*3.3. Soil Fertility*

The RF model with 1000 decision trees and seven features was trained to predict soil fertility at the first step. The ranking of attribute importance in decreasing order was H, Slope, Aspect, Cv, Ch, TWI, second brightness index (BI2), color index (CI), HV, HH, VV, and VH. It was revealed that topographic and soil indices contributed more than SAR backscatters. By dividing into three levels against measured

values, the RF-based soil fertility displayed zonal distribution (Figure 8a). The small and large values were mixed in distribution. The RF model overestimated small values while underestimating large values in comparison to measured soil fertility (Table 2). With range, nugget, and sill values of 14.5 km, 48.6, and 230.5, respectively, semivariogram in OK interpolation was modeled as an exponential type and used to predict soil fertility residuals from RF at the second step. The small value of basal effect (nugget/sill = 0.21) showed a strong autocorrelation of residuals. It was suggested that soil fertility prediction be overestimated by RF in the high-altitude area (Figure 8b). Final predicted soil fertility by RFK with more equal area of each level than RF prediction, which means closer to the measured soil fertility, was shown in Figure 8c. Soil fertility decreased as altitude increased, which agreed with vertical zonal patterns affected by the volcanic eruption hundreds of years ago.

**Figure 8.** Soil fertility in the CMNNR. Soil fertility predicted by random forest was shown in (**a**), and its residuals interpolated by ordinary kriging was (**b**). Final map of soil fertility was (**c**).

#### *3.4. Assessment of Modeling Accuracy and Forest Condition*

The spatial modeling accuracy of five forest parameters was estimated by independent data (n = 601). Canopy closure was modeled with the greatest accuracy among the five parameters, while modeling stand density performed the worst with the least accuracy (Table 5). With large values of *r* and *R*<sup>2</sup> (*r* ≥ 0.75 and *R*<sup>2</sup> ≥ 0.6), it was revealed that all models explained spatial dynamics and characteristics of parameters to a good extent (Figure 9). The modeled parameters were credible (*r* ≥ 0.75) for application in forest condition assessment.

**Table 5.** Accuracy assessment of forest parameter modeling based on independent validation data.


**Figure 9.** Scatter plots of predicted versus ground measured parameters from validation data including canopy closure (**a**), stand density (**b**), stand volume (**c**), forest age (**d**), and soil fertility (**e**). As for forest age, one to five represented young to over-mature.

According to PCA of measured parameters, two components were acquired and shown as Table 6. Forest age contributed the most among the five parameters with a weight of 0.23, followed by stand volume and canopy closure. Stand density had the weakest influence with a weight of 0.12. The normalized parameters scores were shown in Figure 10a–e. The largest score in canopy closure was distributed homogeneously, with almost all above 60. However, the score of soil fertility showed the strongest spatial variations, followed by that of stand density. Weighted by five parameters, forest condition score was mapped as Figure 10f. The forest of the study area in 2017 had major scores were between 50 to 70 and coefficient of variation (CV) as 14.79% (Figure 10g).


**Table 6.** Component matrix and weights of five parameters.

**Figure 10.** Forest parameters and condition in the CMNNR. Forest parameters included canopy closure (**a**), stand density (**b**), stand volume (**c**), forest age (**d**) and soil fertility (**e**). Distribution of condition was in (**f**). Forest condition of different areas was summarized in (**g**).
