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With improved measurement and modelling technology, variability has emergedas an essential feature in non-equilibrium processes. While traditionally, meanvalues and variance have been heavily used, they are not appropriate indescribing extreme events where a significant deviation from mean values oftenoccurs. Furthermore, stationary Probability Density Functions (PDFs) misscrucial information about the dynamics associated with variability. It is thuscritical to go beyond a traditional approach and deal with time-dependent PDFs.Here, we consider atmospheric data from the Whole Atmosphere Community ClimateModel (WACCM) model and calculate time-dependent PDFs and the informationlength from these PDFs, which is the total number of statistically differentstates that a system passes through in time. Time-dependent PDFs are shown tobe non-Gaussian in general, and the information length calculated from thesePDFs shed us a new perspective of understanding variabilities, correlationamong different variables and regions. Specifically, we calculatetime-dependent PDFs and information length and show that the information lengthtends to increase with the altitude albeit in a complex form. This tendency ismore robust for flows/shears than temperature. Also, much similarity amongflows and shears in the information length is found in comparison with thetemperature. These results also suggest the importance of highlatitude/altitude in the information budge in the Earth's atmosphere, thespatial gradient of the information as a useful proxy for the transport ofphysical quantities.

Information length as a useful index to understand variability in the global circulation