Design of groundwater level monitoring sections at river side based on analytical solution

Accurate estimation of the exchange between river water and groundwater requires the establishment of properly designed groundwater level monitoring sections along riverbanks. This study applied the classic Ferris analytical solution and performed Latin Hypercube Sampling to obtain groundwater level data. K-means clustering analysis was then conducted on the groundwater level data, and Kriging interpolation was employed to compare and evaluate the different clustering results, thereby designing a rational groundwater level monitoring section. The results show that preprocessing the data based on the Ferris analytical solution reveals that the initial water level h\left(x,0\right) and the rapid rise height of the river water level \Delta H_0 have insignificant impact on the K-means clustering results. Thus, h\left(x,0\right) was set to 0 and \Delta H_0 was set to 1 to simplify subsequent analyses. For different hydraulic conductivity coefficients a and time t in the analytical solution, the optimal k value for K-means clustering determined by the elbow method was 3, and the number of monitoring wells was also 3. However, the location of the third monitoring well shifts from the third clustering center to the area of maximum influence of river water, facilitating the use of recharge water mound volume for more accurate calculation of river water recharge to groundwater. As a or t increases, the locations of the monitoring wells gradually move away from the riverbank. Therefore, well placement should be determined in consideration of site-specific stratigraphic lithology and river flow duration. This study provides a technical method for the design of groundwater level monitoring sections along riverbanks.