Turbulent Transport in the Atmospheric Surface Layer - Transport in the Atmosphere-Vegetation-Soil Continuum - page 99

for other, similar situations. With such a relationship one needs to measure all variables
but one : the one that has not been measured can then be calculated from the similarity
relationship.

In this section we present one speciic set of similarity laws commonly used in surface
layer meteorology, viz. Monin-Obukhov similarity theory (MOST; Monin and Obuk-
hov, 1954 ; see Foken, 2006 , for an account of the history of MOST). MOST was devel-
oped for use in the surface layer, but above the roughness sublayer (see Section 3.4.3 ).
Although MOST can be applied to many mean turbulent quantities, we focus here on
vertical gradients of mean variables (e.g., mean wind speed, mean temperature).

3.5.1 Dimensionless Gradients: Relevant
Variables in MOST
The relationship between the lux and the vertical gradient of the transported quantity
(Eq. ( 3.1 )) depends on a very large number of factors. To make an analysis possible,
MOST is restricted to situations in which the mean turbulent quantities:

• Do not change in time (stationarity).

• Do not change in space horizontally, that is, the only variation is in the vertical direction

(horizontal homogeneity).
Are not inluenced by processes occurring outside the surface layer (this appears one of •

the weak points of MOST, as there is no strict boundary between turbulence in the sur-
face layer and turbulence in the rest of the boundary layer above).

Then, the main ingredients that shape the vertical gradients in the surface layer are:

1. The surface lux of the quantity of interest. 14
2. The height above the surface (because the domain of the surface layer is bounded at the
lower end). In fact, the height above the zero-plane displacement should be used (see
Section 3.5.6 ).
3. The intensity of the turbulent motion. For this we revert to the TKE budget equation (Eq.
( 3.10 )). We assume that mainly the buoyancy production term and the shear production
term are relevant. 15 Furthermore, in the shear production term ∂
∂

u
z

itself is shaped by


 

g 

  and the shear stress ( u ′′)

w

′′

the turbulence, so that only the buoyancy term θ

θ

v

remain as independent variables.

14 In Monin and Obukhov ( 1954 ) local luxes are used with the restriction that within the surface layer they differ
little from the surface luxes. Here we use surface luxes, based on the premise that scaling should be based on
external variables rather than internal variables In practice, the distinction between local luxes and surface luxes
is not a major issue, except during stable or transition conditions (see Braam et al., 2012 ; van de Wiel et al.,
2012a ).
15 Dissipation a loss term that is always present and which consumes all net production of TKE.