3.1. Electrical Resistivity Imaging Data Acquisition and Processing
We conducted a time-lapse Electrical Resistivity Imaging (ERI) survey at 10 sites (
Figure 4) in February, April, July, September, and November 2019. The resistivity data were measured using a Lippmann 4-point light 10 W resistivity meter [
24]. We used the Wenner and Schlumberger configuration, with 101 electrodes spaced 1.5 m apart. We deployed 1 survey station, PT01, nearby the Pengcuo (PG) observation well to verify the reliability of resistivity data in monitoring GWL. The ERI survey sites PT02, PT03, PT05, PT06, PT07, and PT08 are located to the north of the PG observation well, while PT04, PT09, and PT10 are located to the south. Because of local agricultural activity and nearby artificial noises, the resistivity data of PT01 and PT10 for February, PT09 for May, PT08 for July, and PT05 for September were not included in this study analysis.
Furthermore, we processed and analyzed the resistivity data obtained from the field survey with several steps as shown in
Figure 5. First, we inverted the resistivity data with the software EarthImager2D
TM (Version 2.4.2) [
25]; in this step, we applied a smoothness-constrained least-square inversion method as it helps to reduce the squares of the spatial variations in model resistivity, which is more appropriate for settings with gradually changing resistivity to obtain the 2-D geoelectric model [
26]. Second, we extracted at least 5 sets of 1-D vertical inverted resistivity data from each 2-D inversion result. Then, we converted the 1-D inverted resistivity data to normalized water content by applying Archie’s law. Finally, we estimated the groundwater level (GWL) and theoretical specific yield (
Sy) using Van Gecnuchen (VG) and Brooks–Corey (BC) empirical equations. The spatial distribution of GWL and
Sy was interpolated using the ordinary kriging method. Additionally, we used GWL data from other observation wells near the study region as boundary constraints. The spatial distribution data were then imported into QGIS software to create a contour map.
3.2. Empirical Estimation of Hydraulic Parameter from Resistivity Data
We utilized Archie’s law [
4] to empirically estimate the water content from at least 5 1-D vertical resistivity data in the central part of each resistivity survey line. Several physical factors may affect the resistivity measurements, including water content, porosity, pore structure, and cementation of material. Archie’s law relates resistivity and sediment saturation using the following expression:
where
is the resistivity of the material,
is the pore water resistivity,
is the tortuosity factor,
is the porosity,
is the saturation, and
and
are the saturation index and cementation index, respectively.
Applying the approach used by Dietrich et al. [
27] and Chang et al. [
28] that links the unsaturated and saturated resistivities and shows resistivity variation with the water saturation, we determined normalized volumetric water content,
:
where
is normalized relative saturation and
is the average porosity of the soil. Che, et al. [
29] analyzed soil grain size in Pingtung Plain and determined the porosity using the Vokovic and Soro [
30] empirical equation. The result showed that the Pingtung Plain porosity ranges from 0.26 to 0.30, whereas the porosity of the Pengcuo area varies from 0.26 to 0.27. Thus, this study used the average porosity
of 0.26.
According to the drilling records, the lithology of the uppermost 1 to 2 m consists of surface soil, characterized by clay and sand. Therefore, we eliminated the uppermost 2 m as they represent surface soil layer features rather than gravel aquifer properties.
Figure 6 shows an example of the normalized volumetric water content variation curve with depth extracted from the 1-D vertical resistivity set of PT06 during the April survey, and the variation curve has a similar trend to the Soil Water Characteristic Curve (SWCC). Utilizing the SWCC, we can estimate the GWL and specific yield.
Several studies have applied the SWCC [
31,
32], and the most frequently used of empirical equations are the Brooks–Corey (BC) and the Van Genuchten (VG). The BC can describe the relationships between the suction and water contents in the vadose zone:
where
represents unsaturated water content (L
3L
−3),
represents the residual water content (L
3L
−3),
indicates the saturated water content (L
3L
−3) with the presumed average porosity
,
represents the air-entry suction head (L),
represents the suction head (L), and
indicates the pore size distribution parameter.
The relationship between water content and the suction head was also obtained using the VG:
where
represents the normalized water content (L
3L
−3), 𝛼 is related to the inverse of air entry value, 𝑛 is related to the pore size distribution of the soil, and 𝑚 is associated with the asymmetry of the model [
33], where
m equals
.
The Brooks–Corey (BC) and Van Genuchten (VG) provide a functional relationship to describe the unsaturated soil property in the vadose zone and are widely applied in the SWCC [
31,
34].
Figure 7 depicts the VG with a continuous SWCC. The VG has 3 shape parameters (α, m, and
n); these factors enable more flexibility, allowing the equation to better fit the data for different soil types. The BC has a sharp boundary that corresponds to a capillary head. Because BC has 2 parameters (h and a), obtaining them from BC is simpler than obtaining the VG parameters. To determine hydraulic parameters in the SWCC, this study used both the VG and BC. We inverted the BC and VG parameters by minimizing the root mean square differences between estimated and measured water content. The resistivity measurement yields the measured water content. To optimize the minimum object equation in the inversion, we utilized the Generalized Reduced Gradient (GRG) nonlinear program [
35] with the EXCEL Solver. The Solver is an optimization tool in EXCEL that can be used to determine how changing the assumptions in a model can lead to the desired outcome. This tool can be accessed from the add-ins menu in EXCEL [
36,
37].
The Groundwater Level (GWL) in the study area was estimated using an approach based on the assumption that the saturated layer is a base with a depth of
. Additionally, we assumed that the suction head is proportional to the height of the saturated zone in the unconfined aquifer, as discussed in Krahn and Fredlund [
38]. Then, we estimated the air-entry suction head where water content is in a saturated condition (
) relative to the same base,
. As a result, we were also able to estimate the depth of the saturated surface of the air-entry suction head,
.
The actual groundwater table, however, may differ from the surface that corresponds to the air-entry suction. Therefore, we applied the correction factor,
, to correct the predicted groundwater depth to the groundwater depth obtained from an observation well. Then GWL was obtained by subtracting the groundwater depth (
) from the meter above sea level (MASL). The following is an illustration of the correction equation.
Furthermore, we quantified the theoretical specific yield,
, which represents the average volume of water that can be drained per unit aquifer surface per unit drop of the head. It is an essential hydraulic parameter to describe the groundwater potential of a particular area. Therefore, the
Sy was calculated using the difference between the SWCC saturated water content
and residual water content
: