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

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.