An evaluation of bulk Ri-based surface layer flux formulas for stable and very stable conditions with intermittent turbulence

High-rate near-surface overnight atmospheric data taken during the Cooperative Atmosphere-Surface Exchange Study-1999 (CASES-99) is used to quantify the representativeness of surface layer formulations under statically stable conditions. Combined with weak wind shear, such conditions generate large dynamic stability (Ri > 1.0), intermittency, and nonstationarity, which violate the underlying assumptions of surface layer theory. Still, such parameterizations are applied in atmospheric numerical models from large-eddy to global circulation. To investigate two formulas, their parameterized sensible heat flux and friction velocity (u_*) values are compared, when driven by CASES-99 measurements, to CASES-99 measurements of the same from various heights. Significant inaccuracies in the magnitude and sign of flux are found with 1) a frequent, large underprediction of heat flux for Ri_b > _e1∼1.0, 2) an overprediction of negative sensible heat flux and u_* for _e1∼0.2 Ri_b < _e1∼0.8, 3) a systematic underprediction of u_* for Ri_b > 1.0 for one of the schemes tested, and 4) a misrepresentation of natural heat and u_* intermittency by both schemes for Ri > 1.0. Failures of the "cOnstant flux assuFption" for a given height are proposed as a partial source for the errors. Using experimental data, a surface layer of O(1-10] m is found during dynamically stable conditions. Rather than suggest a revised algebraic fit to the observations, an alternate approach to surface layer parameterization is proposed.