The relationships between crop yields and meteorology are naturally non-stationary because of spatiotemporal heterogeneity. Many studies have examined spatial heterogeneity in the regression model, but only limited research has attempted to account for both spatial autocorrelation and temporal variation. In this article, we develop a novel spatiotemporally varying coefficient (STVC) model to understand non-stationary relationships between crop yields and meteorological variables. We compare the proposed model with variant models specialized for time or spatial, namely spatial varying coefficient (SVC) model and temporal varying coefficient (TVC) model. This study was conducted using the county-level corn yield and meteorological data, including seasonal Growing Degree Days (GDD), Killing Degree Days (KDD), Vapor Pressure Deficit (VPD), and precipitation (PCPN), from 1981 to 2018 in three Corn Belt states, including Illinois, Indiana, and Iowa. Allowing model coefficients varying in both temporal and spatial dimensions gives the best performance of STVC in simulating the corn yield responses toward various meteorological conditions. The STVC reduced the root-mean-square error to 10.64 Bu/Ac (0.72 Mg/ha) from 15.68 Bu/Ac (1.06 Mg/ha) for TVC and 16.48 Bu/Ac (1.11 Mg/ha) for SVC. Meanwhile, the STVC resulted in a higher R² of 0.81 compared to 0.56 for SVC and 0.64 for TVC. The STVC showed better performance in handling spatial dependence of corn production, which tends to cluster estimation residuals when counties are close, with the lowest Moran's I of 0.10. Considering the spatiotemporal non-stationarity, the proposed model significantly improves the power of the meteorological data in explaining the variations of corn yields.

由于时空异质性，农作物产量与气象之间的关系自然是不稳定的。许多研究已经检验了回归模型中的空间异质性，但是只有有限的研究试图说明空间自相关和时间变化。在本文中，我们开发了一种新颖的时空变化系数（STVC）模型，以了解农作物产量与气象变量之间的非平稳关系。我们将提出的模型与专门用于时间或空间的变体模型进行比较，即空间变化系数（SVC）模型和时间变化系数（TVC）模型。这项研究是使用县级玉米产量和气象数据进行的，包括季节性生长日（GDD），致死度日（KDD），蒸汽压亏（（VPD），和降水（PCPN），从1981年到2018年在三个玉米带州，包括伊利诺伊州，印第安纳州和爱荷华州。允许模型系数在时间和空间维度上都变化，可以在模拟玉米对各种气象条件的产量响应时，获得STVC的最佳性能。STVC将均方根误差从TVC的15.68 Bu / Ac（1.06 Mg / ha）和16.48 Bu / Ac（1.11 Mg / ha）的10.68 Bu / Ac（0.72 Mg / ha）降低到10.64 Bu / Ac（0.72 Mg / ha）。同时，STVC导致更高的R TVC为15.68 Bu / Ac（1.06 Mg / ha），SVC为16.48 Bu / Ac（1.11 Mg / ha）从72 Mg / ha）。同时，STVC导致更高的R TVC为15.68 Bu / Ac（1.06 Mg / ha），SVC为16.48 Bu / Ac（1.11 Mg / ha）从72 Mg / ha）。同时，STVC导致更高的R²（0.81），而SVC为0.56，TVC为0.64。STVC在处理玉米产量的空间依赖性方面表现出更好的性能，当县县接近时，STVC倾向于将估计残差聚类，最低的莫兰I为0.10。考虑到时空的非平稳性，提出的模型大大提高了气象数据解释玉米产量变化的能力。