# Use of SMAP Soil Moisture and Fitting Methods in Improving GPM Estimation in Near Real Time
## 3 Model and Method  
### API Model  
[PERSON] et al. (2018) demonstrated that, despite the large computational expense, using a complicated land surface model does not result in a better correction of satellite precipitation estimates than a simple one like the API model. In this study, the assimilation procedure makes use of the API model, which requires precipitation and temperature data as input to derive soil moisture conditions in hydrological catchments. The API model was initially developed by [PERSON] (2016); [PERSON] et al. (2016); [PERSON] et al. (2016) then improved the model by updating the rescaling procedure to a semi-empirical relationship between soil moisture and precipitation, replacing soil moisture index in (mm) with soil moisture in (m3/m3) and accounting for the soil porosity and the selected soil thickness. The model version used in this study is referred to as [PERSON] et al. (2018), which includes modifications to the calculation of the parameter related to soil moisture decreasing with time. In the API model, the current SM at the surface is simulated based on the previous value of SM and the amount of incident precipitation  
\[\text{sm(t)}=\left[\text{sm(t-1)e}^{-\frac{\text{sm}}{\text{t}}}\right]+[\Theta _{\text{sat}}-\text{sm(t-1)}]\left[1-e^{-\frac{\text{sm(t)}}{\text{h}}} \right], \tag{1}\]  
where sm(t) is the modeled soil moisture at the current time t (\(\Delta\)t, the time step, 1 day in this study), with contribution from two different terms. The first term represents the attenuation of soil moisture in the natural state, depending on the previous soil moisture value sm(t\(-\)1) and the time scale of soil drying \(\tau\). The parameter \(\tau\) has to be calibrated on the grid-cell basis using soil information like clay proportion in the original development ([PERSON] et al., 2018). [PERSON] et al. (2018) replaced the calibration with an equation that estimates the \(\tau\) value simply based on air temperature alone  
\[\tau=\left(-7\text{e}^{-5}\text{T}^{4}\right)+\left(0.006\text{T}^{3}\right)- \left(0.03\text{T}^{2}\right)-\left(9.5\text{T}\right)+287, \tag{2}\]  
where the daily air temperature T (\({}^{5}\)C) is obtained from the MERRA-2 dataset directly in this study, which is different from the treatment in [PERSON] (2017) who used the air temperature smoothed on 25 days. The advantage of this method is that \(\tau\) can be inferred without other data such as soil types and can be easily applied worldwide. The second term in Equation (1) represents the increase ofsoil moisture caused by current precipitation P(t), which is limited by saturation soil moisture \(\Theta_{\text{sat}}\) (approximately equal to the soil porosity, taken from the gridded soil characteristics data set of China, as described in Section 2.4)--under no circumstance would this increase cause soil moisture to exceed \(\Theta_{\text{sat}}\). h is the depth of the surface soil layer, fixed to 45 mm, which is similar to the sensing depth of SMAP observations.  
A CDF matching procedure is conducted to correct any bias between the API-modelled SM and the SMAP-based SM. The CDF matching is a grid-cell procedure and can be expressed as  
\[\text{SMSMAP}^{\text{CDF}}=\text{p}_{1}+\text{p}_{2}\text{SMSMAP}, \tag{3}\]  
with  
\[\text{p}_{2}=\sigma(\text{SMAPI})/\sigma(\text{SMSMAP}), \tag{4}\]  
\[\text{p}_{1}=\mu(\text{SMAPI})-\text{p}_{2}\mu(\text{SMSMAP}). \tag{5}\]  
where SMSMAP\({}^{\text{CDF}}\) is the CDF matching corrected SMAP soil moisture to be used in the assimilation procedure, SMSMAP is the original SMAP soil moisture, and SMAPI is the soil moisture modeled by API.