HOW DOES AQUIFER CONNECTIVITY IMPACT GROUNDWATER FLOW TO THE SEA AND SUBSURFACE PATTERNS OF SALINITY? Kaileigh C. Calhoun

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1 HOW DOES AQUIFER CONNECTIVITY IMPACT GROUNDWATER FLOW TO THE SEA AND SUBSURFACE PATTERNS OF SALINITY? by Kaileigh C. Calhoun A thesis submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Master of Civil Engineering Summer Calhoun All Rights Reserved

2 ProQuest Number: All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest Published by ProQuest LLC (2015). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI

3 HOW DOES AQUIFER CONNECTIVITY IMPACT GROUNDWATER FLOW TO THE SEA AND SUBSURFACE PATTERNS OF SALINITY? by Kaileigh C. Calhoun Approved: Holly A. Michael, Ph.D. Professor in charge of thesis on behalf of the Advisory Committee Approved: Harry W. Shenton III, Ph.D. Chair of the Department of Civil and Environmental Engineering Approved: Babatunde A. Ogunnaike, Ph.D. Dean of the College of Engineering Approved: James G. Richards, Ph.D. Vice Provost for Graduate and Professional Education

4 ACKNOWLEDGMENTS Thank you to the following people and organizations. My advisor, Dr. Holly Michael, who mentored me in the field of quantitative hydrogeology and guided me through the research process. The UD Hydrogeology Research Group and the Environmental Engineering Department s student seminar class provided helpful suggestions, support, and feedback. The Department of Public Health Engineering, Bangladesh supplied the core log data and Mohammed Koneshloo provided the geostatistical realizations used in this study. The University of Delaware High- Performance computing department taught me how to run and compile SEAWAT on the Linux Cluster Farber. Dr. Adam Wallace and Dr. Rodrigo Vargas shared their computing resources, ensuring that the project was completed in a timely manner. Project funding was provided by the National Science Foundation (EAR ). iii

5 TABLE OF CONTENTS LIST OF TABLES... vi LIST OF FIGURES... viii ABSTRACT... xi Chapter 1 INTRODUCTION Significant Coastal Groundwater Processes Areas of Further Investigation Research Questions Experimental Approach MODEL APPROACH Geostatistical Modeling Flow and Transport Modeling Two-dimensional Coastal Aquifer Models with Heterogeneous K Fields Extension to 3D Homogeneous Equivalent Models Quantifying Flow and Transport Model Output HORIZONTAL CONNECTIVITY OF HETEROGENEOUS HYDRAULIC CONDUCTIVITY FIELDS Geologic Connectivity Hydraulic Connectivity Other Hydraulic Indicators RESULTS Simulation Error Effect of Connectivity on Steady-state Salinity Distributions Effect of Connectivity on Steady-state Ocean-aquifer Exchange iv

6 4.4 Comparison of Effects of Heterogeneous and Equivalent Homogeneous Hydraulic Conductivity Fields on Steady-state Salinity Distributions Effect of Heterogeneous verses Equivalent Homogeneous Hydraulic Conductivity Fields on Steady-state Ocean-aquifer Exchange Effect of Dimension on Steady-state Salinity Distributions Effect of Dimension on Steady-state Ocean-aquifer Exchange DISCUSSION Hydraulic Connectivity Impacts Recharge Geologic Connectivity Impacts Subsurface Salinity and Patterns of Ocean- aquifer Exchange Geologic Connectivity Impacts Variability of Subsurface Salinity Patterns and Ocean-aquifer Exchange Across Multiple Simulations Heterogeneity Impacts Subsurface Salinity Patterns and Amounts and Patterns of Ocean-aquifer Exchange Dimension Impacts Subsurface Salinity Patterns and Amounts of Ocean-aquifer Exchange Free / Forced Convection Impacts Percent Saltwater Circulation Study Limitations Implications CONCLUSIONS REFERENCES Appendix A DATA B PERMISSION v

7 LIST OF TABLES Table 2.1 Unix verses Windows comparison Table 2.2 Grid refinement test Table 4.1 Table 4.2 Table 4.3 Table A.1 Table A.2 Table A.3 Table A.4 Table A.5 Table A.6 Table A.7 Volumetric and solute mass balance errors for 3D heterogeneous simulations Skew of fresh and saline SGD distributed along sea floor for 2D heterogeneous simulations recharge and PSC for 3D simulations compared to range of results for 2D simulations Effective horizontal and vertical hydraulic conductivities and geometric mean of the hydraulic conductivity values for heterogeneous K fields of the low geologic connectivity case Effective horizontal and vertical hydraulic conductivities and geometric mean of the hydraulic conductivity values for heterogeneous K fields of the medium geologic connectivity case Effective horizontal and vertical hydraulic conductivities and geometric mean of the hydraulic conductivity values for heterogeneous K fields of the high geologic connectivity case Steady-state SEAWAT simulation results with low geologic connectivity heterogeneous K fields Steady-state SEAWAT simulation results with medium geologic connectivity heterogeneous K fields Steady-state SEAWAT simulation results with high geologic connectivity heterogeneous K fields Steady-state SEAWAT simulation results with homogenous equivalent K fields of low geologic connectivity case vi

8 Table A.8 Table A.9 Steady-state SEAWAT simulation results with homogenous equivalent K fields of medium geologic connectivity case Steady-state SEAWAT simulation results with homogenous equivalent K fields of high geologic connectivity case vii

9 LIST OF FIGURES Figure 2.1 Figure 2.2 Figure 2.3 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 4.1 Figure 4.2 Variograms describing geostatistical realizations of low, medium, and high geologic connectivity... 7 One 3D geostatistical facies realization for each geologic connectivity case Model setup and boundary conditions for 2D SEAWAT simulations with heterogeneous hydraulic conductivity fields Heterogeneous 2D hydraulic conductivity fields derived from geostatistical simulation Distribution of horizontal variogram ranges of each facies for each geologic connectivity group for 2D K fields Distribution of hydraulic connectivity as a function of geologic connectivity for 2D K fields extracted from 3D Geostatistical simulation Hydraulic connectivity as a function of horizontal variogram range for each facies Effective horizontal hydraulic conductivity, effective vertical hydraulic conductivity, and anisotropy as a function of geologic connectivity Distributions of volumetric and solute mass balance error for heterogeneous and homogeneous simulations Simulated steady-state salinity distributions for 2D models with heterogeneous hydraulic conductivity fields Figure 4.3 Influence of connectivity on mixing zone area Figure 4.4 Figure 4.5 Influence of connectivity on the ratio of bottom width to top width of the mixing zone Influence of horizontal connectivity on the position of the mixing zone viii

10 Figure 4.6 Simulated submarine groundwater exchange patterns for 2D models with heterogeneous hydraulic conductivity fields Figure 4.7 Influence of connectivity on fresh and saline SGD center of mass Figure 4.8 Influence of connectivity on standard deviation of fresh and saline SGD location weighted by flow magnitude Figure 4.9 recharge as a function of horizontal hydraulic connectivity Figure 4.10 Influence of connectivity on percent saltwater circulation Figure 4.11 PSC as a function of the ratio between free and forced convection Figure 4.12 Steady-state salinity distributions for 2D models with heterogeneous K fields and equivalent homogeneous K fields Figure 4.13 Influence of connectivity on the simulated mixing zone area with heterogeneous K field divided by the mixing zone area with homogeneous equivalent K field Figure 4.14 Influence of connectivity on the difference in location of centroid of mixing zone between each heterogeneous K field and equivalent homogenous K field Figure 4.15 Simulated submarine groundwater exchange patterns for 2D models with heterogeneous hydraulic conductivity fields and corresponding homogeneous equivalent fields Figure 4.16 Influence of connectivity on the difference between the center of mass of SGD in heterogeneous and equivalent homogeneous simulations Figure 4.17 Influence of connectivity on standard deviation of fresh and saline SGD location weighted by magnitude of discharge for simulations with heterogeneous and homogeneous hydraulic conductivity fields Figure 4.18 PSC for heterogeneous K fields v. PSC for corresponding homogeneous K fields Figure 4.19 Selected profiles of steady-state salinity distribution for a 3D heterogeneous K field with low geologic connectivity and steady-state salinity distribution for the 2D heterogeneous K field with low geologic connectivity where the transverse coordinate equals 12.5 km. 48 ix

11 Figure 4.20 Selected profiles of steady-state salinity distribution for a 3D heterogeneous K field with medium geologic connectivity and steadystate salinity distribution for the 2D heterogeneous K field with medium geologic connectivity where the transverse coordinate equals 12.5 km Figure 4.21 Selected profiles of steady-state salinity distribution for a 3D heterogeneous K field with high geologic connectivity and steadystate salinity distribution for the 2D heterogeneous K field with high geologic connectivity where the transverse coordinate equals 12.5 km. 50 Figure 4.22 Steady-state ocean aquifer exchange patterns for the low geologic connectivity 3D simulation Figure 4.23 Steady-state ocean aquifer exchange patterns for the medium geologic connectivity 3D simulation Figure 4.24 Steady-state ocean aquifer exchange patterns for the high geologic connectivity 3D simulation Figure 5.1 Salinity data from Post et al. and a salinity distribution from one of this study s medium geologic connectivity simulations Figure A.1 Permission to reprint figure 2 from Post et al x

12 ABSTRACT In large scale coastal aquifers, the quantification of subsurface salinity patterns is important to water resources management. Meanwhile, the quantification of amounts and patterns of ocean-aquifer exchange is important to protecting coastal waters and understanding long-term ocean chemistry. This study used numerical simulations to investigate the impacts of (1) geologic and hydrologic connectivity, (2) large scale geologic heterogeneity, and (3) model dimension on steady-state variabledensity groundwater flow and salt transport on the continental shelf (200 km) scale. Heterogeneous hydraulic conductivity (K) fields with different geologic connectivities were generated geostatistically and equivalent homogeneous K values were computed. Groundwater flow and solute transport in each heterogeneous and equivalent homogeneous aquifer was simulated. Finally, the size and position of the mixing zone, the distribution and position of fresh and saline submarine groundwater discharge, the quantity of fresh recharge, and the quantity of saltwater circulation were quantified. The results show, first, that as aquifer connectivity increases in the horizontal direction, the fresh-saline mixing zone and fresh and saline SGD occur farther seaward, are spread over a larger area, and become more variable. Next, aquifers with large-scale heterogeneity usually have a larger interface and freshwater that is present further seaward than homogeneous equivalent aquifers do. Third, saltwater circulation is significantly greater in heterogeneous aquifers compared to that of equivalent homogeneous aquifers. Finally, modeling aquifers in 2D rather than 3D exaggerates these results. This study has implications for understanding the variability of field xi

13 data, improving numerical modeling of coastal groundwater systems, estimating the offshore extent of fresh water, and properly quantifying saltwater circulation on continental shelves. xii

14 Chapter 1 INTRODUCTION To properly manage coastal aquifers and the environments they impact, two processes should be considered: (1) subsurface salinity patterns and (2) amounts and patterns of ocean-aquifer exchange. Large scale heterogeneity of the aquifer s geology; connectivity of sands, silts, and clays in the aquifer; and 2D verses 3D conceptualization and modeling of the aquifer are areas in need of further investigation. 1.1 Significant Coastal Groundwater Processes In coastal aquifers, fresh and saline groundwater meet to form a characteristic Ghyben-Hertzberg interface where fresh groundwater sits on top of denser saline groundwater. Tidal cycling, changes in the fresh water table, changes in sea level, and geologic heterogeneity all drive mixing at the interface. This leads to the formation of a mixing zone of considerable width rather than simply a sharp interface. The resulting subsurface salinity patterns are significant for two reasons. First, in coastal communities, where demand for fresh drinking water is high, reliable characterization of this interface is needed for sustainable pumping of fresh groundwater while limiting the risk of saltwater intrusion (Werner et al 2013). Second, and conversely, in some places, brackish groundwater has been discovered as far as 120 km offshore. This could be a potential drinking water resource (Post 2013). 1

15 Submarine groundwater exchange is the movement of water across the coastal zone sea floor, regardless of origin, composition, or flow mechanism. Water flowing into the coastal aquifer is called submarine groundwater recharge (SGR) while water leaving is called submarine groundwater discharge (SGD) (Burnett et al. 2006). groundwater recharge enters the aquifer at the land surface and exits as fresh submarine groundwater discharge. When mixing occurs at the fresh-saline interface, buoyancy forces cause saline water to also exit the aquifer as saline submarine groundwater discharge. water from the ocean then moves into the aquifer to replace it as saline submarine groundwater recharge. This process is called densitydriven saltwater circulation (Cooper 1959). Amounts and patterns of ocean-aquifer exchange are significant for two reasons. First, although estimated worldwide fresh SGD is relatively small in comparison to surface water runoff, it contributes significant material flows of nutrients, metals, carbon, and bacteria to coastal waters and their ecosystems (Johannes 1980, Moore 2010 a). Second, water-rock interactions alter the saline water s chemistry as it moves through the aquifer. Over long timescales, saltwater circulation could cause changes in ocean chemistry (Moore 1999). 1.2 Areas of Further Investigation Geologic heterogeneity has been shown to impact subsurface salinity patterns but further study is needed. Using numerical models, previous studies have assessed the statistical impact of small scale geologic heterogeneity on the size, shape, and position of the mixing zone (Abarca 2007b, Kerrou and Renard 2010). Cohen (2010) modeled transient movement of salinity patterns in the Atlantic continental shelf (from New Jersey to Maine) including large scale geologic heterogeneity. However, impact 2

16 of large scale heterogeneity on the variability of subsurface salinity patterns have not been explored. Geologic heterogeneity has been shown to impact amounts of ocean-aquifer exchange; but further study is needed. recharge is limited by precipitation and the amount of meteoric water that is able to percolate into the aquifer from the land surface. It can be quantified via water balance. Saltwater circulation is limited only by energy balances because the ocean provides an unlimited source of saline water. According to homogeneous numerical models, steady state saline SGD rates that are up to 50% higher than fresh SGD rates can be considered reasonable (Smith 2004). However, near shore seepage meter field studies and coastal scale radium measurements estimate drastically more saltwater circulation than these numerical models. For example, at Indian River Bay seepage meter measurements found SGD to be 50-90% saline (Russoniello et al. 2013). According to Moore (2010 b) radium data suggests total SGD to a large section of the South Atlantic Bight is three times greater than river inputs. Moore proposes that radium mass balances are maintained via cycling of saline water through limestone deposits. At Onslow Bay, NC (located on the South Atlantic Bight), McCoy et al. (2007) estimated that SGD was 80% saline. Geologic heterogeneity is a potential cause of the discrepancy between numerical models and field data. Kerrou and Renard (2010) found that small scale heterogeneity produced saltwater circulation in numerical models up to 20 times greater than in homogeneous equivalent models. The impact of large scale heterogeneity on saltwater circulation has not been studied. Additionally, patterns of fresh and saline discharge from shelf scale aquifers with large geologic features should be investigated. 3

17 Geologic connectivity of heterogeneous media has been shown to impact single-density flow and transport but we don t understand how it impacts coastal systems. Fogg (1986) used geologic interpretation of hydraulic conductivity data to build a simple groundwater model. He found that the continuity and interconnectedness of sand deposits controlled flow rates to a greater extent than the hydraulic conductivity of the geologic materials. Later, Zinn and Harvey (2003) found that multi-guassian conductivity fields with similar statistics and different connectivities can have very different flow and transport patterns. However, the impact of varied geologic connectivity on variable-density flow and transport has not yet been explored. Conceptual and numerical model dimension has been shown to impact flow and transport in heterogeneous aquifers, but further study is needed. Kerrou and Renard (2010) found that modeling aquifers with small scale heterogeneity in 2D rather than 3D exaggerated the offshore position of the saltwater wedge and the amount of density driven saltwater circulation. The coupled impact of large scale heterogeneous K fields and model dimension on coastal systems has not been investigated. Additionally, because most field studies assume that flow in the aquifer is predominantly along transects that are perpendicular to the shoreline, the impact of model dimension on patterns of ocean-aquifer exchange should be studied. 1.3 Research Questions Building on previous research, our study investigates the impact of aquifer connectivity on variable-density flow and transport in coastal aquifers. We ask the following questions. 4

18 1. How does aquifer geologic and hydrologic connectivity impact subsurface patterns of salinity and patterns of ocean-aquifer exchange? 2. What are the potential consequences of modeling flow and transport in a coastal aquifer with a homogeneous representation of its geology? 3. What are the potential consequences of modeling in two dimensions rather than three? 1.4 Experimental Approach To answer these questions, we used geostatistical simulation to create heterogeneous hydraulic conductivity fields with low, medium, and high geologic connectivity. Next, we use the finite-difference model MODFLOW to obtain effective hydraulic conductivity values to represent each heterogeneous field. Then, we use the finite-difference model SEAWAT to simulate variable-density flow and transport conditions at steady state within two and three-dimensional, large-scale heterogeneous and homogeneous aquifers. Finally, we use Matlab to quantify patterns of salinity, density driven saltwater circulation, and patterns of ocean-aquifer exchange. 5

19 Chapter 2 MODEL APPROACH 2.1 Geostatistical Modeling Geostatistical methods were used to create models of subsurface heterogeneity. The fields were created with unconditioned sequential indicator simulation using SGeMS (Remy et al. 2009). Four facies were simulated to represent sediment types found in the Bengal Basin: clay, silt, fine sand, and medium and coarse sand. The geostatistical domain was 200 km in the horizontal direction (perpendicular to the shoreline), 50 km in the transverse direction (parallel to the shoreline), and 402 m deep. Grid size was 1000 m in the horizontal and transverse directions and 3 m in the vertical. The proportion of each facies was determined from 168 driller logs m deep in the Bangladesh coastal zone collected by the Department of Public Health Engineering Bangladesh. The logs characterized the heterogeneous aquifer as 20.5% clay, 28.3% silt, 35.2% fine sand, 16.0% medium and coarse sand. Correlations between facies were controlled by the ranges of the horizontal, transverse, and vertical input variograms. The transverse and vertical variogram ranges were held constant at 5 km and 50 m respectively. To generate facies patterns of differing horizontal connectivity, three horizontal variogram ranges were used: 5 km, 25 km, and 50 km (fig 2.1). The resulting geostatistical facies realizations are shown in figure 2.2. Fifty realizations for each horizontal variogram range were simulated. The intent of these realizations was not to represent the Bengal Basin 6

20 explicitly, but rather to compare an aquifer with similar connectivity to the Bengal Basin to a less connected aquifer and to a more connected aquifer. Figure 2.1 Variograms describing geostatistical realizations of low, medium, and high geologic connectivity. As geologic connectivity increases in the horizontal direction, the range of the variogram increases. 7

21 Figure 2.2 One 3D geostatistical facies realization for each geologic connectivity case. 8

22 2.2 Flow and Transport Modeling Numerical modeling of groundwater flow and salt transport was conducted with the USGS code SEAWAT (Langevin et al. 2007). SEAWAT is a finitedifference model that can simulate variable-density flow and transport. All simulations were run to steady state on the University of Delaware Linux Cluster, Farber. SEAWAT was recompiled for UNIX using the compiler flag Ofast. Windows and UNIX platforms yield identical results for the Henry problem (Henry 1964). When simulations were run for extended periods of time (we ran our simulations for 10 million years or more), truncation differences produced slightly different values for the output variables of interest (table 2.1). Table 2.1 Percent difference for output variables computed from a simulation run on UNIX compared to output variables computed from a simulation run on Windows. Output variables defined in section Output variable Percent difference [%] Area of the mixing zone 0.09 Mixing zone bottom width : mixing zone top width 0.93 Centroid of the mixing zone 0.07 SGD center of mass 0.57 SGD center of mass 0.31 Standard deviation of fresh SGD location weighted by flow magnitude Standard deviation of saline SGD location weighted by flow magnitude Skew of fresh SGD location weighted by flow magnitude -9.1 Skew of saline SGD location weighted by flow magnitude 3.0 recharge Percent saltwater circulation (PSC) 2.2 9

23 2.2.1 Two-dimensional Coastal Aquifer Models with Heterogeneous K Fields Model setup and boundary conditions for the 2D heterogeneous simulations are shown in figure 2.3. The model domain was 200 km in the horizontal direction (perpendicular to the shoreline), 500 m in the transverse direction (parallel to the shoreline), and 402 m in the vertical direction. The coast was placed 150 km from the left boundary, where everything to the left of the shore was considered seaward and everything to the right of the shore landward. Figure 2.3 Model setup and boundary conditions for 2D SEAWAT simulations with heterogeneous hydraulic conductivity fields. BC represents boundary conditions and IC represents initial conditions. The left seaward side boundary and the seaward portion of the top boundary were assigned a prescribed head of 0 m (representing sea level) and a concentration of 35 ppt (that of seawater). A prescribed head of 10 m and a concentration of 0 ppt was assigned to the landward side boundary to imitate fresh groundwater recharge in a topographically limited system. Because the right side boundary was a considerable distance from where the fresh-saline interface developed, the need for a top recharge boundary was assumed insignificant. Therefore, the landward portion of the top boundary was designated as no flow. The bottom boundary was also designated as no 10

24 flow to represent a confining layer at the bottom of the aquifer. To reduce runtime and numerical errors, the entire seaward portion of the model domain was assigned an initial concentration of 35 ppt. For an efficient run time, grid size was 500 m in the horizontal and transverse directions and 3 m in the vertical. To test the grid s robustness, relevant output variables (see section 2.3.2) were quantified for this grid and two refined grid sizes: (1) 250 m in the horizontal and transverse directions and 3 m in the vertical and (2) 125 m in the horizontal and transverse directions and 3 m in the vertical. Percent errors between the 125 m grid and the 500 m grid and between the 125 m grid and the 250 m grid were acceptable for most variables; however, PSC (percent saltwater circulation) continued to increase as the grid was further refined (table 2.2). 11

25 Table 2.2 Refinement test results: (a) percent error between output variables from a 500 m grid simulation and a 125 m grid simulation and (b) percent error between output variables from a 250 m grid simulation and a 125 m grid simulation. Output variable Percent error [%] 500 m v. 125 m Percent error [%] 250 m v. 125 m Area of the mixing zone Mixing zone bottom width : mixing zone top width Centroid of the mixing zone SGD center of mass SGD center of mass Standard deviation of fresh SGD location weighted by flow magnitude Standard deviation of saline SGD location weighted by flow magnitude Skew of fresh SGD location weighted by flow magnitude Skew of saline SGD location weighted by flow magnitude recharge Percent saltwater circulation (PSC) To simulate an aquifer with heterogeneous geology, a 2D profile was extracted from the center of each 3D geostatistical simulation (where the transverse coordinate equaled 25 km). Due to variability within each model, the facies proportions of each 2D profile differed somewhat from the full 3D model and the input proportions. However, only the difference in medium and coarse sand proportion had a relationship with effective horizontal hydraulic conductivity (Kh,eff) and differences in none of the facies proportions had a relationship with effective vertical hydraulic conductivity (Kv,eff). Therefore, 2D profiles with medium and coarse sand proportion differences less than ±25% was considered acceptable. Profiles in which differences exceeded 12

26 this threshold were replaced by a randomly extracted profile from the same 3D geostatistical simulation that did not have a medium and coarse sand proportion error exceeding ±25%. Each facies was assigned a typical hydraulic conductivity value (Fetter 2001): medium and coarse sand: K=10-3 m/s, fine sand: K=10-5 m/s, silt: K=10-8 m/s, and clay: K=10-13 m/s. Anisotropy within each cell was 1 for simplicity. Longitudinal, horizontal transverse, and vertical transverse dispersivity values of 200 m, 20 m, and 2 m, respectively were assigned to the entire domain. The molecular diffusion coefficient was 10-9 m2/s and specific storage was 10-4 /m. Each simulation was run until the total mass in the model reached steady state, million years. Flow was calculated with the geometric multigrid solver (RCLOSE and HCLOSE = 10-3 ). Transport was calculated with the method of characteristics (MOC) solver (maximum number of total moving particles = 10 7 ) Extension to 3D For 3D heterogeneous simulations, the model domain was extended from 500 m to 25 km in the transverse direction (parallel to the shoreline). The remaining model dimensions, boundary conditions, grid size, and parameters were consistent with the 2D heterogeneous model. The heterogeneous hydraulic conductivity values were assigned as above. Due to computational limitations, only the middle 25 km of each geostatistical realization was used in each flow and transport simulation. For efficient runtime, the transport was calculated with the Finite Difference solver rather than the MOC solver. 13

27 2.2.3 Homogeneous Equivalent Models A corresponding 2D homogeneous simulation was run for each 2D heterogeneous simulation. For these simulations, the landward side prescribed head was replaced with a prescribed flow. After each heterogeneous simulation was complete, the resulting fresh recharge was calculated and distributed evenly along the landward side boundary of the corresponding equivalent homogeneous model via injection wells. In this way, each heterogeneous simulation and its homogeneous equivalent received the same quantity of fresh influx. This allowed for the clear comparison of saltwater circulation relative to fresh recharge. All other boundary and initial conditions used in the heterogeneous simulations were applied to the homogeneous simulations. To represent the heterogeneous geology of each aquifer with a homogeneous equivalent, one horizontal and one vertical effective hydraulic conductivity value was assigned to all cells in the model. KH,eff and KV,eff were obtained for each heterogeneous field by applying a head gradient in the horizontal and vertical directions, simulating flow through the model with the USGS code MODFLOW (Harbaugh 2005), and solving Darcy s Law for hydraulic conductivity Quantifying Flow and Transport Model Output Model output was quantified with 7 parameters using Matlab: 1. The area of the fresh-saline mixing zone was defined as the sum of the area of all cells with a concentration between 10% and 90% that of seawater (35 ppt salinity). 2. The ratio of the mixing zone bottom width to the mixing zone top width was defined as the ratio of all cells along the model bottom to all 14

28 cells along the model top with a salinity concentration between 10% and 90% that of seawater. 3. The centroid of the mixing zone was defined as the horizontal average location of all cells with a salinity between 10% and 90% that of seawater. 4. The center of mass of SGD, CMSGD, was calculated separately for fresh and saline SGD as follows: Where qi is the fresh or saline volumetric flow leaving the model through each cell along the model top and xi is the horizontal coordinate of the cell s center. 5. To quantify the spread of the SGD distribution, the standard deviation of SGD location weighted by flow magnitude, σ, was calculated separately for fresh and saline SGD as follows: 6. Skew of SGD location weighted by flow magnitude, S, was calculated separately for fresh and saline SGD as follows: Positive skew indicates landward tailing of the distribution. Negative skew indicates seaward tailing of the distribution. 15

29 7. recharge, FR, was defined as the volumetric flow rate of fresh water entering the model via the landward boundary. 8. Percent saltwater circulation, PSC, was calculated as follows: Where SC is saltwater circulation, the volumetric flow rate of saltwater entering the model via the seaward boundary (Smith 2004). 16

30 Chapter 3 HORIZONTAL CONNECTIVITY OF HETEROGENEOUS HYDRAULIC CONDUCTIVITY FIELDS Connectivity of heterogeneous hydraulic conductivity fields was considered from two perspectives: (1) geologic connectivity and (2) hydraulic connectivity. This study considers connectivity only in the horizontal direction. 3.1 Geologic Connectivity Geologic connectivity was quantified by horizontal variogram ranges: the correlations between medium and coarse sand, fine sand, silt, and clay facies in the simulated aquifers. Three distinct groups were produced with geostatistical simulation: low geologic connectivity K fields, medium geologic connectivity K fields, and high geologic connectivity K fields (fig 3.1). The horizontal input variogram range for the 3D Geostatistical simulations was 5 km for the low geologic connectivity group, 25 km for the medium geologic connectivity group, and 50 km for the high geologic connectivity group. The actual variogram of the simulated fields varied and variability increased with variogram range (fig 3.2). The fields are visually distinct. Greater variogram ranges produced more extensive deposits in the horizontal direction. Long, isolated sand channels are ideal for the formation of preferential flow paths. 17

31 Figure 3.1 Heterogeneous 2D hydraulic conductivity fields derived from geostatistical simulation. Eight cases shown for each geologic connectivity group. Seaward boundary located at 0 km, coastline at 150 km, and landward boundary at 200 km. Seafloor located at top of each plot and aquifer bottom at bottom of plot. Simulated aquifer is 402 m deep. Vertical exaggeration is 100 times. 18

32 Figure 3.2 Distribution of horizontal variogram ranges of each facies for each geologic connectivity group for 2D K fields. Input variogram range used in simulation for each geologic connectivity group is indicated by black dotted line. For each boxplot: center line is median data point, box is middle 50% of data, whiskers are minimum and maximum excluding outliers, and crosses are outliers. 3.2 Hydraulic Connectivity Horizontal hydraulic connectivity was quantified by the ratio of horizontal effective hydraulic conductivity to the geometric mean of all of the hydraulic conductivities in the K field, KH,eff/KG, according to Knudby and Carrera (2005). This value is a metric of flow channeling or how preferential flow paths impact the collective flow through the system (Knudby & Carrera 2005). KG depends directly on the proportions of each facies in the K field. Hydraulic connectivity increased with geologic connectivity (fig 3.3). A plot of hydraulic connectivity as a function of horizontal variogram range for each facies is shown in fig

33 Figure 3.3 Distribution of hydraulic connectivity (KH,eff / KG) as a function of geologic connectivity for 2D K fields extracted from 3D Geostatistical simulation. 20

34 Figure 3.4 Hydraulic connectivity as a function of horizontal variogram range for each facies. Geologic connectivity groups indicated by symbol type. 3.3 Other Hydraulic Indicators KH,eff/KG was the hydraulic indicator that best represented hydraulic connectivity. Horizontal effective hydraulic conductivity (KH,eff), vertical effective hydraulic conductivity (KV,eff), and anisotropy (KH,eff/KV,eff) were also calculated for each field. As geologic connectivity increased, KH,eff increased, KV,eff decreased, and anisotropy increased (fig 3.5). The properties of each geostatistically simulated K field are listed in the appendix (tables A.1-3). 21

35 Figure 3.5 (a) Effective horizontal hydraulic conductivity, (b) effective vertical hydraulic conductivity, and (c) anisotropy as a function of geologic connectivity. 22

36 Chapter 4 RESULTS 4.1 Simulation Error For the 2D, heterogeneous case, 50 of 50 low geologic connectivity simulations, 46 of 50 medium geologic connectivity simulations, and 40 of 50 high geologic connectivity simulations were successfully completed to steady state. All of the corresponding homogeneous equivalent simulations were successfully completed to steady state. Results for each simulation are included in the appendix (tables A.4-9). Distributions of volumetric and solute mass balance errors for the 2D simulations are shown in figure 4.1. The solute mass balance error was high, but when it was less than 10%, no trend was found in the study variables. Simulations with solute mass balance error greater than 10% were therefore removed from the analysis. 46 of 50 low geologic connectivity simulations, 41 of 50 medium geologic connectivity simulations, 37 of 50 high geologic connectivity simulations, and all of the corresponding homogeneous equivalent simulations were included in the following results. 23

37 Figure 4.1 (a) Distributions of volumetric error [%] for heterogeneous and homogeneous simulations. (b) Distributions of solute mass balance error [%] for heterogeneous and homogeneous simulations. One 3D, heterogeneous simulation was completed to steady state for each low, medium, and high geologic connectivity case. Volumetric and solute mass balance errors are shown below in table 4.1. Table 4.1 Volumetric and solute mass balance errors for 3D heterogeneous simulations. 3D heterogeneous simulation case Volumetric error [%] Mass balance error [%] Low geologic connectivity Medium geologic connectivity High geologic connectivity Effect of Connectivity on Steady-state Salinity Distributions The size and variation of the mixing zone area increased with connectivity (fig 4.2, 4.3). The median and range of this area increased with geologic connectivity. A 24

38 positive trend with substantial scatter was observed between mixing zone area and hydraulic connectivity. Figure 4.2 Simulated steady-state salinity distributions for 2D models with heterogeneous hydraulic conductivity fields corresponding to those in Figure 3.1. Seaward boundary located at 0 km, coastline at 150 km (indicated by white dashed line), and landward boundary at 200 km. Seafloor located at top of each plot and aquifer bottom at bottom of plot. Black dot indicates centroid of mixing zone. 25

39 Figure 4.3 Influence of connectivity on mixing zone area for (a) geologic connectivity and (b) hydraulic connectivity. Geologic connectivity groups indicated by symbol type in panel (b). As connectivity increased, the mixing zone became wider at the bottom of the aquifer compared to the top (fig 4.2, 4.4) but the width of the top of the mixing zone was not related to connectivity. For the low geologic connectivity group, the median bottom width to top width ratio was near 1:1 such that 57.4% of simulations resulted in a mixing zone where the top was wider than the bottom and in 40.4% of simulations the bottom was wider than the top. The median and range of the ratio increased with geologic connectivity. The bottom of the mixing zone was wider than the top for 77.7% of the medium geologic connectivity group and 83.8% of the high geologic connectivity group. Similarly, when hydrologic connectivity was low, the ratio tended to be near 1:1. As hydrologic connectivity increased, it became more likely that the bottom of the aquifer was significantly larger than the top. 26

40 Figure 4.4 Influence of connectivity on the ratio of bottom width to top width of the mixing zone for (a) geologic connectivity and (b) hydraulic connectivity. Geologic connectivity groups indicated by symbol type in panel (b). Dotted line in both plots indicates 1:1 ratio. The position of the mixing zone, quantified by its centroid, also changed with connectivity (fig 4.2, 4.5). When connectivity was low, the centroid was near the coast. As connectivity increased, the horizontal position of the mixing zone centroid typically moved seaward and became more variable. As geologic connectivity increased, the median horizontal position of the mixing zone centroid decreased (shifted seaward) and the range increased. The median centroid value for the low geologic connectivity group was 2.6 km seaward of the coast. The median centroid value for the medium geologic connectivity group was 28.3 km seaward of the coast. All of the centroid values for the high geologic connectivity group were seaward of the coast with the median value 47.1 km seaward of the coast. The centroid also shifted seaward as hydraulic connectivity increased. Scatter was considerable, especially for simulations in the high geologic connectivity group. 27

41 Figure 4.5 Influence of horizontal connectivity on the position of the mixing zone for (a) geologic connectivity and (b) hydraulic connectivity. Geologic connectivity groups indicated by symbol type in panel (b). Coastline is located at 150 km (indicated by dotted line). Right of the coast is landward. 4.3 Effect of Connectivity on Steady-state Ocean-aquifer Exchange and saline SGD occurred near the coast when connectivity was low and tended to occur further offshore and with greater variability as connectivity increased (fig 4.6, 4.7). The median locations for both the fresh and saline SGD center of mass were found to move seaward and increase in range with increasing geologic connectivity. Within the medium and high geologic connectivity groups, the fresh and saline SGD center of mass tended to move seaward with increasing hydraulic connectivity. The fresh and saline centers of mass were limited to the area very near to the coastline for the low geologic connectivity group. This resulted in no relationship between SGD center of mass and hydraulic connectivity for the low geologic connectivity group. 28

42 Figure 4.6 Simulated submarine groundwater exchange patterns for 2D models with heterogeneous hydraulic conductivity fields. One simulation selected for each geologic connectivity group. qout is the Darcy velocity out of the sea floor (negative values represent flow into the aquifer). Seaward boundary located at 0 km, coastline at 150 km (indicated by grey dotted line), and landward boundary at 200 km. Note: y axis is not uniform across selected simulations. 29

43 Figure 4.7 (a) and saline SGD center of mass as a function of geologic connectivity. (b) and (c) saline SGD center of mass as a function of hydraulic connectivity. Geologic connectivity groups indicated by symbol type. For both plots the coastline is located at 150 km (indicated by dotted line). Right of the coast is considered landward. Left of the coast is considered seaward. 30

44 As connectivity increased, fresh and saline SGD spread over a larger and more variable area. The spread of discharge location over the simulated seafloor was quantified with the standard deviation of the locations of SGD weighted by the flow magnitude (fig 4.8). The median and range of the weighted standard deviations for both fresh and saline SGD increased with geologic connectivity. A relationship between hydraulic connectivity and the standard deviations for fresh and saline SGD was not found. 31

45 Figure 4.8 (a) Standard deviation of fresh and saline SGD location weighted by flow magnitude as a function of geologic connectivity. Standard deviation of fresh (b) and saline (c) SGD location weighted by flow magnitude as a function of hydraulic connectivity. Geologic connectivity types indicated by symbol type. 32

46 A relationship between connectivity and skew of the SGD distributions either landward or seaward was not found. For both fresh and saline SGD, negative skew, indicating that the distribution tailed seaward, was only slightly more common than positive skew, indicating that the distribution tailed landward (table 4.2). Table 4.2 SGD SGD Skew of fresh and saline SGD distributed along sea floor. Positive skew indicates that discharge was low near the coast and tended to be higher further offshore. Negative skew indicates that discharge was high near the coast and tended to be lower further offshore. If all SGD occurred through one model cell, no skew was quantified. Positive skew: Distribution tailed landward Negative skew: Distribution tailed seaward 36.6% 58.0% 5.3% 40.5% 56.5% 3.1% No skew: Flow through one cell only For all connectivity cases, saline SGR and saline SGD were observed to occur in similar patterns. A positive relationship with significant scatter was found between fresh recharge and hydraulic connectivity (fig 4.9). A relationship between fresh recharge and geologic connectivity was not found. 33

47 Figure 4.9 recharge as a function of horizontal hydraulic connectivity. Geologic connectivity indicated by symbol type. Percent circulation was also quantified, but a relationship between PSC and geologic or hydraulic connectivity was not found (fig 4.10). Figure 4.10 Influence of connectivity on percent saltwater circulation for (a) geologic connectivity and (b) hydraulic connectivity. Geologic connectivity groups indicated by symbol type in panel (b). 34

48 To further understand which variables influenced PSC in heterogeneous aquifers, the relationship between the ratio of free (density driven) to forced convection (head driven) and PSC was explored. The ratio, following Smith (2004) is: Where: Free convection includes the concentration (C) and density (ρ) of both fluids and horizontal (Kx) and vertical (Kz) hydraulic conductivity. Forced convection represents fresh recharge (qf). A positive relationship was found for the variables in this study (fig 4.11). 35

49 Figure 4.11 PSC as a function of the ratio between free and forced convection (calculated by Smith 2004). 4.4 Comparison of Effects of Heterogeneous and Equivalent Homogeneous Hydraulic Conductivity Fields on Steady-state Salinity Distributions The steady-state salinity distributions for selected realizations of each geologic connectivity group and their corresponding homogeneous equivalent are shown in figure For homogeneous equivalent models, in 10.9% of medium and 25.6% of high geologic connectivity simulations, high anisotropy and high fresh recharge caused a complete or near-complete flushing of the system with fresh water. These heterogeneous-homogenous run pairs were not included in the following analysis. 36

50 Figure 4.12 Steady-state salinity distributions for 2D models with heterogeneous K fields and equivalent homogeneous K fields corresponding to those in Figure 3.1. Seaward boundary located at 0 km, coastline at 150 km (indicated by white dashed line), and landward boundary at 200 km. Seafloor located at top of each plot and aquifer bottom at bottom of plot. Black dot indicates centroid of mixing zone. 37

51 The mixing zone area was generally larger for heterogeneous K fields than for homogenous K fields (fig 4.12, 4.13). The median heterogeneous to homogenous mixing zone area ratio was close to 2:1 for all geologic connectivity groups. For approximately 75% of each geologic connectivity group, mixing area was larger for heterogeneous K fields than it was for homogenous K fields. The range of the ratios decreased with geologic connectivity. The ratio also decreased with hydraulic connectivity, but scatter was significant. Figure 4.13 Influence of connectivity on the simulated mixing zone area with heterogeneous K field divided by the mixing zone area with homogeneous equivalent K field for (a) geologic connectivity and (b) hydraulic connectivity. Geologic connectivity groups indicated by symbol type in panel (b). The mixing zone tended to be irregular and widen with depth for simulations with heterogeneous K fields, and it was smoother with a more uniform width for simulations with homogeneous K fields (fig 4.12). For homogeneous simulations within all geologic connectivity groups, the top of the mixing zone was slightly larger than the bottom. Bottom to top width ratio ranged from 0.5 to 0.9, while the ratio 38

52 ranged from 0.4 to 9.4 for heterogeneous simulations. The impact of heterogeneity on this ratio was not found to be related to geologic or hydraulic connectivity. A relationship between the ratio of these ratios ((heterogeneous bottom : top width) : (homogeneous bottom : top width)) and geologic or hydraulic connectivity was not found. A clear relationship between the presence of heterogeneity and location of the mixing zone centroid was not found (fig 4.14). For 57.4% of simulations the mixing zone was further seaward for heterogeneous K fields and for 42.6% of simulations the mixing zone was further seaward for homogeneous simulations. However, the range of differences between heterogeneous and homogeneous centroids was found to increase with geologic and hydraulic connectivity. 39

53 Figure 4.14 Influence of connectivity on the difference in location of centroid of mixing zone between each heterogeneous K field and equivalent homogenous K field for (a) geologic connectivity categories and (b) hydraulic connectivity. Geologic connectivity groups indicated by symbol type in panel (b). Dotted lines indicate zero difference between heterogeneous and homogenous mixing zone centroid. Left of the dotted line, heterogeneous simulations are further seaward than equivalent homogeneous simulations. Left of the dotted line, heterogeneous simulations are farther seaward than corresponding homogeneous simulations. 4.5 Effect of Heterogeneous verses Equivalent Homogeneous Hydraulic Conductivity Fields on Steady-state Ocean-aquifer Exchange SGD tended to extend farther seaward in heterogeneous simulations than in equivalent homogeneous simulations. This discrepancy increased with connectivity. Increasing horizontal geologic and hydrologic conductivity increased the median difference between heterogeneous and homogeneous fresh SGD center of mass and the range of this difference (fig 4.15, 4.16 a and b). A relationship between heterogeneity and location of the saline SGD center of mass was not found. For 58.3% of simulations the center of mass was further seaward for heterogeneous K fields and for 41.7% of simulations the center of mass was further seaward for homogeneous simulations. However, the range of differences between 40

54 heterogeneous and homogeneous centroids was found to increase with both geologic and hydraulic connectivity (fig 4.14, 4.15 a and c). 41

55 Figure 4.15 Simulated submarine groundwater exchange patterns for 2D models with heterogeneous hydraulic conductivity fields and corresponding homogeneous equivalent fields. One simulation selected for each geologic connectivity group. qout is the Darcy velocity out of the sea floor (a negative value indicates flow into the aquifer). Seaward boundary located at 0 km, coastline at 150 km (indicated by grey dotted line), and landward boundary at 200 km. Note: y-axis is not uniform across selected simulations. 42

56 Figure 4.16 Influence of connectivity on the difference between the center of mass of SGD in heterogeneous and equivalent homogeneous simulations for (a) geologic connectivity and fresh and saline SGD, (b) hydraulic connectivity and fresh SGD, and (c) hydraulic connectivity and saline SGD. Geologic connectivity groups indicated by symbol type in (b) and (c). Dotted line indicates zero difference between heterogeneous and homogenous SGD center of mass. Left of the dotted line, heterogeneous simulations are farther seaward than equivalent homogeneous simulations. 43

57 Standard deviation of SGD location weighted by flow magnitude was usually greater for heterogeneous simulations than for homogeneous simulations. For 63.5% of simulations, spread of fresh SGD was greater for heterogeneous fields. For 73.9% of simulations, spread of saline SGD was greater for heterogeneous fields. A relationship between the impact of heterogeneity on spread of SGD over the sea floor and geologic or hydraulic connectivity was not found. Heterogeneity increased the variability in spread of fresh and saline SGD. This discrepancy in homogeneous to heterogeneous standard deviation of SGD location weighted by magnitude of discharge increased with geologic connectivity (fig 4.17a). For homogeneous K fields, a clear relationship was found between hydraulic connectivity and standard deviation of SGD location. The same relationship did not exist for heterogeneous K fields (fig 4.17b). 44

58 Figure 4.17 (a) Standard deviation of fresh and saline SGD location weighted by magnitude of discharge for simulations with heterogeneous and homogeneous hydraulic conductivity fields as a function of geologic connectivity. (b) Standard deviation of fresh SGD location weighted by flow magnitude for simulations with heterogeneous and homogenous hydraulic conductivity fields as a function of hydraulic connectivity. Geologic connectivity groups indicated by symbol type. All fresh SGD distributions resulting from homogenous K fields had a negative skew, indicating that the majority of fresh flow discharged very near to the coast and then the distribution tailed seaward (see characteristic shape of fresh SGD in homogeneous runs, fig 4.15). No relationship was found between this skew and connectivity. In addition, no relationship was found between the ratio of heterogeneous to homogeneous fresh SGD skew and connectivity. 45

59 SGD distributions resulting from homogeneous K fields did not have a consistent skew. 58.0% were negative (tailed seaward) and 42.0% were positive (tailed landward). No relationship was found between this skew and connectivity. In addition, no relationship was found between the ratio of heterogeneous to homogeneous saline SGD skew and connectivity. Percent saltwater circulation for simulations with heterogeneous K fields was found to be 1.5 to 150 times the PSC for corresponding homogeneous K fields (fig 4.18). No relationship was found between geologic or hydraulic connectivity and the heterogeneous PSC to homogeneous PSC ratio. Figure 4.18 PSC for heterogeneous K fields v. PSC for corresponding homogeneous K fields. Geologic connectivity groups indicated by symbol type. Dotted line is 1:1 ratio. 4.6 Effect of Dimension on Steady-state Salinity Distributions For the 3D SEAWAT simulations with heterogeneous K fields, the effect of connectivity was similar to that in 2D, though the magnitude differed. By visually inspecting all 3D slices for each geologic connectivity case, we see that the the mixing 46

60 zone area increased and its center of mass shifted seaward as geologic connectivity was increased. Increasing connectivity also corresponded to an increase in the variability of the size, shape and location of the mixing zone parallel to the shoreline (fig , left). The central salinity profile for each 3D heterogeneous simulation (located at 12.5 km) was compared to the corresponding 2D heterogeneous simulation (fig , right). For all three geologic connectivity cases, the mixing zone was larger when modeled in 2D compared to 3D. A clear relationship between center of mass of the mixing zone in the 2D verses the 3D slices was not found. 47

61 Figure 4.19 Left: Selected profiles of steady-state salinity distribution for a 3D heterogeneous K field with low geologic connectivity. Right: steadystate salinity distribution for the 2D heterogeneous K field with low geologic connectivity where the transverse coordinate equals 12.5 km. Seaward boundary located at 0 km, coastline at 150 km (indicated by white dashed line), and landward boundary at 200 km. Seafloor located at top of each plot and aquifer bottom at bottom of plot. Black dot indicates centroid of mixing zone. 48

62 Figure 4.20 Left: Selected profiles of steady-state salinity distribution for a 3D heterogeneous K field with medium geologic connectivity. Right: steady-state salinity distribution for the 2D heterogeneous K field with medium geologic connectivity where the transverse coordinate equals 12.5 km. Seaward boundary located at 0 km, coastline at 150 km (indicated by white dashed line), and landward boundary at 200 km. Seafloor located at top of each plot and aquifer bottom at bottom of plot. Black dot indicates centroid of mixing zone. 49

63 Figure 4.21 Left: Selected profiles of steady-state salinity distribution for a 3D heterogeneous K field with high geologic connectivity. Right: steadystate salinity distribution for the 2D heterogeneous K field with high geologic connectivity where the transverse coordinate equals 12.5 km. Seaward boundary located at 0 km, coastline at 150 km (indicated by white dashed line), and landward boundary at 200 km. Seafloor located at top of each plot and aquifer bottom at bottom of plot. Black dot indicates centroid of mixing zone. 50

64 4.7 Effect of Dimension on Steady-state Ocean-aquifer Exchange For the 3D SEAWAT simulations with heterogeneous K fields, the center of mass of fresh SGD and saline SGD and SGR moved seaward and spread out over a larger distance along the sea floor as geologic connectivity increased. Increasing geologic connectivity also corresponded to increased variability in both of these variables parallel to the shoreline (fig ). SGD and SGR patterns at 12.5 km in the 3D simulation were not a good match for those in the corresponding 2D heterogeneous simulation. However, similar trends between the output variables and geologic connectivity were observed in both 2D and 3D. 51

65 Figure 4.22 Steady-state ocean aquifer exchange patterns for the low geologic connectivity 3D simulation. qout is the Darcy velocity out of the sea floor (negative values represent flow into the aquifer). Seaward boundary located at 0 km, coastline at 150 km), and landward boundary at 200 km. 52

66 Figure 4.23 Steady-state ocean aquifer exchange patterns for the medium geologic connectivity 3D simulation. qout is the Darcy velocity out of the sea floor (negative values represent flow into the aquifer). Seaward boundary located at 0 km, coastline at 150 km), and landward boundary at 200 km. 53

67 Figure 4.24 Steady-state ocean aquifer exchange patterns for the high geologic connectivity 3D simulation. qout is the Darcy velocity out of the sea floor (negative values represent flow into the aquifer). Seaward boundary located at 0 km, coastline at 150 km), and landward boundary at 200 km. 54

68 When modeled in 3D, fresh recharge and PSC both increased with geologic connectivity (table 4.3). Modeling in 3D rather than 2D resulted in higher values of fresh recharge and lower values of PSC. However, it should be noted that the increase in PSC with geologic connectivity is small compared to the range of 2D PSC values. Table 4.3 recharge [m3/s] and PSC [%] for the 3D simulations of low, medium, and high geologic connectivity compared to range of results for 2D simulations. recharge [m3/s] PSC [%] Geologic connectivity 3D 2D range 3D 2D range Low 2.85E E-6 to 3.75E to 5,927 Medium 8.08E E-6 to 2.40 E to 4,940 High 1.22E E-5 to 3.86E to 3,136 55

69 Chapter 5 DISCUSSION 5.1 Hydraulic Connectivity Impacts Recharge Hydraulic connectivity, also called normalized hydraulic conductivity, impacted fresh recharge. This study maintained a constant width and depth of the model domain and a constant head gradient between land and sea. We assumed that flow was predominantly horizontal in the landward portion of the model. According to Darcy s law, this indicates that freshwater recharge and effective horizontal hydraulic conductivity should have a positive, linear relationship. For heterogeneous and homogeneous K fields we do find a positive trend between Kh,eff and freshwater recharge, but scatter is significant for the heterogeneous case. We suggest that this scatter is caused by the presence of heterogeneity. 5.2 Geologic Connectivity Impacts Subsurface Salinity and Patterns of Oceanaquifer Exchange Geologic connectivity increases local variability of flow and transport within each simulation. This leads to patches of increased dispersion that coexist with high preferential flow paths. In a constant-density system, Zinn and Harvey (2003) showed that as the connectivity of high K patterns in isotropic multi-gaussian hydraulic conductivity fields was increased, velocity variance increased, leading to higher macro dispersivity. 56

70 By finding an increase in mixing zone area with increasing geologic connectivity, we illustrate that their observation holds true in variable-density coastal aquifers. For dispersive Henry problem simulations with anisotropic homogeneous fields, Abarca et al. (2007b) found that while transverse dispersion widened the mixing zone overall, longitudinal dispersion widened the mixing zone bottom. In our heterogeneous systems, we found that increasing geologic connectivity increased not only the overall width of the mixing zone, but to a greater extent increased the bottom of the mixing zone. Therefore, we can suggest that horizontal geologic connectivity increases both longditudinal and transverse dispersion. Both our study and Abarca et al. (2007 b) found that the mixing zone moved seaward as Kh,eff was increased. They suggest that high horizontal K values resulted in greater fresh recharge, which induced greater saltwater circulation. The movement of salt water into the mixing zone and up through the sea floor created a head loss. This loss of potential energy reduced the extent to which the salt wedge intruded (Abarca et al 2007 b). By plotting PSC against Smith s (2004) ratio of free to forced convection, we show that higher fresh recharge leads to lower PSC in our study. We also show that dispersion (indicated by mixing zone area) but not PSC has a relationship to geologic connectivity. Therefore, we suggest that the mixing zone moves seaward when high recharge and high dispersivity, which are both prevalent in our high geologic connectivity simulations, combine. At the same time, geologic connectivity impacted the location and spread of SGD. As geologic connectivity increased, preferential flow paths tended to cause fresh water to discharge further offshore. and over a larger area. Because fresh and saline SGD occur in tandem, saline water tended to discharge further offshore as well. 57

71 5.3 Geologic Connectivity Impacts Variability of Subsurface Salinity Patterns and Ocean-aquifer Exchange Across Multiple Simulations Geologic connectivity creates variability in flow and transport across multiple simulations. This is illustrated by increased variability in mixing zone area, centroid location, and spread and location of ocean-aquifer exchange as geologic connectivity is increased. Geologic connectivity affected variation in mixing zone area. This may be partially explained by whether our medium and high geologic connectivity fields were connected by high or low K deposits. Abarca s dissertation (2007a) studied dispersive and diffusive Henry problem models with anisotropic (small and medium scale) heterogeneous and homogeneous K fields. She found that high K deposits located at the mixing zone caused channeling of outflowing fresh water if they were well connected and local circulation cells if they were isolated. These two opposite occurrences impact the size and shape of the interface and Abarca observed that as K field correlation length increased, a lack of ergodicity led to a wider distribution of results. Relative to model size, our correlation lengths are even larger than Abarca s, so our models likely lack ergodicity. Centroid location and mixing zone area were related; therefore, centroid location varied when mixing zone area varied. Our study and Abarca et al. (2007 b) both found that the mixing zone moved seaward when dispersion increased (here we use mixing zone area as a rough indicator for the relative amount of dispersion in our simulations). Dispersion of saline water into the mixing zone dissipates energy from the seaward portion of the aquifer. Because of this energy loss, saltwater intrusion is limited. 58

72 Location and spread of SGD was related to both mixing zone area and centroid location. From our simulations, we observed that ocean-aquifer exchange occurred where the mixing zone met the sea floor (at the model top). When mixing zone area or width varied, spread of SGD varied. When mixing zone location varied, location of SGD center of mass varied. 5.4 Heterogeneity Impacts Subsurface Salinity Patterns and Amounts and Patterns of Ocean-aquifer Exchange The presence or lack of heterogeneity impacted the area of the mixing zone. Kerrou and Renard (2010) conducted dispersive Henry problem simulations for isotropic and anisotropic multi-gaussian hydraulic conductivity fields and their homogeneous equivalents. They found that heterogeneity increased the area of the mixing zone by up to half. They concluded that the width of the mixing zone is mainly controlled by dispersion, which is greater for heterogeneous K fields. For our study, the ratio of heterogeneous to homogeneous mixing zone area had a much larger range. Heterogeneity could increase the area of the mixing zone by up to 10 times, but it could also decrease the area of the mixing zone. Compared to Kerrou and Renard s work, there is increased likelihood for the formation of preferential flow paths in our K fields. When transport becomes dominated by advection along these preferential flow paths, mixing is reduced. As a result, our study finds that about 25% of heterogeneous fields actually produced smaller mixing zones than their homogeneous equivalents. This is more prevalent as geologic connectivity increases because, although dispersion and advection are always present, advection becomes more dominant. Therefore, the relationship between mixing zone area produced from 59

73 heterogeneous verses homogeneous K fields becomes more difficult to predict as K field geologic connectivity is increased. Dispersion, but not heterogeneity by itself, affected the position of the mixing zone. The quantity of dispersion (indicated by the size of the mixing zone) in each simulation resulted from a balance of dispersion caused by heterogeneity opposed by advective transport through preferential flow paths. This observation differs from other studies where heterogeneous fields consistently produced mixing zones further seaward compared to homogeneous equivalents (Abarca 2007a, Kerrou and Renard 2010). We suggest that this is because previous studies considered small to medium scale heterogeneity that consistently increased dispersion more than they increased advection in the aquifer. The presence of heterogeneity impacted the distribution of SGD along the sea floor. In our homogeneous simulations, fresh SGD was high at the shoreline and tailed seaward. The presence of heterogeneity caused deviation from this characteristic distribution such that fresh discharge could be high at the shoreline and tail seaward, be high further offshore and tail landward, or appear random. This is, again, an effect of preferential flow paths. To our knowledge, patterns of SGD modeled for large coastal aquifers with large scale heterogeneity have not previously been reported. Field studies identifying offshore fresh or brackish groundwater below continental shelves, like those reviewed in Post et al. (2013) are the best support for our results. or brackish groundwater reserves, discovered as far as a few hundred kilometers offshore, have been explained by fresh groundwater recharge during sea-level low-stands. Our 2D simulations 60

74 suggest that with high geologic connectivity, brackish plumes could move low-salinity groundwater from land as far as km offshore at steady state. The presence or lack of heterogeneity impacted PSC. For our study, PSC was 1.5 to 150 times greater for heterogeneous K fields compared to their homogeneous equivalent K fields. In Kerrou and Renard s (2010) study, heterogeneity increased the saline to fresh flux ratio up to 20 times. This increase is attributed to small scale velocity variations caused by the heterogeneous fields. It is interesting to note that while the connectivity of heterogeneous K fields impacts SGD and SGR patterns, the facies arrangement does not impact the quantity of PSC. 5.5 Dimension Impacts Subsurface Salinity Patterns and Amounts of Oceanaquifer Exchange Modeling in 3D rather than 2D increased fresh recharge. recharge is dependent on horizontal hydraulic conductivity which increases with dimension (Kerrou and Renard 2010, Abarca 2007 a). Dimension impacted the width of the mixing zone. Modeling in 2D rather than 3D produced a wider interface. These results are consistent with Kerrou and Renard (2010). However, with small scale heterogeneity they found a discrepancy of less than 10%, but our results are more extreme. In both studies, modeling in 3D increased flow velocity along the flow paths. The added dimension allowed water to move parallel to the shoreline rather than get stuck in clay deposits. In our study, fresh recharge varied at the prescribed head boundary. Because modeling in 3D increased fresh recharge, this decreased mixing in the simulation. Dimension impacted PSC. Because modeling in 3D rather than 2D decreased dispersion, PSC was reduced in 3D models. Kerrou and Renard (2010) saw a similar 61

75 trend. They found that 2D simulations produced PSC up to twice that of 3D simulations. We found that modeling in 2D could produce PSC over 100 times greater than that of 3D simulations. This suggests that as the scale of heterogeneity increases, 2D models are less capable of representing their 3D counterparts. 5.6 Free / Forced Convection Impacts Percent Saltwater Circulation Smith (2004) investigated the impact of dispersivity on PSC with homogeneous models. He found that PSC increased with the ratio of free to forced convection. Our results agree with this conclusion. As mixing (driven by dispersive forces) increased with respect to fresh recharge, PSC increased. Smith also found that the ratio between aquifer depth and vertical transverse dispersivity (D*) impacted PSC. Considering a range of D* values from 2 to 200, PSC peaked at D*=40, where dispersion and the hydraulic gradient were well balanced. But our results suggest that heterogeneity alters this balance. With a D* of 200, our heterogeneous models produced higher values of PSC than any of Smith s homogeneous models. 5.7 Study Limitations This study uses a simple model setup to isolate the impacts of connectivity, heterogeneity, and dimension. As with all numerical models, model decisions impacted results. For example, using a prescribed head of 20 m rather than 10 m on the landward boundary would have increased fresh recharge. This would likely lead to a lower value of PSC (Smith 2004). The study limitation of simulation error has been discussed previously. Additional limitations include grid discretization, the selected dispersivity value and the number of successful 3D simulations. 62

76 Grid discretization tests show higher PSC values as the grid is refined. This indicates that PSC is underestimated in the results reported here. Because PSC is increasing rather than decreasing as the grid is refined, we are confident that numerical dispersion does not cause this significant discrepancy and that higher PSC in the heterogeneous simulations is not an artifact of the decision to use a coarse grid. Rather, similar patterns of saline SGD and SGR for each simulation suggest that heterogeneity increases PSC in shallow circulation cells rather in than deep circulation. We suspect that more of the shallow circulation is quantified as the grid is refined. Because we find a relationship between free to forced convection velocity and PSC similar to Smith (2004), our simulations likely capture deep circulation reasonably well. A longitudinal dispersivity value of 200 m was chosen for this study according to the range of dispersivity values computed from field studies assembled by Gelhar et al. (1992). However, for study scales greater than 300 m (our study is 200 km in length), Gelhar et al classified all collected dispersivity data as unreliable. A conventional 100 : 10 : 1 ratio was specified for longitudinal to horizontal transverse to vertical transverse dispersivity, but there is little evidence available to support this convention (Gelhar et al. 1992). Because this study is a sensitivity analysis not an attempt to represent an aquifer in the field and predict its behavior we believe that this approach is reasonable. A value that is unreasonably low would lead to numerical instabilities. A value that is unreasonably high would lead to the breakdown of free convection (Smith 2004). We are confident that the heterogeneous simulations are not driven primarily by dispersive processes because many heterogeneous 2D simulations produced smaller mixing zones than their homogeneous counterparts. However, 63

77 because dispersion is more dominant in the homogeneous aquifers, mixing and transport in these simulations may be altered to a greater by changes in dispersivity than heterogeneous simulations. Due to time and numerical limitations, most simulations were run in 2D rather than 3D. One simulation of each geologic connectivity case is not sufficient for studying the statistical impact of geologic connectivity on 3D simulations. Neither is it satisfactory for understanding the statistical relationship between heterogeneous 2D and 3D simulations. However, this limited set of 3D simulations and the set of 2D heterogeneous simulations show similar trends in regard to the impacts of connectivity. Additionally, by visually comparing the 3D ensembles to boxplots of our 2D results, we found consistently in 2D compared to 3D that: (1) the mixing zone was wider, (2) fresh recharge decreased, and (3) PSC increased. Therefore, we suggest that while 2D simulations may not accurately portray a 3D heterogeneous aquifer, they are sufficient for understanding the statistical impacts of connectivity on these 3D systems. 5.8 Implications There are four significant implications of this work: First, our findings suggest that when collecting hydrogeologic data in the field, special attention should be paid to aquifers where geologic connectivity is prevalent. This work found that geologic connectivity impacted the size and shape of the mixing zone and patterns of SGD and SGR. As geologic connectivity increased, variability increased parallel to the shore line in the 3D realizations. More complex behavior and higher variability suggest a need for more spatially dense sampling. 64

78 Second, our findings suggest that when modeling large-scale coastal aquifers, the impacts of large scale heterogeneity, geologic connectivity, and model dimension on the simulation should all be considered. Equivalent homogeneous simulations did not adequately represent heterogeneous aquifers. Connectivity impacted patterns of salinity and exchange as well as their variability. Modeling in 2D rather than 3D lead to: exaggerated dispersion at the mixing zone, larger offshore distances of fresh discharge, and inflated PSC. Third, our findings suggest that brackish groundwater could be present tens of kilometers offshore at steady state. In Post et al. (2013), previous studies attribute the presence of brackish groundwater far offshore to transience; freshwater reserves were deposited in the aquifer at sea-level low stands and the freshwater is slowly moving landward as the system tends toward steady state. However, subsurface salinity patterns from field data used to support this theory are similar to salinity patterns from our steady state simulations (fig 5.1). Figure 5.1 Salinity data from Post et al and a salinity distribution from one of this study s medium geologic connectivity simulations. 65