*2.1. Study Area*

The Lin-Bien catchment is located in Pingtung Plain, Taiwan (Figure 1, after [22]). There are three long-term record rainfall stations, namely, Taiwu-1, Xinlaiyi, and Nanhan, which were selected for rainfall data collection (Table 1). Groundwater monitoring wells included Wells 1 to 7, which are adjacent to the catchment boundary (Table 2). The location of each rainfall station and groundwater monitoring well is illustrated in Figure 2.

**Figure 1.** Location map of Pingtung Plain, after [22].

**Table 1.** Rainfall stations in the study catchment.



**Table 2.** Information about each groundwater monitoring well in the study area.

Ting et al. [23] point out that the groundwater catchment in the study area can be divided into three layers, that is, the upper layer, middle layer, and lower layer. The thickness of the upper layer, varying from 10 to 60 m, is assumed to be an unconfined aquifer. The aquifer of the fluvial deposits in the foothills consists of coarse sand and gravel, decreasing in size to sand in a downstream direction with a thickness in excess of 220 m. The middle layer, assumed to be semi-pervious, is a geological formation which has a very low transmissivity compared to the aquifer, with a thickness of about 20 m of clay and sandy clay. The lower layer is assumed to be unconfined in the upper reaches of the area and confined from the mid-fan; the storativity may thus alternate between confined and unconfined values. The aquifers are recharged directly by rainfall, river flow, and subsurface inflow from the northern upstream part of the fluvial fan. The study area is hydraulically bounded in the south by the sea (Taiwan Strait). The screens of each well were all set in the upper layer, which is mainly composed of gravel, and with slice sand, silt, and clay. The transmissivity, storativity, and maximum yield were determined as 9148 m<sup>2</sup>/day, 6.5 × <sup>10</sup>−3, and 7084 m<sup>3</sup>/day, respectively, by the Taiwan Provincial Groundwater Development Bureau [24]. The hydrogeological profile of each well in this study area is redrawn in Figure 3 [25], and the groundwater piezometric map of the Pingtung Plain's dry season is shown in Figure 4 [26].

**Figure 2.** Location map of the study area (W1 to W7 is Well 1 to Well 7, respectively).

**Figure 3.** Hydrogeological profile of the study area (W1 to W7 is Well 1 to Well 7, respectively), after [25]. The A-A' profile of Figure 1.

The infiltration rate in this study area was evaluated by infiltration experiment in a 30 × 30 × 1.63 m test pit in 2002 [27]. The initial infiltration rate was about 22.76 m/day and the average infiltration rate was 17.26 m/day. After a serial infiltration test, the difference in infiltration rate between 2003 and 2005 had a maximum variation from 15.2 to 10.33 m/day due to the sand addition experiment [28]. If one compares the ARL infiltration result to other studies, the infiltration rate is about 5.9 m/day in the Rokugo Alluvial Fan, Northern Japan [29]; Liu et al.'s study on underground reservoirs in the western suburbs of Beijing estimates the infiltration rate between 1.0 m/day and 3.6 m/day [30].

**Figure 4.** Groundwater piezometric map of the Pingtung Plain's dry season (November to May) [26].

#### *2.2. Data Collection and Process*

For this study, around five years of daily rainfall and daily groundwater table data collected from 2010/05 to 2015/12 were used. Before the model was established, original data underwent a pre-procedure process that included the following steps: (1) rainfall data processing, (2) groundwater table data processing, and (3) data normalization. The data collection and processing procedure steps are described in the following subsections.

## 2.2.1. Rainfall Data

Mean catchment rainfall can be calculated by several techniques, such as Thiessen polygon, isohyetal, polynomial, geostatistical, inverse distance weighted, multi-quadratic interpolation, and kriging [31,32]. This study referred to Tsou et al. [33] who used the Thiessen polygon method to calculate the mean catchment rainfall. The separated Thiessen's control area in the Taiwu-1 station was 50.76 km<sup>2</sup> (15%), in the Xinlaiyi station it was 141.13 km<sup>2</sup> (40%), and in the Nanhan station it was 156.97 km<sup>2</sup> (45%). Based on research of the effects of rainfall, rainfall intensity, and groundwater table variation [34], the groundwater table is more sensitive in a five-day time-lag in a shallow layer [35]. Hence, this study combined the rainfall of past 1-day (R1) to past 5-day (R5) and rainfall intensity of past 1-day (RI1) to past 5-day (RI5) as the model inputs.

## 2.2.2. Groundwater Data

This study referred to Nayak et al. using 2-day groundwater differences as output for the model establishment [17]. In addition, considering the hydrogeology in a shallow groundwater aquifer, the groundwater variation is significantly affected by 10 days of rainfall [36]. Therefore, this study separated rainfall and groundwater data by events, where groundwater table rising past 10 days until groundwater drop was regarded as an event.

## 2.2.3. Data Normalization

To prevent an error associated with extreme values, data normalization was conducted for the data regarding rainfall, rainfall intensity, and groundwater differences. In addition, this procedure randomized the data using the concept of stochastic statistics to understand the relative change amount in the database. Therefore, the data employed were bounded between 0 and 1 using Equation (1) below, and then they were reverted by following Equation (2) [37]:

$$\mathbf{x}\_{\text{norm}} = \frac{\mathbf{x} - \mathbf{x}\_{\text{min}}}{\mathbf{x}\_{\text{max}} - \mathbf{x}\_{\text{min}}},\tag{1}$$

$$\mathbf{x} = \mathbf{x}\_{\text{norm}} \times (\mathbf{x}\_{\text{max}} - \mathbf{x}\_{\text{min}}) + \mathbf{x}\_{\text{min}} \tag{2}$$

where *x*norm is the normalized dimensionless variable, *x* is the observed value of the variable, *x*min is the minimum value of the variable, and *x*max is the maximum value of the variable.

#### *2.3. Artificial Neural Network (ANN)*

An artificial neural network is an algorithm for processing information by its dynamic state response to inputs. The neural network computes its output at each iteration (epoch) and compares it with the expected output of each input (exemplary) vector in order to calculate the error. An ANN comprises parallel systems that are composed of processing elements (PEs) or neurons, which are assembled in layers and connected through several links or weights. After feeding input data to the input layer, they pass through and are operated on by the network until the output is produced at the output layer. Each neuron receives numerous inputs from other neurons through some weighted connections. These weighted inputs are then summed, and a standard threshold is added, generating the argumen<sup>t</sup> for a transfer function (usually linear, logistic, or hyperbolic tangent), which in turn produces the final output of the neuron [38,39].

Hsieh et al. and Liao et al. compared MLP, a time lag recurrent network (TLRN), and a time delay neural network (TDNN) for groundwater simulation in the Lin-Bien River catchment. The MLP model is appropriate and suitable for this study area [40,41]. In order to learn more complex decision functions, inputs are fed into a number of perceptron nodes, each with its own set of weights and threshold [42]. The outputs of these nodes are then inputted into another layer of nodes, and so on. The output of the final layer of nodes is the output of the network. Such a network is termed MLP, and the layers of nodes whose input and output are seen only by other nodes are termed hidden [43]. The connection weights are computed by means of a learning algorithm. There are di fferent variants of back-propagation learning algorithms in the literature [44]. The illustration of the MLP model is shown in Figure 5.

**Figure 5.** Illustration of the multilayer perception (MLP) model, after [39].

#### *2.4. Sensitivity Analysis (SA)*

A sensitivity analysis is a tool for model input importance assessment. Referring to Jha and Sahoo [20] and Memarian et al. [45,46], the SA calculation equation (Equation (3)) is given as follows [47]. When the change is small, the input is less sensitive in the model; on the contrary, when the changes are significant, the input is highly sensitive:

$$S\_k = \frac{\sum\_{p=1}^{p} \sum\_{n=1}^{n} \left( y\_{ip} - \overline{y\_{ip}} \right)}{a\_k^2} \tag{3}$$

where *Sk* is the sensitivity index for input *k*, *yip* is the *i*th output obtained with the fixed weights for the *p*th pattern, *n* is the number of network outputs, *p* is the number of patterns, and <sup>α</sup>k<sup>2</sup> is the variance of the input k.
