# Use of SMAP Soil Moisture and Fitting Methods in Improving GPM Estimation in Near Real Time
## 4 Results
### Parameter Values for Seven Correction Methods  
Since the parameters are calibrated for each grid cell, they vary with location. To demonstrate how widely they vary over space, the median, standard deviation, and the values corresponding 25 th and 75 th percentile for each parameter are listed in Table 1. As described in Section 3, the parameter values of each method are calculated using the data from CMPA and GPM during May to September, 2015 to 2016 as the benchmark. For the assimilation algorithm, the parameter values are calibrated based on the explicit minimization of RMSE with respect to CMPA. For other fitting methods, the parameters and their calibration processes are described in Section 3.  
The results in Table 1 indicate that \(\mathrm{N_{SMAP,opt}}\) of assimilation algorithm have a stable range between 4 to 7, whereas \(\mathrm{P_{threshold}}\) shows a strong spatial heterogeneity. That may be because \(\mathrm{N_{SMAP,opt}}\) is related to the observing frequency of SMAP, which is not very different across space. By contrast, \(\mathrm{P_{threshold}}\) is determined by the magnitude of daily precipitation intensity that varies greatly across China, as shown in Figure 1. The median of the parameter \(\mathrm{a_{1}}\) in GPM-Linear correction is 0.67, which shows that GPM greatly overestimates precipitation in most areas. The GPM products is improved by the SM correction, as the median of the parameter \(\mathrm{a_{2}}\) in SMP-Linear correction becomes 0.91. The parameter \(\mathrm{c_{1}}\) in GPM-Nonlinear correction is less than 1 in most areas with the median of 0.57, which indicates a highly nonlinear relationship between CMPA and GPM. The nonlinear relationship still exists after GPM is corrected with SM in SMP-nonlinear, as reflected by the median value (0.74). The parameters in the CDF matching correction method have a larger variability, reflecting stronger spatial heterogeneity.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Product** & **Parameters** & **Median** & \(\boldsymbol{\sigma}\) & **25 th** & **75 th** \\ \hline SMP & \(N_{SMAP,opt}\) & 5 & 1.47 & 4 & 7 \\  & \(P_{threshold}\) (mm/day) & 25 & 13.57 & 15 & 35 \\ GPM-Linear & \(\mathrm{a_{1}}\) & 0.67 & 1.08 & 0.48 & 1.07 \\  & \(\mathrm{b_{1}}\) & 2.3 & 1.66 & 1.43 & 3.40 \\  & \(\mathrm{c_{1}}\) & 0.57 & 0.94 & 0.46 & 0.71 \\  & \(\mathrm{k_{1,0}}\) (\(\mathrm{k_{1,m}}\)) & 0.127(0.104) & 0.097(0.054) & 0.073(0.075) & 0.200(0.141) \\  & \(\mathrm{\theta_{1,0}}\) (\(\mathrm{\theta_{1,m}}\)) & 12.69(13.65) & 12.18(18.44) & 8.18(3.56) & 21.11(29.65) \\  & \(\mathrm{a_{2}}\) & 0.91 & 0.38 & 0.63 & 1.12 \\  & \(\mathrm{b_{2}}\) & 1.46 & 1.21 & 0.83 & 2.30 \\  & \(\mathrm{c_{2}}\) & 0.74 & 0.89 & 0.56 & 0.97 \\  & \(\mathrm{K_{2,0}}\) (\(\mathrm{k_{2,m}}\)) & 0.127(0.163) & 0.097(0.091) & 0.073(0.101) & 0.200(0.223) \\  & \(\mathrm{\Theta_{2,0}}\) (\(\mathrm{\theta_{2,m}}\)) & 12.69(8.99) & 12.18(7.91) & 8.18(5.47) & 21.11(14.19) \\ \hline \hline \end{tabular} \(\sigma\): Standard Deviation; 25 th and 75 th: Percentiles. Note: the parameters \(k\) and \(\boldsymbol{\theta}\) with the subscript \(\epsilon\) denote those are based on CMPA, while the parameters \(k\) and \(\boldsymbol{\theta}\) with the subscript \(m\) denote those are based on GPM or SMP.  
\end{table}
Table 1: Summary statistics of the spatial distribution of the calibrated parameters for the seven correction methods.