HydroGeoSphere (HGS) is a 3D control-volume finite element groundwater model, and is based on a rigorous conceptualization of the hydrologic system consisting of surface and subsurface flow regimes.

[1][2] The model is designed to take into account all key components of the hydrologic cycle.

For each time step, the model solves surface and subsurface flow, solute and energy transport equations simultaneously, and provides a complete water and solute balance.

It was renamed to HydroGeoSphere in 2002 with the implementation of 2D surface water flow and transport.

In order to accomplish the integrated analysis, HydroGeoSphere utilizes a rigorous, mass conservative modeling approach that fully couples the surface flow and transport equations with the 3-D, variably saturated subsurface flow and transport equations.

HydroGeoSphere assumes that the subsurface flow equation in a porous medium is always solved during a simulation, either for fully saturated or variably saturated flow conditions.

The subsurface flow equation can be expanded to incorporate discrete fractures, a second interacting porous continuum, wells, tile drains and surface flow.

The following assumptions are made for subsurface flow: The Richards’ equation is used to describe three-dimensional transient subsurface flow in a variably saturated porous medium: The fluid flux,

is the volumetric fraction of the total porosity occupied by the porous medium,

is the internal fluid exchange rate (e.g. surface water, wells, and tile drains),

is the relative permeability of the medium calculated as a function of saturation,

HydroGeoSphere's surface water flow component is implemented with the following assumptions: The surface flow components are solved by the following three equations, which are given by the following mass balance equation: coupled with the momentum equations, neglecting inertia terms, for the x-direction: and for the y-direction: where

designates parent species for the case of a decay chain.

Graf [2005] incorporated heat transport within the saturated-zone flow regime into HydroGeoSphere together with temperature-dependent fluid properties, such as viscosity and density.

The model’s capability was successfully demonstrated for the case of thermohaline flow and transport in porous and fractured porous media [Graf and Therrien, 2007].

This work extends the model’s capability to include thermal energy transport in the unsaturated zone and in the surface water, which is considered a key step in the linkage between the atmospheric and hydrologic systems.

A complete description of the physical processes and governing flow and solute transport equations that form the basis of HydroGeoSphere can be found in Therrien et al. [2007] and therefore will not be presented here.

The general equation for variably saturated subsurface thermal energy transport following Molson et al. [1992] is given by:

The surface flow equation is solved on a 2-D finite-element mesh stacked upon a subsurface grid when solving for both domains (i.e. the x- and y-locations of nodes are the same for each layer of nodes).

For superposition, the grid generated for the subsurface domain is mirrored areally for the surface flow nodes, with surface flow node elevations corresponding to the top elevation of the topmost active layer of the subsurface grid.

Note that surface flow node elevations may vary substantially to conform with topography.

However, the assumptions of small slope inherent in the diffusion-wave equation will not allow for modeling of inertial effects.

The discretized surface equation is coupled with the 3-D subsurface flow equation via superposition (common node approach) or via leakage through a surficial skin layer (dual node approach).

For both approaches, fully implicit coupling of the surface and subsurface flow regimes provides an integral view of the movement of water, as opposed to the traditional division of surface and subsurface regimes.

Flux across the land surface is, therefore, a natural internal process allowing water to move between the surface and subsurface flow systems as governed by local flow hydrodynamics, instead of using physically artificial boundary conditions at the interface.

When the subsurface connection is provided via superposition, HydroGeoSphere adds the surface flow equation terms for the 2-D surface mesh to those of the top layer of subsurface nodes.

In that case, the fluid exchange flux, which contains leakance term does not need to be explicitly defined.

HGS also dynamically integrates key components of the hydrologic cycle such as evaporation from bare soil and water bodies, vegetation-dependent transpiration with root uptake, snowmelt and soil freeze/thaw.

Features such as macro pores, fractures, and tile drains can either be incorporated discretely or using a dual-porosity, dual permeability formulation.

Additionally, HydroGeoSphere has been linked to Weather Research and Forecasting, a mesoscale atmospheric model for fully coupled subsurface, surface, and atmospheric simulations.