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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)

Catchment-scale hydrological simulations typically require numerical solutions to the Richards equation, which describes variably-saturated water flow in porous media. In recent years, with the widespread use of high-performance computing (HPC), the simulation speed of hydrological models have been significantly enhanced. However, existing numerical schemes for the Richards equation show different performance under different HPC configurations. It remains unclear if the serial Richards solvers scale well in parallel. In this work, four popular numerical schemes (the fully explicit scheme, the predictor-corrector scheme, the iterative Picard scheme, and the fully implicit Newton's scheme) are implemented to solve the three-dimensional Richards equation, aiming at investigating the performance of these schemes on both multi-core CPUs and GPUs. The codes are built under the Kokkos framework to achieve performance portability between CPU and GPU. Two infiltration problems with analytical solutions available are chosen to evaluate the model performance in terms of accuracy and efficiency. As expected, the simulation results indicate that the optimal solution schemes on CPU and GPU could be different. Moreover, the numerical scheme, the linear system solver, and the soil properties all have influence on scaling. A hybrid scheme is promising for minimizing the computational cost under various simulation conditions. The findings of this work will guide the development of the subsurface flow module of the performance-portable, multi-physics model, SERGHEI.

The compartmentalised (modular) design often found in multiphysics Earth system models allows for progressive offloading of compute-intensive kernels to accelerators. The nature of this process implies that some model components will run on accelerators, while other components will continue to run on CPUs, leading to the use of heterogeneous HPC architectures. Furthermore, different hardware architectures (e.g. CPUs, GPUs, quantum, neuromorphic) within an HPC system can be grouped into modules, each tailored to the requirements of a particular class of algorithms and software, and interconnected with other modules via a shared network. Some of these modules may be focused on energy-efficient scalability, whereas others may be disruptive and experimental. Such a conglomerate of different hardware modules, where each module can work stand-alone or in combination with other modules, leads to the idea of modular supercomputer architecture (MSA). The first exascale system in Europe (JUPITER) is expected to be modular, following on from the experience of the JUWELS system. This new paradigm poses questions on how performance and scalability of models change from homogeneous, to heterogeneous to modular systems. The Terrestrial Systems Modelling Platform (TSMP) is a scale-consistent, highly modular, massively parallel, fully integrated soil-vegetation-atmosphere modelling system coupling an atmospheric model (COSMO), a land surface model (CLM), and a hydrological model (ParFlow), linked together by means of the OASIS3-MCT library. Each of these submodels can be considered as a module, with different domain sizes, computational loads and scalability. This implies that optimal configurations for solving a given problem require understanding many levels of non-trivial load balancing. It is currently possible to offload ParFlow to GPUs, while keeping COSMO and CLM on CPUs. This enables both heterogeneous and modular configuration, and thus prompts the need to re-evaluate load distribution and scalability to find new optimal configurations. In a previous study, preliminary results on heterogeneous configurations were presented (https://doi.org/10.5194/egusphere-egu22-10006).In this contribution, we extend our study and present a comparative study of performance and scaling for homogeneous, heterogeneous, and modular TSMP jobs. We study strong and weak scaling, for different problem sizes, and evaluate parallel efficiency on all three configurations in the JUWELS supercomputer. We further explore traces of selected cases, to identify changes in behaviour under the different configurations, such as emergent MPI communication bottlenecks and root causes of the load balancing issues.

Fascinating spatial patterns are found in many ecosystems. For example, patterns in Dryland ecosystems often consist of vegetation patches which alternate with bare soil. The patterns appear strikingly regular, when their formation is driven by scale-dependent feedbacks. Because of their regularity, such patterns are conceptually understood to be periodic. The formation of periodic patterns has been reproduced with idealized numerical models and the vulnerability of pattern forming ecosystems to environmental pressure has been preferentially studied with such models. However, natural patterns appear far from periodic. So does the distance between and the size of the patches vary systematically and the fringes of the patches are ragged. Previously, we revisited tests for periodicity and demonstrated that the large majority of regular patterns found in nature are not periodic. We also introduced a method to quantify the regularity of patterns, and found that natural patterns are of intermediate regularity, in-between uncorrelated noise and periodic functions, which can best be described by stochastic processes, where the irregularity is intrinsic to the pattern and not due to added noise. Here, we corroborate our previous results with a comprehensive metastudy, where we analyze natural and computer-generated patterns found in the leading literature. Furthermore, we extend our theory for the formation of stochastic patterns with arbitrary regularity to two dimensions. We find that our theory captures well the spectral properties of both isotropic, i.e. spotted, labyrinthic and gapped, as well as of anisotropic, i.e. banded patterns. Figure 1: a) Normalized spectral density averaged over the natural and model generated patterns found in the literature. The density of the natural patterns consists of a wide and low lobe, while the density of the model generated patterns consists of a narrow and high peak. b) Median regularity and interquartile range for the natural and model generated patterns. The modelled patterns are 3-5 times as regular as the natural patterns. Number of samples indicated next to the median.

Precipitation scenario analysis is a crucial step in flood risk assessment, in which storm events with different probabilities are defined and used as input for the hydrological/hydrodynamic calculations. Rainfall generators may serve as a basis for the precipitation analysis. With the increase in the use of high resolution spatially-explicit hydrological/hydrodynamic models in flood risk calculations, demand for synthetic gridded precipitation input is increasing. In this work, we present a dynamic spatiotemporal rainfall generator. The model is capable of generating catchment-scale rainfields containing moving storms, which enable physically-plausible and spatiotemporally coherent precipitation events. This is achieved by the tools event-based approach, where dynamic storms are identified as clusters of related data that occur at different locations in space and time, and are then used as basis for event regeneration. The implemented methodology, mainly inspired by Dierden et al. (2019), provides an improvement in the spatial coherence of precipitation extremes, which can in turn be beneficial in flood risk calculations.The model has been validated under different databases such as the radar-based RADALON dataset or spatially-interpolated historical raingauge timeseries of different catchments in Germany, which is also presented in this work. The validation indicates the models ability to adequately preserve observed storm statistics in the generated timeseries. The generator is developed as an extension to the state-of-the-science flood risk modelling tool ProMaIDes (Promaides 2023). The model also puts great focus on user accessibility with offering features such as an easy installation process, support for most operating systems, a user interface and an online user manual. Diederen, D., Liu, Y., 2020. Dynamic spatio-temporal generation of large-scale synthetic gridded precipitation: with improved spatial coherence of extremes. Stoch Environ Res Risk Assess 34, 1369–1383. https://doi.org/10.1007/s00477-019-01724-9ProMaIDes (2023): Protection Measures against Inundation Decision support. https://promaides.h2.de

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.

The Simulation EnviRonment for Geomorphology, Hydrodynamics and Ecohydrology in Integrated form (SERGHEI) model framework is a model framework for environmental hydrodynamics, ecohydrology, morphodynamics, and, importantly, interactions and feedbacks among such processes. SERGHEI is designed to be applicable to both geoscientific questions of coupled processes in Earth system science such as hydrological connectivity and river stability, as well as engineering applications to flooding and transport phenomena. In this contribution we present the SERGHEI model framework, its modular concept and its performance-portable implementation. We discuss the implementation of SERGHEI including the specifics of a highly efficient parallel implementation of the numerical scheme (based on augmented Riemann solvers) and how we achieve portability using the Kokkos programming model as an abstraction layer. The experience in SERGHEI suggests that Kokkos is a robust path towards performance-portability, and sets a realistic path for SERGHEI to be ready for the upcoming European exascale systems. We focus on the SERGHEI-SWE module which solves 2D shallow-water equation. We show that this fully operational module is performance-portable across CPUs and GPUs in several TOP500 systems, as well as first results on portability across GPU vendors. We discuss the computational performance on benchmark problems and show its scalability into the range of hundreds of scientific-grade GPUs. Additionally, we show first results of performance of the upcoming transport module in SERGHEI, and discuss the computational implications and outlook considering further integration of new modules and solvers in SERGHEI.

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).

Runoff generation and the consequent overland flow result from the interactions between gravity-driven flow over complex topography, Earth’s roughness, and infiltration. These processes mostly occur at small spatio-temporal scales, but aggregate throughout the landscape to produce a hydrodynamic response at catchment and stream scales during a rainfall event. While this response is highly transient and spatially heterogeneous, it is mostly studied through aggregated signatures, such as hydrographs. It is therefore of importance to understand how the hydrodynamic response builds up across scales in the landscape into such signatures. Arguably, hydrological (dis)connectivity, which describes how different parts of a hydro-system (dis)connect through fluxes, is a useful concept to describe this multiscale behaviour. In this contribution, we explore the dynamic connectivity behaviour of surface runoff in first order catchments (ranging between 0.06 and 15 km2) in response to singular rainfall events. We further analyse the connectivity response, mainly in terms of the number of disconnected clusters and the flooded areas, together with hydrological signatures. To do this, we use the GPU-enabled shallow water solver SERGHEI-SWE, which allows us to solve the shallow water equations at below-metre resolution (with tens of millions of grid cells per catchment). The extremely high spatial resolution of the model accurately captures spatial heterogeneity of topography and surface properties and thus, correctly represents the structural connectivity of the system. In the same manner, the hydrodynamics obtained on these high-resolution grids accurately capture the dynamic connectivity. Based on the simulated water depths, we assess dynamic connectivity at different spatial scales, and at different stages of runoff development, and study how the connectivity properties vary in different catchments. Furthermore, we perform a first analysis of how connectivity changes with scale and its relation to hydrological signatures and catchment features. Additionally, we explore the effects of coarser resolution simulations on dynamic connectivity on the same catchments.

Multiphysics Earth system models are potentially good candidates for progressive porting of modules to run on accelerator hardware. Typically, these models have an inherently modular design to cope with the variety of numerical formulations and computational implementations required for the range of physical processes they represent. Progressively porting modules or submodels to accelerators such as GPUs implies that models must run on heterogeneous hardware. Foreseeably, exascale systems will make use of heterogeneous hardware, and therefore, exploring early on such heterogeneous configurations is of importance and a challenge.The Terrestrial Systems Modelling Platform (TSMP) is a scale-consistent, highly modular, massively parallel, fully integrated soil-vegetation-atmosphere modelling system. Currently, TSMP is based on the COSMO atmospheric model, the CLM land surface model, and the ParFlow hydrological model, linked together by means of the OASIS3-MCT library.Recently, ParFlow was ported to GPU, therefore enabling the possibility of running TSMP under a heterogeneous configuration, that is COSMO and CLM running on CPUs, and ParFlow running on GPUs. The different computational demands of each submodel inherently result in non-trivial load balancing across the submodels. This has been addressed by studying the performance and scaling properties of the system for specific problems of interest. The new heterogeneous configurations prompts a re-assessment of load balancing, performance and scaling, in order to identify optimal computational resource configurations, and re-evaluate the bottlenecks and inefficiencies that the heterogeneous model system can have.In this contribution, we present first results on performance and scaling assessment of the heterogeneous TSMP, compared to its performance under homogeneous (CPU-only) configurations. We study strong and weak scaling, for different problem sizes, and evaluate parallel efficiency and power consumption, for homogeneous and heterogeneous jobs on the JUWELS supercomputer, and on the experimental DEEP-Cluster, both at the Jülich Supercomputing Centre. Additionally, we explore profiles and traces of selected cases, both on homogeneous and heterogeneous runs, to identify MPI communication bottlenecks and root causes of the load balancing issue.

Rainfall is a complex, spatial and temporally variated process and one of the core inputs for hydrological and hydrodynamic modelling. Most rainfalls are known to be moving storms with varying directions and velocities. Storm movement is known to be an important influence on runoff generation, both affecting peak discharge and the shape of hydrographs. Therefore, exploring the extent rainfall dynamics affect runoff generation and consequently flooded areas, can be an asset in effective flood risk management.In this work, we study how storm movement (e.g. characterized by velocity and direction) can affect surface flow generation, water levels and flooded areas within a catchment. Moreover, the influence of rainfall temporal variability in correlation with storm movement is taken into account. This is achieved by means of numerical-based, spatially explicit surface flow simulations using the tool ProMaIDes (2021), a free software for risk-based evaluation of flood risk mitigation measures. The storm events are generated using a microcanonical random cascade model and further on trajected across the catchment area.The study area is the Kan river catchment located in the province of Tehran (Iran) with a total area of 836 km², which has experienced multiple flooding events in recent years. Due to its semi-arid climate, steep topography with narrow valleys, this area has high potential for flash flood occurrence as a result of high intensity precipitation.The results of this study show a range of possible magnitudes of influence of rainfall movement on the catchment´s runoff response. The resulting flood maps highlight the importance of rainfall velocity and most importantly the direction of the movement in the estimation of flood events as well as their likelihood in catchment area. Moreover, its shown that the magnitude of influence of storm velocity and direction on discharge strongly depends on the location within the river network which it is measured.ProMaIDes (2021): Protection Measures against Inundation Decision support. https://promaides.h2.de

Runoff generation from rainfall events is a complex, spatial and temporally dependent process strongly governed, among other factors, by catchment surface topography. Although it is widely known that many catchments experience morphological evolution, it is often ignored in analysis for different reasons ranging from simplification to lack of data. However, young catchments and early landscapes (such as those which are affected by natural or anthropogenic disturbances) do exhibit topography changes which in turn affect catchment hydrodynamics, hydrology and in particular runoff. In this work, we study the runoff generation and hydrodynamics of the Huhnerwasser artificial catchment (Brandenburg, Germany) during a period of erosion-based topographical changes (2006–2010). Nine Digital Elevation Models from such period were used as topography over which physically-based simulations were performed. The results suggest that topographic evolution in this catchment mostly affects the onset of runoff, whereas peak discharges and receding hydrograph limbs are less affected. These differences in hydrological signatures can be explained through the changes in the spatial distribution of runoff hydrodynamics and their impact on surface runoff connectivity. Relatively small topographical differences produce changing ponding conditions and modify flowpaths which becomes evident only through inspection of the spatial distribution of hydrodynamic variables. Moreover, the study shows that in order for simulations to be able to capture such responses, appropriate computational mesh and topographical data resolution are critical, since connectivity itself can be greatly affected by low resolution data or representation.

In the past decade, shallow water solvers have dramatically improved both in terms of accuracy and computational power. New mathematical models and numerical schemes have been systematically verified against 1D exact solutions and laboratory experiments. Despite the two-dimensional nature of some of these benchmark tests, none of them reports complete 2D water depth fields, but only a few profiles are measured and reported in the best case. This work reports a new benchmarking dataset for validation of shallow water solvers, in which two-dimensional transient water depth measurements are available for complex steady and transient laboratory flume experiments, ranging from transcritical steady flow to dam-break flows around obstacles and complex beds. The transient water surface was measured using a commercial-grade RGB-D sensing device which allows to capture a succession of color-coded point clouds at a high frequency. These experimental measurements are compared with 2D shallow water simulations carried out with an extensively tested finite volume solver. Results asses the suitability of this dataset to perform as benchmark tests, identifying potential limitations of current and future models.

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.

Microtopography is recognised as one of the morphological features which controls runoff generation, surface hydrodynamics, and surface runoff hydrological response. The spatial scales of microtopography are orders of magnitude smaller than typical hydrological domains such as hillslopes or catchments. The hydrodynamic response in the presence of microtopography is complex and its impact on hydrological behaviour is inherently a multiscale problem, influenced by a number of processes and features. In particular, the geometrical properties of microtopography, and the ponded volume in relation to rainfall volume play a role at the micro and meso scales, while the hydrological response at a larger “macro” scale depends on how large such spatial macroscale is: at sufficiently small scales, the hydrological response is ill-defined; at very large scales, microtopography may not be relevant. Yet, at some intermediate scales, the hydrological dynamics can be strongly dominated by microtopography.In this work, a state-of-the-art, high-performance shallow water solver is used to simulate rainfall-runoff processes on an idealised catchment, at a spatial resolution which explicitly and completely resolves microtopography. For simplicity, microtopography is modelled as a 2D sine wave, which is superimposed on a planar hillslope. A four-dimensional parameter space is explored, defined by different slopes, different amplitudes and wavelengths for the microtopography, and different rainfall events. The large parameter space, together with the high resolution and the inherent cost of the solver result in a very large computational cost. In consequence, we implement SERGHEI, a parallelised, high-performance shallow water equations solver based on the Kokkos programming framework. SERGHEI enables computations on heterogeneous systems and multiple graphics processor units (GPU), which allows to address very large computational studies such as this one.Rainfall-runoff-infiltration partitioning is evaluated in terms of runoff, infiltration and ponding volumes, as well as in terms of a contingency table of flooded surfaces for a reference smooth surface and a set of rough surfaces with microtopography. The results are compared both globally (for the entire domain) and in a spatially-distributed manner in order to assess at which spatial scales the hydrodynamic heterogeneity manifests itself as an emergent hydrological behaviour. The preliminary results show a non-linear response of hydrological signatures to the different parameters, and a complex dependency across scales.

Vegetation self-organisation in water-limited ecosystems in semi-arid climates has been studied by means of numerical simulation using a set of reaction-diffusion-equations. The predominant approach in such studies, in particular relating to banded vegetation on slopes, has been to study the long-term steady ecohydrological tates on periodic domains forced by steady rainfall. This default modelling setup does not account for the fact that on a hillslope a net runoff loss may exist at the outlet. Moreover, such runoff loss is modulated by rainfall intensity, i.e., increasing rainfall intensity is likely to favour runoff over infiltration, and therefore affect the banded vegetation formation. Additionally, different inter-storm dry periods prompt different responses from the vegetation. One of the properties of semi-arid climates is a highly intermittent and variable precipitation regime, quite often with a few intense events and a larger number of very mild events. Additionally ecohydrological theory recognises that dryland ecosystems are in a quasi-permanent transient condition, exhibiting non-linear and far-from equilibrium responses to boundary conditions and forcings. The mismatch between the default modelling approach and the properties of rainfall in such systems calls for further complexity in the models and in the forcing. We explore the possible effects that particular rainfall properties can have in banded vegetation dynamics. We solve the well-known Rietkerk model together with a zero-inertia approximation of the shallow-water equations for surface flow. A non-periodic domain with an outlet, i.e., a 2D hillslope with a constant slope is used. We perform simulations forced by a set of variations of idealised temporal distributions of rainfall throughout a year. The reference distribution is a periodic signal of constant intensity storms of a single day, separated by dryspells of equal duration. The total annual rainfall was selected as 270 mm, in the range of semi-arid climates. This annual signal is repeated during the entire simulation. Non-periodic rainfall signals were generated by randomising a single rainfall property but ensuring the same annual rainfall. Randomisations of the inter-storm dryspell duration, the storm duration, and the storm intensity were explored. Although this results also in idealised rainfall signals, it allows for systematic analysis of each property. The banded patterns are assessed both in terms of global signatures (biomass, vegetation cover), spatial properties (number of bands, wavelength and bandwidth), and dynamics (migration velocity of the bands). Our results clearly show qualitatively and quantitatively that the simulated banded vegetation has a strong response to rainfall variability. Moreover, the results also show a high sensitivity to the particular succession of events, e.g., a succession of longer than average dryspells can throw the system away from equilibrium. High sensitivity is also observed to the timing of certain individual events. The system responds differently to events which happen early on in the development, or later, when the system is near equilibrium. The simulated response of the system are arguably too volatile, suggesting that improvements in the vegetation model parametrisation and formulation are warranted to better represent dynamics and allow for stability and resilience studies.

Shallow water modelling is a widely used for a vast range of applications in Hydraulics, Hydrology and Environmental Geosciences. It is at the core of most fluvial flood modelling approaches, and increasingly turning into the model of choice for urban flood modelling, coastal modelling and rainfall-runoff hydrological simulation. Shallow water solvers have significantly matured in the last decade, and currently, robust and accurate first-order solvers are widely available. Relevant developments have also been achieved in terms of higher order solvers, based on MUSCL and WENO reconstructions and on Discontinuous Galerkin (DG) schemes. Despite all this, applying shallow water solvers on realistic problems is constrained by the multiscale nature of environmental surface flows, in which flows in large domains are strongly affected by small-scale features of both the topography and the flow fields. This inherently multiscale problem naturally calls for a multiresolution modelling strategy, which is the topic of this contribution. In this work, we explore the application of a multidimensional Discontinuous Galerkin scheme with dynamic mesh adaptivity driven by multiresolution analysis based on wavelets. The scheme harnesses the locality and high-order properties of DG, and makes use of an additional decomposition into the multiwavelet space driving a multiresolution analysis. By assessing the relevance of local features of the solution across scales, mesh adaptivity is triggered. In previous works, the general scheme has been presented and tested. Herein, we test the capabilities of the scheme on well-known benchmark problems for 2D shallow flows, including both laboratory and field scale flows. The results clearly show that the scheme is capable of solving such problems with a high accuracy and that the dynamically adaptive mesh is capable of tracking physically-meaningful interfaces (wetting and drying fronts, transcritical shocks, rotating vortices) accurately. Moreover, the adaptive scheme is capable of providing very high spatial resolution where and when it is required, while keeping the computational cost orders of magnitude lower than what a uniform high resolution mesh would impose. In particular, the results suggest that this type of adaptive scheme produces more efficient meshes than alternative schemes. The results showcase some of the advantages of high-order solvers, especially when combined with adaptive schemes and are a proof-of-concept of the applicability of this type of solvers for realistic problems. Finally, the results also evidence the capability of the adaptive multiresolution strategy to transparently incorporate the properties of the underlying shallow water solver, allowing for improvements on the core scheme to always benefit the adaptive solution.

The artificial Hühnerwasser catchment was built in a post-mining landscape (Brandenburg, Germany) as a field experiment to observe and monitor early-development ecosystems at first catchment scale. Given that the spatial distribution and temporal dynamics of vegetation affects water redistribution across scales, quantifying changes in vegetation distributions is an obvious indicator for state transitions, especially in the context of early ecosystem development. In this work, we present a semi-automatic image analysis algorithm designed to identify vegetation patches during the early ecosystem development of the Hühnerwasser catchment (throughout 10 years) from aerial photography. Furthermore, the algorithm also allows to characterise vegetation cover, describe spatial structures and their temporal evolution. The earliest stages are especially of interest. The structure is therefore characterized by the area of the catchment covered by vegetation, the number of vegetation patches, the mean and maximum patch size and a form factor (area of patch divided by its perimeter). Base data are aerial images with a resolution at the centimeter scale. Because the imagery was obtained under very different lighting conditions and under different stages of plant growth, a luminance correction was applied in order to normalise colors, and thus be able of consistently binarise the images into vegetated-non vegetated maps. Binary maps were generated by setting thresholds for red, green and blue channels to differentiate between vegetation cover and bare soil. Additionally, bare soil areas were also identified using a similar procedure. To evaluate the consistency of the binary images of each channel these images were stacked and compared. For validation, the binary maps were compared to manually digitised vegetation patches for a subset of the data. The performance of the method was tested by using a set of combinations of thresholds and a comparison with manual mapping of vegetation cover at an image subset was made. The blue channel seems to be very sensitive to detect vegetation and a better differentiation of vegetation and dark/wet soil can be achieved by setting the thresholds of the channels in a specific order. The structures derived by the classification into vegetated and bare soil are more important in the early years of ecosystem development. In those years (2007 to 2011) the largest changes took place. As time advances vegetation became less patchy, and a mix of different vegetation spawns. By comparing the areas identified as (green) vegetation and those areas identified as bare soil, it is also possible to discriminate non-green vegetation, such as dry grasses, and thus achieve a minimal level of decomposition of the imagery into plant functional types.

The onset and generation of runoff, and the overall rainfall-runoff transformation, resulting in hillslope and catchment runoff response, are controlled by multiple interacting small-scale processes. Small scale features such as surface microtopography -small variations around the average terrain shape- can govern large scale signatures of runoff dynamics. This is the net result of local heterogeneities in the flow paths and ponding which in turn control the development of the surface water layer and how it connects and flows downslope. It is therefore relevant to understand which microtopographic features may play a governing role in runoff generation dynamics. Given that it is very difficult to assess such processes experimentally in the field, we turn to computational modelling to assess different features, hydrological conditions and the overall response. In this work, we numerically solve a physically-based surface water model (based on the Zero-Intertia approximation of the shallow-water equations) on an idealised hillslope domain, forced by a single pulse of rain. To explore different topographies and microtopographies, we model 1460 surfaces, based on 10 sloping planes (from 0.1% to 10%) on which a sinusoidal microtopography of various amplitudes (from 1 to 10 cm) and wavelengths (from 15 to 200 cm) is overlaid. In a previous proof-of-concept work, we showed how these microtopograhies have an impact on rainfall-runoff-infiltration partitioning and generate different runoff regimes from disconnected flow to steady sheet flow. In this contribution, we extend our analysis to include a more realistic, time-dependent infiltration capacity, and therefore explore the effects this has in the process of ponding and establishing surface flow connectivity. We extend the number of surfaces (within the same ranges) to better observe the different runoff regimes. We quantitatively assess the results mainly in terms of the increase in total infiltration in the presence of microtopography relative to a smooth plane, and qualitatively in terms of the generated runoff regimes. The results show that microtopography increases total infiltration (up to six times in our simulations) over the whole domain relative to a smooth plane and there is a strong non-linear dependency of infiltration and runoff on slope and on the ratio of the characteristic wavelength and amplitude of microtopography. Moreover, three characteristic regimes of influence of microtopography exist: one in which microtopography plays a negligible role, another in which microtopography increases infiltration, but the particular microtopography features are not very relevant, and one regime in which small changes in microtopography generate significant variations on infiltration. Such regimes are the result of the interplay between small (microtopography) and large scale (slope) system features. Finally, the results also show that the time-dependent infiltration capacity can enhance the effect of microtopography on infiltration. From a modelling perspective, these results hint that neglecting microtopography and time-dependent infiltration in hydrological modelling can lead to an underestimation of infiltration and an overestimation of runoff. The coupled analysis of spatial hydrodynamics and hydrological signatures suggests that the latter can be interpreted and explained by the spatiotemporal variations triggered by surface connectivity.

Surface flows of hydrological interest, including overland flow, runoff, river and channel flow and flooding have received significant attention from modellers in the past 30 years. A growing effort to address these complex environmental problems is in place in the scientific community. Researchers have studied and favoured a plethora of techniques to approach this issue, ranging from very simple empirically-based mathematical models, to physically-based, deductive and very formal numerical integration of systems of partial-differential equations. In this work, we review two families of methods: cell-based simulators – later called Cellular Automata – and Finite Volume solvers for the Zero-Inertia equation, which we show to converge into a single methodology given appropriate choices. Furthermore, this convergence, mathematically shown in this work, can also be identified by critically reviewing the existing literature, which leads to the conclusion that two methods originating from different reasoning and fundamental philosophy, fundamentally converge into the same method. Moreover, acknowledging such convergence allows for some generalisation of properties of numerical schemes such as error behaviour and stability, which, importantly, is the same for the converging methodology, a fact with practical implications. Both the review of existing literature and reasoning in this work attempts to aid in the effort of synchronising and cross-fertilizing efforts to improve the understanding and the outlook of Zero-Inertia solvers for surface flows, as well as to help in clarifying the possible confusion and parallel developments that may arise from the use of different terminology originating from historical reasons. Moreover, synchronising and unifying this knowledge-base can help clarify model capabilities, applicability and modelling issues for hydrological modellers, specially for those not deeply familiar with the mathematical and numerical details.

Summary One of the most difficult issues in the development of hydrologic models is to find a rigorous source of data and specific parameters to a given problem, on a given location that enable reliable calibration. In this paper, a distributed and physically based model (2D Shallow Water Equations) is used for surface flow and runoff calculations in combination with two infiltration laws (Horton and Green–Ampt) for estimating infiltration in a watershed. This technique offers the capability of assigning a local and time-dependent infiltration rate to each computational cell depending on the available surface water, soil type or vegetation. We investigate how the calibration of parameters is affected by transient distributed Shallow Water model and the complexity of the problem. In the first part of this work, we calibrate the infiltration parameters for both Horton and Green–Ampt models under flat ponded soil conditions. Then, by means of synthetic test cases, we perform a space-distributed sensitivity analysis in order to show that this calibration can be significantly affected by the introduction of topography or rainfall. In the second part, parameter calibration for a real catchment is addressed by comparing the numerical simulations with two different sets of experimental data, corresponding to very different events in terms of the rainfall volume. We show that the initial conditions of the catchment and the rainfall pattern have a special relevance in the quality of the adjustment. Hence, it is shown that the topography of the catchment and the storm characteristics affect the calibration of infiltration parameters.

Rainfall-runoff simulations are increasingly being performed with physically-based and spatially distributed solvers. The current computational and numerical technology enables the use of full shallow water equations solvers to be applied for these type of flow problems. Nonetheless, Zero-Inertia (diffusive wave) solvers have been historically favoured due to their conceptual and mathematical simplicity in comparison to shallow water solvers, with the working assumption that the simplifications introduced by Zero-Inertia will have some assumable impact on accuracy but will also allow for computational efficiency. Since both types of solvers have been primarily developed, benchmarked and compared to each other for fluvial and floodplain simulations, it is relevant to assess t-he relative performance for rainfall-runoff problems. In this work, both solvers are applied to a set of six well known test cases with reference solutions. The performance of the solvers is assessed in terms of global signatures such as hydrographs and flooded areas, but also in terms of spatial distributions of depth and velocity, as well as computational cost. Furthermore, the comparisons are performed across different spatial resolutions. The results show that for rainfall-runoff problems explicit, finite volumes solvers for both equations provide a similar accuracy, but the shallow water solver requires less computational time. The Zero-Inertia solver was found to be less sensitive to mesh refining than the full shallow water solver.

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.

Hydraulic phenomena in open-channel flows are usually described by means of the shallow water equations. This hyperbolic non-linear system can be used for predictive purposes provided that initial and boundary conditions are supplied and the roughness coefficient is calibrated. When calibration is required to fully pose the problem, several strategies can be adopted. In the present work, an inverse technique, useful for any of such purposes, based on the adjoint system and gradient descent is presented. It is used to find the optimal time evolution of the inlet boundary condition required to meet the 20 measured water depth data in an experimental test case of unsteady flow on a beach. The partial differential systems are solved using an upwind finite volume scheme. Several subsets of probes were selected and the quality of the reconstructed boundary tested against the experimental results. The results show that the adjoint technique is useful and robust for these problems, and exhibits some sensitivity to the choice of probes, which can be used to properly select probes in real applications.

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.

Dense granular flows are present in geophysics and in several industrial processes, which has lead to an increasing interest for the knowledge and understanding of the physics which govern their propagation. For this reason, a wide range of laboratory experiments on gravity-driven flows have been carried out during the last two decades. The present work is focused on geomorphological processes and, following previous work, a series of laboratory studies which constitute a further step in mimicking natural phenomena are described and simulated. Three situations are considered with some common properties: a two-dimensional configuration, variable slope of the topography and the presence of obstacles. The setup and measurement technique employed during the development of these experiments are deeply explained in the companion work. The first experiment is based on a single obstacle, the second one is performed against multiple obstacles and the third one studies the influence of a dike on which overtopping occurs. Due to the impact of the flow against the obstacles, fast moving shocks appear, and a variety of secondary waves emerge. In order to delve into the physics of these types of phenomena, a shock-capturing numerical scheme is used to simulate the cases. The suitability of the mathematical models employed in this work has been previously validated. Comparisons between computed and experimental data are presented for the three cases. The computed results show that the numerical tool is able to predict faithfully the overall behavior of this type of complex dense granular flow.

Avalanches, debris flows and other types of gravity-driven granular flows are a common hazard in mountainous regions. These regions often have human settlements in the lower parts of valleys, with human structures dangerously exposed to the destructive effects of these geophysical flows. Therefore a scientific effort has been made to understand, model and simulate geophysical granular flows. In order for computer models and simulations to be of predictive value they need to be validated under controlled, yet nature-like conditions. This work presents an experimental study of granular flow over a simplified mountain slope and valley topography. The experimental facility has a rough bed with very high slope at the upstream end and adverse slope on the downstream end, following a parabolic profile. Obstacles are present in the lower regions. Transient measurements of the moving granular surfaces were taken with a consumer-grade RGB-D sensor, providing transient 2D elevation fields around the obstacles. Three experimental configurations were tested, with semispheres of different diameters and a square dike obstacle. The experimental results are very consistent and repeatable. The quantitative, transient and two-dimensional data for all three experiments constitute excellent benchmarking tests for computational models, such as the one presented in a companion paper. A consumer grade RGB-D sensor is used to measure fast transient granular flow.Three highly transient granular flow experiments with obstacles are presented.The technique allows to acquire 2D transient results from the experiments with ease and low cost.The morphology of highly transient and local flow features such as shocks can be detailedly measured.

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.

Summary Richards equation is a non-linear partial differential equation that describes flow in porous media. To solve it, numerical methods that need to be conservative, stable, accurate and efficient, are required. Finite volume methods have not been reported as widely as finite difference or finite element methods. This work is focused on providing numerical results and analysis of several finite volume schemes in one dimension. The formulation of time discretization schemes is revisited, a stability analysis is performed, and analytical and experimental benchmakrs are provided.