OPTIMIZED DESIGNS OF FRAMEWORKS AND ELEMENTS IN SPATIAL SAMPLING FOR CROP AREA ESTIMATION

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1 OPTIMIZED DESIGS OF FRAMEWORKS AD ELEMETS I SPATIAL SAMPLIG FOR CROP AREA ESTIMATIO Wag Di, Zou Qigbo, Liu Jia Agricultural Resources ad Regioal Plaig Istitute, Ciese Academ of Agricultural Scieces, Beijig 0008, Cia - wagdicaas@otmail.com; zouqb@mail.caas.et.c; KEYWORDS: Samplig Teciques; Samplig Frame; Samplig Efficiec; Sample-Square Dimesio; Sample Size ABSTRACT: Te experimets were coducted for moitorig crop area b spatial samplig metods i a witer weat mai productio regio wit a size of 4Km 4Km i Hegsui Cit, Hebei Provice i Cia to optimize desigs of te frameworks ad elemets (sample size, sample-square dimesio), based o Remote Sesig (RS) ad Geograpical Iformatio Sstem (GIS) teciques. 5 sample-square dimesio levels (3000m 3000m, 000m 000m, 000m 000m, 500m 500m ad 300m 300m) were selected ad 3 samplig teciques (simple radom samplig, sstematic samplig ad stratified samplig) were applied. Te experimetal results demostrate tat te samplig efficiec b stratified samplig was te maximal (te average relative error was 0.5%, te average sample size varied from 9 to 0); ad tat of te sstematic samplig was iferior (te average relative error varies from 0.74%~.06%, te average sample size is 9); te samplig efficiec b simple radom samplig was te miimum (te average relative error is.04%, te average sample size is 9) amog 3 samplig teciques. Samplig relative error decreased wit sample-square dimesio simultaeousl. We te sample-square dimesio was reduced to a certai extet (te size of sample is 500m 500m), te error was ot decliig a more. Te samplig relative error was te miimum usig te sample-square wit a size of 500m 500m amog 5 sample-square dimesio levels.. ITRODUCTIO As a importat compoet i te forecastig crop productio, te estimatio of crop acreage as alwas bee a focus durig te assessmets of crop productio usig remote sesig teciques at a large area scale (Xu, 99; Su, 996). At te same time, te accurate estimatio of crop area ad plaed a ver importat role o masterig te crop productio status ad formulatig te reasoable measures. Samplig metods were ofte applied i estimatig crop area b remote sesig teciques, suc as Area Samplig Frame was used i Large Area Crop Ivetor ad Experimet (LACIE) ad Agricultural ad Resources Ivetor Surves toug Aerospace Remote Sesig (AGRISTARS) i Te Uited States. Multiple Frames (a kid of samplig tecique) was also recommeded to surve te crop area i some documets publised b FAO. Stratified samplig tecique was emploed i Te Moitorig Agriculture wit Remote Sesig (MARS) project lauced b Europea Uio (EU), 60 sites were sampled ad 7 crops were moitored wit te samplig metod i Europea couties. Some researces were also coducted usig samplig metods estimatig crop area i Cia, suc as stratified samplig tecique were applied b Ce (000) etc ad Liu (00) to moitor witer weat area all over te coutr. Cotto areas were estimated b Jiao (00) usig a stadard relief map wit a :5000 scale to set up samplig frames. Cluster samplig metod ad trasect samplig frameworks were emploed b Wu ad Li (004) to estimate crop area, based o crop stratificatio all over te coutr. Altoug some progresses ave bee made i moitorig crop area wit samplig metods, tere were still some problems required to be resolved, ad te problems were summarized as follow: Te samplig metods used at preset were simplex. Tere ave ot bee compared wit samplig efficiec amog all of samplig metods, ad spatial samplig frame as ot bee optimized. Te calculatio of sample size was ot reasoable ad te formulatio of sample-square was ot optimized. Terefore, a classical statistical sceme ad RS, GIS teciques were applied i tis paper to improve te curret samplig metods sstems for estimatig crop area.. METHODOLOGY. Geeral feature of te experimetal site Te experimetal site is located i Hegsui Cit, Hebei Provice i Cia. Te regio is suited i te warm temperate latitudes, ad as a tpical temperate cotietal mosoo climate. Te multi-ears average raifall is about 600mm, 70% of te raifall cocetrates i te summer seaso. Tere are most of plai ad witer weat is mai crop cultivated i te regio.. Te desig of samplig frame Firstl, a square wit a size of 4Km 4Km was separated as populatio from SPOT4 image correspodig to te experimetal site b te geerate commad i ArcGIS. Te sample square dimesio was desiged 5 levels (Table ) referrig to te size of sample-square publised i te documets o estimatig crop area usig samplig metods (listed i Table ), ad square was adopted as te sape of sample-square. Te, te image was separated square grids wit 5 sizes of 3000m 3000m, 000m 000m, 000m 000m, 500m 500m ad 300m 300m, respectivel. After te separatio wit square grids, tere were 5 samplig frame i te image correspodig to te experimetal site. Witer weat 979

2 Te Iteratioal Arcives of te Potogrammetr, Remote Sesig ad Spatial Iformatio Scieces. Vol. XXXVII. Part B8. Beijig 008 area was sum up as observatio value of oe square grid usig ArcGIS, ad te sum of observatio value was true value of populatio total. Populatio size ad populatio total ivolved i 5 samplig frame were preseted i table 3. Item RI project i US MARS project MARS project LUCAS project lauced b EU TERUTI surve project i Frec Bettio (00) Crop area estimatio i Ira Padd rice area surve i Cia Zou (996) Deis Tsiligirides Gallego Prada Documets Delic etc(00) (995) (998) (999) (00) Uit m m m m m m m m m m m m m m m m m m m m Size of sample (*) Sape square square square square square square square * deotes te size of sample-square was selected at last. Table A review of sample-square dimesios umber Uit m m m m m m m m m m Size Table Results of sample-square dimesio desiged Sample frame Uit m m m m m m m m m m Populatio size 4 4 (96) (44) 4 4 (764) (7056) (9600) Populatio total(m ) Te total area of experimetal site(m ) Table 3 Populatio size ad populatio total icluded 5 sample frames.3 Samplig teciques.3. Simple radom samplig tecique: ) Te calculatio of sample size Sample size was calculated troug te equatio i () t S 0 ( ) () r Y 0 () 0 + Were 0 is iitial sample size; is modified sample size, we 0 />0.05, is modified wit te equatio i (); is populatio size; t is samplig probabilit, we te cofidece level is 95%, t equals to.96; r is relative error, it was 5%; Y is populatio mea; S is populatio variace. Y, S was calculated troug te equatio i (3) ad (4). Y Y i i (3) S ( Y i Y ) (4) i Were Y i is te it populatio uits observatio. Y, S was usuall estimated wit pre-samplig metods (Ji et al, 00; Du, 005; Li, 006). Y, S was surveed directl accordig to all populatio uit observatios i tis paper, referrig to te metod publised b Ce (00). ) Selectio of samples Te samples were selected usig Pseudo-Radom umber metod. Firstl, te pseudo radom umbers equatig wit sample size were geerated b a computer. Secodl, te square grids icluded i te sample frame were umbered, ad te umberig meas were as follow: te square grid located at te upper left corer of te sample frame was assiged, te, oter grids were assiged, 3,., wic I accordace wit te order from left to rigt. After umberig te grids from te first lie, oter grids from secod, tird,., t lie were umbered. At last, all of te grids was assiged a code amig,,.., i te sample frame. We te umber of a grid equated wit pseudo radom umbers geerated i advace, te square grid was draw as a sample. 3) Settig up estimator ad scalig populatio value 980

3 Te Iteratioal Arcives of te Potogrammetr, Remote Sesig ad Spatial Iformatio Scieces. Vol. XXXVII. Part B8. Beijig 008 Sample mea was cose as te ubiased estimator of populatio mea Y. Sample mea ad variace were calculated troug te equatios i (5) ad (6), te estimator of populatio total was calculated i equatio (7), ad te estimatio of populatio total variace was calculated i equatio (8). i i ( i ) (5) s (6) i Y ( f ) v( Y ) s (7) (8) Were, s are sample mea ad sample variace, respectivel; is sample size; Yˆ is populatio size; populatio total estimator; is te ubiased estimator of populatio total; v(yˆ) is te estimatio of te variace of f is sample fractio..3. Sstematic samplig tecique:tere are ma kid of samplig patters durig applig sstematic samplig metod, sice te samples are draw accordig o some rule. samplig patters were cose i te experimet. )Equal-distace sstematic radom samplig Te programmig implemeted wit te equal-distace sstematic radom samplig metod was as follow: Firstl, samplig iterval k was calculated i te equatio ( k ), if / was ot iteger, te k was modified as a iteger. Secodl, samplig start poit r geerated b pseudo radom umbers geerator i computer was selected amog k populatio uits from te first samplig iterval. After fiisig te selectio of r, te start poit was umbered as rt code, oter samples were cose i term of te patter tat oe sample was selected ever k populatio uits, till all of te samples were draw out. At last, te code of te samples was r + k, r + k,... r + ( ) k umbered as. Te sample size was equal to te correspodig value calculated i simple radom samplig metods )Equal-distace sstematic samplig wit order Te differece betwee Equal-distace sstematic radom samplig wit equal-distace sstematic samplig wit order is tat te populatio uit observatios will be listed i ascedig sequece usig te later metod, ad oter programmig are same i two samplig metods. Te scalig of populatio value is equivalet to tat of simple radom samplig..3.3 Stratified samplig tecique:stratified samplig tecique is also kow as classificatio, tat is te populatio was partitio some strata, ad samples were selected i eac stratum, all of te samples were made up of te samples allocated i ever stratum. Te populatio values were estimated troug sample value from eac stratum. Some sigals used i te samplig metod were demostrated. 5 stratum were partitioed ad subscript deoted te stratum umber (,,, L). Te sigals ivolved i t stratum were preseted as follow: Te populatio size is i t stratum. ; l Te sample size is i t stratum. ; l Te it populatio uit observatio Y i i t stratum; Te it sample uit observatio i i t stratum; Stratum weigt, W ; Te samplig fractio i t stratum, Te populatio mea i t stratum, Te sample mea i t stratum, Te populatio total i t stratum, f ; Y i Y Y i i Y ; i i ; Y i ; Te sample total i t stratum, i ; i Te populatio variace i t stratum, S i ( Y i Y Te sample variace i t stratum, s i ( i ) Te selectio of strata idicator Te fractio tat witer weat area (i oe square grid) accouted for te area of a square was cose as strata idicator, ad te populatio was partitioed 5 strata, tat is 0~0%, 0~40%, 40~60%, 60~80% ad 80~00%, respectivel. ) Te formulatio of strata limits Te strata limits were formulated usig Accumulated Square Root of Frequec (put forward b Hodges i 959). Te total square root of strata idicators divided b te umber of strata was stratum limit. Te programmig implemeted was demostrated i a case, were strata were partitioed usig te metod i te samplig frame wit square grids of 000m 000m (Table 4 ). 3) Te calculatio of sample size Sample size was calculated troug te equatio i (9) ) ). ; 98

4 Te Iteratioal Arcives of te Potogrammetr, Remote Sesig ad Spatial Iformatio Scieces. Vol. XXXVII. Part B8. Beijig 008 WS 0 (9) V Were 0 is iitial sample size; V is te variace of populatio mea estimator, V γ Y ( ) (0) t Were Y is te populatio mea, Y s t L Populatio meay ad populatio variace i ever stratum S were ecessar to calculate 0, Y ad S were surveed directl from te populatio. It is ecessar for 0 to be modified, ad te modified equatio is te same wit tat of simple radom samplig. 4) Allocatios of sample size i eac stratum It was still ecessar to allocate te sample size to eac stratum, tat is (,,.L), after te sample size was calculated. Te ratio allocatio, tat is te allocatio i terms of strata weigt, was adopted. Te equatios are as follow W. W () W () 5) Costitutig estimator ad scalig populatio value Te ubiased estimator of populatio mea ad populatio total were calculated troug te equatio i (3)~(4), ad te variace of populatio total estimator was estimated i te equatio (5). 5 W (3) st Y st v ˆ (4) 5 ( Yˆ) v( st ) s (5) Were st is te sample mea b te stratified samplig metod. f umber Fractio(%) Frequec f(z) f (z) Accumulated f (z) Refereced strata limits ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Strata limits Strata limitsaccumulated f (z) /L74./ Table 4 Strata limits calculated b Accumulated Square Root of Frequec 98

5 Te Iteratioal Arcives of te Potogrammetr, Remote Sesig ad Spatial Iformatio Scieces. Vol. XXXVII. Part B8. Beijig Evaluatios of te samplig results:te relative error r was selected as a criterio to evaluate samplig results betwee te populatio total estimators wit te true populatio total. r Yˆ Y (6) Y Were r is te relative error, %; Y is te true populatio total. 3. RESULTS AD AALYSIS 3. Comparisos of te efficiec amog samplig metods Te results of samplig relative error were preseted i Table 5 usig 4 samplig metods (simple radom samplig, stratified samplig, sstematic samplig wit order ad disorder) at 5 square grid dimesio levels, i order to optimize te spatial samplig frame for estimatig witer weat area. It was foud tat te relative error b stratified samplig metod scalig populatio value was te miimum (te average relative error was 0.5%), ad tat of sstematical samplig was iferior (te average relative error varied from 0.74%~.06%), tat of simple radom samplig was te maximal (te average relative error was.04%) amog 4 samplig metods. At te same time, it was also foud tat te variace of samplig error from stratified samplig metod was te miimum (0.0003%); ad te tat of sstematical samplig was te less (0.0035%~0.035%); tat of simple radom samplig was te maximal (0.07%), compared te results of te variace of samplig error amog 4 samplig metods. Oterwise, sample sizes tat required i 4 samplig metods were listed i Table 6. It was foud tat sample size was te miimum usig stratified samplig (te mea varied from 9 to 0); ad te were tose of sstematical samplig ad simple radom samplig (te mea were 9). Te samplig efficiec usig stratified samplig tecique was te maximal amog 4 samplig metods, compreesivel compared samplig precisio (relative error ) ad samplig cost (sample size). Item Simple radom samplig r(%) Sstematical samplig wit order r(%) Sstematical samplig wit disorder r(%) Stratified samplig r(%) Samplig frame* Samplig frame* Samplig frame3* Samplig frame4* Samplig frame5* Aver Var Std C v * deotes tere is a 3000m 3000m of square grid size i te samplig frame; * deotes tere is a 000m 000mof square grid size i te samplig frame; 3* deotes tere is a 000m 000mof square grid size i te samplig frame; 4* deotes tere is a 500m 500mof square grid size i te samplig frame; 5* deotes tere is a 300m 300m of square grid size i te samplig frame. Table 5 Results of samplig error from scalig populatio value amog 4 metods Item Simple radom samplig Sstematical samplig wit order Sstematical samplig wit disorder Stratified samplig Samplig frame* Samplig frame* 9 Samplig frame3* Samplig frame4* Samplig frame5* Aver Table 6 Sample size required i 4 samplig metods 3. Comparisos of sample-square dimesio Te results of samplig error were preseted i Table 7 usig 4 samplig metods at 5 square grid dimesio levels, i order to optimize te size of sample-square. It was foud tat samplig error decreased wit te size of sample-square simultaeousl (te average error varied from.7% to 0.8%), we te size of sample-square varied from 3000m 3000m to 500m 500m. However, we te size of sample-square cotiued to decrease (from 500m 500m to 300m 300m), te samplig error was ot decliig a more, but it became ascedig somewat ( te average error varied from 0.8% to 0.9%). We te size of sample-square was 500m 500m, samplig error was te miimum amog 5 sample size levels. 983

6 Te Iteratioal Arcives of te Potogrammetr, Remote Sesig ad Spatial Iformatio Scieces. Vol. XXXVII. Part B8. Beijig 008 Item Simple radom samplig r(%) Sstematical samplig wit order r (%) Sstematical samplig wit disorder r (%) Stratified samplig r(%) Aver(%) Std(%) C v (%) Samplig frame* Samplig frame* Samplig frame3* Samplig frame4* Samplig frame5* Table 7 Results of samplig error at 5 sample-square dimesio levels 4. Coclusio 4. COCLUSIO AD DISCUSSIO Te samplig ad scalig sceme experimets for estimatig witer weat area were coducted usig 4 classical samplig teciques at 5 sample-square dimesio levels i tis paper, i order to optimize te desigs of samplig framework ad elemets (sample size ad sample-square dimesio). Te experimetal results sow as follow: Te samplig efficiec is te maximal usig stratified samplig metod (te average relative error is 0.5%, te average sample size varies from 9 to 0); ad te tat of sstematical samplig metod is te iger (te average relative error varies from 0.74% to.06%, te average sample size is 9); tat of simple radom samplig metod is te miimum (te average relative error is.04%, te average sample size is 9), compreesivel compared te relative error meas, variaces ad sample sizes i scalig populatio value b sample value usig 4 samplig metods. Te samplig relative error decreases wit te size of sample-square simultaeousl(te size of sample-square varies from 3000m 3000m to 500m 500m), owever, te samplig relative errors do ot icrease a more, but it becomes ascedig somewat, we te size of sample-square is reduced some degree(te size of sample-square is 500m 500m). Te samplig relative error is te miimum usig te size of sample-square is 500m 500m amog 5 square grid levels. 4. Discussio Te mai issues ivestigated i tis paper are optimizig desigig spatial samplig framework (selectig reasoable samplig metod) ad samplig elemets (sample size ad te size of sample-square ), but it is still scarce o te reasoable formulatio of spatial distributio of samples. I fact, after beig draw out, samples are ofte adjacet wit eac oter. cosequetl, tere is a spatial correlatio amog te samples, wic causes a violatio durig usig te samplig metod scalig populatio value. Terefore, it is ecessar to itroduce variograms from Geostatistics as a tool ad te rage a as a criterio to desig te reasoable spatial distributios. REFERECES Bettio, M., Delic, J., Bruas, P., Croi, W., Eide, G. 00. Area frame surves: aim, pricipals ad operatioal surves. Buildig Agro-evirometal idicators,.pp. -7. Ce, Z. X., Liu, H. Q., Zou, Q. B Samplig ad scalig sceme for moitorig te cage of witer weat acreage i Cia. Trasactios of te Ciese Societ of Agricultural Egieerig, 6(5), pp Delic, J. 00. A Europea approac to area frame surve. Processig of te coferece o agricultural ad evirometal statistical applicatios i Rome(CAESAR),, pp. -0. Deis, D. C., Lawrece, H. C., Katerie, B. E Spatial samplig ad te eviromet. Tecical report umber 38, pp. 0. Du, Z, F Samplig teciques ad practices. Tsigua Uiversit Press, Beijig, pp FAO Multiple frame agricultural surves. Volume I: Curret surves based o area ad list samplig metods, Rome FAO Multiple frame agricultural surves. Volume II: Agricultural surves programs based o area frame or dual frame (area ad list) sample desigs, Rome Gallego, F. J Crop area estimatio i te MARS project. Coferece o te ears of te MARS project, 4, pp. -. Jiao, X. F., Yag, B. J., Pei, Z. Y. 00. Desig of samplig metod for cotto field area estimatio usig remote sesig at a atioal level. Trasactios of te Ciese Societ of Agricultural Egieerig, 8(4), pp Ji, Y. J., Jiag, Y., Li, X. Y. 00. Samplig teciques. Te Ciese People's Uiversit Press, Beijig, pp Li, J. C Applied samplig teciques. Sciece Press, Beijig, pp Liu, H. Q. 00. Samplig metod wit remote sesig for moitorig of cultivated lad cages o large scale. Trasactios of te Ciese Societ of Agricultural Egieerig, 7(), pp Madaa, P. 00. Improvig Lad Use Surve Metod usig Hig Resolutio Satellite Imager. Tesis submitted to te Iteratioal Istitute for Geo Iformatio Sciece ad Eart Observatio for te degree of Master. Prada, S. 00. Crop area estimatio usig GIS, remote sesig ad area frame samplig. JAG,3(), pp

7 Te Iteratioal Arcives of te Potogrammetr, Remote Sesig ad Spatial Iformatio Scieces. Vol. XXXVII. Part B8. Beijig 008 Su, J. L Padect o damic moitorig ad ield estimatio for crop i Cia. Beijig. Cia Sciece ad Tecolog Press, Beijig, pp Tsiligrides, T. A Remote sesig as a tool for agricultural statistics: a case stud of area frame samplig metodolog i Hellas. Computers ad electroics i agriculture, 0, Wu, B. F., Li, Q. Z Crop acreage estimatio usig two idividual samplig frameworks wit stratificatio. Joural of Remote Sesig, 8(6), pp Xu, X. R. 99. Bulleti o eviromet moitorig ad crop ield estimatio wit remote sesig. Beijig Uiversit Press, Beijig, pp Zou, H. M A procedure for samplig ivestigatio of padd area. Soutwest Cia Joural of Agricultural Scieces, 7(3), pp

8 Te Iteratioal Arcives of te Potogrammetr, Remote Sesig ad Spatial Iformatio Scieces. Vol. XXXVII. Part B8. Beijig