River Water‐Quality Concentration and Flux Estimation Can be Improved by Accounting for Serial Correlation Through an Autoregressive Model. Issue 11 (25th November 2019)

• Record Type: Journal Article
• Authors: Zhang, Qian; Hirsch, Robert M.
• Is Part Of: Water resources research. Volume 55:Issue 11(2019)
• Page Start: 9705
• Page End: 9723
• Publication Date: 2019-11-25
• Subjects: flux estimation -- autocorrelation -- autoregressive model -- Kalman filter -- WRTDS -- river water‐quality monitoring; Hydrology -- Periodicals; 333.91
• DOI: 10.1029/2019WR025338
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: Accurate quantification of riverine water‐quality concentration and flux is challenging because monitoring programs typically collect concentration data at lower frequencies than discharge data. Statistical methods are often used to estimate concentration and flux on days without observations. One recently developed approach is the Weighted Regressions on Time, Discharge, and Season (WRTDS), which has been shown to provide among the most accurate estimates compared to other common methods. The main objective of this work was to improve WRTDS estimation by accounting for the autocorrelation structure of model residuals using the first‐order autoregressive model (AR1). This modified approach, called WRTDS‐Kalman Filter (WRTDS‐K), was compared with WRTDS for six constituents including nitrate‐plus‐nitrite (NOx ), total phosphorus, total Kjeldahl nitrogen, soluble reactive phosphorus, suspended sediment, and chloride. Near‐daily concentration records at nine sites were used to generate subsets through Monte Carlo sampling for five different sampling scenarios. Results show that WRTDS‐K provided generally better daily estimates of concentration and flux than WRTDS under these sampling scenarios for all constituents, especially NOx . The degree of improvement is strongly affected by the underlying sampling scenario, with WRTDS‐K gaining more advantage when more samples are available, and hence more residuals can be exploited. The performance of WRTDS‐K depends on the AR1 coefficient (ρ) and that relationship varies with constituents and sampling scenarios. These results provided recommendations on the optimal ρ for each constituent and sampling scenario. Overall, WRTDS‐K has the potential for broad applications to monitoring records elsewhere, as demonstrated by a pilot application to Chesapeake Bay tributaries. Key Points: Estimation of daily constituent concentrations and fluxes can be improved by accounting for the serial correlation in model residuals Model performance depends on the lag‐1 autoregressive coefficient and the optimal coefficients were identified for six constituents The proposed approach for concentration and flux estimation has the potential for broad applications to river monitoring records elsewhere