Spatial modeling of day-within-year temperature time series: an examination of daily maximum temperatures in Arag\'on, Spain

TL;DR

This paper introduces a multi-level spatio-temporal model for daily maximum temperatures in Aragón, Spain, capturing complex dependencies over space, days, and years to improve temperature prediction and climate change analysis.

Contribution

The paper presents a novel multi-level spatio-temporal model that separates fixed and random effects across space, days, and years, enhancing temperature modeling over a 60-year period.

Findings

Model accurately predicts temperatures at unobserved sites.

Effective in capturing spatial and temporal dependencies.

Useful for climate change inference.

Abstract

Acknowledging a considerable literature on modeling daily temperature data, we propose a multi-level 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.