1-D Richards equation or infiltration capacity approaches? A comparative assessment in mesoscale hydrologic modelling across 201 German basins

Soil moisture (SM) infiltration is crucial in hydrological modeling, as it significantly influences runoff, groundwater recharge, and evapotranspiration. This study compares two widely used approaches for modeling SM infiltration in mesoscale hydrology: the one-dimensional Richards equation (1-D RE), which controls vertical flux exchange but is complex and nonlinear, and the infiltration capacity (IC) scheme, which is simpler and only allows downward movement of SM. The challenge in implementing the RE lies in determining effective parameters at the targeted resolution (typically several hundred to thousands of meters) and ensuring computational efficiency. This is because the RE is inherently nonlinear and was developed for much finer scales than those used in typical simulations. As a result, RE-based land surface models (LSMs) have often underperformed compared to those using the IC scheme.

To address this challenge, an experiment was conducted using the mesoscale Hydrologic Model (mHM) equipped with Multiscale Parameter Regionalization (MPR) to parameterize both the RE and IC approaches, keeping everything else equal (Kholis et al. 2024). To improve computational efficiency, Ross’s fast numerical solution was employed, utilizing the Kirchhoff transform to linearize the RE via matric flux potential (MFP). The RE parameterization involved the use of three distinct pedo-transfer functions (PTFs): Cosby for mHM-RE₁, Campbell for mHM-RE₂, and Rawls & Brakensiek for mHM-RE₃. These model parameters were estimated across randomly selected basins in Germany and subsequently validated with streamflow data across 201 basins at multiple resolutions, as well as with soil moisture observations from 46 sites (0-25 cm depth) and 42 sites (25–60 cm and 0–60 cm depths). 

The results demonstrate that mHM-IC and all mHM-RE variants perform comparably well in predicting streamflow. The application of MPR facilitates the transferability of PTF parameters across different scales and areas. Due to its two-way flow mechanism, the mHM-RE variants show better predictability of SM, especially in deeper soil layers. However, for large catchment areas, these variants can be up to six times slower than that with IC. Although the IC approach can sometimes lead to saturation in deeper soil layers, it still provides good predictability for SM anomalies. Importantly, the choice of PTF is critical for the performance of RE models, as parameterization discrepancies, such as overestimated saturated hydraulic conductivity (Ks) and porosity (θs) in mHM-RE₂, can lead to overpredicted SM values, even when streamflow simulations are accurate. This study highlights the potential of mHM-RE for generating transferable parameters and achieving reliable streamflow and SM simulations, provided that appropriate PTFs are carefully selected to minimize parameterization errors. We conclude that the poor performance of RE-based land surface models with respect to streamflow prediction is likely due to deficient parameterization or the use of an inefficient RE solver. 

References:

Kholis, A. N., Kalbacher, T., Rakovec, O., Boeing, F., Cuntz, M., & Samaniego, L. E. (2024). Evaluating Richards equation and infiltration capacity approaches in mesoscale hydrologic modelling. Authorea Preprints. https://doi.org/10.22541/essoar.173532490.04454195/v1