Technical note: Inference in hydrology from entropy balance considerations

Abstract

Abstract. In this study, the method of inference of macroscale thermodynamic potentials, forces, and exchange coefficients for variably saturated groundwater flow is outlined based on the entropy balance. The theoretical basis of the method of inference is the explicit calculation of the internal entropy production from microscale, thermodynamic flux-force relationships using, e.g., hyper-resolution variably saturated groundwater flow models. Emphasis is placed on the two-scale nature of the entropy balance equation that allows simultaneously incorporating movement equations at the micro-and macroscale. The method is illustrated with simple hydrologic cross sections at steady state and periodic sources/sinks at dynamic equilibrium, and provides a thermodynamic point of view of upscaling in variably saturated groundwater flow. The current limitations in the connection with observable variables and predictive capabilities are discussed, and some perspectives for future research are provided.

Simulating coupled surface–subsurface flows with ParFlow v3.5.0: capabilities, applications, and ongoing development of an open-source, massively parallel, integrated hydrologic model

“…The exchange flux term, q e , may be included in the shallow overland flow continuity equation as the exchange rate term with the subsurface (Eq. 9) in a coupled system (Kollet and Maxwell, 2006). Fig.…”

“…That is, the boundary condition links flow processes in the subsurface with those at the land surface. This boundary condition eliminates the exchange flux and accounts for the movement of the free surface of ponded water at the land surface (Kollet and Maxwell, 2006;Williams and Maxwell, 2011). Many IHMs couple subsurface and surface flows by making use of the exchange flux, q e , model.…”

“…Surface water and subsurface (unsaturated and saturated zones) water are connected components of a hydrologic continuum (Kumar et al, 2009). The recognition that flow systems (i.e., surface and subsurface) are a single integrated resource has stimulated the development of integrated hydrologic models (IHMs), which include codes like ParFlow (Ashby and Falgout, 1996;Kollet and Maxwell, 2006), Hy-droGeoSphere (Therrien and Sudicky, 1996), PIHM (Kumar, 2009), and CATHY (Camporese et al, 2010). These codes explicitly simulate different hydrological processes such as feedbacks between processes that affect the timing and rates of evapotranspiration, vadose zone flow, surface runoff and groundwater interactions.…”

“…The Richards equation is employed to simulate variably saturated three-dimensional groundwater flow (Richards, 1931). Overland flow can be generated by saturation or infiltration excess using a free overland flow boundary condition combined with Manning's equation and the kinematic wave formulations of the dynamic wave equation (Kollet and Maxwell, 2006). ParFlow solves these governing equations by employing either a fully coupled or integrated approach, whereby surface and subsurface flows are solved simultaneously using the Richards equation in three-dimensional form (Gilbert and Maxwell, 2017), or an indirect approach whereby the different components can be partitioned and flows in only one of the systems (surface or subsurface flows) is solved.…”

“…ParFlow is well documented and has been applied to surface and subsurface flow problems, including simulating the dynamic nature of groundwater and surface-subsurface interconnectivity in large domains (e.g., over 600 km 2 ) (Kollet and Maxwell, 2008a;Ferguson and Maxwell, 2012;Condon and Maxwell, 2014), small catchments (e.g., approximately 30 km 2 ) (Ashby et al, 1994;Kollet and Maxwell, 2006;Engdahl et al, 2016), complex terrain with highly heterogenous subsurface permeability such as the Rocky Mountain National Park, Colorado, United States (Engdahl and Maxwell, 2015;, large watersheds (Abu-El-Sha'r and Rihani, 2007;Kollet et al, 2010), continental-scale flows Maxwell et al, 2015), and even subsurface-surface and atmospheric coupling (Maxwell et al, 2011;Williams and Maxwell, 2011;Williams et al, 2013;Gasper et al, 2014;Shrestha et al, 2015). Evidence from these studies suggests that ParFlow produces accurate results in simulating flows in surface-subsurface systems in watersheds; i.e., the code possesses the capability to perform simulations that accurately represent the behaviors of natural systems on which models are based.…”