with 
To create a stochastic MODFLOW simulation using parameter zonation, you follow these steps:
First define your zones using key values.
Define parameters that link with your zones.
Select the Stochastic Simulation option from the Global Options dialog.
Select the Parameter Randomization option from the Stochastic Options dialog.
Choose whether you want to use the Random Sampling or Latin Hypercube randomization approaches in the parameters dialog.
Save and Run your model.
View the different model results using the Project EXplorer.
Further analyze the results using the Risk Analysis Wizard.
Random Sampling is the most widely used approach for generating multiple random model simulations. GMS supports both normal and uniform distributions.
A normal distribution can be defined as:
with
where σ is the standard deviation, μ is the mean, and x is the value being sampled. A uniform distribution can be defined as:
with
where α and β are the bounds of the parameter value x.
To set up the Random Sampling, you need to specify the mean, standard deviation, and upper and lower bounds for each parameter. Finally, you choose how many realizations you want to generate.
The Latin Hypercube randomization approach is a method that tries to efficiently probe the probability space for each parameter in a simulation in such a way that there is at least one simulation that represents every probability area for each parameter.
First, we specify the number of segments for each parameter. The total probability, defined by a distribution, mean, standard devation, and upper and lower bounds, is divided up into parts with equal probability (area). GMS then generates a random parameter value so that there is one value that lies within each probability segment.
This is repeated in a combinatorial fashion for each parameter so that there are
number of simulations, where n is the number of parameters and P is the number of segments for the ith parameter. For example, if there were three parameter with four, four and five segments, the number of model runs would be as follows:
Using the Latin Hypercube method has the benefit of needing a fewer number of runs to achieve the same level of confidence than the number required for the Monte Carlo approach because we have guaranteed that the entire probability range will be explored.
Related Links:
Stochastic Modeling