TY - GEN A1 - Caviedes-Voullième, Daniel A1 - Fernández-Pato, Javier A1 - Hinz, Christoph T1 - Cellular Automata and Finite Volume solvers converge for 2D shallow flow modelling for hydrological modelling T2 - Journal of Hydrology N2 - 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 stud-ied 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 exist-ing 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 develop-ments 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. KW - Surface runoff KW - Zero-inertia equation KW - Shallow-water equations KW - Cellular Automata KW - Finite Volume KW - Diffusive-wave equation Y1 - 2018 UR - https://www.sciencedirect.com/science/article/pii/S0022169418304438 U6 - https://doi.org/10.1016/j.jhydrol.2018.06.021 SN - 0022-1694 VL - 563 SP - 411 EP - 417 ER - TY - CHAP A1 - Caviedes-Voullième, Daniel A1 - Fernández-Pato, Javier A1 - Hinz, Christoph T1 - Zero-Inertia vs full shallow water equations: a comparison for rainfall-runoff modelling T2 - Computational Methods in Water Resources XXII (CMWR 2018), Bridging gaps between data, models, and predictions KW - Shallow water equations KW - Diffusive-wave equation KW - rainfall-runoff Y1 - 2018 UR - https://www.irisa.fr/sage/jocelyne/CMWR2018/pdf/CMWR2018_paper_147.pdf ER - TY - GEN A1 - Caviedes-Voullième, Daniel A1 - Fernández-Pato, Javier A1 - Hinz, Christoph T1 - Performance assessment of 2D Zero-Inertia and Shallow Water models for simulating rainfall-runoff processes T2 - Journal of Hydrology N2 - 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. KW - Surface runoff KW - Runoff generation KW - Pluvial flooding KW - Zero-inertia equation KW - Shallow-water equations KW - Diffusive-wave equation Y1 - 2020 UR - http://www.sciencedirect.com/science/article/pii/S0022169420301232 U6 - https://doi.org/10.1016/j.jhydrol.2020.124663 SN - 0022-1694 VL - 584 ER -