GRACE water-storage deficits and surpluses relaxed at similar monthly rates on land in 2002-2026 after precipitation and noise controls; a GRACE-era asymmetry did not repeat in GRACE-FO

We tested if terrestrial water storage (TWS) deficits relax more slowly than surpluses after precipitation is removed. We used CSR GRACE/GRACE-FO RL06.3 mascons (April 2002 to June 2026), GPCP v2.3 precipitation and GHCN-CAMS temperature on a 2.5-degree grid: 1,867 land cells, 1,193 of them snow-free. For each cell we fit the monthly TWS anomaly change against precipitation anomaly and separate relaxation rates for surplus (kp) and deficit (kn) states, with OLS and two-stage least squares. A symmetric linear-reservoir null, driven by observed precipitation, block-bootstrapped innovations and white measurement noise, corrected estimator bias. A 15-degree spatial block bootstrap gave the intervals. In snow-free cells the planned surrogate-corrected OLS asymmetry dk = kp - kn was +0.029 per month (95% interval 0.005 to 0.053), about 7% of the OLS rate. This result was not robust: it was +0.013 (-0.009 to 0.034) with a zero-noise null, the corrected 2SLS median was +0.016 (-0.021 to 0.050), and it was +0.058 in GRACE 2002-2017 but +0.000 (-0.033 to 0.035) in GRACE-FO 2018-2026. Deficit and surplus events took similar times to recover half way (2.23 and 2.14 months; corrected difference 0.1 month, not significant). The S-shaped pooled relaxation curve also appeared in symmetric surrogates, so it comes from noise. A linear reservoir is sufficient at this scale. Limitations: the noise null is approximate (surrogate OLS rates 16% high), GRACE errors are not white, cells are not independent, and slow multi-year or trend asymmetry is not tested.

GRACE · GRACE-FO · terrestrial water storage · drought recovery · storage-outflow nonlinearity · linear reservoir · GPCP · surrogate null · instrumental variables · null result · hydrological memory