Adaptive meshing in a mixed regime hydrologic simulation model

Pettway, Jackie S.; Schmidt, Joseph H.; Stagg, A. K.

doi:10.1007/s10596-010-9179-1

Cited by 7 publications

(7 citation statements)

References 31 publications

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“…The latter problem can be dealt with by either crushing it with massive parallel computing (Kollet, 2010), or by reducing it by avoiding redundant computations. This can be done by exploiting patterns of similarity in time via adaptive time stepping (Minkoff and Kridler, 2006), in space by adaptive gridding (Pettway et al, 2010;Berger and Oliger, 1984), or both (Miller et al, 2006). Due to their generality, adaptive methods have been used to improve distributed modelling of a large variety of systems such as the universe (Teyssier, 2002), the atmosphere (Bacon et al, 2000;Aydogdu et al, 2019), oceans (Pain et al, 2005), and groundwater systems (Miller et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Adaptive clustering: A method to analyze dynamical similarity and to reduce redundancies in distributed (hydrological) modeling

Ehret

Pruijssen

Bortoli

et al. 2020

Preprint

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Abstract. In this paper we propose adaptive clustering as a new way to analyse hydrological systems and to reduce computational efforts of distributed modelling, by dynamically identifying similar model elements, clustering them and inferring dynamics from just a few representatives per cluster. It is based on the observation that while hydrological systems generally exhibit large spatial variability of their properties, requiring distributed approaches for analysis and modelling, there is also redundancy, i.e. there exist typical and recurrent combinations of properties, such that sub systems exist with similar properties, which will exhibit similar internal dynamics and produce similar output when in similar initial states and when exposed to similar forcing. Being dependent on all these factors, similarity is hence a dynamical rather than a static phenomenon, and it is not necessarily a function of spatial proximity. We explain and demonstrate adaptive clustering at the example of a conceptual, yet realistic and distributed hydrological model, fit to the Attert basin in Luxembourg by multi-variate calibration. Based on normalized and binned transformations of model states and fluxes, we first calculated time series of Shannon information entropy to measure dynamical similarity (or redundancy) among sub systems. This revealed that indeed high redundancy exists, that its magnitude differs among variables, that it varies with time, and that for the Attert basin the spatial patterns of similarity are mainly controlled by geology and precipitation. Based on these findings, we integrated adaptive clustering into the hydrological model. It constitutes a shell around the model hydrological process core and comprises: Clustering of model elements, choice of cluster representatives, mapping of results from representatives to recipients, comparison of clusterings over time to decide when re-clustering is advisable. Adaptive clustering, compared to a standard, full-resolution model run used as a virtual reality truth, reduced computation time to one fourth, when accepting a decrease of modelling quality, expressed as Nash–Sutcliffe efficiency of sub catchment runoff, from 1 to 0.84. We suggest that adaptive clustering is a promising tool for both system analysis, and for reducing computation times of distributed models, thus facilitating applications to larger systems and/or longer periods of time. We demonstrate the potential of adaptive clustering at the example of a hydrological system and model, but it should apply to a wide range of systems and models across the earth system sciences. Being dynamical, it goes beyond existing static methods used to increase model performance, such as lumping, and it is compatible with existing dynamical methods such as adaptive time-stepping or adaptive gridding. Unlike the latter, adaptive clustering does not require adjacency of the sub systems to be joined.

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Section: Introductionmentioning

confidence: 99%

Adaptive clustering: A method to analyze dynamical similarity and to reduce redundancies in distributed (hydrological) modeling

Ehret

Pruijssen

Bortoli

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Instead, groups of model elements are dynamically established and adjusted during model runtime by identifying and exploiting patterns of similarity in either time or space. Adaptive time stepping (Minkoff and Kridler, 2006) exploits patterns of similarity in time, and adaptive gridding (Pettway et al, 2010;Berger and Oliger, 1984) exploits patterns of similarity in space; combinations of both approaches are possible (Miller et al, 2006). Due to their generality, adaptive methods have been used to improve distributed modelling of a large variety of systems such as the universe (Teyssier, 2002), the atmosphere (Bacon et al, 2000;Aydogdu et al, 2019), oceans (Pain et al, 2005, and groundwater systems (Miller et al, 2006).…”

mentioning

confidence: 99%

Adaptive clustering: reducing the computational costs of distributed (hydrological) modelling by exploiting time-variable similarity among model elements

Ehret¹,

Pruijssen²,

Bortoli³

et al. 2020

Hydrol. Earth Syst. Sci.

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Abstract. In this paper we propose adaptive clustering as a new method for reducing the computational efforts of distributed modelling. It consists of identifying similar-acting model elements during runtime, clustering them, running the model for just a few representatives per cluster, and mapping their results to the remaining model elements in the cluster. Key requirements for the application of adaptive clustering are the existence of (i) many model elements with (ii) comparable structural and functional properties and (iii) only weak interaction (e.g. hill slopes, subcatchments, or surface grid elements in hydrological and land surface models). The clustering of model elements must not only consider their time-invariant structural and functional properties but also their current state and forcing, as all these aspects influence their current functioning. Joining model elements into clusters is therefore a continuous task during model execution rather than a one-time exercise that can be done beforehand. Adaptive clustering takes this into account by continuously checking the clustering and re-clustering when necessary. We explain the steps of adaptive clustering and provide a proof of concept at the example of a distributed, conceptual hydrological model fit to the Attert basin in Luxembourg. The clustering is done based on normalised and binned transformations of model element states and fluxes. Analysing a 5-year time series of these transformed states and fluxes revealed that many model elements act very similarly, and the degree of similarity varies strongly with time, indicating the potential for adaptive clustering to save computation time. Compared to a standard, full-resolution model run used as a virtual reality “truth”, adaptive clustering indeed reduced computation time by 75 %, while modelling quality, expressed as the Nash–Sutcliffe efficiency of subcatchment runoff, declined from 1 to 0.84. Based on this proof-of-concept application, we believe that adaptive clustering is a promising tool for reducing the computation time of distributed models. Being adaptive, it integrates and enhances existing methods of static grouping of model elements, such as lumping or grouped response units (GRUs). It is compatible with existing dynamical methods such as adaptive time stepping or adaptive gridding and, unlike the latter, does not require adjacency of the model elements to be joined. As a welcome side effect, adaptive clustering can be used for system analysis; in our case, analysing the space–time patterns of clustered model elements confirmed that the hydrological functioning of the Attert catchment is mainly controlled by the spatial patterns of geology and precipitation.

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“…Indeed even one-dimensional approximations have shown that they can pose a significant computational burden and benefit from adaptive resolution, depending on the combination of soil properties, initial conditions, and boundary forcing . However, despite the introduction of sophisticated adaption techniques that have have matured in other computational mechanics fields (Schwab, 1998;Rannacher, 2001;Fidkowski and Darmofal, 2011), including so-called h adaption which modifies the local mesh spacing (Pettway et al, 2010) as well as methods that vary the local mesh spacing and approximation order (i.e., h-p adaption) (Solin and Kuraz, 2011), spatial adaption for Richards' equation is still not widely used in practice.…”

Section: Spatial Discretizationmentioning

confidence: 99%

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Farthing

Ogden

2017

Soil Science Soc of Amer J

262

138

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The flow of water in partially saturated porous media is of importance in fields such as hydrology, agriculture, environment and waste management. It is also one of the most complex flows in nature. The Richards' equation describes the flow of water in an unsaturated porous medium due to the actions of gravity and capillarity neglecting the flow of the non-wetting phase, usually air. Analytical solutions of Richards' equation exist only for simplified cases, so most practical situations require a numerical solution in one-two-or threedimensions, depending on the problem and complexity of the flow situation. Despite the fact that the first reasonably complete conservative numerical solution method was published in the early 1990s, the numerical solution of the Richards' equation remains computationally expensive and in certain circumstances, unreliable. A universally robust and accurate solution methodology has not yet been identified that is applicable across the range of soils, initial and boundary conditions found in practice. Existing solution codes have been modified over years to attempt to increase robustness. Despite theoretical results on the existence of solutions given sufficiently regular data and constitutive relations, our numerical methods often fail to demonstrate reliable convergence behavior in practice, especially for higher-order methods. Because of robustness, the lack of higher-order accuracy and computational expense, alternative solution approaches or methods are needed. There is also a need for better documentation of improved solution methodologies and benchmark test problems to facilitate consistent advances and avoid re-inventing of the wheel.T his review paper is intended to serve as a touchstone on the state of the science of calculating the flow of water through unsaturated porous media. As active researchers we believe it is good to occasionally take stock in what has been accomplished up to date, where things may be headed, and what important issues remain. This review concentrates on computational modeling of flow through the unsaturated zone via Richards' equation.This effort can help provide some focus to the research community and serve to help propel new research forward, particularly by those just joining the field. There are many practical problems that require calculation of one-, two-, and threedimensional fluxes in the unsaturated zone. For a much broader review of modeling soil processes, we recommend the recent paper from Vereecken et al. (2016). A detailed review of mathematical models of infiltration can be found (Assouline, 2013), while Paniconi and Putti (2015) provide historical perspective and an overview of modeling Richards' equation in the context of catchment hydrology.The equation attributed to Richards (1931) that describes the flow of water through unsaturated porous media under the action of capillarity and gravity was first published by the English mathematician and physicist Lewis Fry Richardson in 1922(Richardson, 1922. Therefore, the equation would r...

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Adaptive meshing in a mixed regime hydrologic simulation model

Cited by 7 publications

References 31 publications

Adaptive clustering: A method to analyze dynamical similarity and to reduce redundancies in distributed (hydrological) modeling

Adaptive clustering: A method to analyze dynamical similarity and to reduce redundancies in distributed (hydrological) modeling

Adaptive clustering: reducing the computational costs of distributed (hydrological) modelling by exploiting time-variable similarity among model elements

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

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