Comments on “A New Second-Order Turbulence Closure Scheme for the Planetary Boundary Layer”

Abdella and McFarlane (1997, henceforth AM97) have proposed a second-order turbulence closure scheme for the planetary boundary layer. The scheme contains a prognostic equation for the turbulence kinetic energy and algebraic expressions for the other second-order moments. The expressions for the potential temperature flux and the temperature variance incorporate nonlocal eddy diffusivity and countergradient terms. These expressions are derived through the use of an advanced parameterization of the third-order moments based on convective mass-flux arguments. Remarkably, the AM97 parameterizations for the flux of potential temperature flux, w' super(2) theta ', and the flux of potential temperature variance, w' theta ' super(2) , do not have a traditional downgradient diffusion form. Simultaneously, Zilitinkevich et al. (1997, henceforth ZGLM; see also Zilitinkevich et al. 1999) proposed a ``turbulent advection + diffusion parameterization'' for w' super(2) theta '. Apart from the conventional downgradient diffusion term and the term proportional to the gradient of mean potential temperature, their expression for w' super(2) theta ' contains a nongradient ``advection'' term. That term is identical to the expression for w' super(2) theta ' obtained by AM97 [Eq. (3) below]. In this note we show that the parameterization for the flux of potential temperature variance, w' theta ' super(2) , proposed by AM97 is inconsistent with the physical requirements of symmetry. We then develop a parameterization that possesses necessary physical properties and verify it against large-eddy simulation (LES) and observational data. Reply follows.