Estuarine water quality: One-dimensional model theory and its application to a riverine subtropical estuary in Florida

In this study, analytical solutions were found for nutrients and phytoplankton in an idealized one-dimensional estuary with tidally averaged conditions. Steady forcing conditions and first order kinetics were assumed for freshwater inflow, nutrients, and algal loading input. These analytical solutions consist of two parts, a steady state solution and a non-steady state solution. The steady state solution was determined for a typical advection-dispersion-reaction equation for a nonconservative constituent. For phytoplankton, the non-steady solution has exponential growth or decay depending on the difference between the net growth rate (μnet) and the flushing rate (f). When μnet is greater than f, exponential growth or algal bloom could occur; otherwise, it would be an exponential decay over the time scale of 1/(f- μnet). The steady state solution for phytoplankton predicted the chlorophyll maximum and its location, which would move downstream with increasing freshwater inflows, a phenomenon observed in field studies (Doering et al., 2006; Valdes-Weaver et al., 2006). When applied to the Caloosahatchee River Estuary, a shallow riverine estuary in southwest Florida, the steady state solution for phytoplankton was able to reasonably reproduce the general shape of observed longitudinal phytoplankton distribution. Consistent with the findings of a recent box model study (Sun et al., submitted), this one-dimensional model suggests that there may be important contributions from external loading of phytoplankton to downstream phytoplankton biomass. This finding can inform future improvement of more complex numerical models of estuarine eutrophication as well as practical water management strategies.