Near-Surface Flow and Transport in Tidal Marsh Plains

Abstract

In a tidal marsh plain, salinity and moisture distribution determine the sustainability of the ecosystem. These response patterns are modeled by the marsh plain equations, the governing equations for coupled flow and salinity transport in a saturated/unsaturated tidal marsh plain. The boundary conditions, whose combination is unique to a tidal marsh plain, are established, and evaporation and periodic inundation in a onedimensional soil column is explored. INTRODUCTION In a tidal marsh plain, salinity and moisture distribution determine habitat suitability for local fauna and flora. When the marsh plain is infrequently inundated, large volumes of water evaporate from the surface, creating a dry and hypersaline environment that may be incapable of supporting vegetation. In the creation or restoration of tidal wetlands, the ability to predict when and where such conditions may exist is a crucial factor in success. The unsteady mass conservation equation (Bear 1972), with Darcy’s equations defining the flow velocities, models subsurface flow. The advection-diffusion equation (Fischer et al. 1979), including variable soil saturation, is used to model salinity transport. The governing equations are coupled because fluid density varies with both pressure head and salinity concentration, and the equations must be solved simultaneously. The marsh plain equations are modeled using the numerical technique Method of Lines. A complete discussion of the physics and numerical methods can be found in Greenblatt (1997) and Greenblatt and Sobey (1997). MARSH PLAIN EQUATIONS The marsh plain equations are the governing field equations for coupled flow and salinity transport in the tidal marsh plain, where both saturated and unsaturated flow regions are present (Greenblatt 1997). The full equations are reduced to 1Dept. of Civil & Environmental Engineering, Univ. of California, Berkeley 2Professor, Dept. of Civil & Environmental Engineering, Univ. of California, Berkeley Copyright ASCE 2004 Wetlands 1998 one spatial dimension. Flow will be modeled in the vertical (z) direction, with z positive upwards. The marsh plain flow equation is and the marsh plain salinity transport equation is where p(h, S) [gm/cm3] is the fluid density, K(h) [cm/s] is the hydraulic conductivity, 13(h) is th e moisture content, c(h) [ cm-‘] is the soil moisture capacity, and E [cm2/s], is the diffusion coefficient. The dependent variables are pressure head h = h(z, t) [cm] and salinity S = S(x, t) [psu]. BOUNDARY CONDITIONS The combination of boundary conditions applied to the marsh plain equations is unique to the tidal wetland. Because flow and salinity transport is boundary driven, proper formulation of the boundary conditions is a crucial part of the numerical model. INFILTRATION Infiltration is a downward flux at the surface of the soil column. While the soil surface remains unsaturated, applied water will infiltrate into the soil column. If the applied rate exceeds the infiltration rate, the soil surface becomes saturated, water ponds on the surface, and the actual infiltration rate will be less than the applied rate. A finite control volume approach is implemented to apply the boundary conditions at the top and bottom of the flow domain. Because subsurface flow and salinity transport is slowly varying, sharp gradients may develop at the boundaries if boundary conditions induce large, local changes in the dependent variables. Sharp gradients can cause spurious results in the numerical solution. The control volume approach at the boundaries avoids this purely numerical difficulty without compromising mass conservation. The control volume method treats each end of the soil column as a boundary layer, and uses the boundary conditions at the top and bottom, along with existing conditions in the soil column, to calculate the control volume averaged values of pressure head and salinity. The known applied water rate, qtop, is applied at the top of the control volume. The flow out of the bottom of the control volume, qbot, is a function of the pressure gradient at that location. From Equation 1, mass conservation for the control volume becomes