Hammer and Kadlec [1986] present a model and data describing the dynamics of water flowing horizontally through a wetland. Their model is based on a pair of mass balance equations, one used in the case in which the free surface is above the sediment surface and the other used in the case in which the free surface (water table) is below the sediment surface. This pair of the mass balance equations can be derived from a single mass balance equation. The model of Hammer and Kadlec [1986] is successful in describing the distribution of head in the wetland because their mass balance equations contain the dominant flux terms in the more general equation for the cases of the free surface above and below the sediment surface. The use of two mass balance equations implies that surface water and pore water are decoupled and independent , when in fact there exists a gradual transition between the two regimes in wetlands. The purpose of this commentary is to suggest a form for the general mass balance equation for one-dimensional flow in a wetland that retains the coupling between surface water and pore water. The resulting equation is operationally equivalent to the pair of equations used by Hammer and Kadlec. There is no conflict between discussion presented here and the results and discussion of Hammer and Kadlec regarding the dynamics of surface water flow in wetlands. The advantage of the proposed formulation is that the coupling between surface water and pore water is represented more accurately. This becomes important when one begins to consider the role of the hydrologic cycle in biogeochemical cycles in wetlands. DERIVATION OF THE MASS BALANCE EQUATION The mass balance on water on a vertical slice taken through the full width w of a wetland, perpendicular to the direction of flow (Figure 1), is described by wS dt-dz w vz dy + w[P-E + A-I] (1) b The rate of change of water content in the slice is equal to the total inflow minus outflow due to horizontal velocities perpendicular to the slice, v z, plus the net contribution due to the vertical fluxes of precipitation, P; evapotranspiration, E; lateral inflows and additions, A; and infiltration to an underlying aquifer, I. The rate of change of water content is related to the rate of change of hydraulic head, h, by a storage coefficient S, defined here as the change in water content of the sediment and overlying water column per unit change in head, per unit surface area. The storage coefficient is dimensionless and operationally equivalent to the porosi-ties, •s and (I)g, defined by Hammer and Kadlec, but it differs in concept as will be discussed below. A one-dimensional mass balance is thus developed following the notation of Hammer and Kadlec as much as possible. The integral of horizontal fluxes over the depth interval [hb, h] can be replaced by expressions that give the net horizontal flux above and below the sediment surface: wS •-[ = •zz w(h-hg)a(h-hg) tt + •zz w(hg-hb)[(•zz + W[P-E + A-I] (2) It is assumed that pressure is hydrostatically distributed in the ve...
A simple mathematical model is developed which permits dynamic simulation of wetland hydrology and of nutrient-driven interactions between wastewater and the wetland ecosystem. Spatial variations due to surface water flow are described, and material balance calculations carried out for phosphorus, nitrogen, and chloride. A hydrology model, described elsewhere, predicts overland flow. Ecosystem phenomena are represented, using a one-dimensional, spatially distributed compartmental model. Compartments representing active parts of the ecosystem include soil, surface water, interstitial soil water, and various types of live biomass, standing dead and litter. Solutions to the partial differential equations which comprise these spatial models are demonstrated using finite-difference methods. Computer simulations are compared with operating data from the Porter Ranch wastewater treatment facility at Houghton Lake, Michigan. They accurately predict solute concentrations in surface water, biomass growth patterns, changes in the litter pool, and soil accretion rates.
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