Identifying a land use change cellular automaton by Bayesian data assimilation

Abstract

We present a Bayesian method that simultaneously identifies the model structure and calibrates the parameters of a cellular automaton (CA). The method entails sequential assimilation of observations, using a particle filter. It employs prior knowledge of experts to define which processes might be important in the system, and uses empirical information from observations to identify which ones really are and how these processes should be parameterized. In a case study for the São Paulo state in Brazil, we identify a land use change CA simulating sugarcane cropland expansion from 2003 to 2016. Eight annual observation maps of sugar cane cultivation are used, split over space and time for calibration and validation. It is shown that the identified CA can properly reproduce the observations, and has a minimum reduction factor of 3 in root mean square error compared to a Monte Carlo simulation without particle filter. In the part of the study area where no observational data are assimilated (validation area), there is little reduction in model performance compared to the part with observational data. So, incomplete datasets, regional land survey data, or clouded remote sensing images can still provide useful information for this particle filter method, which is an advantage because good quality land use maps are rare. Another advantage is that in our approach the output uncertainty encompasses errors from expert knowledge, model structure, parameters and observation (calibration) data. This can, in our opinion, be very useful for example to determine up to what future period the results are a secure basis for decisions and policy making.