Recent analyses of hydraulic conductivity data showed that, although the hydraulic conductivity values vary significantly in space, the variation is not entirely random, but correlated in space. Such a correlated nature implies that the parameter values are not statistically independent in space and they must be treated as a stochastic process, instead of as a single random variable.
A. Watch the video below and answer the questions that follow.
Video 1: Different realizations of plume migration in a stochastic K field with lnK variance = 1.0. and a small correlation scale. Mode setup: size of model: 200 x 50m; initial plume size: 10 x 10m; time-step: 1 day.
Video 2: Different realizations of plume migration based on a conditional random field generator (condition points shown in pink). . Mode setup: size of model: 100x 600m; initial plume size: 100 x100m.
- Why is it so difficult to predict contaminant transport in the field using a traditional deterministic approach?
- Why is that solute plume distribution realizations are so sensitive to small scale heterogeneities, while the head distributions for different realizations are - for all practical purposes, essentially the same?
- What is the relationship between variability and uncertainty?
- How does spatial variability in hydraulic conductivity translate into uncertainty in groundwater seepage velocity and contaminant plume distribution?
- How can one systematically analyze solute transport in a risk-based, probabilistic framework?
B. Develop a MAGNET model that can reproduce the above animations, generating multiple likely realizations of conductivity, flow, and solute plume distributions, and perform a sensitivity analysis of predicted plume migration with respect to:
- lnK variance
- correlation scales
MAGNET/Modeling Hints:
Write a 1 page memo discussing the predictability of solute transport in heterogeneous media and how Monte Carlo simulation can be systematically used for risk-based decision making in the presence of uncertainty.
- You may follow the model set-up described in the animation caption above.
- Choose a porosity to use for each realization
- Choose a mean hydraulic conductivity to use for each realization
- Use a zone feature of the entire aquifer area to assign the hydraulic conductivity as a random field
- Use line features as prescribed head boundaries to generate the head difference from the left edge to the right edge of the model.