Estimation bias in water-quality constituent concentrations and fluxes: A synthesis for Chesapeake Bay rivers and streams

Flux quantification for riverine water-quality constituents has been an active area of research. Statistical approaches are often employed to make estimation for days without observations. One such approach is the Weighted Regressions on Time, Discharge, and Season (WRTDS) method. While WRTDS has been used in many investigations, there is a general lack of effort to identify factors that influence its estimation bias. This work was aimed to (1) synthesize and compare WRTDS estimation bias for constituent concentrations and fluxes for rivers and streams in the Chesapeake Bay watershed (including headwater sites) and (2) identify controlling factors from five broad categories (watershed size, sampling practice, concentration and discharge conditions, land use, and geology). Five major constituents were considered, namely, suspended sediment (SS), total phosphorus (TP), total nitrogen (TN), orthophosphate (PO₄), and nitrate-plus-nitrite (NO_x). For both concentration and flux, estimation bias follows the general order of SS > TP > PO₄ > TN ≈ NO_x. Median TN and NO_x bias statistics were near zero, with an equal distribution of small positive and negative bias. TP, PO₄, and SS each showed a median positive bias across sites of <18% for flux and <7% for concentration. Particulate constituents, especially SS, tend to have larger bias at sites with smaller sampling frequencies, shorter sampling record lengths, and smaller watershed sizes. Results of multivariate models showed that both flux and concentration biases are most affected by concentration and discharge variabilities and the length of concentration record. In comparison, flux bias of particulate constituents is more affected by flow variability, whereas flux bias of dissolved constituents is more affected by concentration variability. Moreover, analysis using classification and regression trees provided additional information on how the factors affected flux bias: when all site-constituent combinations are considered, large flux biases are more likely associated with sites that have large concentration and discharge variabilities, small lengths of concentration record, and small sampling frequencies. These results may be useful for identifying sites with large biases, modifying monitoring practice at existing sites to reduce those biases, and choosing new monitoring locations in the Chesapeake watershed and beyond.

Keywords: Water quality, Flux bias, Nutrients, Sediment, WRTDS, Statistical estimation, River monitoring, Chesapeake Bay