Multivariate Bias Correction Procedures for Improving Water Quality Predictions using Mechanistic Models

Water quality observations are usually not available on a continuous basis because of the expensive cost and labor requirements so calibrating and validating a mechanistic model is often difficult. Further, any model predictions inherently have bias (i.e., under/over estimation) and require techniques that preserve the long-term mean monthly attributes. This study suggests and compares two multivariate bias-correction techniques to improve the performance of the SWAT model in predicting daily streamflow, TN Loads across the southeast based on split-sample validation. The first approach is a dimension reduction technique, canonical correlation analysis that regresses the observed multivariate attributes with the SWAT model simulated values. The second approach is from signal processing, importance weighting, that applies a weight based off the ratio of the observed and model densities to the model data to shift the mean, variance, and cross-correlation towards the observed values. These procedures were applied to 3 watersheds chosen from the Water Quality Network in the Southeast Region; specifically watersheds with sufficiently large drainage areas and number of observed data points. The performance of these two approaches are also compared with independent estimates from the USGS LOADEST model. Uncertainties in the bias-corrected estimates due to limited water quality observations are also discussed.