Ross scheme, Newton–Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation

Maina, Fadji Zaouna; Ackerer, Philippe

doi:10.5194/hess-21-2667-2017

Cited by 14 publications

(10 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To compute these processes, CLM uses soil moisture calculated by ParFlow, vegetation characteristics (the type of land use and land cover as well as its physical properties), and the meteorological forcing calculated by WRF. (Homer et al, 2015) and (b) geology (Jennings et al, 1977) and topography (United States Geological Survey, USGS) of the Cosumnes watershed.…”

Section: Numerical-modeling Methodsmentioning

confidence: 99%

Sensitivity of meteorological-forcing resolution on hydrologic variables

Maina

Siirila‐Woodburn

Vahmani

2020

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. Projecting the spatiotemporal changes in water resources under a no-analog future climate requires physically based integrated hydrologic models which simulate the transfer of water and energy across the earth's surface. These models show promise in the context of unprecedented climate extremes given their reliance on the underlying physics of the system as opposed to empirical relationships. However, these techniques are plagued by several sources of uncertainty, including the inaccuracy of input datasets such as meteorological forcing. These datasets, usually derived from climate models or satellite-based products, are typically only resolved on the order of tens to hundreds of kilometers, while hydrologic variables of interest (e.g., discharge and groundwater levels) require a resolution at much smaller scales. In this work, a high-resolution hydrologic model is forced with various resolutions of meteorological forcing (0.5 to 40.5 km) generated by a dynamical downscaling analysis from the regional climate model Weather Research and Forecasting (WRF). The Cosumnes watershed, which spans the Sierra Nevada and Central Valley interface of California (USA), exhibits semi-natural flow conditions due to its rare undammed river basin and is used here as a test bed to illustrate potential impacts of various resolutions of meteorological forcing on snow accumulation and snowmelt, surface runoff, infiltration, evapotranspiration, and groundwater levels. Results show that the errors in spatial distribution patterns impact land surface processes and can be delayed in time. Localized biases in groundwater levels can be as large as 5–10 m and 3 m in surface water. Most hydrologic variables reveal that biases are seasonally and spatially dependent, which can have serious implications for model calibration and ultimately water management decisions.

show abstract

Section: Numerical-modeling Methodsmentioning

confidence: 99%

Sensitivity of meteorological-forcing resolution on hydrologic variables

Maina

Siirila‐Woodburn

Vahmani

2020

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

“…For example, when θ is taken as the primary variable, the newly updated soil moisture might exceed unity, then the pressure head instead will take the primary role for recalculation. Although improvements were made to minimize such deficiency (Hassane Maina & Ackerer, ; Kees & Miller, ; Krabbenhøft, ), the performance of these techniques tends to be problem specific. Moreover, these methods are restricted to Newton–Raphson iteration schemes.…”

Section: Different Forms Of Rresmentioning

confidence: 99%

“…The saturation degree and the Kirchhoff potential (Ross & Bristow, ) are used as the primary variables for unsaturated and saturated nodes, respectively. Previous research has examined the performance the of Ross method (Crevoisier et al, ; Hassane Maina & Ackerer, ; Varado, Braud, & Ross, ; Varado, Braud, Ross, & Haverkamp, ) with problems involving a wide range of soil constitutive models, initial conditions, and boundary conditions. It is shown that the Ross model is intrinsically mass conservative, and can be computationally less expensive than the conventional iterative methods.…”

Section: Iterative and Noniterative Modelsmentioning

confidence: 99%

“…The linearized moisture‐based RRE and mixed form RRE are cost‐effective compared to traditional iterative methods, although the former model is restricted to unsaturated flow only. Hassane Maina and Ackerer () made comparison between the traditional iterative mixed form RRE model and the noniterative Ross method, and highlighted the importance of adjusting time steps using temporal truncation errors for both iterative and noniterative models.…”

Section: Iterative and Noniterative Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

et al. 2019

View full text Add to dashboard Cite

Modeling variably saturated flow in the vadose zone is of vital importance to many scientific fields and engineering applications. Richardson-Richards equation (RRE, which is conventionally known as Richards' equation) is often chosen to physically represent the fluxes in the vadose zone when the accurate characterization of the soil water dynamics is required. Being a highly nonlinear partial differential equation, RRE is often solved numerically. Although there are mature software and codes available for simulating variably saturated flow by solving RRE, the numerical solution of RRE is nevertheless computationally expensive.Moreover, sometimes the robustness and the efficiency of RRE-based models can deteriorate rapidly when certain unfavorable conditions are met. These demerits of RRE hinder its application on large-scale vadose zone hydrology problems and uncertainty quantification, both of which requires many runs of the prediction model. To address these challenges, the accuracy, convergence, and efficiency of the numerical schemes of RRE should be further improved by testing a wide variety of cases covering different initial conditions, boundary conditions, and soil types. We reviewed and highlighted several critical issues related to the numerical modeling of RRE, including spatial and temporal discretization, the different forms of RREs, iterative and noniterative schemes, benchmark solutions, and available software and codes. Based on the review, we summarize the challenges and future work for solving RRE numerically.

show abstract

“…This is why significant efforts have been made in last decades on the development of advanced and appropriate numerical techniques for solving this equation (i.e. Celia et al, 1990;Farthing et al, 2003;Li et al, 2007;Ji et al, 2008;Fahs et al, 2009;Hassane Maina and Ackerer, 2017;Suk and Park, 2019;Ngo-Cong et al, 2020).…”

Section: Introductionmentioning

confidence: 99%