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Bulk Transfer Relations for the Roughness Sublayer

Abstract

In the roughness sublayer (RSL), Monin–Obukhov surface layer similarity theory fails. This is problematic for atmospheric modelling applications over domains that include rough terrain such as forests or cities, since in these situations numerical models often have the lowest model level located within the RSL. Based on empirical RSL profile functions for momentum and scalar quantities, and scaling the height with the RSL height z *, we derive a simple bulk transfer relation that accounts for RSL effects. To verify the validity of our approach, these relations are employed together with wind speed and temperature profiles measured over boreal forest during the BOREAS experimental campaign to estimate momentum and heat fluxes. It is demonstrated that, when compared with observed flux values, the inclusion of RSL effects in the transfer relations yields a considerable improvement in the estimated fluxes.

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Abbreviations

C D :

Drag coefficient for momentum

C H :

Drag coefficient for heat

d :

Displacement height (m)

h :

Canopy height (m)

i :

Index indicating momentum (M) or heat (H) transport

k :

von Kàrmàn constant

L :

Obukhov stability length (m)

L s :

Aerodynamic canopy length scale (m)

u :

Wind speed (m s−1)

u h :

Wind speed at canopy top (m s−1)

u * :

Friction velocity (m s−1)

z :

Height above the displacement height (zZd) (m)

z * :

Roughness sublayer height above the displacement height (m)

z 0 :

Aerodynamic roughness length (m)

z 0H :

Roughness length for heat (m)

Z :

Height above the ground (m)

Z * :

Roughness sublayer height measured from the ground (m)

α i :

Coefficient used in the stability functions

δ :

Average inter-element spacing (m)

\({\phi}\) :

Roughness sublayer profile function

η :

Coefficient used in roughness sublayer function

\({\Phi_{M,H}}\) :

Surface-layer stability function for momentum, heat

χ :

Height scaled with the roughness sublayer height (χ = z/z *)

ζ :

Height scaled with the Obukhov length (ζ = z/L)

λ :

Coefficient in the approximated roughness sublayer correction

μ M,H :

Coefficient in the approximated roughness sublayer correction

ν :

Coefficient in the approximated roughness sublayer correction

ψ M,H :

Integrated stability function for momentum, heat

θ :

Potential temperature (K)

θ * :

Surface-layer temperature scale (K)

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Correspondence to Koen De Ridder.

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De Ridder, K. Bulk Transfer Relations for the Roughness Sublayer. Boundary-Layer Meteorol 134, 257–267 (2010). https://doi.org/10.1007/s10546-009-9450-y

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Keywords

  • Atmospheric numerical modelling
  • Roughness sublayer
  • Surface-layer transfer relations