Improving riverine constituent concentration and flux estimation by accounting for antecedent discharge conditions

Regression-based approaches are often employed to estimate riverine constituent concentrations and fluxes based on typically sparse concentration observations. One such approach is the recently developed WRTDS (“Weighted Regressions on Time, Discharge, and Season”) method, which has been shown to provide more accurate estimates than prior approaches in a wide range of applications. Centered on WRTDS, this work was aimed at developing improved models for constituent concentration and flux estimation by accounting for antecedent discharge conditions. Twelve modified models were developed and tested, each of which contains one additional flow variable to represent antecedent conditions and which can be directly derived from the daily discharge record. High-resolution (∼daily) data at nine diverse monitoring sites were used to evaluate the relative merits of the models for estimation of six constituents - chloride (Cl), nitrate-plus-nitrite (NOx), total Kjeldahl nitrogen (TKN), total phosphorus (TP), soluble reactive phosphorus (SRP), and suspended sediment (SS). For each site-constituent combination, 30 concentration subsets were generated from the original data through Monte Carlo subsampling and then used to evaluate model performance. For the subsampling, three sampling strategies were adopted: (A) 1 random sample each month (12/year), (B) 12 random monthly samples plus additional 8 random samples per year (20/year), and (C) flow-stratified sampling with 12 regular (non-storm) and 8 storm samples per year (20/year). Results reveal that estimation performance varies with both model choice and sampling strategy. In terms of model choice, the modified models show general improvement over the original model under all three sampling strategies. Major improvements were achieved for NOx by the long-term flow-anomaly model and for Cl by the ADF (average discounted flow) model and the short-term flow-anomaly model. Moderate improvements were achieved for SS, TP, and TKN by the ADF model. By contrast, no such achievement was achieved for SRP by any proposed model. In terms of sampling strategy, performance of all models (including the original) was generally best using strategy C and worst using strategy A, and especially so for SS, TP, and SRP, confirming the value of routinely collecting stormflow samples. Overall, this work provides a comprehensive set of statistical evidence for supporting the incorporation of antecedent discharge conditions into the WRTDS model for estimation of constituent concentration and flux, thereby combining the advantages of two recent developments in water quality modeling.