Groundwater Flow Determination Using an Interval Parameter Perturbation Method

Abstract

Abstract:Groundwater flow simulation often inevitably involves uncertainty, which has been quantified by a host of methods including stochastic methods and statistical methods. Stochastic methods and statistical methods face great difficulties in applications. One of such difficulties is that the statistical characteristics of random variables (such as mean, variance, covariance, etc.) must be firstly obtained before the stochastic methods can be applied. The dilemma is that one is often unclear about such statistical characteristics, given the limited available data.To overcome the problems met by stochastic methods, this study provides an innovative approach in which the hydrogeological parameters and sources and sinks of groundwater flow are represented by bounded but uncertain intervals of variables called interval of uncertainty variables (IUVs) and this approach is namely the interval uncertain method (IUM). IUM requires only the maximum and minimum values of the variable. By utilizing the natural interval expansion, an interval-based parametric groundwater flow equation is established, and the solution of that equation can be found. Using a hypothetical steady-state flow case as an example, one can see that when the rate of change is less than 0.2, the relative error of this method is generally limited to less than 5%; when the rate of change is less than 0.3, the relative error of this method can be kept within 10%. This research shows that the proposed method has smaller relative errors and higher computational efficiency than the Monte Carlo methods. It is possible to use this method to analyze the uncertainties of groundwater flow when it is difficult to obtain the statistical characteristics of the hydrogeological systems. The proposed method is applicable in linear groundwater flow system. Its validity in nonlinear flow systems such as variably saturated flow or unconfined flow with considerable variation of water table will be checked in the future.

Editorial of Special Issue “Advances in Groundwater Flow and Solute Transport: Pushing the Hidden Boundary”

“…Focusing on tackling the groundwater flow uncertainties issues, Dong et al [14] has proposed a new method using the Interval Parameter Perturbation (IPP) principle. The IPP method avoids the dilemma faced by many other statistical and stochastic methods in which the statistical characteristics (such as mean, variance, covariance, etc.)…”

“…of random variables of concerns must be known a priori, which is usually not feasible in real-world applications. The new IPP method used in Dong et al [14] did not require the complete statistical characteristics of the random variables. Instead, it only needed the bounded uncertain intervals of variables of concern.…”

A Novel Intelligent Inversion Method of Hydrogeological Parameters Based on the Disturbance-Inspired Equilibrium Optimizer

“…Determination of the hydrogeological parameters is one of the most important stages of scientific evaluation of the sustainability of groundwater resources and numerical simulation [1,2]. The hydrogeological parameters of aquifers are usually inversed using pumping tests in engineering [3,4].…”

Groundwater Flow Calculation Model and Neural Network Prediction Based on Groundwater Modeling System

“…With the rapid development of computer technology, generalized numerical simulation models based on groundwater flow systems have been widely applied in foreign studies [12,13]. In 1935, the appearance of the Theis formula had laid a foundation for the construction of unsteady flow models of groundwater flow systems [14]. After the 1970s, Chinese scholars began to study groundwater flow systems.…”