Tobler’s First Law of Geography
“Everything is related to everything else, but near things are more related than distant things.”
This is the first law of Geography introduced by Waldo R. Tobler’s in 1969.
This concept applies to pollution, noise, soil sciences and countless phenomena.
Let’s examine two ways how to measure Tobler’s First Law of Geography – semi-variograms and autocorrelation.
Semivariograms as Graphs
If you look 1 meter ahead, the terrain elevation is very likely to be the same. When you look 5 meters ahead, chances are that the ground elevation is similar… but may start to vary. But when you look 100 meters away, elevation varies more to the point that they aren’t related.
Often used in kriging interpolation, semi-variograms are useful for understanding patterns related to distance. Semi-variograms take 2 sample locations and denotes the distance between points as h.
In the x-axis, it plots distance (h) in lags, which are just grouped distances. Using pairs of sample locations, it measures the variance between the response variable (in the y-axis) and the distance between those two points in the x-axis.
As distance increases, the response variable becomes less predictable and are less related. Closer things are more predictable and has less variability. Overall, semi-variograms explain Tobler’s First Law of Geography by graphing a variable by close and far distances.
READ MORE: Semi-Variogram: Nugget, Range and Sill
Spatial Autocorrelation and Moran’s I
Tobler’s First Law of Geography can also be described numerically with statistical dependence or autocorrelation. Spatial autocorrelation helps understand how similar closer objects to other nearby objects. Moran’s Index (or simply Moran’s I) is used to measure spatial autocorrelation.
Moran’s I can be classified as: positive, negative and no spatial auto-correlation.
While positive spatial autocorrelation indicates similar values cluster in a map, negative spatial autocorrelation is when dissimilar values cluster together in a map. A value of 0 for Moran’s I typically indicates no autocorrelation.
Using spatial autocorrelation, geographers understand whether or not diseases and other phenomena are isolated. Moran’s I can imply the phenomena is spreading with dispersion or clustering.
READ MORE: Spatial Autocorrelation and Moran’s I in GIS
Tobler’s First Law of Geography is based on cost distance or distance decay, where there is greater hindrance for two places farther apart.
For example, people are less likely to travel greater distance to patron a store as described in Huff’s Gravity Model.
As distance increases, the greater the hindrance for transportation costs and purchase.
Now, bonus points to anyone who can describe the lesser-known Second Law of Geography in the comment section below.