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

TL;DR

This paper introduces the use of information length derived from time-dependent PDFs to analyze variability in Earth's atmosphere, revealing complex altitude-dependent patterns and emphasizing the importance of high-latitude regions.

Contribution

It presents a novel application of information length to atmospheric data, providing new insights into variability and transport processes beyond traditional statistical measures.

Findings

Information length increases with altitude, especially for flows and shears.

Time-dependent PDFs are generally non-Gaussian.

High-latitude/altitude regions are critical for atmospheric information transport.

Abstract

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) model and calculate time-dependent PDFs and the information length from these PDFs, which is the total number of statistically different states that a system passes through in time. Time-dependent PDFs are shown to be non-Gaussian in general, and the information length calculated from these PDFs shed us a new perspective of understanding variabilities, correlation among different variables and regions. Specifically, we calculate time-dependent PDFs and information length and show that the information length tends to increase with the altitude albeit in a complex form. This tendency is more robust for flows/shears than temperature. Also, much similarity among flows and shears in the information length is found in comparison with the temperature. These results also suggest the importance of high latitude/altitude in the information budge in the Earth's atmosphere, the spatial gradient of the information as a useful proxy for the transport of physical quantities.