Mid-season Nitrogen Management for Winter Wheat under Price and Weather Uncertainty

Context: In-season nitrogen (N) management tools are essential for optimizing N application rates, maximizing farmers' economic returns and minimizing adverse environmental impacts. The primary limitation to developing such tools is the risk associated with uncertainties in weather forecasts and crop price projections required to estimate yields and returns for different N rates. Therefore, characterizing the risk associated with these uncertainties is crucial for determining optimum N rates in-season. Objective: This study investigated the N application decision-making process for farmers, accounting for risks associated with weather and crop price uncertainties through crop modeling and economic analysis. Methods: We used field trial data for winter wheat in Kansas to examine how optimal nitrogen rates and economic returns vary over sites, years, and differing farmers' risk attitudes. First, the Environmental Policy Integrated Climate (EPIC) agroecosystem model was used to simulate the distribution of final yields under different N applications during early spring. Then, an autoregressive moving average (ARMA) model estimated the wheat price distribution at harvest based on historical prices. Finally, optimal N application rates for farmers with different risk appetites were estimated using two risk decision models: the constant-absolute-risk-averse (CARA) expected utility model, which treats upside (higher-than-expected returns) and downside (lower-than-expected returns) deviations equally, and the invariant-preference, generalized-deviation (IPGD) model, which focuses on downside risk. Results: We found that optimal N rates vary greatly between sites and years, as well as across farmers with different risk preferences. Due to the positive skewness of economic return distribution, farmers tend to apply lower N rates when considering downside risk. On average, the optimal N rate for farmers with a CARA coefficient of 0.002 is 77 kg/ha in the CARA model and 67 kg/ha in the IPGD model. Compared to the outcome of risk-neutral N usage, risk-averse N usage for a farmer with a CARA coefficient of 0.008 could reduce the uncertainty (standard deviation) of return by 6.2 %, on average, while the expected return decreased by only 1.2 %. Conclusions: By lowering the N rate, risk-averse farmers would reduce the uncertainty of returns and incur a minor return loss, suggesting the possibility of improving agricultural resilience while also improving N use efficiency. Our analysis also underscores the importance of yearly site-specific N management, given the substantial variation in optimal rates across years and locations. Significance: This study provides the foundation for an N application decision framework that considers both weather and price uncertainty. The analysis also demonstrates the potential co-benefit of enhancing agriculture's climate and market resilience while potentially lowering N losses.