# Crop Growth Stage GPP-Driven Spectral Model for Evaluation of Cultivated Land Quality Using GA-BPNN
## 3 Results
### Model Comparison for CLQ Evaluation  
In this study, to reduce the calculation burden, variance inflation factor (VIF) was used to perform the analysis of collinearity of the GPPs among four growth stages given a year for developing the models of evaluating CLQ based on 420 sample points. The results in Table 3 indicate that there is collinearity among the GPPs in the four growth stages. Therefore, all data at the four growth stages were selected to construct spectral models. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Plot\#**} & \multirow{2}{*}{**Field Observations**} & \multicolumn{2}{c}{**30 m MODIS-GPPs**} & \multicolumn{2}{c}{**500 m MODIS-GPPs**} \\ \cline{3-6}  & & **Estimates** & **Absolute Error (\%)** & **Estimates** & **Absolute Error (\%)** \\ \hline  
Mean & 465.49 & 472.73 & 1.64 & 475.09 & 4.80 \\ Stdev & 91.77 & 91.00 & & 97.57 & \\ RMSE & & 7.43 & & 33.43 & \\ NRMSE & & 1.59 & & 7.18 & \\ (\%) & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the original 500 m spatial resolution MODIS-GPPs from the 289 th day in 2013 with their downscaled 30 m products by the Empirical Bayes Kriging (EBK) method based on the dry biomass field observations of 30 sample plots. In this study, three kinds of models including PLSR, SVR, and GA-BPNN were developed for comparing the evaluation accuracy of CLQ. For each of the years from 2011 to 2015, one PLSR model was obtained based on 294 training samples using CLQ as the response variable and GPPs at the four growth stages as the predictors. With the same training datasets for the years, the corresponding SVR and GA-BPNN models were constructed. The prediction accuracies of CLQ from all the models were assessed based on the values of RMSE, NRMSE and the coefficient of determination (R\({}^{2}\)) between the estimated and observed CLQ values [45] according to the training and validation samples. The obtained 2011-2015 PLSR evaluation models are:  
\[ \begin{split}&\hat{CLQ}=2128.457+0.008\times\text{GPP}_{ \text{Tillering}/2011}+9.388\times\text{GPP}_{\text{Jointing}/2011}+14.073 \times\\ &\text{GPP}_{\text{Heading}/2011}-4.620\times\text{GPP}_{ \text{Maturity}/2011}\ \left(\text{R}^{2}=0.38,\text{P}<0.001\right)\end{split}  \tag{12}\]  
\[ \begin{split}&\hat{CLQ}=2562.905+0.238\times\text{GPP}_{ \text{Tillering}/2012}+0.428\times\text{GPP}_{\text{Jointing}/2012}+3.778 \times\\ &\text{GPP}_{\text{Heading}/2012}+5.437\times\text{GPP}_{ \text{Maturity}/2012}\ \left(\text{R}^{2}=0.39,\text{P}<0.001\right)\end{split}  \tag{13}\]  
\[ \begin{split}&\hat{CLQ}=2336.989+6.886\times\text{GPP}_{ \text{Tillering}/2013}+6.834\times\text{GPP}_{\text{Jointing}/2013}-0.401 \times\\ &\text{GPP}_{\text{Heading}/2013}+2.444\times\text{GPP}_{ \text{Maturity}/2013}\ \left(\text{R}^{2}=0.40,\text{P}<0.001\right)\end{split}  \tag{14}\]  
\[ \begin{split}&\hat{CLQ}=2451.9366+0.586\times\text{GPP}_{ \text{Tillering}/2014}+6.341\times\text{GPP}_{\text{Jointing}/2014}+0.516 \times\\ &\text{GPP}_{\text{Heading}/2014}+6.911\times\text{GPP}_{ \text{Maturity}/2014}\ \left(\text{R}^{2}=0.38,\text{P}<0.001\right)\end{split}  \tag{15}\]  
\[ \begin{split}&\hat{CLQ}=2328.035+3.458\times\text{GPP}_{ \text{Tillering}/2015}+3.791\times\text{GPP}_{\text{Jointing}/2015}+5.946 \times\\ &\text{GPP}_{\text{Heading}/2015}-4.830\times\text{GPP}_{ \text{Maturity}/2015}\ \left(\text{R}^{2}=0.35,\text{P}<0.001\right)\end{split}  \tag{16}\]  
For the development of SVR models, the support vector machine (SVM) was selected as epsilon-SVR, its loss function was set as 0.1, and the range of kernel parameter and penalty parameter was set as (\(2^{-8}\), \(2^{8}\)) [47]. Moreover, the obtained GA-BPNN models had a three-layer network and a hidden layer with 13 neuron nodes. A total of 1000 iterations was used with 10 maximum runs. Both learning rate and learning objective were 0.01. The mutation probability, crossover probability and population size were respectively 0.1, 0.3, and 10 [36].