Monin-obukhov similarity functions of the structure parameter of temperature and turbulent kinetic energy dissipation rate in the stable boundary layer

The Monin-Obukhov similarity theory (MOST) functions fe and fT, of the dissipation rate of turbulent kinetic energy (TKE). e, and the structure parameter of temperature, CT2, were determined for the stable atmospheric surface layer using data gathered in the context of CASES-99. These data cover a relatively wide stability range, i.e. Q=z/L of up to 10, where z is the height and L the Obukhov length. The best fits were given by fe = 0.8 + 2.5Q and fT= 4.7[ 1+1.6(Q)2/3], which differ somewhat from previously published functions. e was obtained from spectra of the longitudinal wind velocity using a time series model (ARMA) method instead of the traditional Fourier transform. The neutral limit fe =0.8 implies that there is an imbalance between TKE production and dissipation in the simplified TKE budget equation. Similarly, we found a production-dissipation imbalance for the temperature fluctuation budget equation. Correcting for the production-dissipation imbalance, the 'standard' MOST functions for dimensionless wind speed and temperature gradients (Hm and Hm) were determined from fe and fT and compared with the Hm and Hh formulations of Businger and others. We found good agreement with the Beljaars and Holtslag [J. Appl. Meteorol. 30, 327-341 (1991)] relations. Lastly, the flux and gradient Richardson numbers are discussed also in terms of fe and fT.