Townley, L.R., and Wilson, J.L. (1983), Conditional second moment analysis of groundwater flow: the cumulative effects of transmissivity and head measurements, International Conference on Groundwater and Man, Sydney, Australian Government Publishing Service, December 1983.

The accuracy of predictions of regional groundwater flow using large-scale numerical models is affected by errors in the model parameters which describe the spatial variability of aquifer properties, boundary conditions and inputs. The first and second moments (i.e., means and covariances) of predicted heads can be found to first order using the covariance of uncertain parameters and the sensitivities of heads to parameters. This paper illustrates the use of first order, second moment analysis as transmissivity and head measurements are progressively incorporated in the modelling procedure and better estimates of parameters are obtained. A hypothetical example is presented in which steady flow predictions are affected by uncertainty in the transmissivity field. Kriging is used to interpolate between sparse measurements of transmissivities and a generalised weighted least squares inverse procedure combines the kriged estimates and measurements of heads. The example clearly demonstrates the cumulative effects of additional measurements since the uncertainty in parameters and predicted heads progressively decreases.


Copyright © 2005 by Lloyd Townley
Last revised: 6 May 2005