Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 8. Interface and Common Curve Dynamics

Revisiting Surface-Subsurface Exchange at Intertidal Zone with a Coupled 2D Hydrodynamic and 3D Variably-Saturated Groundwater Model

A new high-performance numerical model (Frehg) is developed to simulate water flow in shallow coastal wetlands. Frehg solves the 2D depth-integrated, hydrostatic, Navier–Stokes equations (i.e., shallow-water equations) in the surface domain and the 3D variably-saturated Richards equation in the subsurface domain. The two domains are asynchronously coupled to model surface-subsurface exchange. The Frehg model is applied to evaluate model sensitivity to a variety of simplifications that are commonly adopted for shallow wetland models, especially the use of the diffusive wave approximation in place of the traditional Saint-Venant equations for surface flow. The results suggest that a dynamic model for momentum is preferred over diffusive wave model for shallow coastal wetlands and marshes because the latter fails to capture flow unsteadiness. Under the combined effects of evaporation and wetting/drying, using diffusive wave model leads to discrepancies in modeled surface-subsurface exchange flux in the intertidal zone where strong exchange processes occur. It indicates shallow wetland models should be built with (i) dynamic surface flow equations that capture the timing of inundation, (ii) complex topographic features that render accurate spatial extent of inundation, and (iii) variably-saturated subsurface flow solver that is capable of modeling moisture change in the subsurface due to evaporation and infiltration.

Using a Distributed Hydrologic Model to Improve the Green Infrastructure Parameterization Used in a Lumped Model

Stormwater represents a complex and dynamic component of the urban water cycle. Hydrologic models have been used to study pre- and post-development hydrology, including green infrastructure. However, many of these models are applied in urban environments with very little formal verification and/or benchmarking. Here we present the results of an intercomparison study between a distributed model (Gridded Surface Subsurface Hydrologic Analysis, GSSHA) and a lumped parameter model (the US Environmental Protection Agency (EPA) Storm Water Management Model, EPA-SWMM) for an urban system. The distributed model scales to higher resolutions, allows for rainfall to be spatially and temporally variable, and solves the shallow water equations. The lumped model uses a non-linear reservoir method to determine runoff rates and volumes. Each model accounts for infiltration, initial abstraction losses, but solves the watershed flow equations in a different way. We use an urban case study with representation of green infrastructure to test the behavior of both models. Results from this case study show that when calibrated, the lumped model is able to represent green infrastructure for small storm events at lower implementation levels. However, as both storm intensity and amount of green infrastructure implementation increase, the lumped model diverges from the distributed model, overpredicting the benefits of green infrastructure on the system. We performed benchmark test cases to evaluate and understand key processes within each model. The results show similarities between the models for the standard cases for simple infiltration. However, as the domain increased in complexity the lumped model diverged from the distributed model. This indicates differences in how the models represent the physical processes and numerical solution approaches used between each. When the distributed model results were used to modify the representation of impermeable surface connections within the lumped model, the results were improved. These results demonstrate how complex, distributed models can be used to improve the formulation of lumped models.

Estimating River Conductance from Prior Information to Improve Surface-Subsurface Model Calibration

Most groundwater models simulate stream-aquifer interactions with a head-dependent flux boundary condition based on a river conductance (CRIV). CRIV is usually calibrated with other parameters by history matching. However, the inverse problem of groundwater models is often ill-posed and individual model parameters are likely to be poorly constrained. Ill-posedness can be addressed by Tikhonov regularization with prior knowledge on parameter values. The difficulty with a lumped parameter like CRIV, which cannot be measured in the field, is to find suitable initial and regularization values. Several formulations have been proposed for the estimation of CRIV from physical parameters. However, these methods are either too simple to provide a reliable estimate of CRIV, or too complex to be easily implemented by groundwater modelers. This paper addresses the issue with a flexible and operational tool based on a 2D numerical model in a local vertical cross section, where the river conductance is computed from selected geometric and hydrodynamic parameters. Contrary to other approaches, the grid size of the regional model and the anisotropy of the aquifer hydraulic conductivity are also taken into account. A global sensitivity analysis indicates the strong sensitivity of CRIV to these parameters. This enhancement for the prior estimation of CRIV is a step forward for the calibration and uncertainty analysis of surface-subsurface models. It is especially useful for modeling objectives that require CRIV to be well known such as conjunctive surface water-groundwater use.

A Hyperbolic–Elliptic Model Problem for Coupled Surface–Subsurface Flow

We consider a model problem for coupled surface–subsurface flow. The model consists of a nonlinear kinematic wave equation for the surface fluid’s height and a Brinkman model that governs fluid velocity and pressure for subsurface dynamics. For this coupled hyperbolic–elliptic model we establish the existence of weak solutions. The proof is based on a viscous approximation and the method of compensated compactness by virtue of appropriate energy estimates. To solve the coupled problem numerically, a finite volume method is applied. The numerical scheme is used to illustrate the influence of the Brinkman parameter on the coupled flow pattern for infiltration scenarios.

Flow-Through Stream Modeling with MODFLOW and MT3D: Certainties and Limitations

This paper aims to assess MODFLOW and MT3D capabilities for simulating the spread of contaminants from a river exhibiting an unusual relationship with an alluvial aquifer, with the groundwater head higher than the river head on one side and lower on the other (flow-through stream). A series of simulation tests is conducted using a simple hypothetical model so as to characterize and quantify these limitations. Simulation results show that the expected contaminant spread could be achieved with a specific configuration composed of two sets of parameters: (1) modeled object parameters (hydraulic groundwater gradient, hydraulic conductivity values of aquifer and streambed), and (2) modeling parameters (vertical discretization of aquifer, horizontal refinement of stream modeled with River [RIV] package). The influence of these various parameters on simulation results is investigated, and potential complications and errors are identified. Contaminant spread from stream to aquifer is not always reproduced by MT3D due to the RIV package's inability to simulate lateral exchange fluxes between stream and aquifer. This paper identifies the need for a MODFLOW streamflow package allowing lateral stream-aquifer interactions and streamflow routine calculations. Such developments could be of particular interest for modeling contaminated flow-through streams.

Averaging Theory for Description of Environmental Problems: What Have We Learned?

Advances in Water Resources has been a prime archival source for implementation of averaging theories in changing the scale at which processes of importance in environmental modeling are described. Thus in celebration of the 35th year of this journal, it seems appropriate to assess what has been learned about these theories and about their utility in describing systems of interest. We review advances in understanding and use of averaging theories to describe porous medium flow and transport at the macroscale, an averaged scale that models spatial variability, and at the megascale, an integral scale that only considers time variation of system properties. We detail physical insights gained from the development and application of averaging theory for flow through porous medium systems and for the behavior of solids at the macroscale. We show the relationship between standard models that are typically applied and more rigorous models that are derived using modern averaging theory. We discuss how the results derived from averaging theory that are available can be built upon and applied broadly within the community. We highlight opportunities and needs that exist for collaborations among theorists, numerical analysts, and experimentalists to advance the new classes of models that have been derived. Lastly, we comment on averaging developments for rivers, estuaries, and watersheds.

Averaging Theory for Description of Environmental Problems: What Have We Learned?

Advances in Water Resources has been a prime archival source for implementation of averaging theories in changing the scale at which processes of importance in environmental modeling are described. Thus in celebration of the 35th year of this journal, it seems appropriate to assess what has been learned about these theories and about their utility in describing systems of interest. We review advances in understanding and use of averaging theories to describe porous medium flow and transport at the macroscale, an averaged scale that models spatial variability, and at the megascale, an integral scale that only considers time variation of system properties. We detail physical insights gained from the development and application of averaging theory for flow through porous medium systems and for the behavior of solids at the macroscale. We show the relationship between standard models that are typically applied and more rigorous models that are derived using modern averaging theory. We discuss how the results derived from averaging theory that are available can be built upon and applied broadly within the community. We highlight opportunities and needs that exist for collaborations among theorists, numerical analysts, and experimentalists to advance the new classes of models that have been derived. Lastly, we comment on averaging developments for rivers, estuaries, and watersheds.

TCAT Analysis of Capillary Pressure in Non-equilibrium, Two-fluid-phase, Porous Medium Systems

Standard models of flow of two immiscible fluids in a porous medium make use of an expression for the dependence of capillary pressure on the saturation of a fluid phase. Data to support the mathematical expression is most often obtained through a sequence of equilibrium experiments. In addition to such expressions being hysteretic, recent experimental and theoretical studies have suggested that the equilibrium functional forms obtained may be inadequate for modeling dynamic systems. This situation has led to efforts to express relaxation of a system to an equilibrium capillary pressure in relation to the rate of change of saturation. Here, based on insights gained from the thermodynamically constrained averaging theory (TCAT) we propose that dynamic processes are related to changes in interfacial area between phases as well as saturation. A more complete formulation of capillary pressure dynamics is presented leading to an equation that is suitable for experimental study.