An Evaluation of Bulk Ri-Based Surface Layer Flux Formulas for Stable and Very Stable Conditions with Intermittent Turbulence

Abstract

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 Rib > ?1.0, 2) an overprediction of negative sensible heat flux and u? for ?0.2 < Rib < ?0.8, 3) a systematic underprediction of u? for Rib > 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 assumption? 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.