# Salinity and Temperature Variations near the Freshwater-Saltwater Interface in Coastal Aquifers Induced by Ocean Tides and Changes in Recharge

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Hydrogeological Setting

^{2}, and its thickness varies from 30 to 50 m in the northernmost sector to more than 250 m in the southern sector [42]. The aquifer is composed of Quaternary detrital sediments with highly variable grain sizes (gravels, sands, and silts), which lie over an impermeable basement of metapelitic materials (schists and phyllites). The hydraulic conductivity of the materials is highly variable, ranging from 1 to 300 m/d [43,44], due to their fluvio-deltaic depositional environment.

^{−3}and 7 × 10

^{−3}[45,46].

**Figure 2.**Location of the Motril-Salobreña aquifer, research boreholes, and the measurement point of the river flow (RF). Cross section of the depositional environments at the study area (modified from Olsen [48]).

^{2}and drains the southern slopes of the Sierra Nevada. The highest mountain peak reaches an elevation of 3482 m, and the average annual precipitation is more than 1000 mm in that area. The hydrologic regime of the Guadalfeo River is pluvio-nival with maximum flows reached from April to June. Upstream from the Motril-Salobreña aquifer (10 km), the Rules Dam interrupts the Guadalfeo River flow. The Motril-Salobreña aquifer has not shown any signs of marine intrusion yet, and the saline wedge does not penetrate more than 500 m [42,43]

^{3}/s at the time of its opening, providing evidence of upward vertical flow in this area of the aquifer [50]. The well intersects the FSI and the three temperature zones described above. Previous studies showed fluctuations in groundwater head attributed to tidal forces [7,51].

## 3. Methodology

#### 3.1. Field Monitoring

#### 3.2. Time Series Analysis

#### 3.3. Numerical Modeling

#### 3.3.1. Models

- -
- Model A (Homogeneous model): the hydraulic conductivity was homogeneous (100 m/d).
- -
- Model B (Heterogeneous layered model): nine layers with different hydraulic conductivity (50 and 400 m/d) were included to modify model A. The thickness of the layers was 15 m for the layers with lower hydraulic conductivity (L1, L2, L3 and L4) and 20–45 m for the layers with higher hydraulic conductivity (H1, H2, H3 and H4) (Figure 4). The alternation of layers with the two values of hydraulic conductivity represented the vertical heterogeneity often found in alluvial coastal aquifers.
- -
- Model C (Changes in recharge conditions): the model parameters were the same as those of model B, but the recharge effect was simulated, modifying the boundary conditions to reproduce a gradually increasing hydraulic gradient, justified by fluctuations of the water table in the upper sector of the aquifer (up to 5 m from summer to winter), and by the lack of recharge of the river near the coastline [45].

#### 3.3.2. Boundary Conditions

**Table 1.**Values of hydraulic head (H), salinity (S) and temperature (T) given to each boundary of the models A, B and C.

Model | Parameter | Freshwater | Sea Bed | Saltwater | Top | Bottom |
---|---|---|---|---|---|---|

Model A | H | Dirichlet 8 m | Dirichlet $H=A\mathrm{sin}\left(\frac{2\pi}{P}t-\phi \right)$ | Neumann No flow | Neumann No flow | Neumann No flow |

S | Dirichlet 350 mg/L | Dirichlet 35,000 mg/L | Neumann No flow | Neumann No flow | Neuman No flow | |

T | Dirichlet 17 °C | Dirichlet 13 °C | Neumann No flow | Neumann No flow | Dirichlet 24 °C | |

Model B | H | Dirichlet 8 m | Dirichlet $H=A\mathrm{sin}\left(\frac{2\pi}{P}t-\phi \right)$ | Neumann No flow | Neumann No flow | Neumann No flow |

S | Dirichlet 350 mg/L | Dirichlet 35,000 mg/L | Neumann No flow | Neumann No flow | Neuman No flow | |

T | Dirichlet 17 °C | Dirichlet 13 °C | Neumann No flow | Neumann No flow | Dirichlet 24 °C | |

Model C | H | Dirichlet 8 to 13 m | Dirichlet $H=A\mathrm{sin}\left(\frac{2\pi}{P}t-\phi \right)$ | Neumann No flow | Neumann No flow | Neumann No flow |

S | Dirichlet 350 mg/L | Dirichlet 35,000 mg/L | Neumann No flow | Neumann No flow | Neuman No flow | |

T | Dirichlet 17 °C | Dirichlet 13 °C | Neumann No flow | Neumann No flow | Dirichlet 24 °C |

#### 3.3.3. Parameters and Time Discretization

## 4. Results

#### 4.1. Vertical Flow in the Borehole

#### 4.2. Water Table Variation Effect on Temperature Oscillation in the FSI

^{3}/s. The lack of surface water prevented the recharge of the aquifer, and thus heads remained low in the aquifer. In March 2018, a period of continuous precipitation started. However, the peak river flow was not reached until May 2018 (7.5 m

^{3}/s) due to the snowmelt in the nearby mountains and the management of river flow by a dam. Since May, the hydraulic heads increased due to the river flow recharge. In July 2018, with the beginning of the summer, a new dry period without precipitation started, and ended in October–November 2018.

#### 4.3. Sea Tides Effect on Temperature and EC Oscillations in the FSI

#### 4.3.1. Model Setup

#### 4.3.2. Continuous Temperature Data

#### 4.4. Numerical Model Results

#### 4.4.1. Model A

^{−3}°C. Still, these small temperature variations must have been generated by the tidal oscillation since, in the case of the mesotidal conditions, the minimum values of temperature and salinity occurred simultaneously, as shown in Figure 9.

#### 4.4.2. Model B

#### 4.4.3. Model C

## 5. Discussion

## 6. Conclusions

- Seasonal variations of aquifer recharge and sea tides produced a displacement of the fresh groundwater and the FSI and, consequently, changes in EC and temperature distribution. EC fluctuations depended on the horizontal gradient of salinity in the proximity of the FSI. However, the oscillations of temperature depended on the presence of the thermal plume generated by the upwelling flow along the FSI, which was also displaced together with the FSI.
- The amplitude of EC and temperature oscillations associated with sea tides decreased with depth and increased in the areas where hydraulic conductivity changed. The convective heat transport was refracted at the interface between layers with different hydraulic conductivity, inducing a bending with different degrees of inclination (verticality) of the thermal contours. The desynchronization of the oscillations registered at the bottom and at the top of the same layer was produced by the variations in verticality of the thermal plume and the FSI.
- EC and temperature fluctuations were related to hydraulic gradient variations and, hence, to groundwater recharge. The presence of the thermal plume induced a different evolution of salinity and temperature. Salinity progressively decreased as the hydraulic gradient increased. However, the evolution of temperature depended on the position of the observation point with respect to the thermal plume.
- The temperature distribution in coastal aquifers is highly sensitive to natural changes or those induced by humans. The position of the FSI and the thermal plume are dependent on groundwater recharge, which, in turn, depends on climate variability and/or water management. Groundwater recharge plays an important role in the amplitudes of temperature oscillations induced by the tides.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Simulation results of model B at different depths of the well W for a mesotidal condition (semi-amplitude of 1.5 m).

## Appendix B

**Figure A2.**Simulation results of model C at different depths of the well W for a mesotidal condition (semi-amplitude of 1.5 m).

## References

- Nielsen, P. Tidal dynamics of the water table in beaches. Water Resour. Res.
**1990**, 26, 2127–2134. [Google Scholar] [CrossRef] - Li, L.; Barry, D.A.; Stagnitti, F.; Parlange, J.Y.; Jeng, D.S. Beach water table fluctuations due to spring-neap tides: Moving boundary effects. Adv. Water Res.
**2000**, 23, 817–824. [Google Scholar] [CrossRef] - Rotzoll, K.; Gingerich, S.B.; Jenson, J.W.; El-Kadi, A.I. Estimating hydraulic properties from tidal attenuation in the Northern Guam Lens Aquifer, territory of Guam, USA. Hydrogeol. J.
**2013**, 21, 643–654. [Google Scholar] [CrossRef] - Xun, Z.; Chao, S.; Ting, L.; Ruige, C.; Huan, Z.; Jingbo, Z.; Qin, C. Estimation of aquifer parameters using tide-induced groundwater level measurements in a coastal confined aquifer. Environ. Earth Sci.
**2015**, 73, 2197–2204. [Google Scholar] [CrossRef] - Pawlowicz, R.; Beardsley, B.; Lentz, S. Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Comput. Geoscien.
**2002**, 28, 929–937. [Google Scholar] [CrossRef] - Levanon, E.; Yechieli, Y.; Shalev, E.; Friedman, V.; Gvirtzman, H. Reliable monitoring of the transition zone between fresh and saline waters in coastal aquifers. Groundw. Monitor. Remed.
**2013**, 33, 101–110. [Google Scholar] [CrossRef] - Sánchez-Úbeda, J.P.; Calvache, M.L.; López-Chicano, M.; Duque, C. The Effects of Non-TIDAL Components, Depth of Measurement and the Use of Peak Delays in the Application of Tidal Response Methods. Water Res. Manag.
**2018**, 32, 481–495. [Google Scholar] [CrossRef] - Carr, P.A.; Van der Kamp, G. Determining aquifer characteristics by the tidal methods. Water Resour. Res.
**1969**, 5, 1023–1031. [Google Scholar] [CrossRef] - Erskine, A.D. The Effect of Tidal Fluctuation on a Coastal Aquifer in the UK. Groundwater
**1991**, 29, 556–562. [Google Scholar] [CrossRef] - Raubenheimer, B.; Guza, R.T.; Elgar, S. Tidal Water Table Fluctuations in a Sandy Ocean Beach. Water Resour. Res.
**1999**, 35, 2313–2320. [Google Scholar] [CrossRef] - Robinson, M.A.; Gallagher, D.; Reay, W. Field observations of tidal and seasonal variations in groundwater discharge to tidal estuarine surface water. Groundw. Monitor Remed.
**1998**, 18, 83–92. [Google Scholar] [CrossRef] - Urish, D.W.; McKenna, T.E. Tidal Effects on Ground Water Discharge through a Sandy Marine Beach. Groundwater
**2004**, 42, 971–982. [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] - Ataie-Ashtiani, B.; Volker, R.E.; Lockington, D.A. Tidal Effects on Sea Water Intrusion in Unconfined Aquifers. J. Hydrol.
**1999**, 216, 17–31. [Google Scholar] [CrossRef] - La Licata, I.; Langevin, C.D.; Dausman, A.M.; Alberti, L. Effect of tidal fluctuations on transient dispersion of simulated contaminant concentrations in coastal aquifers. Hydrogeol. J.
**2011**, 19, 1313–1322. [Google Scholar] [CrossRef] - Robinson, C.; Li, L.; Barry, D.A. Effect of Tidal Forcing on a Subterranean Estuary. Adv. Water Resour.
**2007**, 30, 851–865. [Google Scholar] [CrossRef] - Pool, M.; Post, V.E.A.; Simmons, C.T. Effects of Tidal Fluctuations on Mixing and Spreading in Coastal Aquifers: Homogeneous Case. Water Resour. Res.
**2014**, 50, 6910–6926. [Google Scholar] [CrossRef] - Levanon, E.; Yechieli, Y.; Gvirtzman, H.; Shalev, E. Tide-Induced Fluctuations of Salinity and Groundwater Level in Unconfined Aquifers—Field Measurements and Numerical Model. J. Hydrol.
**2017**, 551, 665–675. [Google Scholar] [CrossRef] - Yu, X.; Xin, P.; Wang, S.S.J.; Shen, C.; Li, L. Effects of Multi-Constituent Tides on a Subterranean Estuary. Adv. Water Resour.
**2019**, 124, 53–67. [Google Scholar] [CrossRef] - Pollock, L.W.; Hummon, W.D. Cyclic Changes in Interstitial Water Content, Atmospheric Exposure, and Temperature in a Marine Beach. Limnol. Oceanogr.
**1971**, 16, 522–535. [Google Scholar] [CrossRef] - Li, L.; Horn, D.P.; Baird, A.J. Tide-induced variations in surface temperature and water-table depth in the intertidal zone of a sandy beach. J. Coast. Res.
**2006**, 22, 1370–1381. [Google Scholar] [CrossRef] - Vandenbohede, A.; Lebbe, L. Heat transport in a coastal groundwater flow system near De Panne, Belgium. Hydrogeol. J.
**2011**, 19, 1225–1238. [Google Scholar] [CrossRef] - Geng, X.; Boufadel, M. Spectral responses of gravel beaches to tidal signals. Sci. Rep.
**2017**, 7, 40770. [Google Scholar] [CrossRef] [PubMed] - Nguyen, T.T.M.; Yu, X.; Pu, L.; Xin, P.; Zhang, C.; Barry, D.A.; Li, L. 2020. Effects of temperature on tidally influenced coastal unconfined aquifers. Water Resour. Res.
**2020**, 56, e2019WR026660. [Google Scholar] [CrossRef] - Kim, K.Y.; Chon, C.M.; Park, K.H.; Park, Y.S.; Woo, N.C. Multi-Depth Monitoring of Electrical Conductivity and Temperature of Groundwater at a Multilayered Coastal Aquifer: Jeju Island, Korea. Hydrol. Process.
**2008**, 22, 3724–3733. [Google Scholar] [CrossRef] - Kim, K.Y.; Park, Y.S.; Kim, G.P.; Park, K.H. Dynamic Freshwater-Saline Water Interaction in the Coastal Zone of Jeju Island, South Korea. Hydrogeol. J.
**2009**, 17, 617–629. [Google Scholar] [CrossRef] - Vallejos, A.; Sola, F.; Pulido-Bosch, A. Processes Influencing Groundwater Level and the Freshwater-Saltwater Interface in a Coastal Aquifer. Water Res. Manag.
**2015**, 29, 679–697. [Google Scholar] [CrossRef] - Blanco-Coronas, A.M.; Duque, C.; Calvache, M.L.; López-Chicano, M. Temperature Distribution in Coastal Aquifers: Insights from Groundwater Modeling and Field Data. J. Hydrol.
**2021**, 603, 126912. [Google Scholar] [CrossRef] - Anderson, M.P. Heat as a ground water tracer. Groundwater
**2005**, 43, 951–968. [Google Scholar] [CrossRef] - Del Val, L. Advancing in the Characterization of Coastal Aquifers: A Multimethodological Approach Based on Fiber Optics Distributed Temperature Sensing. Ph.D. Thesis, Polytechnic University of Catalonia, Barcelona, Spain, 2020. [Google Scholar]
- Taniguchi, M. Evaluations of the saltwater-groundwater interface from borehole temperature in a coastal region. Geophys. Res. Lett.
**2000**, 27, 713–716. [Google Scholar] [CrossRef] - Fidelibus, M.D.; Pulido-Bosch, A. Groundwater temperature as an indicator of the vulnerability of Karst coastal aquifers. Geosciences
**2019**, 9, 23. [Google Scholar] [CrossRef] - LeRoux, N.K.; Kurylyk, B.L.; Briggs, M.A.; Irvine, D.J.; Tamborski, J.J.; Bense, V.F. Using Heat to Trace Vertical Water Fluxes in Sediment Experiencing Concurrent Tidal Pumping and Groundwater Discharge. Water Resour. Res.
**2021**, 57, e2020WR027904. [Google Scholar] [CrossRef] - Parsons, M.L. Groundwater thermal regime in a glacial complex. Water Resour. Res.
**1970**, 6, 1701–2172. [Google Scholar] [CrossRef] - Kurylyk, B.L.; Irvine, D.J.; Bense, V.F. Theory, tools, and multidisciplinary applications for tracing groundwater fluxes from temperature profiles. Wires Water
**2019**, 6, e1329. [Google Scholar] [CrossRef] - Tóth, J. A theory of groundwater motion in small basins in central Alberta. Canada. J. Geophys. Res.
**1962**, 67, 4375–43787. [Google Scholar] [CrossRef] - Domenico, P.A.; Palciauskas, V.V. Theoretical analysis of forced convective heat transfer in regional groundwater flow. GSA Bull.
**1973**, 84, 3803–3814. [Google Scholar] [CrossRef] - An, R.; Jiang, X.W.; Wang, J.Z.; Wan, L.; Wang, X.S.; Li, H. A theoretical analysis of basin-scale groundwater temperature distribution. Hydrogeol. J.
**2015**, 23, 397–404. [Google Scholar] [CrossRef] - Szijártó, M.; Galsa, A.; Tóth, Á.; Mádl-Szőnyi, J. Numerical investigation of the combined effect of forced and free thermal convection in synthetic groundwater basins. J. Hydrol.
**2019**, 572, 364–379. [Google Scholar] [CrossRef] - Befus, K.M.; Cardenas, M.B.; Erler, D.V.; Santos, I.R.; Eyre, B.D. Heat transport dynamics at a sandy intertidal zone. Water Resour. Res.
**2013**, 49, 3770–3786. [Google Scholar] [CrossRef] - Tirado-Conde, J.; Engesgaard, P.; Karan, S.; Müller, S.; Duque, C. Evaluation of temperature profiling and seepage meter methods for quantifying submarine groundwater discharge to coastal lagoons: Impacts of saltwater intrusion and the associated thermal regime. Water
**2019**, 11, 1648. [Google Scholar] [CrossRef] [Green Version] - Duque, C.; Calvache, M.L.; Pedrera, A.; Martín-Rosales, W.; López-Chicano, M. Combined time domain electromagnetic soundings and gravimetry to determine marine intrusion in a detrital coastal aquifer (Southern Spain). J. Hydrol.
**2008**, 349, 536–547. [Google Scholar] [CrossRef] - Calvache, M.L.; Ibáñez, S.; Duque, C.; Martín-Rosales, W.; López-Chicano, M.; Rubio, J.C.; González, A.; Viseras, C. Numerical modelling of the potential effects of a dam on a coastal aquifer in S. Spain. Hydrol. Process.
**2009**, 23, 1268–1281. [Google Scholar] [CrossRef] - Duque, C. Influencia Antrópica Sobre la Hidrogeología del Acuífero Motril-Salobreña. Ph.D. Thesis, University of Granada, Granada, Spain, 2009. [Google Scholar]
- Duque, C.; Calvache, M.L.; Engesgaard, P. Investigating river-aquifer relations using water temperature in an anthropized environment (Motril-Salobreña aquifer). J. Hydrol.
**2010**, 381, 121–133. [Google Scholar] [CrossRef] - Blanco-Coronas, A.M.; López-Chicano, M.; Acosta-Rodriguez, R.; Calvache, M.L. Groundwater recharge-discharge estimation with differential flow gaugings in the final stretch of the Guadalfeo river (Granada). Geogaceta
**2021**, 69, 91–94. [Google Scholar] - Duque, C.; López-Chicano, M.; Calvache, M.L.; Martín-Rosales, W.; Gómez-Fontalva, J.M.; Crespo, F. Recharge sources and hydrogeological effects of irrigation and an influent river identified by stable isotopes in the Motril-Salobreña aquifer (Southern Spain). Hydrol. Process.
**2011**, 25, 2261–2274. [Google Scholar] [CrossRef] - Olsen, J.T. Modeling the Evolution of Salinity in the Motril-Salobreña Aquifer Using a Paleo-Hydrogeological Model. Master’s Thesis, University of Oslo, Oslo, Norway, 2016. [Google Scholar]
- Calvache, M.L.; Duque, C.; Gómez-Fontalva, J.M.; Crespo, F. Processes affecting groundwater temperature patterns in a coastal aquifer. Int. J. Environ. Sci. Technol.
**2011**, 8, 223–236. [Google Scholar] [CrossRef] - Calvache, M.L.; Sánchez-Úbeda, J.P.; Duque, C.; López-Chicano, M.; De La Torre, B. Evaluation of analytical methods to study aquifer properties with pumping tests in coastal aquifers with numerical modelling (Motril-Salobreña aquifer). Water Resour. Manag.
**2015**, 30, 559–575. [Google Scholar] [CrossRef] - Sánchez-Úbeda, J.P.; Calvache, M.L.; Duque, C.; López-Chicano, M. Filtering methods in tidal-affected groundwater head measurements: Application of harmonic analysis and continuous wavelet transform. Adv. Water Res.
**2016**, 97, 52–72. [Google Scholar] [CrossRef] - Pan, H.; Lv, X.; Wang, Y.; Matte, P.; Chen, H.; Jin, G. Exploration of Tidal-Fluvial Interaction in the Columbia River Estuary Using S_TIDE. J. Geophys. Res. Ocean.
**2018**, 123, 6598–6619. [Google Scholar] [CrossRef] - Shumway, H.S.; Stoffer, D.S. Time Series Analysis and its Applications: With R Examples, 2nd ed.; Springer Science + Business Media, LLC.: New York, NY, USA, 2006; 575p. [Google Scholar]
- Larocque, M.; Mangin, A.; Razack, M.; Banton, O. Contribution of correlation and spectral analyses to the regional study of a large karst aquifer (Charente, France). J. Hydrol.
**1998**, 205, 217–231. [Google Scholar] [CrossRef] - Padilla, A.; Pulido-Bosch, A. Study of hydrographs of karstic aquifers by means of correlation and cross-spectral analysis. J. Hydrol.
**1995**, 168, 73–89. [Google Scholar] [CrossRef] - Langevin, C.D.; Thorne, D.T.; Dausman, A.M.; Sukop, M.C.; Guo, W. SEAWAT Version 4: A Computer Program for Simulation of Multi-Species Solute and Heat Transport; U.S. Geological Survey Techniques and Methods; Geological Survey (U.S.): Reston, VA, USA, 2008; Chapter A22.
- Harbaugh, A.W.; Banta, E.R.; Hill, M.C.; Mcdonald, M.G. MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model User Guide to Modularization Concepts and the Ground-Water Flow Process, Geological Survey; CO McDonald Morrissey Associates: Concord, NH, USA, 2000. [Google Scholar]
- Zheng, C.; Wang, P.P. MT3DMS—A Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion and Chemical Reactions of Contaminants in Groundwater Systems: Documentation and User’s Guide; U.S. Army Corps of Engineers: Washington, DC, USA, 1999.
- Yang, X.; Shaoa, Q.; Hoteit, H.; Carrera, J.; Younes, A.; Fahs, M. Three-dimensional natural convection, entropy generation and mixing in heterogeneous porous medium. Adv. Water Resour.
**2021**, 115, 103992. [Google Scholar] [CrossRef] - Tabrizinejadas, S.; Fahs, M.; Ataie-Ashtiani, B.; Simmons, C.T.; di Chiara Roupert, R.; Younes, A. A Fourier series solution for transient three-dimensional thermohaline convection in porous enclosures. Water Resour. Res.
**2020**, 56, e2020WR028111. [Google Scholar] [CrossRef] - Stauffer, F.; Bayer, P.; Blum, P.; Giraldo, N.; Kinzelbach, W. Thermal Use of Shallow Groundwater; CRC Press: Boca Raton, FL, USA, 2014. [Google Scholar] [CrossRef]
- Xiaoqing, S.; Ming, J.; Peiwen, X. Analysis Of The Thermophysical Properties And Influencing Factors Of Various Rock Types From The Guizhou Province. EDP Sciences. E3S Web Conf.
**2018**, 53, 03059. [Google Scholar] [CrossRef] - Pugh, D.T. Tides, Purges and Mean Sea Level; John Wiley & Sons Ltd.: Chichester, UK, 1996. [Google Scholar]
- Saar, M.O. Review: Geothermal heat as a tracer of large-scale groundwater flow and as a means to determine permeability fields. Hydrogeol. J.
**2011**, 19, 31–52. [Google Scholar] [CrossRef] - Wang, Z.; Gao, P.; Jiang, G.; Wang, Y.; Hu, S. Heat Flow Correction for the High-Permeability Formation: A Case Study for Xiong’an New Area. Lithosphere
**2021**, 5, 9171191. [Google Scholar] [CrossRef] - Ma, J.; Zhou, Z. Origin of the low-medium temperature hot springs around Nanjing, China. Open Geosci.
**2021**, 13, 820–834. [Google Scholar] [CrossRef] - Levanon, E.; Shalev, E.; Yechieli, Y.; Gvirtzman, H. Advances in Water Resources Fluctuations of fresh-saline water interface and of water table induced by sea tides in unconfined aquifers. Adv. Water Resour.
**2016**, 96, 34–42. [Google Scholar] [CrossRef] - Mao, X.; Enot, P.; Barry, D.A.; Li, L.; Binley, A.; Jeng, D.S. Tidal influence on behaviour of a coastal aquifer adjacent to a low-relief estuary. J. Hydrol.
**2006**, 327, 110–127. [Google Scholar] [CrossRef] - Costall, A.R.; Harris, B.D.; Teo, B.; Schaa, R.; Wagner, F.M.; Pigois, J.P. Groundwater Throughflow and Seawater Intrusion in High Quality Coastal Aquifers. Sci. Rep.
**2020**, 10, 9866. [Google Scholar] [CrossRef]

**Figure 1.**Simplified schematic diagram of temperature distribution of a coastal aquifer affected by the geothermal gradient.

**Figure 3.**Vertical temperature profiles measured in the Motril-Salobreña aquifer, obtained from the observation well W180 located in Figure 2.

**Figure 4.**Boundary conditions of the numerical model. The specified hydraulic conductivity values were considered for models B and C; however, in model A, the unique value considered was 100 m/d. H: hydraulic head, S: salinity, T: temperature.

**Figure 6.**Data during 2018: Monthly measurements of river water flow (red line) and moving average (MA) of hourly measurements of H obtained from S-4 and S-5 in purple (same values for both sensors), and EC and T obtained from S-4 (green lines) and S-5 (yellow lines). Wet periods are delimited by the grey areas coinciding with the increment of river flow.

**Figure 7.**Vertical logs of EC and T in well W250 during a tidal cycle and the position of the FSI (grey area) and location of the screens (grey bars) where the measurements were obtained (30 September 2019). Log 1 (pink line) during low tide, Log 2 (green line) during tidal rise, Log 3 (brown line) during high tide and Log 4 (blue line) during tidal fall.

**Figure 8.**(

**a**): Continuous measurements of sea level and temperature were obtained from S-3, S-4, and S-5 during February 2018. (

**b**): Density spectra (energy versus frequency) of the temperature data obtained during February 2018. (

**c**): Cross-correlation functions of sea level as input and temperature measured in S-3, S-4 and S-5 as output for February 2018.

**Figure 9.**Simulation results of the homogeneous model (Model A) for microtidal, mesotidal, and macrotidal conditions (semi-amplitudes of 0.75 m, 1.5 m, and 2.5 m, respectively) measured at the observation point L4-T.

**Figure 11.**Simulation results of model B for microtidal, mesotidal, and macrotidal conditions measured at the top of layer L3. (

**a**): Temperature (T) amplitude measured at different distances from the shoreline. (

**b**): T amplitude vs. local horizontal thermal gradient at each observation point ΔT/d.

**Figure 12.**Simulation results of model B at four depths of the well W for a mesotidal condition (semi-amplitude of 1.5 m). (

**a**): At the observation point H3-B (−122 m) (

**b**): At the observation point L3-T (−123 m) (

**c**): At the observation point L3-B (−138 m) (

**d**)

**:**At the observation point H4-T (−140 m).

**Figure 13.**Comparison of the simulation results depending of the location of the observation points (top and bottom of high and low hydraulic conductivity layers).

**Figure 14.**Simulation results of model C at four depths of the well W for a mesotidal condition (semi-amplitude of 1.5 m). (

**a**): At the observation point H3-B (−122 m) (

**b**): At the observation point L3-T (−123 m) (

**c**): At the observation point L3-B (−138 m) (

**d**)

**:**At the observation point H4-T (−140 m).

**Figure 15.**Representation of the effect of sea tides (

**A**,

**B**) and the increase of recharge (

**C**) on the FSI and groundwater temperature distribution obtained from models B and C. The movement and verticality of the thermal contours and the FSI were exaggerated to improve the visualization.

Input Parameters | Value | Source |
---|---|---|

Specific storage | 1 × 10^{−5} m^{−1} | Calvache et al. [50] |

Specific yield | 0.25 | Similar value to Calvache et al. [50] |

$\mathrm{Porosity}\theta $ | 0.3 | Duque et al. [42] |

Longitudinal dispersivity | 20 m | Stauffer et al. [61] |

Vertical transverse dispersivity | 10 m | Stauffer et al. [61] |

$\mathrm{Molecular}\mathrm{diffusion}\mathrm{coefficient}{D}_{m}^{s}$ | 1 × 10^{−10} m^{2}/d | Langevin et al. [56] |

$\mathrm{Thermal}\mathrm{conductivity}\mathrm{of}\mathrm{water}{k}_{Tfluid}$ | 0.58 W/m °C | Langevin et al. [56] |

$\mathrm{Thermal}\mathrm{conductivity}\mathrm{of}\mathrm{sediments}{k}_{Tsolid}$ | 2.9 W/m °C | Approximate value for gravel [62] |

$\mathrm{Specific}\mathrm{heat}\mathrm{of}\mathrm{water}{C}_{Pfluid}$ | 4186 J/kg °C | Langevin et al. [56] |

$\mathrm{Specific}\mathrm{heat}\mathrm{of}\mathrm{sediments}{C}_{Psolid}$ | 830 J/kg °C | Approximate value for gravel [62] |

$\mathrm{Thermal}\mathrm{diffusivity}{D}_{m}^{T}$ | 0.15 m^{2}/d | Langevin et al. [56] |

$\mathrm{Bulk}\mathrm{thermal}\mathrm{conductivity}{k}_{Tbulk}$ | 1.8 W/m °C | Langevin et al. [56] |

$\mathrm{Thermal}\mathrm{distribution}\mathrm{factor}{K}_{d}^{t}$ | 2 × 10^{−7} L/mg | Langevin et al. [56] |

Density change with concentration | 0.7 | Langevin et al. [56] |

Density change with temperature | −0.375 kg/(m^{3} °C) | Langevin et al. [56] |

Density vs pressure head slope | 0.00446 kg/m^{4} | Langevin et al. [56] |

$\mathrm{Bulk}\mathrm{density}{\rho}_{b}$ | 1800 kg/m^{3} | $\mathrm{Calculated}\mathrm{with}{\rho}_{b}={\rho}_{s}\left(1-\theta \right)$ |

Reference temperature | 25 °C | Langevin et al. [56] |

Viscosity vs concentration slope | 1.923 × 10^{−6} m^{4}/d | Langevin et al. [56] |

Reference viscosity | 86.4 kg/ m d | Langevin et al. [56] |

**Table 3.**Observation points of the model (nomenclature and depths) located at a distance of 217 m from the shoreline.

L1-T | L1-B | H2-T | H2-I | H2-B | L2-T | L2-B | H3-T | H3-I | H3-B |
---|---|---|---|---|---|---|---|---|---|

−20 m | −31 m | −34 m | −70 m | −79 m | −88 m | −96 m | −97 m | −110 m | −122 m |

L3-T | L3-I | L3-B | H4-T | H4-I | H4-B | L4-T | L4-I | L4-B | H5-T |

−124 m | −131 m | −139 m | −140 m | −155 m | −168 m | −169 m | −175 m | −182 m | −183 m |

**Table 4.**Main tidal constituents of the Mediterranean Sea and the temperature measured in S-3, S-4, and S-5, obtained with S_TIDE toolbox.

Harmonic Constituent | Symbol | Amplitude (m) | Amplitude (°C) | ||
---|---|---|---|---|---|

Sea Level | S-3 | S-4 | S-5 | ||

Lunisolar synodic fortnightly | Msf | 0.046 | 0.003 | 0.007 | 0.012 |

Principal lunar diurnal | O1 | 0.022 | 0.004 | 0.001 | 0.005 |

Luni-solar diurnal | K1 | 0.029 | 0.004 | 0.001 | 0.006 |

Lunar diurnal | OO1 | 0.013 | 0.001 | 0.002 | 0.001 |

Larger lunar elliptic semidiurnal | N2 | 0.031 | 0.004 | 0.002 | 0.006 |

Principal lunar semidiurnal | M2 | 0.157 | 0.021 | 0.009 | 0.027 |

Principal solar semidiurnal | S2 | 0.064 | 0.008 | 0.003 | 0.011 |

Shallow water overtides of principal lunar constituent | M4 | 0.016 | 0.001 | 0 | 0 |

**Table 5.**Time-lags obtained from the cross-correlation analysis, average amplitudes of the temperature oscillations, and temperature ranges of the dataset for February 2018. ${t}_{la{g}_{TIDE-T}}$ is the delay between tide and temperature, ${t}_{la{g}_{H-T}}$ is the delay between hydraulic head and temperature, ${t}_{la{g}_{EC-T}}$ is the delay between electrical conductivity and temperature.

Depth | ${\mathit{t}}_{\mathit{l}\mathit{a}{\mathit{g}}_{\mathit{T}\mathit{I}\mathit{D}\mathit{E}-\mathit{T}}}\text{}\left(\mathbf{h}\right)$ | ${\mathit{t}}_{\mathit{l}\mathit{a}{\mathit{g}}_{\mathit{H}-\mathit{T}}}\text{}\left(\mathbf{h}\right)$ | ${\mathit{t}}_{\mathit{l}\mathit{a}{\mathit{g}}_{\mathit{E}\mathit{C}-\mathit{T}}}\text{}\left(\mathbf{h}\right)$ | Amplitude (°C) | Range (°C) |
---|---|---|---|---|---|

132 m | 6.4 | 6.1 | −1.1 | 0.04 | 17.7–17.8 |

217 m | 5.6 | 5.6 | - | 0.02 | 18.9–19.0 |

236 m | 5.4 | 5.3 | −0.7 | 0.06 | 19.9–20.0 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Blanco-Coronas, A.M.; Calvache, M.L.; López-Chicano, M.; Martín-Montañés, C.; Jiménez-Sánchez, J.; Duque, C.
Salinity and Temperature Variations near the Freshwater-Saltwater Interface in Coastal Aquifers Induced by Ocean Tides and Changes in Recharge. *Water* **2022**, *14*, 2807.
https://doi.org/10.3390/w14182807

**AMA Style**

Blanco-Coronas AM, Calvache ML, López-Chicano M, Martín-Montañés C, Jiménez-Sánchez J, Duque C.
Salinity and Temperature Variations near the Freshwater-Saltwater Interface in Coastal Aquifers Induced by Ocean Tides and Changes in Recharge. *Water*. 2022; 14(18):2807.
https://doi.org/10.3390/w14182807

**Chicago/Turabian Style**

Blanco-Coronas, Angela M., Maria L. Calvache, Manuel López-Chicano, Crisanto Martín-Montañés, Jorge Jiménez-Sánchez, and Carlos Duque.
2022. "Salinity and Temperature Variations near the Freshwater-Saltwater Interface in Coastal Aquifers Induced by Ocean Tides and Changes in Recharge" *Water* 14, no. 18: 2807.
https://doi.org/10.3390/w14182807