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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

The objective of this study was to determine whether leaf area index (LAI) in temperate mixed forests is best estimated using multiple-return airborne laser scanning (lidar) data or dual-band, single-pass interferometric synthetic aperture radar data (from GeoSAR) alone, or both in combination. ^{2}

Leaf area index (LAI) is an important canopy descriptor used to estimate growth and productivity in forest ecosystems. Watson [

Remote sensing estimation of LAI has been mostly based on empirical modeling, using vegetation indices, generally developed with the spectral reflectance from the near-infrared and red wavelengths, and their correlations with ground-truth estimates. However, the use of optical imagery carries some disadvantages, as follows: (1) it is only suitable when evaluating horizontal variation; (2) optical passive sensors are unable to obtain data from the ground when it is obscured by clouds, and most importantly; (3) vegetation indices calculated using optical imagery tend to reach a saturation point when LAI values are above 3 [

Two fairly recent technologies could potentially improve the estimate of LAI in these forests where canopies can vary greatly not only horizontally but also vertically, and the likelihood of reaching a reflectance saturation point is high. Light detection and ranging (lidar) sensors measure the time between the emission and reception of laser pulses to estimate the location and height of the target feature. They thus acquire information in three dimensions (x, y, and z coordinates) and provide the means to evaluate variation across a vertical profile. Previous studies in which LAI was estimated, in mixed forests (distributed around the world) using lidar data, have reported ^{2}^{2}^{2}^{2}^{2}

Dual-band interferometric synthetic aperture radar (DBInSAR) can now be collected using the geographic synthetic aperture radar (GeoSAR) airborne radar mapping system. GeoSAR acquires X-band (VV, 9.7 GHz) and P-band (HH, 0.35 GHz) simultaneously over 11 km swaths [

Previous attempts to estimate LAI using SAR (Synthetic Aperture Radar) data have found low correlations between ERS-2 (European Remote Sensing Satellite-2) SAR backscatter and LAI or biomass, but significant correlations between a green leaf biomass index (calculated using ERS-2 SAR backscatter) and LAI, in Mediterranean vegetation [^{2}

While these and other studies have used radar backscatter to estimate LAI, none to date has assessed the potential utility of interferometric heights for LAI estimation. Given that lidar data have been shown to enable robust LAI estimation, and both lidar and DBInSAR can be used to estimate canopy heights, we posited that the DBInSAR data from GeoSAR could be useful for remote sensing of LAI. As such, the objective of this study was to determine whether leaf area index in temperate mixed forests is best estimated using multiple-return airborne laser scanning (lidar) data or dual-band, single-pass interferometric synthetic aperture radar data (from GeoSAR) alone or both in combination.

The study area was located in the Appomattox-Buckingham State Forest in Virginia, at 37°25′9″N and 78°40′30″W (

The measurement plots were installed following the US National Forest Inventory and Analysis (FIA) guidelines [

Total tree height (ht) and diameter at breast height (DBH) were assessed for every individual with a DBH > 2.54 cm within the measurement plots using a Haglöf Vertex hypsometer and diameter tape. A 20 m buffer was applied to each plot (from its center) to generate circular plots of 1,256.6 m^{2} of size.

Leaf area index was indirectly estimated during late summer (23–25 September 2008), using the LiCor LAI-2000 Plant Canopy Analyzer. Although, the ground data collection was undertaken in September, the vegetation was mostly green at all levels of the forest vertical profile. The LAI-2000 measures the gap fraction (the probability that a ray of light will go through the canopy without intercepting any plant element), and applies the Beer-Lambert law to estimate leaf area, assuming that the foliage elements (independent of whether they are leaves, needles or shoots) are randomly distributed, and that the leaf size is small compared to the size of the canopy. Thus, when these assumptions are not met, underestimations can occur. However, this instrument has been widely used in previous research, due to it being one of the non-destructive methods to estimate leaf area index, and due to its portability, especially when sampling plots with high amount of understory located in remote areas. Above-canopy readings were recorded remotely every 15 s by placing an instrument in an open field adjacent to the stand during the same date and time that measurements were taken inside the stand. The measurements inside the stand, below-canopy readings, were made holding the instrument at the height of 1 m facing upwards. This same procedure was repeated in every plot regardless of the presence of understory or mid-story vegetation. Due to the instrument design, measurements were taken under diffuse sky conditions to ensure that the sensor used indirect light only. Thus, measurements were taken during the dawn and pre-dusk periods, with the above instrument facing north and using a 90° view cap. Sampling points were distributed in the following manner: one reading at the center of the plot, and one reading at 5 m away from the center in each cardinal direction (north, south, east and west), for a total of 5 readings per plot. The calculation of LAI was accomplished using the FV-2000 software which averaged all the readings per plot. The canopy model used to calculate LAI was Horizontal [

Small footprint lidar data were acquired in late August 2008. The system was an Optech ALTM 3100 with an integrated Applanix DSS 4K × 4K DSS camera. The data have multiple returns with a sampling density of 5 pulses per square meter, with 4 or fewer returns per pulse. The scan angle was less than 15 degrees. Instrument vertical accuracy over bare ground is 15 cm, and horizontal accuracy is 0.5 m. The inverse distance weighted interpolation method was used to generate a digital elevation model (DEM) with the data classified as ground returns [

Frequency of returns (count), calculated from each of the lidar data point classes, was used only to estimate other metrics, such as proportions of returns, but was not used in the development of the models (

GeoSAR data were acquired in late summer 2008. The system recorded data from two microwave bands, X (VV, 9.7 GHz) with a 0.03 m wavelength and P (HH, 0.35 GHz) with a 0.85 m wavelength, in single passes. Postings from the X-band were 3 m; those from the P-band were 5 m. GeoSAR X-band interferometry yields a digital surface model (DSM) and P-band interferometry is used to create a digital elevation model (DEM). Previous research has used the difference between the DSM and DEM to create a canopy height model used to estimate forest biomass [_{0}) or backscatter coefficient from all four looks (North, South, East, West), defined as the backscatter power per unit area on the ground. Analogous to those used with lidar-derived heights and intensities, GeoSAR metrics were developed using the following approach (see also

In order to evaluate the vegetation height, the difference between X-band (mostly backscattered from the vegetation/canopy surface) and P-band (mostly from the ground and lower tree branches) interferometric heights was calculated. In addition, the X-band was divided by the P-band with the purpose of evaluating any other relationship between the two bands.

The high resolution DEM created from the lidar data was used to generate the heights above ground for the X and P bands.

No changes were made to the magnitude or the σ_{0} bands.

The cell values from all the rasters created (10 in total) were extracted and the frequency, mean, standard deviation, coefficient of variation, minimum, maximum, and percentiles (10th to 90th) were calculated for all plots.

A dataset of 81 plots was compiled for all lidar-derived, GeoSAR-derived and ground-truth metrics. However, after deleting plots for proximity to roads and for being outliers (but not influential), the number of plots was reduced to 61. Pearson correlation coefficients were used to evaluate relationships among lidar metrics, GeoSAR metrics and ground estimated LAI. Multiple regressions were used to fit the dataset. Best subset regression models were examined using the RSQUARE method for best subsets model identification [

High coefficient of determination (^{2}

Low residual mean square (RMSE).

Similarity between the adjusted coefficients of determination ^{2}_{adj’} and ^{2}^{2}_{adj’} is a rescaling of ^{2}

Mallows’ _{p}_{p}

Low values from two information criteria, the [

The best models chosen per each subset size (based on number of variables in the models) were evaluated for collinearity issues. Near-linear dependencies between the explanatory variables were evaluated using computational stability diagnostics. In order to make independent variables orthogonal to the intercept and therefore remove any collinearity that involves the intercept, independent variables were centered by subtracting their mean values [

Additional data to test the models were not available, thus cross-validation analysis was performed using the prediction sum of squares (PRESS), which is the sum of squares of the difference between each observation and its prediction when that observation was not used in the prediction equation [_{pred}) was then calculated as the square root of the ratio between the PRESS statistic and the number of observations. The CV-RMSE is an indicator of the predictive power of the model. The significance level used for all the statistical tests was α = 0.05 (

Although the statistical analyses applied to the dataset of 61 plots did not show the presence of outliers, three of these plots with measured low LAI values (1.34 to 1.43) could potentially be influencing the dependent

The 61 plots were distributed within the different forest types as follows: 3 in bottomland hardwoods, 18 in upland hardwoods, 4 in mixed pine-hardwoods, 24 in loblolly pine, 6 in shortleaf pine, and 6 in Virginia pine. For all forest types, stand age ranged between 10 and 164 years.

Mean tree height ranged from 13 m to 16 m, and mean dbh from 13 cm to 24 cm. Mean leaf area index values estimated on the ground, for all forest types, were between 3.1 to 4.1 (^{2}), and for all returns (hag > 0.2 cm) from 4,343 to 5,278 returns/plot area. Mean lidar heights above ground were between 9.9 m to 13.2 m, with standard deviations ranging from 4.5 m to 6.8 m (

Minimum heights were set to 0.2 m, and maximum values ranged from 25.3 m to 37.6 m. Intensity mean values from vegetation returns (hag > 1 m) were observed between 37 to 51 watts/plot. Standard deviations from the intensity values were over 20 watts/plot for all groups of plots. Laser penetration index (LPI) was lowest (0.003) for the pine-hardwoods and shortleaf pine group of plots, and highest (0.039) for the upland hardwood plots.

The mean number of cells per plot from the GeoSAR P-band was 49, and for the X-band was 138. Mean heights from the P-band ranged from 5.46 m to 10.48 m, while for the X-band they ranged from 10.84 m to 16.06 m (

Pearson correlation coefficients were summarized for the variables included in the best models (_{10th} (0.638) and X_{50th} (0.609). Also, d_{2} (−0.347) and X_{cv} (−0.485) were statistically significant. The 10th and 20th percentiles (height values) were the only percentiles of any type significantly correlated with LAI. It is important to mention that in the past, the relationship between LAI and LPI has been reported as linear [^{2}

The best models from lidar metrics had ^{2}^{2}_{10th}, the increase in ^{2}_{10th}, d_{10}, and Cd-3) had a similar contribution (0.053, 0.064, and 0.059). Predicted values from the 4-variable model were plotted against the measured LAI (^{2}^{2}_{adj’} did not, therefore only a 4-variable model with an ^{2}_{50th} (0.127), followed by X_{cv} (0.098), sn01xl_{cv} (0.047), and Xmag_{stdv} (0.035). All variables included in the lidar only and GeoSAR only models had a VIF and CI lower than 5.

The best-performing models from the best subsets regressions using the metrics from lidar and GeoSAR combined are reported in ^{2}_{50th} and X_{50th} variables were included in all models; the latter was the only variable from GeoSAR that was included. Other variables included in these models from lidar were LPI, d_{2}, and two crown density metrics (Cd-1, and Cd-3_{stdv}). The largest contributions (always higher than 0.1) were from the All_{50th} and X_{50th} variables. Between the 5 and 6-variable model, the ^{2}^{2}_{adj’} increased and the RMSE decreased with an extra variable, but the CV-RMSE stayed the same.

There were no collinearity issues flagged by the VIF and CI, which were under 5 for all variables. Predicted values from the 4-variable model and 6-variable model are shown in ^{2}

The best models obtained from the best subset regression analyses applied to the dataset without the low LAI plots (^{2}^{2}^{2}^{2}

Crown density metrics were included in the best models using 5 or more variables. These were removed as independent variables, and the data re-analyzed. The results from these analyses are shown in ^{2}_{stdv} and Pmag_{max}. The VIF values from these two models increased to 7.6 compared to the models with the crown metrics, due to the high correlation between Pmag_{stdv} and Pmag_{max} (0.931).

The LAI range of values, among all plots, was large enough to develop a relationship with lidar metrics. There were few representatives (3) at the low range of LAI. These three plots were influential, and therefore, were not deleted from the dataset. It is important to highlight that even when the estimations from the LiCor LAI-2000 could be conservative and underestimating the actual values of LAI for the plots sampled [

In the past, models for LAI prediction in mixed hardwood and coniferous forests using only lidar data have reported ^{2}^{2} to 500 m^{2}) [^{2} size, reveal an ^{2}^{2}

The high correlation of LPI with leaf area index was expected [

Lidar return percentiles are height values calculated based on the vertical density of returns [

Similar to the 10th percentile of the lidar returns, the density metric d_{10} [_{10}, the density metric d_{2} was selected in the models using lidar and GeoSAR metrics together. This variable relates to the low section of the vertical profile of the stand.

Crown density slice metrics are descriptors of tree crowns, and metrics related with the proportions of returns and standard deviation of the return heights at 1 and 3 meters below the mode value were included in the models. These variables contributed as much as the density metrics. Interestingly, the combination of all returns percentiles, densities, and crown density metrics in the models managed to describe the vegetation at the top, medium, and low level of the vertical profile. For instance, d_{10}, Cd-3, and All_{10th} were together in the 4-variable model for lidar metrics only.

The interferometric heights from the X-band, after being corrected by the DEM developed from lidar data, showed the largest correlations with LAI. The 50th percentile of the height values per plot was positively correlated with LAI. The coefficient of variation from all the height values within a plot correlated negatively, suggesting more variability among the height values in plots with low LAI values. In addition, the metrics of the layer generated from the difference between X-band and P-band (X- minus P-band), and the metrics from the P-band interferometry showed significant correlations with LAI but they were not included in the best models. Moreover, the coefficient of variation obtained from the values of one of the σ_{0} layers contributed significantly to the model when only GeoSAR data were used.

The results from this study support previous success in estimating LAI in mixed forests using lidar metrics [^{2}^{2}^{2}

Ideally, the future inclusion of additional sampled plots covering a wider range of species associations and LAI values for this particular forest type would increase the robustness and accuracy of these models and result in a more trustworthy tool for the estimation and monitoring of leaf area in other states or regions. In addition, X-band interferometry is currently possible using spaceborne sensors, which shows clear utility for LAI estimation at landscape to regional scales.

At present, the growing hardwood utilization industry requires decision support tools that can accommodate a diverse set of management, planning, and policy-making strategies and goals. Leaf area index is a key variable for the estimation of wood production and carbon storage when using such tools. Consequently, robust and accurate models to remotely estimate this variable are essential. The results of our research demonstrate that lidar and DBInSAR data can be important factors in the development and improvement of such models, particularly when the datasets are used in tandem.

This research was possible thanks to support from the Virginia Tech Department of Forest Resources and Environmental Conservation and the help in field data collection provided by Jessica Walker (Virginia Tech), Rupesh Shrestha (Boise State University), Nilam Kayastha (Virginia Tech), Asim Banskota (Conservation International), Wayne Bowman (Virginia Department of Forestry), and John Scrivani (Virginia Information Technology Agency).

Geographic distribution of plots in Appomattox Buckingham State Forest, Virginia, USA. Plots are displayed over a true color aerial photo.

(_{mode} value (height to live crown was not measured on the ground). Five 1-m sections above and below the mode were defined, and the descriptive statistics (

Lidar returns and GeoSAR X- and P-band heights from a 108 yr-old upland hardwood plot with LAI = 3.23. Three-dimensional plots are: (

Vertical profiles for all plots: (

Relationship between estimated LAI and measured LAI using the 4-variable model with lidar metrics only (_{10th}) − 12.498(d_{10}) − 15.113(Cd-3).

Relationship between estimated LAI and measured LAI using the 4-variable model with lidar and GeoSAR metrics (_{50th}) − 3.027 (d_{2}) + 0.201 (X_{50th}).

Relationship between estimated LAI and measured LAI using the 6-variable model with lidar and GeoSAR metrics (_{50th}) − 4.979 (d_{2}) + 0.208 (X_{50th}) − 14.977 (Cd-3_{stdv}) − 7.805 (Cd-1).

Relationship between estimated LAI and measured LAI using the 6-variable model with lidar and GeoSAR metrics and excluding the three plots of low LAI values from the dataset (_{50th}) − 4.800 (d_{2}) + 0.211 (X_{50th}) − 18.042 (Cd-3_{stdv}) − 8.531 (Cd-1).

Explanatory variables derived from lidar and GeoSAR. Return hag refers to the return height above the ground. Statistics in subscripts were as follows: frequency (total), mean, mode, standard deviation (stdv), coefficient of variation (cv), minimum (min), maximum (max), and height percentiles (10th, 20th, …, 90th). The metrics Gr_{total}, All_{total}, Veg_{total}, Gr_{returns}, All_{pulses}, and Veg_{pulses} were determined for calculation of other metrics (

Lidar Metrics | Symbol |
---|---|

Gr_{total} | |

All_{total}, All_{mean}, All_{stdv}, All_{cv}, All_{min}, All_{max}, All_{10th},…, All_{90th} | |

_{total} _{cv} | |

Veg_{total}, Veg_{mean}, Veg_{mode}, Veg_{stdv}, Veg_{cv}, Veg_{min}, Veg_{max}, Veg_{10th},...,Veg_{90th} | |

_{total} _{cv} | |

Gr_{returns}, All_{pulses} | |

LPI = Gr_{returns}/(Gr_{returns} + All_{pulses}) | |

I_{mean}, I_{min}, I_{max}, I_{stdv}, I_{cv} | |

_{cv} | |

R_{i}_{total} | |

d_{i}_{max} − Veg_{min})/10]/Veg_{total} | |

_{min},1,..,10 | |

_{mode} |
Cd_{mean}, Cd_{stdv}, Cd_{cv} |

Cd_{i}_{total} + Gr_{total})] | |

_{mean}, Cd_{stdv}, _{cv} |
( |

_{mode} | |

_{mode} | |

_{mode} | |

GeoSAR Metrics | −Symbol |

_{total}, _{mean}, _{stdv}, _{cv}, _{min}, _{max}, _{10th}, _{20th}, _{25th}, _{40th}, _{50th}, _{60th}, _{75th}, _{80th}, _{and} _{90th} | |

_{total} _{cv}) |
_{0} for flight line 1), sn02xl (σ_{0} for flight line 2), sn03xl (σ_{0} for flight line 3), sn04xl (σ_{0} for flight line 4) |

_{0} ^{2} (dB=decibels) |

Descriptive statistics for tree height, tree dbh, and leaf area index (LAI) at plots per forest type classes. Statistics for total were calculated based on plot means. Column annotation:

Bottomland hardwood | 3 | 89 | 14.0 | 6.4 | 0.4 | 26.8 | 18.7 | 11.2 | 3.1 | 43.7 | 3.94 | 0.40 | 3.68 | 4.40 |

Upland hardwood | 18 | 12–164 | 16.3 | 6.3 | 2.7 | 41.2 | 23.7 | 11.9 | 2.5 | 55.1 | 3.08 | 0.74 | 1.43 | 4.23 |

Pine-hardwood | 4 | 45–118 | 14.9 | 5.9 | 2.4 | 35.4 | 17.0 | 9.0 | 2.5 | 50.0 | 4.06 | 0.68 | 3.41 | 4.90 |

Loblolly pine | 24 | 10–63 | 13.3 | 3.8 | 0.9 | 33.8 | 16.3 | 6.9 | 2.5 | 86.1 | 3.37 | 0.86 | 1.34 | 4.48 |

Shortleaf pine | 6 | 30–38 | 12.9 | 3.8 | 4.0 | 24.1 | 14.1 | 7.4 | 2.5 | 42.7 | 4.09 | 0.28 | 3.68 | 4.39 |

Virginia pine | 6 | 60 | 14.1 | 3.6 | 4.3 | 33.5 | 12.4 | 8.0 | 2.8 | 73.7 | 3.75 | 0.44 | 2.89 | 4.06 |

61 | 10–164 | 14.2 | 3.2 | 0.4 | 41.2 | 17.0 | 5.9 | 2.5 | 86.1 | 3.71 | 0.57 | 1.34 | 4.90 |

Means of lidar returns per forest type and per plot area (1,256.6 m^{2}). Minimum values for all returns heights above ground were set at 0.2 m. Intensity minimum value was 1 for all plots (_{total} (total number of ground returns), All_{total} (total number of all returns), Stdv (standard deviation), Max (maximum value), and LPI (Laser Penetration Index).

_{total} (Mean) |
_{total} (Mean) |
|||||||||
---|---|---|---|---|---|---|---|---|---|---|

Bottomland hardwood | 3 | 222 | 4,343 | 12.7 | 6.8 | 36.6 | 51 | 29 | 136 | 0.019 |

Upland hardwood | 18 | 537 | 5,278 | 13.2 | 6.8 | 31.0 | 44 | 28 | 150 | 0.039 |

Pine-hardwood | 4 | 264 | 5,009 | 12.7 | 5.9 | 34.9 | 49 | 28 | 126 | 0.003 |

Loblolly pine | 24 | 534 | 4,436 | 10.2 | 4.8 | 32.7 | 41 | 24 | 149 | 0.034 |

Shortleaf pine | 6 | 353 | 5,165 | 9.9 | 4.5 | 25.3 | 43 | 27 | 137 | 0.003 |

Virginia pine | 6 | 555 | 4,617 | 13.2 | 5.1 | 37.6 | 37 | 22 | 125 | 0.005 |

61 | 411 | 4,808 | 12.0 | 5.7 | 37.6 | 44 | 26 | 150 | 0.017 |

Means of GeoSAR cell values per forest type. P and X band heights were calculated by subtracting the values from a DEM created from the lidar returns (_{mag} (P-band magnitude values), X_{mag} (X-band magnitude values),

^{2}) |
^{2}) | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Bottomland hardwood | 3 | 10.48 | 1.70 | 14.71 | 16.06 | 2.35 | 25.30 | 5.57 | 1.85 | 11.78 | 0.24 | 0.05 | 0.45 | 0.13 | 0.04 | 0.31 |

Upland hardwood | 18 | 6.65 | 1.35 | 13.53 | 11.96 | 1.81 | 20.91 | 5.20 | 1.99 | 13.40 | 0.26 | 0.05 | 0.62 | 0.11 | 0.03 | 0.25 |

Pine-hardwood | 4 | 8.03 | 1.52 | 16.27 | 13.72 | 1.66 | 24.77 | 5.47 | 1.71 | 11.74 | 0.23 | 0.05 | 0.48 | 0.12 | 0.04 | 0.41 |

Loblolly pine | 24 | 5.46 | 1.30 | 13.26 | 10.84 | 1.22 | 22.55 | 5.46 | 1.70 | 15.40 | 0.36 | 0.08 | 0.99 | 0.07 | 0.02 | 0.27 |

Shortleaf pine | 6 | 6.89 | 1.45 | 11.77 | 11.78 | 1.44 | 18.83 | 4.98 | 1.55 | 12.95 | 0.30 | 0.06 | 0.55 | 0.09 | 0.03 | 0.21 |

Virginia pine | 6 | 6.83 | 1.94 | 18.38 | 15.04 | 1.71 | 30.02 | 8.15 | 1.86 | 15.46 | 0.41 | 0.09 | 0.88 | 0.08 | 0.03 | 0.25 |

61 | 7.39 | 1.54 | 18.38 | 13.23 | 1.70 | 30.02 | 5.80 | 1.78 | 15.46 | 0.30 | 0.06 | 0.99 | 0.10 | 0.03 | 0.41 |

Pearson correlation coefficients for the independent variables used to predict leaf area index (LAI) (

_{10th} |
_{50th} |
_{2} |
_{10} |
_{cv} |
_{50th} |
_{stdv} |
_{stdv} |
_{max} |
_{cv} | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | −0.116 | 0.085 | − |
0.030 | −0.084 | 0.223 | 0.241 | −0.013 | −0.092 | −0.124 | |||||

1 | − |
0.063 | −0.054 | 0.160 | −0.237 | −0.242 | − |
−0.520 | −0.065 | 0.181 | 0.187 | 0.071 | |||

_{10th} |
1 | 0.163 | −0.091 | −0.148 | 0.106 | −0.031 | 0.168 | 0.072 | 0.054 | −0.075 | |||||

_{50th} |
1 | −0.438 | −0.168 | 0.013 | 0.087 | 0.168 | −0.116 | −0.112 | |||||||

_{2} |
1 | −0.083 | 0.085 | 0.050 | 0.086 | 0.078 | 0.031 | 0.105 | |||||||

_{10} |
1 | −0.242 | −0.181 | 0.199 | 0.039 | 0.080 | −0.041 | −0.190 | −0.146 | ||||||

1 | − |
0.136 | 0.216 | −0.251 | |||||||||||

1 | −0.062 | −0.326 | −0.176 | −0.413 | 0.024 | 0.131 | −0.083 | ||||||||

_{stdv} |
1 | −0.127 | 0.176 | − |
− |
0.105 | |||||||||

_{cv} |
1 | 0.222 | −0.074 | −0.109 | 0.044 | ||||||||||

_{50th} |
1 | −0.096 | −0.111 | 0.159 | |||||||||||

_{stdv} |
1 | −0.225 | − |
0.210 | |||||||||||

_{stdv} |
1 | −0.196 | |||||||||||||

_{max} |
1 | −0.185 | |||||||||||||

_{cv} |
1 |

Best predictive models of LAI using lidar metrics only and GeoSAR metrics only, ^{2}_{adj’}, CV-RMSE, SSCC, VIF, and CI are the adjusted coefficient of determination, the RMSE from the cross validation analysis, the squared semipartial correlation coefficient from partial sum of squares, the variance inflation factor and the condition index, respectively. For a description of the variable names refer to

^{2} |
^{2}_{adj’} |
|||||||||
---|---|---|---|---|---|---|---|---|---|---|

2 | 0.58 | 0.57 | 0.52 | 0.53 | Intercept | 3.363 | ---- | ---- | ---- | |

LPI | −6.602 | 0.17 | 1.43 | 1.28 | ||||||

All_{10th} |
0.173 | 0.09 | 1.43 | 1.94 | ||||||

4 | 0.69 | 0.67 | 0.46 | 0.48 | Intercept | 3.405 | ---- | ---- | ---- | |

LPI | −7.480 | 0.20 | 1.58 | 1.24 | ||||||

All_{10th} |
0.134 | 0.05 | 1.50 | 1.28 | ||||||

d_{10} |
−12.498 | 0.06 | 1.06 | 1.56 | ||||||

Cd-3 | −15.113 | 0.06 | 1.14 | 2.16 | ||||||

4 | 0.52 | 0.49 | 0.56 | 0.58 | Intercept | 3.407 | ---- | ---- | ---- | |

X_{cv} |
−0.032 | 0.10 | 1.37 | 1.08 | ||||||

X_{50th} |
0.104 | 0.13 | 1.49 | 1.20 | ||||||

Xmag_{stdv} |
16.887 | 0.04 | 1.37 | 1.38 | ||||||

sn01xl_{cv} |
−0.002 | 0.05 | 1.06 | 2.00 |

Best predictive models of LAI using lidar metrics (including crown density slices) and GeoSAR metrics, ^{2}_{adj’}, CV-RMSE, SSCC, VIF, and CI are the adjusted coefficient of determination, the RMSE from the cross validation analysis, the squared semipartial correlation coefficient from partial sum of squares, the variance inflation factor and the condition index, respectively. All variables in the models were highly significant at a

^{2} |
^{2}_{adj’} |
||||||||
---|---|---|---|---|---|---|---|---|---|

0.66 | 0.65 | 0.47 | 0.47 | Intercept | 3.439 | ---- | ---- | ---- | |

All_{50th} |
−0.153 | 0.29 | 1.43 | 1.27 | |||||

X_{50th} |
0.229 | 0.65 | 1.43 | 1.88 | |||||

0.71 | 0.69 | 0.44 | 0.45 | Intercept | 3.393 | ---- | ---- | ---- | |

LPI | −3.732 | 0.04 | 1.80 | 1.27 | |||||

All_{50th} |
−0.120 | 0.14 | 1.88 | 1.43 | |||||

X_{50th} |
0.176 | 0.21 | 2.57 | 2.97 | |||||

0.73 | 0.71 | 0.42 | 0.44 | Intercept | 3.391 | ---- | ---- | ---- | |

LPI | −3.044 | 0.03 | 1.91 | 1.20 | |||||

All_{50th} |
−0.147 | 0.16 | 2.39 | 1.33 | |||||

d_{2} |
−3.027 | 0.03 | 1.28 | 1.58 | |||||

X_{50th} |
0.201 | 0.24 | 3.00 | 3.34 | |||||

0.76 | 0.74 | 0.40 | 0.42 | Intercept | 3.401 | ---- | ---- | ---- | |

LPI | −4.253 | 0.05 | 2.19 | 1.11 | |||||

All_{50th} |
−0.148 | 0.16 | 2.39 | 1.20 | |||||

d_{2} |
−3.996 | 0.04 | 1.39 | 1.46 | |||||

X_{50th} |
0.183 | 0.18 | 3.20 | 2.00 | |||||

Cd-3 | −11.703 | 0.03 | 1.36 | 3.41 | |||||

0.77 | 0.75 | 0.40 | 0.42 | Intercept | 3.475 | ---- | ---- | ---- | |

LPI | −4.246 | 0.05 | 2.13 | 1.19 | |||||

All_{50th} |
−0.185 | 0.20 | 3.00 | 1.33 | |||||

d_{2} |
−4.979 | 0.05 | 1.65 | 1.41 | |||||

X_{50th} |
0.208 | 0.24 | 3.22 | 2.31 | |||||

Cd-3_{stdv} |
−14.977 | 0.02 | 1.34 | 2.98 | |||||

Cd-1 | −7.805 | 0.04 | 2.07 | 3.92 |

Best predictive models of LAI using lidar metrics (excluding crown density slices) and GeoSAR metrics, ^{2}_{adj’}, CV-RMSE, SSCC, VIF, and CI are the adjusted coefficient of determination, the RMSE from the cross validation analysis, the squared semipartial correlation coefficient from partial sum of squares, the variance inflation factor and the condition index, respectively. All variables in the models were highly significant at a

^{2} |
^{2}_{adj’} |
||||||||
---|---|---|---|---|---|---|---|---|---|

0.74 | 0.72 | 0.42 | 0.44 | Intercept | 3.442 | ---- | ---- | ---- | |

All_{50th} |
−0.180 | 0.34 | 1.72 | 1.16 | |||||

d_{2} |
−4.187 | 0.05 | 1.23 | 1.38 | |||||

X_{50th} |
0.247 | 0.68 | 1.59 | 1.47 | |||||

Pmag_{stdv} |
16.079 | 0.04 | 7.63 | 2.47 | |||||

Pmag_{max} |
−2.731 | 0.04 | 7.61 | 5.50 | |||||

0.77 | 0.74 | 0.40 | 0.42 | Intercept | 3.406 | ---- | ---- | ---- | |

LPI | −3.110 | 0.03 | 2.00 | 1.17 | |||||

All_{50th} |
−0.147 | 0.16 | 2.45 | 1.31 | |||||

d_{2} |
−3.455 | 0.03 | 1.30 | 1.45 | |||||

X_{50th} |
0.199 | 0.23 | 3.04 | 1.75 | |||||

Pmag_{stdv} |
16.643 | 0.04 | 7.64 | 3.71 | |||||

Pmag_{max} |
−2.632 | 0.04 | 7.63 | 0.07 |