Neupauer Roseanna M, Wilson John L
Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904, USA.
Ground Water. 2004 Mar-Apr;42(2):175-89. doi: 10.1111/j.1745-6584.2004.tb02666.x.
Backward location and travel time probabilities can be used to characterize known and unknown sources or prior positions of ground water contamination. Backward location probability describes the position of the observed contamination at some time in the past; backward travel time probability describes the amount of time prior to observation that the contamination was released from its source or was at a particular upgradient location. The governing equation for backward probabilities is the adjoint of the governing equation for contaminant transport, but with new load terms. Numerical codes that have been written to solve the forward equations of contaminant transport, e.g., the advection-dispersion equation, can also be used to solve the adjoint equation for location and travel time probabilities; however, the interpretation of the results is different and some new approximations must be made for the load terms. We present the governing equations for backward location and travel time probabilities, and provide appropriate numerical approximations for these load terms using the cell-centered finite difference method, one of the most popular numerical methods in ground water hydrology. We discuss some additional numerical considerations for the backward model including boundary conditions, reversal of the flow field, and interpretation of the results. We illustrate the implementation of the backward probability model using hypothetical examples in one- and two-dimensional domains. We also present a three-dimensional application of a pump-and-treat remediation capture zone delineation at the Massachusetts Military Reservation. The illustrations are performed using MODFLOW-96 for flow simulations and MT3DMS for transport simulations.
反向位置概率和运移时间概率可用于表征已知和未知的地下水污染源或污染的先前位置。反向位置概率描述了过去某个时间观测到的污染位置；反向运移时间概率描述了在观测之前污染从其源头释放或处于特定上游位置的时间。反向概率的控制方程是污染物输运控制方程的伴随方程，但有新的源项。已编写的用于求解污染物输运正向方程（如平流 - 弥散方程）的数值代码，也可用于求解位置概率和运移时间概率的伴随方程；然而，结果的解释有所不同，并且必须对源项进行一些新的近似。我们给出了反向位置概率和运移时间概率的控制方程，并使用单元中心有限差分法（地下水水文学中最流行的数值方法之一）对这些源项提供了适当的数值近似。我们讨论了反向模型的一些其他数值考虑因素，包括边界条件、流场反转和结果解释。我们使用一维和二维区域的假设示例说明了反向概率模型的实现。我们还展示了马萨诸塞军事保留地的一个抽水 - 处理修复捕获区划定的三维应用。这些示例使用MODFLOW - 96进行水流模拟，MT3DMS进行输运模拟。
