This has been a question which I didn’t find a perfect answer for years: How to express that two maps are correlated in a mathematic way?

I also noticed that someone has asked this question in the ResearchGate community: https://www.researchgate.net/post/How_to_statistically_compare_two_maps

I came into this question when my mentor asked me to provide some correlation coefficient for the statement in my paper. Then I have to think how I can actually calculate the coefficient.

For year, whenever someone talk about correlation efficient, it usually refers to the the Pearson correlation coefficient: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient The Pearson correlation coefficient, however, does not care or specify what kind of data you are dealing with. There are many other different ways to calculate and express correlation, but they are more or less similar.

In Earth science, most data we are dealing with are time series data and spatial data. In GIS, theoretically a data is meaningless if it does not have the location.

To simplify our problem, especially for researcher not familiar with GIS, the location information is often ignored. And in some cases, time is not important as well.

For example, we can calculate the correlation between the weight and height of people without time and location.

In some cases, time is an invisible hand in fact. For example, we are supposed to measure the weight and height simultaneously or close enough. So even time is not a factor in the equation, it is an important factor in the experiment.

But what happens when we add location information, such as a map? What if a map is a vector, such as the state map? Let’s define it as Type A. What if a map is a raster, such as temperature/elevation? Let’s define it as Type B. Some map is raster, but it has been artificially defined, such as soil type and vegetation type. Let’s define it as Type C.