High- Versus Low-Density LiDAR in a Double-Sample Forest Inventory

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1 High- Versus Low-Density LiDAR in a Double-Sample Forest Inventory Robert C. Parker and Patrick A. Glass, Department of Forestry, Forest and Wildlife Research Center, Mississippi State University, Mississippi State, MS ABSTRACT: Light detection and ranging (LiDAR) data at 0.5- and -m postings were used in a double-sample forest inventory on Louisiana State University s Lee Experimental Forest, Louisiana. Phase 2 plots were established with DGPS. Tree dbh ( 4.5 in.) and two sample heights (minimum and maximum dbh) were measured on every 0th plot of the phase sample. Volume was computed for natural and planted pine and mixed hardwood species. LiDAR trees were selected with focal filter procedures and heights computed as the height difference between interpolated canopy and DEM surfaces. Dbh-height and ground-lidar height models were used to predict dbh from adjusted LiDAR height and compute ground and LiDAR estimates of ft 2 basal area and ft 3 volume. Phase LiDAR estimates were computed by randomly assigning heights to species es using the probability distribution from ground plots in each inventory strata. Phase 2 LiDAR estimates were computed by randomly assigning heights to species-product groups using a Monte Carlo simulation for each ground plot. There was no statistical difference between highversus low-density LiDAR estimates on adjusted mean volume estimates (sampling errors of 8.6 versus 7.60% without height adjustment and 8.98 versus 8.63% with height adjustment). Low-density LiDAR surfaces without height adjustment produced the lowest sampling errors for stratified and nonstratified, double-sample volume estimates. South. J. Appl. For. 28(4): Key Words: LiDAR, inventory, double-sample. NOTE: Robert C. Parker can be reached at (662) ; Fax: (662) ; rparker@cfr.msstate.edu. This work was approved for publication as FWRC Publication No. FO248 of the Forest and Wildlife Research Center, Mississippi State University. Copyright 2004 by the Society of American Foresters. Light detection and ranging (LiDAR) is a relatively new remote sensing tool that has the potential for use in the acquisition of measurement data for inventories of standing timber. LiDAR systems have been used in a variety of forestry applications (Magnussen and Boudewyn 998, Lefsky et al. 999, Means et al. 2000) for the quantification of biomass (Nelson et al. 2003), basal area, and tree and stand height estimates. Parker and Evans (2002) used small-footprint, multi-return LiDAR (nominal posting density of approximately 2 m; 0.25 hits per m 2 ) in a double-sample application with a ground-based forest inventory in central Idaho and achieved a sampling error of.5% at a 95% level of confidence. They assumed that volume differences would be adjusted with the ground-lidar height equation prior to volume computation and/or with the regression estimator in the double-sample model if unadjusted heights are used to compute tree volume. The objective of this study was to investigate the use of high versus low posting density LiDAR with height adjustment in a double-sample forest inventory of pine and mixed hardwood stands. This application involved using quantified relationships between ground measurements and LiDAR estimates of tree height, dbh, and number of stems from high versus low-density LiDAR to compare volume estimates. Study Area The study area (,200 ac) was located on the Louisiana State University (LSU), Lee Experimental Forest near Bogalusa in Washington Parish, Louisiana. Forests within this region are dominated by natural and planted stands of loblolly pine (Pinus taeda), natural shortleaf pine (P. echinata), longleaf pine (P. elliottii), and mixed hardwood stands of red oak (Quercus spp.), sweetgum (Liquidambar styraciflua), and hickory (Carya spp). The cooperative project with LSU was funded by NASA Stennis Space Center appropriations through the Mississippi State University, Remote Sensing Technology Center (MSU-RSTC). Methods LiDAR and Field Inventory Data Airborne acquired small-footprint, multi-return LiDAR data of the study area in June 2002 with an Optech ALTM-,225 system to attain nominal posting spacings of m (low density with hit per m 2 and footprint size of 0.23 m) and 0.5 m (high density with 4 hits per m 2 and SJAF 28(4)

2 footprint size of 0.22 m) for two returns plus intensity. Low-density data were obtained at an altitude of,067 m on a swath width of 609 m, and the high-density data from 60 m on a 89-m swath. Each return consisted of a UTM (Zone 5N, NAD 83) x, y, and z coordinate, where z was height above ellipsoid (HAE) in meters. LiDAR data sets were surfaced to produce first return canopy and last return digital elevation models (DEM) with 0.2-m cell sizes using a linear interpolation technique. Tree locations and heights were determined with algorithms and focal filter procedures developed by McCombs et al. (2003) that used a variable search window radius based on relative density. These procedures used moving 2.5-, 4.0-, or 5.5-ft radius search windows to identify each tree peak as the point that is higher than 85% of the surrounding maxima from one of the three search window, radius files. Tree height was interpreted as the difference between canopy and DEM z-values at each tree peak location. Tree heights were converted to point coverages and clipped to sample area boundaries using UTM coordinates to describe sample plot locations and sizes. Inventory design for this double-sample application involved the use of 0.05-ac circular plots with all plots being phase LiDAR plots and every 0th plot as a phase 2 ground plot. A total of 4 phase 2 and,40 phase plots were established within the study area. UTM coordinates were established at the center of each phase 2 plot for navigation with the real-time Differential Global Positioning System (DGPS). Differential corrections were obtained satisfactorily under tree canopies by using a large dome antenna. Ground data on each phase 2 plot included tree diameter at breast height (dbh) on all trees 4.5 in. dbh and total height (ft) on two sample trees determined by minimum and maximum encountered dbh. Ground data were collected for 4 phase 2 plots and LiDAR interpolations were completed for,334 high-density and,302 low-density phase plots and 35 phase 2 plots. The number of phase LiDAR plots are different for the posting densities and with the original allocation because of separate flight missions and plots falling on roads and outside the study area boundaries. Six phase 2 LiDAR plots were lost during height extraction because the actual DGPS location of the plot centers was not field recorded and tree peaks were not located from the theoretical DGPS plot locations. Double-Sample, Regression Estimator Model The double-sample model widely used with groundbased point sampling (Avery and Burkhart 2002) and aerial photogrammetric inventories and adapted for this study was: Y lr y 2 X x 2 () With traditional aerial photogrammetric inventories, the X i and x 2i variables are photographic volume/ac and ground volume/ac from phase and phase 2 plots, respectively, and is the regression slope coefficient for y i (ground volume/ac) over x 2i (photo volume/ac on ground plot). In this study, phase 2 tree measures of dbh (in.) and height (ft) were used to derive LiDAR estimates of basal area (ft 2 ) and volume (ft 3 ) by using field derived dbh-height equations to predict dbh and basal area, and using dbh and height in a standard, standing-tree volume equation to predict volume. Thus, the double-sample models used in this study involved LiDAR mean estimates of basal area (LiBA from phase and liba from phase 2) and volume (LiVOL from phase and livol from phase 2) for the x variables as: Data Analysis Y lr y LiBA liba (2) Y lr y LiVOL livol (3) The per acre number of trees, ft 2 basal area, and ft 3 volumes for 4 phase 2 ground plots, 35 phase 2 LiDAR plots,,302 phase low-density LiDAR plots, and,334 high-density phase LiDAR plots were computed and stored by plot number in text data format for subsequent use in a spreadsheet and custom developed software (Parker 2004). Ground-LiDAR Height LiDAR heights from 99 sample trees on the 4 phase 2 ground plots were used to predict ground height from high- and low-density LiDAR estimates with the species models: High-Density LiDAR: Pine Hardwood H gr H H,Li (I %) (4) H gr H H,Li (I %) (5) Low-Density LiDAR: Pine Hardwood H gr H L,Li (I %) (6) H gr H L,Li (I %) (7) where H H,Li is estimated height (ft) with high-density LiDAR, H L,Li is estimated height (ft) with low density LiDAR, H gr is measured ground height (ft) of trees, and I 2 is the statistical index of fit (Furnival 96), which is equivalent to R 2 for linear models only. dbh Height Measurements of dbh and height from phase 2 ground plots were fitted to species dbh-height models: Pine: dbh [Ln(H gr )] (I %) (8) Hardwood: dbh [Ln(H gr )] (I %) (9) where dbh is diameter at breast height (in.) and H gr is ground height (ft) of measured trees. There was no observed 206 SJAF 28(4) 2004

3 asymptotic relationship between dbh and height and attempts to use a model which had a upper asymptote for height resulted in nonsignificant regression coefficients. Phase Plots Extracted LiDAR heights from the high- and low-density data sets were randomly assigned to a species using ground-based species distribution probabilities in each of three inventory strata: mature natural pine, mixed natural pine-hardwood, and planted pine. The strata contained 369, 354, and 485 phase plots, respectively. LiDAR height was adjusted to ground height for high- and low-density LiDAR estimates with pine and hardwood Equations 4 7. Tree dbh was predicted from ground height (Equations 8 and 9) and used to compute ft 2 basal area and ft 3 volume with a standing-tree volume equation. Phase 2 Plots LiDAR height was adjusted to ground height by species for high- and low-density LiDAR estimates using Equations 4 7. Tree dbh was predicted with the pine and hardwood height Equations 8 9 and used to compute ft 2 basal area and ft 3 volume with a standing-tree volume equation. The three strata contained 37, 52, and 52 phase 2 ground plots, respectively. Basal area and volume on the phase 2 LiDAR plots were obtained by randomly assigning LiDAR-derived tree heights to species-product (pulpwood, chip n saw, and sawtimber) percent distribution es on each plot with a 50 iteration Monte Carlo simulation. Simulations of 50, 00, and 500 iterations showed that 50 iterations were sufficient to approximate ground volume distribution on the phase 2 plots. Prior to the simulation, percent distribution by species-product on each phase 2 plot was ordered from largest to smallest. At each iteration, a new seed was selected from the time clock, and randomly selected heights were randomly allocated to a species-product according to the calculated probability distribution. Once allocated to a species-product, the random LiDAR height was adjusted to ground height with Equations 4 7 depending on species and LiDAR data density. Ground height was used to predict tree dbh with either Equation 8 or 9, calculate ft 2 basal area, and predict ft 3 volume with a standing-tree volume equation. Average heights, basal areas, and volumes by species-product for each ground plot of the three strata were saved in text data format for subsequent combination with the phase 2 ground plot data. Results LiDAR Versus Ground Height Differences between ground-measured and high- and low-density LiDAR estimates of height were significant (at 0.05 with paired t-tests). Because the high- and lowdensity LiDAR data sets were from independent and separate flights, independent, paired t-tests (ground height versus high density LiDAR height and ground height versus low-density LiDAR height) were used instead of analysis of variance (ANOVA). High-density LiDAR underestimated pine heights; the amount varied from 3 ft for a 32-ft tree to 0.5 ft for an 88-ft tree (Equation 4). Low-density LiDAR also underestimated pine heights; the amount varied from 3 ft for a 32-ft tree to.2 ft for an 88-ft tree (Equation 6). Heights for hardwoods were seemingly overestimated on both high- and low-density LiDAR. High-density LiDAR overestimated hardwood heights by 0 ft for a 25-ft tree and 0.4 ft for an 80-ft tree (Equation 5). Low-density LiDAR overestimated hardwood heights by 0 ft for a 25-ft tree and 2.4 ft for an 80-ft tree (Equation 7). The overestimation of hardwood LiDAR heights, as evidenced by the negative intercept values of Equations 5 and 7, is most likely due to the underestimation of the ground hardwood height. LiDAR heights of trees are generally underestimated because the probability of a laser return from the terminal of a crown is low. The narrower and more conical the crown, the greater the likelihood that the pulse return is from a portion of the crown below the terminal. The broader and more irregular the crown of hardwoods, the greater the likelihood that the pulse return is from a lateral limb. Pine heights from low-density LiDAR more closely approximated ground-measured heights than did heights from highdensity LiDAR. Hardwood heights from both high- and low-density LiDAR surfaces were significantly different from ground-measured heights. In general, low-density LiDAR heights had less estimation error and stronger relationships to ground heights than did high-density LiDAR heights. The differences between height estimates from highversus low-density LiDAR is most likely attributable to the footprint size of the LiDAR pulse in relation to the sizes of openings in the canopy layer. The smaller footprint size of high-density LiDAR (0.22 m versus 0.23 m for low density) would result in more pulses passing through a canopy layer than low-density LiDAR. There is a greater likelihood that the larger pulse will be intercepted by crown terminals or foliage than would a smaller pulse. Thus, height estimates from low-density LiDAR surfaces in mature pine and mixed pine-hardwood stands would likely have less noise than estimates from high-density surfaces. Phase Relationships and Values On phase plots, the species-specific ground-lidar height and dbh-height relationships were used to obtain combined per acre estimates of trees, ft 2 basal area, and ft 3 volume (Table ). The data showed that low-density LiDAR produced higher estimates of numbers of trees than did high-density LiDAR or ground plots, thus, resulting in higher estimates of basal area and volume. Phase 2 Relationships and Values Phase 2 ground and LiDAR volumes and basal areas for each species-product are shown in Table. LiDAR volumes and basal areas for individual species-product es were derived from the 50-iteration Monte Carlo allocation of heights. The random assignment of heights to species-product es reasonably approximated the actual ground distribution of volume and basal area, but it was SJAF 28(4)

4 Table. Inventory results for per acre estimates of number of trees (N), ft 2 basal area, and ft 3 volume from,334 high- and,302 low-density phase LiDAR plots versus phase 2 estimates from 4 ground plots and 35 LiDAR plots on the LSU Lee Experimental Forest, Louisiana. Phase Species Product apparent that LiDAR overestimated numbers of trees/ac as compared to ground estimates. Overestimation of trees/ac resulted in overestimates of basal area and volume. Regression relationships between ground and LiDAR basal area and volume were obtained from phase 2 data for combined species-product es (Table 2). LiDAR volume had a stronger relationship to ground volume than LiDAR basal area and low-density LiDAR relationships were stronger than high-density relationships. Double-Sample Estimates Using double-sample models 2 and 3, the adjusted regression estimates of mean volume/ac and associated precision statistics for combined species-product es with low and high-density LiDAR, with and without LiDAR height adjustment to ground values, are shown in Table 2. The low-density regressions had a slightly higher index of fit and a lower sampling error (at a 95% level of confidence) than did the high-density regressions. There were, however, High-density LiDAR Low-density LiDAR N ft 2 ft 3 N ft 2 ft 3 Phase LiDAR Pine Combined 05 6, ,229 Hardwood Combined Total Combined , ,80 Phase 2 LiDAR Pine Pulpwood Chip n saw Sawtimber 33 37, , , ,62 Hardwood Pulpwood Sawtimber Total Combined , ,205 Phase 2 Ground Pine Pulpwood Chip n saw Sawtimber 9 28, ,863 Hardwood Pulpwood Sawtimber Total Combined ,228 no statistical differences between regression estimates of volume based on the different LiDAR densities or the height adjustment procedures. While there were no statistical differences between models involving high and low LiDAR densities with and without height adjustment, the low-density LiDAR volume model with no height adjustment from LiDAR to ground height produced the lowest standard error of the regression estimate and sampling error. The lower errors with low-density LiDAR with no height adjustment estimates were repeated within each stratum (Table 3) and for combined strata estimates (Table 4). The combined strata estimate for volume and standard error of each density/height model was obtained by: Y lr,c n i n 2i N Y lr,i (0) Table 2. Regression estimates ( ) and fit statistics (index of fit, standard error of the regression estimate, correlation coefficient, and sampling error at a 95% level of confidence) for double-sample, high- and low-density LiDAR models, with and without LiDAR-to-ground height adjustment, on the unstratified LSU Lee Experimental Forest, Louisiana. X Variable I 2 Y lr S Y lr SE% Without height adjustment LiBA-High LiVOL-High LiBA-Low LiVOL-Low LiBA-High LiVOL-High LiBA-Low LiVOL-Low Y lr y (LiBA liba); is ft 3 of ground volume per ft 2 of LiDAR basal area. Y lr y (LiVOL livol), is ft 3 of ground volume per ft 3 of LiDAR volume. 208 SJAF 28(4) 2004

5 Table 3. Regression estimates and errors (standard error of the regression estimate and sampling error at a 95% level of confidence) for double-sample, low-density LiDAR volume models, with and without LiDAR-toground height adjustment, for three strata on the LSU Lee Experimental Forest, Louisiana. Stratum X Variable Y lr S Y lr SE% Without height adjustment LiVOL-low 3, LiVOL-low 3, Without height adjustment LiVOL-low 2, LiVOL-low 2, Without height adjustment LiVOL-low, LiVOL-low, Y lr y (LiVOL livol). Table 4. Regression estimates and errors (standard error of the regression estimate and sampling error at a 95% level of confidence) for double-sample, high- and low-density LiDAR models, with and without LiDAR-toground height adjustment, for combined strata on the LSU Lee Experimental Forest, Louisiana. X Variable Y lr S Y lr SE% Without height adjustment LiBA-High 2, LiVOL-High 2, LiBA-Low 2, LiVOL-Low 2, LiBA-High 2, LiVOL-High 2, LiBA-Low 2, LiVOL-Low 2, Y lr y (LiBA liba). Y lr y (LiVOL livol). 2 i n 2i S Y lr,c n N S 2 Y r,i 0.5 () where n i and n 2i are phase and 2 sample sizes respectively for stratum i and i to 3 strata. The combined strata estimates in Table 4 indicated that only a slight reduction in standard error and/or sampling error was achieved with stratification; however, there was no statistical difference between high- and low-density LiDAR estimates with or without height adjustment. Lowdensity LiDAR volume models without height adjustment produced the lowest standard error and sampling error of those models tested. Unstratified and stratified regression estimates for the low-density LiDAR volume model without height adjustment are shown in Table 5. Partitioning of Double-Sample Estimate The volume estimate for species-product es within a stratum was obtained by partitioning the double-sample volume estimate by percent volume distribution of the species-product es. Results for the low-density LiDAR volume model for the combined strata estimate are shown in Table 6. Parker and Evans (2002) reported no difference Table 5. Regression estimates and errors (standard error of the regression estimate and sampling error at a 95% level of confidence) for double-sample, low-density LiDAR volume model, without LiDAR-to-ground height adjustment, by strata on the LSU Lee Experimental Forest, Louisiana. Strata Y lr S Y lr SE% Unstratified 2, , , , Combined 2, Y lr y (LiVOL livol). between partitioning the composite double-sample volume estimate by percent occurrence of trees, volume, or basal area on the phase 2 ground plots into individual species volumes and obtaining individual species estimates with their respective double-sample equations. Discussion Height Adjustment from LiDAR to Ground The height regressions for ground height as a function of LiDAR height contain errors associated with ground measurement as well as any real bias that may exist due to the physics of the LiDAR beam s interaction with crown foliage and structure. The underestimation of conifer heights by LiDAR has been well documented; however, the seeming overestimation of hardwood heights by LiDAR has not received much attention. Collins (2003) and Brandtberg et al. (2003) found that field measurement error of hardwoods was a major contributor to ground versus LiDAR height differences because the ground observer cannot locate a true terminal or crown apex on a rounded hardwood crown. Underestimation of ground height in hardwoods over compensates for the LiDAR height underestimation and results in a negative intercept in the ground-lidar height regressions. Results of this study showed that the error associated with the regression adjustment of LiDAR height to ground height increased the error of the double-sample volume regression estimates. This error is most likely attributed to the positive correlations between height and volume and ground volume and LiDAR volume. Because the doublesample procedure adjusts the bias between phase and phase 2 volume estimates, any additional error introduced by the height equation affects the regression estimate. The height adjustment, in essence, removed the bias in the LiDAR height estimate, thus dampening the inherent variation in heights and volume that is normally adjusted by the regression estimator. There was no significant difference between doublesample regression estimates with or without the LiDAR height adjustment. Standard errors and sampling errors associated with the double-sample estimates were lower when no height adjustment was made. In any event, no statistical gain was recognized for height adjustment, and this translated into reduced field inventory cost. The azimuth and distance of height sample trees were measured with a laser SJAF 28(4)

6 Table 6. Partitioned double-sample regression estimate from the low-density LiDAR volume model without height adjustment into species-product volumes by percent volume distribution for combined strata as compared to ground means for trees per acre (N), basal area (ft 2 ), height (H, ft), and volume (ft 3 ) on the LSU Experimental Forest, Louisiana. Species Product Double-sample partitioned ft 3 Phase 2 ground means N ft 2 H ft 3 Pine Pulpwood Chip n saw Sawtimber, ,043, ,863 Hardwood Pulpwood Sawtimber Total 2, ,228 Standard error of combined estimate is ft 3 or 7.6% sampling error at unit which is expensive, time-consuming to use, and cumbersome in the field. Because the actual plot center should be located with a DGPS, the location of the height sample trees could be obtained with a hand compass azimuth and DME distance. Even though the study results did not indicate the need for the LiDAR-ground height relationship, it would be advisable, however, to collect some height relationship data to validate LiDAR precision. Low- Versus High-Density LiDAR There were no statistical differences ( 0.05) between double-sample regression volume estimates with LiDAR data from nominal posting densities of m(hitperm 2 ) and 0.5 m (4 hits per m 2 ). However, the standard errors and sampling errors of the regression estimates were obviously lower with low-density LiDAR data than with high-density data. These results are most likely attributable to the stand density and species characteristics in the study area. The study area was stratified into a mature natural pine, immature mixed natural pine-hardwood, and planted pine strata. The natural and planted pines were of sufficient height and crown diameter that the low-density LiDAR produced an adequate number of hits in the upper crowns for interpolating tree crown maxima and height. Low-density LiDAR tended to overestimate tree numbers (from the ground or high-density LiDAR values); however, the bias was adequately adjusted with the double-sample procedure. Apparently, there was more noise in the high-density LiDAR data, which translated into additional sampling error about the volume estimate. Heights for pines and hardwoods measured with lowdensity LiDAR appeared to have less bias than those measured with high-density LiDAR, and the ground-lidar height relationships were slightly stronger for low-density LiDAR heights. The height biases for both species groups were adequately adjusted with the double-sample regression estimator. This study indicated that low-density LiDAR ( point/m 2 ) produced acceptable volume results when used with a double-sampling procedure and any increased cost for acquiring high-density data may not be justified. Care must be exercised in extrapolating this conclusion to sampling of immature conifer stands with LiDAR because an adequate number of hits in the small crown area is needed to define tree location and crown maxima for height determination. Literature Cited AVERY, T.E., AND H.E. BURKHART Forest Measurements, 5th Ed. McGraw-Hill, New York, NY. 456 p. BRANDTBERG, T., T.A. WARNER, R.E. LANDENBERGER, AND J.B. MCGRAW Detection and analysis of individual leaf-off tree crowns in small-footprint, high sampling density LiDAR data from the eastern deciduous forest in North America. Remote Sensing Environ. 85(3): COLLINS, C.A Comparing integrated LiDAR and multi-spectral data with field measurements in hardwood stands. M.S. Thesis, Mississippi State University, Mississippi State, MS. 58 p. FURNIVAL, G.M. 96. An index for comparing equations used in constructing volume tables. For. Sci. 7: LEFSKY, M.A., W.B. COHEN, S.A. ACKER, G. PARKER, T.A. SPIES, AND D. HARDING LIDAR remote sensing of the canopy structure and biophysical properties of Douglas-fir western hemlock forests. Remote Sensing Environ. 70(3): MAGNUSSEN, S., AND P. BOUDEWYN Derivations of stand heights from airborne laser scanner data with canopy-based quantile estimators. Can. J. For. Res. 8: MCCOMBS, J.W., S.D. ROBERTS, AND D.L. EVANS Influence of fusing LiDAR and multispectral imagery on remotely sensed estimates of stand density and mean tree height in a managed loblolly pine plantation. For. Sci. 49(3): MEANS, J.E., S.A. ACKER, J.B. FITT, M. RENSLOW, L. EMERSON, AND C.J. HENDRIX Predicting forest stand characteristics with airborne scanning lidar. Photo. Eng. Remote Sensing. 66(): NELSON, R., M.A. VALENTI, A. SHORT, AND C. KELLER A multiple resource inventory of Delaware using airborne laser data. BioScience 53(0): PARKER, R.C., AND D.L. EVANS An application of LiDAR in a double-sample forest inventory. in Proc. of the 2002 ForestSat Conference: Operational Tools in Forestry using Remote Sensing Techniques, Forest Research, Forestry Commission Edinburgh, Scotland. PARKER, R.C Computer automation of a LiDAR double-sample forest inventory. For. and Wild. Res. Center Paper 270. Mississippi State University, Mississippi State, MS. 24 p. 20 SJAF 28(4) 2004