# Contaminant Transport

## Analysis of contaminant transport in an aquifer

All the figures below are generated using `examples/contamination/contamination.jl`

.

### Model setup

There are 20 monitoring wells.
Each well has 2 measurement ports: shallow (3 m below the water table labeled `a`

) and deep (33 m below the water table labeled `b`

).
Contaminant concentrations are observed for 50 years at each well.
The contaminant transport is solved using the `Anasol`

package in Mads.

### Unknown model parameters

- Start time of contaminant release $t_0$
- End time of contaminant release $t_1$
- Advective pore velocity $v$

### Reduced model setup

Analysis of the data from only 2 monitoring locations: `w13a`

and `w20a`

.

### Example model solution

Model parameter values:

- $t_0 = 4$
- $t_1 = 15$
- $v = 40$

### Model calibration

A calibration match between observations and model predictions obtained by model inversion:

### Prior parameter uncertainties

Probabilistic distributions of the prior parameter uncertainties are:

- $t_0$ = Uniform(0, 10)
- $t_1$ = Uniform(5, 40)
- $v$ = LogUniform(0.1, 200)

Spaghetti plots representing the prior uncertainties (note that the uncertainties are not constrained by the observed data):

The observation data are plotted as red dots.

### Bayesian global sensitivity analysis

Histograms and scatter plots of the Bayesian MCMC results:

### Posterior parameter uncertainties

Spaghetti plots representing the posterior uncertainties:

Note that the parameter uncertainties are constrained by the observation data. The observation data are plotted as red dots.

### eFAST global sensitivity analysis

eFAST has proven to be one of the most reliable methods among the existing variance-based techniques for quantification of parameter sensitivity (Saltelli, 2004; Saltelli & Bolado, 1998; Saltelli et al., 2000; Saltelli et al., 1999).

Total and main sensitivity indices over time for monitoring wells w13a and w20a:

The differences between main and total effect estimates suggest correlations among the parameters.

### Saltelli's global sensitivity analysis

Classical Saltelli's (Sobol's) global sensitivity analysis.

Total and main sensitivity indices over time for monitoring wells w13a and w20a:

There are differences between eFAST & Saltelli estimates. The eFAST results should be considered more reliable.