A Phenology-guided Bayesian-CNN (PB-CNN) framework for soybean yield estimation and uncertainty analysis

Abstract

Large-scale crop yield estimation is important for understanding the response of agriculture production to environmental forces and management practices, and plays a critical role in insurance designing, trade decision making, and economic planning. The empirical models (e.g., deep learning models) have been increasingly utilized for estimating crop yields with the ability to take into account a range of yield predictors and complex modeling relationships. Yet empirical estimation of crop yields still faces important challenges, particularly in accommodating spatio-temporal crop phenological development patterns as well as tackling the heterogeneity of a diversity of yield predictors. The different types of uncertainties associated with empirical yield estimations have seldom been explored. The objective of this study is to develop a Phenology-guided Bayesian-Convolutional Neural Network (PB-CNN) framework for county-level crop yield estimation and uncertainty quantification, with soybean in the US Corn Belt as a case study. The PB-CNN framework comprises three key components: Phenology Imagery construction, multi-stream Bayesian-CNN modeling, as well as feature importance (i.e., yield predictor and phenological stage) and predictive uncertainty analysis (i.e., aleatoric and epistemic uncertainty). With the innovative integration of critical crop phenological stages in modeling the crop yield response to a heterogeneous set of yield predictors (i.e., satellite-based, heat-related, water-related, and soil predictors) as well as the associated uncertainties, the developed PB-CNN framework outperforms three advanced benchmark models, achieving an average RMSE of 4.622 bu/ac, an average R2 of 0.709, and an average bias of −2.057 bu/ac in estimating the county-level soybean yield of the US Corn Belt in testing years 2014–2018. Among the yield predictor groups, the satellite-based predictor group is the most critical in soybean yield estimation, followed by the water- and heat-related predictor groups. Throughout the growing season, the soybean blooming to dropping leaves phenological stages play a more crucial role in modeling the soybean yield. The soil predictor group as well as the early growing stages can improve the model estimation accuracy yet potentially brings more uncertainties into the yield estimation. The further uncertainty disentanglement indicates that the dominant uncertainty in yield estimation is the aleatoric uncertainty, mainly stemming from the fluctuations and variations inherent in the modeling input observations. The PB-CNN framework largely enhances our understanding of the complex soybean yield response to varying environmental conditions across crop phenological stages as well as associated uncertainties for more sustainable agricultural development.