A hierarchical spline model for correcting and hindcasting temperature data

Abstract

Weather observations are important for a wide range of applications although they do pose statistical challenges, such as missing values, errors, flawed outliers and poor spatial and temporal coverage to name a few. A Bayesian hierarchical spline framework is presented here to deal with such challenges in temperature time series. Motivated by a real-life problem, the approach uses penalised splines, constructed hierarchically, to pool the data, along with a discrete mixture distribution to deal with outliers and publicly available global reanalysis data sets (climate model data) to integrate physically constrained information. Efficient Bayesian implementation is achieved using conditional conjugacy, which allows thorough model checking and uncertainty quantification. Fitting the model to daily maximum temperature illustrates its flexibility in capturing temporal structures, in pooling of the information and in outlier detection. The model is used to hindcast the time series 50 years into the past while maintaining uncertainty at reasonable levels.