Collecting and
manipulating data
Data are collected by
sampling a population:
Population

Sample

Everybody
in Santa Barbara County

1,000
respondents in a telephone poll, 20 questions

Precipitation
in Colorado

450
rainfall "buckets" across the state

Africa

"Megaflyover", NGS, pictures every 20 seconds, georeferenced by lat/long

Ecology
biodiversity

Transects
and quadrats

From these samples we
can extrapolate, or "go beyond" the sample data
Example: from the 450 rainfall gauges
(points) we can make an isoline map of temperatures
and "thread" the isolines between sample
points. The location of the isoline is dependent on
the point values.
This is called interpolation:
Some forms of
extrapolation:
Interpolation


Inverse distance
weighting (the simplest
spatial interpolation method)

Earthworm prediction from IDW!

Spatial
autocorrelation for prediction (Tobler's Law)

"Everything is
related to everything else, but near things are more related"  Waldo Tobler, 1970

Spatial
smoothing

Smoothing linear features
Tobler's "pycnophylactic
method" for smoothing areas

Choropleth mapping (areal average,
raises "boundary problem")


Geographically
weighted regression (GWR)


