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### 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

### Conclusion

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.

The phenomenon external to an area of interest affects what goes on inside.