**4. Discussion**

#### *4.1. Understanding Forest Parameters with Remote Sensing Predictors*

Close relationships were found for canopy closure and stand density with LAI and FVC from Sentinel-2 (Figure 4). LAI explained more canopy closure ( *R*<sup>2</sup> = 0.81) than FVC ( *R*<sup>2</sup> = 0.52). However, the performances of LAI ( *R*<sup>2</sup> = 0.87) and FVC ( *R*<sup>2</sup> = 0.89) on modeling stand density were similar. The assessment by independent sample sites (Table 5 and Figure 9) showed that LAI and FVC revealed spatial variations of canopy closure and stand density (*r* ≥ 0.9 and *R*<sup>2</sup> ≥ 0.8). While RMSE values showed that stand density was estimated with the largest error among the five parameters (Table 5). This may have resulted from the saturation problems from Sentinel-2. It was indicated that biophysical products of Sentinel-2, especially LAI, had good abilities to delineate the spatial variation of simple horizontal structure, such as canopy closure and stand density, in the study area.

The backscatter from HV was more sensitive to stand volume than HH based on the WCM models (Figure 6) and the attribute importance in the RF model. This revealed that HV backscatter was more helpful than HH to model forest productivity, which was consistent with previous findings of aboveground biomass [110,111]. The extinction coe fficients modeled by WCM models in this study were much larger than previous studies in modeling aboveground biomass with backscatters and without mosaic [55,97]. This resulted in a relatively less accuracy of stand volume among five forest parameters.

The attribute importance in RF models demonstrated that topographic and spectral indices from L band InSAR and MSI contributed more than backscatters from L and C band SAR in modeling forest age and soil fertility. Additionally, backscatters from HV and VV had influenced more on forest parameter modeling than HH and VH, respectively. However, the ranking of predictor importance was di fferent between forest age and soil fertility. The L band InSAR predictors showed the absolute dominance in soil fertility modeling, followed by variables from MSI, L band SAR, and C band SAR. This was on account of the good penetrability of L band and sensitivity to vegetation (CI) and soil humidity (BI2) of indices from MSI. As for forest age modeling, HV backscatter was much more important than second-derivative topographic micro indices (Cv and Ch). Additionally, vegetation indices from near-infrared (Band 8 and 8A), red (Band 4), vegetation red edge (Band 7), and green band (Band 3) had a greater e ffect than the complex macro topographic index (TWI) on forest age modeling. Also, the backscatter from VV was much more significant than that from HH. It was denoted that forest age had a more complex relationship than soil fertility with SAR and MSI data, which contained multisource influences form basic vertical and horizontal forest parameters. Moreover, the multi-sensor modeling of soil fertility based on RF algorithms showed certain limits in predicting minimum and maximum values (Figure 8a) with strongly auto-correlated residuals (nugget/sill = 0.21). It was also revealed that soil fertility had the heterogeneity conveyed by backscatters and reflectance, and the spatial autocorrelation dependence on own attributes.

#### *4.2. Uncertainty of Spatial Modeling*

The uncertainty analysis is crucial for understanding the quality of remote sensing-based forest parameters. RMSE used in this study is the common statistic to characterize the uncertainty [112,113]. Overall, the uncertainty of forest parameter modeling was acceptable with all *r* values above 0.75 and RMSE below 35% based on the independent validation data (Table 5). The uncertainties were from three aspects in this study as field-measurements, predictor variables and modeling. In order to ge<sup>t</sup> representative sample sites, a total of 1803 plots covering forests in the study area were measured (Figure 1). To match the remote sensing data, the plot size was set as 30 m by 30 m. Then, open-access remote sensing data from four di fferent sources were selected to match the field campaign time. Predictor variables were derived from the monthly mosaic of filtered Sentinel-1 images. Limited by the cloud cover, only one cloud-free image from Sentinel-2 acquired on 25 September 2017 was used.

The forest parameters in this study were modeled with e fficient predictor variables from minimum data sources based on previous findings. Specifically, canopy closure, and stand density were modeled by Sentinel-2 and stand volume was modeled by L band SAR. It was accorded from previous studies that SAR data were sensitive to vertical structure and function while MSI were primary in horizontal canopy modeling [18,21]. L band SAR penetrated into the canopy and scatters back from leaves, branches, and stems [114]. Hence, L band SAR was used to model stand volume, and DSM from L band InSAR was chosen to extract topographic indices in this study, rather than SRTM DEM from C band as most researches used. Nevertheless, as complex parameters, forest age and soil fertility were modeled by multi-sensor data to reflect the information on basic structure and function.

The uncertainty of modeling was reduced by using e fficient algorithms combined with remote sensing predictors based on existing researches. First, the physically based models were considered to acquire the basic variables which were directly related to remote sensing data, such as LAI and FVC. Then, basic structure parameters such as canopy closure and stand density were modeled by parametric algorithms to show the explicit relationships with biophysical variables. The physically based model was also used to test the suitability of L band SAR for stand volume modeling. However, the function and comprehensive parameters had complex relationships with remote sensing-derived variables. Therefore, recognized nonparametric algorithms with grea<sup>t</sup> accuracy, such as RF and RFK, were selected to model stand volume, forest age, and soil fertility.

#### *4.3. Forest Condition from Structure and Function*

Forest parameters and condition showed variations along the elevation gradient (Figure 10). Among four vertical vegetation zones, the mixed coniferous and broad-leaved forest had the highest scores, followed by dark-coniferous spruce-fir and Ermans birch forest. While the northern slope area within dark-coniferous spruce-fir forest had large values of stand volume (Figure 7a). This was mainly due to taller and matured trees are distributed in this region [115]. The intensity of soil fauna activities, moisture, temperature, and plant diversity in lower altitudes were more favorable than those at higher elevations in the Changbai Mountain [72,116–119], so that forest parameters and conditions generally decreased with increasing altitude.

Forest conditions in the CMNNR showed spatial variations, which were assessed by the weighted structural and functional parameters (Figure 10). The forests with higher condition scores were located in the area with lager values of soil fertility. While low values of forest condition were mainly consistent with smaller scores of stand volume. It was demonstrated that function parameters were primary in assessment of forest conditions in the CMNNR. Among three functional zones, forests in the core area showed the largest variation and were vital for improving forest conditions.
