# A Multi-Year Study on Rice Morphological Parameter Estimation with X-Band Pulsar Data
## 4 Results and Discussion  
In this section, we present the stochastic inversion results of the same PCE\({}_{\text{EM}}\) metamodel for the estimation of stalk height, leaf length and leaf width parameters from X-band co-polar SAR data on a dataset spanned over three cultivation periods. For the analysis, the noise in the TerraSAR-X data was reduced using 13 \(\times\) 13 boxcar smoothing windows, resulting in 33 m \(\times\) 25 m spatial resolution. The estimation accuracies of the chosen parameters are evaluated based on their correlation against the ground measured values. The results are reported with their coefficient of determination (R\({}^{2}\)) and the root-mean-square error (RMSE) values. Table 1 provides the input parameters for the PCE\({}_{\text{EM}}\) metamodel evolutions that were assumed constant. The details of the EM model, its metamodel, their simulation accuracies and growth phase based global sensitivity analysis results of the PCE\({}_{\text{EM}}\) metamodel are provided in [12]. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Central frequency & 9.65 GHz \\ Dielectric constant (\(\epsilon_{g,l}\)) & 25 + 8 j \\ Dielectric constant (\(\epsilon_{g}\)) & 70 + 20 j \\ Average incidence angle (\(\theta\)) & 31\({}^{\circ}\) \\ Distance to target & 514 km \\ Illuminated area x-size & 2.58 m \\ Illuminated area y-size & 1.79 m \\ Number of MC iterations & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input parameters that are assumed constant during the EM model and PCE\({}_{\text{EM}}\) metamodel simulations. Figure 4: The ground and Synthetic Aperture Radar (SAR) data collection dates for the cultivation period between 2013 and 2015. On the right side, the VV channel PolSAR intensity image is also provided from the 30 June 2013. In the image, rice fields can be detected with their higher backscattering intensities. The chosen EM model and the proposed stochastic inversion approach consider the simplified plant morphology. As observed in Figure 3, the evolution of chosen morphological parameters are related to each other. In the proposed method these morphology based relations provide the base of the optimization constraints. As the stochastic inversion algorithm provides multi-dimensional parameter distributions, the mean values of the estimations are used for the calculation of R\({}^{2}\) and RMSE values. The stochastic inversion results for stalk height, leaf length, and leaf width parameters are presented in Figure 5 and Table 2. The R\({}^{2}\) and RMSE were calculated against the estimated biophysical parameters are given for the cultivation periods from 2013 to 2015. The accuracy analyses were conducted using a total number of 93 different \(\sigma^{o}\) values (32 from 2013, 25 from 2014, and 36 from 2015) measured from different fields having different morphologies, agricultural practices and environmental conditions. The global sensitivity analysis of the PCE\({}_{\text{EM}}\) metamodel was previously discussed in [12]. The analysis results emphasize the importance of stalk height, leaf length and structural density parameters (number of plant components in a unit area) throughout the growth cycle. The following deductions can be made from the stochastic inversion results. **Stalk Height** estimations had the highest accuracy (R\({}^{2}\)\(\geq\) 0.86) considering the entire dataset of three cultivation periods. As presented in Figure 5, the stalk height estimation results are slightly over-estimated for rice canopies shorter than 0.6 m and under-estimated for the taller canopies. The performance of the algorithm for the 2015 dataset was calculated to be lower compared to the other years with an RMSE value of 13.5 cm. This situation can be related to the variance of the \(\sigma^{o}\) values and the PCE\({}_{\text{EM}}\) metamodel simulations for the corresponding morphology parameter ranges in the parameter space.