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Effect of Sea-Level Rise on Salt Water Intrusion

Effect of Sea-Level Rise on Salt Water Intrusion
near a Coastal Well Field in Southeastern Florida
by Christian D. Langevin and Michael Zygnerski

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    Saltwater intrusion model pompano fl Saltwater intrusion model pompano fl Document Transcript

    • Case Study/ Effect of Sea-Level Rise on Salt Water Intrusion near a Coastal Well Field in Southeastern Florida by Christian D. Langevin1 and Michael Zygnerski2 Abstract A variable-density groundwater flow and dispersive solute transport model was developed for the shallow coastal aquifer system near a municipal supply well field in southeastern Florida. The model was calibrated for a 105-year period (1900 to 2005). An analysis with the model suggests that well-field withdrawals were the dominant cause of salt water intrusion near the well field, and that historical sea-level rise, which is similar to lower-bound projections of future sea-level rise, exacerbated the extent of salt water intrusion. Average 2005 hydrologic conditions were used for 100-year sensitivity simulations aimed at quantifying the effect of projected rises in sea level on fresh coastal groundwater resources near the well field. Use of average 2005 hydrologic conditions and a constant sea level result in total dissolved solids (TDS) concentration of the well field exceeding drinking water standards after 70 years. When sea-level rise is included in the simulations, drinking water standards are exceeded 10 to 21 years earlier, depending on the specified rate of sea-level rise. Introduction There is little dispute that global mean sea level has been rising, and there is recent evidence to suggest that the rate of rise is accelerating. Recent satellite altimetry data collected from 1993 to 2003 show an increased rate of 3.1 ± 0.7 mm/year (Cazenave and Nerem 2004). This rate is almost twice the rate observed during the 20th century (1.7 ± 0.5 mm/year; Bates et al. 2008), but owing to the relatively short period of time, it is possible that part of the increased rate could be due to natural variability. Predictions of future rates of sea-level rise continue to improve as the science evolves, as new data are collected, and as associated uncertainties are more fully addressed. In the Third Assessment Report (TAR), 1 Corresponding author: U.S. Geological Survey, 411 National Center, Reston, VA 20192; 703-648-4169; fax: 703-648-6693; langevin@usgs.gov 2 Broward County Environmental Protection and Growth Management Department, 115 South Andrews Avenue, Fort Lauderdale, FL 33301. Received January 2012, accepted September 2012. Published 2012. This article is a U.S. Government work and is in the public domain in the USA. doi: 10.1111/j.1745-6584.2012.01008.x NGWA.org the Intergovernmental Panel on Climate Change (IPCC) reported possible increases for the 21st century that range from 0.24 to 0.88 m, with a median value of about 0.48 m (Church et al. 2001). As part of the Fourth Assessment Report (AR4) by the IPCC, Meehl et al. (2007) provide an estimated range of 0.18 to 0.59 m for the expected rise in sea level by the end of this century. Bates et al. (2008) provide insight into the apparent differences between the 2001 and 2007 studies: “the upper values of the ranges (reported in Meehl et al. (2007)) are not to be considered upper bounds for sea-level rise.” Meehl et al. (2007) noted that dynamic ice flow processes are poorly understood. For this reason, they did not include Greenland and Antarctic ice sheet losses in their projections. By including the effect of land ice, Pfeffer et al. (2008) suggest that a 2.0 m rise in sea level by the end of the century is possible if variables are quickly accelerated but that a 0.8 m rise is more plausible. Improving these projections has been the subject of recent IPCC investigation on ice sheet instabilities (IPCC 2010). Several studies have attempted to quantify and characterize, in a generic way, the effect of sea-level rise on salt water intrusion into a coastal aquifer. Using a steady-state analysis with an analytical solution, Werner GROUND WATER 1
    • and Simmons (2009) identified the major hydrogeologic controls on the impact of sea-level rise on salt water intrusion in unconfined coastal aquifers. They differentiated between flux-controlled and head-controlled systems and showed that sea-level rise is more problematic for headcontrolled systems because inland water levels do not rise with rising sea level. Chang et al. (2011) also found that for flux-controlled confined aquifers, sea-level rise may not have an impact on fresh water volumes. Werner et al. (2012) extended the analysis of Werner and Simmons (2009) to include unconfined and confined aquifers and proposed quantitative vulnerability indicators that can be calculated based on boundary condition type and hydrogeologic parameter values. Webb and Howard (2010) and Watson et al. (2010) investigated the migration aspect and response time of salt water movement. Webb and Howard (2010) focused solely on the head-controlled system as the consequences are more severe for that case. Their simulation results indicated that in certain situations, several centuries may be required for the salt water interface to reach equilibrium with sea-level change. Watson et al. (2010) found markedly different response times depending on the type of indicator. For example, the representative response time for the vertical center-of-mass was much shorter than the response time for the toe position, indicating that care should be given to select indicators relevant to the study purpose. These studies generalize the effect of sea-level rise on salt water intrusion for hypothetical and simplified conditions. Several efforts have addressed the effect of sealevel rise on a specific coastal setting. Masterson and Garabedian (2007) predicted the response for the Lower Cape Cod aquifer system and found that sea-level rise increased groundwater discharge into streams causing a reduction in the total volume of fresh water. Using Werner and Simmons (2009) terminology, the Lower Cape Cod aquifer would be classified as a head-controlled system. In contrast, Rozell and Wong (2010) found that Shelter Island, New York, would act as a flux-controlled system and that the effects of sea-level rise on the fresh water volume would be relatively minor. Interestingly, they found that an increase in sea level might actually increase the fresh water lens volume. They attributed this counterintuitive response to the presence of a marine clay layer that truncates the base of the fresh water lens; thus, the volume of fresh water in the aquifer is less if the marine clay layer were absent. As the prescribed sea level rose in the model, there were no overlying head controls and so fresh water accumulated in the unsaturated zone. Vulnerability of low-lying coastal areas to sea-level rise has been addressed by Lebbe et al. (2008) for the Belgian coastal plain, by Oude Essink (1999) and van der Meij and Minnema (1999) for the Netherlands, by Feseker (2007) for northwestern Germany, and by Giambastiani et al. (2007) for an unconfined coastal aquifer near Ravenna, Italy. Fujinawa et al. (2009) evaluated the effect of climate change (including sea-level rise) for the eastern Mediterranean coastal region of Turkey. Lo´ iciga a et al. (2012) concluded for the seaside area sub-basin in 2 C. Langevin and M. Zygnerski GROUND WATER Monterey County, California, that groundwater extraction would have a larger effect on sea water intrusion than sea-level rise. For northern Miami-Dade and southern Broward Counties, a sensitivity analysis by Guha and Panday (2012) suggests that water levels and chloride concentrations could increase by as much as 15 and 640%, respectively, for coastal parts of the Biscayne aquifer. All of these studies used a mathematical modeling approach to predict the impact of sea-level rise on salt water intrusion. This paper adds to our understanding of the impact of sea-level rise on salt water intrusion by quantifying historical changes in fresh water resources and quantifying process sensitivity for a low-lying coastal aquifer in southeastern Florida subjected to municipal groundwater withdrawals. The shallow coastal aquifers of southern Florida, which include the Biscayne aquifer, offer a unique opportunity to evaluate the effect of sea-level rise; the limestone aquifer is highly permeable, and thus, effects on fresh water resources may be seen more quickly than for less permeable clastic aquifers. Southeastern Florida also generally fits into the head-controlled category of Werner and Simmons (2009) because of an extensive canal network that overlies the entire region; these canals have been shown to be in direct hydraulic connection with the underlying permeable aquifers and act as a strong head control. Combined with a thin unsaturated zone, high propensity for damaging floods and high rates of evapotranspiration, there is little volume available in the thin unsaturated zone for future rises in the water table. Southern Florida is also representative of many coastal areas because of its large population. The combined 2009 population of the three counties comprising mainland southeastern Florida (West Palm Beach, Broward, MiamiDade Counties) is about 5.5 million. Collectively, these conditions suggest that southeastern Florida may be more highly susceptible to accelerated salt water intrusion caused by sea-level rise than other coastal areas. This investigation uses a numerical groundwater flow and dispersive solute transport model to evaluate the relative importance of sea-level rise compared to the other dominant hydrologic processes for a municipal well field in southeastern Florida. The model represents the hydrologic changes that occurred as the area transformed from a natural coastal environment into an agricultural setting and then into an urban corridor (Renken et al. 2005). The model was then used to predict the impact of future rises in sea level on salt water intrusion near the well field. Bredehoeft (2003) summarizes the general premise that model predictions tend to be more accurate when the calibration period contains events and conditions, and encompasses time scales that are comparable to those expected in the future. The model presented here was calibrated for a 105-year period using measured heads and salinity concentrations at monitoring wells. During the calibration period a salt water intrusion event was observed near the well field followed by a subsequent freshening of the aquifer. Also during this period, sea level rose by about 25 cm, which is similar to the lower-bound estimate of the IPCC (Church NGWA.org
    • Figure 1. Map of study area showing physiographic features, surface water control structures, municipal groundwater wells, and monitoring wells. Lines in Florida map delineate county areas. et al. 2001). The model was calibrated using highly parameterized inversion techniques to help ensure that the model was a reasonable representation of the physical system. Challenges encountered with the calibration effort are described here for others working on sea-level rise groundwater simulations. Description of Study Area This study focuses on the Pompano Beach well field in northeastern Broward County, Florida (Figure 1). The study area is defined as the active model domain boundary shown in Figure 1. The climate of the area and southeastern Florida in general is characterized by distinct wet (May through October) and dry seasons. The extreme seasonal rainfall variability combined with the desire to reclaim large parts of the former Everglades for urban and agricultural uses necessitated the construction of an extensive water management system throughout most of southeastern Florida. This water management system consists of a series of levees, canals, pumps, and gates, which are used to control the elevation of the water table. A structure is a spillway, culvert, or weir located within a canal that can be used to control the water surface elevation. Primary structures are controlled and operated NGWA.org by the South Florida Water Management District and by the U.S. Army Corps of Engineers. Secondary and smaller drainage features are operated by the county and local drainage districts. During the wet season and hurricane events, excess water is released in to the Atlantic Ocean as a mechanism for providing flood protection. During the dry season, the canal system is used to provide aquifer recharge in coastal areas to prevent salt water intrusion into municipal well fields. The water management system is also used by the agricultural community during dry periods as a source of irrigation water. East of the easternmost control structure, canals are tidally influenced and can have salinities close to that of sea water. Tidal “finger” canals, which were dredged to provide waterfront property with ocean access, can be seen in Figure 2 in the area east of the Pompano Beach well field. Prior to the extensive development that occurred during the 20th century, northern Broward County was characterized by Everglades fresh water wetlands that extended from inland areas to the western side of the Atlantic Coastal Ridge (Parker et al. 1955). The Hillsboro River and Cypress Creek (presently the Hillsboro Canal and the Cypress Creek Canal) flowed eastward through low areas in the Atlantic Coastal Ridge called the Peat Transverse Glades (Parker et al. 1955). With land C. Langevin and M. Zygnerski GROUND WATER 3
    • sea level, are referenced to the National Geodetic Vertical Datum (NGVD) of 1929. The surficial aquifer system in southern Florida contains the highly transmissive Biscayne aquifer and the gray limestone aquifer. According to Fish (1988) and Reese and Cunningham (2000), the gray limestone aquifer is not present within the study area. The Biscayne aquifer, however, is present within the study area and is the primary water producing part of the surficial aquifer system. Fish (1988) defines the Biscayne aquifer as that part of the surficial aquifer system in southeast Florida comprised (from land surface downward) of the Pamlico Sand, Miami Oolite, Anastasia Formation, Key Largo Limestone, and Fort Thompson Formation all of Pleistocene age, and contiguous highly permeable beds of the Tamiami Formation of Pliocene age where at least 10 feet of the section is very highly permeable (a horizontal hydraulic conductivity of about 1,000 ft/d or more). Figure 2. Map of the area of interest showing the salt water intrusion lines mapped by Dunn (2001) for the top of the production zone. The lines are contours of the 250 mg/L chloride concentration for different years. elevations exceeding 7 m, it is unlikely that the Atlantic Coastal Ridge in this area would ever have been inundated by the fresh water wetlands to the west. During the 20th century, the landscape of northern Broward County changed considerably. What were once the fresh water wetlands of the Everglades were transformed first into agricultural areas and then into the expansive urban corridor of today (Renken et al. 2005). Hydrostratigraphy and Aquifer Properties This study focuses on the highly permeable, shallow surficial aquifer system, which is the primary source of potable water in Broward County (Klein and Hull 1978; Causaras 1985). The underlying Floridan aquifer system, which is hydraulically separated from the surficial aquifer system by an extensive confining unit, is not discussed in this paper or represented in the model. A study on the effect of long-term (100,000 year) sea-level changes on the Floridan aquifer system is reported by Hughes et al. (2009). The surficial aquifer system, which increases in thickness from west to east, is defined on the top by the water table and at the bottom by the top of the Hawthorn confining unit (Fish 1988). The base of the surficial aquifer system slopes downward from an elevation of about −40 to −55 m in the western part of the study area to more than −110 m in the eastern part. In the Pompano Beach well field, Fish (1988) defined the base of the surficial aquifer system at an elevation of about −114 m. In this paper, all elevations, including those referring to 4 C. Langevin and M. Zygnerski GROUND WATER With this definition, Fish (1988) mapped the base of the Biscayne aquifer in the western part of the study area at an elevation of about −37 m. At the Pompano Beach well field, Fish (1988) mapped the base of the Biscayne aquifer at an elevation of about −98 m, which is slightly higher than the elevation of −122 m suggested by Tarver (1964, 8) for the Pompano Beach well-field area. Implicit in the Fish (1988) definition is that the top of the Biscayne aquifer coincides with the water table. Restrepo et al. (1992) and Dunn (2001), however, note that a blanket of less permeable sand (of the Pamlico Sand and Anastasia Formation) is present in most areas. They define the top of the Biscayne aquifer as being the first occurrence of highly permeable limestone. For the present study, a similar distinction is made and the overlying less permeable sands are not included as part of the Biscayne aquifer. Accordingly, this paper discusses three parts of the surficial aquifer system: the upper part, the Biscayne aquifer, and the lower part. Ranges of aquifer properties as summarized from the literature are presented in Table 1. Fish (1988) constructed a transmissivity map using values from selected aquifer tests representative of the surficial aquifer system. The transmissivity estimates used to construct that map were used here with estimates of Biscayne aquifer thickness to calculate hydraulic conductivity. These hydraulic conductivities are thought to be representative of the average hydraulic conductivity over the entire Biscayne aquifer thickness. Hydraulic conductivities of individual zones within the Biscayne aquifer are probably much different than these average values. Nevertheless, these average values are used as starting hydraulic conductivities for the numerical model, which were then adjusted as part of the calibration process. Salt Water Intrusion near the Pompano Beach Well Field Construction of the Pompano Beach well field began in 1926 with the completion of the first well in 1927 (Dunn 2001). The well field was located on the Atlantic Coastal Ridge because the underlying surficial aquifer system near NGWA.org
    • Table 1 Summary of Aquifer Properties for the Surficial Aquifer System Property Value Kh (upper part of surficial aquifer system) Kh (Biscayne aquifer) 15 m/d 80–20,000 m/d References Comment Fish (1988) Fish (1988, Table 4) Kh (lower part of surficial aquifer system) Kv:Kh (Biscayne aquifer) Sy (Biscyane aquifer) Sy (Biscayne aquifer) Sy (Biscayne aquifer) 0.1–20 m/d Fish (1988) 1:7 to 1:49 0.004–0.30 0.093–0.25 0.20–0.25 Camp and McKee, Inc. (1980) Fish (1988) Camp and McKee, Inc. (1980) Merritt (1996a) αL , αT (Biscayne aquifer) 1–10, 0.1–1 m αL , αT (Biscayne aquifer) 76, 0.03 m Merritt (1995) αL , αT (Biscayne aquifer) 2.0–2.5 m Renken et al. (2008) n (Biscayne aquifer and lower part of surficial aquifer system) n (surficial aquifer system) n (Biscayne aquifer) n (Biscayne aquifer) 0.37–0.48 Fish (1988) Values calculated from multiple pumping test results and aquifer thickness at different locations 0.20 0.20 0.4 Langevin (2001, 2003) Merritt (1996b) Langevin (2001) Renken et al. (2008) Analysis based on rainfall-event-based water level fluctuations in Miami-Dade County Calibration of variable-density groundwater model in Miami-Dade County Calibration of solute transport model in Miami-Dade County From a tracer test in Miami-Dade County Analyses performed on core-scale samples Based on one-dimensional simulations of a tracer test in Miami-Dade County Notes: A range is reported for some properties because more than one value is reported in the literature. Kh is horizontal hydraulic conductivity; Kv is vertical hydraulic conductivity; Sy is specific yield; αL is longitudinal dispersivity; αT is transverse dispersivity; n is porosity. the ridge tends to have better groundwater quality than areas to the west (Tarver 1964). Five additional production wells were drilled during the 1950s. By 1972, the well field consisted of a total of 16 production wells (Figure 2). These wells were completed in a production zone of the Biscayne aquifer that extends from about 22 to 43 m below sea level. Production well 1 was abandoned in the mid-1980s (Dunn 2001) because of elevated chloride concentrations. Using measured chloride concentrations at monitoring wells and an estimate of the vertical chloride concentration gradient, Dunn (2001) mapped the temporal evolution of the position of the 250 mg/L isochlor near the well field. Contours of the 250 mg/L isochlor at the top of the production zone (about 22 m below sea level) are shown in Figure 2 for selected years between 1972 and 1999. The isochlor advanced to its furthest inland position in 1984 and then moved seaward to its last mapped position in 1999. Identifying the contributing factors, such as drought and groundwater withdrawals, to the advance and subsequent retreat of saline groundwater is not straightforward as there are likely many factors contributing to salt water movement. Relevant data for the Pompano Beach well-field area are shown in Figure 3 to summarize the hydrologic NGWA.org conditions that led to the advance and subsequent retreat of saline groundwater in the surficial aquifer system. Rainfall variations have been suggested by Dunn (2001) as one of the primary drivers for the salt water intrusion event that began in the mid-1970s. For the 1970 to 1981 period, 11 out of the 12 years had rainfall values less than the long-term mean, and this period corresponds to a time of salt water intrusion. Groundwater withdrawals from the Pompano Beach well field are probably a dominant cause of the salt water intrusion event. From 1950 to 1980, withdrawals at the Pompano Beach well field continued to increase. By 1980, groundwater withdrawals reached 1 × 105 m3 /d (Figure 3). Based on a simple Theis analysis of predicted drawdown, Tarver (1964) warned that withdrawals exceeding about 7.6 × 104 m3 /d could cause salt water intrusion and suggested that an expansion of the well field to the north and west would reduce the potential for salt water intrusion by distributing the withdrawal effects. The withdrawal threshold calculated by Tarver (1964) was first exceeded in 1971. In 1984, the City of Pompano Beach constructed the Palm Aire well field about 5 km west of the Pompano Beach well field (Figure 1). The late 1980s to the present shows a redistribution of groundwater withdrawals from the C. Langevin and M. Zygnerski GROUND WATER 5
    • Figure 3. Plots of rainfall, groundwater withdrawals, water levels, and TDS concentration for selected monitoring wells. Pompano Beach well field to the Palm Aire well field (Figure 3). Reluctance by water managers to construct new well fields in the western part of the county was due to the occurrence of poor quality groundwater (Howie 1987). Water levels of the Atlantic Ocean, Cypress Creek and Hillsboro Canals, and the G-853 monitoring well provide insight into the salt water intrusion event (Figure 3). Both the Hillsboro and Cypress Creek Canals maintain relatively constant stages from about 1970 onward. The Atlantic Ocean, however, shows an increase of about 25 cm from 1900 to 2005. By itself, the rise in sea level does not explain the salt water intrusion event, but it may have been a contributing factor. The most striking feature of the water levels in Figure 3 is the sharp decline in the G-853 monitoring well, which is located near the center of the well field. Water levels in this well remained near or below sea level for the 1970 to 1990 period. A water table map constructed by Sherwood et al. (1973) for May 1971 showed water levels 1-m below sea level for much of the Pompano Beach well-field area. An interesting characteristic of the salt water intrusion event was that salt water intruded more rapidly in the 6 C. Langevin and M. Zygnerski GROUND WATER production zone than in the layer beneath the production zone. The G-2055A monitoring well was open to the production zone and salinity concentrations started to rise in 1974. The G-2055 monitoring well, located next to G-2055A, but open in a deeper zone, did not begin to show elevated salinity concentrations until about 1983. Data from these two wells indicate the presence of an isolated salt water wedge in the middle part of the aquifer. The City of Pompano Beach owns and maintains the municipal golf course adjacent to the Pompano Beach well field (Figure 2). The golf course is irrigated using treated waste water. Irrigation rates were intentionally increased above what is needed to maintain the golf course in order to provide artificial recharge and prevent salt water intrusion. Irrigation with treated waste water began in August 1989. The average irrigation rate from 1989 to 2005 is about 4300 m3 /d. Averaged over the area of the golf course, this rate is about 120 cm/year, which is similar to the average annual rainfall rate of about 150 cm/year. The importance of excess golf course irrigation on minimizing the potential for salt water intrusion was evaluated with a sensitivity analysis. NGWA.org
    • Model Development and Calibration A variable-density groundwater flow and solute transport model was developed for the northern part of Broward County to evaluate the causes of salt water intrusion near the Pompano Beach well field and to determine if historical sea-level rise was a factor. The model was then used to predict the effect of alternative rates of sea-level rise on salt water intrusion. To ensure that the inversion process had the flexibility to extract the most information from the observation data set, the model was calibrated for a 105-year simulation period (1900 to 2005) using a highly parameterized approach. Simulation of this a long time period is computationally intensive, and so it is worthwhile to comment on the rationale for choosing the calibration period length, which was established early in the study. First, sea level has risen by about 25 cm over this calibration period; therefore, sensitivity analyses can be used with the calibrated model to test the effect of that 25-cm rise on salt water intrusion in the area. It may not be possible to resolve the importance of sealevel rise with shorter simulations. Second, it is difficult to assign initial conditions to salt water intrusion models. Models with long simulation periods tend to be less sensitive to errors in initial concentrations than models with short simulation periods. Lastly, there was no way to quantify how long it would take for saline groundwater to respond to hydrologic variability. Because the hydrology changed drastically over the 105-year period, a long calibration period seemed necessary in order to ensure that it contained the hydrologic forcings responsible for causing salt water movement. Parameter estimation with flow and transport observations has not been applied to threedimensional sea water intrusion problems (Carrera et al. 2010); however, Dausman et al. (2010) applied automated inversion techniques for a related problem of buoyancydriven plume migration. This study, therefore, is among the first to apply sophisticated calibration strategies to a three-dimensional salt water intrusion model. Several numerical models of groundwater flow have been developed for Broward County. Restrepo et al. (1992) designed a groundwater model to address problems associated with water supply; however, the model did not include a variable-density component. Two models designed to evaluate salt water intrusion in southern Broward County, south of the present study, are described by Andersen et al. (1988) and Merritt (1996b). Other variable-density models developed for nearby areas to evaluate groundwater flows or salt water intrusion are described by Langevin (2001, 2003), Dausman and Langevin (2005), and Guha and Panday (2012). Simulation Codes SEAWAT is a coupled version of MODFLOW and MT3DMS designed to simulate variable-density groundwater flow and solute transport (Guo and Langevin 2001; Langevin et al. 2003; Langevin and Guo 2006). The program has been used to address a variety of issues, such as submarine groundwater discharge (Langevin 2001, 2003) and salt water intrusion (e.g., Shoemaker NGWA.org and Edwards 2003; Rao et al. 2004; Shoemaker 2004; Masterson 2004; Dausman and Langevin 2005; Hughes et al. 2010), for example. The simulations reported here were performed using SEAWAT Version 4 (Langevin et al. 2008), which is based on MODFLOW-2000 (Harbaugh et al. 2000) and MT3DMS Version 5 (Zheng and Wang 1999; Zheng 2006). For the present application, the solute concentration (C) simulated by the model is the total dissolved solids (TDS) concentration of sea water salts. Fresh water is assumed to have a TDS concentration of zero; sea water is assumed to have a TDS concentration of 35 g/L. Fluid density (ρ) is calculated by SEAWAT using a linear relation subject to the constraints that fresh water has a fluid density of 1000 kg/m3 and sea water has a density value of 1025 kg/m3 . The resulting equation of state used for all of the simulations reported here is: ρ = ρf + 0.714 C. In some instances, chloride concentration measurements were available. These concentrations were converted to TDS concentrations using a simple linear relation between sea water, which has a chloride concentration of about 19,800 mg/L, and fresh water, which is assumed to have a chloride concentration of zero. A chloride concentration of 250 mg/L is commonly used as a maximum concentration for potable water. In terms of TDS, this equates to a concentration of 0.44 g/L. Many of the preliminary simulations used the implicit finite-difference solution method in MT3DMS and SEAWAT to solve the solute transport equation. Later tests revealed, however, that this solution scheme was causing an excessive level of numerical dispersion, resulting in a high level of parameter surrogacy, and difficulties were encountered in trying to reproduce observed salinity variations in monitoring wells. Parameter surrogacy occurs when the inversion process adjusts parameter values in order to compensate for errors in the model, such as numerical dispersion. The simulations reported here used the explicit third order, Total variation diminishing (TVD) scheme in MT3DMS and SEAWAT as an alternative to the standard implicit finite-difference scheme. TVD is mass conservative and can minimize numerical dispersion, but because it is an explicit scheme, it is subject to time step constraints and can be computationally demanding. TVD simulations better represented the presumed level of hydrodynamic dispersion as evidenced by an improved ability to represent observed salinity variations compared with finite-difference transport solutions. Related work by Langevin and Hughes (2009) showed that calibration of a highly parameterized salt water intrusion model can result in parameter surrogacy, such as heterogeneity artifacts in the presence of numerical dispersion. These artifacts can be reduced by using high levels of grid resolution or TVD schemes that minimize numerical dispersion and also by using uniform concentration weighting schemes for calibration instead of assigning weights that are proportional to the concentration value. Preliminary simulations of the salt water intrusion event had difficulties reproducing the relatively quick response of salinity concentrations in groundwater C. Langevin and M. Zygnerski GROUND WATER 7
    • monitoring wells. Numerous attempts to capture the response with alternative parameterization approaches and parameter values repeatedly failed until the conceptual model for transport was revised. The surficial aquifer system in southern Florida is highly heterogeneous in both the vertical and horizontal directions. Recent work in southeastern Florida (Cunningham et al. 2006, 2009; Renken et al. 2008) has identified the presence of preferential flow pathways that likely play a key role in transport even though they comprise only a fraction of the aquifer total thickness. To accommodate these important groundwater flow pathways, the dual-domain capabilities in MT3DMS (and SEAWAT) were used (Zheng and Wang 1999). With the dual-domain approach, the aquifer is conceptualized as having a fast moving mobile domain and an immobile domain. All advective transport occurs within the fast domain, and solute exchange between the two domains occurs based on an exchange coefficient and the concentration difference. Lu and Luo (2010) demonstrate the effect of the dual-domain conceptual model on salt water intrusion simulations. The dual-domain approach was used for all the simulations reported here. The salt water intrusion model was calibrated using the PEST software suite (Doherty 2009a, 2009b). PEST uses the Gauss-Marquardt-Levenberg algorithm to estimate parameters by minimizing weighted residuals between observations and simulated equivalents. To avoid problems with numerical instabilities and to allow for the estimation of many more parameters than there are observations, PEST contains several options for regularizing the problem into one that is tractable. For example, PEST contains subspace regularization methods (singular value decomposition [SVD]) as well as Tikhonov methods. For the present application, the SVD-assist technique (Doherty 2009a, 2009b), which is a combination of both subspace and Tikhonov methods, was the approach used for model calibration. Parameter estimation methods based on perturbation sensitivities can benefit greatly from parallelization (Carrera et al. 2010). To facilitate tractability of the parameter estimation process, a cluster computer with 232 computer cores was used. Spatial and Temporal Discretization The model grid consists of 115 rows and 160 columns (Figure 4). Each model cell is 150 by 150 m. In the Universal Transverse Mercator (UTM) Zone 17 coordinate system and the horizontal 1983 North American Datum (NAD 83), the southwest corner of the model grid is located at x = 570,000 and y = 2,898,350. There is no rotation of the model grid from the UTM coordinate system. The model is bounded on the west by Water Conservation Area 2A, to the north by the Hillsboro Canal, to the south by the Cypress Creek Canal, and to the east by the Intracoastal Waterway and the Atlantic Ocean. Although the extent of the model grid includes the barrier island system, groundwater flow within the shallow isolated lens of the barrier island is only roughly approximated owing to an insufficient grid resolution relative to the island width. 8 C. Langevin and M. Zygnerski GROUND WATER Figure 4. Model grid, inland and coastal pilot points, and layer 1 boundary conditions for stress period 783 (December 2005). Nine model layers were used to discretize the surficial aquifer system. Model layers 1 and 2 correspond to the unconsolidated sediments of low to moderate permeability that overly the Biscayne. Layers 3 through 8 correspond to the highly transmissive Biscayne aquifer, and layer 9 represents the lower part of the surficial aquifer system, which tends to be less permeable than the Biscayne aquifer. Land surface elevation was estimated using 10m horizontal resolution, U.S. Geological Survey (USGS) digital elevation models. The bottom of model layer 1 was set uniformly at an elevation of −5.0 m. This elevation was set lower than the lowest anticipated water table elevation so that wetting and drying problems common to MODFLOW-based codes could be avoided. The bottom of model layer 2 was specified using elevation data from the bottom of layer 2 of an existing Broward County flow model (Restrepo et al., 1992). Layer 2 of that model also corresponded to the lower permeability sands overlying the Biscayne aquifer. Spatial interpolation using estimates of the bottom of the Biscayne aquifer (Fish 1988) was used to assign elevations for the bottom of model layer 8. The thickness of the Biscayne aquifer (bottom of layer 8 subtracted from bottom of layer 2) was then divided equally among model layers 3 through 8. Spatial interpolation using estimates of the bottom of the surficial aquifer system (Fish 1988) was used to assign elevations for the bottom of model layer 9. SEAWAT follows the MODFLOW and MT3DMS convention of stress periods, flow time steps, and transport time steps (Langevin et al. 2003). Hydrologic stresses remain constant for each stress period, with the exception of specified heads. Specified heads are linearly interpolated within a stress period from starting and ending head values assigned for each stress period. Time is further discretized in SEAWAT using transport time steps. NGWA.org
    • For each transport time step, SEAWAT first solves the flow equation and then solves the transport equation. Although SEAWAT contains options for iteratively solving the flow and transport equations until the solution meets a specified convergence criterion, this option was not used for the present study. The 105-year simulation period, beginning January 1, 1900, and ending December 31, 2005, was divided into 783 stress periods. The first three stress periods represent the 40 years from January 1, 1900 to December 31, 1940. The first stress period represents the time period prior to the construction of major canals. The second stress period starts January 1, 1907, which is the approximate construction date of the Hillsboro Canal, and extends through December 31, 1929. The third stress period starts January 1, 1930, which is the approximate construction date of the Pompano Canal, and ends December 31, 1940. One flow time step, which can be used in SEAWAT to control the frequency of writing output, was used per stress period. Lengths of transport time steps were calculated during the simulation using a specified Courant number of 0.75. Representation of Hydrologic Stresses Hydrologic stresses were included in the model as boundary conditions or as internal sources and sinks. In most instances, representation of hydrologic stresses required specification of a flux or head-dependent condition and the specification of a solute concentration or flux. Accordingly, each hydrologic stress is discussed both in terms of its effect on groundwater flow and solute transport. The hydrologic features and the MODFLOW/SEAWAT package used for their representation in the model are summarized in Table 2. A simplified linear equation was used to estimate the Atlantic Ocean stage relative to NGVD 1929 for the 1900 to 1940 period (C. Zervas, National Oceanic and Atmospheric Administration [NOAA], written communication, 2007): Stage = 2.39 mm/year (year − 2000) + 22.6 mm. For the remainder of the simulation period, data from three NOAA tide stations were combined. From January 1941 to June 1981, tide data from the NOAA Miami Beach tide station (station identification number 8723170) were used. From August 1981 to August 1992, data from the Haulover Pier tide station (station identification number 8723080) were used. From February 1994 to December 2005, data from the Virginia Key station (station identification number 8723214) were used. The resulting Atlantic Ocean stage record, as used in the model, is shown in Figure 5. Parameterization, Regularization, and Initial Parameter Values Application of formal parameter estimation techniques requires parameterization of aquifer properties and initial parameter values from which calibration takes NGWA.org place. The initial parameter values should be assigned based on existing system information. For highly parameterized models, some form of regularization must also be applied for the problem to be tractable. For the present study, preferred value regularization was applied to all parameters using the initial parameter value. An irregular distribution of 97 pilot points (Doherty 2003), with a higher density of points near the Pompano Beach well field, was used to parameterize Kh (Figure 4). These 97 pilot points were used for each model layer. Ordinary kriging was used with an isotropic exponential variogram and a range of approximately 7.5 km to interpolate between pilot points. Statistics on the initial Kh parameter fields and the minimum and maximum restricted values during calibration are provided in Table 3. Initial Kh pilot-point values for the Biscayne aquifer (model layers 3 to 8) were assigned using a spatially variable Kh map prepared using the aquifer tests reported in Fish (1988). At each pilot point, 80% of the Biscayne aquifer transmissivity was apportioned evenly among layers 3 through 5 (the production zone) and used as the initial value for calibration. The remaining 20% of the Biscayne aquifer transmissivity was evenly apportioned among model layers 6 through 8. In coastal areas, Kh pilot-point values were allowed to vary for all layers. For inland pilot points, however, a single Kh multiplier was used to scale the initial Kh values in model layers 3 through 8 by a single value. A similar pilot-point methodology was used for the Kh:Kv ratio and n. An initial parameter value of 100 was assigned to Kh:Kv for all model layers. For inland pilot points, the Kh:Kv ratio in model layers 3 through 8 were adjusted by a single factor. The Kh:Kv ratio was restricted to a range between 1 and 10,000. An initial parameter field of 0.25 for the mobile domain porosity (n) was assigned for model layers 1, 2, and 9; based on preliminary simulations of salt water movement, an n value of 0.10 was assigned to the Biscayne aquifer (layers 3 through 8). For calibration, n was restricted to a range between 0.05 and 0.40. Use of a lower n value than found in the literature for layers 3 through 8 was required to match the salt water intrusion event and subsequent flushing. The model could not match the timing of these events with higher n values, providing further support for the concept of preferential flow zones in the Biscayne aquifer. Similar to Kh and Kh:Kv, n values for model layers 3 to 8 were adjusted by a single factor at inland pilot-point locations. During parameter estimation, the conductance for each canal reach was updated using the spatially variable Kh field because these dredged canals typically have good hydraulic connection with the adjacent aquifer. This approach provided the inversion process with a mechanism for adjusting aquifer-canal interaction. Other parameters estimated as part of the calibration process are included in Table 4. These parameters do not vary spatially or temporally. In the absence of literature values, results from preliminary sensitivity simulations were used to determine initial values for these parameters. For example, a relatively low value was required for the C. Langevin and M. Zygnerski GROUND WATER 9
    • Table 2 Hydrologic Feature and the Package Used to Represent the Stress Hydrologic Feature MODFLOW/SEAWAT Package Atlantic Ocean and Intracoastal Waterway CHD Predevelopment fresh water wetlands GHB Primary water management canals GHB Secondary water management canals RIV Tidal canals GHB and RIV Recharge RCH Evapotranspiration EVT Well-field withdrawals WEL Golf course irrigation WEL Comment Cells with center elevations above the Atlantic Ocean sea floor are represented as time-varying specified heads with the TDS concentration for inflow specified as 35 g/L. Intracoastal waterway cells are also included as time-varying specified heads, but with a TDS concentration of inflow specified as 27 g/L (BCDPEP 2001) and only in model layer 1. Everglades fresh water wetlands were represented in western parts of the model in stress period 1 with a TDS concentration of zero. The stage was set to 4 m, and the hydraulic conductance was calculated using the cell area, half the cell thickness of model layer 1, and the estimated vertical hydraulic conductivity of model layer 1. Primary water management canals (Hillsboro, L36, Pompano, and Cypress Creek) were represented in model layers 1 and 2 using historical stage measurements. Canals were activated in the model based on construction date. Hydraulic conductance was calculated for each canal cell using an estimate of the aquifer-canal contact area, the estimated horizontal hydraulic conductivity of the aquifer at that cell, and a flow length of 50 m. A TDS concentration of 8 g/L was specified for the tidal part of the Hillsboro Canal and 18 g/L was assigned for the tidal parts of the Pompano and Cypress Creek Canals. These concentrations were calculated using water-quality data reported in BCDPEP (2001). Secondary and tertiary water management canals were represented in model layer 1 using the RIV Package. Canal activation date, stage, and hydraulic conductance were assigned using the same procedure described for the primary water management canals. Tidal finger canals were assigned Atlantic Ocean stages and TDS concentrations of the adjoining water body (Intracoastal Waterway, Hillsboro Canal, or Cypress Creek Canal). Tidal canal activation date and hydraulic conductance were assigned using the same procedure described for the primary water management canals. A spatially uniform recharge rate was assigned to model layer 1 based on measured rainfall totals. No attempt was made to subtract runoff, interception, and unsaturated zone evapotranspiration quantities. This approach was used by Merritt (1996a) and Langevin (2001, 2003) for similarly constructed groundwater models of Miami-Dade County. The evapotranspiration surface was calculated by subtracting a value of 1.0 m from land surface to approximate microtopographic effects of small depressions. The extinction depth was set to 7.0 m; this relatively large depth was explained by Merritt (1996a) as approximating other processes not represented by the model. For the first three stress periods, a maximum evapotranspiration rate of 151 cm/year was assigned (Merritt 1996a). For the remaining stress periods, the maximum evapotranspiration rate varied by month according to the rates estimated by Merritt (1996a). Withdrawals at public supply wells were specified in the model based on estimated pumping records for each well. For public supply wells with open-hole intervals that spanned multiple model layers, the withdrawal rate was apportioned based on the estimated horizontal hydraulic conductivity at that cell. Excess golf course irrigation (artificial recharge) was modeled by specifying a flux to layer 1 model cells within the Pompano Beach municipal golf course. Measured irrigation totals not available for 1993–1994 and 2002–2005 were estimated from other years. The percentage of the irrigation water that recharges the aquifer was calculated as part of the calibration process. The TDS concentration of the irrigation water was calculated using an average chloride concentration of 400 mg/L. BCDPEP, Broward County Department of Planning and Environmental Protection. 10 C. Langevin and M. Zygnerski GROUND WATER NGWA.org
    • development process; however, steady-state conditions were difficult to estimate, concerns over changes in sea level raised questions about the defensibility of this approach, and long runtimes were required to achieve steady-state conditions. As an alternative, a variant of the pilot-point methodology, as described in Doherty (2009c), was used to parameterize the initial salinity field. Initial heads were not parameterized in this manner as they equilibrated quickly relative to the length of the simulation. Initial interface elevations were assigned to the pilot points shown in Figure 4 using the salinity field from a preliminary steady-state simulation. Ordinary kriging was then used to spatially interpolate the twodimensional interface surface to the model grid. This interface surface was then intersected with the threedimensional model grid. Model cells with centroids above the surface were assigned an initial TDS concentration of zero; model cells with centroids below the interface surface were assigned an initial TDS concentration of 35 g/L. To represent a diffuse interface, an interface width parameter was introduced whereby TDS concentration decreased upward and increased downward according to a sigmoidal function. The interface width parameter was assigned an initial value of 10 m and was limited to a range between 1 and 50 m. Dausman et al. (2010) used a similar approach to parameterize a salinity field. The Figure 5. The Atlantic Ocean stage record (relative to the National Geodetic Vertical Datum of 1929) as used in the model. dual-domain mass transfer rate, which indicates that the system is advection dominated with little mass transfer between the mobile and immobile domains. An advection dominated system with slow exchange between the mobile and immobile domains is supported by the relatively fast rates of observed salt water intrusion and subsequent aquifer flushing, and by the lack of a pronounced tail on the observed TDS concentration plots (Figure 3). Initial conditions can be complicated to estimate for transient salt water intrusion models because they are rarely known with any certainty, and they can have a large effect on model predictions. A common procedure is to perform a steady-state simulation and then use the resulting salinity field as input for a subsequent transient analysis. This approach was used early in the model Table 3 Statistical Description of the Spatially Variable Horizontal Hydraulic Conductivity (Kh) Fields Prior to Calibration Parameter Group Kh1 Kh2 Kh3 Kh4 Kh5 Kh6 Kh7 Kh8 Kh9 Mean (log[Kh]) Standard Deviation (log[Kh]) Initial Kh Pilot Point (Min) Initial Kh Pilot Point (Max) Calibration Minimum Limit 1.176 1.176 2.327 2.327 2.327 1.726 1.726 1.726 0.845 0.0 0.0 0.303 0.303 0.303 0.303 0.303 0.303 0.0 15 15 43 43 43 11 11 11 7 15 15 572 572 572 143 143 143 7 Calibration Maximum Limit 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 100 100 10,000 10,000 10,000 10,000 10,000 10,000 100 Note: Kh values are in m/d. Table 4 Spatially Uniform Model Parameters Estimated as Part of the Calibration Process Parameter Initial Value Calibration Minimum Limit Calibration Maximum Limit Specific storage Specific yield Evapotranspiration Extinction depth Multiplier for golf course Irrigation to Aquifer recharge Dual-domain mass Transfer rate Immobile domain porosity 1 × 10−5 /m 0.20 7m 0.20 1 × 10−7 /m 0.10 0.1 m 0.1 1 × 10−3 /m 0.40 10 m 0.9 1.02 × 10−7 /d 0.30 1 × 10−10 /d 0.2 1.0 /d 0.5 NGWA.org C. Langevin and M. Zygnerski GROUND WATER 11
    • Table 5 Observation Groups Used for Model Calibration Observation Group HEADS HEADS_POMP CONCS CONCS_POMP C_WELL Description Water levels in monitoring wells outside the area of interest Water levels in monitoring wells within the area of interest Salinity concentrations in monitoring wells outside the area of interest Salinity concentrations in monitoring within the area of interest (this group also contains a time series of salinity concentration difference at the G2055 and G2055A nested monitoring wells) Measure of the total salt mass withdrawn at each public supply well over the entire simulation period (concentrations less than 0.4419 g/L not included in calculation) Weight Assigned to Individual Observations Number of Observations with a Nonzero Weight 0.0 0 0 3.45 1735 6347 2.55 1659 2064 7.43 2138 9209 0.04 130 11,085 Objective Function Value Prior to Calibration Note: The area of interest is shown in Figure 2. advantage of this approach is that the parameter estimation process is given the freedom to adjust the initial salinity field, if necessary, in order to better match observed salt water intrusion patterns, and thus lengthy steady-state runs can be avoided. Observations and Weights Water levels and TDS concentrations in groundwater monitoring wells and public supply wells comprised the observation dataset used to calibrate the model. Temporal and spatial interpolation of model results was used to derive simulated values that corresponded in time and space to the observations. The observation data set was divided into five observation groups (Table 5). Weights were assigned uniformly to observations within a group. Weights assigned to each group were manually adjusted to achieve the intended contribution of the observation group to the composite measurement objective function. A wide variety of weighting schemes and weight values were tested as part of the calibration process. For example, concentration weights are typically related to the inverse of the concentration value to accommodate the assumed level of measurement error (Hill and Tiedeman 2007; Sanz and Voss 2006). While this approach tended to improve the match for low concentrations, simulated TDS breakthrough curves did not adequately characterize the salt water intrusion event. Ultimately, the weights presented in Table 5 were used. The contribution of each observation group to the composite objection function was assigned on the basis of modeling objectives, an assessment of measurement error, and experience gained from preliminary calibration runs. The C_WELL observation group was intentionally assigned the highest contribution to the measurement 12 C. Langevin and M. Zygnerski GROUND WATER objection function. Historical water-quality records and discussions with well-field personnel indicated that with the exception of the public supply well at the south end of the well field, TDS concentrations of withdrawn groundwater never exceeded the potable limit (a chloride concentration of 250 mg/L, which equates to a TDS concentration of about 0.4419 g/L). TDS concentrations of withdrawn groundwater simulated by the uncalibrated model (using the initial parameter values), however, exceeded potable limits at certain times indicating that salt water had intruded into the Pompano Beach well field. Accordingly, the C_WELL observation group was assigned a relatively large weight to improve the capability of the model to represent fresh water conditions at municipal wells. TDS concentrations in monitoring wells near the Pompano Beach well field (Figure 2; CONCS_POMP) were weighted the next highest. The CONCS_POMP group also contains a time series of concentration differences at monitoring wells G2055 and G2055A. These derived observations were added to help the inversion process reproduce the isolated salt water wedge in the middle of the aquifer. Water levels near the Pompano Beach well field and then TDS concentration differences at other monitoring wells were weighted the next highest. Outside of the Pompano Beach well-field area, heads were assigned a weight of zero for two reasons. First, there was generally good agreement between simulated and observed heads with the uncalibrated model. This was not by chance, as many different conceptualizations, parameter sets, and boundary implementations were tested. The mean error and mean absolute error for the HEADS group were 0.03 and 0.41 m, respectively. Second, because groundwater levels in the Biscayne aquifer are highly dependent on exchanges with NGWA.org
    • the surface water system, errors in assignment of canal boundary levels have a large effect on simulated heads. Data exist for assigning some canal boundary levels, but they were derived or interpolated when missing. Consequently, when nonzero weights were assigned to the HEADS group, the parameter estimation process adjusted hydraulic conductivity as the sole option for improving the head match (canal levels were not parameterized). Consequently, the resulting parameter fields did not seem reasonable as they tended to compensate for the structural error caused by errors in assigned canal stage. Because of this weighting approach and the focus on the Pompano Beach well field, the domain outside the area of interest was not formally calibrated using PEST. This issue did not seem to affect the area of interest because the secondary canal network is restricted to only the westernmost part of the area of interest, and because historical stage measurements for the Pompano and Cypress Creek Canals were generally of good quality. Model Calibration PEST was used with the SVD-assist methodology for model calibration (Doherty 2009a, 2009b) to estimate a large number of parameter values, many of which were highly correlated. A preferred value regularization constraint was set for all of the estimated parameters based on literature values and results of preliminary calibration attempts with fewer parameters. The strength of the regularization constraints was controlled through PEST using a tuning variable. This variable was adjusted until a good fit was obtained with the measurements and the estimated parameter values and distributions were reasonable. The parameter estimation process made substantial progress in improving the fit between measured values and simulated equivalents as shown in Table 6. The inversion process was manually terminated on the 10th optimization iteration as progress toward reducing the measurement objective function had slowed considerably. For some previous calibration runs, the inversion process was allowed to continue for more than 40 optimization iterations, and while the matches between observed and simulated values were extraordinary, the resulting parameter fields contained a high level of heterogeneity that was not considered reasonable. Overfitting of the model to observations can reduce the accuracy of predictions (Doherty and Welter 2010). Even if the model was provided with the best possible set of parameter values, there would still be disagreement between observed values and simulated equivalents. This is because the model observations contain measurement error and because of structural errors in the model caused by numerical errors, simplifications of physical processes, spatial and temporal averaging, inaccurate boundary values, and other model inadequacies. Thus, if the calibration process is allowed to overfit the observations, parameter values may become polluted by measurement and structural errors. This overfitting may reduce the predictive capability of the model if the prediction is dependent on the affected parameters. To minimize the potential for this problem, the estimated parameter fields and values were carefully evaluated to ensure that the level of calibration achieved with the estimation process was consistent with the quality of the observations and model errors. Selection of the appropriate level of calibration was based on residual statistics, time-series plots of observed versus simulated values, plots of spatially varying parameter fields, and estimated parameter values. To facilitate the discussion, the uncalibrated model is referred to as Opt.0. The calibrated model for the first optimization iteration is referred to as Opt.1, and so forth. Opt.6 was selected as the model used for sensitivity and scenario analyses and is referred to later as the base case calibrated model. Time-series plots of water level and TDS concentration (Figure 6) highlight the progression of the calibration procedure for several of the key wells near the Pompano Beach well field. Simulated water levels at the G-853 monitoring well near the center of the well field are in good agreement with observed water levels. This Table 6 Table of Residual Statistics for Selected Observation Groups Optimization Iteration Group HEADS_POMP CONCS CONCS_POMP Statistics ME MAE RMS ME MAE RMS ME MAE RMS 0 1 2 −0.260 −0.241 −0.193 0.433 0.409 0.364 0.307 0.275 0.219 −13.113 −12.350 −10.891 16.193 15.313 13.541 478.334 426.133 329.704 4.059 3.990 3.791 9.687 9.105 8.178 195.063 173.486 140.950 3 4 5 6 7 8 −0.138 0.314 0.164 −8.641 11.011 216.841 3.151 6.736 98.411 −0.104 0.279 0.130 −6.483 8.685 136.608 2.575 5.631 70.578 −0.077 0.253 0.108 −4.950 7.133 93.741 2.051 4.956 53.031 −0.046 0.228 0.089 −2.207 4.446 43.902 1.844 4.320 39.869 −0.021 0.211 0.077 −0.820 3.032 28.892 1.322 3.951 33.100 −0.030 0.207 0.074 −0.471 2.479 22.575 1.190 3.465 26.653 Notes: Residual statistics were calculated for those with nonzero weights. The number of values used to calculate these statics are listed in Table 5. ME = mean error; MAE = mean absolute error; and RMS = root-mean-square error. NGWA.org C. Langevin and M. Zygnerski GROUND WATER 13
    • Figure 6. Plots of observed and simulated water levels and TDS concentrations for selected monitoring wells. The fit between observed and simulated values improves with increasing optimization number. Solid lines are for the Opt.6 base case model, which was used for the sensitivity analyses. Faint dashed lines are for other optimization iterations. is true for all of the optimization iterations, including the uncalibrated model. Simulated TDS concentrations are highly affected by the calibration process and it is clear that calibration has improved the fit between observed and simulated values, but there are some obvious deficiencies. For monitoring wells G-2054, G-2055A, and G-2063, for example, maximum simulated concentrations do not match with maximum observed concentrations. In the mid-1980s, simulated concentrations are as much as 10 g/L less than observed concentrations. Another model deficiency is the inability to accurately represent the 14 C. Langevin and M. Zygnerski GROUND WATER isolated salt water wedge detected at the G-2055A and G-2055 wells. In addition to the observed TDS concentration values used for calibration, a separate observation set of temporal concentration differences at these two wells was also used for calibration. Although there are many explanations for this model deficiency, the leading explanation is numerical dispersion caused by a lack of vertical model resolution. Thus, while broad salt water transition zone characteristics over the width of the aquifer may be adequately represented, concentration differences between layers may be underestimated. NGWA.org
    • (a) (b) Figure 7. Horizontal hydraulic conductivity (Kh, as a base 10 logarithm) of the Biscayne aquifer estimated from (a) Fish (1988) aquifer tests and from (b) the Opt6. model calibration. In general, estimated parameter values were within 10% of their specified initial values, but there were some exceptions. For example, the multiplier used to convert the irrigation flux to a net recharge flux was increased from 20% in Opt.0 to 70% in Opt.6. Heterogeneity was also introduced in Kh, Kh:Kv, and n. Plots of the Opt.0 and Opt.6 Kh fields (log transformed) for the Biscayne aquifer are shown in Figure 7. The vertically averaged Kh fields were calculated by summing the transmissivity values for model layers 3 through 8 and dividing by the Biscayne aquifer thickness. The Opt.0 and Opt.6 Kh fields share similar characteristics because the Fish (1988) data were used as initial parameter values and as preferred value regularization information. Thus, in the absence of informative observation data, estimated Kh values remained at their initial values. Near the Pompano Beach well field, heterogeneity in the Kh field was introduced as part of the calibration process to improve representation of the spatial and temporal pattern of the salt water intrusion event. Most importantly, a band of lower Kh was identified near the well field. There are no other sources of data to suggest if this lower Kh band is real or not, but the ability of the calibrated model to match G-853 water levels NGWA.org (Figure 6) within the highly stressed well field provides some assurance that the estimated Kh field is reasonable. Plots of Kh:Kv and n (not shown) show similar degrees of heterogeneity as shown for Kh. Prior to calibration, simulated TDS concentrations of groundwater withdrawn at the Pompano Beach well field were higher than observed values. Historical data indicate chloride concentrations of the pumped groundwater never exceeded drinking water standards for chloride (approximately equal to a TDS concentration of 0.44 g/L) except in one withdrawal well. All the simulations show an increase and subsequent decrease in the TDS concentration of pumped groundwater. As the optimization number increases, the TDS concentrations of pumped groundwater decrease to more realistic values near or below the potable limit, which is consistent with historical observations. In particular, there appears to be a large TDS decrease and improvement in the simulated pumped concentration between Opt.5 and Opt.6. This improvement between Opt.5 and Opt.6 is caused primarily by a lowering of the Kh in the area to the east of the well field (Figure 7). The model does a good job representing many of the important characteristics of the flow system at the well-field scale. Simulated heads are in good agreement with measured heads at G-853, for example, and the simulated water table map (Figure 8) is consistent with previously published water table maps (e.g., Tarver 1964). Most importantly for the present investigation, the model qualitatively represents characteristics of the salt water intrusion event and subsequent flushing. Figure 8 shows simulated TDS concentrations in model layer 3 for six of the years evaluated by Dunn (2001). Figure 8 also shows the 0.44 g/L TDS contour mapped by Dunn (2001) for the top of the Biscayne aquifer. Thus, the inland extent of the colored salt water zones in Figure 8 can be compared directly with the Dunn (2001) contours also shown in the figure. The model shows a gradual salinization of the aquifer during the late 1970s and 1980s, when drawdowns are the largest, and a subsequent freshening during the 1990s, after water levels had risen. The model does not, however, represent some details of the events, such as the exact spatial patterns of the intrusion or the precise timing of the retreat. At the coastline, the model simulates a zone with TDS concentrations less than 0.44 g/L. This zone forms at the top of the Biscayne aquifer due to fresh groundwater recharge from above. There are no groundwater salinity data to confirm whether or not the Biscayne aquifer is fresh in this area, and so these results should be evaluated with caution. Deeper model layers show elevated TDS concentrations for this area. Although a slight cone of depression can be seen in the water table for 1999, water levels clearly increased from 1984 to 1999 (Figure 8). The higher water table elevations had a positive impact by flushing out some of the salt water at the top of the Biscayne aquifer. The flushing can be attributed to a reduction in groundwater withdrawals, an increase in rainfall relative to the drought period, and artificial recharge at the golf course. Effects of C. Langevin and M. Zygnerski GROUND WATER 15
    • Figure 8. Comparison between simulated TDS concentrations in model layer 3 and the mapped 0.44 g/L TDS contour of Dunn (2001). Contours of the simulated water table elevation are also shown to indicate the effect of groundwater withdrawals on groundwater flow patterns. the 25-cm rise in sea level over the 105-year simulation period cannot be directly quantified from the calibrated model, nor can the relative importance of the other hydrologic stresses. For this reason, a sensitivity analysis was performed to isolate the relative importance of these factors on salt water intrusion. Effect of Historical Sea-Level Rise A qualitative sensitivity analysis was used to compare the importance of historical sea-level rise to several 16 C. Langevin and M. Zygnerski GROUND WATER other key hydrologic factors: well-field withdrawals, annual recharge variations, and artificial recharge at the golf course. The evaluation was performed by making a targeted adjustment to the input for the base case calibrated model (Opt.6) and then rerunning the simulation. This approach is consistent with the approach outlined by Lo´ iciga et al. (2012) for isolating the effect a of different stresses on salt water intrusion. In the case of historical sea-level rise, a constant sea level at the estimated 1900 level was used for the entire 105-year simulation for the tidal canals, the Intracoastal Waterway, NGWA.org
    • and the Atlantic Ocean. The importance of well-field withdrawals was evaluated by running a simulation without groundwater withdrawals. The next simulation was used to evaluate the importance of droughts and annual variations in recharge. Dunn (2001) hypothesized that the 1971 to 1982 period of below average rainfall was partially responsible for the observed salt water intrusion event at the well field. To evaluate this hypothesis, a simulation was performed using a constant recharge rate calculated from the average annual rainfall total. Lastly, the utility of the artificial recharge system was evaluated by performing a simulation without artificial recharge. As shown in Figure 9, historical sea-level rise does not have a large effect on the position of the 1 g/L TDS contour in model layer 4, compared to the effect of pumping, but the effect is discernible. In 1955, for example, the 1 g/L contour for the simulation without sea-level rise is about 100 m seaward of the 1 g/L contour for the calibrated model. The largest effect from historical sea-level rise can be seen in 1995 near the southeastern part of the well field. In this area, the 1 g/L contour is as much as 1 km farther inland for the calibrated model than for the simulation without sea-level rise. This difference in the contour position is the result of the larger fresh water flux toward the coast for the simulation without sea-level rise. Thus, as sea level rises, the hydraulic gradient is reduced, the fresh groundwater flux decreases, and salt water intrusion occurs. This response is consistent with a head-controlled system. An analysis of simulated well-field TDS concentration (not shown) also indicates the effect of sea-level rise. The calibrated model shows an increase in TDS beginning in about 1971 and with TDS values exceeding the potable limit in 1984. Without a rise in sea level, the increase in TDS occurs within about a year of the calibrated model, but the well-field TDS concentration never exceeds the potable limit. Most importantly, well-field TDS concentrations are consistently about 0.2 g/L less from about 1980 to 2002 for the case without sea-level rise. Although this is a relatively small difference, it equates to a difference in chloride concentration of about 100 mg/L, which is important considering the drinking water standard is 250 mg/L. To further evaluate the head-controlled nature of the system in response to sea-level rise, the simulated water table from the calibrated model was compared to the simulated water table from the sensitivity simulation without sea-level rise. Over most of the model domain, the elevation of the water table compares to within about 0.02 m or less. Along a narrow band near the coast, however, the water table for the calibrated model is higher than the water table for the simulation without sea-level rise. Specifically, to the east of a line that connects structure G56 with G57 (the easternmost structures that separate the fresh water canals from the tidally influenced canals; Figure 1), there are no fresh water canals to act as a strong head control and the relatively high land surface elevations along the Atlantic Coastal Ridge allow the water table to rise without much restriction by evapotranspiration. The sensitivity analysis clearly indicates that wellfield withdrawals have the largest effect on the position Figure 9. Results from the qualitative sensitivity analysis showing simulated results for the base case and for simulations of constant recharge, no sea-level rise, no groundwater withdrawals, and no artificial recharge. Contours are of the 1 g/L TDS concentration in model layer 4. NGWA.org C. Langevin and M. Zygnerski GROUND WATER 17
    • of the 1 g/L TDS contour (Figure 9). By eliminating pumping altogether, the 1 g/L TDS contour does not change appreciably and the slight changes shown in Figure 9 can be attributed to construction of the tidal finger canals, historical sea-level rise, and recharge variations. To further evaluate the effect of well-field withdrawals, a range of different withdrawal increases and decreases were simulated. By eliminating withdrawals altogether, there is no historical rise in TDS concentrations at the well field. Doubling withdrawals, however, show substantial increases in well-field TDS concentrations. Slight decreases in well-field withdrawal rates also have a large effect on well-field TDS concentrations. Had the actual well-field withdrawals been 25% to 50% less, model results suggest that salt water intrusion may not have been a concern. Sensitivity results indicate that rainfall variations and artificial recharge can affect salt water intrusion, but the effects are much less important than effects of well-field withdrawals. Results from the simulation with a constant recharge rate are similar to the base case calibrated model, suggesting that the 1971 to 1982 period of less-thanaverage rainfall was not a predominant cause of salt water intrusion near the well field (Figure 9). A likely explanation is that surface water was brought into the area during that time to maintain water levels of the primary canals (Hillsboro and Cypress Creek). These canals do not show a decrease in stage during that period (Figure 3), and would have provided recharge to the aquifer to compensate for the drought conditions. Model results suggest that artificial recharge at the Pompano Municipal Golf Course has a beneficial impact on salt water intrusion. In 1995, for example (Figure 9), elimination of artificial recharge in the sensitivity simulation results in the 1 g/L TDS contour being located as much as 1.5 km landward of the position in the base case calibrated model. Contour positions in 2005 also suggest that artificial recharge helps to prevent salt water from intruding near the well field. Sensitivity to Projected Rates of Sea-Level Rise A sensitivity analysis was performed with the Opt. 6 model using four different rates of projected sea-level rise and using the average annual hydrologic conditions (well-field withdrawals, canal stages, rainfall and artificial recharge, and evapotranspiration rates) from the last year of the calibration period (2005). Results from these 100year simulations cannot be used to predict future rates of salt water intrusion in response to sea-level rise, because the simulations do not include anthropogenic changes, alternative rainfall patterns from climate change, or well-field management strategies. The results can be used, however, to investigate the sensitivity of salt water movement to different rates of projected sea-level rise. For the first simulation, sea level was held constant at the average annual 2005 level. For the remaining three simulations, sea level linearly increased over the 100year simulation at rates of 24, 48, and 88 cm/century as estimated in the IPCC TAR (Church et al. 2001). Sea-level 18 C. Langevin and M. Zygnerski GROUND WATER Figure 10. Simulated well-field TDS concentration for the sensitivity analysis of projected rates of sea-level rise. The concentrations were calculated as a volumetric average for groundwater extracted from municipal wells at the Pompano Beach well field. rise was represented in the model by linearly increasing the stage of the Atlantic Ocean and tidal canals. Intraannual variations in sea level were not represented in these simulations. Figure 10 shows a plot of well-field TDS concentration relative to time for the four simulations. The well-field TDS concentration was calculated as a volumetric average using the withdrawal rates and simulated TDS concentrations at individual extraction wells. Use of average 2005 hydrologic conditions and a constant sea level result in TDS concentrations of the well-field exceeding drinking water standards after 70 years. This finding suggests that the 2005 withdrawal rates may not be sustainable with the 2005 hydrologic conditions. When sea-level rise is included in the simulations, drinking water standards are exceeded 10 to 21 years earlier (after 60 years for a rise of 24 cm/century; 55 years for a rise of 48 cm/century; and 49 years for a rise of 88 cm/century). Apparent rates of lateral salt water intrusion in model layer 4 were calculated from these sensitivity simulations using the 1 g/L TDS contour. They are referred to here as apparent because there is an upward component of groundwater flow near the well field, and thus, intrusion is not limited to horizontal movement. Apparent lateral intrusion rates are 15, 17, 18, and 21 m/year for the 0, 24, 48, and 88 cm/century sea-level rise rates, respectively. Webb and Howard (2010) reported lateral salt water intrusion rates (referred to as interface velocity in their work) for different ratios of hydraulic conductivity to recharge and for different rates of sea-level rise. Their largest reported intrusion rate was 4 m/year, which is about four to seven times less than the rates reported here, but similar considering the substantial differences between their simplified two-dimensional system and the Pompano Beach well-field area. Discussion The Pompano Beach well-field area and nearby coastal areas in southeastern Florida represent an endmember in the spectrum of impacts of sea-level rise on NGWA.org
    • salt water intrusion. The following are a number of general observations about southeastern Florida that help explain why the shallow coastal aquifer system is particularly vulnerable to salt water intrusion caused by sea-level rise. 1. As shown by Werner and Simmons (2009), systems that are head controlled are more susceptible to salt water intrusion caused by sea-level rise than those that are flux controlled. For confined aquifers that are flux controlled, sea-level rise may not have any effect on salt water intrusion (Chang et al. 2011). The widespread canal system in southern Florida places an extensive head control on water levels in the shallow surficial aquifer. The head control is particularly strong in southeastern Florida due to the direct hydraulic connection between canals and the highly permeable Biscayne aquifer. Also, land surface is relatively flat with little relief, and the unsaturated zone is thin (typically less than a meter or two). Flooding from high water tables can be a problem in many neighborhoods. Evapotranspiration rates are also relatively high and can be similar to rainfall rates during the summer months. These combined conditions effectively eliminate the possibility for groundwater levels to rise as sea level rises. Consequently, the seaward hydraulic gradient and associated fresh groundwater flow toward the coast is expected to decrease. 2. Southeastern Florida has many tidally influenced canals that extend inland into the permeable coastal aquifer. In some cases, tidal canals extend inland as far as municipal well fields. These canals provide ocean access for a thriving boating community. Near the Pompano Beach well field, the tidal portion of the Cypress Creek Canal extends inland as far as the Pompano Beach well field. Tidal canals are also present between the well field and the Intracoastal Waterway. These tidal canals, which have elevated salinities, have stages at or near the stage of the Atlantic Ocean. A rising sea level makes it difficult to maintain a seaward hydraulic gradient that is strong enough to prevent salt water intrusion. 3. The highly permeable shallow aquifer system also contributes to the susceptibility of southeastern Florida to sea-level rise. The high hydraulic conductivities serve to reduce the seaward hydraulic gradient, cause rapid water level declines after aquifer recharge events, and allow salt water to intrude the aquifer at relatively fast rates. 4. Southeastern Florida is heavily populated with a large water demand for potable as well as for environmental purposes; nearly all of the potable water is derived from the shallow aquifer system, although there have been recent efforts to explore alternative water sources. Most groundwater is withdrawn near the coast at well fields located along the Atlantic Coastal Ridge. The Atlantic Coastal Ridge is the preferred location for well fields because additional treatment is often required for poorer quality groundwater withdrawn farther inland. Construction of the Palm Aire well field, located west NGWA.org of the Pompano Beach well field, was an effective mechanism for reducing groundwater withdrawals near the coast; shifting withdrawals inland raised the water table near the coast and reduced the threat of salt water intrusion. The modeling analysis described in this investigation can be used to quantify effects of sea-level rise for other areas. Therefore, it is important to summarize important and transferable lessons such as those related to dual-domain transport, grid resolution, computational issues, and modeling approach. Numerous challenges were encountered in the development and calibration of the county-scale (300 km2 ) dispersive salt water intrusion model. Representing solute transport with a dual-domain approach is consistent with geological knowledge of permeable flow zones in the Biscayne aquifer and seemed to provide a more accurate representation of salt water intrusion than the traditional advection-dispersion approach. Without the dual-domain approach, there was no way to calibrate the model (with a reasonable parameter set) so that it could simultaneously represent the salt water intrusion event and subsequent retreat of saline groundwater. Numerical dispersion and use of appropriate grid resolution and transport schemes were among the most difficult challenges. Sanford and Pope (2010) encountered the same problem for a large 2000 km2 salt water intrusion model of the Eastern Shore of Virginia and questioned whether concentrations at an individual well can be accurately simulated by a numerical model of that scale. They suggest that in some instances, 10-cm thick model layers may be required to accurately characterize the transition zone between fresh and saline groundwater. Owing to computational limitations, Sanford and Pope (2010) were not able to use the TVD scheme in MT3DMS/SEAWAT for their problem, which would have helped to reduce numerical dispersion as it did for the present application. For computation reasons, Sanford and Pope (2010) used the relatively fast, implicit finitedifference scheme for solute transport. This made the problem tractable with present computing technology. Additional numerical resolution would have been useful for the present study. The model was unable to represent some of the observed salinities in monitoring wells (e.g., G-2055); maximum concentrations tended to be underestimated, for example. There are many possible reasons why the model had difficulty in simulating the details of the salt water intrusion event (e.g., errors in the conceptual model or problems with the data); it would have been useful to eliminate numerical dispersion as a possibility. As shown by Langevin and Hughes (2009), calibration of a salt water intrusion model with a high level of numerical dispersion can have deleterious effects on the predictive capability of the model. If, for example, some of the hydraulic conductivity heterogeneity was introduced by the calibration process in order to compensate for the effects of numerical dispersion, then model predictions would be in error if the predictions were sensitive to that heterogeneity. As mentioned by Sanford C. Langevin and M. Zygnerski GROUND WATER 19
    • and Pope (2010), the capability to add resolution where necessary is desirable in this situation. A finite element or finite volume model would have been one option. Another option for future studies would be to implement a local-grid refinement approach (Mehl and Hill 2002) in SEAWAT as a way to increase horizontal and vertical model resolution in areas where transport is important and predictions depend on accurate representation of large hydraulic gradients. For these types of larger-scale studies with potential difficulties in simulating dispersive solute transport, one might also consider an entirely different modeling approach based on an existing sharp interface formulation, which is available in the Salt Water Intrusion (SWI) Package for MODFLOW (Bakker 2003; Bakker and Schaars 2005). The sharp interface approach was designed for regional salt water intrusion modeling, and while it cannot simulate solute concentrations, it is by design, free of any type of dispersion including numerical dispersion. Calibration of the salt water intrusion model within a highly parameterized context was found to be useful for this study. The Pompano Beach well field consists of 16 groundwater withdrawal wells. Extraction rates for the wells are highly variable between wells and throughout time. The system also has many other spatially and temporally variable stresses (variations in fresh and tidal canal levels, recharge, artificial recharge, rainfall, evapotranspiration) that confound interpretation of hydrologic records. Karst aquifers, such as the Biscayne aquifer, are highly discontinuous and heterogeneous, both in their spatial and temporal functioning, and it is commonly difficult to separate the signal caused by a natural hydrologic event from one caused by an anthropogenic event. It was difficult to infer from the data subsurface areas that may be more or less permeable, and there were few reliable point measurements of hydraulic conductivity. With the highly parameterized calibration approach, features of the system were quantified by monitoring where and how parameters changed. In many instances, unrealistic parameter distributions were used to identify deficiencies in the numerical model, such as an erroneous prescribed canal level or an error in a monitoring well location. Although not considered in this assessment, a next step in this type of analysis is to quantify prediction uncertainty. Robust uncertainty measures can be calculated within the highly parameterized context provided one can assign measures of parameter uncertainty. Future efforts to quantify sea-level rise impacts would benefit from considering uncertainty quantification. Uncertainties in the predicted salt water intrusion patterns that result from sea-level rise were not quantified, but experience with the model suggests that there is a high level of uncertainty. As suggested by Konikow (2011) and experienced in this effort, solute transport models are particularly difficult to develop, and one should not expect the same level of reliability as one might expect for a groundwater flow model. Uncertainties caused by structural model errors can be reduced by evaluating differences in model simulations instead of focusing on 20 C. Langevin and M. Zygnerski GROUND WATER a specific numeric value produced from a single forward model run (Doherty and Welter 2010). For the sensitivity analysis of the projected sea-level rise, this means it is preferable to state that well-field concentrations exceed the potable limit 10 to 21 years sooner than for the case without sea-level rise. This study focused on evaluating the sea-level rise projections reported by the IPCC (Church et al. 2001). More recent projections by the IPCC (Meehl et al. 2007) seem to project sea level rising at a slower rate, but the revised estimates do not include some feedback mechanisms that are anticipated to occur, such as rapid ice sheet melting. Recent studies (Pfeffer et al. 2008) have shown that sea level may rise by 0.8 to 2.0 m by 2100. Heimlich et al. (2010) summarize some of the recent sea-level rise projections and their possible effects on southeastern Florida. These larger rates of sea-level rise were not tested with the model. It is reasonable to assume that increased rates of sea-level rise much larger than those considered here would have serious impacts on the fresh coastal groundwater supplies of southeastern Florida. For these larger rates of sea-level rise, it is unclear if adaptation measures and changes to the infrastructure could meet potable water demands while simultaneously providing flood protection. Conclusions Conditions near the Pompano Beach well field in northern Broward County, Florida, provide a unique opportunity to examine the effects of historical and projected sea-level rise on the fresh groundwater resources of a low-lying highly permeable coastal aquifer. Results of a numerical modeling analysis suggest that groundwater withdrawals were the dominant cause of a multi-decade salt water intrusion event, and that historical sea-level rise (about 25 cm for the simulation period) contributed to the extent of the intrusion by about 1 km. The historical rate of sea-level rise was similar to the lower-bound estimate (24 cm) of the IPCC (Church et al. 2001) projection for the next century. A sensitivity analysis of four projected rates of sea-level rise (24, 48, and 88 cm/century) comparatively illustrates the relative severity of the situation in south Florida. Even if sea level does not rise in the future, model simulations suggest that corrective actions would likely be required to protect the aquifer from salinization. Corrective actions would be required as much as 21 years sooner depending on the future rate of sea-level rise. The findings from this study are consistent with general observations about the vulnerability of southeastern Florida to salt water intrusion caused by sealevel rise. Southeastern Florida is particularly vulnerable because of (1) the overlying canal system, which acts as a strong head control, (2) the presence of tidal canals that extend inland, (3) the highly permeable shallow aquifer system, which includes the Biscayne aquifer, and (4) the large groundwater withdrawals from the coastal aquifer. NGWA.org
    • Acknowledgments Special acknowledgments to Darrel Dunn and Katie Lelis of the Broward County Environmental Protection Department/Water Resources Division, Francis Henderson and Dave Markward of the Broward County Office of Environmental Services/Water Management Division, and Randy Brown, Maria Loucraft, and Alan Clark of Pompano Beach Utilities Department for providing extensive information and data on the study site. A special thanks to Winnie Said and Krista Guerrero-Reger of the South Florida Water Management District as well as Guy Bartolotta of Broward County Environmental Operation Division for providing model data sets and historical well-field pumping records, and to John Doherty for his continued support with the parameter estimation program (PEST). Technical assistance was also provided by Alyssa Dausman, Joann Dixon, and Roy Sonenshein. 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