Variograms. Brian Klinkenberg Geography. To get there, we’ll consider. Correlation Tobler’s first law of geography Spatial autocorrelation Three dimensions of scale Units of observation Regionalized variables Variograms. Correlation. What is correlation? What does it measure?
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What is correlation? What does it measure?
"All things by a mortal power,
Near or far
To each other linked are,
That thou canst not stir a flower
Without the troubling of a star"
Francis Thompson, "The Mistress of Vision" 1897
In mathematical terms, the semi-variogram:
Where h represents a distance vector.
Recall that the variance is expressed as:
In graphical terms:
Why ‘semi’-variogram? As the lag distance approaches infinity,
the expression converges to twice the variance. Therefore, dividing by 2 means that the sill approximates the variance.