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An Isotopic Study of Northeast Everglades National Park and Adjacent Urban Areas

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> Box Models
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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:

x + y = 100 % (equation 4)

(δ18Ox)x + (δ18Oy)y = (δ18Op)100 (equation 5)

where x is the percentage of Everglades water at the pumping well, y is the percentage of urban water at the pumping well, δ18Ox is the δ18O value of Everglades water (taken as the δ18O value at G618), δ18Oy is the δ18O value of urban water (taken as the δ18O value at G3555) and δ18Op 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.

simple box model
Figure 23: Simple Box Model [larger image]

  Everglades Water Urban Water
Overall Average 68.9 31.1
1998 Average 65.7 34.3
1996-1997 Average 72.0 28.8
"Summer" Months 59.6 40.4
"Winter" Months 86.4 13.6
"Dry" Months 73.8 26.2
"Wet" Months 66.4 33.6
Table 3: Simple Box Model Results

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

diagram showing flow terms used in complex model
Figure 24: Flow Terms Used in Complex Model [larger image]
For the complex box model, a two-mile by four-mile rectangular area within the focus area (down to the Biscayne aquifer) was selected and broken into five boxes which represent the Everglades area, canal, lakes, deep groundwater, and urban areas (Figures 24 and 25). A water balance and an isotopic balance were then established for each box in order to compute water flows between each of the boxes. Specifications for these boxes are provided in Table 4. Those variables which were measured versus those computed through the complex model described in this section are summarized in Table 5.
diagram showing control volumes used for complex model
Figure 25: Control Volumes Used for Complex Model [larger image]

Values of δG618, δG3660, δG3575, δG3551, δG3662, δWell 29/30, and δG3555 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 (δRain G618) and at the West Wellfield (δRainWW). Values of δE1, δE2, and δE3 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 δL utilized is the average of the δ18O values for RL1 and RL3. Herrera, 2000, showed that values of δL 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 δL 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.

Box # Box Description Inputs Corresponding Values Used Outputs Corresponding Values Used
1 Everglades Everglades water including inflow from S333 (E)

Rainfall (R1) over A1, a 2.00 mile by 2.00 mile area


Rain G618

Evapo-transpiration (ET1) over A1, a 2.00 mile by 2.00 mile area

Shallow Groundwater (X)
Deep Groundwater (Y)

δE1 from Rain
G618, S3575, S3577 & S3578


2 Canal Shallow Groundwater (X)
Rainfall (R2) over A2, a 2.00 mile by 0.02 mile area
Rain WW
Evapo-transpiration (ET2)
over A2, a 2.00 mile by 0.02 mile area
Shallow Groundwater (Z)
δE2 from Rain
WW, 2M3, 3M4 & 4M5
3 Lakes Shallow Groundwater (Z)
Rainfall (R3) over A3, a 2.00 mile by 0.22 mile area
Rain WW
Evapo-transpiration (ET3)
over A3, a 2.00 mile by 0.22 mile area
Shallow Groundwater (L)

Seepage (S)

δE3 from Rain
WW, RL1 & RL3
δL from RL1 & RL3
δL from RL1 & RL3
4 Deep
Deep Groundwater (Y)
Seepage from lakes (S)
δL from RL1 & RL3
Deep Groundwater (D) G3662
5 Urban Shallow Groundwater (L)

Deep Groundwater (D)
Rainfall (R5) over A5, a 2.00 mile by 1.76 mile area

δL from RL1 & RL3


Pumping Well (P)
Urban Water (U)
Well 29/30
Table 4: Complex Box Model Parameters

Box # Measured Variables Calculated Variables
1 R1, ET1, A1, δG618, δRain G618, δE1,
δG3575, δG3660
E, X, Y
2 R2, ET2, A2, δG3575, δRain WW,
δE2, δG3551
X, Z
3 R3, ET3, A3, δG3551, δRain WW,
δE3, δL
Z, L, D
4 δG3660, δL, δG3662 Y, S, D
5 R5, A5, P, δL, δG3662, δRain WW,
δWell 29/30, δG3555
L, D, U
Table 5: List of Measured and Calculated Parameters in Complex Box Model

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:

E + R1*A1ET1*A1XY = 0 (equation 6)

Isotopic Balance:

E*δG618 + R1 *A1*δRain G618ET1 *A1*δE1X*δG3575Y*δG3660 = 0 (equation 7)

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).

diagram of complex model results using isotopic data from 1998
Figure 26: Complex Model Results Using Isotopic Data from 1998 [larger image]
Results of the complex box model for the 1998 and the overall average data sets (Figures 26 and 27) indicate that water leaving the Everglades and seeping under the Levee 31N preferentially moves through the deep groundwater layer. This is observed from the flow ratio of over ten to one in the deep groundwater as compared to shallow groundwater. Deep groundwater travels east until moving into the vicinity of the rock mining lakes. As the lakes cut through the deeper semi-confining layer, the model indicates that nearly sixty percent of the deep groundwater flow travels into the lake. Water from both the lake and deep groundwater migrate eastward into control volume number five, the urban box. Here the model flow terms indicate that the pumping wells draw water from surrounding urban shallow groundwater, the lakes, and deep groundwater. Furthermore, it is important to note that the results of the complex box model are consistent with those from the numerical model (MODBRANCH) developed by Nemeth et al. 2000 and later modified by Herrera 2000 to incorporate lakes. A detailed comparison between the results of the complex model and those of the numerical model are provided by Wilcox 2000. Wilcox, 2000, reports that the results are within the same order of magnitude and within only a 30 to 35% difference between the MODBRANCH and complex models.
diagram of complex model results using entire isotopic data set
Figure 27: Complex Model Results Using Entire Isotopic Data Set [larger image]
The complex model is in many ways an improvement over the simple model. It incorporates rainfall and evapo-transpiration data. In addition, it accounts for the presence of both deep groundwater flow and the rock mining lakes. Another positive aspect of the complex box model is that it utilizes data from several of the isotope monitoring stations rather than only two as in the simple box model.

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.

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