Predicting Joint Frequency Distributions In the Boundary Layer

Joint frequency distributions (JFDs) can be formed using any combination of thermodynamic or dynamic variables, for example vertical velocity vs. temperature or moisture vs. temperature. These JFDs can be a useful tool for investigating turbulent fluxes or cumulus formation in the atmospheric boundary layer. Several authors have proposed theories explaining the shape of JFDs of vertical velocity vs. temperature and moisture vs. temperature. Theoretical JFDs will be compared to those measured with an instrumented aircraft flying near the surface during Boundary Layer Experiment 1996

An extension to the theory for JFDs of vertical velocity vs. temperature will be presented. This extension, which is based on the observed Bowen ratio and the surface energy balance, can be used to generate JFDs using variables that are estimated in numerical models of the atmosphere.

The JFDs of moisture vs. temperature are approximately ellipsoidal, in agreement with theory. Unfortunately, there are differences between the tilt of the theoretical and observed JFDs. However, there appears to be a relationship between the tilt of the observed JFDs and the observed Bowen ratio.