Aggregate Measures of Watershed Health from Reconstructed Water Quality Data with Uncertainty

Abstract

Risk-based measures such as reliability, resilience, and vulnerability (R-R-V) have the potential to serve as watershed health assessment tools. Recent research has demonstrated the applicability of such indices for water quality (WQ) constituents such as total suspended solids and nutrients on an individual basis. However, the calculations can become tedious when time-series data for several WQ constituents have to be evaluated individually. Also, comparisons between locations with different sets of constituent data can prove difficult. In this study, data reconstruction using a relevance vector machine algorithm was combined with dimensionality reduction via variational Bayesian noisy principal component analysis to reconstruct and condense sparse multidimensional WQ data sets into a single time series. The methodology allows incorporation of uncertainty in both the reconstruction and dimensionality-reduction steps. The R-R-V values were calculated using the aggregate time series at multiple locations within two Indiana watersheds. Results showed that uncertainty present in the reconstructed WQ data set propagates to the aggregate time series and subsequently to the aggregate R-R-V values as well. This data-driven approach to calculating aggregate R-R-V values was found to be useful for providing a composite picture of watershed health. Aggregate R-R-V values also enabled comparison between locations with different types of WQ data.