Aggregation of Flow Vectors

The EDEN grid has 57,073 active cells, so a map of flow vectors for every cell corner may be too dense to be a useful visual representation. Aggregating the vectors allows for varying the resolution and density of the map. The grid scheme in figure 2 can be altered so that the flow vectors for a larger set of cells are averaged to get the total flow for the aggregated group. For example, the three-by-three aggregation computes the average of nine flow vector points (fig. 3) and is calculated to occur over a spatial resolution of 1,200 m (3 times 400 m). At a larger scale, the five-by-five aggregation computes the average of 25 points over a spatial resolution of 2,000 m. For the purposes of the presentation used in this report, the three-by-three set of cells with a spatial resolution of 1,200 m is used.

Barriers to Flow

The EDEN study area includes eight subdomains separated by a levee system that divides and controls the wetlands and conservation areas and results in water-level discontinuities (fig. 4). Water levels on opposing sides of levees or any other obstruction to flow are not used to calculate an intervening water-level gradient and surface-water flow vector. The subdomain boundaries shown in figure 4 are used as a basis to define the EDEN grid cells that are not used to compute flow (no-flow cells), except for the boundary between the NPS (Everglades National Park/Big Cypress National Preserve) and L67ext (Levee 67 extension) subdomains. The southern section of this boundary does not correspond to a levee and is only included to complete the subdomain. Additional no-flow cells are identified as areas with features that block flows or water-level data that are affected by nearby flow boundaries (fig. 5). If any of the four cells used to compute a vector is set to no-flow, the flow vector is set to zero. Thus, flow is not computed along or across a levee.

Further determination of no-flow cell locations was made by delineating locations where gradients were not representative of flow at the scale of the grid (hundreds of meters). Such cases may be due to a gage being heavily affected by local structure flows or additional obstructions to flows. Gradients calculated in these areas are affected by canal stage, which may not be the same as the stage in an adjacent wetland, resulting in erroneous flow vectors. Using data from the year 2020, areas with water-level gradients an order of magnitude larger than the average in EDEN are noted as consistently being affected by water-level interpolation to nearby canal levels. These locations are included in the no-flow areas shown in figure 5. Location 1 (fig. 5) is west of the L-31N canal and includes the enlarged inset map in figure 1. Location 2 (fig. 5) is east of L-30 in the Pennsuco Wetlands area (fig. 1). Location 1 (fig. 5) is at the northern corner of EDEN model subdomain WCA2A (fig. 4). Location 1 is characterized by a single gage near a junction of two levees that has nine flow structures (not shown), location 2 is a narrow area between a canal and a boundary, and location 3 has six gages in a cluster near a canal.

Calibration

The modified Manning’s equation was calibrated by using continuous flow measurement sites at coastal rivers in Everglades National Park, for the period January 1–December 31, 2020, to develop friction factors (K) for each river individually and for the total flow. The values of the coefficients K, α, and β in equation 3 depend on the location, vegetation, and the flow regime. For the GARDEN application, the coefficients can be calibrated by the equivalence of water-level gradient S in equation 3 with ∇Z_x and ∇Z_y from equations 1 and 2:

One source of calibration data is the South Florida Water Management District’s computed discharge data at control structures (South Florida Water Management District, 2020), which is based on stages and rating curves upstream and downstream of the control structure. The total discharge in the cells directly downstream from the control structure can be equated to the discharge at the structure. However, multiple sources of flow affecting an area of the wetland or regional flow that is not associated with the structure can interfere with equating the measured structure flow with the wetland water-level gradient, increasing calibration uncertainty. The downstream stages at control structures often are not a good representation of water levels required to calculate a wetland gradient in an area. Considering these difficulties, flow data at control structures were not used to calibrate GARDEN.

Point velocities have been measured in the Everglades (Riscassi and Schaffranek, 2002; He and others, 2010), but measurements lacked adequate temporal and spatial continuity for inclusion in the calibration process. These measurements would have to be multiplied by the EDEN grid-cell widths to compare with computed values. This approach would assume that the point velocity is approximately equivalent to a daily average velocity for the area around the measurement, but the actual vertically averaged velocity is not known. In addition, these measurements are usually made at different locations and at different times, lacking temporal and spatial continuity, so they were not chosen for calibration.

Measured flow at coastal-river gages on the boundary of the EDEN study area provides a timeseries for calibration. Lostmans River, Broad River, Harney River, and Shark River have USGS continuous-discharge gages and receive flow from Everglades National Park along the EDEN domain boundary (figs. 1 and 6). The four coastal river gages measure discharge every 15 minutes and the data extend back as far as 2007 (table 1) (U.S. Geological Survey, 2016). For the calibration of the GARDEN flow vectors, the daily average flow out of one of these rivers should approximately match the sum of the computed GARDEN boundary flows upstream from the river for that day. The rivers monitored by these gages drain flow from Shark River Slough, a primary flow-way in Everglades National Park, so calibration includes flow characteristics important to the study domain. Given that spatially detailed studies have not been implemented in the EDEN domain, the calibration approach chosen is to utilize the timeseries of discharge from the four coastal gages shown on figure 6 to calibrate K values by fitting observed and modeled discharge for temporally averaged values. Potential sources of error include subdaily variations in river flow, groundwater interactions, rainfall, and evapotranspiration between the upstream EDEN cells and location of the river gages.

The three coefficients, K, α, and β, can vary with location, and K can vary with flow direction. With limited data, these coefficients are assumed to be stationary (constant) at a given measured-flow location. Values of α and β are taken from the literature, as described later, and K is used as the calibration parameter. The difference in coefficient values between measured-flow locations indicates frictional resistance variability, although each value is implicitly averaged over the drainage area of the coastal river. Spatial distributions of Everglades vegetation and frictional resistance have been mapped (Wang and others, 2007, fig. 4; Ruiz and others, 2017) but only cover part of the EDEN study area. Frictional resistance was examined in an area north of EDEN model subdomain WCA3A (fig. 4) using a wave-propagation technique (Wasantha Lal, 2017) and spatial variations determined, but also only cover part of the EDEN study area.

Calibrating GARDEN flow vectors to measured coastal flows requires delineating the boundary cell flows corresponding to each of the coastal rivers. The direction of the flow vectors near the known GARDEN area boundary indicates the river destination for different boundary grid cells, and the relative volumes of flow in each river can be used to estimate the distribution. Alternately, the total flows through the four rivers can be equated to the sum of the boundary flow vectors. Although this aggregates the frictional characteristics of the entire area together, it does remove the need to allocate flow vectors to individual rivers.

Computed-Flow Vectors in 2020

Flow vectors at an aggregation of three-by-three 400-m cells to the 1,200-m scale were computed daily for the year 2020. The three-by-three cell aggregation scale is conducive to visualization of the entire EDEN area (fig. 8). The location of each surface-water flow vector is at the base of the arrow, and large flows can place the tip of the arrow in no-flow areas. Compared to dry-season flows on March 1, 2020, higher discharges and inundation are visible on August 1, 2020, during the wet season.

Flow-Vector Calibration

Parameters used to compute flow vectors were calibrated using observed and simulated flows from January 1–December 31, 2020, at the four coastal river outflows (fig. 6), and EDEN boundary cells were selected with corresponding flows to each river. Cells were selected by trial and error to ensure that (1) the range of cells represents the likely flow path to each gage, and (2) the flow distribution among the coastal streams was similar to the distribution indicated by measured data from the gages.

Based on Kadlec (1990) and He and others (2010), coefficient values α = 0.71 and β = 1.12 were used in equations 4 and 5. The value of the coefficient K was calculated as a simple arithmetic average of calibrated K values for the sum of each daily measured and computed flow at each coastal river, as well as for total flows summed at all rivers for a value K = 45.59. The K value for individual coastal river flows ranged from 29.74 at Broad River to 64.26 at Shark River. These values correspond to Manning’s n values of 0.050–0.023, respectively. Although greater than most values assigned to rivers, these values are considerably smaller than values assigned to sites affected by emergent vegetation (He and others, 2010; Wang and others, 2007). However, field estimation of frictional resistance usually concentrates on small-scale measurements of flow or point measurements in the vegetation type of interest (He and others, 2010). Larger-scale flow regimes include subareas of lower vegetative resistance that can carry most of the flow. This results in a lower aggregate frictional resistance for larger-scale areas. Wasantha Lal (2017) computed frictional resistance by means of a wave-propagation technique in various stormwater treatment areas in the “greater Everglades” with flow widths ranging from 6,512 to 16,010 feet. Computed Manning’s n values varied greatly, from 0.18 to 1.42. Another consideration is that the frictional resistance represented by this calibration represents the southern end of Shark River Slough (fig. 6), which, as a major flow-way, may have a lower frictional resistance than areas elsewhere with denser vegetation.

With the area-average value K = 45.59, the flow vectors can be quantified as indicated in figure 8. The flow vectors are separated by 1,200 m (three cells), so the indicated flowrates are occurring on this scale. Flows at the EDEN boundaries were computed using GARDEN and compared to measured river flows for the 2020 calibration period (fig. 9). The measured flows at the coastal rivers fluctuate more than the upstream flows computed along the EDEN boundary by GARDEN, as the coastal-river flows are highly affected by wind and tide. The larger timescale variability in flow in the rivers are reflected in the EDEN boundary flow, although minimal variations are indicated in the boundary flow leading to Lostmans River.

Flow-Vector Validation

To validate GARDEN output, streamflow vectors were calculated for 2021 and the boundary flow to the coastal rivers calculated (fig. 10). Similar to the 2020 calibration period, the longer-term fluctuations in river flows are indicated in the EDEN boundary flows, with the boundary flow upstream of Lostmans River showing little change. Cumulative flow for both 2020 and 2021 indicates the biggest difference between river and EDEN boundary flows occurs from November 2020 to April 2021 (fig. 11).

The temporal variability in flow observed at the four coastal-river gages were not simulated in the flows computed by GARDEN at the EDEN boundary, as the upstream flow is not subject to coastal wind and tidal forcings. Despite these differences, the Pearson’s correlation coefficient between the EDEN boundary flows and the sum of the coastal river flows for the 2020 calibration period is 0.766. For the 2021 flows, the Pearson’s coefficient is 0.566. A Pearson's coefficient over 0.5 indicates that more than one half of the observed variance is explained by the computed data.

Example Application

Although there are many uses for the GARDEN application, one use is to examine the effects of control-structure discharge on wetland flow. The S12A, B, C, and D structures (S12s) discharge into Everglades National Park from the Tamiami Canal (fig. 1) and supply water to Shark River Slough. The combined flow through these structures for June 2020 is shown on figure 12. Flow releases were zero until June 2, 2020, and increased rapidly through June 4, 2020. The effect of these releases from the S12s on flow direction and magnitude in the adjoining wetlands is apparent in the EDEN flow vectors for select days on figure 13.

On June 2, 2020, little flow is indicated south of the S12s, because only 70 cubic feet per second (ft³/s) was flowing through the structures on that date (figs. 12 and 13). On the next day, June 3, flow south of the S12s increased to 273 ft³/s. Flow through S12A did not occur in June 2020, and the flow patterns reflect this (fig. 13; location on fig. 1). Although flow through the structure increased to 508 ft³/s on June 4, very low flow persists farther south of the structures with most of the flow from the S12s appearing to be going to storage in the adjacent wetlands. By June 18, the continuous path of flow vectors from the S12s structures to the coastal boundary indicates that the response of flows in Shark River Slough to flow releases during the dry season may take over a week.