# A Multi-Year Study on Rice Morphological Parameter Estimation with X-Band Pulsar Data
## 4 Results and Discussion
On the other hand, the estimation bias between the measured and estimated values shows an increasing spread with increasing stalk height. The variation in the bias can be interpreted by the presence of plants with varying physical structures and similar backscattering behaviors at later phases of the growth cycle. The RMSE values were calculated to be less than 13.5 cm, which are acceptable for the stalk height estimations calculat \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Stalk Height**} & \multicolumn{2}{c}{**Leaf Length**} & \multicolumn{2}{c}{**Leaf Width**} \\ \cline{2-7}  & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** \\ \hline
**2013** & 0.921 & 0.108 & 0.804 & 0.069 & 0.646 & 0.003 \\
**2014** & 0.891 & 0.092 & 0.831 & 0.048 & 0.628 & 0.002 \\
**2015** & 0.868 & 0.135 & 0.776 & 0.055 & 0.613 & 0.003 \\
**Complete** & 0.894 & 0.116 & 0.848 & 0.057 & 0.717 & 0.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy analysis of the stochastic inversion of PCE\({}_{\text{EM}}\) metamodel given with the calculated R\({}^{2}\) and root-mean-square error (RMSE) values for the years 2013, 2014, 2015 and the complete dataset. Figure 5: The measured values of stalk height, leaf length and leaf width parameters versus their estimations given in a correlation scatter plot for years 2013 to 2015 with a reference line. Symbols are colored with respect to the year: 2013 (\(\star\)), 2014 (\(\star\)) and 2015 (\(\star\)). **Leaf Length** estimation accuracy is calculated to be lower than the stalk height estimation accuracy for the dataset of three cultivation periods. As shown in Figure 5, the leaf lengths are mainly over-estimated when they are shorter than 50 cm and under-estimated when they become longer. The stochastic inversion results of the PCEEM metamodel shows highly accurate results (R\({}^{2}\geq\) 0.78 and RMSE \(\leq\) 7 cm) for the evaluations from the complete dataset. From three different years, the lowest accuracy was obtained from the data acquired during 2015, as it was observed for the stalk height. Regarding the estimation bias, it is noted that the errors tend to increase with increasing leaf length. Similar to the interpretation provided for stalk height estimations, the increasing error with increasing leaf length can be explained by the presence of higher variance in the parameter space at later growth phases. **Leaf Width** is morphologically related to the leaf length due to natural growth limitations. The accuracy analysis on leaf width estimations presented acceptable values with R\({}^{2}\) values higher than 0.61 and RMSE values lower than 3 mm. Similar to stalk height and leaf length parameters, the lowest accuracy was again obtained from the copolar SAR measurements of 2015. The estimation bias of the analysis is observed to vary between \(\pm\)5 mm for the complete growth cycles of three years. The stochastic inversion of the PCEEM metamodel provided successful estimations for stalk height and leaf length parameters for the cultivation periods of three years. However, from the chosen rice morphology parameters, leaf width estimations had lower accuracies with higher relative RMSE values. This situation is supported by the global sensitivity analysis results, which states the importance of stalk height and leaf length parameters on the PCEEM metamodel simulations, while mentions the lower effect of the leaf width [12]. The accuracy analysis exhibited in this study combines 93 different rice plant morphology and SAR measurements collected from the cultivation periods of 2013 to 2015. Concerning the presence of various environmental factors and agricultural practices, the results are considered to be representative for the wet-cultivated and broadcast seeded rice fields that are located in Ipsala (Turkey). Therefore, the results are encouraging for the development of new management practices, which can use the estimated morphology parameters to interpret the yield and the detailed growth stage.