Statistical Surfaces & Interpolation

A statistical surface is any geographic entity that can be thought of as containing a Z value for each X,Y location. A statistical surface can be any numerically measurable attribute that varies continuously over space, such as temperature and population density (interval/ratio data).

Spatial Sampling is the process of selecting points (of an attribute) from a continuous field

• Statistical samples allow the inference of population characteristics from a subset (that is cheap & easy to get)
• Interpolated surfaces are dependent (in part) on the sampling scheme used to create them

Condition for sampling: the variation between the sampling points should be constant and gradual

• For curves, we have to collect more data points
• Density of points and the resolution of points are important

Spatial sampling designs designed based on the variation the data:

• Simple random sampling
• Systematic sampling
• Systematic sampling with local random application
• Contour sampling / adaptive sampling

Geostatistics is a class of statistics used to analyze and predict the values associated with spatial or spatiotemporal phenomena. It incorporates the spatial (and in some cases temporal) coordinates of the data within the analyses.

Spatial Autocorrelation

Spatial autocorrelation is a measure of the degree to which geographic objects tend to be clustered together in space or dispersed.

Tobler’s first law: Formulation of the concept of spatial autocorrelation

Measurement of spatial autocorrelation is the Moran Index (I):

• -1: very strong negative spatial correlation where dissimilar values cluster together in a map
• 0: no spatial autocorrelation (random arrangement)
• 1: very strong positive spatial correlation (similar values cluster together in a map)