## 2 Materials and Methods
### Model Calibration
#### 2.5.2 Regular Pilot Point Placement  
Regular placement is related to the uniform distribution of pilot point locations to form a regular grid. The regularity guarantees the existence of a pilot point at a fixed distance. This pilot point placement structure is known as the ordinary placement for pilot point model calibration. The entire model is about 121,500 m\({}^{2}\); a grid of 60 m \(\times\) 60 m and 40 m \(\times\) 40 m are formed respectively for the low density and high-density pilot point, giving 35 parameters for the low density and 60 for the high. Pilot points are placed regularly in the middle of each grid which is diverse from the finite-difference grid, such as each 3600 m\({}^{2}\) have one arbitrary point for the low density and 1600 m\({}^{2}\) for the high density of pilot points (Figure 4a-c). Figure 4: Pilot points placement design: (**a**) regular placement with 35 pilot points; (**b**) MHMDG placement with 35 pilot points; (**c**) regular placement with 60 pilot points; (**d**) MHMDG placement with 60 pilot points. 2.5.3. Middle Head Measurement Down Gradient Pilot Points Placement  
MHMDG is a pilot point placement concept that considers the head observation measurement and the hydraulic gradient. When using the kriging method to assign the hydraulic conductivity of every cell interpolated from the pilot point, the emplacement of the pilot point must be carefully considered. The assignment of the pilot point value is completed using the zonation technique. The area is divided into upgradient and downgradient zones from the southeast to the northwest. The frequency of the regular pilot point placement is maintained. However, the pilot points are placed in the middle of the head observation, and the downgradient part is more considered. The upgradient position is filled with a spared pilot point to avoid generating a gap in the interpolation (Figure 4b-d). 2.5.4. Pilot Point Placement Criteria  
Placement criteria are the principle by which the pilot point localization is chosen. It must follow a technical condition to meet the requirement of the adopted methodology. Although there is no particular rule for the pilot point placement, criteria must be addressed to fulfill the model calibration target. As presented in the preceding paragraph, the model is a small-scale area of 450 m \(\times\) 270 m. The principle is to cover the entire study area; however, avoiding oversaturation is controlled. This study is conducted using two different pilot point placements, the regular placement, the MHMDG placement, and two other parameters density based on several criteria to achieve a minimum error and maximum accuracy (Figure 4). The number of 35 represents the lower density of the pilot point for calibration, so the distance between two pilot points is 60 m, as the model is entirely covered and has one pilot point each 3600 m\({}^{2}\) and one pilot point every 1600 m\({}^{2}\). The pilot points used here are designed in three-dimensional pilot points placed on the top surface of the aquifer layer. 3. Results  
3.1. Pilot Point Placement and Frequency Effect  
The pilot point placement is related to the localization of each pilot point, while the frequency is the amount of the pilot point placed in the area. The effect of these two structures could be measured by experimental simulation under various circumstances, including the convergence of the model and the measurement of the RMS. The convergence accuracy of the hydraulic head simulation reached 95% with 60 parameters, and the RMS decreased (Table 2). The middle head measurement down gradient placement takes advantage of the regular placement in terms of estimation accuracy, shown by the Standard error of estimate respectively 0.053-0.056 and 0.061-0.063.