Spatial modeling of annual minimum and maximum temperatures in Iceland

Abstract

Bayesian hierarchical modeling is applied to the analysis of annual minimum and maximum temperatures. In both cases the generalized extreme value distribution is selected as the marginal distribution at each site due to its flexibility and theoretical basis. This distribution has three unknown parameters, a location parameter, a scale parameter and a shape parameter. The location and scale parameters are assumed to vary across sites while the shape parameter is assumed to be the same for all sites. The location and the scale parameters are modeled as two independent Gaussian spatial processes which are governed by the Matern correlation function. These spatial processes play a central role in spatial predictions at unobserved sites. The location parameter is also modeled with a common time effect which includes a linear trend and a linear site effect with altitude, distance to open sea, latitude and longitude as covariates. This model allows for spatial predictions for any set of unobserved sites, the scale of the grid can be as fine as possible as long as the covariates are observed at each of the unobserved sites. Data on the annual minimum and maximum temperatures in Iceland from 1961 to 2009 at 72 sites are analyzed and used to predict the 2nd percentile of the minimum temperature for the 12-month period from July 2011 to June 2012 and the 98th percentile of maximum temperature for the year 2011 for a large set of unobserved sites across Iceland at which the covariates are available. The spatial predictions reveal that the 2nd percentile of minimum temperature for 2011 to 2012 reaches −35°C in the central part of Iceland and ranges from −12 to −22°C around the coast of Iceland with the lowest coastal temperatures in the Northern part and the Northeastern part. The 98th percentile of maximum temperature in 2011 ranges from 10 to 30°C where the warmest areas are found in the Eastern part, the North-Eastern part and the Southern part of the country. The estimated increase in minimum and maximum temperatures over the years 1961 to 2009 is 0.71 and 0.47°C per decade, respectively, while the average annual temperature increased 0.24°C per decade over the same period.