LARGE DOMAIN SATELLITE BASED ESTIMATORS OF CROP PLANTED AREA

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1 LARGE DOMAIN SATELLITE BASED ESTIMATORS OF CROP PLANTED AREA Michael E. Bellow, USDA/NASS Reseach Division, 3251 Old Lee wy., Rm. 305, Faifax, VA KEY WORDS: Regession, atio, aea sampling fame, impovements of TM based estimates ove suvey bias based estimates wee found fo cotton and ice in Akansas (Allen, 1990b). I. INTRODUCTION NASS etuned to opeational emote sensing in 1991 with a poject in the Mississippi Rive Delta The USDA's National Agicultual Statistics egion, discussed in Section III. In 1994, Landsafi Sevice (NASS) has long been involved with the TM data wee used fo cop classifications and application of eath esouces satellite data to mapping in a pilot study involving the Cow and cop aea estimation. In cetain egions of the Nothen Cheyenne Resevations in Montana (Gaham United States, estimates of aea planted o and anuschak, 19S4). In addition to cop aea havested in specific cops have been geneated estimation, NASS uses eath esouces satellite using combined satellite and gound suvey data. data in the constuction of aea sampling fames These figues ae used as inputs to NASS's setting (Bush and ouse, 1993). of official state level cop aea estimates. Section II discusses the methodology fo The satellite data used fo this application ae satellite based cop aea estimation, including the usually fom Landsafi o Fench SPOT satellites. A sepaate egession estimato. Section IV multispectal satellite scene consists of many intoduces fou altenative satellite based pixels, each having a vecto of scaled enegy estimatos and discusses thei popeties. Section eflectance values in seveal bands of the V compaes estimatos using empiical data. electomagnetic spectum. SPOT's spatial esolution (pixel length) of 20 metes is fine than TM's 30 II. METODOLOGY metes, but TM has seven bands io SPOT's thee. NASS often uses multitempoal data, consisting of This section summaizes the pocedues NASS two scenes fom diffeent dates ove the same aea. follows io pocess satellite and gound suvey data Cop aea estimates at the state o egional fo cop aea estimation. Moe detailed (lage domain) level ae computed by applying desciptions of the methodology ae povided by egession equations to population level classified Allen (1990a) and Gaham (1993). pixel counts within aea fame land use stata, The PEDITOR softwae system, developed at NASS, then summing ove stata. The use of egession is used fo most data pocessing (Ozga et. al., between gound suvey and satellite data often 1992). PEDITOR is installed on a MicoVax 3500 esults in much lowe vaiance than diect compute and IBM compatible pesonal computes. expansion estimation using suvey data alone. NASS conducts the June Agicultual Suvey (JAS) In 1972, the fist Landsat satellite was annually in almost evey state. The aea fame launched, caying the Multispecfial Scanne (MASS) potion of the suvey uses a statification of each with 80 mete esolution. Fom 1972 to 1979, NASS state's aea based on land use (Bush and ouse, developed the basic methodology fo satellite based ISS3). The sample units ae land aeas called cop aea estimation and tested it in seveal segments, usually one squae mile. Each yea, about states (anuschak et. al., 1982). The fist lage 20 pecent of segments ae otated into o out of a scale opeational emote sensing pogam was the state's aea sample. Duing the suvey, enumeatos Domestic Cops and Land Coves (DCLC) poject inteview the land opeatos in each sampled ( ), involving eight states in the cental segment, ecoding the cove (cop/land use), size United States (Allen and anuschak, 1988). Landsafi and boundaies of evey field. The field boundaies MSS data wee used io geneate annual aceage within segments ae dawn onto aeial photogaphs. indications fo con, soybeans, cotton, ice, Field boundaies ae tansfeed fom segment soghum and winte wheat. The DCLC estimates had photos to digital fom. Fo segments that emain in lowe sampling eos than suvey based estimates the sample fom one yea io the next but have field and wee usually close io the official estimates bounday changes, the pevious yea's digitized issued by NASS's Agicultual Statistics Boad. files ae updated to eflect the changes. The The DCLC pogam was discontinued in 1987 in satellite scenes ae egisteed io a map base in ode to pefom eseach on new sensos and latitude/longitude coodinates, allowing JAS implement advanced computing technology. Duing enumeated fields to be matched with thei , eseach pojects in fou states found coesponding satellite pixels. that use of the Landsafi TM senso led io moe Remote sensing analysts divide a state into efficient cop estimates than eithe the Landsat analysis disticts, within which sepaate analyses MSS o Fench SPOT sensos. The lagest ae done. An analysis distict is an aea coveed 194

2 by one o moe satellite scenes having the same ovepass date, o an aea fo which usable satellite coveage is not available. Cop aea estimates ae geneated at the distict level and late summed to obtain state level estimates. Fo a given analysis distict, the pixels epesenting specific gound cove types ae gatheed into sepaate files and clusteed using a modified ISODATA algoithm to geneate multivaiate disciminant functions known as cove signatues (Bellow and Ozga, 1991). All pixels in the analysis distict ae then categoized to cove types using maximum likelihood classification. The subset of classified pixels epesenting the sample segments is used fo egession. classification accuacy assessment and Analysts use a fist-ode egession model to elate classified pixel counts tic the gound suvey data on a pe statum basis. Regession is pefomed only in stata having sufficient sample sizes to obtain a valid elationship. The egession equations ae applied to statum level classified pixel counts tic obtain statum level cop aea estimates. Suvey based diect expansion estimates ae substituted fo egession estimates in stata whee egession is not done. The estimates ae summed ove stata to get analysis distict level estimates, then ove disticts to obtain state level estimates. Vaiance estimates at the distict and state levels ae also computed. Fo convenience, the egession stata will be labeled... E and the non-egession stata h= +1..., whee is the numbe of egession stata and is the total numbe of stata in the analysis distict. The fomula fo the sepaate egession estimato () of cop aceage in the egession stata is: ~(SRG) = ENh ['}h. +bh(~-~. ) ] whee : N h = numbe of population units in statum h Yh. = mean epoted cop aceage pe sample segment in statum h Xh. = mean pixels pe sample segment classified tic cop in statum h n h f'hi=1 i=1 n h = numbe of sample segments in statum h ~ = mean pixels pe population unit classified to cop in statum h The fomula fo the diect expansion estimato () in the non-egession stata is- ^ y() = E NhYh. h= +I The vaiance estimato of is: v(y (SAG)) = ~[N h (Nh-n h) (n h- 1 )/n h (nh-2) ] [ Syh2-bhSxy h ] Syh2 = [11 (nh-1) ]~(Yhi-Yh. ) i=l Sxy h = [1/(nh-1)]Enh(xhi-%.)(yhi-Yh.) i=1 Yhi = epoted cop aceage in statum h, sample segment i Xhi = numbe of pixels classified to cop in statum h, sample segment i The vaiance estimato of in the non- egession stata is: A 2 v(y()) = E h= +1 [Nh(Nh-nh)/nh]syh The composite state level estimate is the sum of the sepaate egession and diect expansion tems: ~(CMP) = ~(SRG) + ~() Similaly, the vaiance estimate of the composite state level estimato is the sum of the vaiance estimates of the two components. Cochan (1977) emaks that the atio of bias to standad eo of the may become appeciable. Since statum level egession estimates of means can have biases of ode i/n h and the biases may be in the same diection in all stata, the bias of the oveall estimate of total could be of ode Nh/n h. oweve, the isk of that lage a bias is small if the elation between the two vaiables is faily linea. Chhikaa et. al. (1988) identified a poblem known as "ovefitting". The use of the same aea fame se~nents to develop both the cop signatues and the egession elationships additional bias to the estimates. can contibute The methodology fo state and egional level estimation has been adapted fo county level (small domain) estimation, using a Battese-Fulle andom effects model (Bellow, 1993). III. MISSISSIPPI LTA PROJECT NASS' s emote sensing effot in the Mississippi Delta egion began in 1991 as an opeational cop aea estimation pogam. The goal was to povide timely state and county level aceage estimates of majo cops to the Agicultual Statistics Boad and MASS State Statistical Offices involved. The states in the 195

3 pogam have been Akansas (1991- ), Louisiana (1992), and Mississippi ( ). Landsat TM data wee used exclusively fom In addition to estimates, the poject has poduced categoized county level cop maps. The two main cops estimated in the Delta poject ae cotton and ice. Table 1 gives the Landsat composite estimates, JAS diect expansion estimates and NASS official estimates of both cops. The elative efficiency (RE), defined as the atio of the vaiance of the JAS diect expansion estimate to that of the Landsat composite estimate, is also shown. In 1993, two sepaate analyses wee done. The fist analysis used unitempoal satellite data fom the sping and povided inputs in time fo NASS's August Cop Poduction Repot. The second analysis, simila to pevious yeas, used multitempoal satellite data fom sping and summe fie poduce end-of-yea estimates. This analysis also used follow-up gound suvey infomation not available in time fo the ealy season estimation. Both types of estimate ae given in Table I fo compaison. Table 1 shows that the Landsat sepaate egession estimate was always below the JAS diect expansion estimate fo both cotton and ice. The Landsat estimate was below the final NASS estimate in five of seven cases fo cotton and fou of seven cases fo ice, and was close than to the final NASS estimate in thee of seven cases fo cotton and fou of seven cases fo ice. Relative efficiencies anged fom 2.2 to 21.0 fo cotton and 1.5 to 5.5 fo ice. In the 1993 Akansas analyses, the late season RE was moe than twice the ealy season RE fo both cops. Fom the above esults and pevious DCLC findings, the following obsevations can be made. Satellite based estimation can achieve damatic eductions in vaiance ove the taditional suvey based methods. The degee of eduction vaies with cop. oweve, in the Delta poject the Landsafi based estimate was close than the JAS diect expansion estimate fie the final NASS estimate less than half the time, as opposed fie 60 pecent fo the DCLC poject ove eight yeas. The Landsat estimate tended fie fall below the coesponding diect expansion estimate. IV. ALTERNATIVE SATELLITE BASED ESTIMATORS In this section, fou altenative lage domain cop aea estimatos ae descibed. These estimatos ae based on the same pixel classification used to compute the sepaate egession estimato. Thee of the fou estimatos use the oveall (acoss-stata) count of pixels classified fie a cop. The emaining estimato equies the individual statum level pixel counts fo its computation. The ationale fo intoducing these estimatos is fie compae thei bias and vaiance popeties with those of. A. Raw Pixel Count Estimato ~CR~ = ~x = convesion facto (aea units pe pixel) X = numbe of pixels classified to cop of inteest in analysis distict The aw plxel count estimato () is a diect count of pixels classified to the cop of inteest, conveted to aea units. Since it epesents a complete enumeation of classified pixels in an aea, does not have sampling eo. oweve, thee is a theoetical bias due to classification eo, which can be appoximated by : B () = Y [ (~c-~o) I ( I-~ c ) ] Y = tue aea planted fie cop of inteest in analysis distict ~o = pobability that a pixel belonging to cop of inteest is not classified to that cop (omission eo) ~c = pobability that a pixel classified to cop of inteest does not belong to that cop (commission eo) Thus the bias is positive o negative depending upon whethe the pixel level pobability of commission eo is geate than o less than that of omission eo. The denominato tem indicates that the bias is especially sensitive to commission eo, so can seveely oveestimate the tue cop aceage if (x c is high. B. Sepaate Ratio Estimato ~(SR) _ ~ h--'l [Yh./~.lXh Vaiance Estimato - v[y (SR) ] = ~ [N h(nh-n h)/n h] [Syh2+~2Sxh2-2~Sxyh ] Sxh = [ll(nh-l)] E (Xhi-Xh.) 2 i=l 196

4 Chhikaa et. al. (1986) studied atio estimatos fo cop aea estimation at the individual statum level. Ratios can be computed in each statum having a positive numbe of sample segments and fo which a positive numbe of pixels wee classified to the cop of inteest. Diect expansion is used in othe stata to fom an oveall composite estimate. If atios ae computed in all stata, then the following statement can be made about the bias of SRE: B[y (SR)] = o[1/2g(y(sr))cv(~h.)] whee o(.) means "on the ode of", G(.) denotes the fiue standad deviation and CV(.) denotes the tue coefficient of vaiation. Cochan (1977) does not ecommend SRE unless the sample size in each statum is lage enough that the vaiance estimate is valid and the cumulative bias is negligible. C. Combined Ratio Estimato ~(CR) = [Yst/Xst]X N = total numbe of population units ~ - (~/~)F. Nh~" h--1 tt h-1 Vaiance Estimato - v[y(cr)] = Z [Nh(Nh-nh)/nh][Syh2+R2Sxh2-2RSxTh ] The combined atio estimato (CRE) epesents an adjustment of to compensate fo bias. The adjustment facto is the atio of expanded epoted aceage fie expanded classified pixel count fo the cop of inteest. The combining of data fom all stata eliminates the need to use diect expansion in weak stata, as was the case with SRE. The bias of CRE has the following uppe bound (Cochan, 1977) : B[y (CR)] <_ G[y(Ca)lcV[xst] Thus the bias is negligible elative to the standad eo if the CV of the weighted pixel mean is less than 0.1. CRE is much less pone to bias fihan SRE. D. Combined Regession Estimato ~(CRG) = N[~st+~(~_Xs t)] = [ Z AhSxyh]/[ Z AhSxh 2] A h = N h (Nh-n h)/n h R = XIN Vaiance Estimato - v(y(crg)) Z [Nh(Nh-nh)/nh] 2 "2 2 " ffi [Sy h +b Sxh -2bSxy h] The combined egession estimato (CRGE) is analogous to the combined atio estimato in that infomation fom all stata is combined. This estimato equies that sample segment sizes be the same in all stata having a positive numbe of segments in the analysis distict. Cochan (1977) obseves that CRGE is less pone to bias than when sample sizes ae small within individual stata. Futhemoe, the vaiance of has a lage contibution fom sampling eos in the egession coefficients. The vaiance of CRGE is inflated if the population egession coefficients diffe fom statum to statum. CRGE is pefeed if the egessions ae linea with slopes oughly the same in all stata. V. COMPARISON USING EMPIRICAL DATA An empiical compaison of the five satellite based estimatos (SRE, CRE,, CRGE, ) and the suvey based diect expansion estimato () was done using 1991 data fom Mississippi and 1993 data fom Akansas. The Mississippi distict extends the length of the state along the Mississippi Rive, containing all o pat of 33 counties. The Akansas distict contains 12 counties in the east cental pat of the state. The following discussion is intended to illustate estimato pefomance using the two data sets; moe geneal hypotheses o conclusions beyond the context of the study should not be infeed. As a benchmak fo evaluating the estimatos, poated "official" estimates of cop aceage in the two disticts wee calculated. Official county estimates ae issued by NASS's State Statistical Offices. The official cop aea estimates fo counties entiely contained in the analysis distict wee summed, then added to the sum of scaled official estimates fo counties patially inside the distict. The scaling was done by multiplying the full county estimate by the atio of numbe of population units in the included potion of the county to numbe of population units in the whole county. The esults ae given in Tables 2 though 5. The agicultual land use stata ae defined based on pecent cultivation, given in paentheses in the "statum" column. was eithe the highest 197

5 o lowest of the five satellite based estimates in all cases, and was much highe than the othes fo cotton in Mississippi and ice in Akansas. This obsevation is not supising in light of the discussion of 's bias in Section IV. The fou satellite based estimates othe than always fell below the "official" estimates. was much highe than, CRGE, SRE, CRE in both disticts fo ice, while faily close to them fo cotton. The two combined-type estimates (CRE, CRGE) wee highe and close to "official" than both sepaate-type estimates (SRE, ) fo both cops in Mississippi and ice in Akansas. In the same thee cases, the vaiances of those fou estimatos did not diffe appeciably. These empiical esults and the theoetical popeties given in Section IV suggest that the thee altenative estimatos most competitive with ae SRE, CRE and CRGE. While these estimatos exhibit similaities, a given estimato may be pefeed unde cetain conditions based upon its unique attibutes. In paticula, the two combined-type estimatos have moe favoable bias popeties than. Futue eseach will compae the estimatos egions. VI. SiRdMARY fo othe cops in diffeent This pape descibed the histoy and status of lage domain satellite based cop aea estimation at NASS, and compaed seveal estimatos fo this application. Since the onset of satellite data eseach in 1972, NAgS has developed and efined the methodology though a seies of eseach and opeational pogams. The pocedues have been consistently updated to take advantage of impoving emote sensing and computing technology. The shows significantly educed vaiance when compaed with the suvey based diect expansion estimato. oweve, opeational satellite based estimates fom the DCLC and Delta po3ects have geneally fallen below diect expansion estimates. Fou altenative satellite based estimatos wee intoduced and thei popeties discussed. An empiical study evaluated estimato pefomance using cotton and ice data fom the Mississippi Delta aea. Thee of the altenative estimatos (SRE, CRE, CRGE) ae competitive with. Thee will be futhe eseach on these estimatos. REFERENCES Allen, J.D. (1990a),"A Look at the Remote Sensing Applications Pogam of the National Agicultual Statistics Sevice," Jounal of Official Statistics, 6(4), Allen, J.D. (1990b), "Remote Senso Compaison fo Cop Aea Estimation Using Multitempoal Data," Poceedings of the IGARSS '90 Symp0sium, Allen, J.D. and anuschak, G.A. (1988), "The Remote Sensing Applications Pogam of the National Agicultual Statistics Sevice: ," U.S. Depatment of Agicultue, NASS Staff Repot No. SRB Bellow, M.E. (1993), "Application of Satellite Data to Cop Aea Estimation at the County Level," Poceedings 0f the Infienational Confeence on Establis.h~n. ent $uvels, Bellow, M.E. and Ozga, M. (1991), "Evaluation of Clusteing Techniques fo Cop Aea Estimation using Remotely Sensed Data," Poceedings of the Section on Suvey Reseach Methods, Statistical Association, Ameican Bush, J. and ouse, C. (1993), "The Aea Fame: A Sampling Base fo Establishment Suveys," Poceedings of the Intenational Confeence on Establishment Suveys, Chhikaa, R.S., Lundgen, J.C. and ouston, A.G. (1986), "Cop Aceage Estimation Using a Landsat- Based Estimato as an Auxiliay Vaiable," IEEE Tansactions on Geoscience and Remote Sensins, GE-24(1), Cochan, W.G. Yok, N.Y.: John Wiley & Sons. (1977), Sampling Techniques, New Gaham, M.L. (1993), "State Level Cop Aea Estimation Using Satellite Data in a Re~ession Estimato," Poceedings of the Intenational Confeence on Establishment Suveys, Gaham, M.L. and anuschak, G.A. (1994), "Land Cove Maps fo Cow and Nothen Cheyenne Resevations," NASS unpublished memoandum. anuschak, G.A., Allen, R.D. and Wigfion, W.. (1982), "Integation of Landsafi Data into the Cop Estimation Pogam of USDA's Statistical Repofiin~ Sevice ( )," Poceedings of the Eighth Intenational Symposium on Machine Pocessin8 of Remotely Sensed Data, Ozga, M., Mason, W.W. and Caig, M.E. (1992), "PEDITOR - Cuent Status and Impovements", Poceedings of the ASPRS/ACSM/RT92 Convention, U.S. Depatment of Agicultue (1994), Cop Poduction Summay, Statistics Boad. NASS Agicultual 198

6 m Table i: Mississippi Delta Cop Aea Estimates (I000 Aces) COTTON: JAS Landsat Reg. State Yea_. E Estimate S_EE Estimate S EE Akansas (E) (L) Louisiana Mississippi RE Final NASS Estimate i000.0 I RICE: JAS Landsat Reg. State Yea E Estimate S_EE Estimate S E Akansas (E) (L) Louisiana Mississippi E - ealy season; L - late season RE.=== Final NASS Estimate Table 2: Estimated Cotton in Mississippi Reseach Distict (1000 Aces) CRGE SRE CRZ Si atum t ~. Es S.D. ~. t ~. Es S. D_. ~. Est ~. S.D. t ~. Es D ~. S. Est._~. S.D. A (>75Z) B (51-75Z) I C (15-50Z) D (<15Z) 54.0 i0.7 Total Table 3: Estimated Rice in Mississippi Reseach Distict (i000 Aces) CRGE SRE CRE Statum Est ~. S.D._~. Est ~. S.D ~. t ~. Es D ~. S. t =, Es D ~. S. Est_. ~. Est ~. S.D ~. Est ~. A (>752) B (51-752) Total Table 4: Estimated Cotton in Akansas Reseach Distict (I000 Aces) CRGE SRE CRE Statum Est ~. S.D. Est = S.D. A (>752) B (25-75Z) C (<25Z)* Total t ~. Es S.D. t ~ Es S.D Est ~ S.D * - Diect expansion value used fo and SRE Table 5: Estimated Rice in Akansas Reseach Distict (I000 Aces) CRGE SRE CRE Statum S.D. A (>752) B (25-752) Total S.D. Est ~. S.D. Est ~ S.D S.D ,