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. 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. 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. 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 %. 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. 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.

中文翻译：

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价格和天气不确定性下冬小麦季中氮肥管理


当季氮 (N) 管理工具对于优化氮肥施用量、最大限度地提高农民的经济回报和最大限度地减少不利的环境影响至关重要。开发此类工具的主要限制是与天气预报和作物价格预测的不确定性相关的风险，这些风险需要估算不同氮肥的产量和回报。因此，描述与这些不确定性相关的风险对于确定当季最佳施氮量至关重要。本研究调查了农民的施氮决策过程，通过作物建模和经济分析来解释与天气和作物价格不确定性相关的风险。我们使用堪萨斯州冬小麦的田间试验数据来研究最佳施氮量和经济回报如何随地点、年份和不同农民的风险态度而变化。首先，利用环境政策综合气候（EPIC）农业生态系统模型模拟早春不同施氮条件下的最终产量分布。然后，自回归移动平均（ARMA）模型根据历史价格估计收获时的小麦价格分布。最后，使用两种风险决策模型估算了具有不同风险偏好的农民的最佳施氮量：恒定绝对风险规避（CARA）预期效用模型，该模型处理上行（高于预期的回报）和下行（低于预期的回报） -高于预期的回报）偏差，以及不变偏好广义偏差（IPGD）模型，该模型关注下行风险。我们发现，最佳施氮量因地点和年份以及具有不同风险偏好的农民而异。 由于经济回报分布的正偏态，农民在考虑下行风险时倾向于采用较低的施氮量。平均而言，CARA 系数为 0.002 的农民的最佳施氮量在 CARA 模型中为 77 千克/公顷，在 IPGD 模型中为 67 千克/公顷。与风险中性施氮的结果相比，对于 CARA 系数为 0.008 的农民来说，规避风险的施氮可以将回报的不确定性（标准差）平均降低 6.2%，而预期回报仅降低 1.2% %。通过降低氮肥施用率，规避风险的农民将减少回报的不确定性并遭受较小的回报损失，这表明有可能提高农业抵御能力，同时提高氮肥利用效率。我们的分析还强调了每年特定地点氮管理的重要性，因为不同年份和地点的最佳氮管理率存在很大差异。这项研究为同时考虑天气和价格不确定性的 N 应用决策框架奠定了基础。该分析还表明，增强农业气候和市场恢复力同时可能降低氮素损失具有潜在的协同效益。