Interpolation between Businger–Dyer Formulae and Free Convection Forms: A Revised Approach

AbstractIn this study, profile functions for flux calculations during unstable conditions are proposed and examined. These functions are based on a direct interpolation for the dimensionless wind speed and temperature gradients between the standard Businger–Dyer formulae, $$\phi_{{\rm K}u} (\zeta) = (1 - \gamma _{u} \zeta)^{-1/4}$$, $$\phi_{{\rm K}t} (\zeta) = (1 - \gamma _{t} \zeta )^{-1/2}$$, and free convection forms, $$\phi _{{\rm C}u,t} (\zeta) = (1 - \alpha _{{\rm C}u,t} \zeta )^{-1/3}$$, $$\zeta$$ being the Monin–Obukhov stability parameter. A previously presented interpolation between the corresponding profile relationships, in attempting to provide a general relationship for the whole unstable regime, leads to serious restrictions for the values of $$\alpha _{{\rm C}u ,t}$$ in the free convection forms. These restrictions rendered available experimental data almost inapplicable, since the behaviour of the formulae in the near-neutral range controls the values of those parameters. The proposed interpolation provides functions that, firstly, fit the standard Businger–Dyer forms for near-neutral conditions and, secondly, satisfy the asymptotic behaviour as $$\zeta \rightarrow -\infty$$, permitting wider ranges of possible $$\alpha _{{\rm Cu},t}$$ values. This step is very important, taking into account the large spread of the experimental data. Thus, as further and more accurate observations at strong instability become available, this approach could prove very efficient in fitting these data while retaining correct near-neutral behaviour.