# A Hybrid DSCNN-GRU Based Surrogate Model for Transient Groundwater Flow Prediction
## 2 Methodology
### Groundwater Models
#### 2.1.2 Modeling Method  
The three models in this study were designed to depict the general hydrogeological environment of the study area, rather than being specifically tailored to a particular location. Initially, a 3D watershed was established with dimensions of 10 km wide, 10 km long, and 105 m deep. The watershed was discretized into 100 rows, 100 columns, and 21 layers, all configured as convertible layers, but only the first layer of water head field data is taken. The surface elevation in the eastern and western regions was set to 2 m. The bottom of the aquifer was assumed to be a no-flow boundary, while the eastern and western boundaries were designated as time-varying groundwater heads.  
Data for transient head boundary (Figure 2a) were obtained from nearby observation wells (website: [[https://www.waterenonect.sa.gov.au/Systems/GD/Pages/Default.aspx](https://www.waterenonect.sa.gov.au/Systems/GD/Pages/Default.aspx)]([https://www.waterenonect.sa.gov.au/Systems/GD/Pages/Default.aspx](https://www.waterenonect.sa.gov.au/Systems/GD/Pages/Default.aspx)), accessed on 9 November 2024). Transient recharge and evapotranspiration data (Figure 2b,c) were sourced from a calibrated regional water balance model by [PERSON] et al. [1; 22; 23].  
Sixty months, representing a single stress period, are selected from the time span between 2009 and 2013, with each month serving as a time step. The parameter ranges for  
Figure 2: Transient boundary conditions used in the numerical model. (**a**) Groundwater tables of west and east boundaries. (**b**) Recharge from the top surface. (**c**) Maximum evapotranspiration flux.  
this model are primarily derived from the calibration of a regional model in the southeastern part of South Australia, which is used in [PERSON] et al.'s study [22; 23]. Range of other parameters such as horizontal hydraulic conductivity, vertical hydraulic conductivity, initial water head, boundary conditions, pumping rate of wells, and evapotranspiration rate are determined based on expert knowledge and local hydrogeological information.  
In Case 1, the hydraulic conductivity distribution in the study area is segmented into ten blocks, with constant values within each block. Based on available research data for the study area, hydraulic conductivity values for Blocks 1 to 5 are randomly chosen from the range of 1 to 2 m/d, and for Blocks 6 to 10, from 3 to 4 m/d. The specific values of hydraulic conductivity for each block are illustrated in Figure 3a.  
In Case 2, the hydraulic conductivity field of the study area is divided into 20 different blocks, as illustrated in Figure 3b. The values for each block are randomly selected from 2 to 6 m/d, based on existing research data.  
In Case 3, a total of 64 evenly distributed sampling points are set in the study area, as depicted in Figure 4a. Based on existing research data, hydraulic conductivity values randomly selected from 10 to 100 m/d were assigned to sampling points and spatially interpolated across the study area using ordinary Kriging with a linear variogram model to generate the conductivity field shown in Figure 4b [2; 24]. The study area is further divided into a 100 \(\times\) 100 grid. Two randomly placed pumping wells are located at row 5, column 1, and row 74, column 58, with pumping rates randomly selected from 20 to 70 m\({}^{3}\)/d. In these three cases, except for different hydraulic conductivity settings, other common parameters such as initial head field and drainage area are the same.  
Figure 4: Example of using Kriging interpolation to set the global hydraulic conductivity (Case 3). (**a**) Hydraulic conductivity distribution map of sampling points before interpolation. (**b**) Hydraulic conductivity distribution map of the whole domain after interpolation.  
Figure 3: Hydraulic conductivity distribution schematic for the first two examples. (**a**) Case 1. (**b**) Case 2.