# Groundwater Storage Changes in China from Satellite Gravity: An Overview
## 2 Data and Methodology  
### Groundwater Storage Change Estimation from GRACE  
GRACE-derived TWS changes represent an integrated change in various water storage components, i.e., soil moisture storage (SMS), snow water equivalent storage (SWES), surface water reservoir storage (RESS), and groundwater storage (GWS). To separate GWS changes from GRACE-derived TWS changes, other water storage components of TWS have to be estimated from auxiliary data or hydrological models. Thus, changes in GWS can be expressed as follows:  
\[\Delta\text{GWS}=\Delta\text{TWS}-\Delta\text{SMS}-\Delta\text{SWES}-\Delta \text{RESS} \tag{1}\]  
Time series of GWS changes in a given region can be estimated by various methods. As we know, original GRACE products in terms of spherical harmonics (SH) (i.e., Stokes coefficients) contain correlated errors in the spectral domain, i.e., north-south stripes in the spatial domain [49]. Thus, destriping (decorrelation) and Gaussian smoothing have to be applied to the GRACE SH products (i.e., Level-2 data) to remove correlated errors and high-frequency noises. The mass variations outside the study region will leak into the region (i.e., leakage-in effect); meanwhile, the signal in the region can also leak out to its surroundings (i.e., leakage-out effect). In general, the composited leakage effect will cause the actual signal inside the region attenuated. In addition, truncation of GRACE SH products with limited degree and order can also result in leakage effect and signal attenuation. Truncation, destriping, and smoothing of SH are hereinafter referred to as filtering or post-processing. To restore the actual signal in a given region from filtered GRACE products, leakage-in corrections need to be applied, which are estimated by simulated TWS from models generally; and then scaling factor method can be used to restore the leakage-in corrected mass change from filtered GRACE products. There are two methods to estimate scaling factors. In the first method, a basin-scale single scaling factor can be estimated from the ratio of the unfiltered and filtered basin function [50; 51; 52]. The basin function is defined as 1 inside the basin and 0 outside. The basin-scale scaling factor can also be estimated by minimizing the misfit between unfiltered and filtered mass change time series in the basin from models through least-squares fitting [53]. In the second method, however, gridded scaling factor can be estimated from the ratio of the gridded unfiltered and filtered mass changes from models [53]. No matter which method is used, we can finally derive unbiased time series of TWS changes from GRACE. Then, with estimates on other water storage components from models or observations, we can obtain time series of GWS changes as follows:  
\[\Delta\text{GWS}=sf*\Delta\text{TWS}_{f}-\Delta\text{SMS}-\Delta\text{SWES}- \Delta\text{RESS} \tag{2}\]  
where \(sf\) represents scaling factor; subscript \(f\) represents filtered. There is another alternative method to derive more reliable GWS changes with a minimum leakage effect if a priori information on GWS changes is available [18]. In this method, other water storage components (SMS, SWES, and RESS) from models are filtered in the same way as the GRACE data. After removing these filtered model grids from GRACE-derived TWS changes, we can obtain filtered GWS grids as follows:  
\[\Delta\text{GWS}_{f}=\Delta\text{TWS}_{f}-\Delta\text{SMS}_{f}-\Delta\text{ SWES}_{f}-\Delta\text{RESS}_{f} \tag{3}\]  
We assume that GWS changes are concentrated inside the area of interest. Therefore, the leakage-in effect should be negligible because there is no GWS change outside the area. Thus, restoring the actual GWS changes only require rescaling of signal amplitude by a scaling factor and no leakage correction is needed:  
\[\Delta\text{GWS}=sf*\Delta\text{GWS}_{f} \tag{4}\]where \(sf\) represents the scaling factor to restore filtered GWS changes, which needs to be estimated based on independent information on spatial distribution of GWS changes from in situ observations or models.