GIS has evolved into a full-featured environment for a range of modeling approaches to analyze and predict the behavior of complex, spatially- and temporally-varying systems. Given data and empirical or analytical rules for system behavior, GIS can be used to implement models predicting the evolution or expected state of the system due to the process(es) in operation.

Modeling: Empirical

Observed MA snowfall vs. elevation
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Observed and predicted MA snowfall

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Observational data can be combined and analyzed to understand empirically whether there are any significant relationships among two or more variables. Such empirical relationships can then be used to build a predictive model for locations lacking observations.

These images show the relationship between average annual snowfall and elevation in Massachusetts for the handful of climate stations with long enough records to provide meaningful values, and a statewide prediction of snowfall based on the linear model fitted to the observed data. Note that other (non-linear) models could be explored in this way, and models with additional factors other than elevation could also be considered. The empirical relationship can be modeled with a variety of tools (within or outside of the GIS software); the prediction based on the model is implemented within the GIS to produce the spatial output.