The Equatorial Cylindrical Equidistant (ECE) projection is perhaps the most popular projection for researchers working with global scale data. The ECE projection has many aliases including: "Plate-Caree", "simple cylindrical", "lat/lon", and "unprojected". There is no single projection that best suits all purposes. When projecting a map, image, or other data, there are certain tradeoffs. Users of polar data may prefer a polar projection, while users of tropical data may prefer an equatorial projection. If the spatial area of features is of primary interest (e.g., comparing the area covered by sea ice to that of open water), users will want an equal-area projection. If the shape of features is more important (for navigation), users may want a conformal projection.
The popularity of the ECE projection is due to simple transformation functions from (x, y) to (lat, lon) and vice versa. Researchers and developers with limited cartographic experience find the ECE easier to work with because it is the only projection in which trigonometric functions (cos(0) and sin(90)) are no longer relevant. Transformation functions are straightforward and linear. In the simplest case, transformations for a 360x180 Cartesian grid centered at the origin are:
Larger grids just introduce a scale factor.
Graphical applications are a bit more difficult because the screen coordinate system is not centered on the origin. However, transformations are still linear, with scale and shift introducing minor complications. With a left-handed coordinate system (origin in the upper left corner, y positive downward, and x positive to the right), the transformations are:
Apart from simple transformations, the ECE projection has few desirable properties. The ECE projection is neither conformal nor equal-area, thus, NSIDC generally does not use the ECE projection or produce data in ECE grids. However, because of its popularity, we do offer ECE grids as an output option in the Polar Spatial Query (PSQ) tool. We feel it is important for researchers to understand the limitations of the ECE grids. For more detailed information on limitations and advantages of the ECE and other grids, see: EASE-Grid: A Versatile Set of Equal-Area Projections and Grids.
The ECE projection is defined as
r = r0 + C/360 * lon
s = s0 + C/180 * lat
h = 1.0
k = 1.0/cos(lon)
The cylindrical equidistant map is defined as true at at the equator
where:
The values of C, r0, and s0 are determined by the grid that is chosen to overlay the projection.
A grid is always defined in relation to a specific map projection. It involves the same parameters that define a transparent piece of graph paper overlain on a flat map, anchored at the map origin. The following four elements completely describe a grid:
Any number of grid definitions can therefore be used to describe the effect of changing the "graph paper" (e.g., using fewer columns or rows, a higher resolution, anchoring the map origin to the center of the grid, etc.).
An array of gridded data consists of one data element for each grid "cell" or lattice point. The user has complete flexibility to define the meaning of each grid cell value, based on the most appropriate binning technique for those data and applications.
The ECE grid definitions in the PSQ interface have cell resolutions defined in degrees. On a spherical earth, the latitude resolution (in km) along any meridian is the same as the the longitude resolution along the equator. But the longitude resolution along the parallels decreases to zero at the poles. This map suffers from both areal and shape distortion as follows:
| Shape Distortion | Areal Distortion | |
|---|---|---|
| latitude | k/h | kh - 1 |
| 89 | 57 | 5630% |
| 80 | 6 | 476% |
| 60 | 2 | 100% |
| 45 | 1.4 | 41% |
| 0 | 1 | 0% |
By convention, grid coordinates (r,s) start in the upper left corner at cell (0,0), with r increasing to the right and s increasing downward. Rounding the grid coordinates up at .5 yields the grid cell number. Each grid cell is centered at grid coordinates (j,i) and bounded by: j -.5 <=r < j +.5, i -.5 <= s < i +.5.
Higher resolution grids are defined such that some latice coordinates are coincident and have a scalar multiple of the lower resolution latice coordinates. Consequently, the cells are nested. Thus, the (lat, lon) coordinate of the upper left corner of every ECE grid is (90, -180) and the lower right corner is (-90, 180).
The dimensions, center, and extent of the ECE grids are summarized below. It is important to remember that there is nothing data specific in these definitions.
LonRes = EqRes*cos(lat)?
| Equatorial Cylindrical Equidistant Grids | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Grid | Dimensions | Map Origin | Map Origin | Longitudinal resolution in km. (Reseq * cos(lat)) | |||||||
| Name | Width | Height | Column (r0) | Row (s0) | Latitude | Longitude | Equator | +- 45 degrees | +- 60 degrees | +- 80 degrees | +- 89 degrees |
| One degree | 360 | 180 | 179.5 | 89.5 | 0.0 | 0.0 | 111.20 | 78.63 | 55.60 | 19.31 | 1.94 |
| Half degree | 720 | 360 | 359.5 | 179.5 | 0.0 | 0.0 | 55.60 | 39.31 | 27.80 | 9.65 | 0.97 |
| Quarter degree | 1440 | 720 | 719.5 | 359.5 | 0.0 | 0.0 | 27.80 | 19.66 | 13.90 | 4.83 | 0.49 |
| Five minute | 4320 | 2160 | 2159.5 | 1079.5 | 0.0 | 0.0 | 9.27 | 6.55 | 4.63 | 1.61 | 0.16 |
| Thirty second | 43200 | 21600 | 21599.5 | 10799.5 | 0.0 | 0.0 | 0.93 | 0.66 | 0.46 | 0.16 | 0.02 |
Users interested in a more general discussion of projection characteristics and details on defining custom grids should also read Points, pixels, grids, and cells -- a mapping and gridding primer.