GRACE gravity data yield a physics-bounded global groundwater record: 358 cubic kilometers lost per year
Synopsis
GRACE and GRACE-FO satellites sense only total column water, so groundwater must be separated by subtracting soil moisture, snow and canopy storage, and the models used for that step underestimate the largest trends. A physics-constrained decomposition LSTM splits each cell's groundwater signal into a trend, a seasonal cycle and a residual, holding the trend inside the net atmospheric supply and enforcing basin mass balance during training. The reconstruction reached a root mean squared error of 6.97 centimeters and a Nash-Sutcliffe efficiency of 0.69 on withheld months, and its trend error against monitoring wells was lower than an independent hydrological model and a data-assimilation product at every scale tested.
Interpretation
A continuous, physically bounded gridded record of global groundwater storage change now covers April 2002 to December 2022 at half-degree resolution. Earlier GRACE-based groundwater estimates subtracted land-surface model soil moisture, snow and canopy storage from total water storage, and global hydrological models substantially underestimate the largest declining and rising trends relative to the satellite observations, an error the subtraction inherits. On withheld observed months the reconstruction reached a root mean squared error of 6.97 centimeters and a Nash-Sutcliffe efficiency of 0.69; against independent monitoring wells its trend error was lower than WaterGAP 2.2d and a GRACE data-assimilation product at cell, aquifer, basin and basins above 200,000 square kilometers.
The model writes each cell's groundwater anomaly as the sum of a trend, a seasonal cycle and a residual, so physical constraints act only on the long-term term. The trend pathway is driven by static properties alone, passed through a hyperbolic tangent and scaled by a time axis in years, and its slope is held within 1.5 times the cell's mean net atmospheric supply plus 1 centimeter per year, a bound with a median of about 8.33 centimeters per year. A soft penalty during training held the mean predicted trend of 233 basins to the observed basin trend; at matched 45-epoch training, a weight of 0.5 cut basin-closure error from 0.5285 to 0.4172 centimeters per year while held-out error fell 2.4 percent.
The reconstructed depletion was carried through to two planetary consequences, sea level and polar motion. Earlier groundwater depletion estimates ranged from about 126.5 to 550 cubic kilometers per year on differing bases. Across 21,632 significantly declining cells, gross depletion was 357.64 plus or minus 11.6 cubic kilometers per year and net storage change was minus 36.25 cubic kilometers per year, equivalent to 0.100 plus or minus 0.049 millimeters per year of sea-level rise; the associated mass redistribution gave a pole drift of 6.92 centimeters per year toward 68.6 degrees east.
Perspective
The results cover the global land surface at half-degree resolution from April 2002 to December 2022, with 52,427 cells entering training and evaluation; validation uses only the GROW monitoring-well compilation, and well data enter downstream of learning. The authors propose bridging the gap between the two missions with the same physics-constrained framework as GRACE Follow-On extends the record.
Specific yield enters the uncertainty budget as an assumed value of 0.15 or 0.40 rather than a measurement at satellite footprint scale, and it dominates the error in 67.6 percent of cells. At individual-cell scale, sweeping the imputed relative error to about 0.51 collapses the significant fraction, a property of the significance test itself; aggregated to the roughly 6-degree correlation area, the significant fraction is 61.4 percent under the conservative bound and 76.7 percent under the independent bound. The pole-drift rate is sensitive to the analysis window, rising to 8.145 centimeters per year over 2002 to 2019 while the direction shifts only 0.65 degrees.