Variable update strategy to improve water quality forecast accuracy in multivariate data assimilation using the ensemble Kalman filter

Data assimilation in complex water quality modeling is inevitably multivariate because several water quality variables interact and correlate. In ensemble Kalman filter applications, determining which variables to include and the structure of the relationships among these variables is important to achieve accurate forecast results. In this study, various analysis methods with different combinations of variables and interaction structures were evaluated under two different simulation conditions: synthetic and real. In the former, a synthetic experimental setting was formulated to ensure that issues, including incorrect model error assumption problem, spurious correlation between variables, and observational data inconsistency, would not distort the analysis results. The latter did not have such considerations. Therefore, this process could demonstrate the undistorted effects of the different analysis methods on the assimilated outputs and how these effects might diminish in real applications. Under synthetic conditions, updating a single active variable was found to improve the accuracy of the other active variables, and updating multiple active variables in a multivariate manner mutually enhanced the accuracy of the variables if proper ensemble covariance and observation data consistency were ensured. The results of the real case indicated a weakened mutual enhancement effect, and the methods in which variable localization were applied yielded the best analysis results. However, the multivariate analysis methods produced more accurate forecasting results, indicating that these methods could be superior. Therefore, it is suggested that multivariate analysis methods be considered first for water quality modeling, and the application of variable localization should be considered if significant spurious correlations and data inconsistency are present. [Display omitted] •Multivariate DA performance in water quality modeling was investigated.•Synthetic test was used to clarify superiority among analysis methods in EnKF.•Mutual enhancement effect among state variables was presented explicitly.•Multivariate analysis may be superior to univariate analysis on forecast accuracy.•Update strategy in multivariate DA was proposed considering variable localization.