Multivariate bias corrections of mechanistic water quality model predictions

Water quality networks usually do not include observations on a continuous timescale over a long period. Statistical models that use streamflow and mechanistic models that use meteorological information and land-use are commonly employed to develop continuous streamflow and nutrient records. Given the availability of long meteorological records, mechanistic models have the potential to develop continuous water quality records, but such predictions suffer from systematic biases on both streamflow and water quality constituents. This study proposes a multivariate bias correction technique based on canonical correlation analysis (CCA) - a dimension reduction technique based on multivariate multiple regression - that reduces the bias in both streamflow and loadings simultaneously by preserving the cross-correlation. We compare the performance of CCA with linear regression (LR) in removing the systematic bias from the SWAT model forced with precipitation and temperature for three selected watersheds from the Southeastern US. First, we compare the performance of CCA with LR in removing the bias in SWAT model outputs in predicting the observed streamflow and total nitrogen (TN) loadings from the Water Quality Network (WQN) dataset. We also evaluate the potential of CCA in removing the bias in SWAT model predictions at daily and monthly time scales by considering the LOADEST model predicted loadings as the predictand for CCA and LR. Evaluation of CCA with the observed dataset and at daily and streamflow time scales shows that the proposed multivariate technique not only reduces the bias in the cross-correlation between streamflow and loadings, but also improves the joint probability of estimating observed streamflow and loadings. Potential implications of the proposed bias-correction technique, CCA, in water quality forecasting and management are also discussed.