A Multivariate Approach to Accounting for Input Data Uncertainty in Water Quality Assessment

Water Quality Index (WQI) is one of the most popular mathematical approaches for assessing the quality of water resources, which converts several physical, chemical, and biological characteristics of water into a single number representing the condition of water quality. Given the fact that designing optimal treatment strategies and the protection of water quality requires confidence in WQI evaluation, a comprehensive uncertainty analysis will ensure that the uncertainty is reflected in the estimation of WQI, thereby providing reliable assessments. Among various sources, input data uncertainty is a considerable and unavoidable source of uncertainty in WQI, which has been infrequently accounted for in previous studies. Factors such as measurement errors or the use of model-based data both have the potential to produce this type of uncertainty and bias in estimations. In this study, we present a new multivariate framework for uncertainty analysis that is based on uncertainty-aware principal component analysis (UPCA) and hierarchical clustering (HC). We applied our framework to uncertainty analysis of WQI for the South Florida watershed over seven years (۲۰۱۵-۲۰۲۱) and ۱۹ stations. Furthermore, we used a global sensitivity analysis approach to identify water quality parameters that mostly contribute to the uncertainty in WQI. Overall, results reveal how data uncertainty significantly affects traditional, widely-used principal component analysis outcomes. Also, we found that the cluster with the highest level of uncertainty is created with the most significant influences from total phosphate, total hardness and pH. Moreover, alkalinity and nitrogen have the lowest effect. Results indicated the effectiveness of the proposed framework for input data uncertainty analysis that could be replicated for other watersheds.