One of the most restrictive attributes of a Cartesian grid is the limited variability in resolution. By the purest definition, a Cartesian grid consists of square cells, meaning a constant resolution over the entire domain. A method that can be employed to support variable resolution involves the creation/use of what can be called a Telescoping Grid (sometimes referred to as a Quad Tree). A Quad Tree is a two-dimensional recursive spatial subdivision. Each region can be subdivided into four child regions. In the SMS application, the regions are always square or rectangular.
The CMS-Flow model is the only numeric engine currently supported by the SMS which allows computation on a telescoping grid.
The generation of a telescoping grid involves:
- A base grid
- Refinement features
The SMS generates a telescoping grid from a user defined base grid. Define this base grid with the approach that is used in any other grid generation operation in the SMS consisting of the definition of a grid frame to define grid extents and either a base cell dimension or number of cells in each of the coordinate directions (I,J). The base grid parameters are specified as a grid frame properties or when using Map→2D Grid.
Choosing Base Grid Cell Size
Normally this is a single value for both dimensions (I,J) that represents the typical variation in the geometry. Specifying a value of 50 m indicates that the grid will have a depth every 50 m and any feature smaller than about 100 m will be smoothed away. If a single Cartesian grid is used, this dimension must be small enough to capture the smallest desired feature. For a variable cell grid it must be small enough to capture any feature along the row or column. For a telescoping grid, this can be a general value to represent the general geometric shape of the domain. In some situations there may be justification to have a larger base cell size in one direction that another. For example, all of the features may be aligned with a coastline and the cells could generally be elongated in that direction. This situation would be rare, so a square base cell size is a general recommendation.
Theoretically a refinement feature could be a single point, a linear feature (arc) or a region (polygon). Future capabilities may allow for a variety of refinement features, but currently the SMS telescoping grid generation capability allows defining feature polygons that enclose areas for which a specific resolution is desired. Assign a "maximum grid cell size" as an attribute on the polygon (double-click on the polygon and assign polygon attributes).
When the SMS generates the telescoping grid, when a cell is generated, the polygon containing the cell centroid is found (if it exists). If either cell dimension is larger than the maximum specified size for the polygon, the cell is split into four sub-cells and the process repeated.
Note, when rectangular cells are being generated (as specified on the base grid), this constraint will force the larger dimension of the cell to be smaller than the specified maximum size, so the cell may be significantly smaller than the specified size.
Choosing a Maximum Grid Cell Size
The maximum grid cell size for a polygon should be based on a physical length. One example would be a channel that must be represented in the domain. If the base cell size is 250 m, but the channel has a width of approximately 100 m, the channel would not be represented by the base grid. By specifying a cell size of 20 m for a polygon enclosing the channel, it is possible to enforce approximately five cells to represent the shape of the channel. The feature being represented may be a structure such as a jetty, a natural feature like a channel, or a numerically represented feature such as an eddy current. Geometric features can be detected before generating any grids. Numerical features may require modifications based on preliminary simulations.
Impact of Feature Size on Base Cell Size
In addition to the limitation noted above between a single maximum size and a two dimensional cell, the relationship between the selected base cell size and the maximum specified sizes can also cause what appear to be overly refined grids.
Since the cells are created in discrete increments (half of the parent cell dimension), the actual generated size may be smaller than the specified target simply due to binary limitations. For example, if a maximum size of 5 is specified, and the base cell size is 30, the first acceptable cell size that meets the criteria of 5 is actually 3.75 (30/2^3 - 30, 15, 7.5, 3.75). In this case, 3.75 is only 75% of the specified maximum, resulting in cells that are 75% smaller than the user specified acceptable resolution (in the larger direction).
This perceived difference can be reduced by specifying a compatible base cell size. In the previous example, a base cell size of 20 (instead of 30) would result in a cell size of 5 (20/2^2), exactly matching the specified maximum. However, since there are two dimensions to the base cell size, and only one target size, and there can be multiple refinement polygons, each with a specified maximum cell size, the relationship can seem complex.
The SMS includes a tool for telescoping or quad tree grids to compute an ideal base cell size. This option appears in the Grid Frame dialog which is accessible either by right-clicking on the grid frame or when using Map→2D Grid. This tool will increase the base cell sizes defined for a telescoping grid so that the largest dimension will be a multiple of the smallest specified grid size. The specified aspect ratio of the cells will be maintained.
- Note: Telescoping Cartesian grids have been replaced with a more memory efficient Quadtree structure in SMS 12.0.
SMS – Surface-water Modeling System
|Modules:||1D Grid • Cartesian Grid • Curvilinear Grid • GIS • Map • Mesh • Particle • Quadtree • Raster • Scatter|
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