Scale Effects and Correction for Land Surface Albedo in Rugged Terrain

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1 Proceedng of the 8th Interntonl ympoum on ptl Accurcy Aement n turl Reource nd Enronmentl cence hngh P. R. Chn June pp cle Effect nd Correcton for Lnd urfce Albedo n Rugged Terrn Jngung Wen 3 + Qng Lu Qnhuo Lu Qng Xo 2 nd Xowen L tte Key Lbortory of Remote enng cence Jontly ponored by the Inttute of Remote enng Applcton of Chnee Acdemy of cence nd Bejng orml Unerty Bejng 000 Chn 2 Bejng Reerch Inttute of Urnum Geology Bejng Chn 3 Grdute chool of the Chnee Acdemy of cence Bejng Chn Abtrct. It well nown tht nfluence of grphy mut be ccounted when ung hgh-reoluton remote enng dt to etmte lnd urfce reflectnce or lbedo n rugged terrn. Howeer when moderte or low-reoluton tellte remote enng dt re ued the grphc effect on lbedo clculton re generlly condered gnorble becue the lope of the low-reoluton pxel re uully mll. A potentl problem tht grphc effect wthn one low-reoluton pxel he been omtted whch my cue error n lbedo etmton. Th problem come from the cle effect n lnd urfce lbedo. Th pper netgte n theory whether there cle effect n lnd urfce lbedo when upclng hghreoluton urfce lbedo nto low-reoluton urfce lbedo n rugged terrn. Bed on th nly we preent the method to upcle hgh-reoluton urfce lbedo to core reoluton nd fnlly dere correcton fctor for lnd urfce lbedo dered from low-reoluton remote enng dt. The method put forwrd n th pper ueful nd effecte method for cle correcton of lnd urfce lbedo; nd t lo good method to clculte lbedo from low-reoluton remote enng dt n rugged terrn. Keyword: lbedo cle effect rugged terrn grphc effect. Introducton Lnd urfce lbedo defned the rto of the reflected olr rdton t the lnd urfce to the totl ncomng olr rdnce prmry controllng fctor for urfce energy blnce nd thu crtcl prmeter ffectng the erth clmte Dcnon 995. It chrcterze the rdte property of the urfce nd dre the mportnt proce of photoynthe epotrnprton nd urfce energy budget n locl regon nd globl cle. Epeclly the lrge regon nd globl urfce lbedo lwy mong the dered product/dt et for recent moderte to low reoluton tellte mon uch MODIchf et l MIRDnner et l. 998 POLDERLeroy et l nd n the pt AVHRRCzr et l. 999 etc. The trdtonl method of obtnng lnd urfce lbedo from feld meurement. It lnd urfce lbedo of ground pont cle nd necery dt ued to ldte the low reoluton lnd urfce lbedo product. Howeer t not good wy to ldte the low reoluton lbedo product drectly becue of the mmtchng of the pont cle nd low reoluton pxel cle of lbedo. Upclng from ground pont meurement to the low reoluton pxel ung hgh reoluton remote enng dt necery nd crtcl teplng.l. et l In flt re wth homogeneou urfce nd under the umpton tht the tmophere horzontlly homogeneou the feld meurement t one locton or the hgh reoluton dt wthn n mll regon cn be extrpolted oer the whole re. Mny netgton he been conducted to mutully ldte the dfferent reoluton lbedo product Lng.L. et l Wng J.D. et l Jo Z.T. et l But th extrpolton no longer ld when the urfce rugged. clng + Correpondng uthor. Tel.: E-ml ddre: hore_wjg@hotml.com. IB: IB3:

2 the pont cle lbedo or hgh-reoluton lbedo product to the low reoluton n complex terrn tough problem becue of the trong grphc effect. Mny lterture he hown tht the nfluence of grphy on lbedo clculton hould be ten nto ccount n hgh reoluton remote enng dt uch Lndt-5 Themtc Mpper TM Wng J. et l Hnen L.B. et l POT Hgh Reoluton Vble HRV hepherd J. D. et l.2003 nd n low reoluton remote enng dt uch Adnced Very Hgh Reoluton Rdometer AVHRRChlr J. et l.2004 or Moderte Reoluton Imgng pectrrdometer MODIWng K.C. et l Topogrphc effect on remote enng dt depend on t reoluton. Hgh reoluton remote enng dt emphze pxel-pecfc grphc effect on locl rdnce lope/pect relted llumnton dfference reflecton from djcent terrn hdowng whle low reoluton remote enng dt le pxel-pecfc grphc effect becue the grphc lope uully mll. Though pxel-pecfc grphc effect mll nd generlly condered to be gnorble ub-pxel grphy mnly hdow wll cue BRDF-le effect ntenely on the reultnt low reoluton remote enng dt. Thu the low reoluton lbedo clculted from low reoluton prmeter low reoluton reflectnce low reoluton DEM etc. wll dfferent from erge lbedo from hgh reoluton prmeter where we hould remoe the grphc effect or the ground pont meurement. Thee dfference come from the cle effect n upclng lnd urfce lbedo n complex terrn. The objecte of th pper to prode fctor for lbedo cle effect correcton nd method for upclng the hgh reoluton lbedo to low reoluton. We wll trt by dcung low reoluton lbedo clculton n complex terrn to llutrte why t h the cle effect. Then we wll ntroduce fctor for remong the cle effect nd ge n effecte method to clculte low reoluton lbedo. Method error nly nd precon eleton wll be gen n detl by ung the multed dt to ldte the method performnce. 2. cle effect of lbedo n complex terrn Under the umpton of no grphc effect n the pxel cle lnd urfce lbedo cn be obtned by ntegrtng the pxel urfce Bdrectonl reflectnce dtrbuton functon BRDF or drectonl reflectnce. If we ume the lnd urfce BRDF nown then the blc-y lbedo one ntegrted oer ll the ew ngle nd the whte-y lbedo one ntegrted oer ll the ncdent ngle nd ew ngle. The fnl lbedo een from lterture n the form of lner combnton of thee two nd of lbedo. It obou tht the blc-y lbedo h ntene grphc effect becue t depend on olr ncdent ngle nd cue the lbedo cle problem. In th pper we focu on the cle effect of the blc-y lbedo n the complex terrn. Two dfferent ptl cle reflectnce re umed n complex terrn hgh reoluton drectonl reflectnce γ ; nd low reoluton drectonl reflectnce β. It true tht β ncluded n mny γ φ whch umed to be ndependent on grphc effect. The term of β re olr zenth ngle olr zmuth ngle enor zenth ngle enor zmuth ngle grphc lope nd pect repectely. Integrtng thee two reoluton reflectnce we cn get the mcrore lbedo nd the pprent lbedo grphc effect lbedo b pp. When ergng ll the mcrore lbedo wthn one pxel by t re proporton we cn get the ctul lbedo. In ctully the pprent lbedo hould be cloe to the ctul lbedo due to the homogou b 0 mcrore nd no grphc effect o there no ny cle effect n lbedo clculton. Otherwe we hould conder ther dfference whch cued by the cle effect nd try to remoe thee effect to obtn more ccurte low reoluton lbedo n complex terrn. The low reoluton lbedo cle effect cn be expreed : f DEM φ φ b0 pp f DEM the cle effect of low reoluton lbedo clculton n complex terrn. In order to emphze the grphc effect n lbedo cle effect we umed tht the lnd type the me wthn the low reoluton pxel nd only the ub-pxel grphy ffect the pxel reflectnce. 68

3 2.. cle effect of pprent lbedo nd ctul lbedo Accordng to codemu codemu F. et l. 977 when the tmopherc effect re condered to be gnorble the pxel drectonl reflectnce β : co γ φ ; φ co 2 β co co It cler tht th reflectnce nmed grphc effect drectonl reflectnce ffected by the ub-pxel grphy. In the boe equton the number of the mcrore tht ble n both ncdent nd ew drecton wthn the low reoluton pxel. Prmeter ndcte whether the mcrore un lt whle ndcte whether the mcrore ble by enor. They re et to one for unlt or ble mcrore nd et to zero otherwe. tnd for the re of the th mcrore φ re the olr relte ncdent zenth ngle nd zmuth ngle repectely nd φ re the enor relte ew zenth ngle nd zmuth ngle repectely whch cn be expreed : co co co + n n co β 3. co co co + n n co β 3.b In prctce β cn be MODI or AVHRR low reoluton reflectnce when one BRDF model e.g. ernel dre model ued wthout conderng the grphc effect. Integrtng th reflectnce oer ll the enor ew ngle n hempherc pce grphc effect lbedo or pprent lbedo cn be wrtten : 2ππ / 2 pp β co n d d 4 π 0 0 Actul lbedo generlly ued n order to ecern the pprent lbedo whch ffected by the ub-pxel grphy. If the mrcore h no grphc effect t men tht the DEM lope nd pect zero the equton 4 cn be rewrtten : d d 5. 2ππ / 2 b0 γ ; co n π b b where the re of the pxel nd the mcrore lbedo nmed ctul lbedo. It obou tht b the ctul lbedo the um of ll the mcrore lbedo weghted by the rto of mcrore re to pxel re. We cn conclude tht n the ctul bledo there no cle effect cued by grphy cle effect correcton of low reoluton grphc effect lbedo One low reoluton pxel nclude mny lope mcrore whch he dfferent lope nd pect ngle. And t drectonl reflectnce would be ffected by thee mcrore nd ther hdow jut le equton 2 hown. o the model nd method for pxel grphc effect remong my not be utble becue of only grphc effect on pxel lope nd between pxel. A model conderng the ub-pxel grphc effect need to be deeloped to obtn the ctul low reoluton drectonl reflectnce nd t lbedo. Becue the rdnce enterng the enor mnly controlled by the relte olr ncdent ngle nd relte enor ew ngle of the mcrore wthn one low reoluton pxel dfferent mcrore n the enor feld of ew wll contrbute dfferent rdnce to the enor. In order to decrbe the grphc effect on the low reoluton drectonl reflectnce the equlent pxel rble put forwrd to expln the ce tht the mcrore grphy n the enor feld of ew red wth dfferent enor ew ngle. An equlent mooth urfce drectonl reflectnce ntroduced whch h no ubpxel effect wth the equlent effecte re A e nd t equlent relte olr ncdent ngle t nd equlent relte enor ew ngle t. The re of enor ewed cn be expreed : A e co co 6 t 69

4 70 o the equlent relte enor ew ngle cn be wrtten : t co co 7. Jut le the equlent relte enor ew ngle the equlent relte olr ncdent ngle cn be wrtten n the me form: t co co 7.b The rdte ntenty t I from enor nterpreted t come from n equlent effecte e A wth relte olr ncdent ngle t relte enor ew ngle t nd the urfce drectonl reflectnce tht : t t t E I co co π 8 At the me tme the rdte ntenty enter the enor cn be rewrte the functon of pprent low reoluton drectonl reflectnce: t E I co co β π 9 Combnng equton 8 nd equton 9 we wll wrte the equlent mooth urfce drectonl reflectnce the product of n pprent low reoluton drectonl reflectnce β : t t co co co co φ β 0 The term t t co co co co only relted wth DEM nd geometry of un nd enor. And we cn get the cle effect remong fctor: t t DEM T co co co co Combnng wth equton 6 when ll the mcrore urfce wthn low reoluton pxel re both unlt nd ewed the equton 0 cn be rewrten : co co t β φ 2 It lo n equton for correctng the grphc effect on the pecfc pxel. And the o clled corrected lbedo fter cle effect remong cn be wrtten : ππ β π / 0 n co bn d d DEM T 3 Th corrected lbedo n theory equl to ctul lbedo becue the urfce homogenou nd there no grphc effect Error n low reoluton lbedo clculton nd cle effect remong Followng equton 4 3 nd 5.b we cn obtn the dfference between the pprent lbedo the corrected lbedo nd the ctul lbedo. The low reoluton lbedo depend on the mrcrore grphy nd the low reoluton reflectnce nd th lo the ce for the error of low reoluton lbedo. In order to llete the nfluence of the bolute lue on the reult of th nly we dopt the relte low reoluton lbedo error:

5 dp 0 r pp b0 dp 0 r 00% b0 3 bn b0 dn 0 r 00% 4 b0 denote the relte error n lbedo clculton cued by ub-pxel grphy. dn 0 r denote the relte error n lbedo clculton wth ub-pxel grphc effect remong. 3. Dt ne DEM were generted wth Gun heght dtrbuton to prode rton roughne. The DEM grd cell nd men eleton umed to be unt the tndrd error of eleton 0.25 unt. By multplyng rel dtnce n the numercl multon the rel reoluton of grd cell nd the DEM reoluton n eleton cn be multed. Through pproprte exggerton n ertcl eleton but fxng the grd cell ze the DEM wth dfferent lope cn be gotten. For the experment preented here the rel dtnce 30 meter nd lue of exggerton n ertcl eleton 0 nd 20 repectely. We lo ppled Gun moothng flter for the Gun heght feld nd normlzed the reultnt DEM to ge the requred roughne tttc. Flter of extent 3 nd 5 unt were ppled. Fgure multed DEM wth Gun heght dtrbuton Ech DEM w of grd cell. Howeer n the followng experment only the centrl prt of the boe DEM ued to multe low reoluton pxel due to the mbguou blocng of the mcrore n the edge of DEM. The reoluton of the pxel 800 meter becue the multed DEM grd cell 30 meter. The tttc erge lope lted n tble. flter 3 5 Men eleton meter Tb DEM men eleton nd tttc lope Exggerton Exggerton0 Exggerton20 tttc lope Men eleton tttc lope Men eleton degree meter degree meter tttc lope degree The lmbertn reflectnce of 0.3 ued for the mcrore grd cell. Tht we get the ctul 7

6 reflectnce nd the ctul bedo of the low reoluton 0.3.Y 4. Reult nd dcuon 4.. Relte error of grphc effect for drectonl reflectnce Aume the olr zmuth ngle 50 nd the olr zenth ngle nd 60 repectely bed on the lmbertn mcrore reflectnce nd the multed DEM nd ung equton 2 we wll obtn the dfferent ub-pxel grphc effect drectonl reflectnce. Fgure 2 how the relte low reoluton reflectnce error whch ffected by ub-pxel grphy n the un prncple plne oer the nd 37.7 tttc lope repectely. We cn fnd tht the hgher the tttc lope the hgher the relte low reoluton reflectnce error nd the more the effect of the ub-pxel grphy re. Fgure 2 how tht the error re not more thn 0.5% wthn the enor ew ngle from -80 to 80 under the condton of the low tttc lope. When the tttc lope ncree jut fgure 2b 2c nd 2d how there bg dfference between the pprent reflectnce nd the ctul reflectnce nd the error re red ntenely. Fgure 2 low reoluton relte reflectnce error n dfferent tttc lope: tttc lope.33 b: tttc lope 2.84 c: tttc lope d: tttc lope Equton 9 ntroduced cle effect remong fctor whch only relted wth hgh reoluton DEM. Th fctor ge n effecte method to remoe the cle effect for clcultng the low reoluton reflectnce nd lbedo n complex terrn. Compred wth fgure 2 fgure 3 how the low relte reflectnce error of cle effect remong reult for reflectnce. It obou tht there re the lowet relte reflectnce error n the low enor ew ngle n the un prncple plne oer ll tttc lope nd the error re not more thn 5%. Wth the ncree of the enor ew ngle the error re not more thn 20% except thoe error occurred t the hgher tttc lope nd the olr zenth ngle jut le the 60 olr zenth ngle n fgure 3c nd the 45 nd 60 olr zenth ngle n fgure 3d relte hgh reflectnce error would be found. In fgure 3 we lo hould note tht the relte reflectnce error wll be low when the olr zenth low from 0 to 0 n ll dfferent tttc lope nd the error re not more thn 0%. 72

7 Fgure 3 Corrected low reoluton relte reflectnce error n dfferent tttc lope: tttc lope.33 b: tttc lope 2.84 c: tttc lope d: tttc lope Comprng wth the relte reflectnce error of pprent reflectnce the relte reflectnce error re decreed whch how the low reoluton reflectnce more greement wth ctul reflectnce Relte error of lbedo cle effect correcton n dfferent tttc lope o f the pprent reflectnce ntegrted for the low reoluton lbedo clculton the lbedo pprent lbedo nd h the cle effect. We denote the pprent lbedo * jut fgure 4 how. Fgure 4 how the pprent lbedo red wth the tttc lope t would be hrp decreed wth the ncree of the tttc lope. Fgure 4b how the pprent lbedo relte error compred wth the ctul lbedo. The error re lttle red n relte flt re nd t lue mll. Wth the tttc lope ncreed the hgher the tttc lope the lower the pprent lbedo. The error cn be reched 33% n bout 40 tttc lope. b Fgure 4 Compron between the pprent lbedo nd the corrected lbedo n dfferent tttc lope We lo clculted the corrected lbedo ung the reflectnce wth cle effect remong by ung the fctor. The corrected lbedo w denoted. The ub-pxel grphc effect he been remoed nd the corrected lbedo cloe to 0.3 whch equl to ctul lbedo epeclly when the tttc lope le thn 20 degree nd the relte lbedo error re ery low. Fgure 4 how the relte lbedo error wth cle effect remong t much le thn pprent lbedo. The relte lbedo error no more thn 5%. o the method preented n th pper cn remoe the ub-pxel effect nd cle effect n the low reoluton 73

8 reflectnce nd lbedo clculton Relte error of lbedo cle effect correcton n dfferent ptl reoluton A DEM rndom elected n DEM et whch degree of tttc lope. From the center prt of th DEM the nd grd cell re ued to multe dfferent ptl reoluton pxel whch men tht the pxel reoluton 600 meter200 meter 800 meter nd 2400 meter repectely. Followng equton 4 3 nd 5.b we lo clculted the pprent lbedo ctul lbedo nd corrected lbedo wth the boe dfferent ptl cle. Fgure 5 how the pprent lbedo denoted * whch dfferent wth dfferent ptl cle n dfferent olr ncdent ngle. And we cn fnd the lower the pxel ptl reoluton the cloer the pprent lbedo nd ctul lbedo re. It men the grphc cle effect on lbedo become lower when the pxel ptl reoluton decree. The bolute error of lbedo chnged from more thn 0. n pxel reoluton of 600 meter to 0.06 n pxel reoluton of 2400 meter. Compred wth ctul lbedo t obou tht the pprent lbedo relte error hgh nd t cn be more thn 35% when pxel reoluton 600 meter. And wth the decreng of the pxel reoluton the lbedo relte error tll 20% n pxel reoluton of 2400 meter jut hown n fgure 5b. When the cle effect remong fctor ued the corrected lbedo denoted h le ubpxel grphc effect nd cle effect. The lbedo cloe to bout 0.3 of the ctul lbedo n dfferent ptl lbedo epeclly n the lower ptl reoluton. And the lbedo relte error low jut fgure 5b hown. And we cn fnd the relte error le thn 5% n dfferent ptl reoluton except when the olr ncdent ngle lrge. It how tht the cle effect remong fctor ued for clcultng the dfferent ptl reoluton lbedo effecte. 74 Fgure 5 Compron between the pprent lbedo nd the corrected lbedo n dfferent ptl reoluton 5. Concluon It true tht the lbedo clculton wll h cle effect when the urfce unhomogeneou ncludng the lnd urfce type unhomogeneou nd the grphy unhomogeneou. Th pper demontrte tht t necery to conder the grphc effect when clng lnd urfce lbedo n rugged re nd t preent method for cle correcton of lnd urfce lbedo. Becue of the ub-pxel grphc effect the low reoluton lbedo clled pprent lbedo nd clculted ung the hgh reoluton reflectnce h the cle effect. There lrge dfference between the pprent lbedo nd the ctul lbedo whch erged from mcrore lbedo. After ntroducng the cle effect remong fctor the corrected lbedo h le cle effect nd greement wth ctul lbedo. The method put forwrd n th pper ueful nd effecte method for cle trnformton of lnd urfce lbedo nd t lo good method to clculte lbedo from low-reoluton remote enng dt n rugged terrn. Although th method nlyzed nd ldted by multed DEM t hould perform well oer rety of rel DEM nd remote enng dt becue the method theoretcl b phycl nted of mple emprcl. In prctce the lbedo clculted ung the MODI or AVHRR low reoluton drectonl

9 reflectnce wthout conderng the ub-pxel grphc effect th pprent lbedo nd t wll be uffered the cle effect. o n the future the rel remote enng dt hould be ued to ldte the model performnce. 6. Acnowledgement Th wor w upported n prt by Chn pecl Fund for Mjor tte Bc Reerch Project O:2007CB74402 The Acton Pln of Wetern Deelopment of Chnee Acdemy of cence O:KZCX2-XB nd Chnee turl cence Foundton Project O: Reference [] R. E. Dcnon Lnd procee n clmte model. Remote enng Enronment : [2] C. chf F. Go A.H. trhler. et l. Frt opertonl BRDE Albedo nd ndr reflectnce product from MODI Remote enng of Enronment : [3] D. J. Dner J. C. Becert T. H. Relly et l. Mult-ngle mgng pectrordometer MIR ntrument decrpton nd experment oerew IEEE Trncton on Geocence nd Remote enng : [4] M. Leroy nd A.Lfermnn The POLDER ntrument onbord ADEO: centfc expectton nd frt reult. Ad. pce Re : [5] I. Czr G.Gutmn Mppng globl lnd urfce lbedo from OAA AVHRR Journl of Geophycl Reerch : [6].L.Lng H.L. Fng M. Chen et l. Vldtng MODI lnd urfce reflectnce nd lbedo product: method nd prelmnry reult. Remote enng of Enronment : [7] J.D. Wng Z.T. Jo F. Go et l. Vldton of MODI lbedo product by ung feld meurement nd rborne mult-ngulr remote enng oberton. Proceedng of IEEE Interntonl Geocence nd Remote enng ympoum Touloue Frnce 2003 [8] Z.T. Jo J.D. Wng F. Go et l. Intl Vldton of MODI Albedo product by ung feld meurement nd rborne muhngulr remote enng oberton. Journl of Remote enng : [9] J. Wng K. Whte G.J. Robnon Etmtng urfce net olr rdton by ue of Lndt-5 TM nd dgtl eleton model. Interntonl Journl of Remote enng [0] L. B. Hnen. Kmtrup nd B. Ulf Hnen Etmton of net hort-we rdton by the ue of remote enng nd dgtl eleton model- ce tudy of hgh rctc mountnou re Interntonl Journl of Remote enng : [] J. D. hepherd nd J. R. Dymond Correctng tellte mgery for the rnce of reflectnce nd llumnton wth grphy Interntonl Journl of Remote enng : [2] J.Chlr R. Ltfoc J. Chen et l. ytemtc correcton of AVHRR mge compote for temporl tude. Remote enng of Enronment : [3] K.C. Wng X. J. Zhou J.M. Lu et l. Etmtng urfce olr rdton oer complex terrn ung modertereoluton tellte enor dt. Interntonl Journl of Remote enng : [4] F. codemu J. Rchmond J. H et l. Geometrcl Conderton nd omenclture for Reflectnce B U Deprtment of Commerce Whngton D.C