Nonlinear Expression of Groundwater Head Interval Based on the Perturbation Method

Abstract

An investigation of a groundwater system often requires the prediction of the spatiotemporal distribution of groundwater heads, which determine the groundwater flow direction and magnitude, among other applications. How to quantify the uncertainty of groundwater flow has been an important issue of concern to hydrogeologists for more than 40 years, and many methods based on stochastic and statistical approaches have been proposed to resolve this issue, with considerable progress being made. However, the statistical characteristics of parameters (e.g., hydrogeological parameters, boundaries, and sources/sinks) are often difficult to obtain precisely in practical applications. From a perspective of the interval uncertainty of groundwater, this study proposes a nonlinear expression of the groundwater head interval (GHI) using an interval uncertainty approach to quantify the uncertainty of numerical simulations in groundwater flow. This study uses a steady-state groundwater flow example to analyze the computational effectiveness of the acquired expression of GHI. A comparison of the results with the equal interval continuous sampling method (EICSM) shows that when the changing rate (which is the ratio of the absolute change in the numerical value to the numerical value itself) of a hydrogeological parameter is no more than 0.2, the relative discrepancy of the obtained GHI in this study and EICSM is no more than 5%. When the changing rate is no more than 0.3, such a relative discrepancy can be controlled within approximately 10%. In general, the proposed method is computationally efficient and robust for quantifying GHI. Finally, the method of this study is applied successfully to a real case.