Estimating Crop Albedo in the Application of a Physical Model Based on the Law of Energy Conservation and Spectral Invariants

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1 Remote Sen. 25, 7, ; oi:.339/75536 Atice OPEN ACCESS emote enin ISSN Etimatin Cop Abeo in te Appication of a Pyica Moe Bae on te Law of Eney Conevation an Specta Invaiant Jinjin Pen,2, Wenjie Fan,3, *, Xiu Xu,3,, Lizao Wan 4,, Qinuo Liu 2,5, *, Jvcai Li,3 an Pen Zao,3 Intitute of RS an GIS, Pekin Univeity, Beijin 87, Cina; E-Mai: pey@63.com (J.P.); xxu@26.com (X.X.); 423@pku.eu.cn (J.L.); zaopenowen@26.com (P.Z.) 2 State Key Laboatoy of Remote Senin Science, jointy ponoe by Intitute of Remote Senin an Diita Eat of CAS an Beijin Noma Univeity, Beijin, Cina; 3 Te Beijin Key Laboatoy of Spatia Infomation Inteation an 3S Appication, Beijin 87, Cina 4 Beijin Reeac Intitute of Automation fo Maciney Inuty, Beijin 2, Cina; E-Mai: wz22@ina.com 5 Joint Cente fo Goba Cane Stuie, Beijin 875, Cina Tee auto contibute equay to ti wok. * Auto to wom coeponence ou be aee; E-Mai: fanwj@pku.eu.cn (W.F.); iuq@ai.ac.cn (Q.L.); Te.: (W.F.). Acaemic Eito: Xin Li, Yuei-An Liou, Rica Müe an Paa S. Tenkabai Receive: 4 Auut 25 / Accepte: Novembe 25 / Pubie: 8 Novembe 25 Abtact: Abeo caacteize te aiometic inteface of an uface, epeciay veetation, an te atmopee. Abeo i a citica input to many moe, uc a cop owt moe, yooica moe an cimate moe. Fo te extenive attention to cop monitoin, a pyica abeo moe fo cop i eveope bae on te aw of eney conevation an pecta invaiant, wic i eive fom a pio foet abeo moe. Te moe input ave been efficienty an pyicay paameteize, incuin te epenency of abeo on te oa zenit/azimut ane, te faction of iffue kyit in te incient aiance, te canopy tuctue, te eaf efectance/tanmittance an te oi efectance caacteitic. Bot te aniotopy of oi efectance an te cumpin effect of cop eave at te canopy cae ae coniee, wic contibute to te impovement of te moe accuacy. Te compaion between te moe eut an Monte Cao

2 Remote Sen. 25, imuation eut inicate tat te canopy abeo a i accuacy wit an RMSE <.5. Te vaiation uin oun meauement a ao emontate te eiabiity of te moe an tat it can efect te inteaction mecanim between aiation an te canopy-oi ytem. Keywo: abeo; cop; pecta invaiant. Intouction Suface abeo etemine te otwave aiation buet an te eney tanfe at te oi-veetation-atmopee inteface an fute infuence of ecoytem, yooy an meteoooy pocee, uc a potoyntei an evapoation []. A veetation pay a cucia oe in a of tee natua pocee, caefuy epictin te veetation abeo i of pime inteet wen tuyin cop monitoin [2], yooica cyce moein [3,4], weate foecatin an cimate moein [5]. Compae to ote veetation type, ti cop equie exta attention, becaue it ow inificant eaona vaiation an ton fuctuation caue by uman activitie. It pecta caacteitic cane aon wit it owt a te popotion of bae oi eceae. Cuenty, a eat numbe of eeac tuie ae beinnin to focu on te moein an inveion of cop caacteitic, epeciay te cop abeo [5,6]. Peviouy, te abeo of a cetain an cove type wa et to a contant in many appication cae [7]. Aon wit te eveopment of quantitative emote enin (QRS) tecnique, inceain nea ea-time ateite abeo ata ave povie te oppotunity to eveop avance an uface abeo paameteization [8,9], uc a te wie appication of MODIS abeo pouct [9]. Abeo i uuay cacuate a te weite aveae of back-ky abeo (BSA) an wite-ky abeo (WSA). BSA i te anua inteation of te biiectiona efectance itibution function (BRDF) o biiectiona efectance facto (BRF) ove a viewin iection, weea WSA i a fute inteation of BSA ove a iumination iection []. Te veetation abeo vaie inticatey ue to te abunant vaiation of te veetation biiectiona efectance itibution function (BRDF) [8]. Te veetation BRDF moein invove two pyica pocee: uface cattein an voume cattein. Tey ae bet ane by eometic optic (GO) teoy an aiative tanfe (RT) teoy, epectivey []. Howeve, iect inteation bae on tee moe to obtain veetation abeo i too compex to fomuate matematicay [2]. To ove ti pobem, a emi-empiica kene-iven moe bae on te inea combination of iotopic, eometic an voume cattein kene a been eveope [3,4]. Te moe a eaty impifie te inteation poce. Howeve, te moe ie te an cove an cop tuctua infomation in te tatitica kene coefficient, wic cannot be iecty ue in cop monitoin [5]. Futemoe, te inveion of te moe eie on atmopeicay-coecte, cou-ceae, muti-anua an muti-ate efectance obevation [3]. Tu, te tempoa eoution of abeo i a to impove, an te moe i not uitabe fo i patia eoution ata witout pio knowee [6]. A abeo i ao efine a te atio of upwein fux (iaiance) to ownwa fux (iaiance) [], it can be etimate witout inteation by accumuatin te upwa an ownwa iaiance uin

3 Remote Sen. 25, numeica imuation meto [7]. Te ownwa fux, i.e., te um of te iect oa fux an te iffue oa fux, wic i an inteation of te ky aiance ove a iumination iection, vaie wit oa zenit ane an atmopeic viibiity []. Te upwa fux epen on not ony te ownwa fux, but ao te an uface caacteitic. A common meto ue fo cacuation of te aiation efecte by a canopy i te Monte Cae (MC) meto, by wic te intenity of te efecte aiation can be obtaine if a ufficient numbe of poton i tace [8,9]. Accuate a te MC imuation i, it equie a compete eciption of te cene, an te aiation i obtaine by countin witout knowin te matematica eationip between te paamete. Te p-teoy tat by epictin te manne in wic poton inteact wit te canopy an unetoy [2]. Te ecoiion pobabiity (p) i pectay invaiant an can be intepete a te pobabiity tat a poton cattee fom a eaf wi inteact ( coie ) wit anote eaf in te canopy, wic i ue to peict te amount of aiation cattee by te canopy [2]. Bae on te p-teoy, Manninen an Stenbe [22] etimate te veetation-oun (foet foo) mutipe cattein an imuate te foet abeo. Howeve, te p-teoy i effective by aumin tat te catte pae of eave ae iotopou, tat i tat te eivative moe cannot ecibe te anua itibution of te cattee aiation in ea to te coiion of poton wit eave. Ti caue ome icepancy fom te eaitic ituation, wic can be neecte on aveae at ae cae [23]. A te cacuation of te abobe aiation i moe uccinct tan tat of te efecte aiation, te abeo wa cacuate a te compement of te canopy an oi aboption fom te aw of eney conevation by Stenbe [24]. Te moe of Stenbe [24] pyicay expee te eationip between foet abeo an te canopy an unetoy paamete. Te moe wa eive fo a iven iection of iumination (oa zenit ane). Commony, inoin te contibution of iffue kyit may caue a.% 2% etimation eo of canopy abeo [25]. Teefoe, to appy te moe in ea ceneie, an anua inteation i neceay, atou it wou inceae te cacuation compexity. Fan et a. [26] paameteize te compoition of te incient aiation uin te faction of iffue iaiance in cacuatin canopy aboptance, wic pefom we fo bot continuou an non-continuou veetation. Beie, in ea to te cop, te aniotopic efectance caacteitic of te oi ou ao be incue, wic ominate te IFOV befoe te coin of te cop canopy. Ti pape aim to etimate te cop abeo in te bae of te foet abeo moe by Manninen et a. [22] an Stenbe [24]. Coniein te caacteitic of cop canopy, te cumpin inex of cop canopy wa cacuate to faciitate te moe fo non-continuou cop canopy, an te compoition of incient aiation wa paameteize. Beie, te Hapke moe wa ue to cacuate te iectiona-emipeic efectance an bi-emipeic oi efectance, bot of wic ave been ue in te cop abeo moe to epict te aniotopic efectance of te oi [27]. Accoin to te enitivity anayi of te main input, te moe i impifie. Te poce wa ao cecke an veifie uin Monte Cao imuation. Te fina moe wa vaiate uin fie meauement. 2. Moe Deciption Suface abeo i etemine by te uface popetie an te anua an pecta itibution of te incient oa aiation. Veetation canopy abeo epen on te eaf aea inex (LAI), eaf ane

4 Remote Sen. 25, itibution, eaf tanmittance, eaf efectance an unetoy abeo, wic i mainy infuence by te oi moitue of te cop [8]. Te moe i uppoe to make expicit te eationip between tee paamete an te veetation canopy abeo. Continuou veetation i te impet tuctua type fo moein. Ti ection fit intouce te moe fo a continuou canopy an ten ue te cumpin inex to exten te moe to a non-continuou cop. Finay, te moe wa impifie, o te ominant paamete an mecanim ae ceae an moe itinct. 2.. Baic Moe Te moe oiinate fom te abeo moe by Manninen an Stenbe [22], fute ecompoe by Stenbe et a. [24]. To aapt to te cop ceney, te moe wa fute efine, wic aume te actua incomin it a a combination of iect an iffue aiation, cacuate te cumpin inex of te cop to a in te moe an epaate oi efectance into iectiona-emipeica an bi-emipeica efectance to iciminate te eence of te iect an iniect coiion. Te eivation of te moe ao efe to te FAPAR moe by Fan et a. [26]. Accoin to te aw of eney conevation, te abeo (A) of veetation an cove i te compement of te canopy aboptance av an te oi aboptance av, wic can be ecibe a, Te A av a () av incue te iect aboption of aiation by te canopy efecte by te backoun an ten abobe by te veetation Te av av av av2. av an te pat tat i 2 (2) a incue te faction of oa aiation iecty abobe by te oi caue by veetation-oi mutipe cattein a2 (Fiue ). a a a a an tat 2 (3) Te eney eacin te oi (f ) incue two pat, te popotion of te incient aiation tat iecty eace te oi witout inteactin wit te canopy (f) an tat afte one o moe cattein event witin te canopy (f2). f a a cetain incience ane, an te efecte aiation i etemine by te iectiona-emipeic efectance of te oi ( ). Moeove, te efecte aiation fom te popotion tat eace te oi afte one o moe cattein event witin te canopy (f) i infuence by te bi-emipeica efectance of te oi ( ). a f ( ( )) (4) a ( ) f ( ) 2 * i c * 2 c p q (6) (5)

5 Remote Sen. 25, * wee c i te iffue efectance of te veetation canopy. q 2 i te faction of incomin aiation cattee ownwa (i.e., fowa). i i te aveae inteception pobabiity of te iffue kyit by te canopy, wic can be intepete a te anua inteation of te iectiona canopy inteception of te incomin aiation i [22]. G LAI = co Te canopy inteception i i expee a i e bae on te Poion aw. i i inteate fom te iectiona inteception pobabiity i [22]. G LAI co i = e co in 2 (7) In pactice, i can be obtaine fom numeica inteation. Fan et a. [26] popoe an empiica exponentia function of i fo te peica veetation type. f epen on te canopy tanmittance, a we a te compoition of te incient aiation. iciminate te contibution of te iect unit an te iffue kyit. ( f ( ) ( i )+ ( i ) (8) f ( ) i te um of two pat, te efecte iect unit afte te fit coiion wit te oi * f i ) an te popotion tat eace te oi afte one o moe inteception by te canopy tou c cattein ( f 2 ). * f( ) f ic f2 (9) f 2 ao epen on te facto of te iffue kyit an te iectiona/iffue inteception by te veetation canopy tou cattein. * ( ) c f2 i i () Ten, a pyica moe of veetation abeo a been fome a foow (ymbo ite in Tabe ), A av a ( ) v= i ( ) i f i ic p ( ) ( ) ( i)+ ( i) c = ( ) i+ i i c i c ( ) ( i)+ ( i) i c ()

6 Remote Sen. 25, Fiue. Iutation of te compoition of oi aboption. Tabe. Expanation of te ymbo in te abeo moe (te at fou ine it te unknown paamete in te Hapke moe). Symbo Tem / te oa zenit/azimut ane v / v te view zenit/azimut ane te view azimut eative to te oa azimut i / i te canopy iect/iffue inteception te ecoiion pobabiity tat a poton cattee fom a eaf wi inteact ( coie ) p wit anote eaf in te canopy, q 2 te faction of incomin aiation cattee ownwa (i.e., fowa) iffue kyit popotion of tota incient aiation P te ap faction te cumpin inex u te eaf voume enity function; H i te canopy eit G te mean pojection of a unit foiae aea aon te iection wit a zenit ane of R T, wee R an T ae te efectance an tanmittance of eave, epectivey. te aveae ine cattein abeo of te patice compoin te oi uface. ow wit/ow pace at a iven azimut ane ; a i te ow wit, an a 2 i te A /A 2 ap wit pepenicua to te ie ( ) / iectiona-emipeic efectance of te oi/bi-emipeic efectance of te oi te coefficient of te Leene poynomia expanion ue to expe te patice b, c pae function P ( ) B ecibe te manitue of te ot pot caacteize te wit of te ot pot 2.2. Fo Noncontinuou Veetation Cumpin Effect Tee ae two oup of paamete etemine by te canopy tuctue, wic i affecte by te cumpin eee of te canopy. One i te canopy inteception i, i an tanmittance t, an te ote i te ecoiion pobabiity p. Wit an aumption of continuou omoeneou veetation une iea conition, tee paamete can be iecty cacuate fom te eaf aea inex (LAI) [26,28].

7 Remote Sen. 25, Howeve, in natue, canopy tanmittance inceae in ome iection, becaue eave cump witin cown an amon cown [29]. Te cumpin effect a been coniee in te cacuation of te p paamete by Stenbe [28]. Te cumpin inex ( ) i abe to ecibe te cumpin effect [3]. Fo non-continuou o non-unifom veetation, te aveae ap faction can be eive wit te aitance of te cumpin inex [3]. G P(, ) exp( LAI ) (2) Hee, LAI i an equivaent eement aea inex etemine by bot te eave an te tak, wic can be tanfome to effective LAI ( LAI ) by mutipyin. In evee, te cumpin inex can be e etieve fom te aveae ap faction iven te iection ( co( ) ), LAI an G. n P (, ) (3) G LAI Te actua cop i away pante in ow (ie). Te cumpin effect of cop i mainy caue at te canopy cae, i.e., te eua confiuation between te ow. Eac ow i abtacte a a ectanua poou oi tetc aon te ie iection [33] (Fiue 2). In te cacuation of, LAI i ifficut to quantify, becaue te contibution of cop tak at iffeent zenit ane i ay meauabe. Hee, we aopte an appoximation meto. Fo anomy-itibute canopy tuctue, te itibution can be ecibe uin te Poion teoy. Meanwie, fo non-continuou veetation wit patce at vaiou cae, te Neyman-type itibution fit moe accuatey, wic aume canopy fit combine in oup, an te patia itibution of te cente of a oup foow te Poion poce [32]. Tee i a paamete m2 in te Neyman itibution function tat coepon to te a pioi vaue of te mean ize of cute. A te m2 i mae, te Neyman itibution an Poion itibution become coe. Aumin eave itibute anomy witin eac ow, it can be infee tat te cop wi beave ike continuou veetation wen te v i ae tan a teo zenit ane ( c atan( A/ H) ), a te oi i inviibe, wic eut in te cumpin inex eve oin to an aymptote ( ). Teefoe, te LAI can be appoximate to patiay-aveae eaf aea inex LAI in cacuatin te aveae ap faction. Teefoe, te cumpin inex can be appoximatey cacuate fom Equation (4), wic i ao poven by Yan et a. [33], a n P (, ) (4) G LAIa Yan et a. [33] eive te aveae ap faction wit a i accuacy; oweve, an intea meto wa miue in te cacuation. Intea, te canopy ou be emente into many mico-ice, woe ap faction a up to te fina eut.

8 Remote Sen. 25, Fiue 2. Iutation of aveae ap faction cacuation of ow cop in a vetica pane wit x point to an azimut ane of (te azimut inceae in te cockwie iection wit it oiin aon te ow iection). A = A + A2. A ow unit A can be ivie into fou pat, namey a, b, c an. Pat a can be teate a continuou canopy. Pat b an ave equa ap faction. Tey ave been emente into mico-ice, an eac mico-ice can be coniee a continuou canopy, a on a it i tin enou. Te ap faction of te fou pat can be cacuate a foow, G Pa exp uh, ; Pc, co G uix n in G u H e i co co Pb P e, H tan G u H nx H tan wee A a / in, A 2 a 2 / in an a an a 2 efe to te ow wit an ow pace, epectivey, wen te x-axi i pepenicua to te ie ( 9 ). Te aveae ap faction of a cop unit i te weite aveae of te fou pat. A Htan H tan P(, ) Pa 2 Pb A A in A H tan 2 e A2 Htan G u Pc A A in A2 H tan 2 G u G uh co (5) (6) Aniotopic Soi Refectance Fo continuou veetation, te infuence of oi aniotopy on canopy abeo i not a obviou a tat fo te cop, epeciay in te beinnin of te owin eaon [34]. Fo ti cop abeo moe, te Hapke moe wa ue to imuate te BRDF of oi an to bui a ook-up tabe of oi tou

9 Remote Sen. 25, anua inteation. wa fute obtaine tou iumination emipee inteation of Hapke moe i expee a Equation (7); efe to [35] fo etaie infomation. (, v, ) B( ) P( ) H (co ) H (co v) 4 co co wee B B ( ), [ / tan( / 2)] P b c 2 ( ) co [(3co ) / 2], ( 2 x) H( x). [ 2 ( ) x] 2.3. Moe Simpification v. Te Sufficient etai, a Equation (), ow tat te entie moe i ity compicate an a inceae inveion ifficutie. In fact, te contibution of ome component ae eay imite, o muc a to be neecte. Te moe wa impifie an eoanize a Equation (8). Tee ae two impifie pat in av( ), bot of wic eate to te aboption of oi-efecte aiation by te canopy. One i neectin te iffeence between iectiona an emipeica canopy inteception ( i an i ) ony befoe te fit coiion between poton an te oi uface. Te ote i omittin te facto i c in te enominato, a it i coe to zeo. Simiay to a( ), two impification wee mae. One i tat te fit pat of f ( ) (Equation (9)) i neecte, becaue te aboption fom te muti-coiion afte te fit iect coiion between canopy an oi i too ma. Te iffeence between an i mainy emboie in te fit iect coiion an muti-iniect coiion. Secon i tat te facto i c i omitte, te ame a tat in av( ). Te iffeence between te impifie moe an te oiina moe i imuate an iutate in Fiue 3. A av a ( ) av i ( i i ) +( i ) i p ( ) i i i i i i c a ( )+ ( ) Te impifie moe ave a cea pyica expanation of te veetation abeo. Tee ae tee mutua facto fo veetation aboption an oi aboption: te veetation inteception, te facto of iffue kyit an te oi efectance caacteitic. Moeove, te veetation aboption i ao infuence by te pecta aboption coefficient ( ac ( ) ), wic i etemine by te p ecoiion pobabiity p an te eaf ine cattein abeo ( ). (7) (8)

10 Remote Sen. 25, Fiue 3. Te atio between te impifie vaue an te oiina vaue of av (eft) an a (it).., =, A =.3, A2 =.2, Senitivity an Scenaio Anayi Te facto icue above, incuin te popotion of iffue kyit, eaf aea inex an oi efectance, contibute to te vaiation of veetation abeo, a tey infuence canopy aboptance an oi aboptance. Te enitivity of abeo to tee tee paamete i anayze in ti ection. Te anayi of te fit two paamete (Section 3. an 3.2) wa conucte on continuou veetation, weea te at one wa conucte on cop, wee te infuence of oi efectance i moe inificant. In te foowin imuation, G wee et a.5. Te iectiona-emipeica efectance ( G ) of oi wee imuate uin te Hapke moe. Te five paamete of te Hapke moe wee et to: =.54; B =.33; =.2; b =.86; c = Vaiation of Abeo wit te Diffue Faction av an oi a. Fo veetation, te faction of te incient iffue aiation a an impotant In ti aoitm, te veetation abeo wa eive fom veetation aboptance aboptance impact on veetation an oi aboptance. Te enitivity anayi wa conucte on continuou veetation. Te imuation eut in Fiue 4 emontate tat av i ominate by av an tat a i ominate by a. Howeve, a te oppoite effect of on av an a (efein to Equation (8)) offet eac ote, te abeo oe not vay inificanty wit. If te LAI i ae enou an te efectance of te eave i mae tan tat of te oi, te abeo wou ity inceae wit, wic expain te iffeence between veetation abeo on couy ay an unny ay Vaiation of Veetation Abeo aon wit LAI Aon wit te owt of LAI, te faction of eney abobe by te veetation canopy inceae, wie te eney abobe by oi eceae. Howeve, becaue of te mutipe inteaction of poton at te oi-veetation-atmopee inteface, te vaiation of abeo manifet in a compex manne.

11 Remote Sen. 25, Te infuence of LAI on abeo i mainy etemine by te canopy inteception ( i an i ) an te ecoiion poibiity p. Te inceae of LAI wou tie te owt of i, i an p, an ten av wou inceae an a eceae (Fiue 5). Tu, te fina vaiation of abeo eut fom te eative ize of te eaf an oi efectance. In Fiue 5a, te canopy aboptance inceae apy a LAI ow, wic i not aequatey compenate by te eceain of oi aboptance an ea to te eceae of canopy abeo. In Fiue 5b, becaue i ae, te inceain of canopy aboptance i not a inificant a te eceae of oi aboptance. Teefoe, te canopy abeo ity inceae wit te owt of LAI. abeo an component of aboption av av 2 a a 2 abeo Fiue 4. Te eteminant of te canopy abeo a a function of te faction of iffue aiation. Te bae vaue incue LAI 3, 2 an =.23 (at te een ban). wa vaie fom zeo to one in tep of., wie ote paamete wee e contant. av av 2 a a 2 abeo abeo an component of aboption abeo an component of aboption LAI (a) LAI (b) Fiue 5. Te eteminant of te canopy abeo a function of LAI: (a) =.23 (een ban),.22, 2 ; (b) =.7 (nea-infae ban),.22, 2.

12 abeo Remote Sen. 25, Infuence of Leaf Foiae Ditibution on Canopy Abeo G i te mean pojection of a unit foiae aea aon te iection wit a zenit ane of, wic i one of te paamete to ecibe canopy tuctue. Tee ae five commony-ue G function type, incuin eectopie, paiopie, peica (G =.5), extemopie an panopie [36]. In ti moe, te G function i empoye to cacuate te i, i an P(, ). To caify te impact of eaf foiae itibution on cacuate abeo, a compaion wa conucte between te abeo eive fom tee five G function type [36] wit inceain LAI an ote paamete contant. Fiue 6 manifet tat te infuence of G function i not appaent wen LAI i extemey ma o ae (e tan one o moe tan ix) wen =.23,.22, 2. Te maximum icepancy i about.6 wen LAI i tee..2 EREC PLAG SPHE EXTR PLAN LAI Fiue 6. Te canopy abeo eive fom iffeent G function wit canin LAI. (ERECeectopie, PLAG-paiopie, SPHE-peica, EXTR-extemopie an PLAN-panopie) 3.4. Depenence of Canopy Abeo on Waveent Abeo an canopy/oi aboption ( A, av an to te pectum-epenent paamete, incuin, A, av an, a eive by Equation (), wee pecta fie meauement of maize cop. Fiue 7 emontate tat oppoite vaiation ten an toete etemine te caacteitic of a ) cane aon wit waveent, owin an. Fiue 7 ow te vaiation of,, av an A. an ae obtaine fom a appea to ave te av manifet a vaey at te nea-infae ban (76 nm to 3 nm) ue to te tuctue of eaf ce. Te e eney abobe by te eave, te moe eney eace te oun. Teefoe, a eve ae maximum at te neainfae ban.

13 Dicepancy of Abeo Dicepancy of Abeo Remote Sen. 25, abeo an component of aboption av a abeo waveent (nm) Fiue 7. Specta abeo an component of aboption Infuence of Soi Aniotopy on Canopy Abeo Te abeo moe iciminatin te an i efee to a te aniotopy oi moe, an te abeo moe teatin te oi a a Lambetian uface ( ) i cae te iotopy oi moe. Fiue 8 iutate te icepancy between te abeo eive fom te iotopy oi moe, wic ue te oi a a contant, an tat eive fom te aniotopy oi moe uin vayin a epicte in Fiue 9. Wen te oa zenit ane i e tan 6, te abeo eive fom te iotopy oi moe i ae LAI (a) β (b) Fiue 8. Cont.

14 of oi Dicepancy of Abeo Remote Sen. 25, Gap wit (c) Fiue 8. Te icepancy between abeo eive fom te iotopy an aniotopy oi moe. (a,b,c) te icepancy of abeo vayin wit te LAI, an te ap wit of cop. Eac ine coepon to a cetain. Te efaut vaue incue =.23, A =.3, H =, =9 (pepenicua to te ie). (a).2, A2 =.2, LAI wa vaie fom. to nine. (b) LAI = 2, A2 =.2, wa vaie fom. to one. (c) LAI = 2,.2, te ap wit (A2) wa vaie fom. to one. Accoin to Fiue 9, ti i becaue become ae tan (wic i equa to.294 in ti cae) wen te oa zenit ane i beyon 6, an te abeo inceae wie Equation (7) expain..35 inceae, a SZA ( ) Fiue 9. Vaiation of te iectiona-emipeica efectance zenit ane (SZA). aon wit te oa In Fiue 8a, te ap between te abeo at iffeent SZA naow, wie te LAI inceae, becaue oi i ominant in te fie of view (FOV) at ma LAI, weea te faction of veetation in FOV inceae, an te infuence of oi efectance eceae wit te inceae of LAI. In Fiue 8b, te ap between te abeo at iffeent naow wit te inceae of. Ti i becaue te abeo eive fom te iotopy oi moe i baey cane wit, weea te abeo eive fom te aniotopy oi moe ow wit te inceae of. In Fiue 8c, te ap between te abeo wien wit te inceae of te ap wit an a contant ow wit, becaue te ominancy of oi efectance ow wit te ap wit. In ti cae, te iffeence of abeo caue by te aniotopy of te oi i appoximatey ±.2, wic nee to be coniee wen te accuacy eman i i.

15 Remote Sen. 25, Moe Vaiation 4.. Vaiation by MC Simuation 4... Meto Te moe wa vaiate uin a Monte Cao (MC) meto. MC imuation i a numeica tatitica meto by wic te aiative tanfe poce of poton in te canopy i imuate an te tuctua paamete of te canopy ae peefine [8,26,37,38]. Te main tep of te imuation incue: eneatin te incient poton, eteminin te cenaio eain poton coiin wit eave o oi, anomy ainin te cattein iection, cacuatin te fee pat of te poton an countin te poton atifyin pecific conition. Te MC meto wa ue to vaiate te abeo moe une unifom continuou veetation an cop conition, epectivey. Wite ky abeo (WSA) i te anua inteation of back ky abeo (BSA) in te iumination emipee, o te BSA i mainy vaiate ee. Te iuna vaiation of BSA epen on te oa zenit ane, an te on-tem BSA mainy cane wit effective LAI ( LAI e ). Teefoe, te vaiation i conucte on two imenion. One imenion i te LAI, an te ote i te SZA. Fo unifom continuou veetation, BSA emain contant wit. Nevetee, fo te cop canopy, BSA wou cane wit te vaiation of, a tat wou cane te atio between te cop wit an canopy eit. Teefoe, two oup of pepenicua iection wee eecte wit vaue of an 9, epectivey. Te paamete of te Hapke moe wee et a w =.543, B =.33, =.2, b =.86 an c =.7, wic wee uitabe fo te oi caacteitic of te meaue oi in te eeac. Te main paamete invove incue: Leaf aea inex of te canopy: zeo to nine; Poton incient zenit ane ( ): zeo to 6; Poton incient azimut ane ( ): zeo, 9; Leaf ane itibution type: peica (G =.5); Temination teo of poton eney:. (conto wen te oun of imuation i teminate); Poton numbe: 6 ; Soi iectiona-emipeica efectance Soi bi-emipeica efectance :.294; : ee Fiue 9; Te eaf efectance an eaf tanmittance wee obtaine fom te Leaf Optica Popetie Expeiment 93 (LOPEX93) atabae [26] Compaion of Continuou Veetation Te moe-cacuate back ky abeo (BSA) aee we wit te MC imuation eut (Fiue ). Te abeo eceae monotonicay wit LAI. A ae incient zenit ane coepon to a ie abeo vaue. Te icepancy between te two oup of eut wa evauate in tem of Peaon coeation wen te eaf anua itibution type i peica, te coefficient () an te oot mean quae eo

16 RMSE Abeo Remote Sen. 25, (RMSE) (Fiue ). Reut ow tat BSA imuate by MC an te moe a a ton poitive coeation (.999 ) an ma icepancy ( RMSE.3 ) une a oa zenit ane < MC moe 3 MC 3 moe 5 MC 5 moe LAI Fiue. Reationip between LAI an back-ky abeo (BSA) a peicte by te moe (cice an iamon) an MC (oi ine) une iffeent oa zenit ane (SZA, epoye at, 3 an 5 ) at te een ban (53 nm). Te iffeence in te wit of ine an te ize of make ow te vaiation on SZA abeo (moe aaint MC) RMSE Fiue. Peaon coeation coefficient () (ba ap) an oot mean quae eo (RMSE) (ine cat) between te moe-imuate an MC-imuate BSA of continuou veetation une iffeent oa zenit ane at te een ban (53 nm). A we a te BSA, te in Fiue 2 an 3. av an av an av inceae wie a ae of i accuacy accoin to te eut iutate a eceae monotonicay wit LAI an SZA. Bot a eive fom te moe an fom MC at iffeent SZA ave ton aeement, wit a i coeation (.999 ) an a ma icepancy ( RMSE.2 ).

17 a RMSE av RMSE Remote Sen. 25, LAI (a) av (moe aaint MC).994. MC moe MC 3 moe 5 MC 5 moe (b) RMSE.3.2 Fiue 2. (a) Reationip between LAI an av a peicte by te moe (cice an iamon) an MC (ine) une iffeent oa zenit ane at te een ban; (b) te coeponin an RMSE MC moe 3 MC 3 moe 5 MC 5 moe a (moe aaint MC) LAI RMSE (a) (b) Fiue 3. (a) Reationip between LAI an a a peicte by te moe (cice an iamon) an MC (ine) une iffeent oa zenit ane at te een ban; (b) te coeponin an RMSE Vaiation fo te Row Cop Canopy To unetan te vaiation of imuation eo une iffeent LAI an incient zenit ane fo te cop, te ow wit, ap wit an canopy eit wee e contant at.3 m,.2 m an m, epectivey, wie LAI wa vaie fom zeo to nine an SZA vaie fom to 6 in tep. Soi abeo wee pe-imuate uin te Hapke moe. Fiue 4 ow te vaiation eut of te cop canopy wen (aon te ow iection) an 9 (pepenicua to te ow). Te i coeation coefficient an ow RMSE ow tat te vaue eive fom te moe ae accuate fo te cop canopy, a we a te continuou veetation.

18 Abeo RMSE Abeo RMSE Remote Sen. 25, MC moe 3 MC 3 moe 5 MC 5 moe cop abeo (moe aaint MC) LAI RMSE (a).25.2 MC moe 3 MC 3 moe 5 MC 5 moe.998 abeo (moe aaint MC) LAI RMSE (b) Fiue 4. Reationip between LAI an cop abeo a peicte by te moe (cice an iamon) an MC (ine) une iffeent oa zenit ane at te een ban (a) an 9 (b) Vaiation Uin Goun Meauement Te beavio of te abeo moe eveope in ti tuy wa ao tete uin meaue paamete a input, an te eut wa compae to te meaue abeo. Te input paamete incue te LAI, te faction of iffue aiation, te eit an wit of te ow canopy, eaf efectance/tanmittance, oi abeo an te G function, wic ae obtaine fom fie meauement. Te abeo meauement incue te pecta abeo an te otwave abeo. Te conveion fom pecta abeo to boaban abeo a ue te meaue ownwa aiation a te weit, a etaie in Lian (22) Site Deciption Te tuy ite at te Huaiai Remote Senin Station, wic i ocate in Huaiai, Hebei povince, Cina (4.349 N, E), i one of te eco-yooy an fux ite aoun Cina (Fiue 5). Te ominant cop of te Huaiai Site i maize. Te abeo moe wa tete uin oun meauement of maize at two iffeent owin tae. Duin te eein tae, maize can be

19 Remote Sen. 25, coniee a non-continuou canopy, an unti te canopy i coin, te maize can be coniee a continuou canopy Meauement Fiue 5. Poition an aeia view potoap of te Huaiai ite. Te abeo wa coecte at iffeent peio of maize owt (Fiue 6 an Tabe 2). Fiue 6. Poition an aeia view potoap of te Huaiai ite. () Specta abeo of maize an oi: Te pecta abeo wa cacuate a te atio of te pecta ownwa to te upwein aiation. Te pecta uface aioity wa coecte uin an Anaytica Specta Device (ASD) FieSpec3 (FS3) pectoaiomete wit te manufactue' emote coine ecepto (RCR) foeoptic (~8 HFOV) e.5 m above te maize canopy (coeponin to a footpint of 3 m in aiu. Te iffue incomin aiation i meaue at te open teain aea wit a back pane ain te iect incient aiation; te faction of te iffue aiation wa cacuate a te atio of iffue incomin aiation to ownwa aiation. (2) Sotwave abeo: Te otwave abeo wa eive fom te upwa/ownwa otwave aiation, wic wa meaue uin a CNR4. Te CNR4 wa mounte on a poe an upene fom te patfom of te towe cane, wic aowe fo poition, eit an eve ajutment. Te own-ookin pyanomete ooke own at te maize. Raiation wa meaue evey econ an

20 G Remote Sen. 25, time aveae to one-minute inteva. Te ata oe cock wee ynconize to te econ. Abeo wee cacuate a te atio of efecte to incient aiation. (3) G function: G i te mean pojection of te eaf aea unit in a pane pepenicua to te unay (Jonckeee I, 24); G wa etimate tou te meauement of te pobabiity enity of te eaf ane itibution of te obeve maize, wic i te itibution of te eaf noma wit epect to te uppe emipee an wa meaue uin a potacto. Accoin to te tatitica anayi of Ro (98), te G function wa imuate tou te weite aveae eaf ane of te obeve maize (Fiue 7) Zenit ane ( ) Fiue 7. Reationip of te G function vaue wit te zenit ane. (4) Leaf efectance/tanmittance wa meaue uin te Anaytica Specta Device (ASD) FieSpec3 (FS3) pectoaiomete wit a eaf cip (Fiue 8). Te pecta meauement wa aveae fom tee eave, wic wee ampe fom te top, mie an bottom of te pant. efectance tanmittance waveent (nm) Fiue 8. Te meaue efectance an tanmittance of maize eave. (5) Te LAI wa meaue by uin a etuctive ampin meto witin a 5 m 5 m quaant tat beon to te avetin meto. Te LAI wa accuatey cacuate uin a CI-22. (6) Te wit of one cop peio wa meaue at te eay peio of te maize a te itance between two pant ie-by-ie between two ow.

21 abeo Remote Sen. 25, (7) Te un zenit ane vaue wee te actua one at te ocation of te meauement. Date Time LAI Tabe 2. Te meaue paamete on tee iniviua ate. Soa Zenit Ane ( ) Soa Azimut Ane ( ) Row Wit (m) Gap Wit (m) Canopy Heit (m) CNR4 Meaue Abeo 3 May 25 9: June 25 3: Juy 24 3: Compaion Reut Te moe-imuate pecta abeo of te maize canopy aee we wit te oun-bae pecta abeo (Fiue 9). Te pecta vaiation of te maize canopy can be accuatey imuate uin te popoe moe fo 3 May 25. Duin ti peio, te maize wa at te eein tae, o te oi efectance a a inificant infuence on te canopy abeo, wic epeent te ituation on wic te moe focue. Te RMSE between te meaue an moee pecta abeo i.7. Howeve, tee i an obviou icepancy between te cacuate pecta abeo an te meaue pecta abeo fo 5 June 25. Refein to te compaion eut (Tabe 3) between te boaban abeo, it ao pove tat te cacuate eut a oveetimate te canopy abeo. Given te ton coeponence between te cacuate abeo an te ASD pectoaiomete abeo, we upect tat te icepancy wa caue by te oveetimation of oi abeo in cacuatin te abeo. Te oi abeo wa meaue fom te ajacent bae faman in wic te oi wa quite y, wie te maize wa jut iiate an te uneoun oi wa wette. Te ae oi moitue coepon to owe oi efectance. None of te pecta abeo of te maize canopy wa coecte on 8 Juy 25, a te canopy eit wa above 2 m, wic exceee te imit tat te ane -m fibe pobe cou eac, o te cacuate abeo fo 8 Juy 25 wa iecty vaiate uin te boaban abeo meaue wit te CNR4. Te cacuate abeo wa oveetimate by appoximatey.4, wic i.63%. Duin ti peio, te coin of te cop aowe te maize to be teate a continuou veetation May 25 meaue abeo moe abeo.3.2 RMSE = waveent (nm) (a) Fiue 9. Cont.

22 abeo Remote Sen. 25, June 25 meaue abeo moe abeo.4.2 RMSE =.46 (b) Fiue 9. Compaion between te meaue pecta abeo an moe-imuate abeo on (a) 3 May an (b) 5 June. Fom te compaion of te pecta abeo coecte on 3 May 25 an 5 June 25, it a been poven tat te abeo of aicutua uface cane conieaby at iffeent tae of te owin eaon. In te eaie tae, te canopy abeo i mainy etemine by te optica caacteitic of te oi patice, uc a te moitue content of te topoi. A te cop ow, te ominancy of te pyica conition of te eave an te tuctue of te cop become ponounce. Tabe 3. Compaion between te boaban abeo iecty meaue uin te CNR4 fom te Anaytica Specta Device (ASD)-meaue an moe-imuate pecta abeo. Date CNR4 Meaue Abeo ASD Boaban Abeo Moe Boaban Abeo 3 May June Juy Concuion waveent (nm) In ti eeac, a pyica moe epictin cop abeo wa eive fom a foet abeo moe. Te moe cacuate abeo a a compement of canopy an oi aboptance. It conie mutipe cattein, bot witin te canopy an between te canopy an te oi, a we a iffue ky aiation. Te moe can be extene to ow cop an icete veetation canopie uin effective LAI intea of LAI. It a been poven tat te new moe i eiabe an effective at acquiin veetation abeo by compain te eut of te moe an toe of MC imuation. Te moe can typicay be ue in a impifie fom, wic bui a bai fo te moe to be ue fo emote enin ata in te futue. Goun vaiation of te moe owe tat te icepancy between te moe-imuate abeo an te fie meauement of continuou veetation an cop i ma in bot pecta an boaban abeo. A a pyica moe, it i moe obut tan empiica moe in teoy an wou be moe attactive fo te aement o monitoin of biopyica caacteitic of veetation. Fo an abeo iuna coue tuy, it wou be a oo coice to ue ti moe, a te iect an iffue iaiation ae

23 Remote Sen. 25, teate epaatey. Moeove, te moe can be appie in veetation abeo inveion fom emote enin ata. Tee wou be te next tep of te eeac. Acknowement Ti wok wa caie out wit te Nationa Natua Science Founation of Cina (45359, , , , 94253), Potoctoa Science Founation of Cina (25M57886), Open Fun of State Key Laboatoy of Remote Senin Science (OFSLRSS258) an te Majo State Baic Reeac Deveopment Poam of Cina (23CB73342). Te auto tank te eviewe fo tei vauabe an initfu comment an uetion an te Eevie anuae eitin oup fo tei contibution. We atefuy acknowee te eneouy-ae LAI fie meauement fom Ei Cai an Baocen Dou at Beijin Noma Univeity. Specia tank ae extene to Yeu Zen of te Intitute of Remote Senin an Diita Eat fo aitin in te oi abeo imuation, a we a to Biao Cao fo coopeation in te fie meauement. Auto Contibution Jinjin Pen, Wenjie Fan an Xu Xiu conceive of an eine te expeiment. Jinjin Pen, Lizao Wan, Jvcai Li an Pen Zao pocee te ata an pefome te expeiment. Qinuo Liu, Wenjie Fan an Lizao Wan paticipate in te icuion an anayi. Jinjin Pen wote te woe manucipt. Wenjie Fan contibute to te concuion an eviion. Confict of Inteet Te auto ecae no confict of inteet. Refeence. Jacob, F.; Oioo, A. Deivation of iuna coue of abeo an efecte oa iaiance fom aibone POLDER ata acquie nea oa noon. J. Geopy. Re.: Atmo. 25, oi:.29/24jd Batiaanen, W.G.; Canapaa, L. Wate baance vaiabiity aco Si Lanka fo aein aicutua an envionmenta wate ue. Aic. Wate Mana. 23, 58, Otté, C.; Via-Maja, D. Aimiation of oi moitue infee fom infae emote enin in a yooica moe ove te HAPEX-MOBILHY eion. J. Hyo. 994, 58, Mee-Homji, V.M. Pobabe impact of efoetation on yooica pocee. In Topica Foet an Cimate; Spine: Doect, Te Netean, 992; pp Riwe, A.; Sinaaye, J.S.; Heteinton, A.M.; Vae, P.J. Tackin eiona cimate cane by eaf abeo bio-eoenineein. Cu. Bio. 29, 9, Sinaaye, J.S.; Riwe, A.; Ivine, P. Aein te benefit of cop abeo bio-eoenineein. Envion. Re. Lett. 29, 4, Wan, Z.; Zen, X.; Baae, M.; Dickinon, R.E.; Gao, F.; Scaaf, C.B. Uin MODIS BRDF an abeo ata to evauate oba moe an uface abeo. J. Hyometeoo. 24, 5, 3 4.

24 Remote Sen. 25, Reci, D.; Raatz, T.J.; Jacob, D. Paameteization of now-fee an uface abeo a a function of veetation penooy bae on MODIS ata an appie in cimate moein. Teo. App. Cimato. 29, 95, Bonan, G.B.; Oeon, K.W.; Vetentein, M.; Levi, S.; Zen, X.; Dai, Y.; Dickinon, R.E.; Yan, Z. Te an uface cimatooy of te community an moe coupe to te NCAR community cimate moe. J. Cimate 22, 5, Lian, S. Quantitative Remote Senin of Lan Suface; Jon Wiey & Son: Hoboken, NJ, USA, 25.. Ni, W.; Li, X. A coupe veetation oi biiectiona efectance moe fo a emiai ancape. Remote Sen. Envion. 2, 74, Ni, W.; Woocock, C.E. Effect of canopy tuctue an te peence of now on te abeo of boea conife foet. J. Geopy. Re. 2, 5, Scaaf, C.B.; Gao, F.; Stae, A.H.; Luct, W.; Li, X.; Tan, T.; Stune, N.C.; Zan, X.; Jin, Y.; Mue, J.; et a. Fit opeationa BRDF, abeo nai efectance pouct fom MODIS. Remote Sen. Envion. 22, 83, Roujean, J.L.; Leoy, M.; Decamp, P.Y. A biiectiona efectance moe of te Eat uface fo te coection of emote enin ata. J. Geopy. Re.: Atmo. 992, 97, Wite, H.P. Invetiation of Boea Foet Biiectiona Refectance Facto (BRF). P.D. Deee, Yok Univeity, Toonto, ON, Canaa, Suai, Y.; Maek, J.G.; Gao, F.; Scaaf, C.B. An aoitm fo te etieva of 3-m now-fee abeo fom Lanat uface efectance an MODIS BRDF. Remote Sen. Envion. 2, 5, Not, P.R. Tee-imeniona foet it inteaction moe uin a Monte Cao meto. IEEE Tan. Geoci. Remote Sen. 996, 34, Zan, B.; Fan, W.; Xu, X.; Liu, Y. FAPAR an BRDF imuation fo ow cop uin Monte Cao meto. In Poceein of te IEEE Intenationa Geocience an Remote Senin Sympoium (IGARSS), Quebec City, QC, Canaa, 3 8 Juy 24; pp Diney, M.; Lewi, P. Specta invaiant beaviou of a compex 3D foet canopy. In Poceein of te t ISPMSRS meetin, Davo, Switzean, 2 4 Mac 27; pp Rautiainen, M.; Stenbe, P. Appication of poton ecoiion pobabiity in conifeou canopy efectance imuation. Remote Sen. Envion. 25, 96, Mõttu, M. Poton ecoiion pobabiity in icete cown canopie. Remote Sen. Envion. 27,, Manninen, T.; Stenbe, P. Simuation of te effect of now covee foet foo on te tota foet abeo. Aic. Foet Meteoo. 29, 49, Stenbe, P.; Mottu, M.; Rautiainen, M. Moein te pecta inatue of foet: Appication of emote enin moe to conifeou canopie. In Avance in Lan Remote Senin, Spine: Doect, Te Netean, 28; pp Stenbe, P.; Lukeš, P.; Rautiainen, M.; Manninen, T. A new appoac fo imuatin foet abeo bae on pecta invaiant. Remote Sen. Envion. 23, 37, 2 6.

25 Remote Sen. 25, Román, M.O.; Scaaf, C.B.; Lewi, P.; Gao, F.; Aneon, G.P.; Pivette, J.L.; Stae, A.H.; Woocock, C.E.; Baney, M. Aein te coupin between uface abeo eive fom MODIS an te faction of iffue kyit ove patiay-caacteize ancape. Remote Sen. Envion. 2, 4, Fan, W.; Liu, Y.; Xu, X.; Cen, G.; Zan, B. A new FAPAR anaytica moe bae on te aw of eney conevation: A cae tuy in Cina. IEEE J. Se. Top. App. Eat Ob. Remote Sen. 24, 7, Hapke, B. Biiectiona efectance pectocopy:. Teoy. J. Geopy. Re.: Soi Eat 98, 86, Stenbe, P. Simpe anaytica fomua fo cacuatin aveae poton ecoiion pobabiity in veetation canopie. Remote Sen. Envion. 27, 9, Cen, J.M.; Mene, C.H.; Lebanc, S.G. Goba mappin of foiae cumpin inex uin muti-anua ateite ata. Remote Sen. Envion. 25, 97, Cen, J.M.; Cia, J. Pant canopy ap-ize anayi teoy fo impovin optica meauement of eaf-aea inex. App. Opt. 995, 34, Nion, T. A teoetica anayi of te fequency of ap in pant tan. Aic. Meteoo. 97, 8, Cen, J.M.; Lebanc, S.G. A fou-cae biiectiona efectance moe bae on canopy acitectue. IEEE Tan. Geoci. Remote Sen. 997, 35, Yan, B.; Xu, X.; Fan, W. A unifie canopy biiectiona efectance (BRDF) moe fo ow ceop. Sci. Cin. Eat Sci. 22, 55, Jacob, A.; Van Pu, W. Seaona cane in te abeo of a maize cop uin two eaon. Aic. Foet Meteoo. 99, 49, Pinty, B.; Vetaete, M.M.; Dickinon, R.E. A pyica moe fo peictin biiectiona efectance ove bae oi. Remote Sen. Envion. 989, 27, Ro, J. Te Raiation Reime an Acitectue of Pant Stan; Spine Science & Buine Meia: Bein, Gemany, Govaet, Y.M.; Vetaete, M.M. Raytan: A Monte Cao ay-tacin moe to compute it cattein in tee-imeniona eteoeneou meia. IEEE Tan. Geoci. Remote Sen. 998, 36, Ro, J.K.; Maak, A.L. Cacuation of canopy biiectiona efectance uin te Monte Cao meto. Remote Sen. Envion. 988, 24, by te auto; icenee MDPI, Bae, Switzean. Ti atice i an open acce atice itibute une te tem an conition of te Ceative Common Attibution icene (ttp://ceativecommon.o/icene/by/4./).