Separating the ground and airborne laser sampling phases to estimate tropical forest basal area, volume, and biomass

ELSEVIER

Separating the Ground and Airborne Laser Sampling Phases To Estimate Tropical Forest Basal Area, Volume, and Biomass Ross Nelson,* Richard Oderwald, and Timothy G. Gregoire A i r b o r n e laser profiling data were used to estimate the basal area, volume, and biomass of primary tropical forests. A procedure was developed and tested to divorce the laser and ground data collection efforts using three distinct data sets acquired in and over the tropical forests of Costa Rica. Fixed-area ground plot data were used to simulate the height characteristics of the tropical forest canopy and to simulate laser measurements of that canopy. On two of the three study sites, the airborne laser estimates of basal area, volume, and biomass grossly misrepresented ground estimates of same. On the third study site, where the widest ground plots were utilized, airborne and ground estimates agreed within 24%. Basal area, volume, and biomass prediction inaccuracies in the first two study areas were' tied directly to disagreements' between simulated laser estimates and the corresponding airborne measurements of average canopy height, height variability, and canopy density. A number of sampling issues were investigated; the following results were noted in the analyses of the three study areas. I) Of the four ground seg~wnt lengths considered (25 m, 50 m, 75 m, and 100 m), the 25 m segment length introduced a level of variability which may severely degrade prediction accuracy in these Costa Rican primary tropical forests. This effect was more pronounced as plot width decreased. A minimum segment length was on the order of 50 m. 2) The decision to transform or not to transform the dependent variable (e.g., biomass) was' by far the most important factor of those considered in this experiment. The natural log transformation of the dependent °Biospheric Sciences Branch, NASA/Goddard Space Flight Center, Greenbelt College of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, Blacksburg Address correspondence to Ross Nelson, Biospheric Sciences Br,, NASA/GSFC, Code 923, Greenbelt, MD 20771. l~eceived 29 January 1996; revised 5 October 1996. REMOTE SENS. ENVIRON. 60:311-326 (1997) ©Elsevier Science Inc., 1997 655 Avemle of the Amerieas~ New York, NY 10010

variable increased prediction error, and error increased dramatically at the shorter segment lengths. The rru)st accurate models were multiple linear models with forced zero intercept and an untransformed dependent variable. 3) General linear models were developed to predict basal area, volume, and biomass using airborne laser height measurements. Useful laser ~rwasurements inc,lude average canopy height, all pulses (h,,), average canopy height, canopy hits (h,) and the coefficients of variation of these ter~s (c, and c~). Coefficients' of determination range front 0.4 to 0.6. Based on this research, airborne laser and ground sampling procedures are proposed for use fi)r reconnaissance level surveys of inaccessible f~rested regions. ©Elsevier Science Inc., 1997

INTRODUCTION

Airborne laser profiling data may be used to remotely measure tree height. Pulses from a laser transmitter carried aboard an aircraft are directed toward the ground to collect ranging data from aircraft to the top of the canopy, and in some instances, from aircraft to ground. The forward motion of the aircraft in conjunction with the sequential pulses of the laser produce a linear height transect through the vegetation canopy. Mathematical relationships may be established between the sequential laser height measurements and ground and/or photo measurements of forest canopy height, canopy density, timber volume, and forest biomass, These regression relationships can, in turn, be used in conjunction with airborne LIDAR (light detection and ranging) data acquired over a particular study area in order to estimate certain biometric characteristics of that area. Numerous researchers in Canada, the United States, and the former Soviet Union have studied the use of airborne lasers for forest mensuration. Russian investigators 0034-4257/97/$17.00 PII S0034-4257(96)00213-1

312

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developed the theory and hardware to measure tree heights and stand densities and studied the effects of tree canopy shape on laser profilogram measurements (Soludukhin et "al., 1977a,b; 1979; 1985; Stolyarov and Solodukhin, 1987). They found that the more conical the canopy, the greater the laser underestimate of groundmeasured tree height. They analyzed simulated laser profiling data of spruce, pine, dwarf-pine, and larch stands and found that mean laser canopy height underestimated ground-measured heights by 26% in spruce stands, 8-10% in other species. Working in Canada, Sehreier et al. (1984; 1985) characterized the accuracy of airborne laser measurements of tree heights and found that 95% of all laser heights were within 1.8 m of photogrammetrically derived tree heights. They developed a method to discriminate broadleaf and conifer forests based on canopy heights, the power of the laser return, and the variability of the power. Aldred and Bonner (1985) looked at the effects of laser spot size, studied different methods of extracting tree heights from the laser data, and quantified the accuracies of the laser height and canopy density measurements. They found, for instance, that laser measures were within +2 m of photogrammetrie estimates two-thirds of the time, and crown closure classes in increments of 20% were correctly identified 62% of the time. In the United States, preliminary photogrammetric studies to estimate tree heights, canopy density, and forest volume or biomass were initiated by Spurr (1960), Smith (1969), Maclean (1982), and Maclean and Martin (1984). Airborne laser measurements were used in place of photogrammetric measurements to estimate forest heights and canopy density (Nelson et al., 1984) and forest volume or biomass (Maclean and Krabill, 1986; Nelson et al., 1988a,b). In southwestern Georgia (USA), Nelson et al. (1988b) reported that laser-ground comparisons of biomass estimates were with 7-8% on a 6000+ ha study area, but researchers note that the proximity of the flightlines and the ground samples may have lead to an overestimate of the accuracy. These researchers coneluded that laser data can be used to estimate forest volume and biomass remotely, and they have shown that the accuracy of the estimates increased if stands were differentiated by species or species groups. Previous studies that have related laser height measures to various forest canopy attributes have depended on the accurate location of the path of the laser profile on the ground. Once specific sections of the laser transect were located on the ground, regression relationships were developed that estimated the forest characteristic(s) of interest (e.g., ground-measured tree height, total tree biomass, bole volume) as a function of laser measurements of canopy height. This need to accurately locate laser transects on the ground limited the use of the airborne laser data to those areas with adequate ground

control. Accurate registration of tile airborue laser and ground transects required the presence of features which could be precisely located on the ground and in the laser data (e.g., roads, edges of lakes, streams, buildings, forests). Those areas most appropriate fi~r laser ranging-tbr example, inaccessible tropical forest--typically have few ground control features. The tropical forests especially are characterized by extensive regions of unbroken canopy. The primary purpose of this research is to define a procedure that may be used to estimate basal area, volrune, or biomass based on the acquisition of airborne laser data over featureless, t})rested terrain. Necessarily then, this procedure must separate the laser and ground sampling phases. The overall objective of this research is to develop robust sampling and analysis techniques to facilitate the use of airborne laser profiling for forest biomass and volume assessment when no consistent ground control is available. The specific subobjectives which follow provide a general outline of the study approach. 1. Develop and implement an algorithm which can be used to formulate regression equations used to predict basal area, volume, and biomass ibr use with airborne laser data without depending on laser line-ground line coloeation. • Simulate the height characteristics of forest canopies using ground reference information. The simulator utilized fixed-area plot data, including tree location, tree bole, and canopy size inibrmation, to construct a three-dimensional digital representation of the plot. Different forest canopy shapes and ground plot sizes were selected. • Simulate laser transects across the digital model of lbrest canopy heights. Simulated laser measurements of forest canopy height were paired with the corresponding ground measurements of interest, for example, woody bole volume, biomass, tree height, basal area. • Develop predictive equations which linearly relate simulated laser and ground measurements. • Utilize these equations to predict basal area, volume, and biomass using the airborne laser data. Assess the accuracy of these predictions by comparing the airborne laser results to comparable ground measurements. 2. Determine which of various regression models and regression development techniques best predict basal area, volume, and biomass. 3. Look at the issues of ground sampling segment length and ground plot width to describe a sampiing methodology appropriate to the tropical forests of Costa t/ica. The research objectives were addressed using three dif-

Separating Ground and Airborne Laser Sampling Phases 313

Ground Sampling

Computer Simulation

yses called the accuracy of these colocations into question because specific sections of the airborne laser data could not be registered with the ground segments. A third ground data set was collected independently of the laser investigation in the late 1980s on LaSelva. This ground transect data set was located in the neighborhood of a portion of the LaSelva airborne laser data.

CoUect fixed area ground transect data and map locations of stems in forest types similar to airborne laser transects.

Use transect stem maps to construct a two-dimensional array of canopy heights in computer.

t Randomly transect height array to develop I I file of simulated laser measures and coincident [ ground estimates of BA, volume, and biomass.

I

t Regress simulated laser measures (independent variables) and ground measures (dependent variables). Consider:

Model Development

- simple linear regression: v = f(height) - transformed, with intercept, vs. untransformed, thru origin. - parametric vs. nonparametric. - segment lengths, 25, 50, 75, 100m. - airborne laser segment lengths. - multiple linear regression: v = f(multiple laser measures)

Airborne Laser Processing

using predictive models

(og., BA =

f(simulatod laser))

and airborne laser data.

Figure 1. A ttowehart of the general procedure used to develop airborne laser-based estimates of basal area, volume, and biomass.

ferent data sets on two different study sites in Costa Rica (CB). PROCEDURE The research had two distinct components, that is, 1) the development of methods to estimate ground measurements of interest (e.g., biomass) using airborne laser data and ground data which are not necessarily coincident and 2) the development of a statistical framework to produce estimates of the ground measures of interest (e.g., basal area, biomass) using airborne laser data. Figure 1 summarizes the overall procedure used to develop estimates of ground measures of interest using airborne laser data. This procedure was tested using three different ground data sets, one near the town of Tileran, CIt, and two on the LaSelva Biological Station near Puerto Viejo de Sarapiqui, CR. Study Areas and Data Collection Two airborne laser data sets and two ground transect data sets were collected in the mid-1980s, one airground set near Tileran, the second air-ground set at LaSelva (Sader, 1987). At the time of the collections, the ground segments were thought to be coincident with sections of the airborne laser transects. Subsequent anal-

Airborne Laser Data Collection Two study areas in Costa Bica were flown by the NASA P-3a Airborne Oceanographic LIDAB configured with a frequency-doubled Nd:YAC laser transmitting a 9.532 #m beam of green light at 400 Hz. The nominal aircra}} ground speed was 100 m/s, resulting in a nominal alongtrack sampling frequency of 0.25 in (Sader, 1987). Nominal flying height was 400-500 m above terrain; laser beam divergence was set to 5 milliradians (mr), providing a spot size at target of "2.0-2.5 m. The field of view (FOV) of the detector was a 5×5 mr square, providing an actual FOV at the ground of 2.0 m×2.0 m up to 2.5 m×2.5 m. The FOV was boresighted with the transmitted laser pulse. A wavefbrm digitizer was used to record secondary laser pulse returns. These waveform data were processed post-flight to locate ground beneath the forest canopy. The waveform digitizer was described by Hoge et al. (1980), Nelson et al. (1984), and Krabill et al. (1984). The two study sites flown in Costa Rica in October 1984 were located 1) near the town of Puerto Viejo de Sarapiqui at the LaSelva Biological Station on the east side of the continental divide and 2) near the town of Tileran on the west side of the continental divide. On the morning of 19 October 1984, laser profiling data were acquired over the La Selva Biological Station tinder scattered clouds. LaSelva is on the Carribbean side of the continental divide, and it has no distinct, predictable dry season. LaSelva hosts tropical wet and tropical premontaine wet forest (Holdridge et al., 1971); the majorit-/of the then 700 ha biological reserve was in primary forest. Laser data were acquired along two ttightlines oriented approximately NW-SE. Each ftightline incorporated 2-3 km of laser data within the Station borders. The Tileran site was flown on the afternoon of 19 October 1984 under clear skies. The area around Tileran consisted of small, relatively" open, patchy t})rest stands which had been disturbed by selective logging; however, there were remnant primau forest trees. The site was on the Pacific side of the continental divide, which has a distinct d u season. The ground plot was located in the general vicini~ of, but not coincident with, the flightline analyzed in this study. Ground Data Collection The ground data collection varied between sites, but in both instances the ground survey was conducted using the 35 mm and T-11 photography acqnired concurrently

314 Nelson et al.

with the laser data. The aerial photographs were used in an attempt to locate ground plots coincident with the actual laser trace on the ground. Lack of ground control, even in these relatively accessible forests, made this coregistration difficult. In Tileran, a starting point for the ground plot was located in the photography and on the ground and a 500 m compass line was established. Only the start point was used for line location. All trees whose boles were located within 5 m of this line were tallied (i.e., a 10-m-wide fixed-area plot) in May 1985. Tree species at Tileran were not noted because there are too many individual species. At LaSelva, five distinct ground plots were located in the general vicinity of the laser flightlines. Two 1-km ground plots, two 300-m plots, and one 400-m plot, each 5 m wide, were measured in January and February 1985. All trees greater than 10 cm dbh were tallied if their bole centroids fell within 2.5 m of the centerline of the plot. Five tree species that make up the bulk of the woody biomass at LaSelva were noted; all other tree types were classed into a generic sixth category. The five tree species recorded included: Pentaclethra macroloba, Carapa guianensis, Virola spp., Vochysia ferruginea, and Tetragastris foramensis. The location, dbh, total height, height to first branch, and crown diameter of each tree sampled on the Tileran and LaSelva ground plots were recorded. Bole volume or above-ground dry biomass was estimated for each tree tallied on the ground plots using the information collected in the ground survey. Merchantable volume was calculated for each of the 265 trees sampled along the Tileran ground plot. A non-species-specific volume equation published by Lojan (1966) was used; log(v)=2.03986 log(d~)+0.779 log(hb)-4.07682, where v = merchantable volume (ma), db=dbh (cm), hb=tree height to first major branch (m). Approximately 8 km SE of the LaSelva Biological Station, in tropical wet forest, 96 trees were destructively sampled in order to derive dry weight measures for the total above-ground portions of the trees. The dry' weights of the foliage, branches, and commercial stem were measured on each tree. These weight measures were logarithmically related to tree diameter and total height for the five tree species listed above. All other species were grouped together to produce a sixth set of generic biomass equations. The general forms of the biomass equations follow: total tree dry weight (kg) commercial stem dry weighl branch dry weight, or =a0+al ln(d~,ht) foliage dry weight

where a0 and aE are regression coefficients and h, is total heightJ Most B 2 values for these relationships exceeded 0.90; all exceeded 0.76. These biomass equations were used to calculate ground estimates of the components of total tree dry weight for all trees sampled along the ground at LaSelva. A second LaSelva ground data set was acquired by researchers at the University of North Dakota. Stems were mapped on two plots, 20 mXl5O m and 20 m×200 m, located on the west side of the primary forest reserve. These plots were located in the general vicinity of the northwestern end of the southernmost laser flightline acquired over LaSelva. The equations noted above were used to calculate total above-ground dry biomass fbr each of the trees mapped on these two subplots. Although the amount of area incorporated in these two 20m-wide plots was approximately one-ninth of the area encompassed by the 5-m-wide data, consideration of the wider plots permitted at least a cursory look at the effects of ground plot width on canopy simulation and estimation of basal area and biomass. In all, three different ground reference data sets were considered in this study, one near Tileran and two on the LaSelva Biological Station. Although these datasets were not spatially coincident with the airborne laser data, sections of the airborne laser flightlines in the general proximity of the ground plots were identified.

Computational Procedures--Forest Simulator The forest canopy simulator was described in detail in Nelson (1994), but the salient features of the simulator included the following: 1. Each element of the two-dimensional height array represented an area on the ground of 0.25 reX0.25 m. 2. The canopy shape was assumed to be half-elliptic when viewed from the side with one axis of the half-ellipse defined by the vertical distance from the top of the tree to the level of the lowest branch, and the second defined by the crown diameter. 3. The canopy shape was assumed to be circular when viewed from above. 4. A canopy roughness or noise factor was added to the elliptic canopy shapes to account for the unevenness of the canopy's surface. 5. Edge effects were handled by assuming that trees on adjacent plots were located in the same positions as on the primary plot. The net effect of this assumption was that trees that grew out of

IPersonal communication from Edgar Ortiz Malavasi, Director, Departamento de Ingenieria Forestal, Cartago, Costa Rica, to Dr Armond Joyce, Principal Investigator, NASA/NSTL, dated 24 March 1987.

Separating Ground and Airborne Laser Sampling Phases

31,5

Table 1. A Listing of Simulated Laser and Ground Measures Produced by the Simulation Procedure Simulated Laser Measures: For a Particular Segment g=canopy closure (%) t_~0=average canopy height, all pulses (m) h,.=average canopy height, canopy hits only (m)" s,=standard deviation of average canopy height, all pulses (m) s,-standard deviation of average canopy height, canopy hits only (m) c,,=eoefficient of variation of average canopy height, all pulses (m) <=coefficient of variation of average canopy height, eano W hits only (m) w~=weighted sum of deviations, all pulses w,=weighted sum of deviations, canopy hits s,,=standard deviation of canopy heights weighted by average height, all pulses

Ground Reference Measures: per Hectare Estirruztesfor a Parti~dar Segment crown area (mVha) canopy vohlme (mS/ha) number of trees, seen number of trees, total b,=basal area, seen (me/ha) b,=basal area, total (mZ/ha) v,=volume or biomass, seen (m3/ba or kg/ha) v,-volume or biomass, total ( m q m or kg/ha) ~'g, h,,, h,, and p (canopy profile area) are interrelated. For a given transect or segment:

i, Seen and unseen refer to a tree's canopy position with respect to an airborne laser. If any portion of a particular tree's canopy can be potentially sensed by an airborne laser, in other words, if any portion of a tree's canopy is visible when the forest is viewed vertically from above; then that tree is "seen." The terms roughly correspond to overstory and understory. The seen and unseen components are summed in order to calculate the "total."

the 2-D array- on one side "grew into" the array on the side opposite. 6. The simulator kept track of seen and unseen trees. Seen and unseen refer to a tree's canopy position with respect to an airborne laser. If any portion of a particular tree's eanopy can be potentially sensed by an airborne laser (in other words, if any portion of a tree's canopy is visible when the forest is viewed vertically from above), then that tree is "seen.'" The terms roughly eorrespond to overstory and understo U. The simulation program was coded in Fortran-77. Once the two-dimensional height array was constructed, the number of randomly oriented laser lines that transeet the long axis of the height array was specified. A minimum tree height of 5 m was specified below which the canopy was defined as shrub. Table 1 provides a list of the simulated laser and ground measurements which were reported by the canopy height simulator. Five different measures of laser height variability along a given segment were calculated in an attempt to mathematically characterize stand structure. The five variance measures included 1) coefficient of variation of all pulses along a segment; 2) eoefflcient of variation of pulses intercepting the forest canopy only; 3) a weighted sum of laser height deviations of all pulses; 4) a weighted

sum of laser height deviations of pulses intercepting the forest canopy only; and 5) the standard deviation of canopy pulse heights weighted by the average height of all pulses. The weighted sums of laser height deviatkms (3 and 4, directly above) took the following form: i=lkh,,/

,,c(,,,/

w , = ~ F (h~-l~,.), i=l tt,./

(2)

wb e r e ha=total number of pulses in segment, n,,=number of pulses which hit tree canopies, h~=height of pulse/, @=average height of all pulses in a segment, h,.= average height of the canopy hits in a segment. was small in those situations where h~h,,, that is, dense, even-aged stands, and became larger as the stand became less dense, w,: was small in those situations where h~-h,,, regardless of patchiness or canopy density. The fifth variance measure was developed with three basic generalities in mind (exceptions can be easily tbund): 1) the taller the mean height, the higher the biomass; 2) dense stands have greater biomass than open stands for

//.3 a

316

Nelson et al.

Table 2. Coefficients o f D e t e r m i n a t i o n ~br Logarithmic Models

Study Site

Segment Length

F1~ In(BA,seen)

ln(BA,total)

ln(V, seen)

ln(V, total)

Tileran

100 75 50 25

m m m m

0.673 0.310 0.358 0.527

0.778 0.441 (/.510 (I.645

0.868 0.524 (t.556 0.589

0.900 0.601 0.647 0.666

LaSelva-5 m

100 75 50 25

m m m m

0.261 0.239 0.389 0.497

0.303 0.284 0.422 0.527

(t.4(/6 0.379 0.522 /I.33(t

(I.439 0.412 (/.548 0.335

50 m 25 m

0.115 0.343

0.160 0.466

{/.169 0.392

0.199 0.480

LaSelva-20 m

a given height and height variance; and 3) a single superemergent may account for the majority of the woody biomass on a given plot, and a large height variance connotes an all-aged,canopy structure, whieh in turn connotes high biomass. If these premises held, then the following laser measure may have explained significant variation in ground-measured biomass. ,%,= (/~)(10-~0)= (h~)(s~),

(3)

where

g=canopy closure (%), s, =standard deviation of canopy height, canopy hits only. This variable was expected to increase as the canopy grew taller, more dense, and more varied. Establishing Ground-Laser Relationships Linear regression equations were fitted to predict ground measures of interest from laser measurements. A sim~e linear regression model with average canopy height, h~,,

Table 3. A C o m p a r i s o n o f Simulated F o r e s t C a n o p y M e a s u r e m e n t s , Simulated Laser M e a s u r e m e n t s , and Airborne Laser M e a s u r e m e n t s o f T h r e e Study Sites in Costa ttica

Simulated Forest Canopy ~' Tileran

No. stems/ha Basal area/ha (m2/ha): Merch. vol/ha (m:Tha): Total dry biomass (mtons/ha):

LaSelva-5 m

LaSelva- 20 m

Seen

Unseen

Total

Seen

Unseen

Total

Seen

Unseen

Total

282 34.62 342.00

248 7.48 50.73

530 42.10 392.72

346.033 26.871

56.633 1.399

402.667 28.27l

347.142 30.767

146.143 3.141

493.286 33.914

156.679

5.317

161.997

177.470

12.498

189.969

Simulated Laser Measurements# (30 Random Laser Transects)

Average height, all pulses (m) Average height, canopy hits (m) Coefficient of variation, all pulses Coefficient of variation, canopy hits Canopy closure (%)

Tileran

LaSelva-5 m

LaSelva-20 m

19.854 22.909 0.523 0.322 86.665

9.941 17.834 l. 102 0.443 55.116

16.83 19.847 0.541 0.3119 84.738

Tileran

LaSelva-5 m

LaSelva-20 m

12.185 14.263 0.582 0.379 85.425

22.901 24. 128 0.421 0.342 94.912

2(I.548 21.954 0.446 0.349 93.598

Airborne Laser Measurements t'

Average height, all pulses (m) Aveage height, canopy hits (m) Coefficient of variation, all pulses Coefficient of variation, canopy hits Canopy" closure (%)

The LaSelva-5 m and LaSelva-20 m simulated laser transect means are calculated by weighting the individual transects by their length, as per DeVries (19861. h The Tileran airborne laser measurements are compiled from approximately 500 m of laser thought to be closest to the ground transect. The LaSelva-5 m airborne laser measurements are an average of 4 km of laser line in the proximity of the 3 km of ground transect data. The LaSelva-20 m airborne laser measurements are average over 850 m of flightline.

Separating Ground and Airborne Laser Sampling Phases

317

Table 4. Summary of Point Measurement Data Collected during a 1993 Field Trip to the LaSelva Biological

Research Station~ ALl-1

ALl-2

All Points

Mean

Std. Dec,.

n

Mean

Std. Dev.

n

Mean

Std. Dec,.

r~

Avg. perpendicular distance from D/CD trees t{} transect (m) Avg. height D/CD trees (m) Avg. canopy density (%) Avg. height, all trees on pts. (m)

3.76 31.96 94.79 23.21

"2.44 6.34 3.49 11.03

31 3l "28 63

3.58 33.26 94.15 20.66

"2.76 8.58 "2.74 12.34

'29 29 28 74

3.67 32.58 94.47 21,83

")..58 7.47 :3.13 I 1.78

60 60 56 1:37

Largest tree (m) Smallest I)/CD tree (m) Smallest tree (m)

44.41 22.13 4.57

48.19 20.02 4.57

48.19 20.02 4.57

' D/CI) stands for dominant/eodominant trees.

as the independent variable was utilized in order to assess factors which may have had an impact on prediction accuracy. The factors included 1) ground plot segment length and 2) the inclusion or exclusion of a natural logarithmic trausfimnation of the dependent variable to control variance. Those factor levels which were found to improve the accuracy of the prediction were used to develop a single multivariate model. Simple Linear Begres'sion with One Independent Variable

Initial efforts to develop models to predict basal area, volume, and biomass centered on assessing variants of a basic model commonly employed in previous airborne laser studies: In(g) =ao + a[ (p )=ao + a,(/],),

(4)

where y=basal area, volume, or biomass, p =canopy profile area along a 1 km flight transect (m2), /],,=average canopy height, 'all pulses (m) ao, a{, and aj are coefficients such that a~= 0.001 am. Two general regression models were considered, a logarithmic simple linear model, with intercept [ln(y)= a0+a~(/~,,)], and a model involving no transformation with the line forced through the origin [y=a,2(/~,,)]. The natural log model served as a standard. The untransformed model with no intercept was suggested by scatterplots of height with basal area, volume, and biomass. Prediction accuracies might have been improved by fitting an untransformed model in orcler to avoid bias in the detransfbrmed estimates (Miller, 1984), Variants of this simple linear model were assessed to see if mean square error and or prediction accuracy could be improved. Four ground segment lengths were considered: 25 m, 50 m, 75 m, and 100 m. Selection of an appropriate segment length was a trade-off between two competing factors. The shorter the segment length, the larger the sam-

pie size per unit field effort. The larger sample sizes facilitated regression studies. The shorter the segment length, however, the higher the variation in the simulated laser and associated ground measurements (i.e., the greater the noise), Segment length was constrained by canopy diameter. Segments should not be any shorter than the average canopy diameter along a transect; ideally segments should not be aW shorter than the maximum canopy, diameter along any ground plot. This constraint was imposed to avoid situations where the simulated laser and ground attributes of a particular segment were driven by the attributes of a single tree, In Tileran, the maxinmm canopy diameter was 18 m; at LaSelva, the maximum canopy diameter recorded along those ground plots associated with the laser overflight (the 5-m-wide plots) was 20 m. The maxinmm canopy diameter recorded along the 20-m-,adde plots was 25 m. Segment lengths of 25 m, 50 m, 75 m, and 100 m were considered to determine if shorter lengths degraded the accuracy of the equations used to predict basal area, volume, or biomass. Twenty-~bur regressions were fitted (4 ground tra> sect lengthsx2 modelsx3 study areas) to predict basal area, volmne, or biomass as a fimction of simulated, laser-measured tree height. Each of these regressions, in turn, was applied to the actual airborne laser data to estimate basal area, volume, or biomass, and these airborne laser estimates were compared with ground estimates. The airborne laser data were processed in segment lengths identical to those ground segment lengths used to produce the simulated laser measurements. St) regression equations developed using ground transect data divided into 50 m segments, for instance, were used to process 50 m airborne laser segments. In all cases, the airborne laser data segments were processed with a 15 m gap left between each segment. A 15 m gap was introduced to mitigate the effects of" spatial autocorrelation. The presence of a 15 m gap reduced autocorrelation by separating sequential segments by more tlhan the width of an average tree crown. Within-stand antocorrelatk)n may have persisted, but the gap preclude{{ artificial vari-

318 Nelson et al.

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Multiple Independent Laser Variables Parametric multivariate techniques were employed to identify those simulated laser measurements most useful for predicting the ground variables of interest. Only the specific ground segment length identified as optimal in the simple linear regression investigation was considered in the multiple linear regression analyses• As in the simple linear regression investigation above, two generic models were considered: 1) dependent variable (e.g., total merchantable volume) transformed using the natural logarithm with a linear model, with intercept; and 2) dependent variable not transformed, with the linear model forced through the origin (i.e., no intercept term)• Models for seen and total basal area, volume, and above-ground dry biomass were constructed independently. The variable selection process was subjective since different variables and different numbers of variables were "optimal" for the different study areas. A

common suite of variables which explained significant variation in a particular dependent variable on 'all three study sites was selected• This attempt to make models generic meant that most all of the models considered were not optimal in terms of maximizing R 2, or minimizing Cp (Mallow's Cp statistic) or mean square error (MSE) for any particular study area. Thus the predictive capability of the resulting model was compromised in an attempt to derive laser variables which might be commonly employed, or at least considered, in subsequent investigations in other tropical forests• RESULTS Simple L i n e a r R e g r e s s i o n Analyses

The coefficients of determination associated with the simple linear regressions developed for the logarithmic models varied markedly (Table 2). Table 2 indicates that, across most segment lengths and study areas (LaSelva-5 in, 25 m segment length being the exception), merchant-

Separating Ground and Airborne Laser Sampling Phases 319

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able volume and total above-ground dry biomass were better predicted than basal area. No diseernable pattern was noted across study areas with respeet to segment length. R 2 values are not reported for the parametric analyses (breed through the origin sinee, in these situations, the R '2 values may be unbounded at the lower or upper ends, are not eomparable, and/or may be misleadingly inflated (Myers, 1990). The effects of segment length on the mean square error are illustrated in Figure 2. Mean square error, in this table was calculated as follows: n

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As segment length decreased, MSEs generally increased, with the largest rate of increase noted between the 25 m and 50 m segment lengths. The LaSelva-5 m in(total biomass) figure (2.2.C) is note worthy since the MSE increased approximately 1300% as the segment shortened from 50 m to 25 m. This remarkable increase was due to the presence of eight "25 m segments without trees; the relatively large differences between the intercept and the origin inordinately drove up the MSE. The large increases noted as segment length decreased from 50 m to 25 m, across all three study areas, and both models, suggested that segment lengths greater than 25 m should be utilized in these tropical forests. Based on the results presented in Figure 2, of the four segment lengths considered in this study, a 50 m segment was optimal from the standpoints of reducing MSE and field effort. The mean square errors depicted in Figure 2 were cause for concern about the accuracy of this laser inventory approach. For the 50 m segments, the root mean square errors (RMSE) fbr the Tileran basal area and

320

Nelson et al.

woody volume estimates were 27% and 3i% of the ground reference values, respectively, for the untransformed models. The corresponding tlMSEs for predicted basal area and biomass using the LaSelva-5 m data were 52% and 65%. For the LaSelva-"20 m data set, the respective RMSEs were 24% and 24%. In Tileran, the airborne laser values for basal area and volume underestimated comparable ground reference values; at LaSelva, the airborne laser overestimated ground reference values. Basal area, volume, and biomass were predicted as simple linear functions of average height. The simple linear relationship between height and, for instance, biomass, was based on simulated laser measurements (from a canopy height simulator which used mapped stand data) and ground-measured biomass. To the extent that these simulated laser heights mimicked what the airborne laser measured, airborne laser estimates of biomass tracked ground-measured biomass. It was apparent from the results presented in Table 3 that the simulated laser values did not track airborne estimates well. At Tileran, the average airborne laser height estimate was 61% of the simulated height estimate, which led to the 2731% underestimates of basal area and volume when airborne laser height values were used to calculate basal area and biomass. Conversely, the LaSelva-5 m simulated heights were less than half the heights measured by the airborne laser, which led to the 50-65% overestimates. The LaSelva-20 m sinmlated height measurements were within "20% of the airborne laser values, which resulted in (on average) 24% overestimates. The magnitude of these differences between the simulated and airborne laser measurements were troubling. Which data sets were correct (i.e., most accurately described actual ground conditions), and what were the reasons behind the discrepancies? Certainly, natural variation in tree heights and forest structure accounted for some of the differences. However, considering the LaSelva-5 m transect data, 3 km of 5-m-wide mapped stand data were collected and compared to approximately 4 km of airborne laser data. Intuitively, enough data were collected on the ground and from the air to adequately represent forest canopy conditions at LaSelva and to mitigate the effects of natural variation. The 5-m-wide transect data characterized a forest 10 m tall, with a canopy closure of 55%. Comparable airborne measurements described a forest 23 m tall and 95% closed. (Note: This 95% canopy density figure was developed assmning that canopy heights less than 5.0 m were laser pulses to shrubs or ground.) A trip was made to the LaSelva Biological Station in September 199:3, 9 years after the laser data were collected and 8 years after collection of the ground transect data. Point measurements were made along lines roughly parallel to and in the proximity of the airborne laser profiles and 5 m ground plots. The point measurements were made to describe the spatial and

height characteristics of those trees whose crowns would have been intercepted by an airborne laser had the aircraft followed tile same path as the teclmician on the ground. At 25 m intervals along a particular compass bearing, spatial and biometric data were collected on any tree whose canopy was intersected by a line vertically projected from the sample point. In addition, canopy density measurements were made using a spherical densiometer. At a given point, ~)r each tree whose crown was vertically intercepted, the following measurements were taken: 1) crown position in the canopy (dominant, codominant, intermediate, suppressed); '2) distance along and perpendicular to the sample transect (i.e., the compass bearing); 3) tree height; 4) dbh; and 5) shrub height in the general vicini~ of the sample point. A total of 56 points were visited, half in the general vicini~ of the northernmost flightline, half along the southern flightline. These more recent ground observations, smnmarized in Table 4, were studied to tl7 to account for the marked diftbrences between sinmlated and airborne laser measurements. A number of items may be noted Table 4: 1. The average perpendicular distance from the 1993 sample transect to a dominant or codominant tree exceeded 3.6 m. Thirty-seven of the 60 dominant or codominant trees tallied on these points were greater than 2.5 m from the sample transect line. In the primary tropical forests of LaSelva, then, a 5-m-wide ground plot missed 62% of the trees, which an airborne laser would sense if it traversed the same line. 2. Canopy densities along the 1993 sample line ranged from 83.3% to 98.4%, with a mean of 94.5%. Only four of 56 points exhibited crown closures less than 90% when measured with a spherical densiometer. The 1993 average canopy density agrees within 1% with the average canopy densities reported by the airborne laser at LaSelva. The simulated value developed using the ground plot data, 55%, was unrealistic. 3. The tallest tree found in this 56 point sample was 48.2 m as measured using a Suunto hyl)someter; the average dominant/codominant tree height was 3"2.6 m. The average height of all trees tallied on these points was 21.8 m. This average height matched the comparable airborne laser measures to within 1.5 m. The simulated mean height values based on the 5-m-wide ground plot data are unrealistically less than half of the 1993 ground measurements. The LaSelva canopy, a tropical wet primary- ibrest, appeared to be all-aged, multistoried. If one assumed little overall change in general stand structure over the 10year period between the mid-198.0s sampling work and

Separating Ground and Airborne Laser Samplin,~ Pha,ses 321

the data were used to discern such things as effects of segment length and canopy shape on estimated basal area and biomass. The prediction errors for volume and biomass observed at the four segment lengths are illustrated in Figure 3. Based on these results, it was noted that:

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the 1993 field trip [an assumption supported by biometde data reported by Lieberman et al. (1990)], then it was clear that the LaSelva-5 m plot data were not useful for canopy simulation. Such narrow ground sampling missed too many of the trees important for simulating canopy height. The fixed-area plot information was useful Ibr developing estimates of the ground measures of interest (e.g., stems/ha, basal area/ha, and volume or biomass/ha), but it did not aecurately portray the spatial arrangement in the primalT tropical fi)rest. For comparative purposes, however, the 5 m plot data were utilized throughout the investigation for simulation studies. In other words, although the 5-m-wide plot data did not adequately characterize ground conditions sensed by an airborne laser,

• Selection of a particular segment length (25 m, 50 m, 75 m, and 100 m) inw4ved consideration of two offsetting trends. First, shorter lengths are better from the standpoint of mitigating fieldwork. Second, the longer the segment, the greater the number of tree crowns involved in canopy simulation and the smaller the likelihood of highly influential observations due to the presence or absence of large trees. • The large, consistent jump in mean square error (Fig. 2) across 'all three study areas as segment length was reduced to 25 m from 50 m suggested that a 50 m length should be employed to segment the ground plot data. Likewise this same segment length should be used to segment the airborne laser data with a 15 m gap. • The absolute estimation error, ~4th few exceptions, increased when a logarithmically transibrmed model was employed (Fig. 3.). Twosided paired t-tests confirmed the trends illustrated in Figure 3. Considering the LaSelva-5 m and 20 m biomass results jointly, t-tests showed that the natural log transff,rmation significantly exacerbated (p<0.01, n=36) an inherent overestimation problem. At Tileran, the response was reversed as the uatural log model consistently, signifieantb~ exacerbated (p<0.02, n=24) an inherent underestimation problem. No consistent, downward transfbrmation bias was noted in the results involving the log transform; hence no bias adjustment (Miller, 1984) was applied. In summa~, the use of the natural log model improved regression fit, but amplified prediction errors when log estimates were detransformed. Based on these results and keeping in mind that shorter segment lengths reduce field work, laser-based estimates of basal area and volume or biomass should be generated: 1) using a ground segment length greater than 25 m, that is, 50 m; 2) by dividing airhorne laser data into 50 m segments with a 15 m gap between seginents to reduce autoeorrelation; and 3) by using antransformed data with the regression [breed through the origin. Multiple Linear Regression Analyses

Based on the simple linear regression findings, only 50 m segments were considered, and the airborne laser data

322

Nelson et al.

Table 5. Multiple Linear Regression Estimates of Seen, Unseen, and Total Basal Area, Merchantable Volume, and Total Above-Ground Dry Biomass for the A) Tileran, B) LaSelva-5 m, and C) LaSelva-20 m Stud), Areas. Two models are considered: untransformed data forced through the origin and transformed data with an intercept. Only parametric regression techniques are used to estimate M L R coefficients. Simulated Canopy Mean

50 m Seg/15 m Gap

Std. Error

Mean

Std. Error

n

0.510 0.220 0.040 0.010 2.150

12.818 14.447 0.481 0.281 87.698

1.542 1.547 0.049 0.033 2.825

1577 1383 1577 1383 1577

21.228 4.402 25.630 171.958 26.617 198.575

3.020 0.736 3.754 44.999 5.785 5(/.744

8 8 8 8 8 8

12.818 14.447 0.481 0.281 87,698

1.542 1.547 0.049 0.033 2.825

1577 1383 1577 1383 1577

23.734 4.080 27.813 204.787 33.343 238.130

2.209 0.723 2.927 26.420 5.778 32.10(I

8 8 8 8 8 8

A. T i l e r a n

Parametric, no transformation (through origin) Height, all pulses (m) Height, canopy hits (m) Coef. var., all pulses Coef. var., canopy hits Canopy closure (%) BA, seen (m2/ha) BS, unseen (m2/ha) BA, total (m2/ha) Vol, seen (m~/ha) Vol, unseen (m3/ha) Vol, total (m3/ha)

19.854 22.910 0.520 0.320 86.670 34.620 7.480 42.100 342.000 50.730 392.720

Parametric, transformed data (with intercept) Height, all pulses (in) Height, canopy hits (m) Coef. vat., all pulses Coef. var., canopy hits Canopy closure (%) BA, seen (m2/ha) BA, unseen (m2/ha) BA, total (me/ha) Vol, seen (m:Tha) Vol, unseen (m3/ha) Vol, total (ma/ha) B. L a S e l v a - 5 m

Parametrie no transformation (through origin) Height, all pulses (m) Height, canopy hits (m) Coef. vat., all pulses Coef. var., canopy hits Canopy closure (%)

9.940 17.830 1.102 0.443 55.120

23.027 24.189 0.360 0.276 94.836

0.667 0.640 0.027 0.014

1.242

12085 11461 12085 11461 12085

BA, seen (me/ha) BS, unseen (m2/ha) BA, total (m2/ha) Biomass, seen (kg/ha) Biomass, unseen (kg/ha) Biomass, total (kg/ha)

26.870 1.400 28.270 156,680 5,318 161,997

46.207 3.515 49.721 295,123 11,189 306,311

0.879 {).135 0.990 7.571 5411 8,071

61 61 61 61 61 61

Parametric, trans{brmed data (~4th intercept) Height, all pulses (in) Height, canopy hits (m) Coef. var., all pulses Coet: var., canopy hits Canopy closure (%)

23.027 24.189 0.360 0.276 94.836

0.667 0.640 0.027 0.014 1.242

12085 11461 12085 11461 12085

BA, seen (m2/ha) BA, unseen (m2/ha) BA, total (m2/ha) Biomass, seen (kg/ha) Biomass, unseen (kg/ha) Biomass, total (kg/ha)

56.344 5.806 62.150 322,626 22,561 345,186

2.618 0.422 2.967 27.557 1.525 28.634

61 61 61 61 61 61

(continued)

Separating Ground and Airborne Laser Sampling Phases ~ 2 3

Table 5. Continued Simulated Canopy Mean Std. Error

50 m Seg/15 m Gap Mean Std. Error

Parametric, no transformation (.through origin) tteight, all pulses (m) Height, canopy hits (m) Coef. var., all pulses Coef. var., canopy hits Canopy closure (%)

16.830 19.850 0.54l 0.309 84.740

19.869 20.919 0.394 0.293 92.763

1.795 1.469 0.073 0.032 3.461

2598 2410 2598 2410 2598

BA, seen (m2/ha) BA unseen (m'-Tha) BA, total (m~/ha) Biomass, seen (kg/ha) Biomass, unseen (kg/ha) Biomass, total (kg/ha)

30.780 3.140 33.910 177,471 12,499 189,970

33.498 4.059 37.557 215,214 16,794 232,908

1.465 0.548 1.450 13,340 2,403 13,187

13 13 13 13 13 13

Parametric, transformed data (with intercept) Height, all pulses (m) Height, canopy hits (m) Coef. var., all pulses Coef. var., canopy hits Canopy closure (%)

19.869 20.919 0.394 0.293 92.763

1.795 1.469 0.073 0.032 3.461

2598 2410 2598 2410 2598

BA, seen (m'-'/ha) BA, unseen (m2/ha) BA, total (meAm) Biomass, seen (kg/ha) Biomass, unseen (kg/ha) Biomass, total (kg/ha)

37.597 3.804 41.401 219,756 14,744 234,499

3.644 0.745 3.506 23,074 2,963 22,877

l:3 13 13 13 13 13

C. L a S e l v a - 2 0 m

were processed with a 15 m gap between each 50 m segment. Both models--transformed data with intercept and untransformed data forced through the origin--were tested. The results of all the possible subsets regressions indicated that the following models could be applied to the three study area data sets. Basal Area

Volume/Biomass

b,=f(h,,,¢.) b,=f([~,,,c,.) b.=b,-b~

v,=f(h,c,,,c~) v,=f(hc,¢,,c~) v,,=v,-v,

The basal area, volume, and biomass subscripts s, u, and t represent the seen, unseen, and total components, respectively. As noted with the simple linear regression results, Tileran airborne estimates underrepresented ground reference basal area and volume by approximately a factor of 2 (Table 5). The LaSelva-5 m airborne results, conversely, overestimated ground reference data by approximately a factor of 2. The LaSelva-20 m airborne estimates overestimated ground reference data by approximately 23%, reflecting the (relatively) close agreement of simulated and airborne laser measure along these 20-m-wide ground plots. In order to determine the most accurate model for predicting basal area, volume, and biomass, SLR and

MLR airborne laser results were concatenated and error terms were calculated (Table 6). In order to develop comparable measures of prediction errors across 'all three study areas, the merchantable w)lume estimates of Tileran were "scaled" to the biomass metric tonnage figures of LaSelva-5 m and LaSelva-20 m study areas. Tileran's volume estimates were converted to metric tons/ha by dividing by an average wood density of 2.0 ma/metric ton.-' Two error terms were calculated. The average absolute error is the average of the absolute difference between the airborne laser estimate and the ground reference estimate for the three study areas. The root mean square error is the square root of the average squared difference between the airborne laser estimate and the ground reference estimate for the three study areas. The results in Table 6 suggested that the untransformed multiple regression models {breed through the origin were most apt.

DISCUSSION Lasers for forest mensuration are best employed in situations where little inventory information exists and where ~'This conversion factor is equivalent to a current volume specific grayly7 of 0.5 (see Husch et al., 1972). This generic density figure for Costa Rican tropical woods is equivalent to the density of wood found in black cherry', sycamore, red maple, and sweetgnm (Harford County Forest D, Board, no date).

324 Nelson et al.

Table 6. Summary of airborne Laser Estimates of Total Basal Area and Total Merchantable Volume or Total 11U Biomass for the Tileran, LaSelva-5 m, and LaSelva-20 m Study Sites" Simple Linear Regress'ion Study Site

Ground Reference

Untransfmued through 0

42.100 28.270 33.910

27.028 59.032 39.728

Multiple Linear Regression

Transfmn, with Intercept Estimate R2

Untrausfimned through 0

Transfl,rm, with Intercept Estimate R2

Total Basal Area (ina/ha) Tileran LaSelva-5 m LaSelva-2O m Average lerrorl rmse Tileran LaSelva-5 m LaSelva-20 m Average lerrorl rmse

25.432 76.261 37.532

0.5111 0.422 0,160

25,630 49,721 37.557

27.813 62.150 41.401

1/.55:3 0.511 0.422

17.217 22.760 13.856 18.553 20.061 29.406 15.755 21.665 Total Volume (ma/ha)--Tileran, Total Biomass (mtons/ha)--LaSelva-5 m, LaSelva-20 m 392.720 161.997 189.970

255.739 368.543 223.469

208.543 721.224 218.410

102.845 127.115

226.585 327.630

0.647 0.548 0.199

198.57,5 3116.3ll 232.1/08

238.130 345.186 234.499

94.475 103.307

101.671 117.637

0,660 1/.739 11.48t)

Simple linear and multiple linear regression models are considered. Average absolute error and root mean square error are reported. The Tileran merchantable volume estimates are scaled to the LaSelva biomass estimates by multipl~ng volumes hy a density factor of 0.,5 mtons/m 3 of wood. Simple linear regression models use average canopy height, all pulses, as the independent variable. The umltiple linear regression models are reported in the subsection Multiple Linear Regression Analyses.

site access may be limited due to terrain, climate, and/ or a lack of infrastructure. An airborne laser system is not a good site-specific mapper (Nelson et al., 1988b); rather, lasers should be used to assess large tracts or regions where prediction errors can be mitigated by sample size. Areas such as uncolonized regions of the Amazon, the Congo, the circumpolar boreal forests, and the tropical forests of Southeast Asia are candidate areas for airborne laser surveys. Previous studies have depended on the accurate registration of airborne laser and ground survey data in order to develop regressions relating airborne laser and ground measurements. Colocation of the laser and ground transects within 2-3 m has, in the past, required the presence of ground control features that could be definitively located in the laser data. Areas where lasers 1night be flown to best effect typically have few ground control features. Unbroken, often closed-canopy forest make transect registration based on visual clues impossible across broad reaches of the regions. Global Positioning System (GPS) handheld receivers could be employed on the ground to help with transect location, but this technology has its own set of problems with 1) signal reception beneath a forest canopy and 2) locational accuracy. The overall purpose of this research is to define an inventory procedure which utilizes airborne laser data but divorces the air and ground sampling phases. To this end, a simulator which uses mapped stand data digitally recreated the height structure of the top of the forest canopy. The two-dimensional height array was randomly transacted to develop simulated laser measures which were matched directly with the corresponding ground measures of interest. Subsequent statistical analyses resulted in regression equations which predicted basal

area, volume, and biomass as a function of simulated laser measurements. These equations, in turn, were used in conjunction with airborne laser data acquired over the study site to produce regional estimates of basal area, volume, and biomass. The specific suggestions which ~bllow are provided as starting points for further research. • Of the four segments lengths considered, the 50 m segment is optimal for these Costa Riean forests. The 50 m segment is the shortest of the four considered which did not consistently exhibit high mean square errors when laserground regressions were calculated. • It is hypothesized that a 5-m-wide ground plot is too narrow to capture the overstou height characteristics of a Costa Riean primary tropical forest. It is recommended that ground transects be at least 10 m wide (DeVries, 1986) if topof-canopy architecture is to be simulated using fixed area plots. Primary forests may require widths on the order of 20 m in order to adequately model treetop structure. • The logarithmically transformed regression models yield results which are prone to gross overestimation. The overestimation problem is exacerbated at shorter segments lengths. • The following nmltiple linear models proved useful on the three Costa Riean stu@ sites: b,, b,=a~(f~,)+ad¢.),

~, ~,=<(fi,~)+<(co)+,,~(c,:). Based on these results, an inventory procedure was defined which can be used to assess tropical forest basal

Separating Ground and Airborne Laser Sampling Phases 32,5

area, volume, or biomass using airborne laser data without depending on ground registration of the airborne laser track. The procedure produced estimates within 11-24% of ground-estimated values in those situations where cmaopy conditions were simulated within 25% of airborne laser values. In situations where canopy conditions were not accurately reproduced in the computer, estimates suffered. The accuracies of basal area, volume, and biomass estimates were directly tied to the degree to which the simulated canopy architecture represented really. In two of the three ground data sets, the airborne laser either grossly overestimated or grossly underestimated ground-measured basal area and biomass. This simulation work is by no means proven technology. In principle there is no reason that the approach (canopy sinmlation, regression development, estimation using airborne laser data) should not work, yet the fact remains that two out of three ground data sets were markedly at odds with similar measurements (e.g., average height, canopy densi~) made using the airborne laser. Prior to dedicating significant resources to large area inventmT, additional work should be done, perhaps in temperate forests, so that ground-laser discrepancies can be definitively addressed. Pacific Coast old-growth Douglas-fir/ true fir fbrests woukt be a useful test ease from the standpoint of incorporating an all-aged height distribution and large trees which, like a tropical forest, could present problems with highly influential observations. Assuming comparable results in the designed field experiment, the technique should be considered for reconnaissance level surveys of remote tbrested areas worldwide. The technique, if successful, may be applied to the tropical tbrests of South America, Africa, southeast Asia, and the circumpolar boreal forests to estimate above-ground carbon stores. These results may refine components of the global carbon budget. More importantly, these estimates may serve as carbon store benchmarks fbr change detection purposes. Research aircraft outfitted with GPS receivers permit flightlines to be coarsely repeated (within 100 m). Data collection missions may be reflown over the same flightpaths to detect regional biornass accunmlations or losses without the need to repeat the ground sampling phase, the simulations, or the regression work. Such technology may prove most usefid to detect changes in the above-ground carbon stores of the northern boreal forests, where the most rapid and significant climate and vegetation changes are expected oxer the next 200 years.

Most of the data utilized in this study were collected by others and gener~nMy shared. Dr. Ar~rumd Joyce (NASA/Stennis Space Center) and Dr. Steve Sader (University of Maine, Orono) provided the airbomw laser data, the Tileran and LaSelva-5 m gr~nmd transect data, and the allometrie equations for biomass. Drs. Diane and Milton Lieber~tum (University of North Dakota)

kindly ,supplied the 20-m-wide LaSelva gr(nmd transect data. The LaSelva Biological Research Station staff and Drs. Deborah and David Clark in particular supported the 1993 fiehl efforts. This unfunded research could not have been done withtn~t the support and generosity of these people; the authocs appreciate it.

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