The Statistical Differences Between the Gridded Temperature Datasets, and its Implications for Stochastic Modelling

Several research groups around the world collect instrumental temperature data and combine them in different ways to obtain global gridded temperature fields. The three most well known datasets are HadCRUT4 produced by the Climatic Research Unit and the Met Office Hadley Centre in UK, one produced by NASA GISS, and one produced by NOAA. Recently Berkeley Earth has also developed a gridded dataset. All these four will be compared in our analysis.

The statistical properties we will focus on are the standard deviation and the Hurst exponent. These two parameters are sufficient to describe the temperatures as long-range memory stochastic processes; the standard deviation describes the general fluctuation level, while the Hurst exponent relates the strength of the long-term variability to the strength of the short-term variability. A higher Hurst exponent means that the slow variations are stronger compared to the fast, and that the autocovariance function will have a stronger tail. Hence the Hurst exponent gives us information about the persistence or memory of the process.

We make use of these data to show that data averaged over a larger area exhibit higher Hurst exponents and lower variance than data averaged over a smaller area, which provides information about the relationship between temporal and spatial correlations of the temperature fluctuations. Interpolation in space has some similarities with averaging over space, although interpolation is more weighted towards the measurement locations. We demonstrate that the degree of spatial interpolation used can explain some differences observed between the variances and memory exponents computed from the various datasets.