An inverse approach to estimate bacterial loading into an estuary by using field observations and residence time

Pathogen, whose abundance is often measured by the concentration of fecal indicator bacteria, is listed as the top cause of waterbody impairments in the US. An accurate estimation of the bacterial loading from watershed is thus fundamentally important for water quality management. Despite advances in watershed modeling, accurate estimation of bacterial load is still very challenging due to large uncertainties associated with bacterial sources, accumulation, and removal in the watershed. We introduce an inverse method using field-measured bacterial concentrations and numerical model-calculated residence time to estimate the bacterial loading from the drainage basin. In this method, an estuary is divided into multiple segments. Water and bacterial fluxes between neighboring segments are computed from a set of linear equations derived based on mass balance equation and the relationship between residence time and water fluxes. Loading to each segment can then be estimated by combining the computed water fluxes and observed bacterial concentrations. The approach accounts for seasonal and interannual variations in hydrodynamics due to tide, river discharge, and estuarine circulations. The method was applied to Nassawadox Creek, a sub-estuary of Chesapeake Bay, where Fecal Coliform concentrations at 46 stations were continuously monitored. The method is verified by the high consistency between estimated loadings and presumably known input loadings in numerical experiments with either constant or time-varying input loadings. With sparse observational data, the inversely estimated loadings agree well with the loadings from a previously calibrated watershed model, demonstrating the reliability of the method. The inverse approach can be used to cross-check the result of watershed models and assess changes in watershed condition. The method is also readily applicable to other types of materials, such as inorganic nutrients.