Discretization of Estuary to Represent Environment, Habitat and Facilitate Crab Movement

Given a closed boundary specification of the Neuse, the estuary is discretized into a series of triangles by applying an external mesh generation program (NETGEN written by Joachim Schoeberl available at http://www.hpfem.jku.at/netgen/). The initial set of coarse triangles is read into the model and refined (Bänsch 1991) to create a series of nested conforming triangles at different levels (Fig. A1). For our purposes, the advantages of this approach are that it allows representation of more complex domains than is possible with rectangular basis elements, the nested conforming triangulation facilitates the crab movement algorithm (Appendix A.5.4) by enabling fast determination of which fine-level triangle a crab is on, and finally it allows a discrete representation of the continuous environmental variables. If required, this nested triangulation could also enable multigrid methods to be used to numerically solve more detailed partial differential equation models (e.g., Braess 1997) of the environmental variables.

The coarsest discretization in the nested triangulation is constructed to contain the fewest possible triangles while still adequately representing the estuary. The nested triangulation used consists of four refinement levels representing 89, 218, 498 and 1079 triangles with each triangle having an average unscaled area (Appendix A.6) of $\approx$ $2.5\times 10^6$, $1.0\times 10^6$, $4.5\times 10^5$, $2.1\times 10^5$ m$^2$, respectively. The degree of refinement is chosen based on the degree of spatial resolution desired for environment variables, clam, and crab densities.