Flooding impacts are on the rise globally, and concentrated in urban areas. Currently, there are no operational systems to forecast flooding at spatial resolutions that can facilitate emergency preparedness and response actions mitigating flood impacts. We present a framework for real‐time flood modeling and uncertainty quantification that combines the physics of fluid motion with advances in probabilistic methods. The framework overcomes the prohibitive computational demands of high‐fidelity modeling in real‐time by using a probabilistic learning method relying on surrogate models that are trained prior to a flood event. This shifts the overwhelming burden of computation to the trivial problem of data storage, and enables forecasting of both flood hazard and its uncertainty at scales that are vital for time‐critical decision‐making before and during extreme events. The framework has the potential to improve flood prediction and analysis and can be extended to other hazard assessments requiring intense high‐fidelity computations in real‐time.

[1] A novel two-dimensional, physically based model of soil erosion and sediment transport coupled to models of hydrological and overland flow processes has been developed. The Hairsine-Rose formulation of erosion and deposition processes is used to account for size-selective sediment transport and differentiate bed material into original and deposited soil layers. The formulation is integrated within the framework of the hydrologic and hydrodynamic model tRIBS-OFM, Triangulated irregular network-based, Real-time Integrated Basin Simulator-Overland Flow Model. The integrated model explicitly couples the hydrodynamic formulation with the advection-dominated transport equations for sediment of multiple particle sizes. To solve the system of equations including both the Saint-Venant and the Hairsine-Rose equations, the finite volume method is employed based on Roe's approximate Riemann solver on an unstructured grid. The formulation yields space-time dynamics of flow, erosion, and sediment transport at fine scale. The integrated model has been successfully verified with analytical solutions and empirical data for two benchmark cases. Sensitivity tests to grid resolution and the number of used particle sizes have been carried out. The model has been validated at the catchment scale for the Lucky Hills watershed located in southeastern Arizona, USA, using 10 events for which catchment-scale streamflow and sediment yield data were available. Since the model is based on physical laws and explicitly uses multiple types of watershed information, satisfactory results were obtained. The spatial output has been analyzed and the driving role of topography in erosion processes has been discussed. It is expected that the integrated formulation of the model has the promise to reduce uncertainties associated with typical parameterizations of flow and erosion processes. A potential for more credible modeling of earth-surface processes is thus anticipated.

The understanding of reasons leading to nonuniqueness of soil erosion susceptibility is still inadequate, yet indispensable for establishing general relations between runoff volume and sediment yield. To obtain relevant insights, we performed a series of numerical simulations with a detailed hydrodynamic model using synthetic storms of varying intensity, duration, and lag time between events as representations of different hydrologic response conditions in a zero-order catchment. The design targeted to generate surface flow and “perturb” soil substrate by a first rainfall event, creating a set of initial conditions in terms of flow and deposited sediment prior to the onset of a subsequent rainfall event. Due to the differential effect of (re)detachment and (re)entrainment processes on soil particles of varying sizes, the deposited sediment mass formed shielding layer. One of the essential results is that unless the initial condition of flow and sediment is identical, the same volume of runoff can generate different total sediment yields and their variation can reach up to ∼200%. The effect is attributed to two major conflicting effects exerted by the deposited “initialization” (soil antecedent condition) sediment mass: erosion enhancement, because of supply of highly erodible sediment, and erosion impediment, because of constrain on the availability of lighter particles by heavier sediment. Consistently with this inference, long-term simulations with continuous rainfall show that a peculiar feature of sediment yield series is the existence of maximum before the steady state is reached. The two characteristic time scales, the time to peak and the time to steady state, separate three characteristic periods that correspond to flow-limited, source-limited, and steady-state regimes. These time scales are log linearly and negatively related to the spatially averaged Shields parameter: the smaller the rainfall input and the heavier a given particle is, the larger the two scales are. The results provide insights on how the existence of shield operates on erosion processes, possibly implying that accurate short-term predictions of geomorphic events from headwater areas may never become a tractable problem: the latter would require a detailed spatial characterization of particle size distribution prior to precipitation events.

A novel modeling framework that simultaneously improves accuracy, predictability, and computational efficiency is presented. It embraces the benefits of three modeling techniques integrated together for the first time: surrogate modeling, parameter inference, and data assimilation. The use of polynomial chaos expansion (PCE) surrogates significantly decreases computational time. Parameter inference allows for model faster convergence, reduced uncertainty, and superior accuracy of simulated results. Ensemble Kalman filters assimilate errors that occur during forecasting. To examine the applicability and effectiveness of the integrated framework, we developed 18 approaches according to how surrogate models are constructed, what type of parameter distributions are used as model inputs, and whether model parameters are updated during the data assimilation procedure. We conclude that (1) PCE must be built over various forcing and flow conditions, and in contrast to previous studies, it does not need to be rebuilt at each time step; (2) model parameter specification that relies on constrained, posterior information of parameters (so‐called Selected specification) can significantly improve forecasting performance and reduce uncertainty bounds compared to Random specification using prior information of parameters; and (3) no substantial differences in results exist between single and dual ensemble Kalman filters, but the latter better simulates flood peaks. The use of PCE effectively compensates for the computational load added by the parameter inference and data assimilation (up to ~80 times faster). Therefore, the presented approach contributes to a shift in modeling paradigm arguing that complex, high‐fidelity hydrologic and hydraulic models should be increasingly adopted for real‐time and ensemble flood forecasting.

Applications of process‐based models (PBM) for predictions are confounded by multiple uncertainties and computational burdens, resulting in appreciable errors. A novel modeling framework combining a high‐fidelity PBM with surrogate and machine learning (ML) models is developed to tackle these challenges and applied for streamflow prediction. A surrogate model permits high computational efficiency of a PBM solution at a minimum loss of its accuracy. A novel probabilistic ML model partitions the PBM‐surrogate prediction errors into reducible and irreducible types, quantifying their distributions that arise due to both explicitly perceived uncertainties (such as parametric) or those that are entirely hidden to the modeler (not included or unexpected). Using this approach, we demonstrate a substantial improvement of streamflow predictive accuracy for a case study urbanized watershed. Such a framework provides an efficient solution combining the strengths of high‐fidelity and physics‐agnostic models for a wide range of prediction problems in geosciences.