Preprints
https://doi.org/10.5194/hess-2021-426
https://doi.org/10.5194/hess-2021-426

  08 Sep 2021

08 Sep 2021

Review status: this preprint is currently under review for the journal HESS.

It rains and then? Numerical challenges with the 1D Richards equation in kilometer-resolution land surface modelling

Daniel Regenass1,a, Linda Schlemmer2, Elena Jahr1, and Christoph Schär1 Daniel Regenass et al.
  • 1Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland
  • 2Deutscher Wetterdienst DWD, Offenbach, Germany
  • anow at: Federal Office for Meteorology and Climatology, MeteoSwiss, Zurich Airport, Switzerland

Abstract. Over the last decade kilometer-scale weather predictions and climate projections have become established. Thereby both the representation of atmospheric processes, as well as land-surface processes need adaptions to the higher-resolution. Soil moisture is a critical variable for determining the exchange of water and energy between the atmosphere and the land surface on hourly to seasonal time scales, and a poor representation of soil processes will eventually feed back on the simulation quality of the atmosphere. Especially the partitioning between infiltration and surface runoff will feed back on the hydrological cycle. Several aspects of the coupled system are affected by a shift to kilometer-scale, convection-permitting models. First of all, the precipitation-intensity distribution changes to more intense events. Second, the time-step of the numerical integration becomes smaller. The aim of this study is to investigate the numerical convergence of the one-dimensional Richards Equation with respect to the soil hydraulic model, vertical layer thickness and time-step during the infiltration process. Both regular and non-regular (unequally spaced) grids typical in land surface modelling are considered, using a conventional semi-implicit vertical discretization. For regular grids, results from a highly idealized experiment on the infiltration process show poor numerical convergence for layer thicknesses larger than approximately 5 cm and for time steps greater than 40 s, irrespective of the soil hydraulic model. The velocity of the wetting front decreases systematically with increasing time step and decreasing vertical resolution. For non-regular grids, a new discretization based on a coordinate transform is introduced. In contrast to simpler vertical discretizations, it is able to represent the solution second-order accurate. The results for non-regular grids are qualitatively similar, as a fast increase in layer thickness with depth is equivalent to a lower vertical resolution. It is argued that the sharp gradients in soil moisture around the propagating wetting front must be resolved properly in order to achieve an acceptable numerical convergence of the Richards Equation. Furthermore, it is shown that the observed poor numerical convergence translates directly into a poor convergence of infiltration-runoff partitioning for precipitation time series characteristic of weather and climate models. As a consequence, soil simulations with low resolution in space and time may produce almost twice the amount of surface runoff within 24 hours than their high-resolution counterparts. Our analysis indicates that the problem is particularly pronounced for kilometer-resolution models.

Daniel Regenass et al.

Status: open (until 03 Nov 2021)

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Daniel Regenass et al.

Daniel Regenass et al.

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Short summary
Weather and climate models need to represent the water cycle on land in order to provide accurate estimates of moisture and energy exchange between the land and the atmosphere. Infiltration of water into the soil is often modeled with an equation describing water transport in porous media. Here, we point out some challenges arising in the numerical solution of this equation and show the consequences for the representation of the water cycle in modern weather and climate models.