Generating crop sequences in land-use models using maximum entropy and Markov chains

Farm management models often produce average crop shares over a number of years, whereas models from the natural sciences often require inputs of sequences of crops grown on a specific field over several years. In interdisciplinary modelling, this difference can be a relevant obstacle. To bridge this gap, an approach is presented that allows disaggregating results from farm management models to the level required by many natural science models. The approach presented includes two methodological innovations: first, minimum cross entropy is used to ensure a unique solution when modelling a linear programming model at the field level, even when objective and constraint coefficients are identical for different fields. Second, the use of a calibrated Markov chain approach allows the creation of land-use sequences that are closer to the linear programming model's results than an unconditional stochastic simulation would be. The calibrated Markov chain makes use of a prior matrix of transition probabilities that can be empirically derived. Both simulations and analytical calculations with case study data show that the variances of the Markov chain approach are systematically lower than those yielded by a simple stochastic simulation approach. The approach introduced in this paper can improve the coupling of farm-level economic models with natural science models at the field level.