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It remains a challenge to accurately model the runoff behavior in urban areas with a complex topography. The question to be addressed is how varying the urban spatial configurations can quantitatively influence the overland flow response in relation to the hydrodynamic variables. We use a 2D shallow water model to indicate the influence of changing spatial urban factors (such as the orientation of streets and buildings, and adding sidewalks) in small idealized (synthetic) urban catchments with a size of 267.5m*267.5m during a single pluvial flood event. We differentiate between: i) the two-way main street with of 14-m width with sidewalks, and ii) side streets of 10m width. We then define novel spatially integrated indicators over the domain to analyze quantitatively runoff variables in correlation with the urban features. Additionally, local hotspot flood maps were created to assess risk. The modelling results showed that, with respect to the flow velocities in small-scale urban catchments, the main street layout is the dominant urban factor, followed by the side street widths, which were decisively determined by the geometry of the sidewalks. The comparison with real flood risk thresholds shows that the lower part of the main road is the most sensitive to flood risk in the domain. Spatially integrated indicators of the flow variables are showing low sensitivity to the spatial urban features. Our findings offer a new important perspective on the development of urban flood risk assessment, and provide a better understanding of the spatiotemporal rainfall-runoff generation in a small urban catchment., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

An accurate assessment of the physical states of the Earth system is an essential component of many scientific, societal and economical considerations. These assessments are becoming an increasingly challenging computational task since we aim to resolve models with high resolutions in space and time, to consider complex coupled partial differential equations, and to estimate uncertainties, which often requires many realizations. Machine learning methods are becoming a very popular method for the construction of surrogate 5 models to address these computational issues. However, they also face major challenges in producing explainable, scalable, interpretable and robust models. In this manuscript, we evaluate the perspectives of geoscience applications of physics-based machine learning, which combines physics-based and data-driven methods to overcome the limitations of each approach taken alone. Through three designated examples (from the fields of geothermal energy, geodynamics, and hydrology), we show that the non-intrusive reduced basis method as a physics-based machine learning approach is able to 10 produce highly precise surrogate models that are explainable, scalable, interpretable, and robust.

Geoscientific model development 16(3), 977 - 1008 (2023). doi:10.5194/gmd-16-977-2023, Published by Copernicus, Katlenburg-Lindau

The Simulation Environment for Geomorphology, Hydrodynamics and Ecohydrology in Integrated form (SERGHEI) is a multi-dimensional, multi-domain and multi-physics model framework for environmental and landscape simulation, designed with an outlook towards Earth System Modelling. It aims to provide a modelling environment for hydrodynamics, ecohydrology, morphodynamics, and, most importantly, interactions and feedbacks among such processes at different levels of complexity and across spatiotemporal scales. The small scale feedbacks and interactions, which warrant high resolution, can result in emergent behaviours manifesting at larger scales, thus warranting large model domains. At the core of SERGHEI's technical innovation is its HPC implementation, built from scratch on the Kokkos portability layer. Consequently, SERGHEI achieves performance-portability from personal computers to top HPC systems, including GPU-based and heterogeneous systems. SERGHEI relies Kokkos to handle memory spaces, thread management and execution policies for the required backend programming models. In this work we explore combinations of MPI and Kokkos using OpenMP and CUDA backends. In this contribution, we introduce the SERGHEI model framework, and present with detail its first operational module for solving shallow water equations (SERGHEI-SWE). This module is designed to be applicable to hydrological, environmental and consequently Earth System Modelling problems, but also to classical engineering problems such as fluvial or urban flood modelling. We also provide evidence of its applicability by testing it against several well-known benchmarks. We also evaluate its performance on several benchmarks and large scale problems. Finally, SERGHEI-SWE is evaluated in terms of scaling (on several TOP500 HPC systems).

Surface runoff (dis)connectivity manifests across scales, spawning from different spatial flow patterns, which are dominated by both topography (structural connectivity) and hydrodynamics (dynamic connectivity). How the connectivity builds and evolves throughout rainfall events is integrated into observable hydrological signatures (namely, hydrographs and water balance). In this contribution we explore the connectivity properties of runoff generation processes across spatial scales. We revisit three case studies of runoff generation during rainfall, numerically simulated by solving shallow-water equations. This approach provides a full description of the hydrodynamic flow fields, allowing to study both the connectivity properties, as well as the domain-integrated hydrological signatures (namely, hydrographs) that build up in response to flow phenomena. We discuss and link the runoff generation processes arising from (i) runoff generation at the plot scale (20 m2 at cm resolution) with explicit microtopographies, (ii) runoff generation at the hillslope or first-order catchment scale with overland and (ephemeral) rill flows in the Hühnerwasser experimental catchment (4000 m2 at m resolution), and (iii) runoff generation at the catchment scale in the Lower Triangle catchment (15 km2 at m resolution).The detailed study of runoff generation dynamics highlights the needs to use time-evolving connectivity metrics, which are particularly useful to understand spatiotemporal model output. We computed the number of disconnected flooded clusters (and Euler characteristic) as the main connectivity metric.The results of the three different systems suggest similar qualitative behaviours of connectivity across scales, from plot to catchment scales, and therefore also offer the possible use of connectivity to understand how fluxes are re-scaled across the landscape, and as a multiscale indicator of hydrological function. The relationship between the connectivity response at a given scale (e.g., plot) and the hydrological signature observed at the next larger scale (e.g., hillslope) may lead into a hierarchical relationship of connectivities and signatures, in which the time-continuous nature of the connectivity signal may give rise to non-linear and threshold behaviours in the larger scale signature. Additionally, in the context of assessing model quality, connectivity is a feature of the natural system which models (and modellers) should strive to ensure. In this sense, we argue that model formulations, meshing (including resolution/topology and preprocessing/smoothing of the terrain model) and parameterisations should be evaluated not only using integrated signatures (e.g., water balance, hydrographs) or point data (water depth, velocities) but also using (dis)connectivity metrics. In this way, it is possible to evaluate to which extent a model and its setup can simulate natural flow paths and landscape functions.

Microtopography (MT) can govern runoff dynamics as a net result of local heterogeneities in the flow paths and ponding. This in turn controls the development of the surface water layer that connects and flows downslope. It is therefore important to understand which microtopographic features affect runoff generation dynamics and its macroscopic—hillslope scale—hydrological signatures (e.g., hydrographs, runoff and infiltration volumes). In this study, we numerically solve 2D overland flow from a single rain pulse on 1,460 idealized hillslopes with different slopes and sinusoidal microtopographies and different infiltration capacities. We assess hydrodynamic distributions, hydrographs and hydrological indices to assess the effects of MT and infiltration on the (local) hydrodynamic and (larger scale) hydrologic responses in terms of surface runoff regimes. The results show that MT enhances infiltration and that infiltration and runoff depend in a strong non-linear way on slope and the properties of MT. Three regimes of influence of MT were identified: one in which MT plays a negligible role but there is a high sensitivity to the infiltration capacity curve, a second regime in which hydrological partitioning is highly sensitive to MT and the infiltration capacity curve, and a third regime in which MT increases infiltration, but the response is insensitive to particular features, and more affected by the average slopes. The regimes are the product of the interplay between small (MT) and large scale (slope) properties. Furthermore, the results suggest that hydrological signatures can be interpreted and explained by the spatiotemporal variation of surface connectivity.

The Simulation Environment for Geomorphology, Hydrodynamics and Ecohydrology in Integrated form (SERGHEI) model framework is a multi-dimensional, multi-domain and multi-physics model framework. It is designed to provide a modelling environment for hydrodynamics, ecohydrology, morphodynamics, and, importantly, interactions and feedbacks among such processes, at different levels of complexity and across spatiotemporal scales. SERGHEI is in essence, a terrestrial landscape simulator based on a hydrodynamics core, designed with an outlook towards Earth System Modelling applications. Consequently, efficient mathematical and numerical formulations, as well as HPC implementations are at its core. SERGHEI intends to enable large scale and high resolution problems, which will allow to acknowledge and simulate emergent behaviours rising from the small-scale interactions and feedbacks between different environmental processes, that often manifest at larger spatiotemporal scales.At the core of the technical innovation in SERGHEI is its HPC implementation, built from scratch on the Kokkos programming model and C++ library. This approach facilitates portability from personal computers to Tier-0 HPC systems, including GPU-based and heterogeneous systems. This is achieved by relying on Kokkos handling memory models, thread management and computational policies for the required backend programming models. In particular, using Kokkos, SERGHEI can be compiled for multiple CPUs and GPUs using a combination of OpenMP, MPI, and CUDA.In this contribution, we introduce the SERGHEI model framework, and specially its first operational module for solving shallow water equations (SERGHEI-SWE). This module is designed to be applicable to hydrological, environmental and consequently Earth System Modelling problems, but also to classical engineering problems such as fluvial or urban flood modelling. We also provide a first showcase of the applicability of the SERGHEI-SWE solver to several well-known benchmarks, and the performance of the solver on large-scale hydrological simulation and flooding problems. We also show and discuss the scaling properties of the solver (on several Tier-0 systems) and sketch out its current and future development.

A wavelet-based local mesh refinement (wLMR) strategy is designed to generate multiresolution and unstructured triangular meshes from real digital elevation model (DEM) data for efficient hydrological simulations at the catchment scale. The wLMR strategy is studied considering slope- and curvature-based refinement criteria to analyze DEM inputs: the slope-based criterion uses bed elevation data as input to the wLMR strategy, whereas the curvature-based criterion feeds the bed slope data into it. The performance of the wLMR meshes generated by these two criteria is compared for hydrological simulations; first, using three analytical tests with the systematic variation in topography types and then by reproducing laboratory- and real-scale case studies. The bed elevation on the wLMR meshes and their simulation results are compared relative to those achieved on the finest uniform mesh. Analytical tests show that the slope- and curvature-based criteria are equally effective with the wLMR strategy, and that it is easier to decide which criterion to take in relation to the (regular) shape of the topography. For the realistic case studies: (i) slope analysis provides a better metric to assess the correlation of a wLMR mesh to the fine uniform mesh and (ii) both criteria predict outlet hydrographs with a close predictive accuracy to that on the uniform mesh, but the curvature-based criterion is found to slightly better capture the channeling patterns of real DEM data.

The measurement and simulation of 2D free-surface shallow flows is carried out in this work. For the experimental study a 3D-sensing device (Microsoft Kinect) is used to measure both steady and transient water surface elevation fields with different flow characteristics. This procedure provides 640x480 px resolution water surface level point clouds with a frequency ranging from 8 Hz to 30 Hz. The experimental measurements are compared with 2D finite volume simulations carried out by means of a robust and well-balanced numerical scheme able to deal with flow regime transitions and wet/dry fronts. A good agreement is found between experimental and numerical results for all the cases studied, demonstrating the capability of the RGB-D sensor to capture the water free-surface position accurately. This new experimental technique, which allows us to obtain 2D water depth fields in open- channel flows, leads to a wide range of promising capabilities in order to validate new shallow water models and to improve their accuracy and performance.

This paper presents the formulation of an adaptive finite volume (FV) model for the shallow water equations. A Godunov-type reformulation combining the Haar wavelet is achieved to enable solution-driven resolution adaptivity (both coarsening and refinement) by depending on the wavelet's threshold value. The ability to properly model irregular topographies and wetting/drying is transferred from the (baseline) FV uniform mesh model, with no extra notable efforts. Selected hydraulic tests are employed to analyse the performance of the Haar wavelet FV shallow water solver considering adaptivity and practical issues including choice for the threshold value driving the adaptivity, mesh convergence study, shock and wet/dry front capturing abilities. Our findings show that Haar wavelet-based adaptive FV solutions offer great potential to improve the reliability of multiscale shallow water models.

The 2D numerical simulation of river flow requires a large amount of topographic data to build an accurate Digital Terrain Model which must cover the main river channel and the area likely to be flooded. DTMs for large floodplains are often generated by LiDAR flights. However, it is often impossible to obtain LiDAR data of permanently inundated river beds. These areas are often surveyed and discrete cross-sections of the river channel are obtained. This work presents an algorithm to generate the missing information for the areas between cross-sections. The algorithm allows to generate a river bed which preserves important morphological features such as meanders and thalweg trajectory. Two benchmark cases are studied: a synthetic river-floodplain system and a real case application on a reach of the Ebro river in Spain. The cases are analyzed from a geometry and hydrodynamics perspective by performing 2D simulations with good results. This work describes an algorithm designed to reconstruct 2D river beds from 1D cross-section data.The algorithm is designed to interpolate the trajectory of the channel from the cross-section data, as well as the elevation.Tests show that the algorithm is well suited for 2D river bed reconstruction and allows to obtain good hydrodynamic simulations.

Numerical modeling of bed-load transport in shallow flows, particularly oriented toward environmental flows, is an active field of research. Nevertheless, other possible applications exist. In particular, bed-load transport phenomena are relevant in urban drainage systems, including sewers. However, few applications of coupled two-dimensional (2D) shallow-water and bed-load transport models can be found, and their transfer from environmental applications-usually river and floodplain-into sewer applications requires some adaptation. Unlike to river systems, where there is a thick layer of sediment that constitutes a movable riverbed, sewer systems have thin layers of sediment that need to be removed, thus exposing a rigid, nonerodible surface. This problem requires careful numerical treatment to avoid generating errors and instability in the simulation. This paper deals with a numerical approach to tackle this issue in an efficient way that allows large-scale studies to be performed and provides empirical evidence that the proposed approach is accurate and applicable for sewage and channel-flushing problems. (C) 2017 American Society of Civil Engineers.

We provide an adaptive strategy for solving shallow water equations with dynamic grid adaptation including a sparse representation of the bottom topography. A challenge in computing approximate solutions to the shallow water equations including wetting and drying is to achieve the positivity of the water height and the well-balancing of the approximate solution. A key property of our adaptive strategy is that it guarantees that these properties are preserved during the refinement and coarsening steps in the adaptation process.The underlying idea of our adaptive strategy is to perform a multiresolution analysis using multiwavelets on a hierarchy of nested grids. This provides difference information between successive refinement levels that may become negligibly small in regions where the solution is locally smooth. Applying hard thresholding the data are highly compressed and local grid adaptation is triggered by the remaining significant coefficients. Furthermore we use the multiresolution analysis of the underlying data as an additional indicator of whether the limiter has to be applied on a cell or not. By this the number of cells where the limiter is applied is reduced without spoiling the accuracy of the solution.By means of well-known 1D and 2D benchmark problems, we verify that multiwavelet-based grid adaptation can significantly reduce the computational cost by sparsening the computational grids, while retaining accuracy and keeping well-balancing and positivity.

Computer methods in applied mechanics and engineering 294, 56-71 (2015). doi:10.1016/j.cma.2015.05.016, Published by Elsevier Science, Amsterdam [u.a.]