A variance-covariance matrix, often referred to as a covariance matrix, is a square matrix that provides covariances between pairs of elements of a random vector. A covariance matrix of model parameters describes the variance of each parameter and the covariance of that parameter with that of every other parameter. For cases in which parameters represent points in a spatial (or temporal) parameter field (e.g. pilot points), it is reasonable to expect that parameters which are spatially (or temporally) closer together are more likely to be similar than those which are far apart. A covariance matrix provides a means with which to characterizes this relationship.
The present document is a tutorial on how to construct covariance matrix files using PPCOV* utilities from the PEST Groundwater Utility suite. These covariance matrix files can be used for regularisation during calibration (see GMDSI tutorial on calibration), and to define parameter probability distributions prior to linear or nonlinear uncertainty analysis (see GMDSI tutorial on linear uncertainty analysis).