Improving Crop Model Inference Through Bayesian Melding With Spatially Varying Parameters

An objective for applying a Crop Simulation Model (CSM) in precision agriculture is to explain the spatial variability of crop performance and to help guide decisions related to the site-specific management of crop inputs. CSMs require inputs related to soil, climate, management, and crop genetic information to simulate crop yield. In practice, however, measuring these inputs at the desired high spatial resolution is prohibitively expensive. We propose a Bayesian modeling framework that melds a CSM with sparse data from a yield monitoring system to deliver location specific posterior predicted distributions of yield and associated unobserved spatially varying CSM parameter inputs. These products facilitate exploration of process-based explanations for yield variability. The proposed Bayesian melding model consists of a systemic component representing output from the physical model and a residual spatial process that compensates for the bias in the physical model. The spatially varying inputs to the systemic component arise from a multivariate Gaussian process, while the residual component is modeled using a univariate Gaussian process. Due to the large number of observed locations in the motivating dataset, we seek dimension reduction using low-rank predictive processes to ease the computational burden. The proposed model is illustrated using the Crop Environment Resources Synthesis (CERES)-Wheat CSM and wheat yield data collected in Foggia, Italy.