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

Gregory S. PoulosColorado Research Associates, NWRA, Boulder, Colorado

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Sean P. BurnsNational Center for Atmospheric Research, Boulder, Colorado

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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.

Corresponding author address: Gregory S. Poulos, Colorado Research Associates, NWRA, 3380 Mitchell Lane, Boulder, CO 80301. Email: gsp@cora.nwra.com

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.

Corresponding author address: Gregory S. Poulos, Colorado Research Associates, NWRA, 3380 Mitchell Lane, Boulder, CO 80301. Email: gsp@cora.nwra.com

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