## 5 Conclusions  
This paper presents an improved calibration technique for the groundwater flow model based on the pilot point method under various situations and stress circumstances. The experimental simulation is conducted using the MODFLOW model and the PEST calibration numerical code in a small-scale heterogeneous area for an MHMDG design of the pilot point method on steady-state mode. Our main findings are as follows:  
1. The calibration evaluation compared the simulated hydraulic head to the observed data. The conceptualization method has a significant impact on the result, especially the grid structure and elevation, which define the deformation of the grid and the relief of the surface. The geological structure could be well reflected by the surface interpolated from a SGrid model elevation point. The accuracy depends on the interpolation method, which is the primary source of uncertainty. The kriging interpolation remains the most effective and accurate for groundwater model conceptualization.
2. The calibration method based on the pilot point method is effective in the small-scale area, as proved by this experimental study; however, it massively pivots on the pilot point emplacement strategy and density. In our application case, the MHMDG placement method with a large density gives the best R-squared 0.901 compared to 0.880 for the regular placement. The kriging interpolation used in inverse modeling reflects the value of the hydraulic conductivity of every pilot point. The initial value of the pilot points impacts the accuracy of the result and the computation time. The calculation is more complicated in heterogeneous media and generates a computation burden that affects the model stability.
3. The choice of the solution model and the engines adapted to the context is critical for simulation, especially when using the MODFLOW numerical code. It might yield an excellent calculation outcome of unrealistic value. The MODFLOW 2005 and the PEST combination are perfect solutions for small-scale areas. The consideration ofsmall-scale simulation with regularization is a future topic for another research. It helps to understand the calibration solution's uniqueness of using the pilot point method and zonation focused on the middle head measurement on the downgradient technics.  
Conceptualization, T.P.R. and Y.Z.; Data curation, Z.Y.; Formal analysis, T.P.R. and Z.Y.; Methodology, T.P.R. and Y.Z.; Supervision, Y.Z. and Y.H.; Validation, Y.Z. and Y.H.; Visualization, U.K.; Writing--original draft, T.P.R.; Writing--review & editing, T.P.R., Y.Z., Y.H. and U.K. All authors have read and agreed to the published version of the manuscript.  
This study was funded by the National Key R&D Program of China (2019 YFC1805905), the National Natural Science Foundation of China (41872249).  
The dataset of the current study is not publically available, available only for the review of the present article.  
Authors are grateful to the editors and anonymous reviewers for their helpful advice and constructive suggestions, which have significantly improved the paper's quality. We are also thankful to [PERSON] for his valuable help in revising this manuscript.  
The authors declare no conflict of interest.