# Spatial Downscaling of Soil Moisture Based on Fusion Methods in Complex Terrains
## 4 Results and Analysis
### In Situ SM Fusion Results  
To improve the data quality, high-precision but sparse ground measures were incorporated into the downscaled results. The spatial distribution of in situ SM is shown in Figure 6a. In this experiment, the 1 km GABP-downscaled results were used as the calibration object (the HRSM). Thirty percent of the in situ data were randomly selected for verification, which were not involved in the fusion process. The RMSE and MAE were used as the verification scores. As Table 2 shows, the results of the in situ SM fusion were all better than those of the prefusion HRSM. The IDW interpolation had a smaller RMSE and MAE than the Kriging interpolation. For the same interpolation, the GDA was better than the GRA, with a smaller RMSE and MAE.  
In the following, the two datasets before fusion (HRSM and in situ SM) and the four fusion results, GDA_Kriging, GRA_Kriging, GDA_IDW and GRA_IDW, were compared using boxplots (Figure 7a) and PDFs (Figure 7b). The in situ data shown here only include those that had undergone spatiotemporal matching.The boxplots and PDFs show that the in situ data had the highest mean score. In terms of the dynamic range, the in situ data were the widest, the two IDW results were narrower, and the two Kriging results and HRSM were similar. The PDF curves for the two Kriging results resembled HRSM more closely. When using the same interpolation method, the GRA result was slightly higher than that of the GDA. In general, the Kriging method could better preserve the dynamic range and statistical characteristics of the HRSM during fusion.  
Although the result of the GDA was slightly better than that of the GRA, the following only compares GDA_Kring and GDA_IDW because the GDA was unable to compute the ratio (X/0). Figure 8 shows the daily average sequence curves for in situ SM, HRSM, GDA_Kriging, and GDA_IDW. As can be seen from Figure 8, relative to HRSM, the fusion data have a greater variation, and the change trend coincides with the in situ data, especially in summer. This indicates that the fusion results contain in situ information and tend toward the in situ information. This method can realize data fusion and correction at the same time and improve the dynamic ranges of spatial averages.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **HRSM** & **GDA\_IDW** & **GRA\_IDW** & **GDA\_Kriging** & **GRA\_Kriging** \\ \hline RMSE (m\({}^{3}\)/m\({}^{3}\)) & 0.0980 & 0.0944 & 0.0946 & 0.0950 & 0.0960 \\ MAE (m\({}^{3}\)/m\({}^{3}\)) & 0.0784 & 0.0757 & 0.0758 & 0.0761 & 0.0769 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Evaluation indices from the in situ SM evaluation set.  
To compare and analyze the spatial distribution of the data before and after fusion, the spatial distributions of the mean SMs for HRSM, GDA_Kriging, and GDA_IDW are shown in Figure 9. As shown in Figure 9, the Kriging method retains the spatial variation details of HRSM and simultaneously fuses the in situ information, but there are point mutations at the station locations. The IDW method smooths the mutations at stations, but also smooths the spatial variations of HRSM, loses some extreme values, and narrows the data range. Therefore, the Kriging method can retain the spatial variation details of the HRSM and dynamic range of the site better than the IDW method.  
Figure 8: Daily average sequence curves of the in situ SM, HRSM, GDA_Kriging, and GDA_IDW SM in Sichuan from 10 June to 30 November 2017.  
Figure 7: Boxplots (**a**) and PDF curves (**b**) of the in situ SM, HRSM, GDA_Kriging, GRA_Kriging, GDA_IDW, and GRA_IDW SM in Sichuan during summer and autumn of 2017.