# Combined Use of Airborne Lidar and DBInSAR Data to Estimate LAI in Temperate Mixed Forests

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## Abstract

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^{2}to 0.77 with a CV-RMSE of 0.42. This study indicates the clear potential for X-band backscatter and interferometric height (both now available from spaceborne sensors), when combined with small-footprint lidar data, to improve LAI estimation in temperate mixed forests.

## 1. Introduction

^{2}’s between 0.37 and 0.93 related to a number of indices and lidar metrics. For a coniferous and mixed beech forest in Italy, the laser penetration index (LPI, taking into account the transmission of the laser beams through the canopy, as the proportion of laser pulses that hit the ground to the total number of pulses) was created explaining 89% of the variation of LAI [7]. Later, Kwak et al. [8] using the LPI and an interception index (LII) could explain 86% of the variation in a South Korean mixed forest. In Japan, using the ground fraction of returns, Sasaki et al. [9] reported an adjusted R

^{2}of 0.80 for an evergreen and broad-leaved forest. Solberg et al. [10] reported correlations with laser penetration from 0.37 to 0.93 (depending on plot size), in a mixed forest in Norway. Hopkinson and Chasmer [11] evaluated coniferous and mixed forests in Canada, and found R

^{2}’s ranging from 0.58 to 0.78, when using either lidar returns ratios or intensity of returns ratios. In United States, Zhao and Popescu [12] found an R

^{2}of 0.84 in a mixed hardwoods and coniferous (including plantations) from Texas, and Richardson et al. [13] reported R

^{2}values from 0.49 to 0.66 for a Pacific Northwest mixed forest. Other efforts to estimate LAI with lidar, using different approaches than LPI and in either coniferous or hardwood forests only, have shown similar promising results [14–19]. In addition, none of these prior studies have reported a maximum LAI or saturation problem using lidar.

^{2}of 0.78 by using a simulator that could be used for understanding how vegetation changes may affect the InSAR data. Other researchers have found saturation problems for the C-band (radar band that operates at a wavelength of 4–8 cm) backscatter with high values of LAI in tundra ecosystems and plantation forests [28,29]. Manninen et al. [30] used a C-band backscatter ratio from ENVISAT (ENVIroment SATellite)/ASAR (Advanced Synthetic Aperture Radar) in a mixed forest obtaining an RMSE of 0.27.

## 2. Methods

#### 2.1. Study Site

^{2}of size.

#### 2.2. Field Data Collection and Analysis

#### 2.2.1. Leaf Area Measured with an Optical Sensor

#### 2.2.2. Lidar Data

#### 2.2.3. GeoSAR Data

_{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 Table 1):

- 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.

#### 2.2.4. Statistical Analysis

- High coefficient of determination (R
^{2}) value. - Low residual mean square (RMSE).
- Similarity between the adjusted coefficients of determination R
^{2}_{adj’}and R^{2}values. The R^{2}_{adj’}is a rescaling of R^{2}by degrees of freedom, hence involves the ratio of mean squares instead of sum of squares. - Mallows’ C
_{p}statistic values [41]. When the model is correct, the C_{p}is close to the number of variables in the model. - Low values from two information criteria, the [42] Information Criterion (AIC) and [43] Bayesian Criterion (SBC). The AIC is known for its tendency to select larger subset sizes than the true model; hence the SBC was used for comparison, since it penalizes models with larger number of explanatory variables more heavily than AIC.

_{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 (p-value < 0.05). This p-value was used to evaluate if the variables included in the model were statistically significant as well. The squared semipartial correlation coefficients (SSCC) were calculated using partial sum of squares to determine the contribution from each variable to the models, while controlling the effects of other independent variables within the model. These coefficients represent the proportion of the variance of the dependent variable associated uniquely with the independent variable.

## 3. Results

#### 3.1. Summary Statistics from Ground Measurements and Lidar Metrics

^{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 (Table 3).

_{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 [38] and as curvilinear (as the logarithmic transformation of LPI) [48]. In this research, we evaluated both relationships as variables in the models. The Pearson correlation values were similar, −0.689 for the curvilinear model vs. −0.698 for the linear approach. Also, the results from the subset analyses showed consistently similar or higher R

^{2}’s values when using the linear relationship than when using the logarithmic transformation of LPI. This is probably due to a combination of factors, such as ecosystem type and range of LAI values. As a result, the models reported include the variable from the linear relationship only, which not only performed similarly to the curvilinear, but also makes the models easier to use and interpret.

^{2}values up to 0.69 with 4 variables in the model. Adding more variables increased the R

^{2}and resulted in no collinearity problems. However, there was always at least one variable not contributing significantly to the model. Hence, only models with 2 and 4-variables were reported (Table 6). Common variables in these models were LPI and All

_{10th}, the increase in R

^{2}(from 0.58 to 0.69) was given by the d10 and Cd-3 metrics. The largest contribution in both models was from the LPI (0.174 and 0.202), and in the 4-variable model the other three variables (All

_{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 (Figure 5). The results from the best subset analyses for GeoSAR metrics showed that although the R

^{2}values increased when adding more variables to the model, the R

^{2}

_{adj’}did not, therefore only a 4-variable model with an R

^{2}of 0.52 is shown in Table 6. The variable that contributed the most was X

_{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.

#### 3.2. Variable Selection and Modeling

^{2}values ranged from 0.66 from a 2-variable model to 0.77 from a 6-variable model. The All

_{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 R

^{2}and R

^{2}

_{adj’}increased and the RMSE decreased with an extra variable, but the CV-RMSE stayed the same.

^{2}values between these two is only 0.04, but the observations from the 6-variable model are distributed closer to the 1:1 line, suggesting a better fit.

^{2}values were lower (0.1 lower) than the R

^{2}values observed when using the 61 plots (Figure 8), however, this reduction of the R

^{2}values can be attributed to the reduced number of plots representing the low levels of the LAI range. In addition, the fact that the best models included the exact same variables than the models from the 61 plots, and that the reduction of the R

^{2}values is only 0.1 confirms that such plots are not influential enough to drive the relationship in the models. Therefore, since the exclusion of these three plots did not affect the relationship of measured LAI with the lidar and GeoSAR metrics, most of the results reported in this research used the dataset with 61 plots.

^{2}and RMSE values comparable to the models in Table 7. The additional metrics from GeoSAR were Pmag

_{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).

## 4. Discussion

^{2}values ranging from 0.8 to 0.9, using either very few plots (between 10 to 18) or small plot sizes (400 m

^{2}to 500 m

^{2}) [8,9,12,38]. The results reported in this research, using 61 plots of 1,257 m

^{2}size, reveal an R

^{2}of 0.69 (CV-RMSE = 0.48) for lidar only models, and an increased R

^{2}value of 0.77 (CV-RMSE = 0.42) when using lidar and GeoSAR data together.

_{10}[39], defined as the proportion of returns found at the top of the canopy with respect to the total number of returns from the vegetation, was included in the lidar metric models only. The top of the canopy is directly related to tree crowns, and hence LAI. Almost opposite to d

_{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.

_{10}, Cd-3, and All

_{10th}were together in the 4-variable model for lidar metrics only.

_{0}layers contributed significantly to the model when only GeoSAR data were used.

## 5. Conclusions

^{2}values were 0.58 (CV-RMSE=0.53) and 0.69 (CV-RMSE=0.48) for two and four lidar metrics in the model, respectively. Our evaluation showed that the sole use of dual-band synthetic aperture radar to estimate LAI is not as promising as the sole use of lidar data, since the best model had an R

^{2}of 0.52 (CV-RMSE=0.58) by including four metrics in the model. However, the evaluation of the two technologies together showed an important synergistic gain in the explanation of LAI variability, the R

^{2}values increased up to 0.77 with a CV-RMSE of 0.42. The most important metric in the combined model was the 50th percentile of the X-band interferometric height from DBInSAR The set of plots used in this research, comprised a broad range of stand ages (10 to 164 year old), forest types (21 plots of hardwoods, 36 plots of pure pine, and 4 plots of pine-hardwood), and measured LAI values (1.3 to 4.9). Considering this variability, the models developed represent a robust and accurate way to estimate LAI in the temperate mixed forests of Virginia.

## Acknowledgments

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**Figure 1.**Geographic distribution of plots in Appomattox Buckingham State Forest, Virginia, USA. Plots are displayed over a true color aerial photo.

**Figure 2.**(

**a**) Hypothetical representation of crown density slices derived from lidar Veg

_{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 (i.e., frequency, mean, standard deviation, and coefficient of variation) from the returns within each section were obtained. See Table 1 for variable names and how they were calculated. (

**b**) Crown density values for an upland hardwood plot.

**Figure 3.**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: (

**a**) Lidar returns (from ground and vegetation), and (

**b**) GeoSAR interferometric heights from bands X and P, after having been subtracted from a DEM created from the lidar data. Lidar ground returns are drawn for reference.

**Figure 4.**Vertical profiles for all plots: (

**a**) lidar vegetation returns (hag > 1 m) and (

**b**) heights generated from GeoSAR X-band (cells), after corrected by a DEM generated from lidar returns. The mode calculated from the lidar vegetation returns is circled on the y axis: (a) black, (b) gray, drawn as a reference for visual comparison.

**Figure 5.**Relationship between estimated LAI and measured LAI using the 4-variable model with lidar metrics only (n = 61). Plots were classified by forest type. Model (refer to Table 1 for variable names): LAI = 3.405 − 7.480(LPI) + 0.134(All

_{10th}) − 12.498(d

_{10}) − 15.113(Cd-3).

**Figure 6.**Relationship between estimated LAI and measured LAI using the 4-variable model with lidar and GeoSAR metrics (n = 61). Plots were classified by forest type. Model (refer to Table 1 for variable names): LAI = 3.391 − 3.044 (LPI) − 0.147 (All

_{50th}) − 3.027 (d

_{2}) + 0.201 (X

_{50th}).

**Figure 7.**Relationship between estimated LAI and measured LAI using the 6-variable model with lidar and GeoSAR metrics (n = 61). Plots were classified by forest type. Model (refer to Table 1 for variable names): LAI = 3.475 − 4.246 (LPI) − 0.185 (All

_{50th}) − 4.979 (d

_{2}) + 0.208 (X

_{50th}) − 14.977 (Cd-3

_{stdv}) − 7.805 (Cd-1).

**Figure 8.**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 (n = 58). Plots were classified by forest type. Model (refer to Table 1 for variable names): LAI = 3.658 − 8.933 (LPI) − 0.193 (All

_{50th}) − 4.800 (d

_{2}) + 0.211 (X

_{50th}) − 18.042 (Cd-3

_{stdv}) − 8.531 (Cd-1).

**Table 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 (i.e., proportions of returns), but were not used for model development.

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

Total number of ground returns | Gr_{total} |

All returns (return hag > 0.2 m) | All_{total}, All_{mean}, All_{stdv}, All_{cv}, All_{min}, All_{max}, All_{10th},…, All_{90th} |

Units are meters for all metrics except for All._{total} and All_{cv} | |

Vegetation returns (return hag > 1 m) | Veg_{total}, Veg_{mean}, Veg_{mode}, Veg_{stdv}, Veg_{cv}, Veg_{min}, Veg_{max}, Veg_{10th},...,Veg_{90th} |

Units are meters for all metrics except for Veg._{total} and Veg_{cv} | |

Pulses (number of lidar pulses per return class) | Gr_{returns}, All_{pulses} |

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

Intensity values (returns hag > 1 m) | I_{mean}, I_{min}, I_{max}, I_{stdv}, I_{cv} |

Units are watts for all metrics except for I._{cv} | |

Proportion of 1st, 2nd, 3rd and 4th returns | R_{i} = total number of i returns/ Veg_{total} |

Ri is a proportion of returns | i = 1st, 2nd, 3rd, and 4th |

Density | d_{i} = [x + (Veg_{max} − Veg_{min})/10]/Veg_{total} |

di is a proportion of returns | x = Veg_{min},1,..,10 |

i= 1, 2,…,10 | |

Crown density slices around Veg_{mode} | Cdi, Cdi_{mean}, Cdi_{stdv}, Cdi_{cv} |

Refer to Figure 2 for a graphic explanation of the slices | Cd_{i} = [number of returns in i / (All_{total} + Gr_{total})] |

Units are meters for Cdi._{mean}, Cdi_{stdv}, and Cdi_{cv} | (i=+1,+ 2,+3,+4,+5, 0, −1, −2, −3, −4, and −5) |

Cdi is a proportion of returns | i=+1,…,+ 5 at i meters above Veg_{mode} |

i = 0 at Veg_{mode} | |

i = −1,…, −5 at i meters below Veg_{mode} | |

GeoSAR Metrics | −Symbol |

Values from all cells per plot | i_{total}, i_{mean}, i_{stdv}, i_{cv}, i_{min}, i_{max}, i_{10th}, i_{20th}, i_{25th}, i_{40th}, i_{50th}, i_{60th}, i_{75th}, i_{80th}, _{and} i_{90th} |

Units are meters for all metrics (except for i_{total} and i_{cv}) obtained from the interferometric height bands. | i = P (P-band interferometric heights), X (X-band interferometric heights), X-P (X minus P), Pmag (P-band magnitude), Xmag (X-band magnitude), sn01xl (σ_{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) |

Units from magnitude bands are$\sqrt{\mathbf{watts}/{\mathbf{m}}^{\mathbf{2}}}$ | |

Units for σ_{0} are dB/m^{2} (dB=decibels) |

**Table 2.**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: n (number of observations or plots), ht (mean tree height), dbh (diameter at breast height), and Stdv (standard deviation).

Forest Type | n | Stand Age | ht (m) | dbh (cm) | LAI | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Stdv | Range | Mean | Stdv | Range | Mean | Stdv | Range | ||||||

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 |

Total | 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 |

**Table 3.**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 (n = 61). Column annotation: n (number of observations or plots), Gr

_{total}(total number of ground returns), All

_{total}(total number of all returns), Stdv (standard deviation), Max (maximum value), and LPI (Laser Penetration Index).

Forest Type | n | Gr_{total} (Mean) | All_{total} (Mean) | Return Heights (m) | Intensity (W) | LPI | ||||
---|---|---|---|---|---|---|---|---|---|---|

Mean | Stdv | Max | Mean | Stdv | Max | |||||

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 |

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

**Table 4.**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 (n = 61). Column annotation: X − P (X-band minus P-band), P

_{mag}(P-band magnitude values), X

_{mag}(X-band magnitude values), n (number of observations or plots), Stdv (standard deviation), and Max (maximum value).

Forest Type | n | P-Band Heights (m) | X-Band Heights (m) | (X − P) Heights (m) | Pmag (W/m^{2}) | Xmag (W/m^{2}) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Stdv | Max | Mean | Stdv | Max | Mean | Stdv | Max | Mean | Stdv | Max | Mean | Stdv | Max | ||

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 |

Total | 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 |

**Table 5.**Pearson correlation coefficients for the independent variables used to predict leaf area index (LAI) (n = 61). For a description of the variable names refer to Table 1. LAI was measured on the ground. Bold values were significant at α = 0.05.

LAI | LPI | All_{10th} | All_{50th} | d_{2} | d_{10} | Cd-1 | Cd-3 | Cd-3stdv | X_{cv} | X_{50th} | Xmag_{stdv} | Pmag_{stdv} | Pmag_{max} | sn01xl_{cv} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

LAI | 1 | −0.698 | 0.638 | −0.116 | 0.085 | −0.347 | 0.030 | −0.084 | 0.223 | −0.485 | 0.609 | 0.241 | −0.013 | −0.092 | −0.124 |

LPI | 1 | −0.546 | 0.063 | −0.054 | 0.160 | −0.237 | −0.242 | −0.262 | 0.693 | −0.520 | −0.065 | 0.181 | 0.187 | 0.071 | |

All_{10th} | 1 | 0.163 | −0.091 | −0.148 | 0.106 | −0.031 | 0.168 | −0.451 | 0.685 | 0.269 | 0.072 | 0.054 | −0.075 | ||

All_{50th} | 1 | −0.292 | 0.508 | −0.438 | −0.168 | 0.013 | 0.087 | 0.550 | 0.168 | −0.116 | −0.112 | 0.252 | |||

d_{2} | 1 | −0.083 | −0.286 | −0.290 | 0.085 | 0.050 | 0.086 | 0.331 | 0.078 | 0.031 | 0.105 | ||||

d_{10} | 1 | −0.242 | −0.181 | 0.199 | 0.039 | 0.080 | −0.041 | −0.190 | −0.146 | 0.286 | |||||

Cd-1 | 1 | 0.562 | −0.269 | −0.429 | −0.285 | −0.421 | 0.136 | 0.216 | −0.251 | ||||||

Cd-3 | 1 | −0.062 | −0.326 | −0.176 | −0.413 | 0.024 | 0.131 | −0.083 | |||||||

Cd-3_{stdv} | 1 | −0.127 | 0.316 | 0.176 | −0.408 | −0.430 | 0.105 | ||||||||

X_{cv} | 1 | −0.363 | 0.222 | −0.074 | −0.109 | 0.044 | |||||||||

X_{50th} | 1 | 0.345 | −0.096 | −0.111 | 0.159 | ||||||||||

Xmag_{stdv} | 1 | −0.225 | −0.358 | 0.210 | |||||||||||

Pmag_{stdv} | 1 | 0.931 | −0.196 | ||||||||||||

Pmag_{max} | 1 | −0.185 | |||||||||||||

sn01xl_{cv} | 1 |

**Table 6.**Best predictive models of LAI using lidar metrics only and GeoSAR metrics only, n = 61. The statistics R

^{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 Table 1. All variables in the models were highly significant at a p-value < 0.001.

Sensor | # var. | R^{2} | R^{2}_{adj’} | RMSE | CV-RMSE | Variable | Coefficient | SSCC | VIF | CI |
---|---|---|---|---|---|---|---|---|---|---|

Lidar | 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 | ||||||

GeoSAR | 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 |

**Table 7.**Best predictive models of LAI using lidar metrics (including crown density slices) and GeoSAR metrics, n = 61. The statistics R

^{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 p-value < 0.0001. For a description of the variable names refer to Table 1.

# var. | R^{2} | R^{2}_{adj’} | RMSE | CV-RMSE | Variable | Coefficient | SSCC | VIF | CI |
---|---|---|---|---|---|---|---|---|---|

2 | 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 | |||||

3 | 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 | |||||

4 | 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 | |||||

5 | 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 | |||||

6 | 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 |

**Table 8.**Best predictive models of LAI using lidar metrics (excluding crown density slices) and GeoSAR metrics, n = 61. The statistics R

^{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 p-value < 0.0001. For a description of the variable names refer to Table 1.

# var. | R^{2} | R^{2}_{adj’} | RMSE | CV-RMSE | Variable | Coefficient | SSCC | VIF | CI |
---|---|---|---|---|---|---|---|---|---|

5 | 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 | |||||

6 | 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 |

## Share and Cite

**MDPI and ACS Style**

Peduzzi, A.; Wynne, R.H.; Thomas, V.A.; Nelson, R.F.; Reis, J.J.; Sanford, M.
Combined Use of Airborne Lidar and DBInSAR Data to Estimate LAI in Temperate Mixed Forests. *Remote Sens.* **2012**, *4*, 1758-1780.
https://doi.org/10.3390/rs4061758

**AMA Style**

Peduzzi A, Wynne RH, Thomas VA, Nelson RF, Reis JJ, Sanford M.
Combined Use of Airborne Lidar and DBInSAR Data to Estimate LAI in Temperate Mixed Forests. *Remote Sensing*. 2012; 4(6):1758-1780.
https://doi.org/10.3390/rs4061758

**Chicago/Turabian Style**

Peduzzi, Alicia, Randolph H. Wynne, Valerie A. Thomas, Ross F. Nelson, James J. Reis, and Mark Sanford.
2012. "Combined Use of Airborne Lidar and DBInSAR Data to Estimate LAI in Temperate Mixed Forests" *Remote Sensing* 4, no. 6: 1758-1780.
https://doi.org/10.3390/rs4061758