Statistical analysis and time series models for minimum/maximum temperatures in the Antarctic Peninsula

It is now widely known that Antarctic air is warming faster than the rest of the world, and the Antarctic peninsula has experienced major warming over the last 50 years. The monthly mean near surface temperature at the Faraday/Vernadsky station has increased considerably, at a rate of 0.56 degrees C per decade over the year and at 1.09 degrees C per decade over the winter. The increase is not the same over all the stations in the Antarctic region, and the increase is very significant at the Faraday/Verdansky station. Only at this station are the minimum/maximum monthly temperatures, for the period $1951-2004$, separately available, and we believe that the increase in mean surface temperature at this station is mainly due to the increases in minimum temperatures. Therefore our object in this paper is to study the variations in the min/max temperatures using a multiple regression model with non-Gaussian correlated errors. By separately analysing the minimum and maximum temperatures we could clearly identify the source of increase. The average temperature (usually calculated as (max+min)/2) smooths out the variation, and may not be that informative. We model the correlated errors using a linear Autoregressive Moving Average model with innovations which have an extreme value distribution. We describe the maximum likelihood estimation methodology and apply this to the data sets described above. The methods proposed here can be widely used in other disciplines as well.

Our analysis has shown that the increase in the minimum monthly temperatures is approximately 6 degrees C over 53 years (1951-2003), whereas we did not find any significant change in the maximum temperature over the same period.

We also establish a relationship between the minimum monthly temperatures and ozone levels. We use these models, fitted upto December 2003, to obtain monthly forecasts for the year 2004 and compare it with the true values available upto December 2004.