Trend evaluation in records with long-term memory: Application to global warming

Previous statistical detection methods indicate that, on a global scale, the observed warming cannot be attributed solely to natural fluctuations. Here we estimate the probability W(Delta) that an observed trend Delta occurs naturally, and determine the anthropogenic part A(Q)(Delta) of the temperature increase within a given confidence interval Q. To obtain these quantities, we do not use climate simulations, but assume as statistical null hypothesis that monthly temperature records are long-term correlated with a Hurst exponent alpha > 0.5 (including also nonstationary records with alpha values above 1). We show that for confidence intervals with Q above 80% analytical expressions for W(Delta) and A(Q)(Delta) can be derived, which request as input solely the Hurst exponent, as well as the temperature increase Delta obtained from the linear regression line and the standard deviation sigma(t) around it. We apply this approach to global and local temperature data and discuss the different results. Citation: Lennartz, S., and A. Bunde (2009), Trend evaluation in records with long-term memory: Application to global warming, Geophys. Res. Lett., 36, L16706, doi: 10.1029/2009GL039516.