Evaluating desirable geometric characteristics of Discrete Global Grid Systems: Revisiting the Goodchild criteria Matthew Gregory 1 , A Jon Kimerling 1 , Denis White 2 and Kevin Sahr 3 1 Oregon State University 2 US Environmental Protection Agency 3 Southern Oregon University
34
Embed
Evaluating desirable geometric characteristics of Discrete Global Grid Systems: Revisiting the Goodchild criteria Matthew Gregory 1, A Jon Kimerling 1,
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Evaluating desirable geometric characteristics of Discrete Global Grid Systems:
Revisiting the Goodchild criteria
Matthew Gregory1, A Jon Kimerling1, Denis White2 and Kevin Sahr3
1Oregon State University2US Environmental Protection Agency
3Southern Oregon University
Objectives
Develop metrics to address desirable shape characteristics for discrete global grid systems (DGGSs)
Characterize the behavior of different design choices within a specific DGGS (e.g. cell shape, base modeling solid)
Apply these criteria to a variety of known DGGSs
The graticule as a DGGS
commonly used as a basis for many global data sets (ETOPO5, AVHRR)
well-developed algorithms for storage and addressing
suffers from extreme shape and surface area distortion at polar regions
has been the catalyst for many different alternative grid systems
Equal Angle 5° grid (45° longitude x 90° latitude)
DGGS Evaluating Criteria
Topological checks of a grid system Areal cells constitute a complete tiling of the globe A single areal cell contains only one point
Geometric properties of a grid system Areal cells have equal areas Areal cells are compact
Metrics can be developed to assess how well a grid conforms to each geometric criterion
Intercell distance criterion
on the plane, equidistance between cell centers (a triangular lattice) produces a Voronoi tessellation of regular hexagons (enforces geometric regularity)
classic challenge to distribute points evenly across a sphere
most important when considering processes which operate as a function of distance (i.e. movement between cells should be equally probable)
Points are equidistant from their neighbors
A
B
D
C
Cell center
Cell center
Cell wall midpoint criterion
derived from the research of Heikes and Randall (1995) using global grids to obtain mathematical operators which can describe certain atmospheric processes
criterion forces maximum centrality of lattice points within areal cells on the plane
The midpoint of an edge between any two adjacent cells is the midpoint of the great circle arc connecting the
centersof those two cells
Cell wall midpoint ratio =length of d
length of BD
d
Midpoint of arc between cell centers
Midpoint of cell wall
Center as defined by method
Maximum centrality criterionPoints are maximally central within areal cells
Maximum Centrality Metric1. Calculate latitude/longitude of points
on equally-spaced densified edges
2. Convert to R3 space
3. Find x, y, z as R3 centroid
4. Normalize the centroid to the unit sphere
5. Convert back to latitude/longitude
6. Find great circle distance (d) between this point and method-specific center
Asymptotic behavior of normalizing statistic DSS has lowest maximum centrality
measures as centroids are coincident with cell centers by definition
Snyder method has relatively large offsets along the radial axes
Tesselating shape seems to have little impact on the standardizing statistic
General Results
Asymptotic relationship between resolution and normalized measurement allows generalization
Relatively similar intercell distance measurements for triangles, hexagons and diamonds implies aggregation has little impact on performance for Platonic solid methods
Generally, projective DGGSs performed unexpectedly well for cell wall midpoint criterion
Implications and Future Directions
Grids can be chosen to optimize one specific criterion (application specific)
Grids can be chosen based on general performance of all DGGS criteria
Study meant to be integrated with comparisons of other metrics to be used in selecting suitable grid systems
Study the impact of different methods of defining cell centers
Extend these metrics to other DGGSs (e.g. EASE, Small Circle)