Estimating the Impact of Climate Variables on Crop Yield Using Hierarchical Bayesian Models with Spatial and Temporal Dependencies

Project Abstract

This study develops a hierarchical Bayesian framework to quantify how climate variables influence crop yield while explicitly modeling spatial and temporal dependencies across diverse agro-ecological zones. Leveraging multi-level structures, the model accommodates heterogeneity in crop response due to soil type, management practices, and regional climatic regimes, enabling robust inference in data-sparse settings. We integrate high-resolution climate covariates (temperature, precipitation, vapor pressure deficit, solar radiation) with agronomic indicators (fertilizer application, irrigation, planting density) and remote-sensed soil moisture to capture both direct and indirect pathways affecting yield. Spatial dependence is modeled via conditional autoregressive priors on region-specific intercepts and slopes, allowing neighboring locations to share information and reflect local adaptation processes. Temporal dynamics are addressed through state-space components that distinguish year-to-year variability from long-term trends, while a temporal random effect captures autocorrelation in climate-crop responses. The hierarchical structure facilitates partial pooling across spatial units, mitigating overfitting and improving predictive performance in data-limited districts. We allow non-linear response relationships using flexible spline-based functions and employ a log-normal likelihood to accommodate yield distribution characteristics, including skewness and potential heteroscedasticity. Model comparison is conducted using information criteria and posterior predictive checks to evaluate alternative specifications of climate interactions, lag structures, and the inclusion of extreme weather indicators. We address missing data through a fully Bayesian data augmentation scheme, ensuring coherent uncertainty propagation from climate variables to yield projections. Computationally, we implement Markov chain Monte Carlo with efficient Hamiltonian Monte Carlo sampling to handle high-dimensional parameter spaces, coupled with sparse matrix techniques to exploit spatial structure. The dataset comprises multi-year harvest records from multiple counties, paired with gridded climate datasets and agronomic management data spanning a 20-year horizon. We perform out-of-sample validation across held-out years and locations to assess predictive accuracy under climate variability and potential future climate scenarios. Sensitivity analyses explore the impact of prior choices, lag lengths for climate effects, and alternative spatial neighborhood configurations. Key findings demonstrate that incorporating spatial and temporal dependencies markedly improves yield prediction accuracy compared to conventional fixed-effect regressions. Temperature and precipitation interact nonlinearly, with lagged moisture deficits amplifying yield losses in drought-prone regions, while solar radiation exhibits diminishing returns beyond optimal thresholds. Spatially varying climate-response coefficients reveal substantial heterogeneity in adaptation, with some regions showing stronger resilience due to management practices and soil properties. The probabilistic framework yields coherent uncertainty quantification for yield forecasts and scenario analyses, informing risk-aware decision-making for farmers and policymakers. implications include targeted irrigation planning, climate-smart agronomic strategies, and refinement of regional yield forecasting systems under future climate projections.

Project Overview

What This Project Is About

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A plain-language overview of the topic and what the project investigates.

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The Problem It Addresses

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What problem or gap this project tackles and why it matters to the field or society.

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Objectives of the Project

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1. Identify key climate factors that influence crop yield.
2. Build a simple model to link climate data with yields using hierarchical ideas.
3. Explain how spatial (where) and temporal (when) patterns affect results.
4. Assess uncertainty in predictions and how it changes with data size.

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What You Will Do Step by Step

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1. Review basic climate and crop data sources that are publicly available.
2. Preprocess data to align dates, locations, and units.
3. Learn concepts behind hierarchical models and why they help with grouped data.
4. Implement a simple hierarchical model that accounts for location and year effects.
5. Test the model with subsets of data and check prediction accuracy.
6. Interpret results in plain language and create visuals to explain findings.

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Expected Outcome

The project should produce a clear, easy-to-understand explanation of how climate variables impact crop yield, with a simple model and useful visuals to communicate uncertainty and spatial patterns.