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A water quality model has four major components:

(1) The Equations: the mathematical formulation of the fundamental principles (e.g. that momentum and mass are conserved) and the empirical relationships that describe the effects of processes that are not entirely understood or included (e.g. how the rate of production of organic matter depends upon light and nutrient concentration); and

(2) The Numerical Methods: the equations are generally too complicated to solve analytically and approximate versions that can be solved using numerical algorithms are necessary; and

(3) The Geometry and Forcing Data: for each location and time that the model is to be used the details of the geometry (e.g. the shape of the estuary and locations of rivers etc.) must be defined and the variation in the meteorological and hydrological conditions (winds, light and river flow) must be prescribed; and

(4) The Computer Programs: the techniques for the solution of the approximate equations with the geometry and forcing data must be translated to instructions that can be executed by computers to create predictions.
In most water quality model The equations are divided into at least two groups, those that describe the physical processes (the evolution of density, currents and vertical mixing) and those that describe the biogeochemistry. However, these are linked because the transport processes move and mix the biogeochemical variables. Some models have a third set of equations that describe the transformations of organic matter and nutrients in the sediments.

SWEM (System Wide Eutrophication Model) is the name that is used to refer to the water quality model of Long Island Sound, the harbors of New York and New Jersey and the adjacent continental shelf. It is a specific set of equations, methods, geometry and forcing data all combined into two main programs. The equations and approximations for the physical processes use the ECOM hydrodynamic model (see http://www.hydroqual.com/ehst_ecomsed.html) and the equations and approximations for the biogeochemical processes are based on a model called RCA (see http://www.hydroqual.com/wr_rca.html).

The documentation for the most recent version of RCA (Release 3.0) is provided here:

RCA Release 3.0 Documentation

The best description of the benthic processes included in the SWEM model is provided in a report about water quality in Massachusetts Bay and Cape Cod Bays (The Bay Eutrophication Model) and it is provided here:
N-164-BEM and B-158 BEM 92-94.

SWEM was applied in a project to assess the consequences of upgrades to the Newtown Creek Water Pollution Control Plant in Brooklyn, NY, which discharges into the East River. The report of the formulation of water quality part of the model, and the calibration and verification of the predictions is provide here: G-176 SWEM.  Appendices to the report contain detailed graphical comparisons of observations and model predictions and are provided here: G-177 SWEM Appendix B, G-178 SWEM Appendix C.

An independent assessment of the sensitivity of the performance of SWEM in the simulation of dissolved oxygen in Long Island Sound and recommendations for improvements was reported by O’Donnell et al. 2010 and is provided here: O’Donnell et al., 2010 ReportFinal.pdf.