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Scalar Concentration Profiles in the Canopy and Roughness Sublayer

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Abstract

The mean flow and scalar concentration profiles within and above a tall canopy are well known to violate the standard boundary-layer flux-gradient relationships. We present a theory for the scalar concentration profile that is comprised of a canopy exchange model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing-layer analogy for the flow at canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the profiles depend and a set of criteria that allows a reduction in the empiricism associated with earlier forms in the literature. Predictions of the mean scalar concentration profiles are shown to match observations over a wide range of diabatic stabilities for both potential temperature and water vapour.

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Abbreviations

a :

Frontal leaf area per unit volume (m2 m−3)

c d :

Drag coefficient at the leaf level

c * :

Scale of the turbulent scalar concentration fluctuations above the canopy

C :

Time and spatially averaged scalar concentration

C h :

Value of C at canopy top

C 0 :

Reference scalar concentration

d t :

Virtual origin for profiles above the canopy

\({\tau \ \ (F_{c})}\) :

Vertical flux of momentum (scalar C)

F D :

Kinematic drag force (m s−2)

f :

Parameter for the within-canopy scalar concentration profile

g c :

Leaf level boundary-layer conductance for scalar transfer

K m (K c ):

Turbulent diffusivity for the vertical momentum (scalar) flux (m2 s−1)

l m (l c ):

Mixing length for the vertical turbulent momentum (scalar) flux (m)

ℓ m (ℓ c ):

Value of l m (l c ) within the canopy

L :

Obukhov length (m)

L c :

Length scale for the absorption of momentum by the canopy (m)

r :

Leaf level Stanton number (Nusselt number if heat is the scalar)

S c (z):

Turbulent Schmidt number (as a function of height)

S cc (P tc ):

Turbulent Schmidt number at canopy top (Prandtl number if heat is the scalar)

S χ :

Source/sink of scalar

u * :

Friction velocity (m s−1)

U :

Time and spatially averaged profile of wind speed (m s−1)

U h :

Value of U at canopy top

z :

Vertical co-ordinate with the origin at canopy top

z0m (z0c ):

Roughness length for momentum (scalar concentration)

β (β N ):

u*/U h (value of β in neutral conditions)

κ :

von Karman constant

ρ :

Density of air (kg m−3)

\({\phi_{m} \ \ (\phi_{c})}\) :

MOST stability functions for momentum (scalar)

\({\hat{\phi}_{m} \ \ (\hat{\phi}_{c})}\) :

RSL function for momentum (scalar)

\({\phi_{m} \ \ (\phi_{c})}\) :

Generalized stability functions for momentum (scalar)

\({\psi_{m} \ \ (\psi_{c})}\) :

Integrated forms of the MOST stability functions

\({\hat{\psi}_{m} \ \ (\hat{\psi}_{c})}\) :

Integrated forms of the RSL functions

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Authors and Affiliations

  1. CSIRO Marine and Atmospheric Research, FC Pye Laboratory, Canberra, Australia

    Ian N. Harman & John J. Finnigan

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  1. Ian N. Harman
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  2. John J. Finnigan
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Correspondence to Ian N. Harman.

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Harman, I.N., Finnigan, J.J. Scalar Concentration Profiles in the Canopy and Roughness Sublayer. Boundary-Layer Meteorol 129, 323–351 (2008). https://doi.org/10.1007/s10546-008-9328-4

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