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Massachusetts Estuary Project(MEP) <br /> Linked Waterslied Embayment Model Peer Review <br /> 5.2.2.1.Estuarine Hydrodynamic Model <br /> Key Issue 1 -Are the RMA2 and RMA4 Numerical Models Appropriate/Adequate for Computing <br /> TMDLs for Cape Cod Estuaries and Bays? <br /> In the analysis of the adequacy of these models there are four sub-issues;namely,1.Is the vertically- <br /> averaged assumption appropriate?2.Are the numerical grids adequate?3.Is mass conserved? 4.Are <br /> computational times excessive? <br /> Is the vertically-averaged assumption appropriate?There are numerous fully three-dimensional(31)) <br /> models that could have been selected for application by the SMAST Team. The RMA2 and RMA4 <br /> models are based on the assumption that vertical variations in the salinity and flow fields are negligible. <br /> The SMAST Team has presented data demonstrating that this assumption is valid for all but one(i.e. <br /> Pleasant Bay)of the estuaries and bays for which TMDLs will be developed. There are some kettle <br /> ponds in Pleasant Bay where vertical stratification can occur at times. However,these ponds generally <br /> have a layer of heavy saline water very near the bottom that perhaps acts as a barrier to the exchange of <br /> nitrogen from the bottom sediments with the water column but do not significantly result in the <br /> generation of residual currents due to gravitational circulation. <br /> A full 3D hydrodynamic and mass transport model would theoretically give more accurate computations <br /> of flow and mass concentration fields. However,the Panel concludes that the two-dimensional(2D) <br /> approach is adequate and more preferable because it is more cost-effective for scenario analyses of <br /> nitrogen loads needed by policy and management planning. <br /> Are the numerical grids adequate?The RMA2 and RMA4 models are based on the finite element method <br /> for solving the governing equations of motion in RMA2 and the conservation of mass equation for a <br /> constituent such as nitrogen in RMA4. The other commonly employed solution method is referred to as <br /> the finite difference method. With the finite element method, one assumes the solution and then attempts <br /> to minimize the error when the assumed solution is inserted into the governing equations. The most <br /> common form of the assumed solution is a polynomial. In the case of RMA2 and RMA4,a quadratic <br /> polynomial is assumed. With the finite difference solution method,the derivatives in the governing <br /> equations are approximated by finite differences. <br /> There are two major differences in the two most common solution methods. The fast is that finite <br /> element models generally utilize unstructured grids,whereas the finite difference method utilizes <br /> structured grids. With structured grids,there is an order to the labeling of the computational cells. In <br /> other words,each cell knows its neighbor by an(I,J,K)accounting. With an unstructured grid,a <br /> connectivity table must be constructed so that each computational element knows its neighbor elements. <br /> A major advantage of the finite element method of solution and the resulting unstructured numerical grid <br /> is that physical features such as the geometry of the water body,interior channels,etc. can be more <br /> accurately resolved than with a structured grid representing the water body. The Panel considers this a <br /> major strength of using the RMA2 and RMA4 models. <br /> Is mass conserved?The second major difference between the two commonly employed solution methods <br /> concerns the conservation of mass. If a staggered structured numerical grid is employed with the finite <br /> difference method such that the value of a constituent such as nitrogen is computed in the center of a <br /> computational cell and transport(water velocity)is specified on the cell boundaries,mass is absolutely <br /> conserved. With the finite clement solution method,mass over the entire grid is also absolutely <br /> conserved. However,mass in the interior of the grid is not constrained to be absolutely conserved <br /> (Galland et al. 1991). When modeling water quality parameters,this is often a concern. However,the <br /> problem can be minimized through the construction of a grid that accurately resolves the bathymetry of <br /> the water body and gradients in the variable being computed, e.g.;nitrogen. In the November 14,2011 <br /> meeting with the SMAST Team, including Applied Coastal and Research Engineering,the concern about <br /> December 30,2011 <br />