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A performance comparison between nonlinear similarity functions in bulk parameterization for very stable conditions

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Abstract

Three sets of nonlinear similarity functions for strong stability are selected to compare their performance in bulk parameterization. To uncover their advantages and disadvantages, theoretical and measurement analyses are made with four profile metrics and the Deacon number technique. Main disadvantages include the negligence of the different transfer efficiency between momentum and heat, the flux cutoff due to the upper limit in gradient Richardson number (Ri) and the ignorance of limited stability range where the dimensionless gradient functions (\({\varphi_{{\rm M}}}\) and \({\varphi_{{\rm H}}}\)) approach constants. Accordingly, three suggestions are made for future improvement. First, the functions for wind velocity and potential temperature should have the same function form, but with different coefficients. Second, \({\varphi_{\rm M}}\) and \({\varphi _{\rm H}}\) should approach constants only within a certain stability range. Third, the limit value in Ri should be avoided to widen their applicability in flux modeling. Furthermore, quantitative comparisons in transfer coefficients for moment and sensible heat (C D and C H) are made among the similarity functions in the bulk Richardson number (Ri B) range 0 < Ri B < 1. Generally, significant discrepancy is found, which may approach a factor of two and three at large Ri B in C D and C H, respectively. Finally, a new recommendation is made to one of the three sets, mainly because of its ability to predict C D and C H that decrease rather slowly in very stable conditions.

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Abbreviations

C D :

bulk transfer coefficient for momentum

C H :

bulk transfer coefficient for heat

c p :

specific heat capacity of air

d :

zero-plane displacement

D H :

Deacon number for potential temperature profile

D M :

Deacon number for wind velocity profile

g :

gravity acceleration

H :

sensible heat flux

L :

Obukhov length

Pr:

turbulent Prandtl number

Ri :

gradient Richardson number

Ri B :

bulk Richardson number

T 0 :

reference temperature near the ground

\({\overline u }\) :

mean wind velocity

\({u_\ast }\) :

friction velocity

z :

height above the ground

z 0H :

roughness length for heat

z 0M :

roughness length for momentum

\({\varphi_{\rm M }}\) :

dimensionless gradient function for wind velocity

\({\varphi_{\rm H }}\) :

dimensionless gradient function for potential temperature

κ:

von Karman constant

\({\overline \theta }\) :

mean potential temperature

\({\overline \theta_0}\) :

mean potential temperature at the roughness length for heat

\({\theta_\ast }\) :

temperature scale

ρ:

air density

τ:

turbulent momentum flux

\({\Psi_{\rm H}}\) :

stability correction function for potential temperature

\({\Psi _{\rm M }}\) :

stability correction function for wind velocity

ζ:

dimensionless stability parameter

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Authors and Affiliations

  1. Department of Atmospheric Science, School of Physics, Peking University, Beijing, 100871, People’s of Republic China

    Xiaofeng Guo & Hongsheng Zhang

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  1. Xiaofeng Guo
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  2. Hongsheng Zhang
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Correspondence to Hongsheng Zhang.

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Guo, X., Zhang, H. A performance comparison between nonlinear similarity functions in bulk parameterization for very stable conditions. Environ Fluid Mech 7, 239–257 (2007). https://doi.org/10.1007/s10652-006-9015-2

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