Global random walk stochastic simulations for the assessment of the contamination risk in groundwater systems

地下水系统污染的可预测性将通过使用全局随机漫步方法（GRW）的随机模拟进行研究。为此目的，在高性能并行计算机上通过GRW模拟计算的运输实现的统计集合将用于估计遍历范围。后者由实际观测值与随机模型提供的预测值的均方根偏差定义，并在很大程度上量化遍历性。研究将集中于前渐近状态和由输运对初始溶质羽流的形状和尺寸的非线性依赖引起的记忆效应。基于Fokker-Plank和Itô方程的随机分析将被开发并用于解释随机模拟结果。为了提高计算效率，GRW算法也将被用作遍历模拟过程的一部分。该方法利用有限相关范围的地下水速度场地质统计模型的遍历性，通过对单一速度实现的模拟从空间平均推断输送统计。

The predictability of contamination in groundwater systems will be investigated via stochastic simulations using the Global Random Walk method (GRW). To this aim, statistical ensembles of transport realizations, computed by GRW simulations on high performance parallel computers, will be used to estimate ergodicity ranges. The latter are defined by the root mean square deviation of actual observables from predictions provided by stochastic models and quantify the ergodicity in a large sense. The investigations will focus on pre-asymptotic regime and on memory effects induced by the nonlinear dependence of transport on the shape and dimensions of the initial solute plumes. Stochastic analyses based on Fokker-Plank and Itô equations will be developed and used for the interpretation of the stochastic simulations results. To increase the computational efficiency, the algorithm GRW also will be used as part of an ergodic simulations procedure. This approach exploits the ergodicity of the geo-statistical model of the groundwater velocity field with finite correlation range by inferring transport statistics from space averages over simulations done for a single velocity realization.