Application of Karhunen-Loève Transform Algorithms in Hydrogeological Parameter Compression: A Comparative Study

ABSTRACT This paper proposes a parameter compression method using the Karhunen-Loève Transform (K-L) to reduce the computational burden of parameter inversion in groundwater models. Two spatial distributions of hydraulic conductivity (K) were generated using Kriging interpolation and Sequential Gaussian Simulation (SGS), and the K-L transform was applied to reduce their dimensionality. The method’s generality was assessed by varying model boundaries, extreme values of K, and simulation periods. The results showed that sequentially adding different boundary conditions resulted in high accuracy in model output. The model was most accurate when K values were within the range of 50-100 m/d, and its performance decreased as the range of K expanded. The model also exhibited high accuracy across various time periods within a single stress period. Dimensionality reduction through Kriging-KL and SGS- KL resulted in high accuracy of model-simulated heads, with R2 values exceeding 0.80 and 0.98 respectively. Overall, the K-L transform efficiently reduces parameter dimensions without compromising model performance. SGS-KL showed greater robustness under varying parameters, indicating its suitability for complex groundwater systems. This study contributes to efficient groundwater model inversion and provides valuable insights into the characteristics of groundwater systems.