METHODOLOGY

Water Budget

The water-budget equations that apply to the surface-water/ground-water interaction at the ENR are presented here. Using the conceptual model of water flow in the ENR (Figure 2) and mass conservation, the governing water-budget equation is

    [1]     D

Figure 2. Conceptual model of water flows in the ENR [larger image]

where S_i and G_i are the rates of surface-water inflow and ground-water discharge, respectively, and S_o and G_o are the rates of surface-water outflow and ground-water recharge, respectively. P and ET are the rates of precipitation and evapotranspiration, respectively. V is the volume of water in the ENR at the present and previous time step, and t and t are time and time interval, respectively. There are also several measured fluxes that are unique to the ENR site that must be included in the balance. L_i is shallow seepage through the L-7 levee collected by a ditch and delivered by culverts into ENR. In addition, R_i is the rate of surface-water pumping to the ENR from a seepage canal that collects ground water on the western and northern side of the ENR. R_o is the rate of surface-water outflow from the ENR to the seepage canal (R_o is almost always zero).

For our water balance, we used four years of data (1994-1998) that were supplied to us by the South Florida Water Management District. Among the main components of water balance, areal average precipitation was computed as a Thiessen-weighted average of a seven-gage network. Daily evapotranspiration was computed based on percent type of vegetative cover and the area of each cell. A Penman-Monteith model was used to determine evapotranspiration for cattails and mixed macrophytes, and a Penman-Combination model was used for shallow open water. The reader is refered to Abtew and Mullen (1997) for a more complete description of hydrologic monitoring at ENR. For our study, all components of input and output (L³/T) are averaged over two-week periods in order to consider both the hydrologic residence time of approximately 20 days in surface water (Guardo 1999) and time interval of chemical monitoring by South Florida Water Management District (14 days). We chose to use units of flow (hectare-meter/day) that were consistent with the data base of South Florida Water Management District (1 hectare-m/day = 0.116 m³/second). Using the 14-day averaged fluxes, equation [1] is rewritten as

    [2]     D

where t equals 14 days and the overbars denote 14-day averaged fluxes. Using equation [2], we can solve for the two unknowns (G_i and G_o) in terms of a net exchange between ENR surface water and ground water by substituting V(t) - V(t - 1) by V and rearranging [2] to yield

    [3]     D

Combined Water and Solute Mass Balance

Using only the surface-water-budget balance data, we cannot take the further step of partitioning the net ground-water exchange (G_i - G_o) to solve for G_i and G_o individually. In order to solve for the two unknowns (G_i and G_o), we need a second mass balance equation, such as one for solute tracer. Using the same conceptual model for water fluxes in the ENR, the solute mass balance for a solute in surface water is

    [4]     D

where

M is the mass storage of the designated solute in the ENR,

C(t) is the area-averaged solute concentration in ENR surface water at time t,

_Si is the solute concentration in surface inflow from ENR supply canal,

_P is the solute concentration in precipitation,

_Ri is the solute concentration in surface inflow from seepage canal,

_Li is the solute concentration in shallow seepage collected by L-7 culverts,

_Gi is the solute concentration of ground-water discharge into ENR,

_So is the solute concentration of surface outflow from ENR

_Ro is the solute concentration of surface outflow to seepage canal, and

_Go is the solute concentration of ground water recharge from ENR.

Being able to calculate G_i and G_o is the main advantage of the combined approach using water and solute mass balance relationships. This is accomplished by rearrangement of [3] and substitution for G_o in [4]

    [5]     D

The result for _i from equation [5] can be substituted back into equation [3] to compute ground-water recharge.

The following steps were undertaken in the estimation procedure. First, hydrologic and chemical data were acquired for the ENR from the South Florida Water Management District (Table 1 and Figure 1b). The initial volume of surface water in ENR (V_o) was estimated using measurements of surface-water depth (ranging from 0.5 m to 0.8 m) and the area of each cell. Chemical concentrations monitored by the South Florida Water Management District were available on approximately biweekly basis at each surface input and output flow locations and at each interior site in ENR (Table 1 and Figure 1b). We evaluated several potential tracers (Cl, Na, Mg, and Ca) for the present study and selected chloride as the best ionic solute tracer for the ENR.

The average Cl concentration in surface water of the ENR (C_t) was estimated using water-volume fractions in each cell and average Cl concentrations in each cell determined from 3 or 4 representative monitoring sites in each cell (Table 1 and Figure 1b). The Cl concentration of ground-water discharge (_Gi) was estimated by averaging the Cl measurements from 3 wells located on the eastern side of the ENR (near L-7 Canal) (Figure 1b). Boreholes were drilled by the mud-rotary drilling method and wells emplaced with 0.6-m screen located at approximately 9 m below land surface in a limestone layer with interbeded sand lenses (Harvey et al. 2000). In addition, the Cl concentration of ground-water recharge (_Go) was estimated from average concentration of surface water in cell 2, where hydraulic gradient and seepage-meter data suggest that most ground-water recharge is likely to occur (Harvey et al. 2000). Using the combined hydraulic and chemical data set and equations [3, 4, and 5], the ground-water discharge (_i) and recharge (_o) were estimated every 14 days over the study period of 4 years (1994 to 1998).

Uncertainty Analysis

A general characteristic of hydrologic mass balance equations is that they appear deceptively simple, i.e., mass in equals mass out plus or minus change in storage (Equation [1] and [4]). In reality, however, the errors in inputs to the mass balance equations affect the reliability of the outcome. Errors are usually generated from three major sources: first, measurement errors from imperfect instruments and inadequate sampling design and data collection procedures; second, interpretation errors resulting from spatial interpolation of point data; and third, model errors that are caused by inaccurate statement of the problem, for example, not including an important flux in the mass balance equation. Ideally, all of these errors should be assessed before final conclusions are drawn. For this study, we estimated the uncertainty of net ground-water exchange and ground-water discharge using standard techniques for propagating error through numerical calculations. For the case where a quantity y is determined as a function of multiple variables x₁, x₂, ... , x_n, the uncertainty in y is expressed by following (Meyer 1975, Taylor 1982)

    [6]     D

where _y represents the uncertainty in a calculated variable y and _x1,x2,...,xn represent uncertainties of measured variables x₁, x₂, ... , x_n. The relative contribution of each variable to uncertainty in calculated variable y can be determined by comparing ²_y and each term under the square root of the right hand side of equation [6]. In the present study, we adhered to the usual assumption in hydrologic studies that the uncertainty of each variable was independent of that of other variables (Winter 1981). Equation [6] is therefore the simplified form of the more general expression that considers covariance between variables (i.e., where the uncertainty in one variable depends on another) (Winter 1981). We referred to previous works (e.g., Winter 1981, Nuttle and Harvey 1995) in developing our uncertainty estimates of hydrologic components, such as precipitation, evapotranspiration, and surface-flow measurements (Table 2). However, to our knowledge, an equally defensible approach to define uncertainty of chemical measurements originating from both instrument error and interpolation error has not been attempted (LaBaugh 1985, Stauffer 1985, LaBaugh et al. 1997). Therefore, we estimated uncertainties of measured chemical variables at ENR by using our best judgment to qualitatively estimate instrument errors and interpolation errors associated with averaging point data to represent larger area of the ENR.

Table 2. Estimated uncertainties involved in hydrologic and chemical components.
Hydrologic Components		Chemical Components
Components	Uncertainty (%)	Components	Uncertainty (%)
Si	10.0	Ct and Co	15.0
So	10.0	CSi	10.0
Ri	10.0	CSo	10.0
Ro	10.0	CRi	10.0
Li	10.0	CRo	10.0
P	8.5	CP	15.0
ET	20.0	CLi	10.0
V	15.0	CGi	15.0
Vo	15.0	CGo	20.0

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