#### Residual Analysis

Assessing the goodness-of-fit is a crucial step in inverse modeling. If the goodness-of-fit criterion suggests that the model is an unlikely match to the data, then the estimated parameter set is bound to be meaningless. **iTOUGH2** performs a detailed residual analysis which includes:

- Residual plot
- Statistics of residuals (mean, median, variance, absolute error, bias)
- Statistical model test
- Covariance matrix of calculated system response and residuals
- Normalized residuals
- Influence function
- Outlier identification
- Contribution of each data set and data type to the objective function

#### Estimation Error Analysis

The covariance matrix of the estimated parameter set is calculated to assess estimation uncertainty. The error analysis in **iTOUGH2** contains the following elements:

- Covariance matrix of estimated parameters
- Correlation matrix of estimated parameters
- Correlation chart
- Direct correlations between pairs of parameters
- Eigenanalysis of covariance matrix
- Measure of overall parameter sensitivity and parameter independence
- Correction procedure to account for non-linearities

#### Uncertainty Propagation Analysis

Uncertainty in the parameters entering a **TOUGH2** model lead to uncertainties in the model predictions. Given the distributions of the parameters considered uncertain, **iTOUGH2** calculates prediction uncertainty using one of the methods listed below. An application is described in *James and Oldenburg* [1997].

- Linear uncertainty propagation analysis
- Monte Carlo simulations; the predefined covariance matrix of correlated parameters is accurately reproduced using Empirical Orthogonal Functions.