Diagnostic tools to evaluate a spatial land change projection along a gradient of an explanatory variable

This paper proposes a method to quantify the goodness-of-fit of a land change projection along a gradient of an explanatory variable, by classifying pixels as one of four types: null successes, false alarms, hits, and misses. The method shows: (1) how the correctness and error of a land change projection are distributed along the gradient of an explanatory variable, (2) how the gradient of the explanatory variable relates to the stationarity of the land transition processes, and (3) how to use the insights from the previous two points to search for additional explanatory variables. The paper illustrates the method through a case study that applies the model Geomod in Central Massachusetts, USA. Results reveal that the model predicts more than the observed amount of change on flat slopes and less than the observed amount of change on steep slopes. One reason for these types of errors is that the land change process during the calibration interval is different than the process during the prediction interval with respect to slope. The method allows modelers to use the validation step as a diagnostic tool to search for potentially influential missing variables and to gain insight into land transition processes. The technique is designed to be applicable to a variety of types of land change models.