Hydrological Storage Diagnostics: A Framework for Separating Model Error in State, Memory, and Trend Using GRACE

<jats:p>A hydrological simulation can match one skill score and still hold the wrong water volume, carry the wrong storage memory, or miss a storage trend. One number cannot say which failure is large. The Hydrological Storage Diagnostics (HSD) framework separates a simulation’s disagreement with GRACE into three model diagnostics and one machinery check, each in its own units: the distribution of storage values (state); the lagged dependence of the storage history (memory), the amplitude and persistence of variability across timescales; the closure trend, the signed storage trend a simulation must add to follow GRACE (trend); and a conditioning check, the trajectory residual after month-by-month conditioning on GRACE, which verifies the machinery and sets the observation noise floor rather than scoring the model. I evaluate 920 cases, 184 river basins by four GRACE solutions and five hydrological models, over 2002 to 2025. The closure trend equals the observed trend gap per case (r = 0.996) and carries a per-case uncertainty from a moving-block bootstrap in time; its median is near zero and its 95th-percentile magnitude is 13mmyr−1. Each entry is a target that revised physics must reduce or explain on the same window. The three models sharing one forcing need similar corrections in the same basin, while the two sharing only a process class do not; the clustering is consistent with the shared forcing, and the design cannot identify its cause. Conditioning lowers the median trajectory residual from 55 to 11mm, and a model-blind reference does as well, so the residual verifies the machinery rather than measuring model skill. Plain Language Summary A river basin stores water in soil, snow, rivers, lakes, and groundwater. Simulations estimate that total from the movement of water; GRACE estimates it by weighing the basin from orbit through small changes in Earth’s gravity. GRACE does not say which store holds the change. The two often disagree, and one error score does not say why. A simulation can match the long-term trend while still missing the seasonal range or the persistence of wet and dry periods. The Hydrological Storage Diagnostics replaces that one score with four numbers: the storage values, the storage memory, the storage trend the simulation still needs to add on its own, and a check that the steering machinery itself works. The trend is a target: better groundwater, reservoir, or irrigation physics should reduce it or explain why it remains. Across 184 basins, four GRACE versions, and five hydrological models, steering the simulation onto GRACE month by month shrinks the typical error to about a fifth of its raw size, and to about a third of what a standard statistical correction achieves by adjusting values but not their order in time.</jats:p>