**3. Results**

#### *3.1. Accuracy Assessment of WorldView-2 Classification*

Relatively high pairwise JMD values (Table 4) indicated very high spectral dissimilarity among the most of land cover classes. The overall accuracy of classification was 81.3% and the Cohen's Kappa coefficient was 0.790. Mature trees had strong spectral similarity with tree saplings, resulting in a high rate of commission errors (41.6%) for mature tree classification and high omission error (66.5%) for tree sapling classification. Similarly, spectral separability between shrublands and grasslands

was also relatively low, preventing us from distinguishing the two classes in subsequent analyses. Mature trees and tree saplings together occupied about 23.6% of the total burned area, while shrublands and grasslands occupied approximately 51.9% of the total burned area (Figure 3). Bare rock, where vegetation has difficulty establishing, accounted about 10.2% of the total burned area. The remaining 14.3% consisted of bare soil, water bodies, shadow areas and moss.

**Table 4.** Pairwise Jeffries–Matusita distance (JMD, values within brackets) and confusion matrix for evaluating intra-classes separability and classification accuracies respectively. The bold represents the number of verified samples.


**Figure 3.** Land cover mapping of the burned area (**a**) based on WorldView-2 imagery. Small windows (**b**–**<sup>e</sup>**) show zoomed views of land cover maps (**b**,**d**) compared to the RGB imageries (**<sup>c</sup>**,**<sup>e</sup>**) for two sites (black box for **b**,**c**, red box from **d**,**<sup>e</sup>**) respectively.

#### *3.2. Correlations between Remote Sensed Variables and LAI and TSA*

All Landsat-derived indices exhibited significant correlations with LAI and TSA (Table 5). In two Landsat cases, the EVI2 (R<sup>2</sup> = 0.427, RMSE = 0.348, Figure 4a) and NBR (R<sup>2</sup> = 0.489, RMSE = 0.331, Figure 4d) were found the most explanative Landsat-derived indices for LAI, while the NBR (R<sup>2</sup> = 0.499, RMSE = 0.953, Figure 4b) and NDMI (R2 = 0.478, RMSE = 0.983, Figure 4e) were the most explanative variables for TSA. Spectral indices derived from SWIR bands (e.g., NBR and NDMI) generally performed better than vegetation indices (e.g., NDVI, EVI, and SAVI). The PPCT variable of WorldView-2 (VHR) explained the highest proportions of variance for LAI (R<sup>2</sup> = 0.676, RMSE = 0.257, Figure 4c) and TSA (R<sup>2</sup> = 0.508, RMSE = 0.977, Figure 4f) among all variables, but image texture represented relatively weak correlations (Table 5).

**Table 5.** Coefficients of linear regression models for evaluating relationships between remotely sensed variables and leaf area index (LAI) and tree sapling abundance (TSA). Landsat-derived spectral index abbreviations see footnote of Table 2. PPCT—Pixel Percentage of Canopy Tree; Co\_Means—Means of Co-occurrence Texture; ASM—Angular Second Moment. RMSE—Root Mean Square Error.


**€**: Model fits using logarithmic transformation; †: Significance code: \*\* *p* < 0.01; \* *p* < 0.05.

The spatial distributions of LAI (Figure 5a) and TSA (Figure 5b) 14 years post-fire were mapped based on the correlation models with highest R<sup>2</sup> in Table 5. We found about 51.1% (~4098 ha) of the burned area exhibited high LAI recovery (greater than 1), which corresponded to approximately 10,790~74,380 sapling/ha TSA. About 14.6% (~1169 ha) of the burned area exhibited moderate LAI recovery (between 0.5 and 1) of 4770~10,680 sapling/ha, and approximately 2745 ha of the burned area exhibited recovered poor recovery (LAI < 0.5, and TSA < 4630 sapling/ha).

**Figure 4.** Scatter plots depict the best relationships (Table 4) between leaf area index (LAI) and two Landsat indices (**<sup>a</sup>**,**b**), and WroldView-2 case (**c**); and relationships between Tree sapling abundance (TSA) and two Landsat indices (**d**,**<sup>e</sup>**), and WroldView-2 case (**f**).

**Figure 5.** Two maps show spatial distribution of Leaf Area Index (LAI, **a**) and Tree Sapling Abundance (TSA, **b**) based on Pixel Percentage of Canopy Tree (PPCT) derived from WorldView-2 image.

#### *3.3. Relative Importance of Predictors to LAI Recovery*

Because WorldView-2 derived PPCT was the most predictive indicator for both LAI and TSA, and LAI and TSA are highly correlated with each other, the RF model produces the same results for both LAI and TSA. Thus we only represented the RF model results for LAI. The 50 RF models explained a maximum of 62.4% (Mean R<sup>2</sup> = 55.5%, SD = 3.0%, MSE = 0.382, N = 50) of the variation in estimated LAI. The coverage of understory vegetation and shadow pixels were the top-two most important predictor variables, decreasing MSE about 43.3% (SD = 4.6%) and 42.89% (SD = 3.8%) respectively when incorporated in RF models (Figure 6). The dNBR contributed about a 23.4% (SD = 2.9%) decrease

in MSE, while contributions of topography variables ranged from 9.6% to 16.7%, followed by Solar Radiation (SD = 3.7%), Topographic Position Index (TPI) (SD = 2.3%), TWI (SD = 3.9%) and Elevation (SD = 2.1%). The edge effect was found to be the least important factor, contributing about a 7.2% (SD = 3.2%) decrease in MSE.

**Figure 6.** Relative importance from 50 random forest models, measured as the normalized difference between the mean square errors (MSE) when permuting the out-of-bag portion of the data and the MSE when permuting given variable. Magnitude of decrease of in MSE indicates relative importance of predictor variable (see Table 3 for variable abbreviations).
