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Geographic Standard Deviation
As you might now expect, the Cartesian definition of standard deviation provided in the standard MATLAB function std is also inappropriate for most geographic data. Depending upon your purpose, you may want to use the separate geographic deviations for latitude and longitude provided by the function stdm, or the single standard distance provided in stdist. Both methods measure the deviation of points from the mean position calculated by meanm.
The Meaning of stdm
The stdm function handles the latitude and longitude deviations separately.
The function returns two deviations, one for latitudes and one for longitudes.
Latitude deviation is a straightforward standard deviation calculation from the mean latitude (mean parallel) returned by meanm. This is a reasonable measure for most cases, since a degree of latitude always has the same arc length.
Longitude deviation is another matter. Simple calculations based on sum-of-squares angular deviation from the mean longitude (mean meridian) are misleading. The arc length represented by a degree of longitude at extreme latitudes is significantly smaller than that at low latitudes.
The term departure is used to represent the arc length distance along a parallel of a point from a given meridian. For example, assuming a spherical planet, the departure of a degree of longitude at the Equator is a degree of arc length, but the departure of a degree of longitude at a latitude of 60° is one-half a degree of arc length. The stdm function calculates a sum-of-squares departure deviation from the mean meridian.
If you want to plot the one-sigma lines for stdm, the latitude sigma lines are parallels. However, the longitude sigma lines are not meridians; they are lines of constant departure from the mean parallel.
This handling of deviation has its problems. For example, its dependence upon the logic of the coordinate system can cause it to break down near the poles. For this reason, the standard distance provided by stdist is often a better measure of deviation. The stdm handling is useful for many applications, especially when the data is not global. For instance, these potential difficulties would not be a danger for data points confined to the country of Mexico.
The Meaning of stdist
The standard distance of geographic data is a measure of the dispersion of the data in terms of its distance from the geographic mean. Among its advantages are its applicability anywhere on the globe and its single value:
In short, the standard distance is the average, norm, or cubic-norm of the distances of the data points in a great circle sense from the mean position. It is probably a superior measure to the two deviations returned by stdm except when a particularly latitude- or longitude-dependent feature is under examination
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