Stochastic analysis of groundwater based on scale factor

The ergodic hypothesis will become invalid in a small domain.Therefore,the modified covariance functions of aquifer parameters are evaluated from the ensemble average,and an improved numerical model is developed based on the K-L (Karhunen-Loeve)expansion and chaos expansion.This study analyzes the impact of the domain scale on groundwater flow. The results show that the investigation scale causes the change of the eigenvalue and eigenfunction series,and the investigation scale impacts the total head,water content and velocity in different degree.The variances of total head and velocity increase as the investigation scale increases,and the mean of total head,velocity and water content are scaled independent.