SYMPOSIA PAPER Published: 01 January 1996

Model Validation and Uncertainty Analysis — An Example Using a Nitrate Percolation Model


Model validation and uncertainty analysis are demonstrated using a model previously developed for estimating nitrate-nitrogen (nitrate) concentrations in percolation water from land application of sewage sludge. The objectives are to demonstrate alternate validation techniques and to analyze uncertainty associated with model use following validation. Field data from three published sludge application studies and two separate methods are used for the validation. The first method, point validation, is accomplished by inserting mean values into the model to make point predictions. Model accuracy is then assessed by calculating coefficient of determination (r2), relative error and standard error. Statistical accuracy is tested using the Wilcoxon Signed Rank Test. The second method, statistical validation, uses Monte Carlo simulation to obtain distributions of model predictions. The hypothesis that field data represent reasonable samples from the distribution of model predictions is tested by checking whether observed values are within a range bounded by the 5 and 95 percent quantiles of the distribution. Both validation methods demonstrate that the land application model generally overestimates nitrate concentrations. Point validation provides quantitative values that can be compared with industry standard values for predictive models. Stochastic validation, on the other hand, allows uncertainty in model input to be considered during the validation process. Monte Carlo simulation is used to identify which model input parameters are the largest contributors to the uncertainty in model predictions. During successive simulations, individual random variables are set equal to their mean values. The decrease in the variance of model predictions is assumed to be the amount of uncertainty attributable to the random variable that had been set constant. This uncertainty analysis demonstrates that the rate of organic mineralization generally accounts for more than 50 percent of the uncertainty in model predictions.

Author Information

Mummert, MC
R. E. Wright Environmental, Inc., Middletown, Pennsylvania
Price: $25.00
Contact Sales
Reprints and Permissions
Reprints and copyright permissions can be requested through the
Copyright Clearance Center
Developed by Committee: D18
Pages: 187–200
DOI: 10.1520/STP38386S
ISBN-EB: 978-0-8031-5563-3
ISBN-13: 978-0-8031-2021-1