This study introduces an innovative Cumulative Link Modeling approach to monitor crop progress over large areas using remote sensing data. The models utilize the predictive attributes of calendar time, thermal time, and the Normalized Difference Vegetation Index (NDVI). Two distinct issues are tackled: real-time crop progress prediction, and completed season fitting. In the context of prediction, the study presents two model variations, the standard one based on the Multinomial distribution and a novel one based on the Multivariate Binomial distribution. In the context of fitting, random effects are incorporated to capture the inherent inter-seasonal variability, allowing the estimation of biological parameters that govern crop development and determine stage completion requirements. Theoretical properties in terms of consistency, asymptotic normality, and distribution-misspecification are reviewed. Model performance was evaluated on eight crops, namely corn, oats, sorghum, soybeans, winter wheat, alfalfa, dry beans, and millet, using in-situ data from Nebraska, USA, spanning a 20-year period. The results demonstrate the wide applicability of this approach to different crops, providing real-time predictions of crop progress worldwide, solely utilizing open-access data. To facilitate implementation, an ecosystem of R packages has been developed and made publicly accessible under the name Ages of Man.

翻译：本研究提出了一种创新的累积链接建模方法，利用遥感数据对大面积作物生长进程进行监测。该模型使用日历时间、热时间以及归一化差分植被指数（NDVI）作为预测属性，解决了两个不同的问题：实时作物生长进程预测与完整生长季拟合。在预测方面，本研究提出了两种模型变体：基于多项分布的标准模型和基于多元二项分布的新型模型。在拟合方面，通过引入随机效应来捕捉固有的季节性间变异，从而能够估算控制作物发育并决定阶段完成要求的生物学参数。研究还从一致性、渐近正态性和分布误设角度对理论性质进行了综述。模型性能评估基于美国内布拉斯加州20年间的实地数据，涵盖玉米、燕麦、高粱、大豆、冬小麦、苜蓿、干豆和小米等八种作物。结果表明，该方法具有广泛的跨作物适用性，仅利用开放获取数据即可实现全球范围内的作物生长实时预测。为促进应用，已开发并公开了名为"Ages of Man"的R语言包生态系统。