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A geodesic grid allows local to global assimilation of ecologically significant information at its own level of granularity. [ 13 ] When modeling the weather , ocean circulation, or the climate , partial differential equations are used to describe the evolution of these systems over time.
In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the locally [a] shortest [b] path between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection.
Mathematically it is a space partitioning: it consists of a set of non-empty regions that form a partition of the Earth's surface. [1] In a usual grid-modeling strategy, to simplify position calculations, each region is represented by a point, abstracting the grid as a set of region-points. Each region or region-point in the grid is called a cell.
The MODLAND Integerized Sinusoidal Grid, based on the sinusoidal projection, is a geodesic grid developed by the NASA's Moderate-Resolution Imaging Spectroradiometer science team. [ 4 ] See also
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English: Part a shows a rectilinear grid in the horizontal plane. Part b shows a curvilinear grid in the horizontal plane. Part c shows a z-level grid structure in the vertical plane. Part d shows a s-level grid structure in the vertical plane. This figure is taken from Delandmeter and van Sebille 2019 (Delandmeter, P. and van Sebille, E.:
A grid-based spatial index has the advantage that the structure of the index can be created first, and data added on an ongoing basis without requiring any change to the index structure; indeed, if a common grid is used by disparate data collecting and indexing activities, such indices can easily be merged from a variety of sources.
This is analogous to the Earth's surface, where the geodesic between two points along a great circle is the shortest route only up to the antipodal point; beyond that, there are shorter paths. Beyond a conjugate point, a geodesic in Lorentzian geometry may not be maximizing proper time (for timelike geodesics), and the geodesic may enter a ...