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.

In the 30 years of its availability, satellite altimetry has established itself as an important tool for understanding the Earth system. Originally developed for oceanography and geodesy, it has also proven valuable for monitoring water level variation of lakes and rivers. However, when using altimetry for inland waters, there is always a critical issue: retracking i.e. the procedure in which the range from the satellite to the water surface is (re)estimated. The current retracking methods heavily rely on single waveforms, which results in a high sensitivity to every individual peak in the waveform and in a strong dependency on the waveform's shape. Here, we propose the Bin-Space-Time (BiST) retracking method that moves beyond finding a single point in a 1D waveform and instead seeks a retracking line within a 2D radargram, for which the temporal information over different cycles is also considered. The retracking line divides the radargram into two segments: the left (Front) and right-hand side (Back) of the retracking line. Such a segmentation approach can be interpreted as a binary image segmentation problem, for which spatiotemporal information can be incorporated. We follow a Bayesian approach, exploiting a probabilistic graphical model known as a Markov Random Field (MRF). There, the problem is arranged as a Maximum A Posteriori estimation of an MRF (MAP-MRF), which means finding a retracking line that maximizes a posterior probability density or minimizes a posterior energy function. Our posterior energy function is obtained by a prior energy function and a likelihood energy function, both of them depending on signal intensity and bin: 1) The prior: the bin-space energy function defined between firstorder neighbouring pixels of a radargram modeling the spatial dependency between their labels for given intensities and bins and 2) The likelihood: the temporal energy function of a pixel for labeling Front or Back given its overall temporal evolution. The realization of the field with the minimum sum of the bin-space and the temporal energy functions is then found through the maxflow algorithm. Consequently, the retracking line, the boundary between the Back and Front region is obtained. We apply our method to both pulse-limited and SAR altimetry data over nine lakes and reservoirs in the USA with different sizes and different altimetry characteristics. The resulting water level time series are validated against in situ data. Across the selected case studies, on average, the BiST retracker improves the RMSE by approximately 0.5 m compared to the best existing retracker. The main benefit of the proposed retracker, which operates in bin, space, and time domains, is its robustness against unexpected waveform variations, making it suitable for diverse inland water surfaces.

The forthcoming Surface Water and Ocean Topography (SWOT) mission will vastly expand measurements of global rivers, providing critical new datasets for both gaged and ungaged basins. SWOT discharge products will provide discharge for all river reaches wider than 100 m, but at lower accuracy and temporal resolution than what is possible in situ. In this paper, we describe how SWOT discharge produced and archived by the US and French space agencies will be computed from measurements of river water surface elevation, width, and slope and ancillary data, along with expected discharge accuracy. We present here for the first time a complete estimate of SWOT discharge uncertainty budget, with separate terms for random (standard error) and systematic (bias) uncertainty components in river discharge timeseries. We expect that discharge uncertainty will be less than 30% for two thirds of global reaches and will be dominated by bias. Separate river discharge estimates will combine both SWOT and in situ data; these “gage constrained” discharge estimates can be expected to have lower systematic uncertainty. Temporal variations in river discharge timeseries will be dominated by random error and are expected to be estimated to within 15% for nearly all reaches, allowing accurate inference of event flow dynamics globally, including in ungaged basins. We believe this level of accuracy lays the groundwork for SWOT to enable breakthroughs in global hydrologic science.