# Aquifer Parameters Estimation from Natural Groundwater Level Fluctuations at the Mexican Wine-Producing Region Guadalupe Valley, BC

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{−6}to 2.78 × 10

^{−6}m

^{−1}), porosity (14–34%), storage coefficient (3.10 × 10

^{−5}to 10.45 × 10

^{−5}), transmissivity (6.67 × 10

^{−7}to 1.29 × 10

^{−4}m

^{2}∙s

^{−1}), and hydraulic conductivity (2.30 × 10

^{−3}to 2.97 × 10

^{−1}m∙d

^{−1}) were estimated. The values obtained are consistent with the type of geological materials identified in the vicinity of the analyzed wells and values reported in previous studies. This analysis represents helpful information that can be considered a framework to design and assess management strategies for groundwater resources in the overexploited Guadalupe Valley Aquifer.

## 1. Introduction

## 2. Methods

#### 2.1. Aquifer Response to Earth and Atmospheric Tides

#### 2.2. Groundwater-Level Response to Atmospheric Pressure

#### 2.3. Groundwater-Level Response to Solid Earth Tide

_{zz}) associated with SET through the tidal efficiency (γ

_{e}), which is obtained according to Jacob [8] as follows:

_{v}). Nevertheless, considering the induced deformation associated with SET and tectonic activity, the ε

_{v}is not well-known as a priori [17,20]. Moreover, the ε

_{zz}value measured on the terrain surface is approximately equal to the value of a horizontal strain component but with an opposite sign [20]. Therefore, it is more appropriate to analyze the WL response to an areal tidal strain (ε

_{A}) defined by Rojstaczer and Agnew [13] and calculated as follows:

_{zz}has an opposite sign, ε

_{A}value is higher than ε

_{v}. Thus, the WL response may be lower when ε

_{v}is used rather than ε

_{A}.

_{2}[28]. This differs from the measured gravitational potential due to geological and topographical local discontinuity effects [28,29,30]. Geologic and topo-graphic influence is complicated to define a priori. Thus, in the absence of strain measurements, the use of the theoretical gravitational strain is appropriate [20].

#### 2.4. Aquifer Parameters Estimation

_{k}is the rock matrix compressibility, φ corresponds to porosity, and β

_{W}is water compressibility. If both expressions are added, the result is unity. Therefore, in calculating any of the previous parameters, it is possible to define the other one (BE = 1 − γ

_{e}).

_{S}) of the rock materials. Bredehoeft [10] indicated that S

_{S}could be calculated from the water-table fluctuations record (dh), and assuming a characteristic value of Poisson’s ratio (ν) in undrained conditions. Van der Kamp and Gale [11] derived an expression to estimate S

_{S}as follows:

_{U}is the rock matrix compressibility under undrained conditions, h = 0.6031 and l = 0.0839 are the Love numbers [31]; Er corresponds to the Earth’s radius, and g indicates gravity acceleration.

_{2}and dh is equivalent to the relation among the amplitude of the dominant harmonic components of W

_{2}denoted as (A

_{2}(τ, θ)), and the amplitude of the dh (A

_{dh}(τ)) at the same period (τ). Merrit [14] proposed that the derivatives (dW

_{2}and dh) can be approximated by a finite differential scheme; thus, Equation (6) can be written as follows:

_{2}(τ, θ) is calculated as follows:

_{2}is to represent it through a finite set of harmonic functions, sinus, and cosines. Each k-tidal harmonic component has a particular frequency (f

_{Tk}), amplitude (A

_{Tk}), and phase angle (Φ

_{Tk}) [32]. Amplitude (A

_{dhk}) and phase-angle (Φ

_{dhk}) estimations from the WL variations at the exact frequencies of the harmonic components of W

_{2}are calculated from the regression coefficients (a

_{dhk}and b

_{dhk}) obtained as follows [17]:

_{Tk}and Φ

_{Tk}are computed from the theoretical strain-tensor associated to Earth tides, using Equations (9) and (10). Thus, areal strain sensitivity (A

_{SK}) is calculated based on A

_{dhk}and A

_{Tk}according to Rojstaczer and Agnew [13]:

_{k}) is determined by Hsieh et al. [34] as follows:

## 3. Study Area and Database

#### 3.1. Study Area

^{−3}to 52.40 × 10

^{−3}m

^{2}∙s

^{−1}, prevailing higher values of 1.00 × 10

^{−3}m

^{2}∙s

^{−1}. CNA [4] estimated transmissivity values ranging from 0.04 × 10

^{−3}to 60.00 × 10

^{−3}m

^{2}∙s

^{−1}, hydraulic conductivity values between 0.05 to 64.80 m∙d

^{−1}; and mean values of storage coefficient of 0.00005 and specific yield of 0.065.

^{−1}. The exception to this was the southwestern region of EPSB, where the characteristic value determined was 68.49 m∙d

^{−1}. Hydraulic conductivity and storage coefficient values ranging from 2.00 to 8.00 m∙d

^{−1}, and 0.10 to 0.28, respectively; were used to simulate the groundwater-table response to extraordinary rainfall events within GV by [3].

^{−1}were calculated by using the Vukovic–Soro and Kozeny–Carman empirical equations proposed by [42]. Molina-Navarro et al. [38] and Montecelos-Zamora [43] modeled the Global warming hydrogeological impact on the northern zone of the Guadalupe River, using a SWAT model. As a result of the simulation, typical values of hydraulic conductivity, ranging from 2.14 to 2.71 m∙d

^{−1}, were calculated.

#### 3.2. Data

#### 3.3. Data Processing

_{2}) and its strain tensor (ε

_{A}) were calculated at each well location, using the SPOTL package ver. 3.3.0.2 [44,45]. The geologic–topographic discontinuities and oceanic tide influence were not considered. The WL, BP, and ε

_{A}time-series were processed and analyzed by using a set of MatLab codes written particularly for this study. The recorded time-series were detrended by using polynomial functions to represent it in a stationary fashion. A third-degree polynomial better reproduces the influence of annual and semi-annual cycles. Using the characteristic polynomial equation, the very low frequency effect was calculated and removed from the measured time-series. From the detrended data, BE was calculated with the method proposed by Rahi [24]. This technique estimates BE only considering BP perturbations and filtering the areal strain effect.

_{dhk}) and phase angle (Φ

_{dhk}) values were determined at the exact frequencies of the tidal harmonic components, using the t-tide code [46], and applying Equations (9) and (10). Similarly, A

_{Tk}and Φ

_{Tk}were calculated. Areal strain sensitivity was calculated based on A

_{dhk}and A

_{Tk}, using Equation (11). Moreover, the phase shift was estimated based on Φ

_{dhk}and Φ

_{Tk}, using Equation (15). Therefore, the transmissivity magnitude order was estimated by utilizing Equation (13) and considering the values of R

_{WC}and R

_{WS}reported in Table 1.

_{SK}estimates, the specific storage was calculated by using Equation (7). For this, gravitational acceleration at a GV representative latitude was calculated as g = 9.795 [m∙s

^{−2}]. Moreover, the Earth’s radius of 6,371,000 m and Poisson’s ratio equal to 0.25 [47] were assumed. Using estimations of BE and S

_{S}, porosity values were calculated applying Equation (12). For this β

_{W}= 4.40 × 10

^{−10}[Pa

^{−1}] and ρ = 998.20 [kg∙m

^{−3}] were used.

_{HE}), borehole depth (B

_{D}), and water-table elevation (W

_{TE}) reported in Table 1. From B, approximation of the storage coefficient was conducted based on the relation (S

_{C}= S

_{S}∙B). Similarly, the hydraulic conductivity magnitude-order was estimated from the relation (K = T∙B

^{−1}).

## 4. Results and Discussion

_{A}were five, two of them are diurnal (O1, Lunar; K1, Lunar-Solar) and three are semi-diurnal (N2, Lunar; M2, Solar; and S2, Lunar). Its period and nomenclature also are indicated in inset Figure 4c. The amplitude of the tidal harmonic components calculated in the three monitoring wells was comparable. On the reference well P254, amplitudes estimated were O1 = 5.3, K1 = 7.1, N2 = 1.7, M2 = 8.2, S2 = 4.2 nstr. These last harmonic components are responsible for 95% of tidal potential and play an essential role in hydrogeological studies [10,48].

_{dhk}and Φ

_{dhk}at the specific frequencies of the O1 and M2 harmonic components was carried out from the regression coefficients a

_{dhk}and b

_{dhk}, using Equations (9) and (10). The highest amplitudes were determined in well P122 (O1 = 1.06 mm-WEC and M2 = 0.59 mm-WEC). These last values were approximately two times the observed value on the amplitude spectra. The amplitudes determined from wells P452 and POP2 were minor relative to well P122 and are shown in Table 3. Similarly, values of A

_{Tk}and Φ

_{Tk}at the exact frequencies of O1 and M2 were calculated. The amplitude value for O1 was 10.67 nstr and 19.88 nstr for M2. These last two values are nearly two times the observed value on the amplitude spectra. The underestimated amplitude from the frequency spectra may be related to digital filtering and Discrete Fourier-Transform inherent problems, for example, the aliasing.

_{SK}was calculated in well P122 for the harmonic component O1 = 9.90 × 10

^{−2}mm∙nstr

^{−1}; this value was approximately three times the value determined for M2. Added to this, a negative phase shift was determined in well P122 (η

_{k}-O1 = −34°, and η

_{k}-M2 = −83°). These last results indicate that the WL variations are produced as a result of the areal tidal strain effect. In wells, P452 and POP2 values of areal strain sensitivities ranging between 1.13 × 10

^{−2}to 2.13 × 10

^{−2}mm∙nstr

^{−1}of A

_{SK}were calculated. WL variations as a result of the areal tidal strain effect were determined in wells P452 (M2, harmonic component) and POP2 (O1 harmonic component). In contrast, a positive phase shift was determined for the O1 harmonic component in well P452 and for the M2 component in well POP2. In previous studies, the positive phase shift has been related to the borehole storage effect and water diffusion processes [18,25,26,49].

_{S}in the GVA has not been obtained because previously conducted studies have considered an unconfined aquifer, where the specific yield is much higher than S

_{S}. Nevertheless, the results of this study suggest local semi-confined behavior in the GVA. The determined S

_{S}values ranged from 1.27 × 10

^{−6}to 2.78 × 10

^{−6}m

^{−1}(Table 4). The lowest value was calculated for well P122, while the highest value was estimated for well P452. The comparison between the S

_{S}estimations and the expected values as a function of the rock-materials type is shown in Figure 5. In general, the S

_{S}estimations were two orders of magnitude lower than the expected values related to the rock materials that dominate the lithologic column of wells P01, P02, and PG2 reported by Campos-Gaytán [2]. However, these stratigraphic columns also showed the presence of clay lens (P01 and P02), granite (P01), and altered/fractured granite (P02). Based on these last rock materials, the calculated S

_{S}values for wells P452 and P122 are slightly in agreement with the expected S

_{S}values (Figure 5). S

_{S}estimations for well POP2 showed relevant discrepancies concerning the expected S

_{S}values as a function of the rock materials observed in the lithologic column of well PG2 (sand and gravel). Nonetheless, shallow clay layers have been interpreted on recent electromagnetic surveys (TEMs) conducted in the CSB [52]. This last geological feature may explain the calculated S

_{S}values in well POP2 and support the GVA local semi-confined hydraulic behavior deduced.

_{S}and BE. The estimated porosity values ranged from 14 to 34% (Table 4). The lowest value was calculated for well P122, located in the EPSB in which a shallow hydraulic basement has been reported. The highest porosity value was estimated for well POP2 situated in the CSB and is consistent with the expected value associated with the rock materials that constitute the PG2 reference stratigraphic column. Furthermore, calculated porosity values are comparable with the porosity values (26–38%) determined in El Mogor, GVA’s tributary sub-basin [40]. Additionally, estimated porosity values are consistent with the expected porosity values reported in the classic hydrogeological literature [50,53]. For practical purposes and in the absence of local determinations, a representative porosity value for the rock materials in the CSB is 30%, 20% for EPSB, and 25% for the GVA.

_{S}and B. The estimated S

_{C}values ranging from 3.10 × 10

^{−5}to 10.45 × 10

^{−5}(Table 4). The lowest S

_{C}value was calculated for well P122, and the highest S

_{C}value was in well P452; both wells are in the EPSB. The S

_{C}value estimated for well POP2 situated in the CSB was lower than the calculated value for well P452. The estimated S

_{C}values were up to four orders of magnitude lower in comparison to those used in the water-table simulations by González-Ramírez and Vázquez-González [3]. Nevertheless, estimated S

_{C}values are similar in the order of magnitude (10

^{−5}) with those determined through pumping tests by CNA [4].

_{k}, the order of magnitude of S

_{C}, and Figure 2 from Hsieh et al. [34]. The estimated T-values were ranging from 6.67 × 10

^{−7}to 1.29 × 10

^{−4}m

^{2}∙s

^{−1}(Table 4). The lowest T-value was calculated for well P122, and the highest T-value in well P452, both wells are in the EPSB. Estimated T-values are comparable with those (3.40 × 10

^{−4}to 52.40 × 10

^{−3}m

^{2}∙s

^{−1}) determined by Andrade-Borbolla [1], and to those (4.00 × 10

^{−5}a 60.00 × 10

^{−3}m

^{2}∙s

^{−1}) calculated by CNA [4]. Finally, hydraulic conductivity values were calculated from estimations of T and B. The estimated K-values ranged between 2.30 × 10

^{−3}to 2.97 × 10

^{−1}m∙d

^{−1}(Table 4). The highest K-value was calculated for well P452 located at the SW of EPSB; a similar hydraulic behavior was described by Campos-Gaytán and Kretzschmar [41]. The lowest K-value was calculated for well POP2 located on the CSB. In general, the estimated K-values were up to two or four orders of magnitude lower in comparison (Figure 6) to those determined from water-table elevation modeling [3,38,41,43]. In contrast, the estimated K-values are comparable with those reported in the classic hydrogeological literature [50,53]. Moreover, the estimated K-values are pretty similar to those determined from the soil grain-size analysis by Del Toro-Guerrero et al. [40] and with those calculated from pumping tests in wells of the GVA by CNA [4].

## 5. Conclusions

^{−6}to 2.78 × 10

^{−6}m

^{−1}), porosity (14–34%), storage coefficient (3.10 × 10

^{−5}to 10.45 × 10

^{−5}), transmissivity (6.67 × 10

^{−7}to 1.29 × 10

^{−4}m

^{2}∙s

^{−1}), and hydraulic conductivity (2.30 × 10

^{−3}to 2.97 × 10

^{−1}m∙d

^{−1}) were calculated. These results were consistent with previous determinations. Moreover, based on our literature review, the calculated specific storage values correspond to the first estimations reported in the Guadalupe Valley Aquifer.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Macro and regional location of the Guadalupe Valley Aquifer. Monitoring wells (P452, P122, and POP2) instrumented are shown. Reference wells (P01, P02, and PG02) included as a part of the study (lithology column availability) are shown. The location of the barometer (P254) is also shown. Geological features are illustrated and described at inset legend [35,36].

**Figure 2.**(

**a**) Schematic hydrogeological conceptualization of the Guadalupe Valley Aquifer, after Reference [5]. The approximate location of the monitoring wells included as a part of this study is shown. (

**b**) Simplified stratigraphic columns of the rock units drilled by the reference wells (P01, P02, and PG2) [2]. The water level measured in 2010 is indicated.

**Figure 3.**(

**a**) Records of water level (P452, P122, and POP2) and barometric pressure (P254) in terms of centimeters of Water Equivalent Column (cm-WEC) and hectopascals. (

**b**) Calculated tidal strain (P254) expressed as nanostrain (1 nstr = 1 ppb).

**Figure 4.**Discrete amplitude spectra for water levels in wells P452, P122, and POP2 (

**a**); barometric pressure expressed as centimeters of Water Equivalent Column (cm-WEC) (

**b**); and the calculated areal tidal strain (

**c**). The dominant Earth tides’ frequencies are indicated in the spectra.

**Figure 5.**Comparison between the estimated specific storage values (P452, P122, and POP2) and the expected values as a function of the rock-material type.

**Figure 6.**Comparison between the estimated hydraulic-conductivity values (P452, P122, and POP2) and the expected values as a function of the rock-material type, and determined values from previous studies.

**Table 1.**Summary of the characteristics of the three monitoring wells studied. Nomenclature: well head elevation (W

_{HE}, meters above sea level (masl)), borehole depth (B

_{D}), water-table elevation (W

_{TE}), radius well-casing (R

_{WC}), radius well-screened (R

_{WS}), and saturated thickness (B).

Well ID | Coordinates ^{1} | W_{HE} | B_{D} | W_{TE} | R_{WC}/R_{WS} | B | |
---|---|---|---|---|---|---|---|

Longitude X (m) | Latitude Y (m) | (masl) | (m) | (msnmm) | (m) | (m) | |

P452 | 532,619 | 3,546,036 | 301.80 | 40.00 | 299.40 | 0.33/0.10 | 37.60 |

P122 | 536,402 | 3,550,067 | 323.07 | 40.00 | 307.50 | 0.30/0.10 | 24.43 |

POP2 | 543,576 | 3,552,069 | 345.40 | 80.00 | 317.30 | 0.10/0.10 | 51.90 |

^{1}Projected coordinates, Universal Transversal Mercator UTM. Datum: World Geodetic Systems, year 1984, WGS-84.

Well ID | Name | Location | Depth | Lithology |
---|---|---|---|---|

(m) | Material (Interval) | |||

P01 | Porvenir-1 | ~1000 m NE-direction from P452 | 28.57 | 1. Sand (0 to 8 m) |

2. Sand and gravel (8 to 14 m) | ||||

3. Sandy clay (14 to 16 m) | ||||

4. Sand, gravel, clay (16 to 24 m) | ||||

5. Granite (24 to 30 m) | ||||

P02 | Porvenir-2 | ~650 m W-direction from P122 | 41.70 | 1. Sandy clay (0 to 2 m) |

2. Sand (2 to 6 m) | ||||

3. Altered granite (6 to 16) | ||||

4. Fractured granite (16 to 40 m) | ||||

PG2 | Guadalupe-2 | ~400 m NE-direction from POP2 | 83.90 | 1. Alternating layers of sand and gravel. The igneous basement was not drilled. |

**Table 3.**Summary of results of the regression analysis, areal strain sensitivity, and barometric efficiency.

Well ID | A_{dhk}∙(10^{−1}) | Φ_{dhk} | A_{Tk} | Φ_{Tk} | η_{k} | A_{Sk}∙(10^{−2}) | BE |
---|---|---|---|---|---|---|---|

(mm) | (°) | (nstr) | (°) | (°) | (mm∙nstr^{−1}) | (%) | |

O1/M2 | O1/M2 | O1/M2 | O1/M2 | O1/M2 | O1/M2 | ||

P-452 | 1.61/4.24 | −68/−83 | 10.67/19.89 | −81/−44 | 13/−39 | 1.51/2.13 | 41.46 |

P-122 | 10.57/5.98 | 55/−35 | 10.67/19.88 | 89/48 | −34/−83 | 9.90/3.01 | 48.32 |

POP-2 | 1.21/2.66 | 66/78 | 10.68/19.87 | −78/16 | −12/62 | 1.13/1.34 | 79.79 |

**Table 4.**Summary of estimations of hydrogeological parameters for the rock materials that constitute the Guadalupe Valley Aquifer.

Well ID | S_{S} (10^{−6}) | φ | S_{C} (10^{−5}) | T (10^{−6}) | K (10^{−2}) |
---|---|---|---|---|---|

(m^{−1}) | (%) | (m^{2}∙s^{−1}) | (m∙d^{−1}) | ||

O1/M2 | O1/M2 | O1/M2 | O1/M2 | O1/M2 | |

P-452 | 2.78/1.93 | 26.88/18.60 | 10.45/7.26 | 129.46/74.28 | 29.75/17.07 |

P-122 | 1.27/2.53 | 14.22/28.46 | 3.10/6.18 | 32.05/0.66 | 11.33/0.23 |

POP-2 | 1.83/1.52 | 33.95/28.27 | 9.49/7.88 | 12.38/1.99 | 2.06/0.33 |

_{S}; porosity, φ; storage coefficient, S

_{C}; transmissivity, T; hydraulic conductivity, K.

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**MDPI and ACS Style**

Fuentes-Arreazola, M.A.; Ramírez-Hernández, J.; Vázquez-González, R.; Núñez, D.; Díaz-Fernández, A.; González-Ramírez, J. Aquifer Parameters Estimation from Natural Groundwater Level Fluctuations at the Mexican Wine-Producing Region Guadalupe Valley, BC. *Water* **2021**, *13*, 2437.
https://doi.org/10.3390/w13172437

**AMA Style**

Fuentes-Arreazola MA, Ramírez-Hernández J, Vázquez-González R, Núñez D, Díaz-Fernández A, González-Ramírez J. Aquifer Parameters Estimation from Natural Groundwater Level Fluctuations at the Mexican Wine-Producing Region Guadalupe Valley, BC. *Water*. 2021; 13(17):2437.
https://doi.org/10.3390/w13172437

**Chicago/Turabian Style**

Fuentes-Arreazola, Mario A., Jorge Ramírez-Hernández, Rogelio Vázquez-González, Diana Núñez, Alejandro Díaz-Fernández, and Javier González-Ramírez. 2021. "Aquifer Parameters Estimation from Natural Groundwater Level Fluctuations at the Mexican Wine-Producing Region Guadalupe Valley, BC" *Water* 13, no. 17: 2437.
https://doi.org/10.3390/w13172437