A STATISTICALLY VALID METHOD FOR USING FIA PLOTS TO GUIDE SPECTRAL CLASS REJECTION IN PRODUCING STRATIFICATION MAPS

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1 A STATISTICALLY VALID METHOD FOR USING FIA PLOTS TO GUIDE SPECTRAL CLASS REJECTION IN PRODUCING STRATIFICATION MAPS Micael L. Hoppus and Andrew J. Lier ABSRACT. A Landsat TM classification metod (iterative guided spectral class rejection) produced a fore cover map of soutern We Virginia tat provided te ratification layer for producing eimates of timberland area from Fore Service FIA ground plots using a ratified sampling tecnique. Tese same ig quality and expensive FIA ground plots provided ground reference data for te classification metod. Dividing te counties in te soutern portion of te ate into two groups, and using te FIA plots in eac county group to make te rata for te oter, avoids te potential bias incurred by aving te plots ratify temselves. Tis procedure acieved te required precision of 3 percent sampling error per million acres of timberland. BACKGROUND Te Fore Inventory and Analysis (FIA) program of te USDA Fore Service is responsible for inventory and monitoring of te Nation s fores. Congress mandates, troug te Fore and Rangeland Renewable Resources Planning Act of 974 and te McSweeny-McNary Fore Researc Act of 98, tat FIA continuously determine te extent, condition, volume of timber, growt, and depletion of te Nation s fore land. In te Ea, atiical eimates derived from FIA inventories mu meet specified sampling errors; for example, a 3-percent error per million acres of timberland is te maximum allowable sampling error for area. Timberland is defined by FIA as fore land tat is producing or capable of producing crops of 0 cubic feet of indurial wood per acre per year (Hansen and oters 99). Until now, FIA as reaced tis precision in part by ratifying te FIA ground plots using aerial potos and implementing a ratified sampling tecnique (Cocran 977). However, te Agricultural Researc, Extension, and Education Reform Act of 998 (PL 05-85) directs all FIA units to cange from an inventory frequency of 0 to 4 Researc Foreer and Foreer, respectively, U.S. Department of Agriculture, Fore Service, Norteaern Researc Station, Newtown Square, PA Pone (60) ; moppus@fs.fed.us 44 years per ate to an annual inventory syem tat ground samples 0 percent of eac ate per year (Gillespie 999). Tis new inventory design requires plot ratification every 5 years. Te Norteaern FIA unit, responsible for surveying 3 Norteaern States, uses aerial potos from te National Aerial Potograpy Program (NAPP) for FIA ground plot ratification. NAPP currently is on a 7-year cycle. Te ig co of additional qualified potointerpreters necessary to complete aerial poto ratification in all te ates on a 5- year cycle plus te 7-year cycle of NAPP as led to inveigations of te use of satellite imagery to create a ratification layer for ratifying te ground plots into omogeneous groups in order to reduce te variance of eimates (Cocran 977). Furtermore, satellite image classification provides a fore cover map tat can be used to evaluate fore diribution and cange over space and time. OBJECTIVES Te primary purpose of tis project was to eimate te timberland area contained witin te 4 soutern counties of We Virginia. Additionally, we wanted to make and evaluate FIA s fir practical application of satellite imagebased ratification. Preliminary results of tis analysis were requeed by te State foreer of We Virginia. An

2 important goal of te image classification design was to use te FIA ground plots as reference data in a atiically valid way. Te plots provide abundant ig quality ground trut tat is well diributed, recent, and accurately located wit GPS. Te risk, of course, is tat use of te plots to make ratification maps may produce atiically invalid eimates from a po-ratified random sampling metod, i.e., te plots migt erroneously be used to derive te ratification layer tat will ten in turn be used to ratify tem. We ypotesized tat timberland area eimates produced from ratification of te plots based on satellite imagery would be more precise tan eimates provided by simple random sampling of ground plots. METHODS Ground Plots FIA ground plots were diributed randomly over te landscape in te 4 counties of te FIA s Soutern unit of We Virginia wit an intensity of approximately one plot per 6,000 acres or one plot about every 3 miles. Data were collected in 000 and 00. Many data were obtained on eac plot in accordance wit FIA protocol, including current land use class. Timberland is one land use class wose area can be eimated from te survey (USDA Fore Service 00). Te plot coordinates were converted to a vector GIS representation of te information. ERDAS Imagine (ERDAS, Atlanta, Georgia 3039) image processing software was used for image classification. Satellite Image Classification An innovative classification tecnique called Iterative Guided Spectral Class Rejection (IGSCR) was used to produce a fore/nonfore map of te area from te six non-termal bands of Landsat TM. Tis tecnique was developed wit te specific objective of producing FIA pase inventory: FIA plot ratification to improve te precision of eimates (Wayman and oters 00). At its core, te metod uses a large number of reference pixels, wose spectral signatures and fore or nonfore information class are known, to label te spectral classes created from an unsupervised classification. An unsupervised classification is a common tecnique used to group pixels tat ave similar spectral caracteriics. Acquiring sufficient amounts of accurate fore reference data tat can be used for creating te pool of reference pixels is often very difficult and expensive (Congalton and Biging 99). Tis project made use of te large number of exiing FIA ground plots as its source of ig quality, accurately located reference data to be used as training sites for image classification. Te layout and geometry of te ground plots ave implications for use as image classification reference data. Two issues mu be considered wen comparing te pixel brigtness values of Landsat TM images and teir corresponding FIA plot data. Fir, te FIA plot consis of four 48-foot-diameter circular subplots: one in te center, and tree symmetrically separated from te central subplot by 0 feet (fig. ). Tis means tat te plot places a subplot on a minimum of 4 pixels. Eac subplot covers only 9 percent of te area of a pixel. Second, te location accuracy of te pixel is plus-or-minus 30 m on average and te GPS location accuracy of te plot center is about plus-or-minus 0 m. Terefore, tere is not a clear one-to-one relationsip between plot data and a single pixel. We ave found from previous work tat plots closer tan about 90 m (3 pixel widts) to a different land cover type sould not be used for reference data to classify pixels. For te same reason, only plots tat ave a single land use class over te four subplots sould be used to elp classify te satellite image. Figure. Te FIA ground plot geometry versus 30-m TM pixels. Te plot consis of a cluer of four 0.07-a subplots. Te dark gray circles represent te area of locational error due to GPS errors. Te larger gray circles represent te potential locational error due to image regiration. 45

3 For details of te image classification algoritms and te ERDAS Imagine Software usage, see ERDAS (997). Reference pixels for foreed areas were identified by overlaying te location of omogeneous timberland plots onto te satellite image using ERDAS Imagine. By using a region growing tool in tis software, a cluer of spectrally similar pixels was created for eac timberland plot. Reference pixels for nonfore areas were created by interpreting digital orto-maps and growing a region of spectrally similar pixels at te corresponding location on te satellite imagery. We did not use nonfore FIA plots for locating nonfore training sites because FIA plots do not caracterize nonfore areas well from a spectral point of view. Areas covered wit trees may ave a nonfore definition, suc as city parks. Typical nonfore areas, suc as roads, buildings, quarries and paures, are easy to identify on digital orto-maps. Four raw Landsat TM images tat cover te area were mosaicked togeter. Documentation on ow te software performs tis task is weak, and tere was some concern tat differences in pixel brigtness values between scenes at te overlap area would create spectral confusion. A careful examination of te finised fore/nonfore map sowed no evidence of mapping inaccuracies along te seams of te mosaicked images. However, it is important to note tat wen maps were produced from te same mosaic, using more traditional supervised and unsupervised classification metods, definite inconsiencies occurred at te seams. Te classification metod we used did not appear to produce any noticeable inconsiencies at te seam lines of te scenes. Te satellite scenes were all acquired during late May and early June 000. maximum-likeliood decision rule. Tis resulted in a fore/ nonfore raer map tat was used as a basis for all ratification metods. STRATIFICATION METHOD A simple metod was used to keep te plots from being ratified by te same map tat tey produced. Te 4 counties were divided into two sets. FIA plots from eac of te two county sets were used to create reference pixels tat were used to produce two independent fore/nonfore maps using te IGSCR tecnique. Te fore/nonfore maps of county set A were produced wit te elp of plots located only in county set B and vice versa. Te result was tat all FIA plots located in eac of te counties were labeled, and teir eimates weigted, by rata created from a map produced by plots located outside te county. Stratified random sampling procedures were applied to te FIA plots located witin te 4 counties of FIA unit 3 of We Virginia to eimate timberland area. For details of te ratified random sampling protocol, see Cocran (977). Tree ratification designs were compared in tis project:. Two rata Fore and Nonfore;. Four rata Fore, Nonfore, Fore witin pixels of Nonfore, and Nonfore witin pixels of Fore; 3. Four rata (based on te number of foreed pixels witin a 5 X 5 pixel window) 0-6 foreed pixels, 7-7 foreed pixels, 8- foreed pixels, and 3-5 foreed pixels. An unsupervised classification (ISODATA) metod cluered te mosaicked image into 00 spectrally similar classes. Te IGSCR algoritm accepts and labels a spectral class wen 90 percent of te reference pixels contained witin a given class ave te same information class: fore or nonfore. At lea 0 reference pixels ave to be located witin te class. All classes not labeled in te fir iteration are rejected into a single group of pixels tat are again subjected to an unsupervised classification. A portion of tese second iteration classes is labeled, and a tird iteration of te process is performed. Te signature files for all te classes labeled as pure fore or nonfore are ten merged into one signature file and used in a supervised classification using te A previous udy found tat nearly all of te significant Landsat TM predictor variables for timberland area on an FIA plot were based on images created by 3 X 3 or 5 X 5 filters. Tese filters were designed to calculate te average or andard deviation of pixel brigtness values (raw bands and transformed layers) witin te window or, wen applied to classified images, tey summed te count of foreed pixels witin te window (Hoppus and oters 00). Tis indicates tat te geometry matc between te plots and te TM pixels requires a measurement of eac pixel s neigborood for be results wen using Landsat TM derived maps to ratify FIA ground plots. Te numbers of foreed pixels in eac of te four rata based on te 5 X 5 pixel neigborood were cosen based on te results of tis udy (fig. ). 46

4 Figure. Filtering te fore/nonfore map into rata. A 5 X 5 pixel filter window is passed over te fore/ nonfore map. All foreed pixels witin te window are counted and te sum placed in te center of te window. Tis results in a new raer map of fore pixel counts. Pixels wit values equal to foreed neigborood counts are grouped into rata. Placement of an FIA plot into a given ratum was based on te value of te pixel coinciding wit te center of te central subplot. It was predicted tat te four rata designs would reduce te variance of te eimate of timberland area more tan te two rata fore/nonfore design because tey would be more likely to group plots based on teir proximity to fore edges and/or areas of differing eterogeneity. Stratified Eimation Formulae Using Satellite Derived Strata Te data collected were calculated using te FINSYS computer syem developed at te Norteaern Researc Station. Te inventory eimates are based on ratified random sampling metodology. Assumptions for te Image Strata:. Eac image pixel in te entire rata is assigned to one of te classes, e.g., fore or nonfore.. Eac plot is also assigned to one of te same set of classes. Notation: Eac class is called a rata and for rata (Cocran 977) N = total number of pixels N = number of pixels in class n = number of plots in class W = N / N proportion of total pixels in ratum y i = proportion of plot i in ratum tat is timberland = mean proportion of timberland for ratum, wic y i n y i = / n = eimate of te proportion of land area tat i= is timberland for ratum L = total number of rata. To obtain an eimate of te proportion of timberland for te entire area, calculate a weigted mean of te individual ratum means. Weigts sould be proportional to te ratum size because it is improper to weigt te mean representing a very small area te same as one representing a very large area. Te overall ratified eimate is =. Te eimated variance of is obtained wit te sums of squares about te mean s = ( y y ) /( n ) n i= and te variance of te mean is var( ) = s / n 3. Te eimated variance of, wit a correction factor for a finite population, is var( ) =, were L 4. To calculate an eimate of total timberland area, multiply te eimate of te mean proportion by te known total land area A ^ = A Te variance of var( y ) = y y i L W = is y y y y W var( y )( f ) = ^ ŷ y ) ( ^ ŷ ˆ A var( y ) f = n / N 47

5 Te andard error is te square root of A ^ SE( ŷ ) = A 5. Te sampling error is equal to te andard error divided by te eimate y SE = A SE( ) / / var( y ) RESULTS var( Te eimates, sampling errors, and relative sampling efficiencies for total timberland in FIA unit 3 are presented in table. Simple random sampling of te plots, witout ratification, provided an eimate of 4,005,380 acres of timberland wit a sampling error of.6 percent. Te required precision for tis area is.5 percent in order not to exceed an FIA limit of 3 percent sampling error per million acres of timberland. All tree of te ratification designs, based on fore/nonfore maps produced by applying te IGSCR tecnique to four mosaicked Landsat TM scenes, provided eimates wit precisions less tan.5 percent. It is clear tat te ratification metod tat grouped and weigted te plots based on te number of foreed pixels in te surrounding 5- pixel neigborood reduced te variance of te eimate te mo (table ). ŷ^ y ) Anoter way to compare te efficiency of a ratification metod is to calculate ow many extra plots would be required to reduce te variance to te same level. Te percent increase in precision is equal to - (original number of plots / original number plus extra plots) 0.5. A total of,7 plots are required to reduce te variance from.6 percent to. percent, te sampling error for te ratified sampling eimate provided by te 5 X 5 foreed pixel sum. Tat s an increase of 908 plots at an additional co of $700,000. DISCUSSION Our results were consient wit tose of McRoberts and oters (in press), were fore land eimates of portions of four ates were produced wit more precision using a satellite-based ratification metod wit four rata wit a - pixel edge. We ad expected tat ratified random sampling would lead to an increase in te precision of eimates of timberland area over tose from simple random sampling. Our main concern, owever, was tat te satellite ratification tecnique would not reduce te variance below te acceptable limit. Furtermore, we wanted to devise a metod tat did not use te FIA plots to make a map tat would be used to ratify te same plots. Our metod of splitting te counties into two groups and using te opposite counties plots for ratification does not violate te assumptions of independence of rata and te corresponding plots. Table. Eimates, sampling errors, and efficiencies for total timberland in FIA unit 3 of We Virginia provided by sampling FIA plots ratified tree different ways using a fore/nonfore map. Four mosaicked Landsat TM scenes were classified using te IGSCR tecnique to produce te map Landsat TM map rata Timberland Sampling error Efficiency Acres Percent a Percent b Simple Random Sampling 4,005, (3.0) n/a IGSCR (F/NF Plot-Pixel) 4,038,696.3 (.47) 69 IGSCR (F/NF/-Pixel Edge) 4,038,55.6 (.33) 90 IGSCR (5X5 Pixel F Sum) 4,056,300.0 (.) a Sampling error for entire udy area (per million acres of timberland). b Sample sizes would ave to be increased by tis percent to acieve te same precision witout ratification. 48

6 Our results indicate tat even witout ratification, we would almo ave met our requirements. It sould be noted, owever, tat tis region of We Virginia is approximately 80 percent foreed. Wen sampling for proportions (fore and nonfore), te variance is generally greater wen te two classes are nearly equal. In tis udy, te classes are not equal, and tus te variance is expected to be lower. Our results also indicate tat ratification using te classification derived from te iterative guided spectral class rejection metod detailed in Wayman and oters (00) can reduce variance below tat from simple random sampling. We tus conclude tat tere is a clear benefit to using classified satellite imagery, not only from a variance reduction andpoint, but also for its possible use in oter applications suc as fragmentation analysis, cange detection, and grapical display of fore land diribution. LITERATURE CITED Cocran, W.G Sampling tecniques. 3d ed. New York, NY: Jon Wiley and Sons. 48 p. Congalton, R.G.; Biging, G. 99. A pilot udy evaluating ground reference data collection efforts for use in fore inventory. Potogrammetric Engineering and Remote Sensing. 58(): ERDAS, Inc ERDAS field guide, 4 t ed. Atlanta, GA: ERDAS Inc. 656 p. Gillespie, A Rationale for a national annual fore inventory program. Journal of Forery. 97(): 6-0. Hansen, M.; Frieswyk, T.; Glover, J.; Kelly, J. 99. Te Eawide fore inventory database: users manual. Gen. Tec. Rep. NC-5. St Paul, MN: U.S. Department of Agriculture, Fore Service, Nort Central Researc Station. 48 p. Hoppus, M.; Arner, S.; Lier, A.J Stratifying FIA ground plots using a 3-year old MRLC cover map and current TM derived variables selected by decision tree classification. (on file at te Norteaern Researc Station, USDA Fore Service, Newtown Square, PA 9073). In: Proceedings of te 000 FIA Symposium; 000 October 7-8; Salt Lake City, UT: 9-4. McRoberts, R.E.; Wendt, D.G.; Nelson, M.D.; Hansen, M.H. In press. Using a land cover classification based on satellite imagery to improve te precision of fore inventory area eimates. Submitted to Remote Sensing of Environment. September 00. (On file at te Nort Central Researc Station, USDA Fore Service, St. Paul, MN.) USDA Fore Service. 00. Fore Inventory and Analysis Nortea Field Guide. Newtown Square, PA: U.S. Department of Agriculture, Fore Service, Norteaern Researc Station, Fore Inventory and Analysis Unit. 98 p. Wayman, J.P.; Wynne, R.H.; Scrivani, J.A.; Reams, G.A. 00. Landsat TM-based fore area eimation using iterative guided spectral class rejection. Poto-grammetric Engineering and Remote Sensing. 67(0):