**3. Results**

### **3.1 Models run using fixed pixel windows to extract the radiometric information**

Table 3 shows the correlation coefficients tendency of the original bands and some of the variables derived from them correlated to FRB in the first nine groups delimited using the CV. As expected, higher correlations were obtained with increasing spectral homogeneity

Using Remote Sensing to Estimate a Renewable Resource: Forest Residual Biomass 309

exponential –exp- and inverse –inv-) (Hair et al., 1998). Table 4 shows linear regression models performed with each one of the five random divisions of its sample. All of them include only one variable, which is always related to water content in vegetation. The lack of a second variable in these models is due to the high degree of auto-correlations between the spectral variables. This avoids violation of one of the principles of multiple linear regression models. Even so, the R2 values achieved were higher than 0.7. Consequently, they are suitable for FRB estimation in our study area. The results obtained from validation using 20% of the sample showed that the model run with MID57 (TM5+TM7) is the most suitable, because the RMSEr was only 26.67%, significantly lower than the others. As a result, it was selected to obtain FRB cartography with the 1994 Landsat image, using the pine forest areas

*<sup>a</sup> β0 β1*

N1 ln\_MID57 0.711 18.879 -4.663 4.843 26.67 N2 ln\_TM5 0.713 17.933 -5.073 4.591 43.38 N3 ln\_TM5 0.750 17.900 -5.053 4.767 51.91 N4 ln\_TM7 0.735 12.603 -3.906 6.144 42.92 N5 ln\_TM5 0.750 18.253 -5.204 4.792 34.93

Fig. 6. The regression model selected using fixed pixel windows and the FRB map produced

**3.2 Models completed using visual analysis to extract the radiometric information**  Correlation analysis completed using homogeneous areas derived from visual analysis showed that spectral variables related to wetness yielded the highest Pearson coefficients. Among them, TM5, TM7, TC3, MSI and MID57 were identified as the best predictor variables, with an R > 0.68. In addition, vegetation indices were again the second group of variables that showed high correlation levels, with NDVI showing the strongest correlation

Table 4. Linear regression models obtained from 3 x 3 pixel windows

*RMSE (ton/ha)*  *RMSEr (%)* 

in the Aragon 1:50,000 cartography as a mask (Figure 6).

**Model Variable** *R2*

applying it

and a decreasing number of plots. All of the groups showed significant correlations, with the majority of the considered variables yielding p-values of generally p < 0.05, with the one exception being the first CV group, as this group contained only three plots. In all groups, the highest coefficients of correlation were obtained for variables related to wetness information (TM band 5 –TM5-, TM band 7 –TM7-, the third principal component -PC3-, the third tasseled cap component -TC3-, the moisture stress index –MSI-, and the sum of TM5 and TM7 -MID57-), reaching similar coefficients than the Normalized Difference Vegetation Index (NDVI). The coefficients of these variables increased from values of 0.450–0.460 in the group of percentile 10 to more than 0.850 in the group of percentile 3 with all results being statistically significant.


Table 3. Pearson's coefficient of correlation (*R*) between spectral variables and plots at the level of 3 x 3 pixel windows (\* correlation is significant at the 0.05 level); TM, Thematic Mapper; PC, principal component analysis; TC, tasseled cap transform; NDVI, normalized difference vegetation index; SAVI, soil adjusted vegetation index; MSI, moisture stress index; MID57, sum of middle infrared wavelengths

These results show that the degree of spectral heterogeneity determines the feasibility of building accurate predictive models. Thus, if the groups with more plots are used, the models will have low prediction capacity. By contrast, if the groups with lower numbers of plots are used, the models will have higher predictive capacity, but, in turn, the models will be biased to the sample, being not representative of all of the forests of Teruel Province. Therefore, we selected the CV4 group because, among the groups characterized by an elevated homogeneity of plots (allowing execution of models with high R2), it is the one with the most number of plots (68). Scatter plots comparing FRB and the spectral variables clearly reveal nonlinear relationships. As a result, the most suitable standard transformation was applied to the independent and dependent variables in order to guarantee the linearity principle in the multiple linear regression model (logarithmic –ln-, square root –sq-,

and a decreasing number of plots. All of the groups showed significant correlations, with the majority of the considered variables yielding p-values of generally p < 0.05, with the one exception being the first CV group, as this group contained only three plots. In all groups, the highest coefficients of correlation were obtained for variables related to wetness information (TM band 5 –TM5-, TM band 7 –TM7-, the third principal component -PC3-, the third tasseled cap component -TC3-, the moisture stress index –MSI-, and the sum of TM5 and TM7 -MID57-), reaching similar coefficients than the Normalized Difference Vegetation Index (NDVI). The coefficients of these variables increased from values of 0.450–0.460 in the group of percentile 10 to more than 0.850 in the group of percentile 3 with all results being

 **CV10 CV9 CV8 CV7 CV6 CV5 CV4 CV3 CV2**  Nº plots 482 381 285 208 149 111 68 36 14 TM1 -0.435\* -0.493\* -0.500\* -0.529\* -0.550\* -0.513\* -0.542\* -0.708\* -0.647\* TM2 -0.409\* -0.468\* -0.470\* -0.484\* -0.499\* -0.454\* -0.495\* -0.713\* -0.638\* TM3 -0.413\* -0.474\* -0.477\* -0.492\* -0.512\* -0.464\* -0.512\* -0.734\* -0.673\* TM4 -0.199\* -0.257\* -0.232\* -0.189\* -0.163\* -0.110 -0.213 -0.267 -0.573\* TM5 -0.451\* -0.524\* -0.521\* -0.552\* -0.576\* -0.552\* -0.641\* -0.793\* -0.791\* TM7 -0.452\* -0.521\* -0.523\* -0.562\* -0.603\* -0.571\* -0.639\* -0.788\* -0.780\* PC1 -0.429\* -0.498\* -0.493\* -0.509\* -0.528\* -0.489\* -0.560\* -0.737\* -0.743\* PC2 -0.032 0.012 -0.037 -0.087 -0.153 -0.194\* -0.115 -0.213 0.410 PC3 0.421\* 0.474\* 0.508\* 0.590\* 0.656\* 0.663\* 0.754\* 0.869\* 0.853\* TC1 -0.414\* -0.482\* -0.475\* -0.483\* -0.493\* -0.451\* -0.521\* -0.707\* -0.721\* TC2 0.310\* 0.334\* 0.371\* 0.436\* 0.494\* 0.506\* 0.546\* 0.664\* 0.425 TC3 0.453\* 0.525\* 0.541\* 0.603\* 0.654\* 0.645\* 0.750\* 0.852\* 0.852\* NDVI 0.457\* 0.510\* 0.525\* 0.587\* 0.634\* 0.605\* 0.684\* 0.807\* 0.737\* SAVI 0.455\* 0.507\* 0.523\* 0.585\* 0.632\* 0.603\* 0.682\* 0.805\* 0.735\* MSI -0.458\* -0.518\* -0.540\* -0.618\* -0.669\* -0.674\* -0.772\* -0.883\* -0.864\* MID57 -0.454\* -0.525\* -0.525\* -0.558\* -0.590\* -0.562\* -0.641\* -0.792\* -0.787\* Table 3. Pearson's coefficient of correlation (*R*) between spectral variables and plots at the level of 3 x 3 pixel windows (\* correlation is significant at the 0.05 level); TM, Thematic Mapper; PC, principal component analysis; TC, tasseled cap transform; NDVI, normalized difference vegetation index; SAVI, soil adjusted vegetation index; MSI, moisture stress

These results show that the degree of spectral heterogeneity determines the feasibility of building accurate predictive models. Thus, if the groups with more plots are used, the models will have low prediction capacity. By contrast, if the groups with lower numbers of plots are used, the models will have higher predictive capacity, but, in turn, the models will be biased to the sample, being not representative of all of the forests of Teruel Province. Therefore, we selected the CV4 group because, among the groups characterized by an elevated homogeneity of plots (allowing execution of models with high R2), it is the one with the most number of plots (68). Scatter plots comparing FRB and the spectral variables clearly reveal nonlinear relationships. As a result, the most suitable standard transformation was applied to the independent and dependent variables in order to guarantee the linearity principle in the multiple linear regression model (logarithmic –ln-, square root –sq-,

statistically significant.

index; MID57, sum of middle infrared wavelengths

exponential –exp- and inverse –inv-) (Hair et al., 1998). Table 4 shows linear regression models performed with each one of the five random divisions of its sample. All of them include only one variable, which is always related to water content in vegetation. The lack of a second variable in these models is due to the high degree of auto-correlations between the spectral variables. This avoids violation of one of the principles of multiple linear regression models. Even so, the R2 values achieved were higher than 0.7. Consequently, they are suitable for FRB estimation in our study area. The results obtained from validation using 20% of the sample showed that the model run with MID57 (TM5+TM7) is the most suitable, because the RMSEr was only 26.67%, significantly lower than the others. As a result, it was selected to obtain FRB cartography with the 1994 Landsat image, using the pine forest areas in the Aragon 1:50,000 cartography as a mask (Figure 6).


Table 4. Linear regression models obtained from 3 x 3 pixel windows

Fig. 6. The regression model selected using fixed pixel windows and the FRB map produced applying it
