Uncertainty in extrapolations of predictive land-change models

This paper gives a technique to extrapolate the anticipated accuracy of a prediction of land-use and land-cover change (LUCC) to any point in the future. The method calibrates a LUCC model with information from the past in order to simulate a map of the present, so that it can compute an objective measure of validation with empirical data. Then it uses that observed measurement of predictive accuracy to anticipate how accurately the model will predict a future landscape. The technique assumes that the accuracy of the model will decay to randomness as the model predicts farther into the future and estimates how fast the decay in accuracy will occur based on prior model performance. Results are presented graphically in terms of percentage of pixels classified correctly so that nonexperts can interpret the accuracy visually. The percentage correct is budgeted by three components: agreement due to chance, agreement due to the predicted quantity of each land category, and agreement due to the predicted location of each land category. The percentage error is budgeted by two components: disagreement due to the predicted location of each land category and disagreement due to the predicted quantity of each land category. Therefore, model users can see the sources of the accuracy and error of the model. The entire analysis is computable for multiple resolutions, so users can see how the results are sensitive to changes in scale. We illustrate the method with an application of the land-use change model Geomod to Central Massachusetts, where the predictive accuracy of the model decays to 90% over fourteen years and to near complete randomness over 200 years.