Statistical methods are required to evaluate and quantify the uncertainty in environmental processes, such as land and sea surface temperature, in a changing climate. Typically, annual harmonics are used to characterize the variation in the seasonal temperature cycle. However, an often overlooked feature of the climate seasonal cycle is the semi-annual harmonic, which can account for a significant portion of the variance of the seasonal cycle and varies in amplitude and phase across space. Together, the spatial variation in the annual and semi-annual harmonics can play an important role in driving processes that are tied to seasonality (e.g., ecological and agricultural processes). We propose a multivariate spatiotemporal model to quantify the spatial and temporal change in minimum and maximum temperature seasonal cycles as a function of the annual and semi-annual harmonics. Our approach captures spatial dependence, temporal dynamics, and multivariate dependence of these harmonics through spatially and temporally varying coefficients. We apply the model to minimum and maximum temperature over North American for the years 1979–2018. Formal model inference within the Bayesian paradigm enables the identification of regions experiencing significant changes in minimum and maximum temperature seasonal cycles due to the relative effects of changes in the two harmonics.

中文翻译：

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年和半年谐波驱动的典型季节温度循环的时空变化

需要使用统计方法来评估和量化环境过程中的不确定性，例如在不断变化的气候中陆地和海面温度。通常，年度谐波用于表征季节性温度循环的变化。然而，气候季节周期的一个经常被忽视的特征是半年谐波，它可以解释季节周期方差的很大一部分，并且在空间上的幅度和相位变化。总之，年度和半年度谐波的空间变化可以在与季节性相关的驱动过程（例如生态和农业过程）中发挥重要作用。我们提出了一个多元时空模型来量化最低和最高温度季节性周期的空间和时间变化，作为年度和半年度谐波的函数。我们的方法通过空间和时间变化的系数来捕捉这些谐波的空间依赖性、时间动态和多元依赖性。我们将该模型应用于 1979-2018 年北美的最低和最高温度。贝叶斯范式内的正式模型推断能够识别由于两个谐波变化的相对影响而经历最低和最高温度季节性周期显着变化的区域。以及这些谐波通过空间和时间变化系数的多变量依赖性。我们将该模型应用于 1979-2018 年北美的最低和最高温度。贝叶斯范式内的正式模型推断能够识别由于两个谐波变化的相对影响而经历最低和最高温度季节性周期显着变化的区域。以及这些谐波通过空间和时间变化系数的多变量依赖性。我们将该模型应用于 1979-2018 年北美的最低和最高温度。贝叶斯范式内的正式模型推断能够识别由于两个谐波变化的相对影响而经历最低和最高温度季节性周期显着变化的区域。