Emergence of global scaling behaviour in the coupled Earth- atmosphere interaction (original) (raw)

Scale invariance property in the global geometry of Earth may lead to a coupled interactive behaviour between various components of the climate system. One of the most interesting correlations exists between spatial statistics of the global topography and the temperature on Earth. Here we show that the power-law behaviour observed in the Earth topography via different approaches, resembles a scaling law in the global spatial distribution of independent atmospheric parameters. We report on observation of scaling behaviour of such variables characterized by distinct universal exponents. More specifically, we find that the spatial power-law behaviour in the fluctuations of the near surface temperature over the lands on Earth, shares the same universal exponent as of the global Earth topography, indicative of the global persistent role of the static geometry of Earth to control the steady state of a dynamical atmospheric field. Such a universal feature can pave the way to the theoretical understanding of the chaotic nature of the atmosphere coupled to the Earth's global topography. The estimation of future climate variability is of the major concerns of the recent century. Exploring the intrinsic properties of the climate system will improve the understanding of the characteristics of dynamical processes involved within the climate system so as to the downscaling procedures (e.g., stochastic parametrization schemes). Lower boundary conditions as a large-scale forcing may lend predictability to climate system 1–4. Lower boundary conditions (e.g., topography, sea surface temperature, etc.) are usually prescribed in the General Circulation Models (GCMs). GCMs can realistically simulate the dominant modes of variations in the tropo-sphere 5. Earth-atmosphere interactions between the surface and the free troposphere are mainly influenced by the characteristics of the atmospheric boundary layer. Thus, the net exchange of heat, mass and momentum are determined by the lower boundary conditions. Outside the boundary layer, the unresolved scales of motion may not be a big deal for the forecasting of synoptic and large-scale circulations 6. However, they are crucial for the mesoscale forecasting. The Earth's surface is the main heat source and sink for the atmosphere. The inhomoge-neous distribution of land properties leads to the temperature gradient within the boundary layer 7. The complex climate system transports heat (driven by solar insolation) from tropics to the higher latitudes. The midlatitude topographies are the main driver of Rossby waves which contribute to the heat transport in the atmosphere 6,8–10. The Rossby waves control the formation of the atmospheric flows up to very remote regions and modify the wind pattern in the atmosphere 6. Previous studies revealed that, for a wide spectrum of scales, there exists a " power law " behaviour in the linear transects of the Earth's topography (i.e., S ∝ k −2 , where k is the wave number) 11–15. However, much less attention has been paid on the scale invariant analysis within the atmospheric system in connection with the scaling behaviour of the underlying topographic system. Power spectrum of temporal changes of atmospheric temperatures have been previously studied for different time scales 16–19. It has been shown that the rainfall amounts do not obey an overall scaling (power-law) form within the hydrological scales 20. The power spectrum analysis is not applied to different length scales in such studies. Here, we report, for the first time, on a novel observation that the fingerprint of the power-law relationship in the global Earth's topography also exists in the atmospheric dynamics as a result of Earth-atmosphere interaction.