Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Larger foraminiferal biostratigraphy, systematics and paleoenvironments of the Avon Park Formation and Ocala Limestone, Highlands County, Florida

This study investigates the use of larger foraminifera in determining the biostratigraphy of the Avon Park Formation and the Ocala Limestone in central Florida. Sedimentary rocks of the Avon Park Formation are the oldest exposed deposits in the state of Florida, and together with the Ocala Limestone comprise a part of the confining unit of the Floridan Aquifer, a major source of Florida's water supply. ^ Material from the ROMP 29A core collected by the U.S. Geological Survey was evaluated and compared to previous studies of the biostratigraphy of the formations. The larger foraminifera of the Avon Park Formation were examined in thin section, and those of the Ocala Limestone were free specimens. The larger foraminifera from both units were described and identified, and the biostratigraphy determined. The morphological features of the larger foraminifera of the Ocala Limestone were measured and analyzed at various depths within the ROMP 29A core.^ The Avon Park Formation contains predominantly the shallow-water, conical foraminifera Fallotella cookei, Fallotella floridana, Pseudochrysalidina floridana, Coleiconus christianaensis, Coleiconus sp. A, Coskinolina sp. A, Coskinolina sp. B, Fallotella sp. A, Fallotella sp. B, Fabularia vaughani and larger miliolids. ^ The Ocala Limestone contains a different, deeper water assemblage that included the larger foraminifera Heterostegina ocalana, Lepidocyclina ocalana varieties, Lepidocyclina chaperi, Lepidocyclina pustulosa, Nummulites willcoxi, Nummulites striatoreticulatus, Nummulites floridensis and Pseudophragmina spp. A, B, and C. The age of the Avon Park Formation was corroborated by the occurrence of the biomarker echinoid Neolaganum dalli as Eocene, and the Ocala Limestone also contained Eocene larger foraminifera with Eocene to possibly Oligocene calcareous nannofossils. The distribution of the larger foraminifera of the Avon Park Formation was correlated with the subtidal and peritidal zones of the continental shelf. Analyses of variance showed that the changes in measurements of the morphology in Heterostegina ocalana, Lepidocyclina spp. and Nummulites spp. were correlated with change in the depositional environments.^

Development of an integrated surface and subsurface model of Everglades National Park

An integrated surface-subsurface hydrological model of Everglades National Park (ENP) was developed using MIKE SHE and MIKE 11 modeling software. The model has a resolution of 400 meters, covers approximately 1050 square miles of ENP, includes 110 miles of drainage canals with a variety of hydraulic structures, and processes hydrological information, such as evapotranspiration, precipitation, groundwater levels, canal discharges and levels, and operational schedules. Calibration was based on time series and probability of exceedance for water levels and discharges in the years 1987 through 1997. Model verification was then completed for the period of 1998 through 2005. Parameter sensitivity in uncertainty analysis showed that the model was most sensitive to the hydraulic conductivity of the regional Surficial Aquifer System, the Manning's roughness coefficient, and the leakage coefficient, which defines the canal-subsurface interaction. The model offers an enhanced predictive capability, compared to other models currently available, to simulate the flow regime in ENP and to forecast the impact of topography, water flows, and modifying operation schedules.

Chilling damage in a changing climate in coastal landscapes of the subtropical zone: a case study from south Florida

Extensive portions of the southern Everglades are characterized by series of elongated, raised peat ridges and tree islands oriented parallel to the predominant flow direction, separated by intervening sloughs. Tall herbs or woody species are associated with higher elevations and shorter emergent or floating species are associated with lower elevations. The organic soils in this “Ridge-and-Slough” landscape have been stable over millennia in many locations, but degrade over decades under altered hydrologic conditions. We examined soil, pore water, and leaf phosphorus (P) and nitrogen (N) distributions in six Ridge and Slough communities in Shark Slough, Everglades National Park. We found P enrichment to increase and N to decrease monotonically along a gradient from the most persistently flooded sloughs to rarely flooded ridge environments, with the most dramatic change associated with the transition from marsh to forest. Leaf N:P ratios indicated that the marsh communities were strongly P-limited, while data from several forest types suggested either N-limitation or co-limitation by N and P. Ground water stage in forests exhibited a daytime decrease and partial nighttime recovery during periods of surface exposure. The recovery phase suggested re-supply from adjacent flooded marshes or the underlying aquifer, and a strong hydrologic connection between ridge and slough. We therefore developed a simple steady-state model to explore a mechanism by which a phosphorus conveyor belt driven by both evapotranspiration and the regional flow gradient can contribute to the characteristic Ridge and Slough pattern. The model demonstrated that evapotranspiration sinks at higher elevations can draw in low concentration marsh waters, raising local soil and water P concentrations. Focusing of flow and nutrients at the evapotranspiration zone is not strong enough to overcome the regional gradient entirely, allowing the nutrient to spread downstream and creating an elongated concentration plume in the direction of flow. Our analyses suggest that autogenic processes involving the effects of initially small differences in topography, via their interactions with hydrology and nutrient availability, can produce persistent physiographic patterns in the organic sediments of the Everglades.

Use of tritium and helium to define groundwater flow conditions in Everglades National Park

The concentrations of tritium (3H) and helium isotopes (3He and4He) were used as tracers of groundwater flow in the surficial aquifer system (SAS) beneath Everglades National Park (ENP), south Florida. From ages determined by 3H/3He dating techniques, groundwater within the upper 28 m originated within the last 30 years. Below 28 m, waters originated prior to 30 years before present with evidence of mixing at the interface. Interannual variation of the 3H/3He ages within the upper 28 m was significant throughout the 3 year investigation, corresponding with varying hydrologic conditions. In the region of Taylor Slough Bridge, younger groundwater was consistently detected below older groundwater in the Biscayne Aquifer, suggesting preferential flow to the lower part of the aquifer. An increase in 4He with depth in the SAS indicated that radiogenic 4He produced in the underlying Hawthorn Group migrates into the SAS by diffusion. Higher Δ4He values in brackish groundwaters compared to fresh waters from similar depths suggested a possible enhanced vertical transport of4He in the seawater mixing zone. Groundwater salinity measurements indicated the presence of a wide (6–28 km) seawater mixing zone. Comparison of groundwater levels with surface water levels in this zone indicated the potential for brackish groundwater discharge to the overlying Everglades surface water.

Adsorption and desorption of phosphate on limestone in experiments simulating seawater intrusion

This study investigates the potential release of from carbonate aquifers exposed to seawater intrusion. Adsorption and desorption of in the presence of deionized water (DIW) and seawater were conducted on a large block of Pleistocene age limestone to simulate the effects of seawater intrusion into a coastal carbonate aquifer at the laboratory scale. The limestone showed strong adsorption of in DIW, while adsorption was significantly less in the presence of seawater. Dissolution of CaCO3 was found to prevent adsorption at salinities less than 30 psu. Adsorption of was limited at higher salinities (30–33 psu), due to competition with ions for adsorption sites. At a salinity3 precipitated. Concentrations of between 2 and 5 μmol/L were released by desorption when the limestone was exposed to seawater. The results of this study suggest that as seawater intrudes into an originally freshwater coastal aquifer, adsorbed may be released into the groundwater. Consequently, adsorbed is expected to be released from coastal carbonate aquifers world-wide as sea level continues to rise exposing more of the freshwater aquifer to seawater.

Coastal groundwater discharge – an additional source of phosphorus for the oligotrophic wetlands of the Everglades

In this manuscript we define a new term we call coastal groundwater discharge (CGD), which is related to submarine groundwater discharge (SGD), but occurs when seawater intrudes inland to force brackish groundwater to discharge to the coastal wetlands. A hydrologic and geochemical investigation of both the groundwater and surface water in the southern Everglades was conducted to investigate the occurrence of CGD associated with seawater intrusion. During the wet season, the surface water chemistry remained fresh. Enhanced chloride, sodium, and calcium concentrations, indicative of brackish groundwater discharge, were observed in the surface water during the dry season. Brackish groundwaters of the southern Everglades contain 1–2.3μM concentrations of total phosphorus (TP). These concentrations exceed the expected values predicted by conservative mixing of local fresh groundwater and intruding seawater, which both have TPμM. The additional source of TP may be from seawater sediments or from the aquifer matrix as a result of water–rock interactions (such as carbonate mineral dissolution and ion exchange reactions) induced by mixing fresh groundwater with intruding seawater. We hypothesize that CGD maybe an additional source of phosphorus (a limiting nutrient) to the coastal wetlands of the southern Everglades.

Evidence for the removal of CFC-11, CFC-12, and CFC-113 at the groundwater–surface water interface in the Everglades

Poor agreement between 3H/3He ages and CFC-11 and CFC-12 ages suggests that CFCs may not be conservative tracers in the Everglades National Park. 3H/3He ages were used to calculate the expected concentration of CFC-11 and CFC-12 in groundwater from wells 2 to 73 m deep. The expected concentrations of CFCs were compared to the measured concentrations and plots of the % CFC-12 and CFC-11 remaining offered no evidence that significant CFC removal was occurring in the groundwater at depths ≥2 m, suggesting that CFC removal occurs at shallower depths. Except where CFC contamination was suspected, CFC-11, CFC-12 and CFC-113 concentrations in fresh surface water were nearly always below solubility equilibrium with the atmosphere. Measurements of CFC-11, CFC-12 and CFC-113 in pore water indicate a 50–90% decrease in concentration 5 cm below the groundwater–surface water (GW–SW) interface. In the same 5 cm interval CH4 concentrations increased by 300–1000%. This suggested that CFCs were removed at the GW–SW interface, possibly by methane-producing bacteria. CFC derived recharge ages should therefore be viewed with caution when recharging water percolates through anoxic methanogenic sediments.

Hydrologic Dynamics of the Ground-Water-Dependent Sian Ka’an Wetlands, Mexico, Derived from InSAR and SAR Data

The 5,280 km2 Sian Ka’an Biosphere Reserve includes pristine wetlands fed by ground water from the karst aquifer of the Yucatan Peninsula, Mexico. The inflow through underground karst structures is hard to observe making it difficult to understand, quantify, and predict the wetland dynamics. Remotely sensed Synthetic Aperture Radar (SAR) amplitude and phase observations offer new opportunities to obtain information on hydrologic dynamics useful for wetland management. Backscatter amplitude of SAR data can be used to map flooding extent. Interferometric processing of the backscattered SAR phase data (InSAR) produces temporal phase-changes that can be related to relative water level changes in vegetated wetlands. We used 56 RADARSAT-1 SAR acquisitions to calculate 38 interferograms and 13 flooding maps with 24 day and 48 day time intervals covering July 2006 to March 2008. Flooding extent varied between 1,067 km2 and 2,588 km2 during the study period, and main water input was seen to take place in sloughs during October–December. We propose that main water input areas are associated with water-filled faults that transport ground water from the catchment to the wetlands. InSAR and Landsat data revealed local-scale water divides and surface water flow directions within the wetlands.

Assessment of the occurrence and potential effects of pharmaceuticals and personal care products in South Florida waters and sediments

A LLE-GC-MS method was developed to detect PPCPs in surface water samples from Big Cypress National Park, Everglades National Park and Biscayne National Park in South Florida. The most frequently found PPCPs were caffeine, DEET and triclosan with detected maximum concentration of 169 ng/L, 27.9 ng/L and 10.9 ng/L, respectively. The detection frequencies of hormones were less than PPCPs. Detected maximal concentrations of estrone, 17β-estradiol, coprostan-3-ol, coprostane and coprostan-3-one were 5.98 ng/L, 3.34 ng/L, 16.5 ng/L, 13.5 ng/L and 6.79 ng/L, respectively. An ASE-SPE-GC-MS method was developed and applied to the analysis of the sediment and soil area where reclaimed water was used for irrigation. Most analytes were below detection limits, even though some of analytes were detected in the reclaimed water at relatively high concentrations corroborating the fact that PPCPs do not significantly partition to mineral phases. An online SPE-HPLC-APPI-MS/MS method and an online SPE-HPLC-HESI-MS/MS method were developed to analyze reclaimed water and drinking water samples. In the reclaimed water study, reclaimed water samples were collected from the sprinkler for a year-long period at Florida International University Biscayne Bay Campus, where reclaimed water was reused for irrigation. Analysis results showed that several analytes were continuously detected in all reclaimed water samples. Coprostanol, bisphenol A and DEET's maximum concentration exceeded 10 μg/L (ppb). The four most frequently detected compounds were diphenhydramine (100%), DEET (98%), atenolol (98%) and carbamazepine (96%). In the study of drinking water, 54 tap water samples were collected from the Miami-Dade area. The maximum concentrations of salicylic acid, ibuprofen and DEET were 521 ng/L, 301 ng/L and 290 ng/L, respectively. The three most frequently detected compounds were DEET (93%), carbamazepine (43%) and salicylic acid (37%), respectively. Because the source of drinking water in Miami-Dade County is the relatively pristine Biscayne aquifer, these findings suggest the presence of wastewater intrusions into the delivery system or the onset of direct influence of surface waters into the shallow aquifer.

Spatial and Temporal Changes in Groundwater Salinity in South Florida

A combination of statistical and interpolation methods and Geographic Information System (GIS) spatial analysis was used to evaluate the spatial and temporal changes in groundwater Cl− concentrations in Collier and Lee Counties (southwestern Florida), and Miami-Dade and Broward Counties (southeastern Florida), since 1985. In southwestern Florida, the average Cl− concentrations in the shallow wells (0–43 m) in Collier and Lee Counties increased from 132 mg L−1 in 1985 to 230 mg L−1 in 2000. The average Cl− concentrations in the deep wells (>43 m) of southwestern Florida increased from 392 mg L−1 in 1985 to 447 mg L−1 in 2000. Results also indicated a positive correlation between the mean sea level and Cl− concentrations and between the mean sea level and groundwater levels for the shallow wells. Concentrations in the Biscayne Aquifer (southeastern Florida) were significantly higher than those of southwestern Florida. The average Cl− concentrations increased from 159 mg L−1 in 1985 to 470 mg L−1 in 2010 for the shallow wells (<33 m) and from 1360 mg L−1 in 1985 to 2050 mg L−1 in 2010 for the deep wells (>33 m). In the Biscayne Aquifer, wells showed a positive or negative correlation between mean sea level and Cl− concentrations according to their location with respect to the saltwater intrusion line. Wells located inland behind canal control structures and west of the saltwater intrusion line showed negative correlation values, whereas wells located east of the saltwater intrusion line showed positive values. Overall, the results indicated that since 1985, there was a potential decline in the available freshwater resources estimated at about 12–17% of the available drinking-quality groundwater of the southeastern study area located in the Biscayne Aquifer.

The Influence of Hydrologic Restoration on Groundwater-Surface Water Interactions in a Karst Wetland, the Everglades (FL, USA)

Efforts to rehydrate and restore surface water flow in karst wetlands can have unintended consequences, as these highly conductive and heterogeneous aquifers create a close connection between groundwater and surface water. Recently, hydrologic restoration efforts in the karstic Taylor Slough portion of the Everglades has changed from point source delivery of canal water (direct restoration), to the use of a series of surface water recharge retention basins (diffuse restoration). To determine the influence of restoration on groundwater-surface water interactions in the Taylor Slough headwaters, a water budget was constructed for 1997–2011 using 70 hydro-meteorological stations. With diffuse restoration, groundwater seepage from the Everglades toward the urban boundary increased, while the downstream delivery of surface water to the main portion of the slough declined. The combined influence of diffuse restoration and climate led to increased intra-annual variability in the volume of groundwater and surface water in storage but supported a more seasonally hydrated wetland compared to the earlier direct tactics. The data further indicated that hydrologic engineering in karst wetland landscapes enhances groundwater-surface water interactions, even those designed for restoration purposes.

Essays on intergenerational and regional aspects of water management

This dissertation consists of three essays on different aspects of water management. The first essay focuses on the sustainability of freshwater use by introducing the notion that altruistic parents do bequeath economic assets for their offspring. Constructing a two-period, over-lapping generational model, an optimal ratio of consumption and pollution for old and young generations in each period is determined. Optimal levels of water consumption and pollution change according to different parameters, such as, altruistic degree, natural recharge rate, and population growth. The second essay concerns water sharing between countries in the case of trans-boundary river basins. The paper recognizes that side payments fail to forge water-sharing agreement among the international community and that downstream countries have weak bargaining power. An interconnected game approach is developed by linking the water allocation issue with other non-water issues such as trade or border security problems, creating symmetry between countries in bargaining power. An interconnected game forces two countries to at least partially cooperate under some circumstances. The third essay introduces the concept of virtual water (VW) into a traditional international trade model in order to estimate water savings for a water scarce country. A two country, two products and two factors trade model is developed, which includes not only consumers and producer's surplus, but also environmental externality of water use. The model shows that VW trade saves water and increases global and local welfare. This study should help policy makers to design appropriate subsidy or tax policy to promote water savings especially in water scarce countries.^

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Essays on Intergenerational and Regional Aspects of Water Management

This dissertation consists of three essays on different aspects of water management. The first essay focuses on the sustainability of freshwater use by introducing the notion that altruistic parents do bequeath economic assets for their offspring. Constructing a two-period, over-lapping generational model, an optimal ratio of consumption and pollution for old and young generations in each period is determined. Optimal levels of water consumption and pollution change according to different parameters, such as, altruistic degree, natural recharge rate, and population growth. The second essay concerns water sharing between countries in the case of trans-boundary river basins. The paper recognizes that side payments fail to forge water-sharing agreement among the international community and that downstream countries have weak bargaining power. An interconnected game approach is developed by linking the water allocation issue with other non-water issues such as trade or border security problems, creating symmetry between countries in bargaining power. An interconnected game forces two countries to at least partially cooperate under some circumstances. The third essay introduces the concept of virtual water (VW) into a traditional international trade model in order to estimate water savings for a water scarce country. A two country, two products and two factors trade model is developed, which includes not only consumers and producer’s surplus, but also environmental externality of water use. The model shows that VW trade saves water and increases global and local welfare. This study should help policy makers to design appropriate subsidy or tax policy to promote water savings especially in water scarce countries.