Overland Flow Module
Note that this module is not a standard part of HYDRUS (2D/3D) or version 5 of HYDRUS. It is a nonstandard extension that we share with HYDRUS users without guaranteeing its numerical stability and robustness.
Warning: This boundary condition, i.e., the atmospheric boundary condition with overland flow, is less numerically stable than the regular atmospheric boundary condition!
Water flow and transport on a hillslope is a complex nonlinear problem. Precipitation water infiltrates into the soil profile at a rate that is equal to the rainfall rate until the soil infiltration capacity is reached. Surface runoff is generated once the soil infiltration capacity is exceeded. Surface runoff redistributes water at the land surface and moves it to lower parts of the hillside where it can infiltrate providing there is larger soil infiltration capacity. HYDRUS software package (its twodimensional computational module) (Šimůnek et al., 2006) has been modified so that it can now simulate overland flow. For that purpose the existing numerical solver for subsurface flow was coupled with the newly developed overland flow routine. The updated HYDRUS program was tested using multiple examples given below.
The overland flow module does not consider solute transfer from the soil into the surface water layer present during overland flow. Infiltrating water from the surface layer is assumed to have concentration equal to the specified boundary condition concentration.
Download a brief description of implementation of overland flow into HYDRUS, as well as selected test examples below (pdf).
Download the executable module h2d_calc.exe, which considers overland flow (HYDRUS Version 1, (Version 2, (Version 3), and (Version 5). To use this module, copy h2d_calc.exe into the folder where HYDRUS (2D/3D) is installed (After first making a backup of the standard h2d_calc.exe for future use!).
 Project Group: Overland Flow
 Description: Examples demonstrating the use of the special module of HYDRUS2D that considers overland flow
 Availability: Download HYDRUS projects now (Version 1, Version 2, Version 3, and Version 5) (24.3 MB)
Flow Examples
Project

Description

Test1

Transect dimensions: 100*0.5 m, q=0.00666 cm/s, N=201, T=600 s, slope=0.01, n=0.01.+ Regular Hydrus2d is run without the overland flow. Excess water is removed instantaneously.

Test2

The same conditions as for Test1, but with the enabled overland flow. Loam with very low Ks=2.8889e09 cm/s. Comparison with the analytical solution.

Test2a

The same conditions as for Test2, but with Ks=2.8889e06 cm/s, T=300 s, and simulation time = 3600 s. This run considers larger infiltration and also simulates the overland flow recession.

Test2b

The same conditions as for Test2a, but with Ks=2.8889e05 cm/s.

Test2c

The same conditions as for Test2b, but with roughness of 0.05 for nodes with x < 50 m and 0.01 for nodes with x > 50m.

Test2d

The same conditions as for Test2a, but with evaporation.

Test3

The same conditions as for Test2, but with Ks=2.8889e04 cm/s, i.e., regular loam, T=300 s, and simulation time of 3600 s.

Test4

Surface runoff with multiple rainstorms (otherwise the same conditions as for Test3). Transect dimensions: 100*0.5 m, q=0.00666 cm/s, N=201, T=600 s, slope=0.01, n=0.01, ET=0.4 cm/d.

Test5

The same conditions as for Test3, but with variable slope, i.e., Ks=2.8889e04 cm/s, regular loam, T=300 s, and simulation time of 3600 s.

Test6

The same conditions as for Test3, but with inflow at the upper end of the slope, i.e., Ks=2.8889e04 cm/s, regular loam, T=300 s, and simulation time of 3600 s.

Test6s

The same conditions as for Test6, but with solute transport, i.e., Ks=2.8889e04 cm/s, regular loam, T=300 s, and simulation time of 3600 s.

MultiLay

The same conditions as for Test3, but with Ks=2.8889e02 cm/s for the material in the middle of the transect. This run generates overland flow in one section of the transport domain and allows infiltration in another.

MultiLaZ

The same conditions as for MultiLay, but with the slope in the opposite direction.

MultiMat

The same conditions as for MultiLay, but with the each material repeated four times within the transect.

Transport Examples
Project

Description

Test2Sr

The same conditions as for Test2, but with T=300 s, and simulation time T_end=3600 s. Solute of unit concentration in rainfall in the top half of the domain.

Test2bSr

The same conditions as for TestSr, but with Ks=2.8889e05 cm/s. T=300 s, T_end=3600 s. Solute of unit concentration in rainfall in the top half of the domain.

Test2Si

Uphill inflow (h_Top=1 cm) with a concentration of 0.5 (c=0.5) for T=300 s, and simulation time T_end=3600 s.

Test2Sri

Both uphill inflow (h_Top=1 cm) with a concentration of 0.5 (c=0.5) and rainfall with a unit concentration for T=300 s. Simulation time T_end=3600 s.

Additional Examples with Irregular Geometries
Project

Description

Irreg

Transect dimensions: 100*2.0 m, q=0.00666 cm/s, N=544, T=600 s, simulation time = 3600 s, average slope=0.02, n=0.01, regular loam. Irregular surface of the transport domain.

Irreg1

Transect dimensions: 50*1.0 m, q=0.00666 cm/s, N=425, T=600 s, simulation time = 3600 s, average slope=0.08, n=0.01, regular loam. Irregular surface of the transport domain.

Irreg2

The same conditions as Irreg1, but with fixed vertical discretization at the soil surface using internal lines.

Irreg3

The same conditions as Irreg2, but with finer discretization.

Irreg4

The same conditions as Irreg3, but with time units of days.

Irreg5

The same conditions as Irreg4, but with multiple rainstorms.

+ q  rainfall, N  number of surface nodes, T  duration of the rainfall, T_end  simulation time, n – surface roughness, h_Top  inflow depth.
References
The mathematical description of the module:
 Šimůnek, J., HYDRUS2D Code Modification: Modeling Overland Flow and Dynamic Interactions Between Plants and Water Flow in a Hillslope Transect, Idaho National and Environmental Laboratory, Final report for project under contract number 00021013, 55 pp., 2003.
 van Genuchten, M. Th., and J. Šimůnek, Integrated modeling of vadose zone flow and transport processes, Proc. Unsaturated Zone Modelling: Progress, Challenges and Applications, Eds. R. A. Feddes, G. H. de Rooij, and J. C. van Dam, Wageningen UR Frontis Series, Vol. 6, Chapter 2, pp. 37 69, xxi, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004.
 Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Modeling Subsurface Water Flow and Solute Transport with HYDRUS and Related Numerical Software Packages, In: GarciaNavarro & Playán (eds.), Numerical Modelling of Hydrodynamics for Water Resources, An International Workshop, Centro Politecnico Superior, University of Zaragoza Spain, June 1821 2007. Taylor & Francis Group, London, ISBN 9780415440561, 95114, 2007.
The Overland module has been extensively used in multiple studies, including:
 Köhne, J. M., T. Wöhling, V. Pot, P. Benoit, S. Leguédois, Y. Le Bissonnais, and J. Šimůnek, Coupled simulation of surface runoff and soil water flow using multiobjective parameter estimation, J. of Hydrology, 403, 141156, 2011.
 Chen, L., J. Šimůnek, S. A. Bradford, H. Ajami, and M. B. Meles, A computationally efficient hydrologic modeling framework to simulate surfacesubsurface hydrological processes at the hillslope scale, Journal of Hydrology, 614, 128539, 15 p., doi: 10.1016/j.jhydrol.2022.128539, 2022.
 Chen, L., J. Šimůnek, S. A. Bradford, H. Ajami, and M. B. Meles, Coupling water, solute, and sediment transport into a new computationally efficient hydrologic model, Journal of Hydrology, 628, 130495, 14 p., doi: 10.1016/j.jhydrol.2023.130495, 2023.