Uncertainties in Digital-Computer Modeling of Ground-Water Basins

Abstract

Much future computer modeling of the responses of groundwater to water development stresses may be poorly done if the errors and limitations of digital models are not fully appreciated by groundwater hydrologists. Two digital models were constructed of the Tucson basin, one with 1,890 nodes of 1/4 square mile area each and one with 509 nodes of 1 square mile each. The starting point for the digital model was the 2-dimensional, linear, parabolic, time-and space-invariant differential equation of incompressible flow through porous media. An explicit finite-difference equivalent was determined, and a set of 1,890 equations were put in implicit form and solved on a computer in less than 20 seconds at a cost of 2.00 dollars. The errors associated with the model are discussed. In deciding what new data collected in the Tucson basin would give the most improvement in the digital model, a statistical decision theory approach was utilized in which expected opportunity loss and expected worth of sample were calculated for 5 variables. The data was computed using about 110 seconds of computer time, costing about 13.00 dollars. This technique has the advantage of including basin dynamics in estimating worth of additional data by means of using the digital model to compute all values of predicted and 'true' water levels included in the loss function.