Detecting systemic change in a land use system by Bayesian data assimilation

A spatially explicit land use change model is typically based on the assumption that the relationship between land use change and its explanatory processes is stationary. This means that model structure and parameterization are usually kept constant over the model runtime, ignoring potential systemic changes in this relationship resulting from societal changes. We have developed a methodology to test for systemic changes and demonstrate it by assessing whether or not a land use change model with a constant model structure is an adequate representation of the land use system given a time series of observations of past land use. This was done by assimilating observations of real land use into a land use change model, using a Bayesian data assimilation technique, the particle filter. The particle filter was used to update the prior knowledge about the model structure, i.e. the selection and relative importance of the explanatory processes for land use change allocation, and about the parameters. For each point in time for which observations were available the optimal model structure and parameterization were determined. In a case study of sugar cane expansion in Brazil, it was found that the assumption of a constant model structure was not fully adequate, indicating systemic change in the modelling period (2003-2012). The systemic change appeared to be indirect: a factor has an effect on the demand for sugar cane, an input variable, in such a way that the transition rules and parameters have to change as well. Although an inventory was made of societal changes in the study area during the studied period, none of them could be directly related to the onset of the observed systemic change in the land use system. Our method which allows for systemic changes in the model structure resulted in an average increase in the 95% confidence interval of the projected sugar cane fractions of a factor of two compared to the assumption of a stationary system. This shows the importance of taking into account systemic changes in projections of land use change in order not to underestimate the uncertainty of future projections.