CROP-AREA ESTIMATES FROM LANDSAT;TRANSITION FROM RESEARCH ANDDEVELOPMENT TO TIMELY RESULTS

by

George Hanuschak, Richard Sigman, Michael Craig.Martin Ozga. Raymond Luebbe, Paul Cook,

Dave Kleweno. Charles Miller

Economics, Statistics, and Cooperatives ServiceU.S. Department of Agriculture

Washington. D.C.

I. INTRODUCTION

The utility of LANDSAT data in developingdata in crop-area statistics has been demonstratedby a number of investigators. Generally suchstudies have had "proof of concept" in a researchand development (R&D) mode as their primaryobjective. Obtaining timely results for consump-tion by agricultural data users has been ofsecondary importance in most R&D studies. Incontrast, this paper describes recent efforts bythe Economics, Statistics, and CooperativesService (ESCS) of USDA in developing timely crop-area estimates from LANDSAT with measurable andimproved precision. The 1978 Iowa corn and soy-bean crops were the key items of interest for thisprojeel.

One of the functions of ESCS is to estimatecrop areas planted at national and state levels.These estimates are published by ESCS's CropReporting Board starting on June 30 of the cropyear. 2stimates are updated monthly up untilmid-January at which time final national and stateestimates for the crop year are made. Estimatesfor individual counties and in some states formulti-county areas, called Crop ReportingDistricts, are made by ESCS's State StatisticalOffices (SSO's) in cooperation with state govern-ment agricultural agencies. Small area estimates,however, are often not published until April ofthe year following the crop year.

From 1972 to 1977, ESCS has investigated theability of LANDSAT data to improve crop-areaestimates at state, multi-county and individualcounty levels. The results from these svudieshave been mixed. For winter wheat, substantialimprovements in the precision of crop-areaestimates were obtained in Kansas. For corn andsoybeans, however, good results were obtained onlyfor a subset of investigation areas. Theseprevious R&D efforts took over a year on theaverage to complete and thus the results were notuseable for setting final area estimates for thecurrent crop year. In 1978, on the other hand,ESCS strove to develop timely LANDSAT-based crop-area estimates to supplement current area surveyestimates. These estimates were then input to the

1978 Annual Crop Summary released by the USDA'sCrop Reporting Board on January 16, 1979. Theestimates were also used by the Iowa SSO in makingmulti-county estimates.

II. STATISTICAL METHODOLOGY

A. DIRECT EXPANSION ESTIMATION (GROUND DATA ONLY)

Aerial photography obtained from the Agri-cultural Stabilization and Conservation Service isvisually interpreted using the percent of culti-vated land to define broad land-use strata.Within each stratum, the total area is dividedinto N elementary area frame units. Thiscollec~ion of area frame units for all strata iscalled an area sampling frame. A simple randomsample of ~ units is drawn within each stratum.ESCS conducts a survey in late May, known as theJune Enumerative Survey (JES). In this generalpurpose survey, area devoted to each crop or landuse is recorded for each field in the sampled areaframe units (segments). The scope of informationcollected on this survey is much broader than croparea alone. Items estimated from this surveyinclude crop~rea by intended utilization, grainstorage on farms, livestock inventory by variousweight categories, agricultural labor and farmeconomic data. Intensive training of fieldstatisticians and interviewers is conducted pro-viding rigid controls to minimize nonsamplingerrors. The notation used for the stratifiedrandom sample is as follows.

Let h~1,2, •••,L be the land use strata. Fora specific crop (corn, for example) the estimateof total crop area for all purposes and theestimated variance of the total area is asfollows:

Let Y~Total corn area for a state (Iowa, forexample).

YDE=Estimated total of corn area for a state.Yhj~Total area in the jth sample unit in the

stratum.

1979 .Machine Processing of Remotely Sensed Data Symposilrn

Then, jth sample unit in the hth stratum.

The estimated (large sample) variance for theregression estimator is:

where

Note that,

nh[I:j=ln

h[I:j=l

2r =h

r~ = sample coefficient of determination betweenreported corn area and classified corn pixels inthe hth land-use stratum.

N2 N - nhL h h nh - 2v(YDE)= I: (n - 1) !: (Yhj - Yh)h=l nh h Nh j=l

B. REGRESSION ESTIMATION (GROUND DATA ANDCOMPUTER CLASSIFIED LANDSAT DATA)

The regression estimator utilizes both grounddata and classified LANDSAT pixels'l The estimateof the total Y using this estimator is:

Note that we have not yet made use of an auxiliaryvariable such as computer classified LANDSATpixels. The estimator is commonly called a direct~pansion estimate, and we will denote this byYDE

The estimated variance of the total is:

LY = I: Nh· Yh (reg)R h=l

L n - 1v(Y

R)= I: _h (1

h=l ~ - 2

where2and so lim v (YR) = 0 as rh + 1 for fixed nh.

Thus a gain in lower variance properties is sub-stantial if the coefficient of determination islarge for most strata.

and Yh the average corn area per sample unitfrom the ground survey for hth land use stratum.

b = the estimated regression coefficient for theh~h land-use stratum when regressing ground-reported corn area on classified pixels for the~ sample units.

Xh = the average number of pixels of corn perframe unit for all frame units in the hth land-use stratum. Thus entire LANDSAT scenes must beclassified to calculate~. Note that this is themean for the population and not the sample.

~i = number of pixels classified as corn in theith area frame unit of the hth stratum.

xh = the average number of pixels of corn per. thsample unit 1n the h land-use stratum.

The relative efficiency of the regressionestimator compared to the direct expansionestimator will be defined as the ratio of therespective variances:

Since the entire state of Iowa cannot becovered by LANDSAT imagery of the same date, itwas necessary to define post-strata (analysisdistricts) which where wholly contained within aLANDSAT pass or scene. The formulas for thedirect expansion estimate and regression estimatehold f02 post-strata as presented by Gleason,et. al. The regression estimator described above~c~ed the separate form of the regressionestimator. An alternate form for the regressionestimator, called the combined form, is describedby Craig, et. al.3 Conditions under which use ofthe combin~forrn are appropriate are discussed byCochran. 1 Several types of estimates have alsobeen developed for individual counties.2,4

xhj = number of pixels classified as corn in the

1979 Machine Processing of Remotely Sensed Data Symposium

III. GROUND DATA

The ground data required were: land usestrata boundaries digitized from a latitude-longitude map base, individual field data for allfields in the JES sample segments, aerial photo-graphs with accurate field boundary locatio~s anda follow-up survey of JES fields that were not yetplanted at the time of the JES.

Digitizatio~ of the land use strata bound-aries began in mid-January. The land use bound-aries were located and digitized from Iowa CountyHighway Maps. The vertices were digitized from alatitude-longitude coordinate system and thentransformed to the row-column system of LANDSATdata using each individual scene's registrationtransformation. The digitization of the land uc;estrata boundaries was completed in May. Averagetime to digitize an individual county was one day.

The sample segments had land use or crop typeand area recorded for each field during late Mayand early June during ESCS's June EnumerativeSurvey. The field boundaries were drawn onto Asesaerial photographic prints with a scale of approx-imately 8" = 1 mile. The field level informationwas then recorded on a questionnaire and drawnonto an aerial photograph. In the LANDSAT study,a special edit of each field using photo andquestionnaire data was done to insure accuratefield boundary locations. The questionnaire datawas collected, edited at the individual farmlevel, and keypunched by Iowa Crop and LivestockReporting Service personnel. The data was thentransmitted to Washington, D.C. for individualfield level editing. After editing the JES data,a computer tape with all ground data informationwas sent to Bolt, Beranek, and Newman (BBN) dataprocessing facility in Cambridge, Massachusetts.However, at the time of the JES, all fields hadnot yet been planted. Thus, a follow-up surveywas conducted from July 21 to August 1. Thefollow-up survey questionnaire and aerialphotography were used to determine the land coverfor any fields that were not planted at the timeof the JES. The follow-up survey data was thenused to update the ground data computer files atBBN.

Digitization of fields in the JES segmentswas the next step. All field boundaries weredigitized from the aerial photographs using poly-gonal vertices which were transformed to latitude-longitude. Boundaries of 8600 fields from the 298JES segments were digitized. the process began inmid-July and ended in mid-September. Average timeto calibrate and digitize a segment was one hour.

IV. LANDSAT DATA ACQUISITION

Twelve LANDSAT scenes were required tovirtually cover the state of Iowa. The LANDSATscene covering the northwest ,corner of Iowa wasnot analyzed because only 200 square kilometers ofIowa was not contained in LANDSAT scenes further

to the east. This unimaged area in northwest Iowawas less than 0.2 percent of the total area of thestate. The location of the twelve LANDSAT scenescan be seen in Figure 1.

Based on ESCS's previous LANDSAT analysisexperience in Illinois and on the 1978 plantingtimes, LANDSAT imagery was desired during early tomid-August. Table 1 lists images which wereregistered for the Iowa project. Image datesranged from August 7 to September 4, 1978. As canbe seen from the table, some of the registeredimages contained clouds.

Attempts to obtain cloud-free imagery werenot successful. For path 29. row 31, both August18 and September 5, were cloud free. However, theAugust 18 image was of poor quality, while theSeptember 5 image was not delivered to ESCS byDe~ember 15 in time for it to be registered andanalyzed by December 31. Consequently, thepartially cloud covered August 9 scene wasregistered for path 29, row 31. Path 27 on August16 was cloud free. However, this imagery wasnever received by NASA's Goldstone receivingstation. Thus, partially cloud covered imageryfor August 7 was used for path 27.

Because of the various dates of the IowaLANDSAT imagery, the associated cloud-coverproblems, and the different times at which ESCSreceived LANDSAT data, Iowa was partitioned intoten separate areas, called analysis districts.(See Figure 2) The smallest analysis district,number 2C, contained three counties; the largest,number I, contained twenty counties. Analysisdistrict 3A consisted of the thirteen cloud-covered counties.

A number of analysis districts--for example,3B, 3C, and 3D--have the same image date. Sep-arate analysis districts were formed in such casesinstead of a single large one because the LANDSATdata were received by ESCS for the separate areasat different times. Because of time pressure,analysis districts were formed when data werereceived, instead of waiting until all data for agiven image data were on hand.

For each LANDSAT scene uaed in crop-areaestimation, three major processing activitiestranspired from time of satellite overpass to com-pletion of crop-area estimates. These were:

1. NASA delivery of LANDSAT data productsto ESCS,

2. LANDSAT tape reformatting and sceneregistration, and

3. LANDSAT data analysis and calculationof crop-area estimates.

Figure 3 displays by analysis district thebeginning and ending dates for the LANDSAT pro-cessing activities. The first analysis districtto be completed was 2A on October 26; the last.

1979 A1achine Processing of Remotely Sensed Data Symposium

2B, was completed on December 21. Table 2 dis-plays various summary statistics for the timerequired by each processing activity. As can beseen from the table, on the average,data deliverytook the longest and was the most variable induration of the three processing activities.

By examining daily GOES satellite weatherphotos, ESCS was able to select candidate cloud-free LANDSAT scenes within one to two days after aLANDSAT overpass. LANDSAT computer compatibledata tapes and 1:1,000,000 black and white trans-parencies were supplied to ESCS by NASA's GoddardSpace Flight Center (GSFC). Twenty-four tapeswere ordered from GSFC, twelve of which wereregistered for the calculation of crop-areaestimates. A histogram of delivery times, i.e.time from date of satellite overpass to IPceiptby ESCS, for the twenty-four ordered tapes isshown in Figure 4(a). Figure 4(b) displays thetape delivery times for the twelve scenes whichwere registered.

V. DATA PROCESSING SYSTEMS HARDWARE

ESCS purchases computer time on a number ofdifferent types of computers. These include:

1. A PDPlO computer in Cambridge, Massachu-setts (BBN) , used by ESCS for interactive process-ing such as photo and map digitization, LANDSATanalysis for sample segments, and calculation ofcrop-area estimates;

2. AN IBM 370-168 at the USDA's WashingtonComputer Center (WCC) in Washington, D.C., usedfor computer editing of ground truth data, refor-matting LANDSAT tapes, and batch printing of grey-scales; and

3. The ILLIAC IV computer in Sunnyvale,California, used by ESCS for clustering and "wall-to-wall" classification of LANDSAT scenes.

For electronic data transmission ESCS usesComputer Science Corporation's INFONET data net-work and the Department of Defense's ARPANETcomputer network. Additional pieces of hardwareused by ESCS for LANDSAT data analysis are thefollowing:

two digitizer tablets,

Zoom Transferscope,

Terminal plotter with controller,

leased phone line with muliplexor, and

fifteen KRS (keyboard send-receive)terminals of various types.

The total purchase price of this equipment isapproximately $90,000.

Total IB"!370-168 computer charges for theIowa project were $7,000 (includes usage for com-

puter program testing). PDPIO computer usage forthe Iowa project (including usage for developmentand testing of associated computer programs) wasapproximately $69,000.

VI . SOFTWARE AND DATA MANAGEMENT

A. SOFTWARE

All LANDSAT data analysis for Iowa was doneusing the EDITOR software system with the excep-tion of reformatting tapes and some of the grey-scale printing for registration. The latterfunctions were performed using the IBM 370-168 atWCC.

EDITORS is an interactive image processingsystem which runs under the TENEX operatingsystem. EDITOR provides a link via the ARPA net-work to the ILLlAC IV for large-scale batch pro-cessing. EDITOR is a large collection of programsall called from a single main program using simplecommands describing the function of the programs.The programs communicate with each other throughvarious files. For the Iowa project, EDITOR wasnot changed in any substantial or basic manner.However, a number of improvement~ were made tofacilitate its use.

B. DATA MANAGEMENT

The overall flow of data for the Iowa projectwas as follows:

1. Ground-truth data was keypunched in DesMoines, Iowa, and transmitted via INFONET to WCCin Washington, D.C.

2. Ground-truth data was edited in Washing-ton, D.C. and a ground-truth tape mailed to BBN inCambridge, Massachusetts.

3. LANDSAT tapes from NASA's Goddard SpaceFlight Center in Greenbelt, Maryland were refor-matted and tapes mailed to Cambridge, Massachu-ssetts and Sunnyvale, California.

4. The PDPlO in Cambridge, Massachusetteswas accessed via ARPANET, leased line, or FederalTelephone Service (FTS) dial-up for interactiveprocessing of LANDSAT data for sample segments.

S. Classification parameters were trans-mitted to Sunnyvale, California, via ARPANET for"wall to wall" LANDSAT scene classification.

6. Aggregated ILLlAC IV classificationresults were transmitted back to Cambridge,Massachusetts, over ARPANET for interactive cal-culation of crop-area estimates.

VII LANDSAT SCENE REGISTRATION

LANDSAT data registration procedures used forthe twelve scenes were. data reformatting,selection of control points, determination oflatitude-longitude from USGS quad maps and

W79 Jl.1achine Processing of Remotely Sensed Data Symposium

row-column from grey-scales, third order poly-nomial regression analysis, and the matching ofpredicted segment locations with grey-scales forprecise segment location. Root mean square errorsfor LANDSAT scene registration ranged from 45.3meters to 91.7 meters. Registration procedurestook, on the average, two weeks to complete whichwas a considerable improvement over previous ESCSLANDSAT projects.

VIII. LANDSAT CLASSIFICATION

Based upon the stratified random sample ofground data segments, the estimated avera~e fieldsize was 12 hectares for corn and 13 hectares forsoybeans. Consequently the number of pure fieldinterior pixels was approximately 59 percent oftotal pixels for these two major crops. The mod-ified supervised approach6 was used in developingtraining data for crop signatures.

Within each known cover type, several methodswere used to train the classifier:

Resubstitution, in which all the fieldinterior pixels for the cover type are used; the1/2 sample partition method, in which the datafor 50 percent of the sample segments- are used;and a method where small fields « 5 hectares)were excluded from the training data. Once thetraining data for a cover type was established,there were two additional considerations indeveloping classification parameters. These werethe use of prior probabilities for a cover typeand clustering within a cover type's trainingdata. Types of prior probabilties used werethose proportional to the reported acres in thesample segments or equal prior probabilities.

The primary objective of classification wasto mini~ize the variance of the resulting regres-sion estimates, thus little attention was givento estimating the traditional percent correctclassification measures. As previously shown,the variance of the regression estimate is mini-mized when the corresponding r2 is maximized.

IX. CROP-AREA ESTIMATES

Crop-area estimates for corn and soybeanswere developed at the state, multi-county(analysis district), and individual county levels.At the state and multi-county level, improvementsin precision for the regression estimate (LANDSATand ground data) versus the direct expansionestimate (ground data only) were substantial. Atthe analysis district level, the range of relativeefficiencies for corn was 0.93 to 5.98 and soy-beans ranged from 2.73 to 7.59. Specific-valuesfor all analysis district estimates and theircorresponding relative efficiencies are listed inTables 3 and 4. Clouds covered 13 of the 99counties in Iowa for the available LANDSAT data.Loss of LANDSAT data for portions of a stateduring the optimum period for crop discriminationdue to cloud cover isn't an unusual event. Theconventional direct expansion estimate of ground

data had to be used for the 13 county area inIowa. 7 Individual county estimates had C.V. 'sranging from 7.1 to 59.9 percent for corn and 9.0to 100 percent for soybeans. C.V.'s above 20 per-cent are not suitable for operational data use byESCS.

The state level estimates were input to USDA'sCrop Reporting Board's 1978 Annual Crop Summary forIowa. The analysis district estimates were inputto the Iowa Crop and Livestock Reporting Service'smulti-county level estimates. However, theseLANDSAT based regression estimates were not thesole source of data in determining the state andmulti-county estimates.

X. SUMMARY

The primary project goal of developing timelyand precise crop-area estimates at the state andmulti-county level utilizing both LANDSAT data andconventional ESCS ground data was accomplished.These estimates were used as input to officialUSDA crop reports for Iowa. The major benefit ofLANDSAT regression estimates to ESCS is substantialimprovements in precison with no increase inrespondent burden associated with ground surveys.The repeatability of such an effort, however, iscrucially dependent upon timely delivery ofLANDSAT data to ESCS. It is important to note thatthese estimates must be considerably more precisethan those provided by ESCS's efficient JuneEnumerative Survey to be useful to USDA's CropReporting Board. Cloud cover is a serious problemis estimating crop areas at the sub-state level.At the individual county level the sampling errorsassociated with the crop-area estimate~ aregenerally too large to warrant use of the data.

ACKNOWLEDGMENTS

The authors wish to acknowledge severalindividuals and organizations for their deeplyappreciated contributions to this project: fellowmembers of ESCS's New Techniques Section; IowaCrop and Livestock Reporting Service; NASA-Goddard;NASA-Ames; Bolt, Beranek and Newman in Boston;Charles Caudill, Galen Hart, and William Wigton ofESCS for their overall managment support; KathyMorrissey, ESCS for ground data management, andTricia Brookman, ESCS, for her fine typing efforts.

REFERENCES

1. Cochran, William G., Sampling Techniques,(Third Edition), John Wiley and Sons, 1977.

2. Gleason, C., Starbuck, R., Sigman, R.,Hanuschak, G., Craig, M., Cook. P., andAllen, R., "The Auxiliary Use of LANDSAT Datain Estimating Crop Acreages: Results of the1975 Illinois Crop Acreage Experiment,"Statistical Reporting Service, U.S. Departmentof Agriculture, Washington, D.C., October 197~

1979 Ai1achine Processing of Remotely Sensed Data Symposium

3. Craig, M., Sigman, R., and Cardenas, M.,"Area Estimates by LANDSAT: Kansas 1976Winter Wheat", Economics, Statistics, andCooperatives Service, U.S. Department ofAgriculture, Washington, D.C., August 1978.

4. Cardenas, M., Blanchard, M., and Craig, M.,"On the Development of Small Area EstimatorsUsing LANDSAT Data As Auxiliary Information"·,Economics Statistics, and CooperativesService, U.S. Department of Agriculture;Washington, D.C., August 1978.

5. Ozga, M., Donovan, W., and Gleason, C., "AnInteractive System for Agricultural A~reageEstimates Using LANDSAT", Proceedings of the1977 Symposium on Machine Processing ofRemotely Sensed Data, Purdue University,West Lafayette, Indiana.

6. Fleming, M. D., Berkebile, J. S., Hoffer, R.,"Computer Aided Analysis of LANDSAT-l MSSData: A Comparison of Three ApproachesIncluding a Modified Clustering Approach",Proceedings of the 1975 Symposium on MachineProcessing of Remotely Sensed Data, PurdueUniversity, West Lafayette, Indiana.

7. Hanuschak, G., "LANDSAT Estimation with CloudCover", Proceedings of 1976 Symposium onMachine Processing of Remotely Sensed Data,Purdue University, West Lafayette, Indiana.

Path 30

Row 32

Path 29 Path 28 Path 27

-~~---.~-------"]

// Path 26

Figure 1. LANDSAT Imagery Paths and Rows

Table 1. Iowa LANDSAT Scenes Used in Crop-Area EstimationPercentIowaPath Row Date Cloud-Cover Scene ID

30 30 August 19 0 30167-1627431 August 19 0 30167-1628029 30 August 9 0 21295-1601331 August 9 40 21295-1602032 August 18 0 30166-1622428 30 September4 60 30183-1616231 September4 0 30183-1616432 September4 0 30183-1617127 30 August 8 10 21293-1550031 August 8 15 21293-1550232 August 8 10 21293-1550526 31 August 6 0 21292-15444

1979 Machine Processing of Remotely Sensed Data Symposium

4(8-7)

3D(9-4)

3C(9-4)

3D (9-4)

(8-9)

2A

2B(8-9)

II1II LANDSAT Data not analyzed~ Cloud covered

1

Figure 2. Analysis Districts and Images Dates.

(a) All Tapes Ordered

(b) Tapes Analyzed

Ntunber

8

6

4

2Io

xx x xx x x x X

I I I I20 40 60

Delivery Days

Delivery Dayso 20 40 60 80 100

* = Bad initial tape.Data tape reordered.

Figure 4. De Iivery Times for lA'lDSAT Tapes (Heasured in Calendar Daysfro~ Date of Satellite Overpass to Receipt by ESCS):(a) For all Tapes Ordered, and(b) For Tapes Analyzed

1979 Machine Processing of Remotely Sensed Data Symposilnl

ANALYSISDISl'RICf

1

']A

2Il2C

3B

3C

3D

4

5

~~~~

~"~"~~~~~A

~""~ r~I ~'''''~~. \IP".•••••~

I~""l'~ ,...•••...•••...•••..~~~CC~C~CCC~}.~

~C:CQ«~

I I ~~~I I~~ ,....•...~

•• !lATA DEliVERY.

~ BAD INITIAL TAPE. &TA TAPE REffillERED.

_ REFORMATIII«> AND REGISTRATlOO.

_ ~YSIS AND ESTIMATIOO.

fu;1

SEPT1

(b1

ItN1

LEe1

.IAN1

Figure 3. LANDSAT Data Processing ActivitiesBeginning and Ending Dates

Table 2. Durations for LANDSAT data processingactivities: Summary Statistics

Duration in calendar daysActivity median min max quartiles

Data delivery 49 32 93 37 66

Reformatting,Rel!.istration 16 4 25 8,20

Analysis,Estimation 13.5 7 26 10,18

'1979.I\f1achine Processing of Remotely Sensed Data Symposilm

TABLE 3. 1978 IOWA CORN RESULTS (PLANTED HECTARES)

Coefficient Coefficient Range ofAnalysis ¥DE = 1978 Direct of Variation y '" 1978 LANDSAT of V~riation r

2 for h=l, RelativeDistrict Expansion for YDE R Regression for YR ..,L Efficiency

1 1,462,074 3.48 1,460,234 2.20 .57-.92 2.512A 828,772 4.47 818,892 2.50 .71 3.282B 332,050 1l.50 454,252 3.40 .78-.94 5.982C 106,036 10.98 109,959 9.50 .30 1.24

*3A 657,462 4.36

3B 276,1l2 10.05 268,022 8.47 .38 1.493C 550,581 7.46 542,081 6.02 .34-.40 1.583D 83,658 17.76 82,798 18.65 .07 0.93

4 1,029,688 6.72 896,084 4.47 .65-.71 2.995 148,148 1l.10 149,820 6.03 .75 3.32

State JES= 5,525,807 2.3 5,439,604 1.5 .07-.94 2.43

*LANDSAT data not available.

TABLE 4. 1978 IOWA SOYBEANS RESULTS (PLANTED HECTARES)

Coefficient Coefficient Range ofAnalysis YDE

1978 Direct of Vl1riation ¥ _ 1978 LANDSAT of Vl1riation r2 for h=l, RelativeDistrict Expansion for YDE R Regression for YR " ,L Efficiency

747,759 8.ll 781,566 4.04 .58-.88 3.70

2A 655,049 6.75 675,293 3.42 .74 3.68

2B 256,944 12.91 255,540 6.11 .74-.98 4.55

2C 95,196 24.97 97,497 11.67 .80 4.37

*3A 401,671 9.20

3B 86,550 28.00 125,300 9.37 .79 4.26

3C 328,662 14.51 338,363 7.06 .77 3.98

3D 82,633 32.55 95,933 10.20 .89 7.59

4 441,032 12.68 424,782 7.97 .45-.83 2.73

5 47,060 29.20 48,580 12.53 .86 5.10

State JES=3,205,320 3.91 3,244,525 2.50 .45-.98 2.38

*LANDSAT data not available.

1979 Machine Processing of Remotely Sensed Data Symposium

...

PRECISION OF CROP-AREA ESTlt1ATES

George A. HanuschakStatistical Research Division

Economics, Statistics, ~ Cooperatives ServiceU.S. Department of Agriculture

Washington, D.C. 20250

Invited Paper at theThirteenth International

Symposium of Remote Sensingof Environment

Apri 1 1979Ann Arbor, Michigan

FilE COpy

PRECISION OF CROP-AREA ESTIMATES

GEORGE A. HANUSCHAK

Statistical Research DivisionEconomics, Statistics, and Cooperatives Service

U.S. Department of AgricultureWashington, D.C.

1. INTRODUCTION

The utility of LANDSAT data in developing crop-area estimates has been demonstrated byseveral investigators. The major issue in evaluating crop-area estimates is how to measure theprecision and accuracy of the estimates. This paper describes the methods used by theEconomics, Statistics, and Cooperatives Service (ESCS) of the U.S. Department of Agriculture(USDA) for evaluating crop-area estimates.

Annually in late lillyand early June ESCS conducts a nationwide agricultural survey,referred to as the June Enume~ative Survey (JES), consisting of interviews with farm operatorsin randomly sampled areas of land called segments. Segments enter the JES by selection throughstratified random sampling. The strata are land use categories determined by visual inter-pretation of aerial photography or LANDSAT imagery and delineated on county highway maps. TheJES segments are typically 2.59 square kilometers in size. Strict survey quality controlmethods are used prior to, during, and after the data collection period to minimize nonsamplingerrors at the elementary sample unit (segment) level. l1ethods such as training of statisticiansand interviewers prior to each JES, use of aerial. photographs during the interview with thefarm operators, reinterviews by supervisory interviewers, follow-up survey interviews, dataediting-manual and machine, current aerial photography for comparison, etc. are used to insuredata quality. The relative sampling errors for major crops at the national and regional levelare on the order of 1-3 percent. At the state level they are on the order of 2-10 percent.

Any use of LANDSAT data by ESCS must be an improvement over the extremely efficient JES.The Statistical Research Division (SRD) of ESCS has developed techniques using LANDSAT and JESdata together that produce lower sampling errors than the JES alone. The basic method used bythe SRD is a simple application of regression estimation as described in William Cochran's,Sampling Techniques. This technique has been applied in Illinois (1975), Kansas (1976), andIowa (1978). The Iowa project was completed during the 1978 crop year and in time for theregression estimates to be input to the official USDA Crop Reporting Board's Annual Crop Summaryfor Iowa released on January 16, 1979.

2. STATISTICAL METHODOLOGY

2.1 Direct Expansion Estimation (Ground Data Only)

Aerial photography obtained from the Agricultural Stabilization and Conservation Serviceis visually interpreted using the percent of cultivated land to define broad land-use strata.Within each stratum, the total area is divided into Nh area frame units. This collection ofarea frame units for all strata is called an area sampling frame. A simple random sample of nhunits is drawn within each stratum. ESCS then conducts a survey in late May, known as the JES.In this general purpose survey area devoted to each crop or land use is recorded for eachfield in the sampled area frame units. The scope of information collected on this survey ismuch broader than crop-area alone. Items estimated from this survey include crop-area byintended utilization, grain storage on farms, livestock inventory by various weight categories,and agricultural labor and farm economic data. Intensive training of field statisticians andinterviewers is conducted providing rigid controls to minimize nonsampling errors.

The form of an estimated state total _for a crop from a stratified random sample is asfollows:

Let h = I, 2, ..., L be the land-'llsestrata. For a specific crop (corn, for example) theestimate of total crop-area for all purposes and the estimated variance of the total area is asfollows:

Let Y

Then,

Total corn area for a state (Iowa, for example).

Estimated total of corn area for a state.

Total area in the jth sample unit in the hth stratum.

Y

The estin~ted variance of the total is:

v(Y)

Relative Samping Error =

Note that we have not yet made use of an auxiliary variable such as computer classified LANDSATpix~ls. The estimator is commonly called a direct expansion estimate,l and we will denote thisby Y

DE•

As an example, for the state of Iowa in 1978, the direct expansion estimates were'

Corn YDE = 5,525,807 Hectares/ v(Y)/ Y = 2.4%

Soybeans YDE = 3,205,320 no.ctaresRelative Sampling Error = Iv(Y) / Y 3.9%

2.2 Regression Estimation (Ground Data and Computer Classified LANDSAT Data)

By means of a regression estimator both ground data and classified LA!IDSAT data can beutilized to estimate crop hectarage.2 (Regression estimators are discussed in most samplingtexts, e.g. Cochranl) The estimate of Y using the separate form of the regression estimator is

LL Nh· Yh (reg)h=l

where

Yh (reg)

and bh = the estimated regression coefficient for the hth land-use stratum when regressing

ground-reported hectares on classified pixels for the ~ segments.

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