User's guide of Proceessing Modflow 5.0

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6.7.2 An Example of Stochastic Modeling
Folder: \pm5\examples\misc\misc2\
Overview of the Problem
Aquifer remediation measures are often designed by means of groundwater models. Model
results are usually uncertain due to the imperfect knowledge of aquifer parameters. We are
uncertain about whether the calibrated values of parameters represent the real aquifer system.
We never know the actual small-scale distribution of some parameters, e.g. hydraulic
conductivity or recharge. Thus, all groundwater models involve uncertainty. Stochastic models
are often employed to take into accoung uncertainty. In the stochastic modeling, the model
parameters appear in the form of probability distributions of values, rather than as deterministic
sets.
We use the same aquifer described in chapter 2 to illustrate a conception of stochastic
modeling. Using a two-dimensional approach to model the aquifer, we may ultilize the Field
Generator to create lognormal correlated distributions of the horizontal hydraulic conductivity.
The mean horizontal hydraulic conductivity of the aquifer is equal to (4 × 0.0001 + 6 ×
-4
0.0005) / 10 = 3.4 × 10 m/s. The standard deviation is assumed to be F = 0.5. The correlation
length of 60m is used.
In chapter 2, the pumping rate of the well was determined such that the contaminated area
lies within the capture zone of the well. When realizations of the heterogeneous distribution of
hydraulic conductivity are introduced, it is obvious that the capture zone not always covers the
entire contaminated area. The safety criterion for the measure can be defined as the percentage
of the covered area in relation to the entire contaminated area. The expected value of the safety
criterion can be obtained from stochastic simulation.
Modeling Approach and Simulation Results
Using the Field Generator, lognormal distributions of the horizontal hydraulic conductivity are
generated and stored in ASCII Matrix files. First, each generated realization is imported into the
horizontal hydraulic conductivity matrix, then a flow simulation is performed. The capture zone
of the pumping well, as well as pathlines, are computed with PMPATH. The resulting safety
criterion is obtained by a Monte Carlo simulation. This implies that many realizations of the
parameter field are produced and used in the flow simulation.
Fig. 6.68 shows results of five realizations and the calculated mean safety criteria. Mean
6.7.2 An Example of Stochastic Modeling