Chapter II: Technical Results

II.4 Box Models

Two box models were developed for this study and are referred to herein as the "simple" and "complex" box models.

II.4.a Simple Box Model

A simple box model was developed in order to determine the percent contribution of Everglades water to the West Wellfield. This model is based upon the assumption that two isotopically different waters are being drawn to and mixed at the pumping well site (Figure 23). These waters include Everglades type water (water west of L-31N) and urban type water (water east of Levee 31N). An isotopic balance is therefore represented by the following two equations:

where x is the percentage of Everglades water at the pumping well, y is the percentage of urban water at the pumping well, δ¹⁸O_x is the δ¹⁸O value of Everglades water (taken as the δ¹⁸O value at G618), δ¹⁸O_y is the δ¹⁸O value of urban water (taken as the δ¹⁸O value at G3555) and δ¹⁸O_p is the δ¹⁸O value of water at pumping well 29/30. This model was evaluated using different sets of input data. These sets included the overall average of all samples, the 1998 yearly data average, and the 1996/1997 combined data average. Also used as input for model runs were the averages of "Summer" months (considered to be May through October), "Winter" months (November through April), "Dry" months (those having less than four inches of rainfall during the thirty days prior to sampling), and "Wet" months (those having more than four inches of rainfall during the thirty days prior to sampling). Rainfall measurements were those collected at S338. Results of the model for these data sets are provided in Table 3.

Figure 23: Simple Box Model [larger image]

This model, using data for the entire study period, shows that 69% of the water being pumped from the well is indicative of Everglades water while only 31% is indicative of urban water. This supports the hypothesis that Everglades type water is reaching the pumping well and may be the major contributing source. Furthermore, for all conditions, over 50% of the water at the pumping well is Everglades type. The simple model results also show that during "dry" conditions, when a smaller quantity of recharge is available, a greater demand is placed upon the contribution from Everglades groundwater. This causes the percent composition of Everglades water in the pumping well to increase. This observation also holds true when comparing summer and winter months. Summer months in general correlate with the wet season in South Florida during which rainfall recharges groundwater more consistently than during winter months. Consequently, an increase in the quantity of Everglades water reaching the pumping well is observed during the drier winter conditions. The difference between the "1998 Average" model results and those of the "1996-1997 Average" is also likely the result of rainfall differences. On average, there was less rainfall during 1996 and 1997 (50.5 inches) than in 1998 (52.5 inches) in the study area. Accordingly, the percentage of Everglades water returned by the model is higher during the drier 1996-1997 years.

While this simple box model is useful for assessing general trends, certain conceptual problems are inherent as a result of the simplicity of this type of model. These include the lack of compensation for the direct isotopic influence of rainfall and inflow from water conservation areas at gate S333 on the system as well as the influence of any mixing across geologic layers in the rock mining lakes and evaporation of water at the lake surface. There is no simple way to correct these problems within the framework of the simple model. While introducing only rainfall to the model would result in a higher Everglades influence (as additional heavy Everglades water would be needed to balance the light rain input in the isotope balance), introducing only isotopically heavy lake water as an inflow would cause an increase in the observed urban influence. In order to address some of these problems, a more complex box model was developed. Results of the complex model are provided in the next section.

II.4.b Complex Box Model

Figure 24: Flow Terms Used in Complex Model [larger image]

Figure 25: Control Volumes Used for Complex Model [larger image]

Values of δ_G618, δ_G3660, δ_G3575, δ_G3551, δ_G3662, δ_{Well 29/30}, and δ_G3555 utilized for the complex model were the average values measured at the corresponding well locations (given by the subscripts). Isotopic values for the rainfall were also measured directly at sampling stations located next to well G618 (δ_{Rain G618}) and at the West Wellfield (δ_RainWW). Values of δ_E1, δ_E2, and δ_E3 for evaporated water were calculated using the method developed by Gonfiantini (1986). The computation was a function of the δ values for rainfall and surface water corresponding to a particular site. Details concerning this computation are provided by Wilcox, 2000, and Herrera, 2000. The value of δ_L utilized is the average of the δ¹⁸O values for RL1 and RL3. Herrera, 2000, showed that values of δ_L for RL1 and RL3 were similar to one another and the values did not vary considerably with depth within each lake. Please refer to Herrera, 2000, or Solo-Gabriele and Herrera, 2000, for more details concerning δ_L values for the lakes. The rainfall depths, R1, R2, R3, and R5, were obtained from station S336. Values of ET1, ET2, and ET3 were obtained from the Tamiami Trail weather station located roughly 15 miles west of the study site. P was obtained from chart records from each well. Charts were provided by Miami Dade Water and Sewer Department. The value used for the model was 4.53 x 10⁸ cubic feet per year (9.3 mgd) which was found to be representative of the pumping well data evaluated. A1, A2, A3, and A5, correspond to the surface area of the Everglades, canal, lakes, and urban control volumes. The Everglades control volume corresponds to a surface area of 2 miles by 2 miles (A1). The canal is 2 miles by 0.02 miles in area (A2). The urban side (A5) is assumed to represent an area of 2 miles by 1.76 miles. The value of A3, which corresponds to the lakes, was determined by summing the surface area of the two rock-mining lakes included within this study (1.24 x 10⁷ sq ft, Herrera 2000). Conceptually, the model accounts for the lakes as a thin strip which is 0.22 miles long and two miles wide. While the lakes actual shapes are in fact very different, for the purposes of the model flow balances, only the surface area is important.

The model incorporated a seepage term from deep groundwater into the lake control volume. This seepage term, while drawn as an input through the bottom of the lake in the figure, in fact incorporates both movement through the bottom of the lakes (vertical flow) and any inflow through the side (primarily horizontal flow) of the lake between the bottom of the canal and the base of the lakes (between 30 and 40 feet). The model does not distinguish between horizontal and vertical flow across the boundary between box 3 and box 4. Canal seepage, on the other hand, is considered to be only through the sides of the canal. This arrangement is considered to physically describe the system given that hydraulic gradients are very flat in the area of the canal resulting in horizontal flow lines. Furthermore this conceptualization is consistent with the existing MODBRANCH model of the study site (Nemeth et al. 2000). This model utilizes the a relationship which simulates canal seepage through the sides of the canal rather than the bottom.

The unknown flow values were calculated in the model by simultaneously solving a series of mass balance equations. The equations assume steady state conditions and include both volumetric and isotopic balances. Equations were developed for six control volumes (Figure 25). Details of these computations are provided in Wilcox 2000. An example of the equations utilized are provided for box 1 below:

Volumetric Water Balance:

Isotopic Balance:

For these equations, all variables are defined in Table 4. All flows are measured in cubic feet per year (cfy), all areas are in square feet (sq. ft) and rainfall/evapo-transpiration values are measured in feet per year (ft/yr).

Figure 26: Complex Model Results Using Isotopic Data from 1998 [larger image]

Figure 27: Complex Model Results Using Entire Isotopic Data Set [larger image]

Despite all of the positive aspects of the complex box model, it has its limitations. The complex box model does not fully account for north/south water migration or surficial Everglades flow. In addition, some of the sites used in the complex box model were not monitored until the start of 1998 or later. As a result, at sites such as G3660 too few data points were available to accurately perform additional model runs such as those done in the simple box model (section II.4.a) that assess the impact of seasonal variations on the system. It is also important to note that the areal size of the complex model was chosen so as to incorporate the rock mining lakes, the West Wellfield and Everglades isotope monitoring stations. As such, redefining the boundaries of the model could result in different model output.