Acknowledging a considerable literature on modeling daily temperature data, we propose a two-stage spatio-temporal model which introduces several innovations in order to explain the daily maximum temperature in the summer period over 60 years in a region containing Arag\'on, Spain. The model operates over continuous space but adopts two discrete temporal scales, year and day within year. It captures temporal dependence through autoregression on days within year and also on years. Spatial dependence is captured through spatial process modeling of intercepts, slope coefficients, variances, and autocorrelations. The model is expressed in a form which separates fixed effects from random effects and also separates space, years, and days for each type of effect. Motivated by exploratory data analysis, fixed effects to capture the influence of elevation, seasonality and a linear trend are employed. Pure errors are introduced for years, for locations within years, and for locations at days within years. The performance of the model is checked using a leave-one-out cross-validation. Applications of the model are presented including prediction of the daily temperature series at unobserved or partially observed sites and inference to investigate climate change comparison.
翻译:我们承认关于每日温度数据建模的大量文献,我们建议采用一个两阶段时空模型,采用若干创新,以解释西班牙阿拉格登(Arag\'on)所在地区60年来夏季的每日最高温度;该模型在连续空间运行,但每年采用两个独立的时间尺度;通过年中几天和年中自动回归,捕捉到时间依赖性;通过拦截、斜系数、差异和自动反射的空间过程建模,捕捉空间依赖性。该模型以一种将固定效应与随机效应区分开来的形式表达,也为每种效应的空间、年和天数分列。该模型受到探索性数据分析的驱动,采用固定效应来捕捉海拔、季节性和线性趋势的影响。该模型在年中多年、年中地点和年中地点引入纯误差。该模型的性能通过一次空空的交叉校验得到检查。模型的应用包括预测未观测或部分观察的地点的每日温度序列,并参照气候变化的比较。