# Modeling the Potential of Submarine Groundwater Discharge to Facilitate Growth of Vibrio cholerae Bacteria

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Setup

_{S}) were particularly in focus as gradient-driven exchanges and small-scaled variations of flow directions took place mainly in that area. To maximize the representation of the hydrodynamic and solute transport processes right at the coast, the spatial resolution of the mesh was increased in this area using the implemented triangle generator (Delaunay triangulation). Based on model setups in [12], the sea side boundary featured a small vertical part at its lower end to avoid highly acute angles leading to distorted mesh elements and potential numerical issues.

#### 2.2. Governing Equations

^{−1}] is the specific storage coefficient of the fluid, h [m] is the hydraulic potential, t [T] is the time, v [L T

^{−1}] is the Darcy velocity vector, and q [L T

^{−1}] is the outflow/inflow rate (sink/source) of the model system [46].

^{−3}] is the mass concentration. D [L

^{2}T

^{−1}] represents the hydrodynamic dispersion tensor including effects of molecular diffusion D

_{D}and longitudinal and transverse dispersivities (α

_{L}, α

_{T}), respectively [47].

^{−1}] is the hydraulic conductivity tensor, f

_{µ}[–] is the fluid-specific viscosity ratio function, h [L] is the hydraulic potential, and $\tilde{\rho}=$ relative density $=\left(\frac{\rho -{\rho}_{0}}{{\rho}_{0}}\right)$. $\rho $ and ${\rho}_{0}$ [M L

^{−3}] describe the fluid density and reference fluid density. e quantifies the gravitational unit vector with respect to global coordinates [48].

_{D}is the effective molecular diffusion [L

^{2}T

^{−1}], α

_{L}and α

_{T}are longitudinal and transverse dispersivities [L], and I [-] is the unit tensor [49].

#### 2.3. Parametrization

_{Min}= 0°) and the maximum value (β

_{Max}= 76.1°) approached more natural (shallow) conditions. Besides six different slope angles (Table 1), model runs varied individual parameters to elucidate their impact on SGD and V. cholerae growth. Values of controlling factors of SGD were selected to represent a realistic spectrum based on literature (Table 1).

_{X}= 0.8 m d

^{−1}) and varying hydraulic conductivities (8 m d

^{−1}≤ K ≤ 85 m d

^{−1}).

#### 2.4. Model Evaluation

^{−5}s

^{−1}). SGD zone lengths are determined by a digital measuring tool implemented in FEFLOW and represent the sea-side boundary part at which streamlines outflow from the aquifer (Figure 2a). Potentially optimal conditions for V. cholerae growth were measured likewise, as their requirements were met along a restricted part of the SGD zone—referred to as V. cholerae habitat zone, represented by local salinity values C

_{S}≤ 1000 mg L

^{−1}at the direct interface between sea and aquifer (Figure 2b).

## 3. Results

_{X}) on both the SGD zone and the V. cholerae habitat zone. The habitat zones expand non-linearly with increasing inflow, while saltwater intrusion diminishes (Figure 3). V. cholerae habitat zones are generally smaller than the SGD area and disappear below q

_{X}= 0.07 m d

^{−1}. Also, specific SGD flux and hydraulic gradient correlate linearly with inflow (Figure 4). Altered hydraulic conductivities impact SGD and V. cholerae zones; the observed changes in SGD zone, V. cholerae habitat zone (Figure 5), and hydraulic gradient (Figure 6) decrease exponentially with increasing aquifer conductivity with higher rates of change at low K-values. Specific SGD fluxes show a weak positive correlation to changes of hydraulic conductivity (Figure 6).

_{X}and lowest K, respectively. For the considered K-values (Table 1), the V. cholerae habitats in this study range from 1 m to a maximum of 36 m, which corresponds to a possible habitat extension from 1.2% to 42.3% of the entire seaside boundary. With a constant inflow of q

_{X}= 1.3 m d

^{−1}and 85 m d

^{−1}≥ K ≥ 8 m d

^{−1}we note a range from 4 m to 36 m (4.7 % to 42.3 %). Furthermore, the model shows that there is no linear relation between V. cholerae habitat zones and volumes of SGD; while SGD rate increases with increasing permeability (Figure 6), habitat areas decrease (Figure 5).

_{L}, α

_{T}) on the hydraulic potential distribution in coastal aquifers is described in [13,44], which is in accordance with the results obtained here. Accordingly, SGD zones only show minor changes with varying dispersivity parameters (Figure 7). Different from previous results, V. cholerae habitats do not follow the SGD zone response. Higher mixing potential between groundwater and intruding seawater significantly decreases the preferred habitat of V. cholerae assuming a static concentration cap of C

_{max}= 1000 mg L

^{−1}(Figure 7). The maximum expansion of V. cholerae habitat zones at different dispersivities (75 m ≥ α

_{L}≥ 2.5 m) ranges between 15 m and 30 m (the difference corresponds to 17.6 % of the entire seaside boundary) for K = 8 m d

^{−1}.

^{−1}) but converge as the hydraulic conductivity decreases. Specific SGD fluxes correspond to the SGD zone growth behavior in much smaller dimensions (Figure 8). Highest potential changes in V. cholerae zone lengths caused by different coastal slope angles are 6.5 m at K = 17 m d

^{−1}.

## 4. Discussion

_{X}. This is also true for different values of influx q

_{X}. The exponential growth of SGD and V. cholerae habitat zone lengths as only the hydraulic conductivity changes is attributed to the FEFLOW-implemented Darcy equation

_{T}and α

_{L}—slight positive correlations can be attributed to the fact that higher dispersivities reduce density contrasts which weakens the SWI and favors a larger discharge zone for groundwater [12,59]. The strong influence of groundwater and seawater mixing on V. cholerae habitats in this study originates in their assumed dependence solely on salinity. As high mixing potential spreads the transition zone between groundwater and SWI, more discharging groundwater is enriched with salt and higher mass concentrations arise along the SGD zones.

_{L}and α

_{T}values.

_{S}≤ 1000 mg L

^{−1}). Regarding the global frequency of coastal slope angles, most relevant simulation results range between 54° < β < 76° [60]; within these bounds SGD and V. cholerae habitats increase as the sea-side boundary inclines, which could be partially owed to an increasing hydraulic gradient to overcome a growing hydrostatic potential on an expanding slope.

## 5. Conclusions

- Sufficient fresh groundwater inflow and hydraulic conductivity of a coastal aquifer are the most important controls that govern V. cholerae growth. Demanding a high freshwater supply (C
_{S}≤ 100 mg L^{−1}) to the coastal slope and thus a high hydraulic gradient between the hinterland and sea to displace saltwater intrusion, a preferably high groundwater inflow and low hydraulic conductivity within the bounds of a highly conductive material (e.g., sand) create the most favorable conditions for V. cholerae growth, which is not necessarily linked to the specific SGD flux. - Although not significantly affecting the SGD volume, dispersion facilitates non-halophilic bacterial expansion at decreasing values, keeping the fresh groundwater flow low in salt by preventing mixing processes between fresh and saline groundwaters.
- Coastal slope had substantially less impact on the estimated habitat areas than the other analyzed parameters.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Burnett, W.C.; Bokuniewicz, H.; Huettel, M.; Moore, W.S.; Taniguchi, M. Groundwater and pore water inputs to the coastal zone. Biogeochemistry
**2003**, 66, 3–33. [Google Scholar] [CrossRef] - Moore, W.S. The effect of submarine groundwater discharge on the ocean. Annu. Rev. Mar. Sci.
**2010**, 2, 59–88. [Google Scholar] [CrossRef] [PubMed] - Burnett, W.C.; Aggarwal, P.K.; Aureli, A.; Bokuniewicz, H.; Cable, J.E.; Charette, M.A.; Moore, W.S.; Krupa, S.; Kulkarni, K.M.; Loveless, A.; et al. Quantifying submarine groundwater discharge in the coastal zone via multiple methods. Sci. Total Environ.
**2006**, 367, 498–543. [Google Scholar] [CrossRef] [PubMed] - da Rocha, C.M.; Barboza, E.G.; Niencheski, L.F.H. Radon activity and submarine groundwater discharge in different geological regions of a coastal barrier in Southern Brazil. Environ. Earth Sci.
**2018**, 77, 527. [Google Scholar] [CrossRef] - Taniguchi, M.; Burnett, W.C.; Cable, J.E.; Turner, J.V. Investigation of submarine groundwater discharge. Hydrol. Process.
**2002**, 16, 2115–2129. [Google Scholar] [CrossRef] - Johannes, R.E. Ecological significance of the submarine discharge of groundwater. Mar. Ecol. Prog. Ser.
**1980**, 3, 365–373. [Google Scholar] [CrossRef] - Li, X.; Hu, B.X.; Burnett, W.C.; Santos, I.R.; Chanton, J.P. Submarine ground water discharge driven by tidal pumping in a heterogeneous aquifer. Groundwater
**2009**, 47, 558–568. [Google Scholar] [CrossRef] - Antonellini, M.; Mollema, P.; Giambastiani, B.; Bishop, K.; Caruso, L.; Minchio, A.; Pellegrini, L.; Sabia, M.; Ulazzi, E.; Gabbianelli, G. Salt water intrusion in the coastal aquifer of the southern Po Plain, Italy. Hydrogeol. J.
**2008**, 16, 1541. [Google Scholar] [CrossRef] - Michael, H.A.; Mulligan, A.E.; Harvey, C.F. Seasonal oscillations in water exchange between aquifers and the coastal ocean. Nature
**2005**, 436, 1145. [Google Scholar] [CrossRef] - Mulligan, A.E.; Charette, M.A. Intercomparison of submarine groundwater discharge estimates from a sandy unconfined aquifer. J. Hydrol.
**2006**, 327, 411–425. [Google Scholar] [CrossRef] - Cable, J.E.; Burnett, W.C.; Chanton, J.P.; Corbett, D.R.; Cable, P.H. Field evaluation of seepage meters in the coastal marine environment. Estuar. Coast. Shelf Sci.
**1997**, 45, 367–375. [Google Scholar] [CrossRef] - Walther, M.; Graf, T.; Kolditz, O.; Liedl, R.; Post, V. How significant is the slope of the sea-side boundary for modelling seawater intrusion in coastal aquifers? J. Hydrol.
**2017**, 551, 648–659. [Google Scholar] [CrossRef] - Wilson, A.M. Fresh and saline groundwater discharge to the ocean: A regional perspective. Water Resour. Res.
**2005**, 41. [Google Scholar] [CrossRef] - Santos, I.R.; Eyre, B.D.; Huettel, M. The driving forces of porewater and groundwater flow in permeable coastal sediments: A review. Estuar. Coast. Shelf Sci.
**2012**, 98, 1–15. [Google Scholar] [CrossRef] - Adolf, J.E.; Burns, J.; Walker, J.K.; Gamiao, S. Near shore distributions of phytoplankton and bacteria in relation to submarine groundwater discharge-fed fishponds, Kona coast, Hawai‘i, USA. Estuar. Coast. Shelf Sci.
**2019**, 219, 341–353. [Google Scholar] [CrossRef] - Lecher, A.; Mackey, K. Synthesizing the effects of submarine groundwater discharge on marine biota. Hydrology
**2018**, 5, 60. [Google Scholar] [CrossRef] - Kopprio, G.A.; Streitenberger, M.E.; Okuno, K.; Baldini, M.; Biancalana, F.; Fricke, A.; Martínez, A.; Neogi, S.B.; Koch, B.P.; Yamasaki, S.; et al. Biogeochemical and hydrological drivers of the dynamics of Vibrio species in two Patagonian estuaries. Sci. Total Environ.
**2017**, 579, 646–656. [Google Scholar] [CrossRef] - Cook, D.W. Effect of time and temperature on multiplication of Vibrio vulnificus in postharvest Gulf Coast shellstock oysters. Appl. Environ. Microb.
**1994**, 60, 3483–3484. [Google Scholar] - Blackwell, K.D.; Oliver, J.D. The ecology of Vibrio vulnificus, Vibrio cholerae, and Vibrio parahaemolyticus in North Carolina estuaries. J. Microb.
**2008**, 46, 146–153. [Google Scholar] [CrossRef] - Esteves, K.; Mosser, T.; Aujoulat, F.; Hervio-Heath, D.; Monfort, P.; Jumas-Bilak, E. Highly diverse recombining populations of Vibrio cholerae and Vibrio parahaemolyticus in French Mediterranean coastal lagoons. Front. Microb.
**2015**, 6, 708. [Google Scholar] [CrossRef] - Adyasari, D.; Hassenrück, C.; Oehler, T.; Sabdaningsih, A.; Moosdorf, N. Microbial community structure associated with submarine groundwater discharge in northern Java (Indonesia). Sci. Total Environ.
**2019**. under review. [Google Scholar] [CrossRef] - Morris, J.J. Non-O group 1 Vibrio cholerae: A look at the epidemiology of an occasional pathogen. Epidemiol. Rev.
**1990**, 12, 179–191. [Google Scholar] [CrossRef] [PubMed] - Johnston, M.D.; Brown, M.H. An investigation into the changed physiological state of Vibrio bacteria as a survival mechanism in response to cold temperatures and studies on their sensitivity to heating and freezing. J. Appl. Microbiol.
**2002**, 92, 1066–1077. [Google Scholar] [CrossRef] [PubMed] - Oliver, J.D. Wound infections caused by Vibrio vulnificus and other marine bacteria. Epidemiol. Infect.
**2005**, 133, 383–391. [Google Scholar] [CrossRef] [PubMed] - Howard, R.J.; Bennett, N.T. Infections caused by halophilic marine Vibrio bacteria. Ann. Surg.
**1993**, 217, 525. [Google Scholar] [CrossRef] [PubMed] - Fleming, L.E.; Broad, K.; Clement, A.; Dewailly, E.; Elmir, S.; Knap, A.; Pomponi, S.A.; Smith, S.; Solo Gabriele, H.; Walsh, P. Oceans and human health: Emerging public health risks in the marine environment. Mar. Pollut. Bull.
**2006**, 53, 545–560. [Google Scholar] [CrossRef] [PubMed] - Feglo, P.K.; Sewurah, M. Characterization of highly virulent multidrug resistant Vibrio cholerae isolated from a large cholera outbreak in Ghana. BMC Res. Notes
**2018**, 11, 45. [Google Scholar] [CrossRef] [PubMed] - Dupke, S.; Akinsinde, K.A.; Grunow, R.; Iwalokun, B.A.; Olukoya, D.K.; Oluwadun, A.; Thirumalaisamy, P.V.; Jacob, D. Characterization of Vibrio cholerae strains isolated from the Nigerian cholera outbreak in 2010. J. Clin. Microbiol.
**2016**, 54.10, 2618–2621. [Google Scholar] [CrossRef] [PubMed] - Chowdhury, G.; Bhadra, R.K.; Bag, S.; Pazhani, G.P.; Das, B.; Basu, P.; Nagamani, K.; Nandy, R.K.; Mukhopadhyay, A.K.; Ramamurthy, T. Rugose atypical Vibrio cholerae O1 El Tor responsible for 2009 cholera outbreak in India. J. Med.l Microbiol.
**2016**, 65, 1130–1136. [Google Scholar] [CrossRef] - Kohout, F.A. Ground-water flow and the geothermal regime of the floridian plateau (1). GCAGS Trans.
**1967**, 17, 339–354. [Google Scholar] - Bratton, J.F. The three scales of submarine groundwater flow and discharge across passive continental margins. J. Geol.
**2010**, 118, 565–575. [Google Scholar] [CrossRef] - Kim, G.; Swarzenski, P.W. Submarine groundwater discharge (SGD) and associated nutrient fluxes to the coastal ocean. In Carbon and Nutrient Fluxes in Continental Margins: A Global Synthesis, Part III. Arising Issues and New Approaches; Liu, K.-K., Atkinson, L., Quinones, R., Talaue-McManus, L., Eds.; Springer: New York, NY, USA, 2010; pp. 529–538. [Google Scholar]
- Sugimoto, R.; Kitagawa, K.; Nishi, S.; Honda, H.; Yamada, M.; Kobayashi, S.; Shoji, J.; Ohsawa, S.; Taniguchi, M.; Tominaga, O. Phytoplankton primary productivity around submarine groundwater discharge in nearshore coasts. Mar. Ecol. Prog. Ser.
**2017**, 563, 25–33. [Google Scholar] [CrossRef] - Schlüter, M.; Sauter, E.J.; Andersen, C.E.; Dahlgaard, H.; Dando, P.R. Spatial distribution and budget for submarine groundwater discharge in Eckernförde Bay (Western Baltic Sea). Limnol. Oceanogr.
**2004**, 49, 157–167. [Google Scholar] [CrossRef] - Oehler, T.; Mogollón, J.M.; Moosdorf, N.; Winkler, A.; Kopf, A.; Pichler, T. Submarine groundwater discharge within a landslide scar at the French Mediterranean coast. Estuar. Coast. Shelf Sci.
**2017**, 198, 128–137. [Google Scholar] [CrossRef] - Heiss, J.W.; Michael, H.A. Saltwater-freshwater mixing dynamics in a sandy beach aquifer over tidal, spring-neap, and seasonal cycles. Water Resour. Res.
**2014**, 50, 6747–6766. [Google Scholar] [CrossRef] - Park, C.H.; Aral, M.M. Saltwater intrusion hydrodynamics in a tidal aquifer. J. Hydrol. Eng.
**2008**, 13, 863–872. [Google Scholar] [CrossRef] - Righetti, C.; Gigliuto, A.; Chini, A.; Rossetto, R. Saltwater intrusion in a coastal contaminated aquifer density-dependent finite element model of flow and transport to assess remediation strategies and saltwater intrusion at a coastal gas plant site. In Proceedings of the 2nd International FEFLOW User Conference, Potsdam, Germany, 14–18 September 2009. [Google Scholar]
- Essink, G.H.O. Salt water intrusion in a three-dimensional groundwater system in the Netherlands: A numerical study. Transport Porous Med.
**2001**, 43.1, 137–158. [Google Scholar] [CrossRef] - Giambastiani, B.M.; Antonellini, M.; Essink, G.H.O.; Stuurman, R.J. Saltwater intrusion in the unconfined coastal aquifer of Ravenna (Italy): A numerical model. J. Hydrol.
**2007**, 340, 91–104. [Google Scholar] [CrossRef] - Bobba, A.G. Mathematical models for saltwater intrusion in coastal aquifers. Water Resour. Manag.
**1993**, 7, 3–37. [Google Scholar] [CrossRef] - Ghassemi, F.; Jakeman, A.J.; Jacobson, G.; Howard, K.W.F. Simulation of seawater intrusion with 2D and 3D models: Nauru Island case study. Hydrogeol. J.
**1996**, 4.3, 4–22. [Google Scholar] [CrossRef] - Diersch, H.J.G. FEFLOW-Finite Element Modeling of Flow, Mass and Heat Transport in Porous and Fractured Media; Springer: Berlin/Heidelberg, Germany, 2014. [Google Scholar]
- Smith, A.J. Mixed convection and density-dependent seawater circulation in coastal aquifers. Water Resour. Res.
**2004**, 40. [Google Scholar] [CrossRef] - Kolditz, O.; Ratke, R.; Diersch, H.J.G.; Zielke, W. Coupled groundwater flow and transport: 1. Verification of variable density flow and transport models. Adv. Water Resour.
**1998**, 21, 27–46. [Google Scholar] [CrossRef] - Diersch, H.J.G. Modeling variable-density problems in 2D horizontally schematized aquifers using projected gravity. White Pap.
**2004**, 3, 5–12. [Google Scholar] - Diersch, H.J.G. An efficient method for computing groundwater residence times. White Pap.
**2002**, 1, 141–150. [Google Scholar] - Diersch, H.J.G. Consistent velocity approximation in the finite-element simulation of density dependent mass and heat transport processes. White Pap.
**2002**, 1, 141–150. [Google Scholar] - Diersch, H.J.G. Nonlinear dispersion in density-dependent mass transport. White Pap.
**2002**, 1, 277–282. [Google Scholar] - Walther, M.; Delfs, J.O.; Grundmann, J.; Kolditz, O.; Liedl, R. Saltwater intrusion modeling: Verification and application to an agricultural coastal arid region in Oman. J. Comput. Appl. Math.
**2012**, 236, 4798–4809. [Google Scholar] [CrossRef] - Huo, Z.L.; Feng, S.Y.; Kang, S.Z.; Cen, S.J.; Ma, Y. Simulation of effects of agricultural activities on groundwater level by combining FEFLOW and GIS. New Zeal. J. Agr. Res.
**2007**, 50, 839–846. [Google Scholar] [CrossRef] - Lu, J. Identification of forensic information from existing conventional site-investigation data. Introduction to Environ. Forensics
**2015**, 3, 149–164. [Google Scholar] - Grant, S.A. Hydraulic properties, temperature effects. In Encyclopedia of Soils in the Environment; Hillel, D., Ed.; Elesevier: Amsterdam, The Netherlands, 2005; Volume 2, pp. 207–211. [Google Scholar]
- Kaleris, V.; Lagas, G.; Marczinek, S.; Piotrowski, J.A. Modelling submarine groundwater discharge: An example from the western Baltic Sea. J. Hydrol.
**2002**, 265, 76–99. [Google Scholar] [CrossRef] - Bear, J.; Verruijt, A. Modeling Groundwater Flow and Pollution, 2nd ed.; Reidel, D., Ed.; Springer: Dordrecht, the Netherlands, 1987. [Google Scholar]
- Datta, B.; Vennalakanti, H.; Dhar, A. Modeling and control of saltwater intrusion in a coastal aquifer of Andhra Pradesh, India. J. Hydro-Environ. Res.
**2009**, 3, 148–159. [Google Scholar] [CrossRef] - Robinson, C.; Gibbes, B.; Li, L. Driving mechanisms for groundwater flow and salt transport in a subterranean estuary. Geophys. Res. Lett.
**2006**, 33. [Google Scholar] [CrossRef] - Narayan, K.A.; Schleeberger, C.; Bristow, K.L. Modelling seawater intrusion in the Burdekin Delta irrigation area, North Queensland, Australia. Agr. Water Manag.
**2007**, 89, 217–228. [Google Scholar] [CrossRef] - Abarca, E.; Carrera, J.; Sanchez-Vila, X.; Dentz, M. Anisotropic dispersive Henry problem. Adv. Water Resour.
**2007**, 30, 913–926. [Google Scholar] [CrossRef] - Doran, K.S.; Long, J.W.; Overbeck, J.R. A method for determining average beach slope and beach slope variability for US sandy coastlines. USGS
**2015**, 2015-1053, 5. [Google Scholar] [CrossRef] - Boufadel, M.C. A mechanistic study of nonlinear solute transport in a groundwater-surface water system under steady state and transient hydraulic conditions. Water Resour. Res.
**2000**, 36, 2549–2565. [Google Scholar] [CrossRef] - Robinson, C.; Li, L.; Prommer, H. Tide-induced recirculation across the aquifer-ocean interface. Water Resour. Res.
**2007**, 43. [Google Scholar] [CrossRef] - Ghabayen, S.M.; McKee, M.; Kemblowski, M. Ionic and isotopic ratios for identification of salinity sources and missing data in the Gaza aquifer. J. Hydrol.
**2006**, 318, 360–373. [Google Scholar] [CrossRef] - Davis, R.A. The Evolving Coast; Scientific American Library: New York, NY, USA, 1997. [Google Scholar]
- Houben, G.J.; Stoeckl, L.; Mariner, K.E.; Choudhury, A.S. The influence of heterogeneity on coastal groundwater flow-physical and numerical modeling of fringing reefs, dykes and structured conductivity fields. Adv. Water Resour.
**2018**, 113, 155–166. [Google Scholar] [CrossRef] - Weinstein, Y.; Burnett, W.C.; Swarzenski, P.W.; Shalem, Y.; Yechieli, Y.; Herut, B. Role of aquifer heterogeneity in fresh groundwater discharge and seawater recycling: An example from the Carmel coast, Israel. J. Geophys. Res.
**2007**, 112. [Google Scholar] [CrossRef]

**Figure 1.**Sketch (not to scale) of the conceptual model build regarding geometrical and parametrical properties along the boundaries, where q

_{X}describes the horizontal and q

_{Y}the vertical groundwater inflow, C the solute concentration of the fluids and h corresponds to the static hydraulic potential of the sea. The depth of the aquifer is z and β shows the coastal slope angle.

**Figure 2.**(

**a**) Typical flow pattern, solute distribution and Darcy velocities within homogeneous aquifer models. The submarine groundwater discharge (SGD) zone length extends across the area of seaward directed flow arrows along the seaside boundary. (

**b**) Salinity distribution in the aquifer model and marine sediments (seaside BC), isolines indicate concentration limits such as optimized areas for V. cholerae growth (C

_{S}≤ 1000 mg L

^{−1}).

**Figure 3.**(

**a**) Length of SGD zones and (

**b**) length of V. cholerae zones plotted against the groundwater inflow q

_{X}. Each differently colored data series reflects a hydraulic conductivity value K [m d

^{−1}].

**Figure 4.**(

**a**) Specific SGD flux and (

**b**) hydraulic gradient plotted against the groundwater inflow q

_{X}. Each differently colored data series reflects a hydraulic conductivity value K [m d

^{−1}] as seen in Figure 3.

**Figure 5.**(

**a**) Length of SGD zones and (

**b**) length of V. cholerae zones plotted against the hydraulic conductivity K. Each differently colored data series reflects an inflow value q

_{X}[m d

^{−1}].

**Figure 6.**(

**a**) Specific SGD flux and (

**b**) hydraulic gradient plotted against the hydraulic conductivity K. Each differently colored data series reflects an inflow value q

_{X}[m d

^{−1}] as seen in Figure 5.

**Figure 7.**(

**a**) Length of SGD zones and (

**b**) V. cholerae zones plotted against the longitudinal dispersivity α

_{L}. Each differently colored data series reflects a hydraulic conductivity value K [m d

^{−1}].

**Figure 8.**(

**a**) Length of SGD zones and (

**b**) V. cholerae zones plotted against the coastal slope angle tan(β). Each differently colored data series reflects a hydraulic conductivity value K [m d

^{−1}].

**Table 1.**Parameters and related values that varied or remained constant throughout the simulations. The density ratio corresponds to assumptions made in [50].

Varying Parameter | Symbol | Unit | Value |

Groundwater inflow | q_{X} | m d^{−1} | 0.07; 0.17; 0.4; 0.8; 1.3 [12,51] |

Hydr. conductivity | K | m d^{−1} | 8; 17; 34.4; 43; 85 [36,38,52,53,54] |

Long. dispersivity | α_{L} | m | 2.5; 5; 10; 15; 25; 35; 50; 75 [12,55] |

Trans. dispersivity | α_{T} | m | α_{L} × 0.1 [12,55] |

Coastal slope angle | β | ° | 0; 11.3; 28.1; 53.8; 69.7; 76.1 |

Constant Parameter | Symbol | Unit | Value |

Porosity aquifer | ϕ_{S} | – | 0.3 [56,57] |

Salinity groundwater | C_{F} | mg L^{−1} | 100 [44] |

Salinity seawater | C_{S} | mg L^{−1} | 35000 [44] |

Density groundwater | ρ_{F} | kg m^{−}^{3} | 1000 [58] |

Density seawater | ρ_{S} | kg m^{−}^{3} | 1026 [58] |

Density ratio | d | – | 0.026 |

Molecular diffusion coefficient | D_{M} | m^{2} s^{−1} | 1 × 10^{−9} [58] |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vollberg, F.; Walther, M.; Gärdes, A.; Moosdorf, N.
Modeling the Potential of Submarine Groundwater Discharge to Facilitate Growth of *Vibrio cholerae* Bacteria. *Hydrology* **2019**, *6*, 39.
https://doi.org/10.3390/hydrology6020039

**AMA Style**

Vollberg F, Walther M, Gärdes A, Moosdorf N.
Modeling the Potential of Submarine Groundwater Discharge to Facilitate Growth of *Vibrio cholerae* Bacteria. *Hydrology*. 2019; 6(2):39.
https://doi.org/10.3390/hydrology6020039

**Chicago/Turabian Style**

Vollberg, Felix, Marc Walther, Astrid Gärdes, and Nils Moosdorf.
2019. "Modeling the Potential of Submarine Groundwater Discharge to Facilitate Growth of *Vibrio cholerae* Bacteria" *Hydrology* 6, no. 2: 39.
https://doi.org/10.3390/hydrology6020039