Small Area Estimation for Crop Acreage in Remote Sensing Assisted Crop Survey

Transcription

1 Sall Ara Estaton for Crop Acrag n Rot Snsng Assstd Crop Survy A Cas of Major Crop Acrag Estaton n Laozhong County W Zhou Dpartnt of Rural Survys, Natonal Burau of Statstcs of Chna 75 Yutan Nanj, Bjng, Chna wzhou@63.nt DOI: /casVII.016.g44 ABSRAC Applyng rot snsng to stat th plantd acrag s typcally by usng rgrsson stator or calbraton stator whch s takng advantags of cobnng th sapl data fro ground survy wth satllt ag classfcaton. For ost cass of rgrsson stator, th crop acrag staton for a targt populaton such as a provnc or county only satsfs th prcson for tslf but could not b dsaggrgatd to sall aras, such as county and town lvl statstcs. akng th Laozhong county afflatd to Shnyang cty, Laonng provnc as a study ara, th satllt ags fro th odrat rsoluton Landsat 8 OLI s classfd for rc and corn as auxlary nforaton for populaton, and hgh rsoluton Chns GF-1 and ZY-3 ar vsually ntrprtd for rc and corn whch s rgardd as ground truth. h whol county s sgntd nto grds of 100*100 as saplng unts, a spl rando saplng s adoptd to slct sapls wth rplcats 1000 ts to do sulaton of buldng sall ara odls. Fro our sulaton study, t rvals that a basc lvl sall ara odl n th for of on-rspons ultpl rgrsson wth rando ffcts and fxd ffcts ar both fasbl to produc th stats at town and townshp lvl. Manwhl, th aggrgat of stats of vry town could (approxatly) b th stats for th county undr th assupton of lnar rgrsson. It s concludd that th sall ara staton thod s applcabl to solv crop acrag staton fro provnc to county lvl sultanously whn targtng an ntr provnc. Kywords: Crop Acrag, Sall Ara Estaton, Rot Snsng PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016 1

2 1. Introducton Chna s a ajor agrcultural producton country as wll as a larg consupton and trad country n trs of far products. Dpndng on th varous agrcultural nforaton spcally on th plantd acrag statstcs of ajor gran crops, t has bn an portant gst for dcson akng wth rspct to gran and food polcy as wll as conoc dvlopnt plans at natonal lvl. o acqur th plantd acrag of ajor gran crops and thr spatal dstrbuton n a tly, accurat, quanttatv way s of sgnfcanc for akng dcson on agrcultural producton at varous lvls of govrnnts, n ordr to nsur food scurty, str and adjust th crop plantng structur through acro-conoc control, as wll as prov th opratonal anagnt for rlvant ntrprss and fars (Blas and Vanhall t al.; ao and Yokozawa t al.; Chauhan and Arora t al.). h tradtonal approach to obtan crop acrags ar usually conductd by a sapl survy usually by a natonal statstcs agncy. Howvr, ths procss s t-consung, labor-ntnsv and lackng n spatal nforaton (Ma t al.). Rot snsng has bn usd for crop acrag staton ovr th last fw dcads and s consdrd to b an ffctv tool for dtctng th crop ara xtnts and changs at rgonal or global scals (Hall and Badwar; Yang t al.; Xao t al.). So countrs has alrady conductd a srs of opratonal progras whch as at th staton for land covr/land us and crops acrag, such as th USA (LACIE, ; AGRISARS, ; CDL, ), Europan Unon (MARS,1998; LUCAS, ; Goland, 008(011)) and ROK (Iplnt RS Applcaton Syst, IRSAS, ). Slarly to th Arcan and Europan rot snsng progras for crop acrag staton, snc yar 010 th Natonal Burau of Statstcs (NBS) of Chna has collaboratd wth xtrnal rsarch nsttut to prlnary stablsh an opratonal busnss od Rot Snsng Assstd Crop Survy (RSACS) for ajor provncs n trs of gran outputs n Chna. h RSACS bascally nvolvs (1) slctng sapl sgnts for ach ndvdual provnc basd on ara fra, () conductng fld survy and collctng crop data, (3) crop spatal classfcaton basd on odrat satllt ags, (4) crop acrag staton. Many studs hav bn carrd out on crop acrag staton for rot snsng assstd crop survy. o produc th stats of crops acrag for a targt populaton, thr ar usually thr approachs could b adoptd (F.J. Gallgo). h frst s drct xpanson stator whch s a typcal saplng approach to produc th stats by only usng survy sapls. h scond s calld calbraton stator whch s basd on th crop classfcaton rsult fro rot snsng through adjustng th classfcaton by confuson atrx. h thrd s rgrsson stator whch rfrs to buld a lnar rgrsson odl by cobnng th ground survy data wth th classfcaton rsults fro rot snsng. hortcally, th rgrsson stator could gan prcson of staton du to cobng th ground survy data wth crop classfcaton fro rot snsng, whch s takn as an auxlary nforaton for populaton. h rgrsson stator s ssntal drvd fro lnar rgrsson thod whch could b wdly adaptd to a partcular probl solvng, for xapl, Yaozhong Pan proposd an approach to stat wntr what ara through buldng rgrsson on Crop Proporton Phnology Indx (CPPI) whch dsaggrgatd fro th MODIS vgtaton ndx (VI) (Pan t al.). h Chns RSACS has also dvlopd a fasbl soluton on acrag staton for ajor crops such as what, corn, rc at provncal lvl by usng lnar rgrsson thod. Howvr, th currnt thods of crop acrag staton ostly concntrat on producng th stats for th targt populaton (provnc) but could not b dsaggrgatd to sub-rgonal (county) lvls. PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016

3 In th Chns contxt of rot snsng assstd crop survy, th sapl sgnts and crop classfcaton ar drctly lnkd to t th rqurnts for th targt provnc, whl th stats for crop acrags ar xpctd to t th prcson for both provnc and county lvl. Fro ltratur study, sall ara staton s th ost donant approach to solv th ult-lvl staton such as stats for both county and provnc lvl sultanously. In 1988 a nstd-rror sall ara odl s spcfd for th rlatonshp btwn th rportd hctars of corn and soybans wthn sapl sgnts fro ground survy and th corrspondng satllt dtrnaton for aras undr corn and soybans, and prdctons of an hctars of corn and soybans pr sgnt for th 1 Iowa counts ar prsntd (Batts G.E. t al). In 003 sall ara staton s appld n a survy conductd n th Rathbun lak Watrshd n Iowa, rosons ar statd for 61 sall aras wthn th study rgon (Opsor J.D. t al). In 006 Sall ara odl whch ncludd saplng and odl wghts was proposd and appld n agrcultur for prdctng nor crops (Mltno A.F.). In ths study, w attpt to produc th crop acrag staton at ult-lvls by usng thod of sall ara staton. h study ara s chosn n Laozhong county whch s afflatd to Shnyang cty, Laonng provnc of Chna. wo knds of spatal rsoluton satllt ags has bn acqurd and procssd for yar 014. h vsual ntrprtaton rsults fro hgh rsoluton GF-1 and ZY3 for rc and corn was rgardd as ground truth, whl xtractd crop classfcaton for rc and corn fro th odrat rsoluton Landsat 8 OLI was takn as th auxlary nforaton for populaton. W xplord th sall ara odl of basc unt lvl wth rando ffcts and fxd ffcts rspctvly by cobnng th ground truth data wth auxlary nforaton of populaton. Gvn dffrnt saplng fracton undr spl rando saplng by usng Mont Carlo sulaton, th rsult of coffcnt of varaton (C.V) drvd both fro th odl basd an squar rror (MSE) and sulaton basd MSE ar coputd and ak coparson.. Exprntal Ara and Procdurs.1 Exprntal ara W choos th Laozhong county, whch s afflatd to Shnyang cty of Laonng provnc, as xprntal ara or targt populaton n saplng trnology. hr ar altogthr 0 towns and townshps wthn th Laozhong county, rgardd as sall aras or doans n our study. Laozhong locatd n 1 8~13 6 longtud ast and 41 1 ~41 47 lattud north, havng th total trrtory ara around 1460 squar klotrs. Laozhong s stuatd n lowr tr of Laoh rvr watrshd, blong to a washd plan pactd by Laoh rvr and Hunh rvr. On annual avrag, th cuulatv sunshn hours ar 575 hours and cuulatv prcptaton s 640 lltr, t s sutabl for agrcultural producton. h ajor spcs for gran crops ar rc, corn and soyban.. Modrat spatal rsoluton ags For larg scal crop ontor progra by usng rot snsng, usually th odrat rsoluton satllt ags ar adoptd to xtract optcal spctru to dstngush th crops. In ths study, Landsat 8 OLI satllt agry on Jun 4, August 7 and Sptbr 8 ar acqurd rspctvly, and gotry corrcton as wll as radaton corrcton ar procssd. Basd on post-procssd standard orthophoto ags, a axu lklhood classfr (MLC) s adoptd to xtract th rc and corn on pxl-bas. h thr tporal ags ar classfd for rc and corn ndvdually by usng MLC, and thn th fnal dstngushd crops of rc and corn ar obtand by dtctng th dynac chang of PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016 3

4 thr tporal rsults. In th procss of MLC appld to dstngush dffrnt crops, th ral crop survy data n 014 fro Laonng Survy Organzaton of Natonal Burau of Statstcs(NBS) had bn usd as tranng st of sapls whn applyng MLC. Fro th ongong crop sapl survys conductd n Laozhong county by th survy organzaton of NBS, w had 15 sapl vllags and ach vllag allocatd 5 sapl sgnts n th sz of hctars. Altogthr thr ar 75 sapl sgnts of survy data could b usd as ground truth n th procss of satllt ag classfcaton. Fnally th classfd rsults and spatal dstrbuton for rc and corn ar obtand n forat of vctor data, whch covrs th whol county and srvs as auxlary nforaton of populaton..3 Hgh spatal rsoluton ags W acqurd th Chns GF-1 and ZY-3 satllt ags (hgh spatal rsoluton agry) to b vsually ntrprtd to dstngush corn and rc corrspondng to ach arabl fld or plot rspctvly. Subjct to th ltaton of acquston of qualfd satllt ags, w hav acqurd on tporal GF-1 ags datd on Octobr 7, 014 and on tporal ZY-3 ags datd on Jun 4 and Jun 14, 014 bfor th autun harvst. h acqurd hgh rsoluton ags ar pr-procssd by gotry and radotrc corrcton as wll as a fuson of panchroatc and 8 ult-spctral ags. akng th advantags of th covrag of dlnatd cropland for ths county bng obtand fro a prvous land survy, t facltatd th vsual ntrprtaton to dstngush of rc and corn wthn th cropland ffctvly. h rsult of vsual ntrprtaton s usd as an approxat ground truth for corn and rc, and s also appld to assss th accuracy of crop classfcaton fro odrat rsoluton ags. Fgur 1: Plantd dstrbuton of rc and corn fro odrat and hgh rsoluton satllt ags rspctvly..4 Saplng dsgn Wth th faclty of GIS syst, w dlnatd th whol trrtory of Laozhong county nto squard grds n sz of 100 trs 100 trs. hr ar altogthr grds, whch ar rgardd as saplng unts. A spl rando saplng s adoptd to slct sapls, and saplng PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016 4

5 fracton ar chosn as 0.07%, 0.14%, 0.5%, 0.5%, 1%, %, 5% rspctvly to ak coparson. In our study, th crop classfcaton fro th satllt ags of Landsat 8 s takn as th auxlary nforaton for populaton, whl th crop ntrprtaton fro th GF-1 and ZY-3 s rgardd as data of ground truth..5 Analyss for ult-lvl staton W prob th ult-lvl staton for ajor crop acrag n th contxt of rot snsng assstd survy n Laozhong county, whch as to produc th crop acrag stats at town lvl and sultanously gnrat th stats for th county. h thod of sall ara staton s adoptd, and a basc unt lvl odl for sall ara s spcfd. h sall ara odl s st n two scnaros for th ffcts of sall ara, on s th rando ffcts and th othr s fxd ffcts. Gvn th saplng sch of spl rando, a rplcat of 1000 sapls ar slctd for crop acrag staton and consqunt prcson assssnt. For ach town and townshp, th stat prcson drvd fro th sall ara odl s copard wth th prcson fro drct doan staton. In our study, w prsnt sulaton rsults as th followng: (1) Coputng th MSE of th odl accordng to paratr staton such as Eprcal Bst Lnar Unbasd Prdcton (EBLUP) and ts CVs, () Basd on th stats fro ach ndvdual odl fro rplcats, coputng th MSE and ts CVs by sulaton, (3) Basd on th drct doan xpanson, coputng th an squard rror (MSE) and ts coffcnt of varaton (CVs). 3. Mult-lvl Estaton by Sall Ara Modl 3.1 Sall ara odl wth rando ffcts Modl sttng For th crop of ntrst yj, assung th rando ffcts for sall ara, th adoptd unt lvl sall ara odl s as follows: y j X j v j, j1,,..., n, 1,,..., (1) y Whr, j s a spcfd crop (rc or corn) acrag for th jth sapl grd n th th town and townshp, s th total nubr of towns and townshps, n our cas =0,whl n s th sapl sz n th th town and townshp, Xj (xj1,..., xjp )' s th ntrcpt n th odl, rfrs to th 1 crop classfcaton rsults fro th odrat satllt whch s coposd of th varabls x,..., j x jp. Rando ffcts v and rror tr ar ndpndnt and dntcally dstrbuton,subjct to noral dstrbuton wth an 0 and dntcal varanc v and Fro th gnralzd ordnary last squar thod, w hav ˆ rspctvly. ' 1 ' 1 X V X X V Y () 1 1 vˆ ( ) v y ˆ x v / n (3) PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016 5

6 V 11 Whr, ' I v n n n X (X 1 Xn,,..., )' Y (y,..., y )' 1 n,, x s th sapl an for th auxlary nforaton of th th town and townshp. Hnc,th stat for th sub-populaton total of th th town and townshp s as follows: Whr, Yˆ ( v N [X uˆ y x v / n ˆ)] X u s th sub-populaton an of classfd rsult of rc or corn fro odrat N satllt ags of th th town, s th total nubr of grds n th th town and townshp. For th varanc staton of rando ffcts thod ntroducd by Fullr and Batts(1973): ˆ SSE(1) /(n p 1), ˆ v v and rror t ax{[ SSE (4), w adopt th ont () (n p)ˆ ]/,0} Whr, SSE(1) yj y s th su of squard rsduals fro th rgrsson X x on j, SSE() s th su of squard rsduals fro th rgrsson yj X on j p, 1 s th nubr of ' 1 ' n ( ) X x non-zro n j n x X X x, 1 1. If th stats of varanc pluggng nto forula (3) and (4), thn w hav th total stat staton: Whr, ˆ E E Yˆ E E ˆ v E N X u y xˆ ˆ v ˆ / n for th th town and townshp by EBLUP ˆ Yˆ [ ( )] (5) s th stat of whn pluggng nto th stats of varanc n forula (). Altrnatvly th paratr stats could b statd by th ML or REML thod, thr ar no sgnfcant dffrnc aong th stats MSE of EBLUP at town lvl For ach sall ara (town) of th odl, th MSE of Eprcal Bst Lnar Unbasd Prdcton dpnds on th odl, Rao(003) gav th forula as follows. MSE(Yˆ ) g 1 (ˆ v,ˆ ) g(ˆ v,ˆ ) g 3(ˆ v,ˆ ) (6) Whr th dfnton of g (.) 1 g, (.) Estaton Populaton total at county lvl and (.) g 3 ar rfrrd to Rao s ltratur Sall Ara In th rando ffcts odl, th su of acrag stat Y for th total nubr of sall ara 1 to s approxatly qual to th total acrag at county lvl n th assupton of PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016 6

7 gnral lnar rgrsson. In fact, su of th xpctaton of ach Y s qual to xpctaton of total Yˆ. Du to th E(v ) 0, w hav th follows. E(Yˆ) E(Yˆ 1) E(Yˆ )... E(Yˆ ) (7) 3. Sall Ara odl wth fxd ffcts 3..1 Modl sttng h foraton of prdcton odl wth fxd ffcts of sall ara s th sa as th odl n quaton (1). h only dffrnc s that v s assung as fxd ffcts nstad of rando ffcts, that s to say for ach sall ara (town) thr s a fxd valu of By dffrntal thod for th paratr staton, w hav: ˆ X Q X X QY 1 1 vˆ y x ˆ y v n th odl. (8) (9) Whr 1 11 Q In n n n,..., ) X (x, 1 x n Y 1,,..., ) ( y yn auxlary nforaton fro th th town and townshp. h stat for th populaton an of sall ara s as follows: Y ˆ X ˆ ( y x ˆ ), x s th sapl an of u (10) Whr X u s th sub-populaton an of classfd rc or corn fro odrat satllt ags of th th town. y s th sapl an of th ground truth for rc or corn of th th town. x th sapl an of th classfd rc or corn of th th town. hn th stat for th populaton total of sall ara s NY ˆ. s h stat for th rror tr s as follows: ˆ SSE(1) /( n ) (11) Whr, SSE(1) yj y X s th su of squard rsduals fro th rgrsson on j x. 3.. MSE of odl prdcton at town lvl For ach sall ara (town), th MSE whch dpnds on th odl s as follows: MSE(Yˆ 1 ) E(Yˆ Y ) n (X x ) ( X Q X ) ( X x ) nˆ 1 (1) Whr, Yˆ s th stat of crop acrag fro th th town, Y s th approxatly ral PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016 7

8 plantd acrag whch s vsually ntrprtd fro th hgh rsoluton satllt agry. ar sub-populaton an and sapl an of th crop acrag whch ar classfd fro odrat satllt agry. h dfnton of X and X s th sa as n forula (8), and th dfnton of ˆ th sa as n forula (11) Populaton total at county lvl In th fxd ffcts odl, for total stats of ach town and townshp lvl, w hav: Y N X ˆ N ( y x ˆ ) ˆ u (13) x s o su up Y ntr county as follows: ovr th nubr of towns and townshps, w hav th total stats for Yˆ [ N X 1 ˆ N ( y x ˆ)] u N N X u 1 1 y ( x ) ˆ (14) Y 1 to hrfor, th su of acrag stats for th total nubr of sall ara s xactly qual to th total acrag at county lvl n th assupton of gnral lnar rgrsson. Slarly, undr th contxt of saplng wght to b appld, th su of acrag stats ovr all of sall aras s also xactly qual to th total acrag at county lvl n th assupton of gnral lnar rgrsson. 4. Sulaton Rsults 4.1 Exprntal Data For th xprntal ara Laozhong county, w hav dlnatd th whol trrtory nto grds n sz of 100 trs 100 trs. hr ar altogthr grds whch s usd as th saplng unts (PSU). h nforaton usd n sall ara odl buldng ar as follows (abl 1), aong th colun (5) and (6) ar usd as dpndnt varabls, colun (7) and (8) ar usd as ndpndnt varabls. In our study, th Laozhong county s th targt populaton, and ts afflatd 0 towns and townshps ar rgardd as sall aras (doans). wo ajor crops of rc and corn ar our varabls of ntrst. abl 1: Crop ara fro vsual ntrprtaton and classfcaton by town and townshp Unt:Hctar own ID (1) own Cod () own Na (3) Nubr of PSU (4) Rc Ara: ruth (5) Corn ara: ruth (6) Rc Ara fro OLI8 (7) Corn Ara fro OLI Laozhong Cyutuo Yujafang Lngzpu Manduhu Zhujafang (8) PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016 8

9 Lurpu Xnntun Yangshgang Xaojan Changtanzhng Sfangta Chngjaozhn Lujanfang Yangshpu Panjapu Laoguantuo Laodafang Dah Gangz Nuxntuo otal W adoptd spl rando saplng to slct sapls, and dsgnatd svn dffrnt saplng fracton rspctvly as follows: (1) 0.07%, ()0.14%, (3)0.5%, (4)0.5%, (5)1%, (6) %, (7) 5%. Wth rspct to ach saplng fracton, w do th sulaton by slctng th sapls k=1000 ts. In our cas, w adoptd sall ara odl to stat th rc and corn acrag for ach town and townshp. W attptd two scnaros for th sall ara wth rando ffcts and fxd ffcts rspctvly. Manwhl, In ordr to assss th stat prcson fro th thod of sall ara odl, w copard th rsults wth that fro th drct xpanson staton for sall ara. For th 1000 rplcat sapls, n ordr to copar th stat prcson of crop acrag, w coputd th MSE and C.Vs wth rspct to rc and corn acrag for ach town and townshp by th followng thr approachs: (a) drct xpanson for doan stats; (b) odl prdcton (EBLUP) fro th sall ara odl; (c) th stats (prdcton) for ach town and townshp basd on ach ndvdual sall ara odl fro rplcats. For th abov approachs (a) and (c), th an squar rror (MSE) for ach sall ara could b coputd by rplcats. ( Yˆ r Yr ) MSE s(yˆ ) E(Yˆ r Yr ) (15) k Whr, Yˆr and townshp. Whl s th rc or corn plantd acrag statd fro th rth rplcat of th th town Yr s th rc or corn truly plantd acrag fro th rth rplcat of th th town and townshp. Convrtng to coffcnt of varaton (CV), w hav: MSE s(yˆ ) C.V (Yˆ ) 100% (16) Y For th abov approach (b), for ach rplcat w got MSE (Yˆ ) r and C.V (Yˆ ) r fro odl tslf, thn takng th avrag of all ths C.V (Yˆ ) r as a rsult of C.V (Yˆ ). 4. Sulaton rsults for rc and corn Rfrrng to th foraton of quaton (1), yj rfrs to rc or corn ral plantd acrag fro PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016 9

10 approxat ground truth, X j rfrs to rc and corn acrag whch s classfd fro ag. hr ar =0 towns and townshps n Laozhong county. W llustrat th sulaton rsults fro th sall ara odl wth rando ffcts and fxd ffcts. Fgur : C.Vs of rc acrag fro MSE of Prdcton for sall ara odl Fgur 3: C.Vs of rc acrag fro MSE basd on ndvdual stats drvd fro odls Fgur 4: C.Vs of corn acrag fro MSE of Prdcton for sall ara odl Fgur 5: C.Vs of corn acrag fro MSE basd on ndvdual stats drvd fro odls PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr

11 Fgur 6: C.Vs fro th drct xpanson for doan stats h abov Fgur and Fgur 3 ar C.Vs of rc acrag coputd fro odl basd MSE (approach b) and sulaton basd MSE (approach c) rspctvly. Slarly, Fgur 4 and Fgur 5 ar C.Vs of corn acrag coputd fro odl basd MSE (approach b) and sulaton basd MSE (approach c) rspctvly. For sall ara odl, f odl ftnss s good nough, thn th MSE drvd fro th odl should b vry clos to th MSE calculatd fro th sulaton. o splfy th assssnt of stat prcson for sall aras, w could focus on th C.Vs rsults of Fgur 3, Fgur 5 and Fgur 6 to ak coparson. Obvously, th prcson of stats gan sgnfcant provnt for sall aras thr n rando ffcts odl or fxd ffcts odl spcally for a sallr saplng fracton, copard wth th drct doan staton approach. For sall ara odl wth fxd ffcts, t holds on an addtv proprty undr th assupton of lnar odl that th aggrgat of all stats of ach town and townshp s strctly qual to th populaton total for th whol county. Whl for th sall ara odl wth rando ffcts, th abov qulbru s approxatly hold on. In our sulaton, w also xand th C.Vs of aggrgat at county lvl fro suaton of ndvdual stats of towns and townshps n thr rando ffcts or fxd ffcts odl. h C.Vs ar vn outprford than that of a drct xpanson at county lvl (abl ). abl : C.V of rc and corn acrag at county lvl Saplng Fracton Drct Expanson: Ground truth C.V of Rv C.V of Corn Modl Sulaton Rando Effcts C.V of Rc C.V of Corn Modl Sulaton C.V of Rc Fxd Effcts C.V of Corn r=0.07% 14.60% 1.8% 8.% 10.74% 6.06% 5.77% r=0.14% 8.6% 6.65% 7.1% 8.69% 4.0% 4.1% r=0.5% 7.0% 5.6% 6.76% 6.75% 3.04% 3.3% r=0.5% 4.8% 3.6% 4.78% 3.83%.14%.53% r=1% 4.1% 3.1%.55%.0% 1.35% 1.78% r=%.5% 1.81% 1.53% 1.5% 1.15% 1.0% r=5% 1.18% 1.08% 0.79% 0.71% 0.71% 0.63% 5. Dscusson and Concluson 5.1 Prcson Effcncy Espcally n th scnaro of sall saplng fracton, our study llustrats that odl ftnss of sall ara odl wth rando ffcts s bttr than that of odl wth fxd ffcts, whch s rflctd n th rsults of statstcal tst for paratrs as wll as th ffcncy gan of prcson. o xan th prcson of stats for ach ndvdual town and townshp, t s obvously that th C.Vs (dfns as n scton 4.1) s rlatvly lowr whn applyng rando ffcts odl copard PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr

12 to fxd ffcts odl spcally for a sallr saplng fracton. Whn saplng fracton s 0.07%, takng th avrag C.Vs of rc acrag and corn acrag for all th 0 towns as ndcators, th rato of th C.Vs fro rando ffcts ovr th C.Vs fro fxd ffcts s around 44% and 60% rspctvly, ths pls that odl ftnss of rando ffcts n ths scnaro s bttr. Whn saplng fracton s ncrasd to 5%, th rato of th C.Vs fro rando ffcts ovr th C.Vs fro fxd ffcts s around 98% and 99%, ths pls thr s no sgnfcant dffrnc btwn rando or fxd ffcts odl. On avrag, th ratos corrspondng to all th othr scnaros of saplng fracton ls n btwn of lowr lvl 44% and uppr lvl 99%. Fgur 7: h rato of CVs fro MSE undr odl wth rando ffcts vrsus fxd ffcts 5. Modl Ftnss In ral stuaton, th sttng of sall ara odl thr wth rando ffcts or fxd ffcts ostly dpnds on th usr s assupton and undrstandng to th probl solvng. In conotrcs, usually th Hausan tst s usd to chck whthr thr s a fxd or rando ffcts prfrrd to th undrlnd coponnt. But th valdty of th Hausan tst not always guarantd, that ans sots t s dffcult to dtrn whthr to choos fxd ffcts or rando ffcts. In ths study, vn f th sall ara odl wth fxd ffcts dos not hav a suffcnt odl ftnss copard wth that of odl wth rando ffcts spcally whn a sallr saplng fracton, t s also robust to prdct a rasonabl rsults for ach town and townshp whn w scrutnz th stats and ts C.Vs. hrfor, t pls that sall ara odl wth thr rando ffcts or fxd ffcts ar ostly fasbl to produc stats for doans lk town and townshp n ths cas. Wth rgard to th ult-lvl staton both for th town and county lvl sultanously, for th odl wth fxd ffcts th suaton of ach stat of towns xactly quals th stat for th whol county undr th assupton of gnral lnar rgrsson. Whl for th odl wth rando ffcts th suaton of ach stat of towns approxatly quals th stat for th whol county undr th assupton of gnral lnar rgrsson. 5.3 Modl Snstvty of Classfcaton Accuracy As w hav sn, sall ara odl of basc unt lvl wth rando ffcts or fxd ffcts s constructd by cobnng th ground truth data wth classfd ag data rgardd as auxlary nforaton of populaton. Snc th satllt ag classfcaton affctd by any factors such as th ag qualty and classfcaton thods, th accuracy of classfcaton ay vard fro good to du. Gvn th crtan saplng fracton, th odl prcson for stats at town lvl could b pactd by th classfcaton accuracy. Basd on th orgnally classfd vctor data fro Landsat 8 OLI, whch ovrall accuracy for PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr 016 1

13 rc and corn ar around 85% and 90% rspctvly. In ordr to sulat dffrnt accuracs for classfcaton, w addd a dsturbng tr whch s a crtan constant ultply a rando nubr subjct to th standardzd noral dstrbuton for ach grds. hn w calculatd th accuracy of classfcaton agan by coparng th psudo classfd data wth ground truth fro vsually ag ntrprtaton. For th rando ffcts odl, th avrag C.Vs of rc acrag and corn acrag at town lvl corrspondng to varous accuracs ar shown n Fgur 8. akn rc as an xapl, whn saplng fracton s 0.07% and classfcaton accuracy s 80%, th avrag C.Vs at town lvl s around 10.7%. Gvn th classfcaton accuracy at 65%, n ordr to obtan th sa avrag C.Vs at around 10.7%, w nd to hav th saplng fracton at 0.14% whch ans a doubld sapl sz. It rvals that both classfcaton accuracy and sapl sz dtrns an xpctd CVs at town and townshp lvl. In practc, w nd to consdr th trad-off of or accurat classfcaton or fld work of sapls. Fgur 8: h avrag CVs at town lvl undr rando ffcts odl wth varous accuracy 5.4 Concluson In ths study, t s llustratd that a basc lvl sall ara odl n th for of on-rspons ultpl rgrsson wth rando ffcts and fxd ffcts ar both fasbl to produc th stats at town and townshp lvl. Copard wth th fxd ffcts odl, th rando ffcts odl gans or ffcncy n trs of ts C.Vs for town and townshps lvl. akng th advantags of sall ara odl whch cobns th sapl data wth auxlary nforaton of populaton, ths thod could produc th stats for ach sall ara vn f thr s rar or non sapl wthn th doan. Gvn a crtan saplng fracton, a or accurat classfcaton for crops whch s takng as auxlary nforaton for populaton wll bnft th stat prcson for ach town and townshp fro sall ara odl. Sall ara odl provd a soluton to produc stats not only for th towns and townshps but also for th ntr county sultanously. For fxd ffcts odl, th aggrgat of stats of vry town and townshp s xactly qual to th stats for th county undr th assupton of lnar rgrsson. Whl for rando ffcts odl, ths addtv proprty s approxatly hold on. hrfor, t s provd a soluton for ult-lvl staton by applyng sall ara odl. In practc, for th crop survys whch sapls ar slctd fro provnc as targt populaton lk th busnss od of Chna s agrcultural statstcs, thr would b a sgnfcant prcson gans of applyng sall ara odl whch could produc th stats for vry county as wll as provnc tslf n a cohrnt way. PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr

14 REFERENCES [1] Blas, X. and Vanhall, L. t al. Effcncy of crop dntfcaton basd on optcal and SAR ag t srs[j]. Rot snsng of nvronnt, 005,96 (3-4): []Chauhan, H. J. and Arora, M. K. t al. Estatng land covr class ara fro rot snsng classfcaton[j]. Journal of Appld Rot Snsng, 008, : 1-1. [3] Batts, G.E. Hartr, R.M. and Fullr, W.A. An rror-coponnts odl for prdcton of county crop aras usng survy and satllt data[j]. Journal of th Arcan Statstcal Assocaton, 1988(83): [4]Carfagna, E., & Gallgo, F. J. Usng rot snsng for agrcultural statstcs[j]. Intrnatonal Statstcal Rvw, 005(73): [5] Fay, R.E. and Hrrot, R.A. Estaton of nco fro sall placs: an applcaton of Jas-stn procdurs to cnsus data[j]. Journal of th Arcan Statstcal Assocaton, 1979(74): [6] Gallgo F.J. Rot snsng and land covr ara staton[j]. Intrnatonal Journal of Rot Snsng, 004, 5(15): [7] Gallgo, J. and C. Baps. Usng CORINE land covr and th pont survy LUCAS for ara staton[j]. Intrnatonal Journal of Appld Earth Obsrvaton and Gonforaton, 008, 10 (4): [8]Sth, J.H. Sthan, S.V. Wckha, J.D. t al. Effcts of landscap charactrstcs on land-covr class accuracy[j]. Rot Snsng of Envronnt, 003, 84(3): [9] Pan Y.Z., L L., Zhang J.S. t. al. Wntr what ara staton fro MODIS-EVI t srs data usng th Crop Proporton Phnology Indx [J]. Rot Snsng of Envronnt, 01(119): 3 4. [10] Rao, J.N.K. Sall Ara Estaton[M], Nw York:Wly, 003. [11] Opsor J.D., Botts C., and K J. Y. Sall ara staton n a watrshd roson assssnt survy[j]. Journal of Agrcultural, Bologcal, and Envronntal Statstcs, 003, 8(): [1] Mltno A.F., Ugart M.D., and Gocoa. Cobnng saplng and odl wghts n agrcultur sall ara staton [J]. Envrontrcs, 007(18): PROCEEDINGS ICAS VII Svnth Intrnatonal Confrnc on Agrcultural Statstcs I Ro 4-6 Octobr