Before we classify models, a note on what requirements a process must meet to be called a spatial model, requiring construction using a GIS:
- There is variation in variable(s) across geographic space
- Results of modeling change when location changes
Several main types of spatial models:
- Static models
Static models border on being an analysis by our earlier definition, but they usual involve some abstraction through an algorithm that justifies classifying them as a model. Static models represent a system at a single point in time. A great example of a static model is the famous Universal Soil Loss Equation (USLE):
where A denotes the predicted erosion rate, R is the Rainfall and Runoff Factor, K is the Soil Erodibility Factor, LS is the Slope Length Gradient Factor, C is the Crop/Vegetation and Management Factor, and P is the Support Practice Factor.
USLE doesn’t strictly meet the two criteria needed to call it a spatial model: changing the points at which A is evaluated doesn’t change result. Despite this weakness, USLE is best analyzed as a spatial model because it’s inputs vary with space, and are best visualized as a function of geography.
Here’s a story map illustrating how USLE can be derived from GIS data: https://storymaps.arcgis.com/stories/718ed18ce5de41708e9525cfb22ec2d2
- Individual or Aggregate models
Individual models forecast the behavior of each constituent part of a model: the earlier LA traffic example would be an individual model, where the modeler is attempting to predict the behavior of each individual driver during an evacuation.
These are often called agent-based models (ABMs). See below for example of structure of a tsunami evacuation ABM for Seaside, oregon. Note how GIS inputs are fitlered throguh agent-based decision filters before producing mapped output.
Aggregate models, in contrast, are too complex to simulate the behavior of each constituent. Think of a groundwater contamination model: it would be computationally impractical to simulate the behavior of each molecule of water in the aquifer. So instead groundwater models typically simulate water’s behavior as a continuous fluid. See this example of the DRASTIC groundwater model for an idea of how this kind of aggregation works:
- Cellular models
Where the above aggregate model structure needs raster data inputs or requires raster data outputs, we call it a cellular model. Famous example of cellular models –> urban growth forecasts, first pioneered by Keith Clarke.
Example of cellular modle from one of Clarke’s classsic papers
- Cartographic models
This is yet another flavor of aggregate models, whereby the cellular model is represented by map algebra expressions. You know what I mean when I say map algebra: remember in our last lab, how you used the Raster Calculator to average together two different rasters? You were performing map algebra analysis. For cartographic models, you are designing a chain of such processes, sometimes dynamically updating or iterating over the outputs.