Can Recurrence Quantification Analysis Be Useful in the Interpretation of Airborne Turbulence Measurements?

In airborne data or model outputs, clouds are often defined using information about Liquid Water Content (LWC). Unfortunately LWC is not enough to retrieve information about the dynamical boundary of the cloud, that is, volume of turbulent air around the cloud. In this work, we propose an algorithmic approach to this problem based on a method used in time series analysis of dynamical systems, namely Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA). We construct RPs using time series of turbulence kinetic energy, vertical velocity and temperature fluctuations as variables important for cloud dynamics. Then, by studying time series of laminarity (LAM), a variable which is calculated using RPs, we distinguish between turbulent and non-turbulent segments along a horizontal flight leg. By selecting a single threshold of this quantity, we are able to reduce the number of subjective variables and their thresholds used in the definition of the dynamical cloud boundary. Cloud is defined by the presence of liquid (or solid) water in the atmosphere. By agreeing on a certain threshold of liquid water content, one can define a cloud boundary. Cloud processes result in disturbances in the airflow around the cloud (turbulence). Its presence should allow the cloud dynamical boundary to be defined in a similar manner. However, a single simple variable, which could be used in an analogous way is not well defined. In this study we propose a method to define such a variable to distinguish between turbulent and non-turbulent volumes around the cloud (i.e. determining dynamic cloud interface), adopting a method used in the study of dynamical systems. Based on recorded temperature and air velocity fluctuations characteristic for turbulent transport and mixing, a threshold of a variable named "laminarity" is used to define the dynamic cloud boundary on the aircraft trajectory. A vector characterizing turbulence along the aircraft track based on velocity and temperature fluctuations is constructed A time series of this vector allows the construction of a Recurrence Plot, a tool used in studies of dynamical systems A quantity named laminarity, derived from the Recurrence Plot, is used to detect turbulent and non-turbulent regions