A Bayesian hierarchical framework for emulating a complex crop yield simulator

Emulation of complex computer simulations have become an effective tool in the exploration of the behaviour of the simulated processes. Agriculture is one such area where the simulation of crop growth, nutrition, soil condition and pollution could be invaluable in any land management decisions. In this paper, we study output from the EPIC simulation model to investigate the behaviour of crop yield in response to changes in inputs such as fertilizer levels, soil, steepness, and other environmental covariates. We build a model for crop yield around a non-linear Mitscherlich Baule growth model to make inferences about the response of crop yield to changes continuous input variables (fertiliser levels), as well as exploring the impact of categorical factor inputs such as land steepness and soil type. A Bayesian hierarchical approach to the modelling was taking for mixed inputs, requiring Markov Chain Monte Carlo simulations to obtain samples from the posterior distributions, to validate and illustrate the results, and to carry out model selection. Our results highlight a strong response of yield to nitrogen, but surprisingly a weak response to phosphorus and also shows the substantial improvement of the model after adding factor effects response to maximum yield for this particular simulator configuration and catchment.