SIMULATING SAMPLING EFFICIENCY IN AIRBORNE LASER SCANNING BASED FOREST INVENTORY

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1 SIMULATING SAMPLING EFFICIENCY IN AIRBORNE LASER SCANNING BASED FOREST INVENTORY L. Ene, E. Næsset b, T. Gobkken b Norwegin University of Life Sciences, Grdute student - liviue@student.umb.no b Norwegin University of Life Sciences, Dep. of Ecology nd Nturl Resource Mngement - (erik.nesset, terje.gobkken)@umb.no KEY WORDS: Airborne lser scnner, Simultor, Forest inventory ABSTRACT: A simple simultor ws developed to test whether irborne lser scnning cn be used s strip smpling tool for forest inventory purposes. The simultor is bsed on the existing two stges, grid bsed lser inventory procedure. A popultion of trees ws creted using n existing forest stnd structure genertor. Ech tree ws represented by mens of its 3D-crown model derived from irborne lser scnning mesurements nd field mesured prmeters, i.e. totl tree height, height of crown bse nd verge crown dimeter. Monte Crlo simultions were run to ssess the efficiency of volume estimtes obtined from irborne lser scnning nd ground bsed inventory. The lowest RMSE for the lser bsed estimtes ws 5.1 m 3 h -1 (2.0%) nd the highest ws 8.4 m 3 h -1 (3.3%), while RMSE for the ground bsed estimtes vried between 13.7 m 3 h -1 (5.4%) nd 18.4 m 3 h -1 (7.2%). The LIDAR bsed estimtion ws on verge 6.3 times more efficient in terms of MSE thn ground bsed smpling. The RMSE of the volume estimtes incresed with incresing plot size, for given smpling intensity. The results indicted tht forest surveys over lrge res crried out using irborne lser scnning s strip smpling tool cn provide ccurte estimtes, nd cn be more effective thn trditionl systemtic ground plot bsed inventories. 1. INTRODUCTION During the pst two decdes, remote sensing techniques hve proven to meet some of the demnd for environmentl relted dt t firly low cost. Among these techniques, smll footprint LIDAR (LIght Detection nd Rnging) hs become one of the most common remotely sensed dt sources for nlyzing the cnopy structure t the scle of opertionl forest mngement (Wynne, 2006). Reserch hs shown tht profiling LIDAR cn provide relible biomss smpling bsed estimtes t low costs (e.g. Nelson et l., 2006). The LIDAR bsed procedure consists of two stge smpling scheme. LIDAR trnsects re tken by flying prllel fight lines seprted by mny kilometers over the re in question. Systemticlly distributed ground plots or ground trnsects re mesured long the LIDAR trnsect. Ground bsed estimtes re regressed ginst LIDAR mesurements, nd the resulting regression eqution re used for prediction long the LIDAR trnsects cross the entire smpled re (Nelson et l., 2004). In contrst to profiling LIDAR systems which only collects nrrow line of dt on the ground, commercil irborne lser scnners provide n ccurtely geolocted cloud of 3- dimensionl observtions, which cn be relted to ground mesurements such s plots of vrious shpes nd sizes. Scnning LIDAR is tody used opertionlly for stnd-bsed wll-to-wll inventories of forest stnds in Norwy (Næsset, 2004). For lrger regions such s counties or ntions, wll-towll inventories re not fesible. However, even scnning systems cn be used in regionl forest inventory, considering the flight lines s prt of strip smpling design by flying prllel, eqully spced strips over the study re nd collecting smple plots only within strips, using for exmple systemtic smpling schemes. Smpling pplictions re often relevnt in res with size where it is not fesible to estblish ground truth reference vlue. Consequently, designing n optiml inventory system hs to rely on some kind of simultion, where different combintions of field nd irborne dt collection cn be explored. The im of this study ws to develop prototype of simple, smll-scle simultor in order to ssess the efficiency of lser scnning bsed volume estimtes reltive to the corresponding ground plot bsed estimtes, when irborne lser scnning ws used s strip smpling tool. This simultor ws bsed on the two stges, grid bsed smpling procedure developed nd tested by Næsset & Bjerknes (2001) nd Næsset (2002, 2004). 2. MATERIAL AND METHODS Forest stnd dt nd combintions of ground mesurements of single tree prmeters nd irborne lser dt were used to build 3D crown models for Norwy spruce trees. Then, existing forest stnd genertor softwre nd these models were employed to obtin virtul forest s input for the simultions. 2.1 Stnd dt The empiricl stnd dt nd single tree prmeters were comprised in two dtsets. The first dtset (see Bollndsås & Næsset, 2007; Solberg et l., 2006) ws collected in summer Twenty circulr plots of 0.1 h were collected from borel nture reserve locted in south-estern Norwy. The forest ws multilyered with brod rnge of tree sizes nd stnd ges, nd dominted by Norwy spruce [Pice bies (L.) Krst.] nd Scots pine (Pinus silvestris L.). The plots were estblish in subjectively selected spruce dominted sites. On ech plot, ll trees with height (d bh ) 3cm were cllipered nd tree heights were mesured on trees selected with probbility proportionl to stem bsl re. Men 114

2 IAPRS Volume XXXVI, Prt 3 / W52, 2007 dimeter ws defined s dimeter corresponding to men stem bsl re (d BA ) nd men height ws defined s the verge bsl re weighted (Lorey s) height (h L ). Both Globl Positioning System (GPS) nd Globl Nvigtion Stellite System (GLONASS) were used to determine the plnimetric coordintes (Euref89) of the plot centers. The verge estimted ccurcy of the plot coordintes ws 10 cm. For the first dtset, polr coordintes from the plot centre were registered for ll trees with d bh 3 cm. Totl tree height, height of crown bse, crown rdius in four crdinl directions, nd verge crown dimeter were mesured on trees selected from ech plot. The finl coordintes for ll single trees were computed in Euref89, using plot centre coordintes nd plotwise polr tree coordintes. The second dtset (see Næsset, 2004) comprised 60 lrge plots locted in productive forest re of pproximtely 5000 h in the municiplity of Krødsherd, south-estern Norwy. The forest composition ws dominted by Norwy spruce nd Scots pine, while younger stnds were dominted by deciduous species, minly birch (Betul pubescens Ehrh.). The plot res were from 3121 to 4219 m 2, with n verge of 3739 m 2. Within ech plot, ll trees with dimeter t brest height d bh 4 cm nd d bh 10 cm were cllipered in young nd mture stnds, respectively, using 2 cm dimeter clsses. Height mesurements were tken from trees selected with probbility proportionl to stem bsl re t brest height. For ech plot, the men height corresponding to Lorey s height ws computed from the men height of the individul dimeter clsses, weighted by totl plot bsl re for ech dimeter clss. 2.2 Lser dt Lser scnner dt were cquired during June 2005 (lef-on cnopy condition) from the sme re s the first dtset, with n Optech ALTM 3100 sensor operting t 100 khz lser pulse repetition rte nd 70 Hz scnning frequency. The ircrft ws flown pproximtely 750 m bove ground with n verge speed of 75 ms -1. The mximum hlf scn ngle ws 10, nd the corresponding swth width ws bout 264 m. Pulses trnsmitted t scn ngles tht exceeded 8 were excluded from the finl dtset. The verge footprint size ws bout of 21 cm, with n verge point density of 5.09 m -2. First nd lst echo were recorded. 2.3 Lser-derived single tree models Lser dt nd the ground mesurements collected in summer 2003 from 0.1 h stnd plots comprised into the first dtset were used to obtin crown representtion of Norwy spruce trees. Lser pulse hits were relted to tree crown projections by the men of plnimetric coordintes, nd then the resulted lser point clouds were considered s sptil crown models for Norwy spruce trees. Lser pulses with heights below 2 m were considered s ground points. The reltionships between field nd lser mesurements were estblished for totl of 435 spruce trees. Hence, ech of these trees were represented s unique combintions of dimeter (d bh ), height (h), crown height (c h ), crown projection rdius (c r ), stem volume (v) (Tble 1), nd the ssocited 3D crown models. For ech of these trees, the volume ws clculted by the mens of functions for Norwy spruce with brk (Vestjordet 1967). Further in this study, the trees were clled single tree models. Metrics Men S.D. Min Medin Mx d bh (cm) h (m) c h (m) c r (m) v (m 3 ) d bh -dimeter; h-height; c h crown height; c r crown rdius; v-volume; S.D.-stndrd error Tble 1. Descriptive sttistics for individul tree model prmeters. 2.4 Virtul forest The progrm pckge SILVA 2.2 (Pretzsch et l., 2002) ws used to generte virtul forest. The stnd genertor provides tree list with ssocited prmeters. For ech tree, the following informtion ws recorded: tree species, dimeter t brest height, totl height nd height of crown bse, crown dimeter nd tree coordintes (x, y). To generte the tree lists, the input prmeters were tree species, d BA (cm), d mx (cm), h L (m), nd N, obtined from ground mesurements. Only 13 plots from the first dtset nd 25 plots from the second dtset provided cceptble combintions of input prmeters which could be used to obtin tree lists by mens of SILVA 2.2 (Tb. 2). The other plots were rejected due to indvertencies between the test plot reference dt nd model clibrtion of the stnd genertor. Totlly, number of 38 tree lists were obtined nd ech of them ws considered s possible reliztion of forest stnd, given the ground-mesured input prmeters. The virtul forest study re ws defined in 2D-locl coordinte system with xes being multiples of 100 m, nd the terrin ws ssumed to be flt. The frme of study re ws considered to be two-dimensionl rry, where ech (i, j) position is squred re representing forest stnd of 1.0 h. Stnd prmeters First dtset (0.1 h plots) Second dtset (lrge plots) d BA s d mx s h L s Ns d BA s d mx s h L s Ns d BA p d mx p h L p Np d BA b d mx b h L b Nb Mx Min Men d BA =bsl re men dimeter (cm); d mx =mximum dimeter (cm); h L =bsl re weighted men height (m); N=stem number per h; s=norwy spruce; p=scots pine; b =deciduous trees (ssimilted with birch). Tble 2. Summry of stnd metrics for 13 selected plots from the first dtset nd 25 plots from the second dtset. 115

3 To crete the popultion, one of the 38 virtul forest stnds of 1.0 h generted by mens of SILVA 2.2 ws rndomly llocted to ech (i, j) rry position, nd then the stnd coordintes for ech tree were trnslted ccording to the new loction within the rry. The neighborhood effects mong forest stnds were ignored. Thus, the sptil structure of ech cell ws supposed to be independent of the position in the rry. The study re ws defined s squre of 36 km 2. Further, ech tree from the tree list ws substituted with dimeter-equivlent single tree model. Becuse of the reltively smll number of single tree models (i.e. 435 trees) which could be derived from vilble dtset, only d bh ws used s key. The rest of the single tree model prmeters, i.e. height, crown height, crown rdius, lser pulse heights, nd stem volumes, were then trnsferred to the corresponding dimeter-equivlent trees from the tree list positioned t (x i, y i ) coordintes in the study re. The mtching results often consisted of more thn one single tree model with equl dimeters. In this sitution, only one of these tree models ws rndomly selected to replce the tree t the position (x i, y i ) from the generted forest stnd. For the situtions when dimeter mtching did not occur- which mens tht some trees from generted forest stnds hve dimeters tht were not mong the dimeters of single tree models, single tree model with dimeter closest to the missing vlue, either lrger or smller, ws selected insted. Thus, the study re ws re-populted with lser derived tree models, nd the volume of the entire popultion ws clculted s the sum of individul trees. For other species thn Norwy spruce, i.e. Scots pine nd birch, there were no vilble lser dt for building 3D crown models. For this reson, dimeter mtching ws done regrdless of species, which mens tht trees of different species could be mtched if they hd the sme dimeter. After dimeter mtching, trees from the tree list generted by mens of forest stnd genertor were replced with dimeter equivlent Norwy spruce single tree models, regrdless tree species. Lser scnning dt consist of clouds of lser hits relted to tree crowns. In this study, ech lser hit (first echo) hs known x, y nd z-coordintes, but in this nlysis, the (x i, y i ) coordintes of ech lser hit were discrded. It ws ssumed tht lser hits relted to trees inside grid cell fll inside the sme cell where these trees re locted, nd tht ll the hits inside tree crown projection belong only to tht tree. 2.5 Simultor The strip smpling simultion ws bsed on the two-stge procedure described by Næsset & Bjerknes (2001) nd Næsset (2002, 2004) nd follows the pproch proposed by Gobkken et l. (2006). In prllel, n estimtion of men volume by mens of ground plot systemtic smpling ws done, s kind of conventionl inventory. The smpling units consist of equl strips contining the sme number of grid cells. The totl volume ws estimted s the sum of predicted volume for ll grid cells over ll strips. Monte Crlo (MC) estimtes of popultion men volume nd smpling error were derived running 50 itertions for ech smpling scheme. Bis, stndrd devition nd RMSE for estimted men vlues were used to ssess the smpling estimtes ginst the reference volume of the predefined popultion. The systemtic smples of lser scnning strips nd ground plots were treted s rndom smples. Reltive efficiency of regression bsed estimtes obtined from lser scnning strip smpling ginst ground bsed systemtic plot smpling estimtes ws ssessed for ech smpling scheme. Computtions Multiple regression nlysis ws used to estblish strtumspecific reltionships between field mesurements nd lser derived metrics. Bsed on previous findings (e.g. Mgnussen & Boudewyn, 1998; Næsset, 1997, 2002, 2004), two independent vribles derived form first lser pulse returns were used for volume prediction within ech grid cell: the percentile corresponding to the 9 th quntile of lser cnopy height (h 90 ) considering the lowest cnopy height ( 2m), nd the cnopy density corresponding to the proportion of the first pulse lser hits (d 0 ). Cnopy density ws defined s the proportions of first pulse lser hits bove 2 m to totl number of first pulse returns. To clculte the cnopy density, it ws necessry to find the totl number of lser hits within ech grid cell. Becuse the lst echoes from initil lser scnning dt were not vilble, it ws ssumed tht ech grid cell hd uniform coverge of lser hits. Thus, the totl number of lser hits within grid cell could be linerly extrpolted from the number of hits tht fll inside the crown projection. Lser hits with heights below 2 m were considered s ground points s well. The full second order regression model bsed on these vribles ws subject to stepwise vrible selection to develop finl models for prediction. Explortory regression nlysis ws run to detect possible devitions from model ssumptions. Vrious vrince stbilizing trnsformtions of the dependent vrible (smple plot volume) were nlyticlly ssessed by the mens of the Box-Cox method. Five regression models were finlly proposed: (1) multiplictive model, (2) liner model without trnsformtions, nd three different models with trnsformed response vrible: (3) log(y), (4) sqrt(y), nd (5) sin(sqrt(y)). For the multiplictive model, only two independent vribles (h 90 nd d 0 ) were used, nd consequently this model ws not subject to stepwise selection. For the other regression models, n empiricl pproch ws used to obtin regression equtions. Before ech simultion, number of 20 itertions were used to select the finl regression models. First, stripe smpling scheme ws rndomly generted over the study re, nd the loction of ech stripe nd correspondent smple plots were hold fixed. Initil smpling trils were run, nd for ech itertion new popultion outcome ws generted nd smpled. Stepwise regression (p in = 0.05, p out = 0.10) ws used for model selection, nd ech resulted subset model ws registered. After running ll itertions, the most frequently used model form for ech regression model ws selected s finl model to be used for prediction during smpling simultions. Since serious muliticollinerity problems occurred, best subsets regression models were lso derived nd compred to the stepwise regression subsets, in order to select unbised regression models. To estimte the popultion volume, Monte Crlo experiments were run to derive lser scnning nd ground-bsed men volume estimtes. Initil tests showed tht cumulted men volume estimtes over 50 itertions converged towrds the vlue of MC estimtes, while the smpling error decresed symptoticlly. However, the number of itertions should vry with the study re, smple design, nd popultion vribility. Squred smple plots of 200, 400, nd 600 m 2 were used to provide ground estimtes. Using squred plots significntly improves the computtionl performnce during simultion. 116

4 IAPRS Volume XXXVI, Prt 3 / W52, 2007 Prllel lser strips with widths of 160, 180, nd 200 m spced t 1500 m were generted. The smpling intensity for different plot sizes ws held lmost constnt round 0.6% of stripe smpling re, nd the smple size vried with plots size. Compred to smpling intensities in ongoing reserch studies, which typiclly re less thn 0.003% (Gobkken et l., 2006), the smpling intensity t stnd plots level is much higher, but necessry to rech ground smples lrge enough to get relible regression estimtes. Finlly, the MC estimtes for both lser strip nd ground bsed systemtic smpling were ssessed by the mens of two-tiled t-test ginst the popultion vlue. Bis, stndrd devition, nd RMSE for the MC estimtes of men volume were then used to ssess the smpling designs nd regression models. Reltive efficiency of regression bsed lser scnning estimtes ginst corresponding ground bsed estimtes ws clculted s rtio of their respective MSE. Smpling error(m 3 h -1 ) smpling error for lser-bsed estimtes smpling error for ground plot-bsed estimtes stndrd devition for lser-bsed estimtes stndrd devition for ground plot-bsed estimtes Itertions 4. RESULTS Except the multiplictive model, finl regression equtions were built using stepwise regression. A number of 45 men volume estimtes nd their RMSE vlues were derived using five regression models (Tble 4). In ddition, for ech smpling scheme, n estimte of men volume nd the corresponding RMSE were derived by ground bsed systemtic plot smpling (Tble 4). The reference vlue of men volume per h ws 254 m 3, i.e., totl popultion volume of 914,400 m 3 divided by the size of the study re of 3600 h. The simulted study re included over 2.7 million trees. The number of itertions used for ech simultion ensured convergence for both regression nd ground plot bsed estimtes. For men timber volume estimtes, the convergence occurred fter c itertion for smpling schemes using ground plots of 200 m 2, c itertions for plots of 400 m 2, nd fter c itertions for plots of 600 m 2. As the number of itertions incresed, the smpling error decresed symptoticlly (Figure 1). The regression models comprised two to five predictor vribles. The most frequently used prediction vrible ws the interction term, followed by squred height percentile nd cnopy density. Generlly, the R 2 rnged between 0.79 nd The bis of men volume estimtes during itertions in ech simultion rnged between m 3 h -1 (6.5%) nd 10.2 m 3 h -1 (4.0%) for regression estimtes, while the bis of ground bsed estimtes rnged from m 3 h -1 (13.4%) to 31.8 m 3 h -1 (12.5%). MC estimtes of men volume derived by regression rnged between -5.7 m 3 h -1 (2.2%) nd 0.3 m 3 h -1 (0.1%), nd stndrd error between 5.0 m 3 h -1 (2.0%) nd 7.4 m 3 h -1 (2.9%). For plot-bsed MC estimtes, the rnge of bis ws between -2.6 m 3 h -1 (1.0%) nd 3.9 m 3 h -1 (1.5%), with stndrd error between 13.7 m 3 h -1 (5.4%) nd 18.4 m 3 h -1 (7.2%). The lowest RMSE for regression bsed MC estimtes ws 5.1 m 3 h -1 (2.0%) nd the highest ws 8.4 m 3 h -1 (3.3%). RMSE for ground plot MC estimtes vried from 13.7 m 3 h -1 (5.4%) to 18.4 m 3 h -1 (7.2%). Among ll regression models, only the multiplictive nd liner models gve unbised estimtes (p > 0.05) under ll smpling schemes. Ground bsed systemtic plot smpling derived estimtes provided unbised estimtes (p >0.05) for ll smpling designs. Reltive efficiency of lser bsed estimtes reltive to ground plot estimtes vried between 0.11 nd 0.28, with n verge of 0.16, which indictes efficiency in verge 6.3 times higher for lser scnning strip smpling method (Tble 5). Figure 3. Exmple of smpling error estimtion, for multiplictive regression model nd ground plot bse estimtes using strip width of 180 m nd plot size of 400 m DISCUSSION The mjor findings of this study indicted tht: 1) Lser scnning-bsed stripe smpling forest inventory cn provide ccurte nd precise estimtes of men volume for reltively lrge forest res. The LIDAR bsed estimtion ws on verge 6.3 times more efficient in terms of MSE thn ground-bsed smpling. 2) For both inventory methods, the inverse reltionship between plot size nd smple size seemed to be the dominnt fctors tht led to generl increse of RMSE s the plot size incresed. 3) For the ground-bsed systemtic plot smpling method, the plot size ws the dominnt fctor which led the overll trends for the MC estimtes of men volume. The RMSE of volume estimtes incresed by incresing plot size. However, generliztions cnnot be drwn from this study, since mny ssumptions were not relistic compred to relworld pplictions, i.e. smll size of trget re nd smll popultion vribility. Another importnt issue is tht ll metrics derived from the popultion were considered to be error free nd the effects of error propgtion were neglected. As possible error sources could be mentioned errors concerning ground loction of trees nd ground plots, lser smpling nd field mesurements. Nevertheless, we believe development nd ppliction of this first smll-scle simultor hs provided useful insight into some of the chllenges we will hve to fce in the continued work to develop simultors tht cn operte on lrger model forests where lso sptil correltion nd regionl trends in the popultion vlue my be ccounted for. Furthermore, forest stnd genertor clibrted for Norwegin conditions should be developed, nd there is lso need for building up n empiricl dtbse of lser derived individul tree models for ll min tree species in Scndinvi. 117

5 Strip Plot re width Model 200 m m m 2 (m) bis S.D RMSE bis S.D RMSE bis S.D RMSE Lser scnning bsed estimtes (m 3 h -1 ) ns ns ns * ns ns * ns ns * * * ns ns ns ns ns ns * ns ns ns ns ns * * * ns ns ns ns ns ns * s ns ns ns ns * * * ns ns ns Ground plot bsed inventory (m 3 h -1 ) ns ns ns ns ns ns ns ns ns significnce level: * p < 0.05; not significnt: ns > 0.05; Models: 1 multiplictive; 2 log(y); 3 sqrt(y); 4 sin (sqrt(y)); 5-liner. Strip (MSE / MSE b ) width Model Plot size (m 2 ) (m) MSE of lser-bsed estimtes b MSE of lser-bsed estimtes Models: 1 multiplictive; 2 log(y); 3 sqrt(y); 4 sin (sqrt(y)); 5-liner. Tble 5. Reltive efficiency of lser bsed ginst ground plot estimtes. Tble 4. Bis, stndrd error (S.D) nd RMSE of men volume estimtes (m 3 h -1 ). REFERENCES Bollndsås, O. M. nd Næsset, E Estimting percentilebsed dimeter distributions in uneven-sized Norwy spruce stnds using irborne lser scnner dt. Scnd. J. For. Res., 22: Gobkken, T., Næsset, E. nd Nelson, R Developing regionl inventory procedures bsed on scnning LiDAR. In: Hirt, Y., Awy, Y., Tkhshi, T., Swed, T. & Tsuzuki, H. (Eds.). Proceedings of the Silvilser 2006 Conference, Mtsuym, Jpn. Pp Mgnussen, S. nd Boudewyn, P Derivtions of stnd heights from irborne lser scnner dt with cnopy-bsed quntile estimtors. Cn. J. For. Res., 28: Nelson, R., Short, A. nd Vlenti, M Mesuring biomss nd crbon in Delwre using n irborne profiling LIDAR. Scnd. J. For. Res., 19: Nelson, R., Næsset, E., Gobkken, T., Ståhl, G. nd Gregoire, T.G Regionl forest inventory using irborne profiling LiDAR. In: Hirt, Y., Awy, Y., Tkhshi, T., Swed, T. & Tsuzuki, H. (Eds.). Proceedings of the Silvilser 2006 Conference, Mtsuym, Jpn. Pp Næsset, E Determintion of men tree height of forest stnds using irborne lser scnner dt. Photogrmm. Eng. Remote Sensing, 52: Næsset, E. nd Bjerknes, K Estimting tree heights nd number of stems in young forest stnds using irborne lser scnner dt. Remote Sens. Environ., 78: Næsset, E., Predicting forest stnd chrcteristics with irborne scnning lser using prcticl two-stge procedure nd field dt. Remote Sens. Environ., 80: Næsset, E Prcticl lrge-scle forest stnd inventory using smll-footprint irborne scnning lser. Scnd. J. For. Res., 19: Pretzsch, H., Biber, P. nd Ďursky, J The single treebsed stnd simultor SILVA: construction, ppliction nd evlution. For. Ecol. Mnge., 162: Solberg, S., Næsset, E. nd Bollndsås, O.M Single tree segmenttion using irborne lser scnner dt in structurlly heterogeneous spruce forest. Photogrmm. Eng. Remote Sensing, 72: Vestjordet, E Functions nd tbles for volume of stnding trees. Norwy spruce. Rep. Norw. For. Res. Inst. 22: (In Norwegin with English summry). Wynne, R. H Lidr remote sensing of forest resources t the scle of mngement. Photogrmm. Eng. Remote Sensing, 72: