E S -7 ) , w e fo cu so n t h e P a t h f in d e r b e n c h m a r k p e r i o d o f M a r c h 1 9 8 7t h ro u g h N o v emb er 1 9 8 8 . A f t e r p r e s en t i n g t h e g en e ra lca l i br a t io n me t h o d o l o g y (n ex t sec t io n ) , w e d e s c r i b e t h er ad i a t i v e t r an s f e r mo d e l , t h e r e f e r en ce t a rg e t s , an d t h esa te l l it e da ta se t ( th i rd , four th , an d f i f th sec t ions , respec-t iv e ly ) . T h e n w e d e t a i l t h e d e s t r i p i n g an d c l o u d s c r een -ing o f the sa te l li t e image s ( s ix th and seve n th sec t ions ) ,an d w e d es c r i b e t h e co mp u t a t i o n a l p ro ced u re s ( e i g h t hs ec ti o n ). N ex t w e p r e s e n t t i me s e r ie s o f c a li b r a ti o nco e f f i c i en t s o b t a i n ed 1 ) b y co n s i d e r i n g s ep a ra t e l y t h eb r i g h t n es s co u n t o f i n d i v id u a l d e t ec t o r s u s i n g s t r e t ch edd a t a, 2 ) b y av e rag i n g t h e b r i g h t n es s co u n t s o f t h e e i g h td e t ec t o r s ag a in u s i n g s t r e t ch e d d a t a , an d 3 ) b y av e rag i n gt h e b r i g h t n es s co u n t s o f th e e i g h t d e t ec t o r s a f t e r f u r th e rdes t r ip in g ( i .e ., S im pson e t a l ., 1995) o f the s t re tch edd a t a (n i n t h s ec t i o n ) . W e p ro ceed w i t h a d i s cu s s i o n o fd i f feren ces am ong de tec to rs , an analys i s o f average ca l i-b r a t i o n co e f f i c i en t ch an g es o v e r t i me , an a s s e s s men to f ca l i b ra t i o n u n ce r t a i n t i e s , an d a co mp ar i s o n o f o u rca l ib ra t ion coef f i c ien t s wi th tho se o f o the r s tud ies ( t en th


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s ec t i o n ) . W e co n c l u d e w i t h a s t r a t eg y t o ma i n t a i n aper io d ic in - f l igh t chec k-of -ca l ib ra t ion o f the VIS SR v is i-b l e s en s o r ( e l ev en t h s ec t i o n ) .

M E T H O D SA p p ro a chFo r in - fl ight ca l ib ra t ion o f i t s so lar channel s , the VIS SRco n t a i n s an o p t ica l s u b as s e mb l y w i t h r ed u ced s ize ap e r -t u r e fo r d i r ec t l y v i ew i n g t h e s u n . T h i s o p t ica l s u b as s em-b l y , u n fo r t u n a t e l y , i s n o t b e i n g u s ed b eca u s e o f u n ce r -t a in t i es in the cha rac ter i s t i cs o f i t s op t i ca l e l emen ts .T h e re fo r e , o n e h a s t o r e l y o n i n d i r ec t me t h o d s t o ca l i -b r a t e t h e s o l a r ch an n e l s o f t h e o rb i t i n g i n s t ru men t .A v a r i e ty o f i n d i r ec t c a l i b r a t io n me t h o d s can b eap p l i ed t o t h e V ISSR s o l ar ch an n e l s ( s ee t h e r ev i ew s o fCh e an d P r i ce , 1 9 9 2 ; T e i ll e t an d H o l b en , 1 9 9 4 ; Mi t ch e l l,1 9 9 4 ) . O n e c a n u s e c o n c o m i t a n t m e a s u r e m e n t s t a k e nby a su i t ab ly equ ipped h igh-f ly ing a i rcraf t (e .g . , Smi thand Vonder Haar , 1980; Smi th e t a l . , 1988 ; Abel e t a l . ,1988 ; 1992) , o r by a ca l ib ra ted sa te l l i t e ins t rumentwi th s imi lar spec t ra l charac ter i s t i cs (e .g . , Smi th andLoran ger , 1977; Rosso w e t a l. , 1992). One can a l soanalyze s t a t i s t ica l ly the t em pora l var ia t ions o f the top-of -a t mo s p h e re s ig n a l o v e r in v a r i an t ta rg e t s s u ch a s d e s e r t s(S t ay l o r , 1 9 9 0 ; K au fman an d H o l b en , 1 9 9 3 ; Bre s t an dRo s s o w , 1 9 9 2 ; Rao an d Ch en , 1 9 9 3 ; W u an d Z h o n g ,1 9 9 4 ) , o r s i mu l a t e t h e u p w e l l i n g r ad i an ce r each i n g t h es a t e l l i t e w h en v i ew i n g s e l ec t ed t a rg e t s a t t h e s u r f ace(K o ep k e , 1 9 8 2 ; F r a s e r an d K au fman , 1 9 8 6 ; F ro u i n an dGautier , 1987; Slater et al . , 1987; Tei l let et al . , 1990;Vermote e t a l . , 1992 ; Mi tchel l e t a l . , 1992 ; Kaufmanan d H o l b en , 1 9 9 3 ) . T h e r e f e r e n ce t a rg e t s a l so ma y b el o ca t ed i n t h e a t mo s p h e re , f o r i n s t an ce c l o u d s (Mu en ch ,1981; Par i s and Jus tus , 1988; San ter e t a l . , 1991) . Them e t h o d s b a s e d o n c o n g r u e n t a i r c r a f t /s a t e l li t e o b s e rv a -t ions o r s t a t i st i ca l ana lys i s o f s t ab le s i t es p rov ide re la t iveca l i b r a t i o n co e f f i c i en t s . T h ey may n o t r eq u i r e accu ra t ek n o w l ed g e o f t h e ch a rac t e r i s t i c s o f e i th e r t a rg e t o r a t mo -s p h e re . Cro s s - ca l i b r a t i n g t w o s en s o r s , f o r ex amp l e , r e -q u i r e s k n o w l e d g e o f t h e s p e c t r a l d e p e n d e n c e o f t h etarge t , no t i t s ac tua l re f l ec tance . Abso lu te ca l ib ra t ionco e f f i c ien t s a r e d ed u c ed f ro m t h o s e o f t h e s en s o r o fr e f e r en ce ( c ro s s -b an d ca l i b r a t i o n ) o r t h o s e k n o w n o rd e t e r m i n e d i n d e p e n d e n t l y a t a p o in t i n t im e ( in t e rt e m -p o ra l c a l i b r a t i o n ) . Me t h o d s b a s ed o n s i mu l a t i n g t h erad iance a t sa te l l i t e a l t i tude , on the con t rary , p rov ideab s o l u t e ca l i b ra t i o n co e f f i c ien t s d i r ec tl y . A ccu ra t e ch a r -ac t e r i za ti o n o f t h e s u r f ace an d o v e r l y i n g a t m o s p h e re i scr i t i ca l in th i s case , making the resu l t s very sens i t ive tou n ce r t a i n t i e s i n s u r f ace r e f l ec t an ce an d ae ro s o l o p t i ca lp ro p e r t i e s .Fo r ca l i b r a t i n g t h e V ISSR s o l a r ch an n e l s o n ano p e ra t i o n a l , r o u t i n e b a s is , o u r ap p ro ach i s t o u s e s u i t ab l er e f e r en ce t a rg e t s a t t h e s u r f ace , n ame l y , t h e W h i t e

S a n d s M o n u m e n t a r e a i n N e w M e x i c o ( h e r e a f t e r r e -f e r r ed t o a s W h i t e San d s ) an d t h e So n o ra D es e r t i nMexico . The t a rge t s i t es a re fa i r ly s t ab le (p roper t i esinvar ian t wi th t ime) ; they have ref l ec tance charac ter i s -t i c s t h a t h av e b een meas u red an d r ep o r t ed i n t h e l i t e r a -t u r e , an d t h ey a r e l o ca t ed i n r eg i o n s w h e re a t mo s p h e r i ccondi t ions are favorab le (e .g . , c l ear sk ies , low aeroso lload ings ). Th e s t ab i l i ty o f the ca l ib ra t ion s i t es and th ek n o w l ed g e o f t h e i r r e f l ec t an ce p ro p e r t i e s ma k es i t p o s si -b l e t o p e r fo rm b o t h r e l a t i v e an d ab s o l u t e ca l i b r a t i o n s ,b u t w e l i mi t o u r s t u d y t o ab s o l u t e ca l i b r a t i o n . O t h e rt a rg e ts co u l d h av e b ee n s e l ec t ed , in p a r t icu l a r t h e o ceans u r f ace a t h ig h v i ew i n g zen i t h an g l e s [me t h o d o f V e r -mote e t a l . (1992)] o r h igh ly ref l ec t ive c louds [e .g . ,m eth od of San te r e t a l. (1991)] , bu t the i r loca t ion mayv a ry w i t h t i me , m ak i n g t h e s e l ec t i o n an d an a l y si s o fuseful images more diff icul t . Similarly, cross-cal ibrat ingt h e V ISSR so la r ch an n e ls a n d A d v an c ed V ery H i g h Res o -l u t i o n Rad i o me t e r (A V H RR) Ch an n e l 1 i s ap p ro p r i a t e ,a l l t h e mo re s o a s ex t en s i v e w o rk h as b een d o n e o n t h erad io me t r i c ca l ib ra t ion o f th i s channe l (e .g ., Tei l l e t e ta l. , 1990 ; Tei l l e t and H olbe n , 1994) . Managing da ta f romd i f f e r en t s en s o r s , n o t o p e ra t ed b y t h e s ame o rg an i za ti o n ,h o w ev e r , co mp l i ca t e s an o p e ra t i o n a l p ro ced u re . T h ech o s en s t r a t eg y r e f l ec ts o u r o b j ec t i v e o f d e fi n i n g ano p e ra t i o n a l , au t o ma t ed ca l i b r a t i o n s ch eme t h a t , f o rprac t i ca l purposes , u t i l i zes VISSR data on ly . Th i s doesn o t ex c l u d e ap p l y i n g o t h e r ca l i b r a t io n m e t h o d s o r u s i n go t h e r t a rg e t s i t e s . O n t h e co n t r a ry , i n d ep en d en t r e s u l t sa r e n eces s a ry t o en s u re t h e q u a l i ty o f t h e o p e ra t i o n a lca l ib ra t ion ( i . e . , to c ross -check resu l t s and to p rov ideuncer ta in ty l evel s ) .Formal i smIn V ISSR s o l a r b an d i , t h e d e t ec t o r meas u re s t h e av e r -ag e r ad i an ce / ~ i (W m -2 s r - 1 /~m-1 ) :

f ~, = I o R ~ ' L ~ d 2 , (1 )I o R , e xw h ere ~ i s th e w av e l en g t h an d Ra i i s t h e s p ec t r a l r e -s p o n s e o f t h e i t h d e t ec t o r . T h e d e t e c t ed an a l o g si g na li s d i g i t i z ed an d ex p re s s ed i n n u mer i ca l co u n t s C N ~ ,w h i ch a r e r e l a t ed t o L i b y

L = a, CN~ + b,. (2)a~ is an in ver se ra dio m etric gain fa ctor a nd b~ is arad iomet r i c o f fse t fo r the i th de tec to r . Beca use the rad i-om eter v iew s space dur ing each sp in , a m easure o f b~ i sfeasible ( the radiance of space is nul l ) , which leads to

L , = a , ( C N ~ - CN~0,), (3)w h e r e C N o ~ i s the space count . Cal ib ra t ing the ins t ru -men t f o r b an d i , t h e r e fo r e , i s r ed u ced t o d e t e rmi n i n ga~, exp resse d in W m -z s r -1 /~ m /cou nt2 ; b~ i s g iven by


4/21

98 F r o u i n a n d S i m p s o n

b , = - a , c ~ , . ( 4 )T o e l i m i n a t e t h e v a r i a t i o n s d u e t o s o l a r i r r a d i a n c e ,

i t i s c o m m o n t o c o n v e r t / ~ i n t o r e f l e c t a n c e . T h e m o n o -c h r o m a t i c r e f l e c t a n c e p~ is d e f i n e d a s

P ~ = n L ~ ( r / r )e , (5 )w h e r e r 0 / r is t h e r at io o f m e a n t o a ct u a l e a r t h - s u nd i s t a n c e , / ~ i s t h e c o s i n e o f t h e s u n z e n i t h a n g l e , a n dE s a i s t h e s p e c t r a l e x t r a t e r r e s t i a l s o l a r i r r a d i a n c e . T h ee q u i v a l e n t r e f l e c t a n c e i n b a n d i i s e x p r e s s e d a s

/ ) /= r t ( r / r 0 ) ~ /~ i~ s L , ( 6 )

W o r k i n g w i th /i ~ , o n e h a s t o c o r r e c t t h e C N ~ f o r v a r i a t i o n si n i n c i d e n t s o l a r i r r a d i a n c e d u e t o b o t h s u n a n g l e a n de a r t h - s u n d i s t a n c e . T h e c o r r e c t e d c o u n t s a r e d e f in e d b y

C N ~ * = ( C N ~ - C N ~ o , ) ( r / r o ) ~ (7 )W i t h t h is d e f i n i t io n , t h e r e l a t io n b e t w e e n ~ a n d C N~ ~b e c o m e s

~, = a , c ~ * ( 8 )w i t h

aiT~a , = - - : - . ( 9 )T h e a d v a n t a g e o f u s i n g r e f l e c t a n c e s i n s t e a d o f r a d i-

a n c e s i s t h a t t h e c a l i b r a t i o n d o e s n o t d e p e n d o n t h es o l a r i r r a d i a n c e i n t e g r a t e d o v e r t h e s p e c t r a l b a n d . T h i sf a c i l i t a t e s c o m p a r i s o n s a m o n g t h e v a r i o u s V I S S R s . Ad r a w b a c k i s t h a t t h e e f f e c t o f i n s t r u m e n t n o i s e is a m p l i-f i e d a t l a r g e s o l a r z e n i t h a n g l e s ( / ~ c l o s e t o 0 ) . S u c hc o n d i t i o n s , f o r t u n a t e l y , a r e n o t f a v o r a b l e f o r p e r f o r m i n gr a d i o m e t r i c c a l i b r a t i o n . I t w i l l b e e a s y , h o w e v e r , t od e d u c e r a d i a n c e c a l i b r a t i o n c o e f f ic i e n t s f r o m r e f l e c -t a n c e c a l i b r a t i o n c o e f f i c i e n t s [ E q . ( 9 ) ] .

R A D I A T I V E T R A N S F E R M O D E LT h e a v e r a g e r a d i a n c e m e a s u r e d b y th e s p a c e - b o r n es y s t e m i n a n y s p e c t r a l b a n d i s m o d e l e d a s

f - , (I , t ~ , ~ , , ~ o ) , .~ I : - R , ~ L , ~ ( l ~ s , / t t ,, ~ o ) d 2 , (10)w h e r e R z i s t h e a v e r a g e s p e c t r a l r e s p o n s e o f t h e d e t e c -t o r s ( n o r m a l i z e d ) . R a a s a f u n c t i o n o f w a v e l e n g t h i s g i v e nb y R o s s o w e t a l . ( 1 9 9 2 ) , a n d T a b l e 1 s u m m a r i z e s t h ec h a r a c t e r i s t i c s o f t h e V I S S R s o l a r b a n d s .

I n o r d e r t o s i m u l a t e L z , w e u s e t h e r a d i a t i v e t r a n s f e rm o d e l o f T a n r 6 e t a l. ( 19 7 9 ) . T h i s m o d e l e x p r e s s e s t h es igna l r ece iv ed a t sa t e l l i t e a l t i tude a s a func t ion o f success -i v e o r d e r s o f r a d i at i o n i n t e ra c t io n s i n t h e c o u p l e d g r o u n d -a t m o s p h e r e s y s t e m . A s s u m i n g t h a t t h e s u r f a c e r e f l e c -t a n c e is s p a t ia l l y h o m o g e n o u s , L~ c a n b e w r i t t e n a s

T a b l e 1 . Charac t e r i st i c s o f t he GO ES-7 V ISSR So la rChanne l s ~P a r a m e t e r V a l u e

gm 0.623f :R a E , ~ d 2 (W m-Z) 336.0

t[Ra d~ (/~m) 0.205R~ = spectral resp onse; 2 = equivalent wavelength, where

[ :R ~ E ~ ~ d 22 ~ f :R ~ E ~ d ~

7t+ p ~ , ( ~ , ~ , ~ ) e x p ( - r , / ~ ) e x p ( - r , / ~ )+ ~ , ( ~ , ~ , ~ ) e x p( - r , / ~ ) t ~ ( ~ )+ ~ , ( ~ , # o , ~ ) [ t o , ( ~ ) + e x p ( - r , / ~ ) ] t a ~ ( ~ , )+ ~a(Zt,,/~,(a)S~,[to~(/~,,)+ ex p( - ra //~o)]x [t~(/~,) + ex p( - r~//~ ) / [1 - ~ a(/~,,/~,~)S~] },

(11)w h e r e r~ i s t h e o p t i c al t h i c k n e s s o f t h e a t m o s p h e r e , ta ai s t h e d i f f u s e a t m o s p h e r i c t r a n s m i t t a n c e ( e x c l u d i n g t h ed i r e c t c o m p o n e n t ) , a n d ~ i s a d i r e c t i o n a l l y a v e r a g e dr e f l e c t a n c e [ s e e t h e d e f i n i t i o n s i n T a n r ~ e t a l . ( 1 9 7 9 ) ] .I n t h e c a s e o f W h i t e S a n d s a n d t h e S o n o r a D e s e r t ,w h i c h e x h i b i t r e l a t i v e l y s m a l l b i d i r e c t i o n a l e f f e c t s , w eh a v e ( p s~ - ~ ) ~ S a ~ ~ 0 a n d La b e c o m e s ( s e e T a n r ~ e ta l . , 1979):

1 T +~ = ~ / tt sE s ~ g ~ I P ~ ( A p s . ~ + B P s ~ ) ] (1E)l_w i t hA = ex p( - rz / / .t ,) ex p( - ra / /. t~),B = ta(gs) ex p ( - r~//.tv) + ta(/.tv)ex p( - r~//~s) + t a ( l ~ , ) t a ( l ~ v ) .(13)

N o t e i n E q s . ( 1 1 ) a n d ( 1 3 ) th a t a b s o r p t i o n b y a t m o -s p h e r i c g a s e s ( t h e t e r m T ~ ) i s c o n s i d e r e d a s a s i m p l em u l t i p l i c a t i v e f a c t o r d e p e n d e n t o n t h e d i r e c t p a t h s b e -t w e e n t h e S u n a n d t h e t a r g e t a n d t h e t a r g e t t o t h es a t el li t e. D e c o u p l i n g a b s o r p t i o n a n d s c a t t e r i n g i s j u s ti -f i e d b e c a u s e i n t h e s p e c t r a l r a n g e o f t h e V I S S R s o l a rc h a n n e l , 0 . 5 - 0 . 8 / ~ m , t h e m a i n a b s o r b e r ( o z o n e ) i s l o -c a t e d h i g h i n t h e a t m o s p h e r e w h e r e m o l e c u l e s a r e r a r -e f ie d . C o n s e q u e n t l y , p h o t o n s f o l l o w p r a c t i c a l ly a d i r e c tp a t h t h r o u g h t h e a b s o r b i n g l a y e r , m a k i n g i t p o s s i b l e t op a r a m e t e r i z e T ~ a s a f u n c t i o n o f /~ s a n d g v ( f o r a g i v e na m o u n t o f a b s o r b e r) .

T h e a t m o s p h e r e t h n c t i o n s p G ~ , t a a , S a a , an d f fs~ a rec o m p u t e d u s i n g t h e " 6 S " c o d e ( V e r m o t e , p e rs o n a l c o m -m u n i c a t i o n ) . T h e 6 S c o d e i s a n i m p r o v e d v e r s i o n o f t h es i m u l a t i o n o f t h e S a t e ll i te S i g na l in t h e S o l a r S p e c t r u m( 5 S ) c o d e ( T a n r ~ e t a l ., 1 9 9 0 ) t h a t a c c o u n t s f o r b i d i r e c -t i o n a l e f fe c t s o f t h e s u r f a c e r e f l e c t a n c e . I n t h e 6 S c o d e ,


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Radiometric Calibration of GOES-7 Solar Channels 9 9

c o m p u t a t i o n s a r e p e r f o r m e d u s i n g t h e s u c c e s si v e o r d e rso f s c a t te r i n g m e t h o d ( D e u z 6 e t a l ., 1 9 89 ) . M u l t i p l es c a t t e r i n g , i n c l u d i n g m o l e c u l e - a e r o s o l c o u p l i n g e f f e c t s ,a r e f u l l y t a k e n i n t o a c c o u n t . A c c u r a c y is h i g h ( t y p i c a ll y1 0 -3 i n r e f l e c t a n c e ) , a n d e s s e n t i a l ly d e p e n d s o n t h en u m b e r o f G a u s s a n g l e s u s e d i n t h e n u m e r i c a l i n te g r a-t io n . T h e a t m o s p h e r i c f u n c t i o n s d e p e n d o n a e r o s ol t y p ean d am o u n t ( o r v i s i b i l i t y ) . T h e ae r o s o l m o d e l s av a i l ab l ea r e m i x t u r e s o f b a s i c c o m p o n e n t s ( d u s t , o c e a n i c , w a t e r -s o l u b l e , an d s o o t ) . B ecau s e t h e ae r o s o l ch a r ac t e r i s t i c sa t W h i t e S a n d s a n d o v e r t h e S o n o r a D e s e r t a r e n o t w e l lk n o w n a n d a r e n o t m e a s u r e d r o u t in e l y , w e s e l e c t e dt h e c o n t i n e n t a l m o d e l o f t h e I n t e r n a t io n a l R a d i a t i onC o m m i s s i o n ( W C P 5 5 , 1 9 8 3 ) . T h i s m o d e l c o n t a i n s 7 0 %o f d u s t li k e a e r o s o ls , 2 9 % o f w a t e r - s o l u b l e a e r o so l s , a n d1 % s o o t .T h e m o d e l i n p u t p a r a m e t e r s a r e b i d i r e c t i o n a l s u r -f a c e r e f l e c t a n c e , a e r o s o l t y p e , a e r o s o l o p t i c a l t h ic k n e s sa t 5 5 0 n m ( o r, eq u i v a l en t l y , v i s ib i l it y ) , o zo n e an d w a t e rv a p o r a m o u n t s , a l t i t u d e o f t h e t a r g e t , a n d g e o m e t r i c a lc o n d i t i o n s ( s o la r a n d v i e w i n g z e n i t h a n g l e s a n d r e l a t i v e

' a z i m u t h a n g l e ) . T h e b i d i r e c t i o n a l s u r f a c e r e f l e c t a n c e i sd e f i n e d w i t h r e s p e c t t o t h e d i r e c t s o la r fl u x a n d , t h e r e -f o r e , d o e s n o t d e p e n d u p o n s k y c o n d i t i o n s , w h i c h a r eh i g h l y v a ri a b l e . T h i s i s o n e o f t h e a d v a n t a g e s o f t h es i g n a l d ec o m p o s i t i o n o f T an r 6 e t a l . ( 1 9 7 9 ) a s g i v eni n E q . ( 11 ). F r o m t h e a l t i t u d e o f t h e t a r g e t , R ay l e i g hs c a t te r i n g co r r e c ti o n s a r e m a d e , a n d t h e r e d u c e d m o l e c -u l a r o p t ic a l d e p t h i s u s e d t o c o m p u t e g a s e o u s a b s o r p t i o ni n th e n a r r o w o x y g e n b a n d n e a r 0 . 7 6 / 2 m .R E F E R E N C E T A R G E T SI n p r i n c i p l e , o n e ca l i b r a t i o n p o i n t ( i .e . , o n e / ~ , C N~ p a i ro r one ~ , CN~* pai r ) i s su f f ic ien t to de ter m ine a~ o r o~ inthe ca l ib ra t ion e qua t ion [Eqs . (3 ) o r (8 )] . Thu s , a s ing ler e f e r en ce t a r g e t , o f k n o w n an d p r e f e r en t i a l l y h i g h r e f l ec -t an ce , m ay b e u s ed . U n ce r t a i n t i e s i n t h e s u r f ace r e fl ec -t a n c e o f t h e t a rg e ts , h o w e v e r , w h i c h a r e n e v e r c o m p l e t e l yc h a r a c t e r i z e d a n d a r e s u b j e c t t o u n p r e d i c t a b l e e f f e c t s( e .g . , s o i l m o i s t u r e ch an g es ) , s u g g es t t h a t w o r k i n g w i t hs ev e r al t a r g e t s i s p r e f e r ab l e . T h e t a r g e t s s e l ec t ed , n am e l y ,t h e S o n o r a D e s e r t a n d W h i t e S a n d s , p r o v i d e l o w a n dh i g h c a l i b r a t i o n p o i n t s , m a k i n g i t p o s s i b l e t o d e s c r i b ep r o p e r l y t h e c a l i b r a t i o n c u r v e / ~ i =f(C N~ i - CN~o~)or p~ =f ( C ~ * ) .T h e S o n o r a D e s e r t , l o c a t e d a t a b o u t 3 2 N a n dl 1 4 W , i s a l a r g e ( > 5 0 k m ) , fl a t a r e a p a r t i a l ly v e g e t a t e di n a f a i rl y u n i f o r m m a n n e r ( W h i t l o c k e t a l. , 1 98 7 ).A v e r ag e a l t i t u d e i s 0 .2 k m , an d t y p i c a l h o r i zo n t a l v i s ib i li -t i e s a r e 3 0 - 4 5 k m ( Y u m a A i r p o r t W e a t h e r S e r v ic e ,p e r s o n a l c o m m u n i c a t i o n ) . T h e s i t e i s p a r t i c u l a r l y s u i t -a b l e f o r c a l i b r a t i o n p u r p o s e s b e c a u s e i ts r e f l e c ta n c e , a so b s e r v e d b y A V H R R B a n d 1 ( 0 . 5 7 - 0 . 7 0 / ~ m ) , e x h i b i t sl i t t l e s p a t ia l v a r i a t i o n ( ch an g es a r e w i t h i n _+ 5 % ) ( Wh i t -l o c k e t a l ., 1 9 8 7) . T h e r e f l e c t a n c e o f t h e S o n o r a D e s e r t

( a ) 9 0

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Figure 1. Sonora des er t ref lectanc e as func tion of viewinggeometry. Wavelength is 0 .623/~m, the equivalent wave-length o f the GOES-7 V ISSR solar channels; sun zen ithangle is 30 (top) and 60 (bottom). In the polar diagrams,the r coordinate is the viewing zenith angle and the 0 coor-dinate is the relat ive azimuth angle. * indicates solarvector.

i s ab o u t 0 .3 , w i t h s m a l l d i r ec t i o n a l e f f ec t s , ex cep t a ts o l a r a n d v i e w i n g z e n i t h a n g l e s a b o v e 6 0 % e s p e c i a l l yi n f o r w ar d r e f l ec t i o n ( Wh i t l o ck e t a l . , 1 9 8 7 ) . F i g u r e 1s h o w s t h e b i d i r e c t i o n a l r e f l e c t a n c e f u n c t i o n ( B D R F ) o ft h e t a r g e t f o r s o l a r z en i t h an g l e s o f 3 0 ( t o p ) an d 6 0 ( b o tt o m ) . B D R F i s n L / E c o s /9 ,. T h e s p h e r i c a l a lb e d oo f t h e t a r g e t i s 0 .3 9 9 , co n f i r m i n g t h e v a l i d i t y o f E q . ( 13 )f o r t h e s o l ar a n d v i e w i n g z e n i t h a n g l e s b e l o w 6 0 . T h ee f f e c t o f s o il m o i s t u r e , e s t i m a t e d i n t h e l a b o r a t o r y u s i n gs a n d s a m p l e s f r o m t h e S o n o r a D e s e r t , i s s i g n i f i c a n t( Wh i t l o ck e t a l . , 1 9 8 7 ) . A 1 6 % i n c r ea s e i n m o i s t u r ef r om d r y c o n d i t io n s m a y r e d u c e r e f le c t a n c e b y a s m u c ha s 5 0 % . T h e r e d u c t i o n , h o w e v e r , i s n o n l i n e a r a n d c o n -f i n e d to t h e f i r st 3 - 4 % o f m o i s t u r e i n c r e a s e .W h i t e S a n d s , lo c a t e d a t t h e 3 2 0 52 q ~ a n d 1 0 6 1 7rW ,i s a m u c h s m a l l e r ta r g e t t h a n t h e S o n o r a D e s e r t . A p p r o x -i m a t e l y 3 0 k m i n d i a m e t e r , i t is n o t h o r i z o n t a l l y u n i f o r m .O n e d i s t i n g u i sh e s a l k a li fi a ts in t h e w e s t a n d s o u t h a n dg y p s u m d u n e s a l o n g t h e e a s t e r n e d g e o f th e a l k al i p o r -t i o n o f t h e b a s i n . A l t i t u d e i s 1.2 5 k m an d ae r o s o l lo ad i n gi s g en e r a l l y s m a l l [ o p t i ca l t h i ck n e s s l e s s t h an 0 .1 a t 0 .5 5


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, . . .[ ~ " ' " ' - . . .+ .C - . . , ZX . . . . . . . . . . . . . . A)4 -. . . . . . . ~ - - : ~ . . . . . . . . _ _ Z : t' I~. . . . . . - - ~ - - - ~ ~

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Figure 2. Sur face r e f l ec t ance o f Whi t e Sands dunes a s r e -t r ieved from a i rcraf t Adv anced Sol id-Sta te Array Spect ron at i -ometer da ta (Markham et a l . , 1990) and ground-based PA-RABOLA da ta (D ee r ing e t a l. , 1990) , and meas ured in t helabora to ry (Wa lraven and Coulson, 1972) . W aveleng th is0.66/~m and sun zen i th angle i s 54 .

l t m t h r o u g h o u t t h e y e a r ( L e c r o y e t al ., 1 9 9 4 )] . A v e r yh i g h w a t e r t a b l e k e e p s t h e v e r y l o w p a r t s o f t h e a l k a lif ia ts p e r m a n e n t l y w e t . T h e d u n e s o c c u p y a 6 0 0 k m 2a r e a . T h e y a r e h i g h l y r e f l e c t i v e , w i t h t y p i c a l a l b e d o o f0 . 7 at 0 . 6 2 / tm . T h e m a i n p r o b l e m w i t h t h e d u n e s i s t h e i rh e i g h t ( 6 m o n a v e r a g e ) , w h i c h c h a n g e s s i g n if i c an t l y t h es u r f a c e r e f l e c t a n c e b y c a s t in g s h a d o w s . W h e e l e r e t a l.( 1 9 9 4 ) i n d i c a t e t h a t s h a d o w v a r i a t i o n s c o m p l i c a t e t h eb i d i r ec t i o n a l re f l e c t a n c e p r o b l e m a n d m a k e t h e d u n e sl e s s d e s i r a b l e t h a n a l k a l i f i a t s f o r c a l i b r a t i o n p u r p o s e s .T h e d a t a o f W h e e l e r e t a l. ( 19 9 4 ), h o w e v e r , s h o w t h a ts e a s o n a l f l u c t u a t i o n s i n t h e d u n e s " a l b e d o d e r i v e d f r o mc a l i b r a t e d G O E S - 7 v i s i b l e r a d i a n c e s ( c a l i b r a t e d w i t hr e s p e c t t o a l b e d o m e a s u r e m e n t s a t s e v e r a l s i t e s i n t h ea l k a l i f i a t s ) a r e s i m i l a r t o t h o s e i n t h e f i a t s a l b e d o ,i n d i c a t i n g t h a t s h a d o w i n g e f f e c ts c a n n o t b e r e s p o n s i b l ef o r t h e f l u c t u a t i o n s i n t h e d u n e s a l b e d o . T h i s i s c o n s i s -t e n t w i t h t h e o b s e r v i n g g e o m e t r y o f G O E S - 7 , w h i c h isc l o s e to t h a t o f t h e s u n ( s i m i l a r a z i m u t h a n g l e s n e a rl o c a l n o o n ) .T h e s p e c tr a l r e f l e c ta n c e o f g y p s u m s a n d f r o m W h i t eS a n d s w a s m e a s u r e d i n th e l a b o r a t o r y b y W a l r a v e n a n dC o u l s o n ( 1 97 2 ). D r y a n d w e t s a n d s w e r e c o n s i d e r e d .C o m p a r e d t o a i r c r a f t m e a s u r e m e n t s ( a v e r a g e d o v e r 1 - k mr e s o l u t i o n o f a t y p ic a l s a t el l it e s e n s o r ) r e p o r t e d b y M a r k -h a m e t a l . ( 1 9 9 0 ) a n d g r o u n d m e a s u r e m e n t s m a d e b yD e e r i n g e t a l. ( 1 9 9 0 ), th e l a b o r a t o r y m e a s u r e m e n t s a r et o o h i g h b y a f e w p e r c e n t i n b a c k w a r d r e f l e c t i o n a n db y u p t o 2 0 % i n f o r w a r d r e f l e c t i o n ( F i g . 2 ) a t 0 . 6 6p m . I n t h e f i g u re , th e l a b o r a t o r y c u r v e c o r r e s p o n d s t o

( a ) 9 0

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1 8 0 oW h i t e S a n d s , e = = 6 0

Figure 3. W hite Sands ref lec tan ce as a funct ion of viewinggeom e t ry . Wav e leng th i s 0 .623 gm, t he equ iva l en t wave-length o f the G OE S-7 VISSR solar channels; sun zeni thangle i s 30 ( top) and 60 (bottom). Data are f rom Walra-ven and Clouson (1972) . * indica tes solar vector .g y p s u m s a n d c o n t a i n i n g 2 1 % m o i s t u r e , a t y p i c a l v a l u em e a s u r e d b y W i l li a m s o n ( 1 9 7 5) o v e r t h e d u n e s r e g io n .T h e l a r g e d i s c r e p a n c y i n f o r w a r d r e f l e c t i o n is th e d i r e c tc o n s e q u e n c e o f d u n e - i n d u c e d s h a d ow i n g . B e c a u s e t h em e a s u r e m e n t s o f W a l r a v e n a n d C o u l s o n ( 1 9 7 2 ) a r e c om -p l e t e ( a n g u l a r e f f e c t s , s p e c t r a l d e p e n d e n c e ) , t h e y a r eu s e d i n t h e r a d i a t i v e t r a n s f e r m o d e l . T h e y a r e m u l t i p l i e d ,h o w e v e r , b y a f a c t o r o f 0 . 9 4 s o t h a t t h e y m a t c h t h ea i r c r a f t a n d s u r f a c e m e a s u r e m e n t s i n b a c k w a r d r e f l e c -t i o n ( G O E S - 7 c o n d i t i o n s o f o b s e r v a t io n s ) . F i g u r e 3s h o w s t h e c o r r e c t e d b i d i r e ct i o n a l r e f l e c ta n c e o f W h i t eS a n d s a t 0 . 6 2 / ~ m f o r s u n z e n i t h a n g l e s o f 3 0 ( t o p ) a n d6 0 ( b o t t o m ) . U n l i k e t h e S o n o r a D e s e r t , W h i t e S a n d se x h i b i t s m a x i m u m v a l u e s i n f o r w a r d r e f l e c t i o n f o r b o t hs u n z e n i t h a n g l e s. T h e b i d i r e c t i o n a l e f f e c t s a r e l a r g e rf o r a s u n a t 6 0 f r o m z e n i t h , but Eq. (12) i s s t i l l app l i ca -b l e f o r s u n - v i e w i n g z e n i t h a n g l e s b e l o w 6 0 .D A T A S E T SS a t e l l i t eT h e V I S S R d a t a u s e d t o p e r f o r m t h e c a l i b r a t i o n o r i g i -n a t e f r o m t h e S p a c e S c i e n c e a n d E n g i n e e r i n g C e n t e r


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Radiometric Calibration of GOES-7 Solar Channels 101

(SSE C) o f t h e U n i v e r s i t y o f W i s co n s i n , Mad i s o n . T h e yh a d b e e n b r o a d c a s t t o S S E C b y th e G O E S t r a n s m i ss io ns y s t em a f t e r r ep ro ces s i n g a t t h e N E SD IS CD A fac i l i t yi n W a l l o p s I s l an d an d r e t r an s mi s s i o n b ack t o t h e s a t e l -l i te . The da ta a re in th e fo rm of fu l l reso lu t ion , 6 -b i tp r ec i s i o n 5 1 2 x 5 1 2 p i x e l v i s ib l e co d e d o n an 8 b i t s cal ean d 1 0 b i t t h e rma l i n f r a r ed i mag es co d ed a s i n t eg e r * 2d a t a. Se l ec t i o n o f t h e i m ag es w as mad e b y s can n i n gme t eo ro l o g i ca l ch a r t s f o r c l ea r s k y co n d i t i o n s . Mo ret h an 1 0 0 0 i mag es each o f s p ace , W h i t e San d s, an d t h eSo n o ra D es e r t i n t h e v i s i b l e an d t h e rma l i n f r a r ed w e reacq u i r ed a t 1 8 3 1 G MT , 1 9 0 1 G MT , 1 9 3 1 G MT , an d2 0 0 1 G M T o v e r t h e p e r i o d f r o m J u n e 1 9 8 7 t h r o u g hN o v e m b e r 1 9 88 . E a c h o f t h e s e i m a g e s w a s d e s t r ip e du s i n g N O A A 's o p e ra t i o n a l d e s t r i p i n g p ro ced u re p r i o r t or ece i p t o f t h e d a t a a t t h e Sc r i p p s In s t it u t i o n o f O cean o g -r ap h y . T h es e d a t a a r e r e f e r r ed t o a s s t r e t ch ed d a t a i nt h is p ap e r . E ach o f t h e s e s t r e t ch ed i mag es a l s o co n -ta ine d l a rge am ounts o f res idual s t r ip ing . In add i t ion tot h i s d a t a s e t , o b t a i n ed a f t e r r e fo rma t t i n g a t W a l l o p s , ad a t a s e t c o m p o s e d o f u n t a m p e r e d i m a g es , a c q u i re d e v e r yW e d n e s d a y a t 1 8 4 8 G M T ( h e r e a f t e r r e f e r r e d t o a s t h e" W ed n es d ay " d a t a s e t) , a l s o w as ma d e av a i lab l e b y SSE C.Th e "We dnesday" da tase t inc ludes 390 images o f space ,W h i t e San d s , an d t h e So n o ra D es e r t i n t h e v i s i b l e an dt h e rma l - i n f r a r ed an d co v e r t h e s ame t i me p e r io d . T h es es p ec i a l W ed n es d ay d a t a a r e n o t o p e ra t i o n a l l y d e s t r i p edw i t h t h e N O A A a l g o ri th m. T h e y co n t a i n v e ry h i gh l ev e l so f s en s o r n o i s e a s s o c i a t ed w i t h t h e s t ri p e s. T h e t h e rma li n f r a r ed d a t a a r e n o t u s ed d i r ec t l y i n t h e ca l i b r a t i o n o ft h e V ISSR v is i b le ch an n e l s, b u t t h ey a r e i n s t ru men t a li n en s u r i n g t h a t t h e ca l i b r a t i o n s i t e s s e lec t ed f ro m m e t e -o ro l o g ica l ch a r t s a r e co m p l e t e l y f r ee o f c l o u d s ( s ee t h es ec t i o n o n c l o u d s c r een i n g ) .S u r f ac eT h e r ad i a t i v e t r an s f e r mo d e l r eq u i r e s a k n o w l ed g e o fg en e ra l me t eo ro l o g i ca l p a r ame t e r s ch a rac t e r i z i n g t h ea t mo s p h e re o v e r l y i n g t h e t a rg e t , n ame l y , o zo n e amo u n t ,aeroso l amount (e i ther v i s ib i l i ty o r op t i ca l th ickness a t0 . 5 5 / ~m) , an d w a t e r v ap o r amo u n t .Fo r ae ro s o l am o u n t , o b s e rv a t i o n s o f v is i b il it y a t t h ec l o s e s t me t eo ro l o g i ca l s t a t i o n s , n ame l y , A l mag o rd o fo rW h i t e S a n d s a n d Y u m a f o r t h e S o n o r a D e s e r t , w e r e 2 5k m an d 8 k m, r e s p ec t i v e l y , mo s t o f t h e t i me . T h es ev a l u es a r e q u es t i o n ab l e . S l a t e r ( p e r s o n a l co mmu n i ca -t ion) , dur ing h i s ca l ib ra t ion exper iments a t the a lka l if i a t s , f requen t ly observed v i s ib i l i t i es above 100 k in . TheY u m a A i r p o r t W e a t h e r S e r v i c e ( p e r s o n a l c o m m u n i c a -t i o n ) u s u a l l y r ep o r t s v i s i b i l i t i e s b e t w een 3 0 k m an d 4 5k m, w i t h o ccas i o n a l ly l o w e r v a l u es d u r i n g d u s t s t o rms .A t W h i t e San d s , L ec ro y e t a l . ( 1 9 9 4 ) , meas u red t h eae ro s o l o p t i ca l t h i ck n es s a t 0 . 5 5 / ~m d u r i n g a s ev e ra l -y ea r p e r i o d s t a r t i n g i n J an u a ry 1 9 8 9 an d en d i n g i nJ a n u a r y 1 9 9 3. T h e y f o u n d t h a t b e f o r e P i n a t u b o e r u p t e d

in 1991 , the op t i ca l th ickness exh ib i t ed a seasonal t rendw i t h a h i g h o f ab o u t 0 , 1 3 i n J u l y an d a l o w o f 0. 0 1 i nD e c e m b e r . T h e y f u rt h e r m o d e l e d t h e s e a so n a l t r e n d a sra(0 ,55 /Jm) = 0 .08 + 0 .057 co sT - 0 .01 cos 2T (14)

wi thT = [ 2 n ( A P - 2 6 1 ) ] /3 6 5 , (1 5)

w h e re r a i s t h e ae ro s o l o p t i ca l t h i ck n es s an d A D i s t h ed i f f e r en ce b e t w een ac t u a l an d 1 O c t o b e r J u l i an d ay s .T h es e o p t i ca l t h ick n es s e s a r e ch a rac t e r i s ti c o f a v e ryc l ean a t mo s p h e re (v i s i b i l i t y ab o v e 2 3 k m) . Becau s e n oma j o r v o l can i c e ru p t i o n o ccu r r ed d u r i n g o u r s t u d y p e -r i od , t h e mo d e l o f L ec ro y e t a l. ( 1 9 9 4 ) w as u s ed o v e rW h i t e San d s. B ecau s e o f th e l a ck o f d a ta , v i s ib i li ty w asf i x ed a t 3 5 k m fo r al l So n o ra D e s e r t o b s e rv a t io n s . W i t hsuch h igh v i s ib i l i t i es , aeroso l e f fec t s on the VISSR rad i -an ce b ec o m e f a ir l y i n d e p en d en t o f a e ro s o l t y p e , s i mp li -fy ing the rad ia t ive t rans fer m odel ing . T heref ore , a s t an-d a rd co n t i n en t a l a e ro s o l mo d e l (W CP 5 5 , 1 9 8 3 ) w asse lec ted fo r the ca lcu la t ions .F o r w a t e r v a p o r a m o u n t , w e u s e d r a d i o s o n d e o b s e r-v a t i o n s a t E1 Pas o (W h i t e S an d s ca s e ) an d Y u m a (So n o raDeser t case) . E1 Paso i s loca ted a t the same a l t i tude andl o n g i t u d e a s W h i t e San d s . N o co r r ec t i o n i s p e r fo rm ed t oaccount fo r the l a t i tud ina l d i s t ance be tween Whi te Sandsan d E 1 Pas o (1 2 0 k m) . T h is p ro ced u re i s r o u g h l y co r r ec tb ecau s e t h e w a t e r v ap o r e f f ec t o n t h e t o p -o f - a t mo s p h e res ignal i s smal l . Yuma i s loca ted about 50 km nor th o ft h e So n o ra D es e r t , b u t t h e a t mo s p h e r i c co n d i t i o n s a r es imi lar . Over bo th s i t es , water vapor amount i s lowd u r i n g w i n t e r , w i t h v a l u es o f 0 . 5 g c m -2 , an d h i g hd u r i n g s u m mer , w i t h v a l u es ab o v e 3 g c m -2 . I n t h eV ISSR v i s i b l e b an d s , w a t e r v ap o r ab s o rp t i o n i s w eak ,an d i t i s a ccep t ab l e t o u s e t h e 1 8 3 1 G MT v a l u es fo ro b s e rv a t i o n s a t 1 8 4 8 G MT , 1 9 0 1 G MT , 1 9 3 1 G MT , an d2 0 0 1 G M T . In f ac t, it w o u l d h av e b ee n a d eq u a t e t os i mp l y u s e c l i ma t o lo g i ca l v a l u e s o f w a t e r v ap o r amo u n t ,b u t t h e r ad i o s o n d e d a t a w e re r ead i l y av a i l ab l e .Fo r o zo n e am o u n t , w e u s ed t h e c l i ma t o l o g y o f L o n -don e t a l . (1976) . Th i s i s jus t i f i ed because var ia t ions inozo ne am oun t affect l it t le the V ISSR vis ible s ignal (Frouinan d G au t i e r , 1 9 8 7 ) . U s i n g d a t a f ro m t h e T o t a l O zo n eM a p p i n g S p e c t r o m e t e r w o u l d n o t h a v e c h a n g e d t h eresul ts s ignificant ly.D E S T R I P I N G O F G O E S D A T AU n fo r t u n a t e l y , G O E S v i s i b l e d a t a a r e ch a rac t e r i zed b ya p a t t e rn o f sh a rp , r ep e t i t i v e s t r i p e s o v e r t h e en t i r eimag e (e.g. , We inre b e t a l ., 1989). I f unc orre c ted , thes es t r ipes can l ead to e i ther improper image c lass i f i ca t ion(e . g . , W e i n reb e t a l . , 1 9 8 9 ) an d / o r i n accu ra t e c l o u dd e t ec t i o n (S i mp s o n e t a l . , 1 9 9 5 ) . Mo reo v e r , t h e N O A Ao p era t i o n a l d e s t r i p i n g p ro ced u re l e av es l a rg e l ev e l s o fres idual s t r ip ing in the da ta , and the de gre e o f res idual


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102 F r o u in a n d S i m p s o n

s t r ip ing i s h igh ly var iab le . Therefore , res idual s t r ipes int h e ca s e o f mo s t d a t a an d r aw s t r ip e s i n t h e ca s e o f t h eW e d n e s d a y 1 8 4 8 G M T p a s s e s w e r e r e m o v e d f r o m t h ed a t a u s in g a f r eq u en cy d o m a i n i mp l em en t a t i o n o f af in i t e impulse response (FIR) t a rge t f i l t e r . Th i s newm e t h o d o f d e s t ri p in g w a s u s e d b e c a u s e i t p r o v e d s u p e -r io r (based on s ignal to no i se and f i l t e r - in t roduced d i s -t o r t i o n meas u re s co mp u t ed b e fo re an d a f t e r d e s t r i p i n g )to a l l o ther methods evalua ted (Simpson e t a l . , 1995) .C L O U D D E T E C T I O NT h e G O E S Sp l i t - an d Merg e C l u s t e r i n g (G SMC) c l o u dd e t ec t i o n a l g o r i t h m (S i mp s o n an d G o b a t , 1 9 9 5 a ) w asused to c loud screen the ca l ib ra t ion t a rge t s . Th i s a lgo-ri thm consis ts of thre e s teps: 1) a spl i t -and-merge cluster-ing o f the inpu t da ta (1 km reso lu t ion ref l ec tance , 1 kmg rad i en t o f re f l ec t an ce , an d t h e rm a l IR d a t a s p a ti a ll yi n t e rp o l a t ed f ro m t h e o b s e rv ed 4 k m r e s o l u t i o n t o 1 k mres o l u t i o n ) , w h i ch s eg men t s t h e s cen e i n t o i t s n a t u r a lg ro u p i n g s ; 2 ) a c l u s t e r l ab e l i n g p ro ced u re w h i ch u s e ss cen e s p ec i fi c j o i n t t h r ee -d i men s i o n a l ad ap t i v e t h r e s h -o lds (as opposed to s t a t i c cons tan t th resho lds ) to l abe lthe c lus ters as c loud or c loud-f ree l and ; and 3 ) a pos t -p ro ces s i n g s t ep w h i ch i mp o s es a d e g ree o f s p a ti a l u n ifo r -mi t y o n t h e l ab e l ed l an d an d c l o u d p i x e l s . A n a p r i o r imas k f ea t u r e a l so en h an ces c l o u d d e t ec t i o n i n t r ad it io n -a l ly d i f f i cu l t scenes (e .g . , c louds over b r igh t deser t , seeb e l o w ) . Res u l t s s h o w t h a t t h e G SMC a l g o r i t h m i s n e i -t h e r r eg i o n a l l y n o r t emp o ra l l y s cen e s p ec i f i c .

In cer ta in reg ions (e .g . , the b r igh t deser t t a rge tareas used in th i s s tudy) , h igh ref l ec tance na tu ra l lyo ccu r s an d t h u s r e f l ec t an ce i s n o t a r o b u s t c l o u d d e t ec -t io n p a r am e t e r . M o reo v e r , t h e s p a ti a l r e s o l u t i o n o f t h eG O E S t h e rm a l d a t a ( 4 k m) fu r t h e r co mp l i ca t e s t h e c l o u ddetec t ion p rob lem in these reg ions because in terpo la t ingthe thermal data to ful l spat ial resolut ion (1 kin) canp r o d u c e a s o m e w h a t b l u r r y i m a g e , w h i c h c a n l e a d t omi s l o ca t io n o f f ea t u r e b o u n d a r i e s i n th e t h e rm a l d a ta .T o c i r cu m v en t t h e s e n a t u r a l l y o ccu r r i n g an d s en s o r -s p ec if i c p ro b l em s , t h e G S M C a l g o ri t h m a l lo w s fo r i n co r -pora t ion o f anci ll a ry in format ion ( i. e. , the a p r i o r i mas k )i n t o t h e c l o u d d e t ec t i o n p ro ces s . A n c i l l a ry mas k i n fo r -ma t i o n fo r t h e t w o d es e r t t a rg e t s u s ed i n t h is s t u d y w asfo rmed a s f o l l o w s . A W h i t e San d s c l o u d f r ee t emp l a t e(5 5 x 5 5 p i x e l s 2) an d a So n o ra D es e r t c l o u d f r ee t em p l a t e(6 5 x 6 5 p i x el s 2) w e re fo rmed . T a rg e t b o x es w e re l o ca t edi n t h e cen t e r o f e ach o f t h e s e t emp l a t e s . T h e t a rg e tboxe s w ere 8 8 p ixe l s z and 24 24 p ixe ls 2 fo r W hi teSan d s an d So n o ra D es e r t , r e s p ec t i v e l y . A s u b s ec t i o nma t ch i n g t h e t em p l a t e d i m en s i o n s an d l o ca t i o n fo r e acht a rg e t w as ex t r ac t ed f ro m each o f t h e 2 0 0 0 s cen e s (1 0 00a t W h i t e San d s an d 1 0 0 0 o v e r So n o ra D es e r t ) u s edin the ca l ib ra t ion s tudy . Each subsec t ion was spa t i a l lyco r r e l a t ed w i t h t h e can o n i ca l l y c l ea r i mag e t emp l a t e f o rt h a t t a rg e t. A L ap l ac i an o f t h e G au s s i an (L O G ) ed g e

detec t ion opera to r (e .g . , Ja in , 1989; Simpson , 1990) wasu s ed t o g en e ra t e ed g e s h ap es fo r b o t h can o n i ca l l y c l ea rt a rg e t t emp l a t e s an d fo r e ach ex t r ac t ed i mag e s u b s ec -t io n . T h es e ed g e m ap s w e re u s ed t o a l i gn t h e can o n i ca l lyc l ea r t a rg e t t emp l a t e s an d t h e s u b s ec t i o n s u s i n g anau t o co r r e l a t i o n p ro ced u re . O n ce t h e t w o a r e a l i g n ed , as i mp l e meas u re o f co r r e l a ti o n w as u s ed t o d e t e rmi n e i fa g iven sub sec t ion w as c loud-f ree . I f a subsec t ion i sc l o u d y , t h e t w o ed g e map s w i l l n o t co r r e l a t e w e l l , an dt h e r an d o m s h if ti n g t h a t r e s u l ts f r o m t h e au t o co r r e l a t io nwi l l no t s ign i f i can t ly improve the f ina l cor re la t ion . Int h e c l ea r c a s e , h o w ev e r , t h e s h i f ted s u b s e c t i o n w i ll h av ea mu ch h i g h e r co r r e l a ti o n t h an i f i t h ad n o t b een ex ac t lya l ig n ed w i t h t h e c l o u d f r ee t em p l a t e . T y p i ca ll y , a c l o u d -f ree subs ec t ion wi l l have a cor re la t ion t> 0 .8 wi th th ec l o u d - f r ee t emp l a t e w h e rea s a c l o u d y s u b s ec t i o n t y p i -ca l ly has e i ther a negat ive o r on ly s l igh t ly pos i t ive (0 .1 )co r r e l a ti o n w i t h t h e c l o u d f r ee t emp l a t e . U s e o f t h ist ech n i q u e i s d i s cu s s ed fu r t h e r b y S i mp s o n an d G o b a t(1995a; the i r F igs . 11 and 12 show a Whi te Sandsex amp l e ) .

C A L I B R A T I O N C O M P U T A T I O N A L P R O C E D U R E ST h e ca l i b r a t i o n co mp u t a t i o n a l p ro ced u re s f a l l i n t o t w odis t inc t s t eps : 1 ) va l ida t ion o f t a rge t c la r i ty and 2 ) rad io -me t r i c c a l ib r a ti o n . E ach i s d e s c r i b e d b r i e f l y b e l o w .

G O E S d a t a f r om t h e U n i v e rs i ty o f W i s c o n s in w e r er e c e i v e d in t h e M c l D A S f o r m a t a n d c o n v e r t e d f o r e a syu s e i n a U N IX w o rk s t a t i o n en v i ro n men t (S i mp s o n an dAI-Rawi , 1995) . VISSR data in the v i s ib le we re d es t r ipe d(Simpson e t a l . , 1995) , and c loud-masked (Simpson andGobat , 1995a) us ing the two procedures descr ibed above .Becau s e t h e c l o u d d e t ec t i o n p ro ces s r eq u i r e s ca l i b r a t edre f l ec t an ce , a p r e l i mi n a ry ca l ib r a t io n o f t h e G O E S v is i-b l e co u n t s t o r e f l ec t an ce w as p e r fo rmed u s i n g t h e ca l i -b ra t ion coef f i c ien t s o f Ro ssow e t a l . (1992) . The se ca li -b r a t ed v a l u es w e re u s e d o n l y fo r c l o u d d e t ec t i o n an dcer t i f i ca t ion o f t a rge t c la r ity . Da ta fo r a g iven d a te an dt i me w ere r e t a i n e d fo r u s e i n t h e r ad i o m e t r i c ca l i b r a ti o ni f an d o n l y i f b o t h t h e So n o ra d e s e r t an d W h i t e San d st a rg e t s w e re j u d g ed c l o u d - f r ee b y t h e c l o u d d e t ec t i o np r o c e d u r e .Radiom et r i c ca lib ra tion was per fo rm ed th ree d i f feren tways : 1 ) gen era te ca l ib ra t ion c oef f i c ien t s fo r the ind iv id -ual v i s ib le sensors us ing da ta co n ta in ing res idual s t r ipes ;2 ) g en e ra t e ca l i b ra t i o n co e f f i c i en ts f o r th e av e rag e o f t h eind iv idual v i s ib le sensors us ing da ta con ta in ing res iduals t r ipes ; and 3 ) genera te ca l ib ra t ion coef f i c ien t s fo r theav e rag e o f t h e v i s ib l e s en s o r s w i th d a t a d e s t r i p ed u s in gt h e d e s t r i p i n g p ro c ed u re o f S imp s o n e t a l. ( 1 9 9 5) t orem ove res idual s tr ipes. Re m em ber tha t res idual s t rip ingrefers to s t r ipes l e f t in the da ta a f t e r des t r ip ing byN O A A u s i n g i t s o p e ra t i o n a l d e s t r i p i n g p ro ced u re . T h erad i at i v e t r an s f e r mo d e l s u s ed i n a ll t h r ee c o mp u t a t i o n s


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Radiometric Calibration of GOES-7 Solar Channels 103

S o n o r a O e N r t T a r g et~ c , o , 6 , o ~ , F ~ A ~W h i t e , S a n d s T a c g e t

I M c l D A S o V I F F

S p a c e T a r g e tI M l o , s , o V , F

Prelim.Calibration ~ J CloudScreening

Preliro.Calibration ~ Cloud Screening

DO

Figure 4. Overview of the calibration computational p roce-dure.

a r e de sc r ibe d in de ta i l a bove . An ove r v ie w o f the e n t i r ec om puta t io na l p r oc e dur e i s g ive n in F igu r e 4.

A tot a l o f 602 c l oud- f r e e t r ip l e t s ( Whi t e S a nds ,S onor a De se r t , a nd spa c e ) we r e a va i l a b le f o r ca l ib r a t ion .The r e a r e two wa ys to p r oc e e d wi th th e a na lys i s . I nm e thod 1 the c a l ib r a t e d r a d ia nc e is c om pute d us ing

L = A + B1X2, (16)wher e B1 is the c ompu ted s lope , A is the co mput edof fse t, a nd X 2 c o r r e spond s to the c oun t s squa r e d ob -se r ve d ove r the t a r ge t . I n th i s c a se , t he c a l ib r a t ione qua t ion [ Eq. ( 16) ] doe s no t ne c e ss a r i ly go th r oug hthe o r ig in . B e c a use the spa c e c oun t shou ld be z e r othe or e t i c a l ly , i t i s de s i r a b le th a t t he c a l ib r a t ion be f o r c e dth r ough the o r ig in . Th i s p r oduc e s the phys ic a l ly de s i r -a b le s i tua t ion tha t a z e r o c oun t m e a su r e m e n t c o r r e -sponds to z e r o r e f l e c t a nc e . The n , t he a ppr opr i a t e m ode l(method 2) i s

L = B2(X 2 - X~). (17)Mean s lopes for al l thre e ca l ibra t ion proce dure s ( individua lc ha nne l s t r e t c he d , a ve r a ge d s t r e t c he d , a ve r a ge d s t r e t c he da nd de s t r ipe d ) c o m pute d us ing the s t a t i s t ic a l m ode l t oprod uce B1 and the physi ca l model to prod uce B2 andthe s t a nda r d de v ia t ion f o r t he se s lope s a r e g ive n inTa b le 2 . The se da ta show tha t t he m e a n c a l ib r a t ion

Table 2b. 1901 Dataset Mea n and Sigma Value forStatistical Metho d Slope Coefficient for Reflectance

Mean Standard DeviationStriped 1.94 x 10 -5 1.94 10 -6Destri ped 1.94 10 -5 1.94 x 10 -6Sensor 1 1.86 10 -5 2.04 10 -6Sensor 2 1.94 x 10 -5 2.34 x 10 -6Sensor 3 1.98 10 -5 2.09 10 -6Sensor 4 2.00 10 -5 2.16 x 10 -6Sensor 5 1.94 x 10 -5 1.10 10 -6Sensor 6 1.95 10 -s 2.11 x 10 -6Sensor 7 1.88 10 -5 2.11 10 -6Sensor 8 1.99 10 -~ 2.35 10 -6

Table 2c. Comparison of Slope Coefficients: Root MeanSquared Difference betwe en Coefficients Generat edfrom Statistical and Physical Methods for Reflectance

1831 1901 1931 2001Striped 3.46 10 -7 4.02 10 -7 4.1 6x1 0 -7 4.28 10 -7Destriped 3.4710 -7 4.0210 -7 4.16x1 0 -7 4.2810 -7Sensor 1 4.6710 -7 4,93x 10 -7 5.4110 -7 4.84x1 0 -7Sensor 2 4.77 10 -7 5.02 10 -7 4.86x 10 -7 5.28 10 -7Sensor 3 4.0 7x 10 -7 4.88 10 -7 4.85 x 10 -7 5.07 10 -7Sensor 4 4.08x 10 -7 4,75 1 0 - 7 4.97 10 -7 5.28 10 -7Sensor 5 4.35 10 -7 4,81 x 10 -7 5.02 x 10 -7 4.99 10 -7Sensor 6 4.82x 10 -7 5.15 x 10 -7 5.3 01 0 -7 5.34 10 -7Sensor 7 5.0610 -7 5.32 x 10 -7 5.59 10 -7 5.56 10 -7Sensor 8 4.41 10 -7 4.71 X 10 -7 4.86 10 -7 5.01 10 -7

Table 2d. Average Values of r z for Physical Meth odReflectance Coefficients for 1901 Datase t

Mean Standard DeviationStriped 0.98 0.03Dest ripe d 0.98 0.03Sensor 1 0.97 0.03Sensor 2 0.95 0.05Sensor 3 0.97 0.03Sensor 4 0.96 0.05Sensor 5 0.97 0.03Sensor 6 0.97 0.04Sensor 7 0.97 0.03Sensor 8 0.96 0.04

Table 2a. 1901 Dataset Mean and Sigma Value forPhysical Method Slope Coefficient for Reflectance

Mean Standard DeviationStriped 1.94 10 -5 1.97 10 -6Des tri ped 1.94 10 -5 1.97 10 -6Sensor 1 1.89 x 10 -5 2.06 x 10 6Sensor 2 2.90 x 10 -s 1.31 x 10 -6Sensor 3 1.98 x 10 -5 2.05 x 10 -6Sensor 4 1.98 10 -5 2.16 x 10 -6Sensor 5 1.94 x 10 -5 1.91 x 10 -6Sensor 6 1.96 x 10 -5 2.02 10 -6Sensor 7 1.91 x 10 -5 2.13 x 10 -6Sensor8 1.9710 5 2.35x10 6

Table 2e. Average Values of r ~ for Statistical M etho dReflectanc e Coefficients for 1901 Data set

Mean Standard DeviationStriped 1.0 0.01Dest ripe d 1.0 0.01Sensor 1 1.0 0.00Sensor 2 0.99 0.01Sensor 3 0.99 0.01Sensor 4 0.99 0.01Sensor 5 0.99 0.01Sensor 6 0.99 0.01Sensor 7 0.99 0.01Sensor 8 0.99 0.01


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1 0 4 F r ou in a n d S i m p s on

s lopes are near ly iden t i ca l reg ard less o f m ode l [Eqs . (16)o r ( 1 7) ] u s ed t o c o m p u t e t h em. Mo reo v e r , r 2 co r r e l a ti o ncoeff i c ien t s (Tab les 2d and 2e) show tha t the l inear i tyof the f i t i s no t on ly h igher , w hich jus t i f i es us ing th reeca l i b ra t i o n p o i n t s , b u t a l s o u n a f f ec t ed b y ch o i ce o f co m-p u t a ti o n m o d e l . R o o t m e a n s q u a r e d d i f f e re n c e s b e t w e e nt h e ca l i b r a t i o n s l o p es co m p u t e d u s i n g t h e s t a ti s ti c a l an dphys ica l model (Tab le 2c) fo r a l l the da ta dur ing thefour ca l ib ra t ion t ime per iods (1831 , 1901 , 1931 , and2001) are smal l . Thus , we conclude tha t impos ing thep h y s i ca l co n s t ra i n t o f z e ro r ad i an ce fo r z e ro o b s e rv e dcou nt i s jus t i f i ed and cons i s te n t wi th th e avai l ab le da ta .R E S U L T SA s i n d i ca t ed ab o v e , t h e ca l i b r a t i o n w as p e r fo rmed i nt h r ee d i f f e r en t w ay s : 1 ) u s i n g c l o u d - s c r een ed d a t a co n -ta in ing res idual s t r ipes and cons ider ing ind iv idual de tec-t o r s s ep a ra t e ly ; 2 ) u s in g c l o u d - s c r e en ed d a t a co n t a i n i n gre s i d u a l s t r i p e s av e rag ed o v e r t h e e i g h t d e t ec t o r s ; an d3) us ing des t r ip ed [ i. e. , meth od of Sim pson e t a l. (1995)],c l o u d - s c r een ed d a t a av e rag ed o v e r t h e e i g h t d e t ec t o r s .I n t h e f i r s t ap p ro ach , eq u a l i za ti o n o f t h e d e t ec t o r s o c -curs when app ly ing the ca l ib ra t ion coef f i c ien t s to ind i -v i d u a l d e t ec t o r s . T h u s , d e s t r i p i n g o f th e d a t a f ro m t h er e f e r en ce t a rg e t s i s a cco mp l i s h ed t w i ce , t h e f i r s t t i meu n i q u e l y fo r c l o u d s c r een i n g p u rp o s es . I n t h e s eco n dap p ro ach , t h e d i f f e r en ces b e t w een d e t ec t o r s a r e l o s tw h en av e rag i n g t h e co u n t s s q u a red . T h i s ap p ro ach i sn o t r e c o m m e n d e d , b u t h a s b e e n u s e d i n t h e p a s t ( F ro u i nand Gau t ier , 1987; R ossow e t a l. , 1992). In the th i rdap p ro ach , a s i n t h e s eco n d ap p ro ach t h e d e t ec t o r s a r eno t d i s t ingu i shed ; the same ca l ib ra t ion coef f i c ien t s app lyto a l l de tec to rs . In th i s case , however , the removal o ft h e r e s i d u a l s t r i p e s u s i n g t h e me t h o d o f S i mp s o n e ta l. (1995) ef fec t ive ly norm al izes th e de te c to r s p r io r toaverag ing . Ope ra t iona l use o f such ca l ib ra t ion coef f i -c ien t s requ i res des t r ip ing the V ISSR data p r io r to app ly ingthe ca l ib ra t ion coef f i c ien t s , a t ask tha t migh t be t ime-consuming when deal ing wi th fu l l d i sk , ha l f -hour ly im-ag es . H o w ev e r , S i mp s o n e t a l . ( 1 9 9 5 ) s h o w ed t h a t t h ed e s t ri p in g p r o c e d u r e c a n b e i m p l e m e n t e d i n t h e s p a ti ald o ma i n fo r o p e ra t io n a l p u rp o s es . N o t e a l s o t h a t d e s t r i p -i n g mu s t b e acco mp l i s h ed p r i o r t o c l o u d s c r een i n g t oavo id s ign i f i can t e r ro rs in c loud de tec t ion (Simpson e ta l . , 1995) . Th i s sugges t s tha t rad iomet r i c ca l ib ra t ionm i g h t b e c o n s i d e r e d a s p a r t o f a p r o c e d u r e a i m e d a tp ro v i d i n g n o t o n l y r ad i o me t r i ca l l y co r r ec t ed d a t a , b u ta l s o p ro p e r l y c l o u d - s c r een ed ( an d , a f o r t i o r i , d es t r i p ed )data . Our ob jec t ive here i s to quan t i fy the l imi ta t ionso f n o t eq u a l i z i n g t h e d e t ec t o r s p r i o r t o ca l i b r a ti o n o rn o t co n s i d e r i n g t h e d e t ec t o r s i n d i v i d u a l l y .In F i g u re 5 t h e t i me s e r i e s o f co u n t s s q u a re d o v e rspac e (Fig. 5a), W hite Sands (Fig. 5b), and the Sonora Desert(Fig . 5c) a re p rese n ted . Ind iv idual de tec to rs a re co ns ideredsepara te ly . (The da ta have been c loud-screened us ing

4 0 0

3 0 0

t- 2 0 00(5

10 0

4 0 0 0 0

3 0 0 0 0

cJt-

2 0 0 0 00

1 0 0 0 0

0

2 0 0 0 0

1 5 0 0 0

-"~ 1 0 0 0 000

5000

I IS p a c e , 1 9 : 0 1

( a ) ,2 00

I I I

I I I I- - Sonsor 1....... S e n s o r : ). . . . S e n s o ~ 3- - + S e n e m 4- -- S4nsor5- - - S e n s o r 6.......... Sensor 7

' l i ~ b

~ - ', . ~ , - ~ [.,~ ' ' - 4 " -~' ' I ~ [

400 600I I I I

W h i t e S a n d s , 1 9 :0 1

( b )I P P I I I

200 400 600I I I I I I I

S o n o r a D e s e r t ,1 9 01 ~1 t. -~-'-'......

( c )I

80 0

8 00

I I I I I0 2 0 0 4 0 0 6 0 0 8 0 0

Days s i nce Janu a r y 1 , 1987Figure 5. Time series of the count squared of a) space, b)White Sands, and c) the S onora De sert for individual VISSRsolar detectors.t h e s ch ema d es c r i b ed t w o s ec t i o n s ea r l i e r . ) O n l y d a t aob ta ined a t 19 :01 GMT are p resen ted , and they are aver -ages over the t a rge t s (a l l da ta f rom a g iven de tec to r a reaveraged). Short- term fluctuat ions in the count squaredof space are l a rge (up to 300) and er ra t i c . No seasonalt r en d i s d e t ec t ed . O n e o f t h e d e t ec t o r s ( l ab e l ed 1 i nFig . 5a) exh ib i t s much h igher changes than the o thers .


11/21


12/21

] 0 6 Frouin and Simpson

3 0 0 . 0

2 5 0 . 0

2 0 0 . 0

~ E 1 5 0 . 0

8c. ~ 1 0 0 . 0 f5 0 . 0 W h i t e S a n d s 1 9 : 01 G M TS o n o r a D e s e r t , 1 9 : 0 1 G M T

0 .0 2 0 0 4 0 0 6 0 0d a y s s i n c e J a n . 1 , 1 9 8 7

800

Figure 7. Time series of simulated top-of-atmosphere radi-ance o f Whi te Sands ( ) and Sonora Deser t ( - - - - - ) .

0 . 8 0

0 . 60

80 . 4 0

0 . 2 0

0 . 00

- - W h it e S a nd s, 1 9 : 0 1 G M TS o n o r a D e s e r t , !9 ; 0 1 G M T

2 00 4 00 - - 6 00 8 00d a y s s i n c e J a n . l , 1 9 8 7

Figure 8. Time series of simulated top-of-atmosphere reflec-tance o f Whi te Sands ( ) and Sonora Deser t ( - - - - - ) .

3 . 0 O e - 0 5

2 . 5 0 e - 0 5

2 . 0 0 e - 0 5

1 . 5 0 e - 0 5

1 . 0 0 e - 0 5 O

-- Sens or1Sensor 2Sensor 3- Sens orSensor5. . . . . . . i ,Se~or 7

2 0 0 4 0 0 6 0 0 8 0 0d a y s s i n c e J a n . 1 , 1 9 8 7

Figure 9. Reflectance calibration coefficients for eachVISSR solar detector.

f l u c tu a t i o n s a r e n o t co r r e l a t ed w i t h t h e Su n zen i t h an g le .O v e r a p e r i o d o f ab o u t 1 5 0 d ay s s t a rt in g a ro u n d d ay250 , a~ d rop s by 1 . 0x 10 -5 (40%). The n a i increase smo re p ro g re s s i v e l y u n t i l d ay 6 0 0 , w h en s o me r eco v e ry( l o w er a i v a l u e s ) o ccu r s ag a i n . Su p e r i mp o s ed o n t h e s el o w f r eq u en cy f l u c t u a t i o n s a r e h i g h f r eq u en cy s p i k esw h o s e a m p l i tu d e m a y b e o f t h e s a m e m a g n i tu d e a st h e l o n g - t e rm ch an g e . D u r i n g t h e s e p e r i o d s o f ab ru p tchange, one, several , or al l the detectors may be affected.The average ca l ib ra t ion coef f i c ien t s (before and af t e rdestr iping) exhibi t s imilar tem poral variabi li ty (not show nh e re ) . T h i s i s ex p ec t ed b ecau s e t h e av e rag ed co u n t ss q u a red b e fo re an d a f t e r d e s t r i p i n g a r e s i mi l a r ( s eeabove). T he same type o f h igh and low f requ ency changeso b t a i n ed fo r in d i v id u a l d e t ec t o r s a l s o is o b t a i n ed w h ent h e d e t ec t o r s a r e n o t co n s i d e r ed s ep a ra t e l y . T h u s , av e r -ag ing counts squared does no t smooth s ign i f i can t ly thevar iab i l i ty in th e ca l ib ra t ion coef f i c ien t o f ind iv iduald e t ec t o r s .D I S C U S S I O NT h e d i f f e r en ces b e t w een ca l i b ra t i on co e f f ic i en t s o f in d i-v i d u a l d e t ec t o r s mi g h t b e l i n k ed t o t h e n o rma l i za t i o np r o c e d u r e a p p l i e d b y N O A A N E S D I S o r m i g h t b e t h eresu l t o f unce r ta in t i es in the ca l ib ra tion . F or ins tance ,each V ISSR d e t ec t o r d o es n o t v i ew t h e s ame t a rg e t ,an d s p a t i a l h e t e ro g en e i t y i n t h e W h i t e San d s o r So n o raD ese rt reflectan ce ma y t ranslate into s ignificant ly differe ntca l ib ra t ion coef f i c ien t s . In add i t ion , the de tec to rs don o t h av e ex ac t l y t h e s am e s p ec t r a l r e s p o n s e . E x ami n i n gthe c oun t squa red o f space (Fig. 5a) sugges t s tha t nor -ma l i za ti o n o f t h e d a t a d o es n o t ex p l a in t h e o b s e rv edvar iab i l i ty and , therefore , tha t the f luc tua t ions in theca l ib ra t ion co ef f i c ien t s a re the r esu l t o f chang es in in-s t rument behav ior . I t i s poss ib le , however , tha t thev a r i ab il i ty i n t h e co u n t s q u a red o f s p ace ( an d , t h e r e fo r e ,p a r t o f t h e v a r i ab i li t y i n t h e c o u n t s q u a red o f t h e ea r t htarge t s ) i s due to res idual e r ro rs associa ted wi th theN O A A o p e ra t io n a l n o rma l i za t io n p ro ced u re , w h i ch isi mp e r f ec t , o r s i mp l y t o d e t ec t o r n o i s e ( r ememb er i nF i g . 5 a t h a t t h e d a t a a r e 6 -b i t p r ec i s i o n , t h o u g h co d edon a 8-bi t scale) .T o ex ami n e t h is p o i n t f u r t h e r , t h e u n t am p ered 1 8 4 8G M T " W e d n e s d a y " d a t a s e t is c o m p a r e d t o t h e p r o c e s s e d(d es t r i p ed b y N O A A ) 1 83 1 G M T an d 1 9 0 1 G M T d a ta -s e ts . T h e t i m e s e r i e s o f s p ace , W h i t e San d s, an d t h eSo n o ra D es e r t a r e d i s p l ay ed i n F i g u re s 1 0 , 1 1 , an d 1 2 ,r e s p ec t i v e ly . T h e co u n t s s q u a red o f s p ace a t 1 8 3 1 G M Tand 1901 GMT (Figs . 10a and 10c) a re s imi lar , un l iket h e co u n t s q u a red o f s p ace a t 1 8 4 8 G M T (F ig . 1 0 b ) . T h eam p l i t u d e o f t h e f l u c t u a ti o n s an d t h e i r e r r a t ic p a t t e rn ,h o w ev e r , a r e a l i k e fo r a l l t h e d a t a s e t s ( u n t amp ered an dd es t r i p ed b y N O A A ) , t h o u g h t h e amp l i t u d e o f t h e 1 8 4 8GM T f luc tua t ions i s def in i t e ly h igher . Th e ano ma lous lyh i gh c o u n t s q u a red o f s p ace a ro u n d d ay 6 4 0 in t h e


13/21

Radiometric Calibration o f GO ES-7 Solar Channels 1 0 7

-

00

c-

O0

t-

o0

400

300

200

100

040 0

300

200

I 0

0400

300

2 0 0

100

I I I I

W e d n e s d a y Data, 18:31

(a )I

I I I

S e n s m " IS p a c e

' , V " ~ - . \ _ i ; - ',......~!, i ~, - .' ,.

............ S e n s o r 2

. . . . S e n ~ x 3- - - S 4 m s o r 4.... Sensors- - Sensor6........... ~ 0sor;

200 400 600I I I I I I IW ednesday D a ta , 18 :48S p a c e

( b )I I I ~ ' l I I I200 400 600I I t I 1 I I

W e d n e s d a y Data, 19:01S p a c e

( c )I

800

200 400 600Days since January 1, 1987

800

00 800

Figure 10. T i m e s e r i e s o f t h e c o u n t s q u a r e d o f s p a c e f o r i n -d i v i d u al d e t e c t o r s a t a ) 1 8 31 G M T , b ) 1 8 4 8 G M T , a n d c )1 9 0 1 G M T .

1 8 4 8 G M T d a t a s e t i s n o t p r e s e n t i n t h e o t h e r d a t a s e t s ,p r o v i d i n g f u r t h e r e v i d e n c e t h a t t h e c o u n t s q u a r e d v a r i -a b i l it y i n F i g u r e s 1 0 a a n d 1 0 c i s l i n k e d t o t h e n o r m a l i z a -t i o n p r o c e d u r e . O n e s h o u l d a d d t h a t, a p a r t f r o m d e t e c -t o r 1, t h e n o r m a l i z a t i o n p r o c e d u r e g e n e r a l l y s u c c e e d si n e q u a l i z i n g t h e d e t e c t o r s t o b e l o w t h e 1 0 0 c o u n t

40000

30000

Nr- 20000O

10000

I I I I I I I

4 0 0 o 0

3 0 0 0 0

. . 200000

10000

40000

30000

r-~ 2ooooO10000

......... Sen~2 I "% .v-~ J '-~.- - - S e n s o r 5- - S e n s o r 6. . . . . . S e n s o r 7. . . . S e n s o r I I

( a )I I20 0I I

Wednesday Data , 18:31Whi te S ands00 800

" - - . . . .

" d

I I I I I400 600I I 1 I I

r

'g,< ,y ,. ,...,,

(b )I

Wednesday Data , 18 :48Whi te S andsI I I I I t200 400 600I I I I I I

. . - ~ - " ~ ' " . . . .

"~ ~t , il '"

( c )I

Wednesday Data , 19:01Whi te S ands

800

0 I t I I I I0 200 400 600 800Days since January 1, 1987

Figure 11. S a m e a s F i g u r e 1 0, b u t c o u n t s q u a r e d o f W h i t eS a n d s .


14/21

] 08 Frouinand Simpson

2 0 0 0 0 i

1 5 0 0 0

1 0 0 0 00

5 0 0 0

0 02 0 0 0 0

1 5 0 0 0

t - 1 0 0 0 00

5 0 0 0

0 02 0 0 0 0

1 5 0 0 0

::1 0 0 0 00

0

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I I I I I I I

iI L. .i - - : ...........

~ .........I ~ / " ~ ,- - S e n s o r I ~ ".../,',,(~ x l........... - :. . . . s e n s o ~ 3- - - , ~ m l ~ ' 4- - - S e n s o r 5- - s e n ~ r 6. . . . . . . . . . . . S e n s o r 7. . . . S e n s o r 8( a )

I

W e d n e s d a y D a t a , 1 8 : 3 1S o n o r a D e s e r t

I I I I I I2 0 0 4 0 0 6 0 0

-

...........

( b )I

W e d n e s d a y D a t a , 1 8 : 4 8S o n o r a D e s e r t

I I I t I I2 0 0 4 0 0 6 0 0

I I I I I

' " , , . .. .. ~ , ~ t , .

W e d n e s d a y D a t a , 1 9 : 0 1( c ) S o n o r a Desert

I I I I I I I2 0 0 4 0 0 6 0 0Da ys since January 1, 1987

8 0 0

8 0 0

8 0 0

Figure 12. Same a s F igure 10 , bu t co un t squa red o f t he So-nora Dese r t .

3 . 5 x 1 0 " 5

3 . 0 x 1 0 - 5c-(D

~ 2 . 5 x 1 0 sOe-. ~ . 2 . 0 x 1 0 - 5

r r1 . 5 1 0 s

1 . 0 x 1 0 .53 . 5 x l 0 . 5

3 . 0 x l 0 . 5E2 . 5 x 1 0 - 5

0(D2 . 0 x 1 0 "5

n -1 . 5 x 1 0 " 5

1 . 0 x 1 0 4 03 . 5 x 1 0 " 5

3 . 0 x 1 0 - 5E.Q )~E~ 2 . 5 x 1 0 5O-, ' ~ 2 . 0 x l 0 - So

n -1 . 5 x 1 0 - 5

I i I I I I I

W e d n e s d a y D a t a , 1 8 : 3 1 - - se ,.,o ,,. . . . . . . Sen$or 2. . . . s e m i " 3- - - - s e t n ~ t 4- - - s e l ' t ~ r 5- - S e r t t ~ 6. . . . . . . . . . sensor 7/ ; ! t , . . . . Seneor 8

' ~ . . . . ,~

I I I2 0 0 4 0 0

I I6 0 0i

W e d n e s d a yData, 18 :48

( / 'i

- f / ; , ' ,~ '> , . . . - . ' ,Y.." A'.'.I ~ " . - - . . . . . : - ~ " , : ~,

I I I I I I2 0 0 4 0 0 6 0 0

I I I I I I

W e d n e s d ay D at a , 19 :01

~L

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.v

8 0 0

8 0 0

1 . 0 x 1 0 - 5 I I I I I I I0 2 0 0 4 0 0 6 0 0 8 0 0Days s ince January 1 , 1987

Figure 13. Reflec tance ca l ibra t ion coeff ic ients for eachVISSR solar de tec tor a t a ) 1831 GMT, b) 1848 GMT, and c)1901 GMT.

s q u a r e d l e v e l s ( l e s s t h a n 3 c o u n t s o n t h e 6 b i t s c a l e ) ,w h i c h i s t h e t y p i c a l a m p l i t u d e o f t h e 1 8 4 8 G M T f l u ct u a -t io n s o f e a c h d e t e c t o r e x c e p t d e t e c t o r 1 ( a g o o d m e a s u r eo f t h e d e t e c t o r n o i s e) . M o r e o v e r , c o m p a r i n g t h e c o u n t ss q u a r e d o f s p a c e o f t h e v a r i o u s d a t a s e t s ( n o t s h o w nh e r e ) r e v e a ls t h a t d e t e c t o r 6 m a y h a v e b e e n s e l e c t eda s t h e r e f e r e n c e c h a n n e l i n th e n o r m a l i za t i o n p r o c e d u r e ,a t l e a s t a f t e r d a y 4 2 0 .

T h e c o u n t s s q u a r e d o f W h i t e S a n d s a n d t h e S o n o r aD e s e r t ( F i g s . 1 1 an d 1 2 ) a t 1 8 4 8 G M T a r e v e r y d is t i n c tf r o m t h o s e a t t h e o t h e r t i m e s . T h e d i f f e r e n c e s a m o n gd e t e c t o r s a r e m u c h l a r g e r i n t h e u n t a m p e r e d d a t a s e t ,i n d i c a t i n g t h a t s e v e r e s t r i p e s c h a r a c t e r i z e t h e u n s t r e t c h e d" W e d n e s d a y " 1 8 4 8 G M T d a t a t r a n s m i t t e d t o t h e N O A AC D A f a c i li ty . T h e c o n s p i c u o u s p e a k o f h i g h c o u n t ss q u a r e d i n t h e 1 8 3 1 G M T a n d 1 9 3 1 G M T S o n o r a D e s e r t


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Radiometric Calibration o f GO ES-7 Solar Channels 109

datasets around day 410, less visible in the respect ive 3-5x10sWhite Sands datasets because of the higher brightnessof Whi te Sands, is not present in the 1848 GMT datasets 3.0xl0-sand must be an artifact of the normalization procedureapplied by NOAA NESDIS. 2.5x10 sThus, one may conclude that the low 1831 GMT and o1901 GMT reflectance calibration coefficients around Ot--da y 410 (Figs. 13a and 13c, respectively) are not due ~ 2,0x10 5to inst rument changes, but are the result of NOAA's =normalization procedure. In fact, around day 410 the n- 1.5x10 51848 GMT calibration coefficients are relatively higherthan those at 390 and 430 (Fig. 13b). Because theprominen t stripes in the untamper ed 1848 GMT dataset 1.0xlo50yie ld significantly higher counts squared after averaging 3.5x10-5striped data than after averaging destriped data, theaverage calibration coefficients are higher by a few 3.0x10 5percent when using destri ped data (Fig. 14). The differ- Eences, however, are much smaller than the fluctuations ._5over the study period. ~ 2.~x105

In Figure 15 the average reflectance calibration o(.}coefficients obta ined for the 1831 GMT, 1901 GMT, = 2.0x10 s1931 GMT, and 2001 GMT datasets are compared to ~values reported in the literature. During the period ofinterest, the calibration data available are the ISCCP 1-sx15calibration results reported by Rossow et al. (1992),those of Whi tlock et al. (1994) obtained from ground- 1.0x10-5based measurements at White Sands, and those of Abel 3.sxl0.set al. (1992) obta ined from ER-2 aircraft measurementsover White Sands. The average calibration coefficientsobtained by averaging the count-squared of destriped ~ 3xlsdata are similar for the 1831 GMT, 1901 GMT, 1931 "~GMT, and 2001 GMT datasets , though some occasional ~ 2.sxl0-sdiscrepancies do exist (e.g., around days 220, 445, 500 oetc.). The ISCCP values are generally lower than those =o_,~ 2.0x10 5of the prese nt study by about 15%, but in some in- ostances the differences are as large as 20%. The Whit-lock et al. (1994) and Abel et al. (1992) values, obtained 1"5x10"5around day 670, are generally closer to our values, butsometimes differ by about + 5-10%. Variabili ty in the 1.Oxl0-SWhit lock et al. (1994) coefficient is high, about 20% 0over a 50-day period, but corresponds to the variabilityin our coefficients. Our findings seem to confirm theresults of Whitlock et al. (1994), who reported evenlarger discrepancies between their coefficients and theISCCP coefficients (lower ISCCP values) after the timeperiod analyzed here.

The accuracy of the radiometric calibration is esti-mated to be on the order of + 8% when consideringtypical uncertainties on aerosol type, visibility, watervapor and ozone amounts, and surface reflectance (dueto spatial heterogeneity, soil moisture variations, etc.)(see Frouin and Gautier, 1987). The most penalizinguncertainties are those on surface reflectance. Becauseeach VISSR detector does not view the same spot on

I I I I

Wednesday Data, 18:31I I I

(a )I

- - S t r i p e d A v e r a g e. . . . D e s t t i p e d Average

I I I I I t200 400 600

I I I i I I

Wednesday D ata, 18:48

( b )I I I I I I I

200 400 600i i I l I I I

Wednesday Data, 19:01

( c )I I I I I t

2 0 0 4 0 0 6 0 0Days s ince January 1 , 1987

800

800

8 00

Figure 14. Average reflectance calibration coefficients at a)1831 GMT, b) 1848 GMT, and c) 1901 GMT.

the earth's surface and because spatial heterogeneitymay be significant, a large part of the differences be-tween calibration coefficients of individual detectorsmay not be actual, but the result of surface reflectancevariations. The problem is less dramatic with aerosolvariability, because the effects are smaller (aerosol load-ing is low). The low frequency fluctuations in the averagecalibrat ion coefficients (Fig. 15), however , are defin itelyabove the uncertainty level, and the rather systematic


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] ] 0 Frouin and Simpson

2 , 5 e - 0 5

2 . 0 e - 0 5"0o8

" ~ 1 . 5 e - 0 5

1 . 0 e - 0 5

Ii, !

i

1 8 : 3 1 \1 9 : 0 1

- 19 : 31- - - 2 0 : 0 1

I S C C P ( R o s s o w e t a l . , 1 99 2 )O N A S N L A R C[ ] N A S N G S F C E R - 2

r I '

/ < : / .2 0 0 4 0 0 6 0 0

d a y s s i n c e Ja n . l , 1 9 8 780 0

Figure 15. Reflectance calibration coeffi

radiometric calibration of goe s - 7

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