Characteristics of the Heat Flux in the Unstable Atmospheric Surface Layer

The behavior of the heat flux H with respect to the stability parameter (=z/L, where z is the height above the ground, and L is the Obukhov length) in the unstable atmospheric surface layer is analyzed within the framework of Monin–Obukhov similarity (MOS) theory. Using MOS equations, H is expressed as a function of and vertical surface-layer potential temperature gradient . A mathematical analysis is carried out to analyze the theoretical nature of heat flux with the stability parameter by considering the vertical potential temperature gradient as (i) a constant and (ii) a power-law function of heat flux. For a given value of H, two values of associated with different stability regimes are found to occur in both the conditions, suggesting the nonuniqueness of MOS equations. Turbulent data over three different sites—(i) Ranchi, India; (ii) the Met Office’s Cardington, United Kingdom, monitoring facility; and (iii) 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99; United States—are analyzed to compare the observed nature of H with that predicted by MOS. The analysis of observational data over these three sites reveals that the observed variation of H with is consistent with that obtained theoretically from MOS equations when considering the vertical temperature gradient as a power-law function of heat flux having the exponent larger than 2/3. The existence of two different values of the stability parameter for a given value of heat flux suggests that the application of heat flux as a boundary condition involves some intricacies, and it should be applied with caution in convective conditions.