We analyzed the relationship between resolution and predictability and
found that while increasing resolution provides more descriptive info
rmation about the patterns in data, it also increases the difficulty o
f accurately modeling those patterns. There are limits to the predicta
bility of natural phenomenon at particular resolutions, and ''fractal-
like'' rules determine how both ''data'' and ''model'' predictability
change with resolution. We analyzed land use data by resampling map da
ta sets at several different spatial resolutions and measuring predict
ability at each. Spatial auto-predictability (P(a)) is the reduction i
n uncertainty about the state of a pixel in a scene given knowledge of
the state of adjacent pixels in that scene, and spatial cross-predict
ability (P(c)) is the reduction in uncertainty about the state of a pi
xel in a scene given knowledge of the state of corresponding pixels in
other scenes. P(a) is a measure of the internal pattern in the data w
hile P(c) is a measure of the ability of some other ''model'' to repre
sent that pattern.We found a strong linear relationship between the lo
g of P(a) and the log of resolution (measured as the number of pixels
per square kilometer). This fractal-like characteristic of ''self-simi
larity'' with decreasing resolution implies that predictability may be
best described using a unitless dimension that summarizes how it chan
ges with resolution. While P(a) generally increases with increasing re
solution (because more information is being included), P(c) generally
falls or remains stable (because it is easier to model aggregate resul
ts than fine grain ones). Thus one can define an ''optimal'' resolutio
n for a particular modeling problem that balances the benefit in terms
of increasing data predictability (P(a)) as one increases resolution,
with the cost of decreasing model predictability (P(c)).