Exploring Self-Correlation in Flux–Gradient Relationships for Stably Stratified Conditions

In this paper, the degree of scatter in flux–gradient relationships for stably stratified conditions is analyzed. It is generally found that scatter in the dimensionless lapse rate ϕh is larger than in the dimensionless shear ϕm when plotted versus the stability parameter z/Λ (where Λ is the local Obukhov length). Here, this phenomenon is explained to be a result of self-correlation due to the occurrence of the momentum and the heat flux on both axes, measurement uncertainties, and other possibly relevant physical processes left aside. It is shown that the ratio between relative errors in the turbulent fluxes influences the orientation of self-correlation in the flux–gradient relationships. In stable conditions, the scatter in ϕm is largely suppressed by self-correlation while for ϕh this is not the case (vice versa for unstable stratification). An alternative way of plotting is discussed for determining the slope of the linear ϕm function.