# Two Decades of Groundwater Variability in Peru Using Satellite Gravimetry Data
## 2 Materials and Methods
### Methods  
#### 2.3.1 Calculation of GWS Changes  
The calculation of groundwater storage changes (\(\Delta\)GWS) and their conversion to percentiles is part of the GRACE-DA-DM GLV3.0 data processing and assimilation system. This system applies statistical transformations by comparing the estimates with a reference climatology, allowing users to directly access processed results--including percentiles--without having to perform the complex chain of calculations from raw satellite data. The GRACE-DA-DM GLV3.0 dataset integrates observations from the GRACE (2002-2017) and GRACE-FO (2018-2023) missions to estimate monthly \(\Delta\)GWS changes at an interpolated linear or spatial resolution of 0.25\({}^{\circ}\) (-28 km). Although the effective resolution of the satellites is approximately 300 km, the assimilation of hydrological models significantly improves the spatial accuracy of the product. This study applies a basin-wide coverage approach to assess GWS at the national scale in Peru, using the full GRACE satellite grid without restricting the analysis to specific aquifer boundaries. This strategy enables continuous assessments across broad hydroclimatic regions. Finally, a water balance approach is used to decompose total water storage (TWS) into its surface components--soil moisture, snow, and surface water--in order to isolate the groundwater component GWS across the country's three natural regions: the coast, Andes, and Amazon. The following section outlines the procedure applied:  
1. Water Balance Method  
Groundwater storage change (\(\Delta\)GWS) is estimated by subtracting surface water components from total terrestrial water storage (\(\Delta\)TWS), according to Equation (1), based on satellite gravimetry data from GRACE/GRACE-FO [37]. \[\Delta\text{GWS}=\Delta\text{TWS}-(\Delta\text{SMS}+\Delta\text{SWES}+\Delta \text{RESS}) \tag{1}\]  
where:  
- \(\Delta\)TWS (change in total water storage) is obtained from the GRACE/GRACE-FO products. - \(\Delta\)SMS (change in soil moisture storage). - \(\Delta\)SWES (change in snow water equivalent) are obtained from hydrological balance models integrated into the GRACE-DA-DM GLV3.0 product or from the GLDAS-2.1 model. - \(\Delta\)RESS (surface reservoir storage) was derived from reservoir monitoring data. \(\Delta\)GWS values are expressed in millimeters (mm) of equivalent water height and can be converted to volume (km\({}^{3}\)) by multiplying by the pixel area (~700 km\({}^{2}\) at 0.25\({}^{\circ}\) resolution in mid-latitudes). This method is consistent with global groundwater assessments [37], though GRACE's ~300 km resolution limits local-scale accuracy. Uncertainties from component separation and ~5% from interpolation were propagated into final \(\Delta\)GWS estimates. For national-scale calculations, GRACE pixel area (0.25\({}^{\circ}\)) was used, while aquifer-specific conversions supported in situ validation. _Percentile Transformation: Statistical Normalization_  
Percentiles compare the current \(\Delta\)GWS with a reference climatology (2003-2023) for each month and pixel, following these steps:  
- _Baseline construction_: For each month (e.g., July), a historical time series of \(\Delta\)GWS (2003-2023) is compiled for each pixel. - _Percentile calculation_: The current value is positioned within the ordered historical distribution. The formula is as follows:  
P = [(N\({}^{\circ}\) historical values \(\leq\) Current value)/Total number of historical records] \(\times\) 100  
- _Percentile 0-10_: Extreme drought (\(\Delta\)GWS among the lowest 10% of the historical record)  
- _Percentile 90-100_: Water surplus (\(\Delta\)GWS among the highest 10%). _Practical example_  
If, for a given pixel, the \(\Delta\)GWS for July 2023 is 7 mm, and 6 out of 21 historical values (2003-2022) are \(\leq\) 7 mm, then: P = (6/21) \(\times\) 100 \(\approx\) 29  
This indicates drier conditions than 71% of historical July. Regression Model for Climatic and Anthropogenic Factors This regression model is explained in Section 2.3.5.