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This study introduces a novel theoretical model for upscaling colloid transport from the grain scale to the Darcy scale under both favorable and unfavorable conditions. The model integrates colloid interception history, where an interception occurs when colloids enter the near-surface zone within 200 nm of a collector, to capture the traditional exponential retention profile, as well as the anomalous, non-exponential behaviors observed under unfavorable conditions. The development of this theoretical model is based on a two-stage framework: first, upscaling from the grain scale to the single-interception scale, followed by upscaling from the single-interception scale to the Darcy scale. The initial stage addresses the distribution of colloids corresponding to a given interception order. The second stage focuses on the distribution of colloids across multiple interception orders. The key innovation of this work is the inclusion of the colloid removal process, where a fraction, denoted by $$\alpha$$, is removed at each encountered interception, rather than with each grain passed, as specified by classical colloid filtration theory. Our model accounts for scenarios under unfavorable conditions wherein if $$\alpha$$ remains constant, the distribution is exponential, albeit shallower relative to favorable conditions. Additionally, the model considers cases where $$\alpha$$ varies with interceptions, leading to multi-exponential and nonmonotonic retention profile shapes. In both scenarios, the proposed theoretical model offers a mathematical representation of colloid retention profiles under favorable and unfavorable conditions, including those exhibiting anomalous shapes. 

Compound flooding, the concurrence of multiple flooding mechanisms such as storm surge, heavy rainfall, and riverine flooding, poses a significant threat to coastal communities. To mitigate the impacts of compound flooding, forecasts must represent the variability of flooding drivers over a wide range of spatial scales while remaining timely. One approach to develop these forecasts is through subgrid corrections, which utilize information at smaller scales to “correct” water levels and current velocities averaged over the model scale. Recent studies have shown that subgrid models can improve both accuracy and efficiency; however, existing models are not able to account for the dynamic interactions of hydrologic and hydrodynamic drivers and their contributions to flooding along the smallest flow pathways when using a coarse resolution. Here, we have developed a solver called CoaSToRM (Coastal Subgrid Topography Research Model) with subgrid corrections to compute compound flooding in coastal systems resulting from fluvial, pluvial, tidal, and wind-driven processes. A key contribution is the model’s ability to enforce all flood drivers and use the subgrid corrections to improve the accuracy of the coarse-resolution simulation. The model is validated for Hurricane Eta 2020 in Tampa Bay, showing improved prediction accuracy with subgrid corrections at 42 locations. Subgrid models with coarse resolutions (R2 = 0.70, 0.73, 0.77 for 3-, 1.5-, 0.75-km grids) outperform standard counterparts (R2 = 0.03, 0.14, 0.26). A 3-km subgrid simulation runs roughly 50 times faster than a 0.75-km subgrid simulation, with similar accuracy.