Surface runoff is commonly described in numerical models using either the diffusion wave or kinematic wave equations, which assume that surface runoff occurs as sheet flow with a uniform depth and velocity across the slope. In reality, overland water flow and transport processes are rarely uniform. Local soil topography, vegetation, and spatial soil heterogeneity control directions and magnitudes of water fluxes. These spatially varying surface characteristics can generate deviations from sheet flow such as physical nonequilibrium flow and transport processes that occur only on a limited fraction of the soil surface. In this study, we first adapted the HYDRUS-1D model to solve the diffusion wave equation for overland flow at the soil surface. The numerical results obtained by the new model produced an excellent agreement with an analytical solution for the kinematic wave equation. Additional model tests further demonstrated the applicability of the adapted model to simulate the transport and fate of many different solutes (non-adsorbing tracers, nutrients, pesticides, and microbes) that undergo equilibrium and/or kinetic sorption and desorption and first- or zero-order reactions. HYDRUS-1D includes a hierarchical series of models of increasing complexity to account for both uniform and physical nonequilibrium flow and transport, e.g., dual-porosity and dual-permeability models, up to a dual-permeability model with immobile water. This same conceptualization was adapted to simulate physical nonequilibrium overland flow and transport at the soil surface. The developed model improves our ability to describe nonequilibrium overland flow and transport processes and our understanding of factors that cause this behavior.

A root growth module was adapted and implemented into the HYDRUS software packages to model root growth as a function of different environmental stresses. The model assumes that various environmental factors, as well as soil hydraulic properties, can influence root development under suboptimal conditions. The implementation of growth and stress functions in the HYDRUS software opens the opportunity to derive parameters of these functions from laboratory or field experimental data using inverse modeling. One of the most important environmental factors influencing root growth is soil temperature. The effects of temperature in the root growth module was the first part of the newly developed HYDRUS add-on to be validated by comparing modeling results with measured rooting depths in an aeroponic experimental system with bell pepper (Capsicum annuum L.). The experiment was conducted at root zone temperatures of 7, 17, and 27°C. Inverse optimization was used to estimate a single set of parameters that was found to well reproduce measured time series of rooting depths for all temperature treatments. A sensitivity analysis showed that parameters such as the maximum rooting depth and cardinal temperatures had only a small impact on the model output and can thus be specified using values from the literature without significantly increasing prediction uncertainties. On the other hand, parameters that define the growth rate or the shape of the temperature stress function had a high influence. The root growth module that considers temperature stress only slightly increased the complexity of the standard HYDRUS models.