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A spheroid is a model of the earth represented by either a sphere of a specified radius or a prolate ellipsoid with specified values for the equatorial and polar radii.
A datum specifies the dimensions of a specific spheroid, a point of origin, an azimuth from the origin to a second point, and the spatial orientation of the spheroid relative to the earth.
A Geographic Coordinate System (GCS) assigns unique coordinate values to locations on the surface of a spheroid. The system is usually based on latitude and longitude and is fully specified by a unit of measure (typically degrees), a prime meridian and a datum (e.g. WGS-84).
A Projected Coordinate System (PCS) is a combination of a map projection, projection parameters, and an underlying GCS that determines the set of x,y coordinates (typically in meters) assigned to a map.
A projected raster data image consists of a raster image for a specified PCS consisting of a specified number of columns and rows, at specified horizontal and vertical resolutions (typically meters per cell), each cell of which is a specified data type (e.g. a single precision floating-point number), with the upper left corner of the upper left cell at a specified PCS x,y coordinate.
The GeoTIFF specification as well as many GIS applications that depend on GeoTIFF for importing projected raster data (including ArcGIS) appear only to support the geolocation of a projected raster data image for which the spheroid associated with the underlying GCS (e.g. WGS-84) is the same spheroid used to define the PCS (e.g. an elliptical sinusoidal projection based on the WGS-84 spheroid). Put another way, the dimensions of the projection spheroid are not specified as projection parameters but simply as inherited parameters of the underlying GCS.
For all Land MODIS level 3 projected products, the underlying GCS is WGS-84, but the spheroid used for the projection is either a sphere of radius 6371007.181 meters in the case of the sinusoidal products (e.g. MOD10A1), or a sphere of radius 6371228.0 meters in the case of the polar EASE-Grid azimuthal equal-area products (e.g. MOD29P1D). This means that a valid GeoTIFF cannot be created for these products in their "native" projection: the data must first be reprojected into a grid using the WGS-84 spheroid as the projection spheroid before a valid GeoTIFF may be created.
The implications of the above situation will be discussed in terms of current MODIS products and software tools, with suggestions for possible future enhancements to both.
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