One of the main problems in statistical climatology is to construct a parsimonious model of natural climate variability. Such a model serves for instance as a null hypothesis for detection of human induced climate changes and of periodic climate signals. Fitting thismodel to various climatic time series also helps to infer the origins of underlying temporal variability and to cross validate it between different data sets. We consider the use of a spectral power-law model in this role for the surface temperature, for the free atmospheric air temperature of the troposphere and stratosphere, and for the total ozone. First, we lay down a methodological foundation for our work. We compare two variants of five different power-law fitting methods by means of Monte-Carlo simulations and their application to observed air temperature. Then using the best two methods we fit the power-law model to several observational products and climate model simulations. We make use of specialized atmospheric general circulation model simulations and of the simulations of the Coupled Model Intercomparison Project 3 (CMIP3). The specialized simulations allow us to explain the power-law exponent spatial distribution and to account for discrepancies in scaling behaviour between different observational products. We find that most of the pre-industrial control and 20th century model simulations capture many aspects of the observed horizontal and vertical distribution of the power-law exponents. At the surface, regions with robust power-law exponents—the North Atlantic, the North Pacific, and the Southern Ocean — coincide with regions with strong inter-decadal variability. In the free atmosphere, the large power-law exponents are detected on annual to decadal time scales in the tropical and subtropical troposphere and stratosphere. The spectral steepness in the former is explained by its strong coupling to the surface and in the latter by its sensitivity to volcanic aerosols. However power-law behaviour in the tropics and in the free atmosphere saturates on multi-decadal timescales. We propose a novel diagnostic to evaluate the relative goodness-of-fit of the autoregressive model of the first order (AR1) and the power-law model. The collective behaviour of CMIP3 simulations appears to fall between the two statistical models. Our results suggest that the power-law model should serve as an upper bound and the AR1 model should serve as a lower bound for climate persistence on monthly to decadal time scales. On the applied side we find that the presence of power-law like natural variability increases the uncertainty on the long-term total ozone trend in the Northern Hemisphere high latitudes attributable to anthropogenic chlorine by about a factor of 1.5, and lengthens the expected time to detect ozone recovery by a similar amount.

One of the main problems in statistical climatology is to construct a parsimonious model of natural climate variability. Such a model serves for instance as a null hypothesis for detection of human induced climate changes and of periodic climate signals. Fitting thismodel to various climatic time series also helps to infer the origins of underlying temporal variability and to cross validate it between different data sets. We consider the use of a spectral power-law model in this role for the surface temperature, for the free atmospheric air temperature of the troposphere and stratosphere, and for the total ozone. First, we lay down a methodological foundation for our work. We compare two variants of five different power-law fitting methods by means of Monte-Carlo simulations and their application to observed air temperature. Then using the best two methods we fit the power-law model to several observational products and climate model simulations. We make use of specialized atmospheric general circulation model simulations and of the simulations of the Coupled Model Intercomparison Project 3 (CMIP3). The specialized simulations allow us to explain the power-law exponent spatial distribution and to account for discrepancies in scaling behaviour between different observational products. We find that most of the pre-industrial control and 20th century model simulations capture many aspects of the observed horizontal and vertical distribution of the power-law exponents. At the surface, regions with robust power-law exponents—the North Atlantic, the North Pacific, and the Southern Ocean — coincide with regions with strong inter-decadal variability. In the free atmosphere, the large power-law exponents are detected on annual to decadal time scales in the tropical and subtropical troposphere and stratosphere. The spectral steepness in the former is explained by its strong coupling to the surface and in the latter by its sensitivity to volcanic aerosols. However power-law behaviour in the tropics and in the free atmosphere saturates on multi-decadal timescales. We propose a novel diagnostic to evaluate the relative goodness-of-fit of the autoregressive model of the first order (AR1) and the power-law model. The collective behaviour of CMIP3 simulations appears to fall between the two statistical models. Our results suggest that the power-law model should serve as an upper bound and the AR1 model should serve as a lower bound for climate persistence on monthly to decadal time scales. On the applied side we find that the presence of power-law like natural variability increases the uncertainty on the long-term total ozone trend in the Northern Hemisphere high latitudes attributable to anthropogenic chlorine by about a factor of 1.5, and lengthens the expected time to detect ozone recovery by a similar amount.