Simple relationships between residence time and annual nutrient retention, export, and loading for estuaries

Simple mathematical models are derived from mass balances for water and transported substance to provide insight into the relationships between import, export, transport, and internal removal for nonconservative substances in an estuary. Extending previous work, our models explicitly include water and substance inputs from the ocean and are expressed in terms of timescales (i.e., mean residence time and the timescale for net removal). Steady-state, timescale-based expressions for ratios of export to import, retention to import, and net export to loading, as well as for loading and annually averaged concentration, are provided. The net export:loading model explains the underlying mechanisms for a well-known empirical relationship between fractional net export and residence time derived by other authors. Although our simplified models are first-order approximations, the relative importance of physical and biochemical processes influencing export or retention of a substance can be assessed using mean residence time and the timescale for net removal. Assumptions employed in deriving the simplified models (e.g., well-mixed, dynamic steady state) may not be met for real estuaries. However, model application to Chesapeake Bay for 1985–2012 demonstrates that interannual variations in total nitrogen (TN) net export:loading can be evaluated, and annual nutrient loadings can be well estimated using numerically modeled time-varying mean residence time, observation-based mean concentration, freshwater inflow, and an appropriately estimated removal timescale. Our model shows that net fractional export of TN loading ranges from 0.3 to 0.5 over the 28-yr period. The models can be employed for other substances and water bodies if the underlying assumptions are applicable.