The study area is on Tinker Air Force Base in central Oklahoma, USA (latitude: 35°25′35.43″N; longitude: 97°24′37.73″W) (Figure 1). The area represents a typical suburban residential area with detached and row houses with trees, both broadleaves and conifers, growing along the road and in the yards and parks. The base is around 20 km² (5,000 acres) in area and has 472 buildings [61]. There are about 6,600 trees, the most common species being Eastern red cedar (Juniperus virgiana), Austrian pine (Pinus nigra) and Siberian elm (Ulmus pumila) [62].

Lidar data were acquired using an Optech ALTM 2050 lidar system in July 2004 in leaf-on condition. The Optech ALTM 2050 is a small-footprint multiple-return lidar system which uses a 1,064 nm laser. The provided lidar data did not have any return numbers. There were about 8 pulses per m². The system was flown at a 640 m flight height with a swath overlap of 40%. The pulse repetition frequency was 50 KHz and the scan frequency 45 Hz. The scan angle was less than 15 degrees.

To do away with any complications arising from classifying lidar data using height-filtering algorithms in urban areas, a 2 m-resolution bare-earth digital elevation model (DEM) delivered by the vendor (Tobin Aerial Surveys, Texas) was used. The DEM was evaluated by the vendor using ground control points and vertical accuracy within ±15 cm was reported. A normalized point cloud was computed by subtracting the digital elevation model (DEM) of the area from the elevation of lidar returns. In the normalized point cloud, all points with less than 1 m height were filtered out, which resulted in retaining only the lidar returns from trees and other urban objects. With the help of the normalized point cloud and a color orthophoto (acquired 17 February 2004 with a spatial resolution of 10.2 cm), lidar points within each tree with distinctly separable crowns (3,564 in total) were manually selected. The boundary of each crown was delineated by computing the planimetric convex hull around the lidar points within each tree in ArcGIS. We opted for a manual approach to avoid the discrepancies common when using an automated crown-delineation algorithm, especially in cases where tree crowns are overlapping with other trees or with buildings. Only a few individual tree crown delineating algorithms have been tested in urban landscapes (e.g., [63]), where conditions are different than forested environments. Various lidar metrics were computed for lidar returns within each individual tree (Table 2).

High-resolution satellite data of the area was obtained from a Quickbird satellite image (DigitalGlobe Inc., USA) acquired 17 May 2005. The image was radiometrically corrected, sensor corrected, and geometrically corrected. The image consisted of a panchromatic image with 0.6 m spatial resolution and a 4-band multispectral image with 2 m resolution. The spectral resolution of the Quickbird image is shown in Table 3.

Subsequent to preprocessing, three vegetation indices were computed as follows: normalized difference vegetation index (NDVI) [64], soil-adjusted vegetation index (SAVI) [65], and modified soil-adjusted vegetation index (MSAVI) [66]. For each of these three indices, and for spectral bands one through four, tree-specific descriptive statistics (minimum, maximum, mean, and standard deviation) were calculated (Table 4). NDVI enhances vegetation but is sensitive to optical properties of soil background, especially in areas with considerable soil-brightness variation. SAVI minimizes the effect of soil by introducing an adjustment factor to NDVI to account for first-order soil variation and differential red and near-infrared flux extinction through vegetation [65]. Unlike NDVI, SAVI vegetation isolines do not converge to the origin and are independent of soil background [67]. The constant factor varies from 0 to infinity depending on the vegetation density. A factor of 0.5 was used for this study as it has been found optimal in a wide range of conditions. MSAVI replaces the constant factor of SAVI with an iterative self-adjusting factor.

Field measurements of the urban trees used for this study were made in 2006. The coordinates of each individual tree were recorded using a GPS unit. A high resolution digital orthoimage was used in the field to verify the location of each tree. Various tree attributes were recorded including species, diameter at breast height, tree height, condition of tree, crown radius, age class, etc. [62]. Diameter at breast height (dbh) was measured to the nearest inch using a logger’s tape. If the tree was co-dominant, the largest leader at breast height (1.37 m) was measured and recorded. Tree height was measured to the nearest foot (0.3048 m) using an Opti-Logic 100 LH Laser Rangefinder Hypsometer. On windy days several measurements were taken and averaged. Crown radius was measured at two directions perpendicular to each other with a logger’s tape to the nearest foot from the center of the trunk to the drip line of the canopy by using a nail to secure the tape to the trunk. For this study, a total of 3,562 trees, 60 broadleaf species and 12 conifer species, were used (Table 5). Most of the conifers are shorter than the broadleaf trees. Among broadleaf species, Platanus occidentalis and Acer saccharinum are, in general, taller than the other species. The descriptive statistics for diameter at breast height and crown size are shown in Table 6. Ulmus pumila, Acer saccharinum, and Platanus occidentalis are among those having larger diameter and crown widths. Conifers generally have smaller dbh and crown size than broadleaf trees.

The biophysical parameters of the trees, including tree height, diameter at breast height, mean crown radius, and biomass were estimated. Tree biomass is usually estimated either through direct measurement such as destructive sampling, or through use of biomass equations and tables [68]. Because the direct method of biomass measurement is often impractical, allometric equations developed for specific tree species and localities are often used to estimate biomass. As there are few allometric equations developed specifically for urban trees (e.g., [69]), most studies rely on the equations based on forest trees. Allometric equations developed for a tree species in different parts of the world differ little in the values of the parameters [70,71]. This suggests that biomass equations developed for certain tree species in one part of the world can satisfactorily predict the biomass of the species in another part of the world, albeit with some bias in the predictions [72]. The USDA Forest Service has developed and evaluated models to quantify the benefit of urban trees—namely i-Tree Streets (http://www.itreetools.org/streets) and Urban Forest Effects Model (http://nrs.fs.fed.us/tools/ufore). These models also use allometric equations from urban trees of the specific region where available.

For the present study, due to lack of availability of urban tree allometry, forest-derived aboveground biomass equations were used in most cases. The species-specific allometric equations were chosen such that they represent the climatic conditions of the study area, where available, and were based on trees with sufficient range of dbh. Equations used to estimate above ground biomass for major species are listed in Table 7. McHale et al. [8] compared biomass equations derived from terrestrial lidar scanning of urban trees to equations developed from traditional forests and found that variability ranged from 60–300%, but when a variety of equations are used for the entire urban forest community, variability was reduced to 10%. In the present study, we used multiple species-specific biomass equations, rather than one or two general biomass equations for all the trees in the area, as this should reduce the potential errors associated with using forest-based allometry.

Once all significant variables were identified among the lidar descriptive statistics (Table 3), best subsets regression was used in Minitab version 16.1.1 software (Minitab Inc., Pennsylvania, USA) to select the best subset of candidate predictor variables to be included in each final model. Multicollinearity of all the independent variables were tested using variance inflation factors (VIF) [79]. If any of the variables had VIF value >10, then the variables with the highest VIF was removed, and the VIF computed again with the new set of variables. This process was repeated until all the variables had VIF of ≤10. The best subsets regression was performed with the remaining independent variables that were significant (α = 0.05). The regression models were evaluated using the following three criteria to select the best model [80]: (1) maximum adjusted coefficient of determination (R²_adj), (2) minimum Mallows C_p, and (3) minimum mean square error (MSE). In this study, the most parsimonious models with C_p ≤ (p + 1), where p is the number of variables in the model, were chosen.

Each resulting model was subjected to residual and influential analysis. While selecting the final model, the parsimony principle was employed whereby fewer variables were preferred over slightly better values of R²_adj or C_p. The predictive capability of the selected model was assessed using cross-validation multiple-correlation [81] and prediction sum of squares (PRESS) [82]. Outliers in the model were identified using jackknife residuals [83], where the multivariate distance for each observation is calculated using means, variances, and covariances that do not include the observation itself. Each outlier, as defined by jacknife residuals, was investigated carefully to determine the cause of the outlier. Only when the outlier was due to unnatural causes, such as lidar returns from power wires or dead trees, or anomalous measurements, was it discarded from the data analysis. Outlier removal was particularly important for this study because there was a lapse of two years between the lidar flight and the field data collection. In the two years between lidar data collection in 2004 and field data collection in 2006, some trees had growth in height and crown diameter, others were pruned, and some were completely removed.

The lidar return with maximum height (H_MAX) from an individual tree is representative of the return coming from the topmost branch of the tree, and is most often related to the field-measured height of the tree. The mean field-measured height was higher compared to mean H_MAX in both conifers (field measured 7.2 m, H_MAX 7. 1 m) and broadleaf trees (field measured 10.1 m, H_MAX 9.6 m). The height underestimation may have become compounded because of the two year lapse between the lidar flight (2004) and field data collection (2006), in which time the height of tree could have increased.

Previous studies (e.g. [84]) using individual tree height with lidar have found similar underestimation in forested environments. Hyyppä et al. [85] and Persson et al. [36] found an underestimation of 0.14 m and 1.73 m respectively in Norway spruce and Scots pine forests. The difference in bias between the two studies was attributed to lidar point density. Hyyppä et al. [85] used a point density of 24 points/m², which was considerably denser than the present study. Using fairly dense lidar data (10 points/m²) in a mixed Bavarian forest, Heurich et al. [86] obtained similar underestimation of 0.42 m for deciduous trees, but a much larger underestimation of 0.65 m for coniferous trees. The smaller underestimation of conifers in the present study can be attributed to lower growth during the two year lapse period compared to broadleaf trees.

The distribution of the field-measured total height and H_MAX for broadleaf trees shows a larger number of trees in taller height classes having lower H_MAX than field-measured height, while for shorter trees fewer numbers of trees had lower H_MAX (Figure 2). This positive shift in height distribution of field-measured broadleaf trees is likely due to growth during the two year lapse. In conifers, however, the total number of trees was lower for most of the trees in the middle height range (Figure 2). For very tall and very short trees, H_MAX overestimated the total height. This result does not conform to the findings by other studies showing lidar underestimates the tree height consistently. In mixed temperate forests of Northern Idaho, Falkowski et al. [87] found that lidar underestimated high tree height and overestimated low tree height, which is similar to the results obtained for broadleaf trees by the present study. Brandtberg et al. [19] also found similar results in an oak-dominated forest in West Virginia using leaf-off lidar data. Since the overall height growth for the conifers over two years’ period was minimal, the height underestimation in the upper height class may also be due to lidar pulses missing the conifer top or to random errors in field measurement where it is sometimes harder to locate the tree-tops, leading to over- or under-estimation of tree heights [25,88].

The field-measured tree height and H_MAX of 3562 total trees had an R² of 0.887 and RMSE of 1.34 m (Figure 3). Conifers (R² = 0.789), had a poorer relationship with H_MAX than the broadleaf trees (R² = 0.889) (Figure 4). The increased probability that lidar pulses missed the conical and pointed tip of the conifers may have contributed to the lower R² than in broadleaf trees, whose tips are not as pronounced as that of conifers.

The less-pronounced tips of broadleaf trees also contribute to error in field-measured height. The well-defined tips of conifers, on the other hand, make it easier to spot the tip in the field. Two factors are important for achieving good height estimation of individual trees using lidar: (1) correct height filtering and hence accurate estimation of bare-earth surface, and (2) correct delineation of the crown, which reduces error due to false tree tops. Poorer crown boundary delineation can contribute to false tree tops and reduce the R² considerably [89].

Some species had a better relationship and others had a worse relationship with H_MAX (Figure 5). Ulmus parviflora and Acer saccharinum had R² below 0.7. These species have a rounded crown with no distinct tree top, thus making it difficult to identify the tree top for the lidar as well as for the field measurer.

Diameter at breast height (dbh) was estimated with crown-based metrics and height-based metrics separately (Table 8). For both sets, one variable with the best relationship was chosen. Among crown-metrics, crown perimeter, C_p, performed best in all cases, and among height-based metrics different variables performed best in different cases. H_MEAN had a good fit with all trees, broadleaf trees, and both conifer species, while for broadleaf species the best variables were H_MAX or one of the upper quantiles. Crown metrics had a better R² value than height-based metrics. The result is similar to that reported by Chen et al. [38] who also found that crown metrics performed better than height metrics to predict basal area and stem volume for individual trees in a deciduous oak woodland in California.

Broadleaf dbh is better estimated using either crown or height metrics than conifer dbh. If measuring crown size with relatively high accuracy is achievable, crown metrics are better predictors of dbh than height-based metrics. Height-based metrics can also give a robust estimate of dbh for individual broadleaf trees, but are not as good for conifers. Persson et al. [36] and Popescu et al. [48] found both height and crown width significant for predicting dbh for individual trees in forested areas. Estimation of diameter at breast height can be greatly improved through complementary use of terrestrial lidar, as has been demonstrated for urban trees by Omasa et al. [90].

A strong correlation (R² = 0.90) was obtained from the relationship between field measured crown radius and the radius measured on the trees identified with lidar (Figure 6(a)). Field-measured crown radius was the average of the two perpendicular measurements taken in the field. Lidar-based radius was computed by assuming the tree crown as a circle: radius = crown   area / π.

Because crown radius is often a function of tree height—taller trees have larger crowns and smaller trees have smaller crowns—field-measured crown radius is related to lidar-measured maximum height but has a lower R² of 0.75 (Figure 6(b)).

An attempt was made to estimate the crown radius using only height-based lidar distribution metrics (Table 9). Lidar height metrics from conifers have a poorer relationship with crown radius compared to those from broadleaf trees. Among broadleaf species only Acer saccharinum has the lowest R². Among the metrics, H_MEAN, H_MAX, and the upper quantiles resulted in the best fit with crown-diameter.

Aboveground biomass of conifers had the lowest R² value among broadleaf trees and all trees combined (Table 10). The lower performance of the biomass models for all trees, broadleaf trees, and conifers compared to individual species (Table 11) might have resulted from aggregating the species-wise models to estimate biomass for broader categories. This might have compounded the variation of biomass between species within the category.

Predictors based on Quickbird performed poorly for all trees, broadleaves and conifers (Table 10). While studies have found good stand-level biomass prediction capacity using hyperspectral or multispectral data in forested areas [91–95], studies exploring the relationship between spectral metrics from high-resolution imagery and forest biomass are largely lacking. Instead of using spectral metrics, most studies have used crown-size information from high-resolution imagery to predict forest biomass. Leboeuf et al. [96] used Quickbird-derived tree shadow fraction, which is calculated as the ratio of the area of tree shadows to the ground reference, to predict biomass in black spruce stands in Canada. Gonzalez et al. [97] used Quickbird-derived crown diameter to predict biomass of old-growth forests in California, but found higher uncertainty and lower accuracy than with lidar-derived height. This is due to the poorer relationship between crown diameter and biomass than between lidar-derived height and biomass.

Species-specific relationships had a much higher R² (from 0.68 to 0.84), Table 11 and Figure 7. Naesset [49] also suggested the use of careful stratification to improve accuracy. The metric crown area (CA) performed well in all the species biomass models, except for Q. schumardii. In Q. schumardii the number of crown returns explained more variance than crown area. Popescu et al. [40] similarly found that lidar-derived crown diameter alone explained 78% of the variance associated with pine biomass.