Estimating the unresolved geophysical processes from resolved geophysical fluid dynamics is the key for improving numerical weather-climate predictions. While data-driven parameterization for unresolved geophysical processes shows potential, most practices fail to capture the diversity of unresolved geophysical processes that agree with resolved geophysical fluid state. This pitfall undermines the likelihood or severity of simulated weather extremes, and erodes the fidelity of climate projections. We propose the criteria of READS (Realism, Efficiency, Adaptability, Diversity, Sharpness) for generative models to yield reasonable stochastic parameterization. We introduce probabilistic diffusion model, a non-equilibrium thermodynamics inspired deep generative modeling approach, to better meet these criteria. Using a case example of numerical precipitation estimation, we demonstrate the advantage of the proposed methodology in quickly delivering diverse and faithful estimates for the target unresolved process, as compared to other popular data-driven deterministic and stochastic methods (UNet, variational autoencoder, generative adversarial net), as well as dynamical downscaling method (WRF). We conclude that generative models, in particular, probabilistic diffusion model, can significantly enhance the representation of unresolved geophysical processes in numerical weather-climate predictions.

Numerical weather prediction models often struggle to accurately simulate high-resolution precipitation processes, due to resolution limits and difficulties in representing convection and cloud microphysics. Data-driven methods often offer more accurate approximation of these unresolved processes by learning from high-fidelity referential data. Yet, existing approaches fail to yield fine-resolution, spatially coherent, reliable ensemble simulations/predictions, particularly for high-impact extreme events. To address these limitations, we develop a latent diffusion modeling (LDM) framework for quantitative precipitation estimation and forecast. The LDM leverages low-resolution (25 km) circulation and topographic information to estimate precipitation at a 4 km resolution. The latent diffusion model (LDM) learns the probability distribution of precipitation patterns by first compressing high-resolution spatial data into a compact, Quasi-Gaussian latent space. It then gradually refines estimates through a deep neural network parameterized reverse diffusion process, effectively capturing complex precipitation dynamics and delivering superior ensemble predictions. This approach enables LDMs to outperform traditional deep learning models like convolutional neural nets and generative adversarial neural nets, particularly for extreme events, while avoiding issues such as mode collapse, blurring artifacts, or underestimation of extremes. Compared to the dynamical method (WRF and GFS), the LDM offers significant performance gains, particularly for extreme precipitation events, improving over 30% in root mean squared error and over 40% in critical success index. For the extreme precipitation (> 300 mm/d) in California on October 25, 2021, LDM can provide effective forecasting up to 7 days in advance, forced by circulation prediction from a data-driven weather forecasting model.

Accurate global river discharge estimation is crucial for advancing our scientific understanding of the global water cycle and supporting various downstream applications. In recent years, data-driven machine learning models, particularly the Long Short-Term Memory (LSTM) model, have shown significant promise in estimating discharge. Despite this, the applicability of LSTM models for global river discharge estimation remains largely unexplored. In this study, we diverge from the conventional basin-lumped LSTM modeling in limited basins. For the first time, we apply an LSTM on a global 0.25° grid, coupling it with a river routing model to estimate river discharge for every river reach worldwide. We rigorously evaluate the performance over 5332 evaluation gauges globally for the period 2000-2020, separate from the training basins and period. The grid-scale LSTM model effectively captures the rainfall-runoff behavior, reproducing global river discharge with high accuracy and achieving a median Kling-Gupta Efficiency (KGE) of 0.563. It outperforms an extensively bias-corrected and calibrated benchmark simulation based on the Variable Infiltration Capacity (VIC) model, which achieved a median KGE of 0.466. Using the global grid-scale LSTM model, we develop an improved global reach-level daily discharge dataset spanning 1980 to 2020, named GRADES-hydroDL. This dataset is anticipated to be useful for a myriad of applications, including providing prior information for the Surface Water and Ocean Topography (SWOT) satellite mission. The dataset is openly available via Globus.

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.

Floodplain inundation links river and land systems through significant water, sediment, and nutrient exchanges. However, these two-way interactions between land and river are currently missing in most Earth System Models. In this study, we introduced the two-way hydrological coupling between the land component, ELM, and the river component, MOSART, in Energy Exascale Earth System Model (E3SM) to study the impacts of floodplain inundation on land and river processes. We calibrated the river channel geometry and developed a new data-driven inundation scheme to improve the simulation of inundation dynamics in E3SM. The new inundation scheme captures 96% of the spatial variation of inundation area in a satellite inundation product at global scale, in contrast with 7% when the default inundation scheme of E3SM was used. Global simulations including the new inundation scheme performed at resolution with and without two-way land-river coupling were used to quantify the impact of coupling. Comparisons show that two-way coupling modifies the water and energy cycle in 20% of the global land cells. Specifically, riverine inundation is reduced by two-way coupling, but inland inundation is intensified. Wetter periods are more impacted by the two-way coupling at the global scale, while regions with different climates exhibit different sensitivities. The two-way exchange of water between the land and river components of E3SM provides the foundation for enabling two-way coupling of land-river sediment and biogeochemical fluxes. These capabilities will be used to improve understanding of the interactions between water and biogeochemical cycles and their response to human perturbations.

The elevation of the mountain rain-snow transition is critical for short-term hazard forecasting and longer-term water supply considerations. Despite the transition’s importance, direct in-situ observations are rare. Here we present two new methods that utilize “anomalous” snow observations to detect rainfall during rain-on-snow: (1) a mass fluctuation at snow pillow sites, and (2) inflated remotely sensed snow grain sizes. Using auxiliary data, we show snow pillows respond to rain-on-snow with distinct perturbations that appear as pulses, collapses and declines within the snow water equivalent. We use these responses to identify mountain-scale rain-snow transitions across California’s Sierra Nevada. We also show how a threshold approach (>200 mm) for remotely sensed snow grain size can identify rain-on-snow as snow grain sizes artificially inflate due to a liquid water film. While the methods are not predictive, if paired retroactively with hydrometeorological models, these new methods have the potential to improve predictive streamflow capabilities.