Uncertainty and spatial analysis in wheat yield prediction based on robust inclusive multiple models

Reliable prediction of wheat yield ahead of harvest is a critical challenge for decision-makers along the supply chain. Predicting wheat yield is a real challenge for better agriculture and food security management. Modeling wheat yield is complex and challenging, so robust tools are needed. The main aim of this study is to predict wheat yield using an advanced ensemble model. A multilayer perceptron model (MLP) was combined with optimization algorithms to determine MLP parameters as the first step in the study. Several optimization algorithms were used as optimizers, including Particle Swarm Optimization (PSO), Honey Badger Algorithms (HBA), Sine-Cosine Algorithms (SCA), and Shark Algorithms (SA). Meteorological data were inserted into models. Next, the outputs of optimized MLP models were incorporated into an inclusive multiple MLP model (IMM). A new hybrid gamma test was used to determine the most appropriate input combination. A hybrid gamma test was created by coupling the HBA with GT. This paper introduces a robust IMM model, develops an MLP model using optimization algorithms, develops a new hybrid gamma test, uses Generalized Likelihood Uncertainty Estimation (GLUE) to analyze uncertainty, and presents a spatial map of wheat yield prediction. Based on the Gamma Test analysis, mean air temperature (T_a), wind speed (WS), relative humidity (RH), evapotranspiration (ET), and precipitation (P) were the most important input parameters for reliable and accurate winter wheat yield predictions. At the testing level, the IMM model decreased the mean absolute error (MAE) of the MLP-HBA, MLP-SCA, MLP-SA, MLP-PSO, and MLP models by 47%, 52%, 55%, 58%, and 61%, respectively. In the study, the uncertainty of models based on input data was significantly lower than that of the model parameters. In addition, the GLUE analysis revealed that the wheat yield predictions were more stable and confident by considering the ensemble IMM technique. The pattern of root mean square error (RMSE) maps demonstrated that higher error produces in the northeast of Urmia Lake. The developed framework provides insight into rainfed yield responses to weather conditions and is simple and inexpensive. Accurate and reliable wheat yield prediction is essential for agricultural monitoring and food policy analysis.