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

With improved measurement and modelling technology, variability has emerged as an essential feature in non-equilibrium processes. While traditionally, mean values and variance have been heavily used, they are not appropriate in describing extreme events where a significant deviation from mean values often occurs. Furthermore, stationary Probability Density Functions (PDFs) miss crucial information about the dynamics associated with variability. It is thus critical to go beyond a traditional approach and deal with time-dependent PDFs. Here, we consider atmospheric data from the Whole Atmosphere Community Climate Model (WACCM) and calculate time-dependent PDFs and the information length from these PDFs, which is the total number of statistically different states that a system evolves through in time. Specifically, we consider the three cases of sampling data to investigate the distribution of information (information budget) along the altitude and longitude to gain a new perspective of understanding variabilities, correlation among different variables and regions. Time-dependent PDFs are shown to be non-Gaussian in general; the information length tends to increase with the altitude albeit in a complex form; this tendency is more robust for flows/shears than temperature. Much similarity among flows and shears in the information length is also found in comparison with the temperature. This means a strong correlation among flows/shears because of their coupling through gravity waves in this particular WACCM model. We also find the increase of the information length with the latitude and interesting hemispheric asymmetry for flows/shears/temperature, with the tendency of anti-correlation (correlation) between flows/shears and temperature at high (low) latitude. These results suggest the importance of high latitude/altitude in the information budget in the Earth's atmosphere, the spatial gradient of the information length being a useful proxy for information flow.