large patch or several smaller patches. If the goal is to measure the quantity of carbon emission, then the configuration of the patches is probably less important. It can be tricky to select a metric that is mathematically rigorous, intellectually assessable, intuitively interpretable, and practically useful (see Box 3.1). A necessary best practice is to match the measurement of the model with the purpose of the modeling exercise for the particular application. This is an area that requires more research.
Whatever metrics the modeler adopts, it is important to use the metrics to
The Challenge of Selecting a Pattern Metric
Selecting an appropriate pattern metric that can indicate process is a challenge. Many modelers are interested in measuring the output of maps based on the spatial pattern metrics of the maps, such as number of patches. The figure below contrasts three cases where we compare the land change between two time points. All three cases have one patch of forest at time 1 and demonstrate a process where deforestation occurs on the edge between forest and nonforest. However, this single process generates different patterns due to interaction between various initial configurations and quantities of change. In this example, case A has a different initial configuration than cases B and C, while case C has less deforestation than cases A and B. Cases A and C have one forest patch at time 2, while case B has two forest patches. This illustrates how the number of patches can be sensitive to an interaction between the configuration of the initial landscape and the quantity of change.