In the recent past, the Gravity Recovery and Climate Experiment (GRACE) satellite mission and its successor GRACE Follow-On (GRACE-FO), have become invaluable tools for characterizing drought through measurements of Total Water Storage Anomaly (TWSA). However, the existing approaches have often overlooked the uncertainties in TWSA that stem from GRACE orbit configuration, background models, and intrinsic data errors. Here we introduce a fresh view on this problem which incorporates the uncertainties in the data: the Probabilistic Storage-based Drought Index (PSDI). Our method leverages Monte Carlo simulations to yield realistic realizations for the stochastic process of the TWSA time series. These realizations depict a range of plausible drought scenarios that later on are used to characterize drought. This approach provides probability for each drought category instead of selecting a single final category at each epoch. We have compared PSDI with the deterministic approach (SDI) over major global basins. Our results show that the deterministic approach often leans towards an overestimation of storage-based drought severity. Furthermore, we scrutinize the performance of PSDI across diverse hydrologic events, spanning continents from the United States to Europe, the Middle East, Southern Africa, South America, and Australia. In each case, PSDI emerges as a reliable indicator for characterizing drought conditions, providing a more comprehensive perspective than traditional deterministic indices. In contrast to the common deterministic view, our probabilistic approach provides a more realistic characterization of the TWS drought, making it more suited for adaptive strategies and realistic risk management.

Previous work based on Gravity Recovery and Climate Experiment (GRACE) data has shown that for certain large river basins like the Amazon, the empirical storage-discharge relationship reveals an underlying dynamics that is approximately linear and time-invariant. This is particularly true for the catchment upstream of the Óbidos stream gauge station on the Amazon river. We build on this observation to put forward, in this case, a simple first-order differential equation that approximates the observed dynamics. The model formulation includes one parameter that can be physically interpreted as an offset determining the total drainable water stored in the catchment, while a second parameter characterizes the typical time constant of the draining of the basin. We determine a value of 1925 km³ for the average total drainable water stored in the catchment during the period 2004 to 2009 and a draining time constant of 27.4 days. The same approach is also tested over eight smaller catchments of the Amazon to investigate whether or not the storage-discharge relationship is governed by a similar dynamics. Combined with the water mass balance equation, we eventually obtain two coupled linear differential equations which can be easily recast into a discrete state-space representation of the rainfall-storage-discharge dynamics of the considered basin. This set of equations is equivalent to defining an analytical instantaneous unit hydrograph for the whole basin. Besides, the proposed model is particularly suitable for Bayesian filtering and smoothing or the reconstruction of past unobserved states.