On the turbulent Prandtl number in the stable atmospheric boundary layer

This study focuses on the behaviour of the turbulent Prandtl number, Prt, in the stable atmospheric boundary layer (SBL) based on measurements made during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA). It is found that Prt increases with increasing stability if Prt is plotted vs. gradient Richardson number, Ri; but at the same time, Prt decreases with increasing stability if Prt is plotted vs. flux Richardson number, Rf, or vs. ζ =  z/L. This paradoxical behaviour of the turbulent Prandtl number in the SBL derives from the fact that plots of Prt vs. Ri (as well as vs. Rf and ζ) for individual 1-h observations and conventional bin-averaged values of the individual quantities have built-in correlation (or self-correlation) because of the shared variables. For independent estimates of how Prt behaves in very stable stratification, Prt is plotted against the bulk Richardson number; such plots have no built-in correlation. These plots based on the SHEBA data show that, on the average, Prt decreases with increasing stability and Prt <  1 in the very stable case. For specific heights and stabilities, though, the turbulent Prandtl number has more complicated behaviour in the SBL.