## 4 Results
### Soil Moisture Index Estimation and Validation  
Soil moisture indices were calculated for each of the 15 observation sites, based on the Equation (4), using soil moisture time series measured and predicted from the linear mixed and fixed effects models, respectively. As an example, the temporal variation of soil moisture index derived from ground measurements, along with the daily accumulated precipitation and mean temperature over site 9 (Nanchang) are plotted in Figure 3. The daily mean temperature shows a similar pattern for the year 2015 and 2016, with the highest temperature observed between July and August and the lowest temperature between January and February. The precipitation increased significantly between April and June in both years. Moreover, due to the El Nino event, precipitation occurred frequently from the winter of 2015 to the spring of 2016. Calculated with soil moisture measurements at the depth of 0-10 cm, which represents the uppermost soil layer, the measured soil moisture indices are rather sensitive to precipitation and temperature. In response to the El Nino event and the lower evaporation rate during the non-growing season, the measured soil moisture indices over site 9 remained high from December 2015 to June 2016. In contrast, with the higher evaporation rate during the growing \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Temporal R\({}^{2}\)** & **Spatial R\({}^{2}\)** & **Overall R\({}^{2}\)** & **RMSE (\%)** & **MPE (\%)** \\ \hline Fixed & 0.558 & 0.671 & 0.219 & 6.88 & 5.14 \\ Mixed (full) & 0.641 & 1 & 0.894 & 2.53 & 1.87 \\ Mixed (without \(s_{i}\)) & 0.613 & 0.052 & 0.171 & 7.16 & 5.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance statistics for three linear fixed and mixed effects models. Figure 2: Scatter plots of measured versus predicted soil moisture from (**a**) the linear fixed effects model; (**b**) the mixed effects model without site effect; and (**c**) the mixed effects model with site effect. The solid black line and dashed red line represent the regression line and 1:1 line, respectively. season and little precipitation, the measured soil moisture indices decreased dramatically from July to August in both years. Figure 4 shows the measured soil moisture index curve of each site (black solid lines). All of the curves vary remarkably with time, reflecting the strong temporal variability of surface soil moisture during the study period. On the other hand, the soil moisture index curves of different sites share a similar pattern, which is supposed to be related to the large scale atmospheric factors, such as precipitation and evapotranspiration. During the period from April 2015 to December 2016, the measured soil moisture index curves generally start with several irregular fluctuations and rise rapidly in November 2015, followed by a plateau till June 2016, and then drop sharply to the bottom in August or September 2016 and rise again gradually till the end of 2016. Unlike regular years with little precipitation during dry season from October to March, the winters of both years were rainy over the whole study area, leading to the relatively high soil moisture indices. In addition, the decreasing soil moisture indices in August of both years could be attributed to the constantly high temperature and low precipitation. The soil moisture index curves that were predicted by the linear fixed effects model (blue dash lines) and the LME model (red dash lines) are also presented in Figure 4. For each site, both of the predicted curves capture the major trends of the measured soil moisture index curve well, with that of the LME model fitting the measured curve better. The R\({}^{2}\) value of the LME model at each site ranges from 0.52 to 0.88, totally exceeding that of the fixed effects model, which ranges from 0.44 to 0.81. At most sites, the LME model largely improves the R\({}^{2}\) by reducing the bias between the measured and predicted soil moisture indices.