Turbulent Transport in the Atmospheric Surface Layer - Transport in the Atmosphere-Vegetation-Soil Continuum - page 97

Figure 3.13 Deinition of layers within the surface layer (height scale is roughly
logarithmic).

Question 3.11: In Eq. ( 3.16 ) the change with height of the sensible heat lux is coupled to
the change in time of the mean temperature of a layer between the surface and a height z .
a) Derive a similar expression for the change with height of the latent heat lux (take
care that the units are correct on both sides of the equality sign).
b) For the same date as depicted in Figure 3.3 , the increase of the speciic humidity in
the lowest 20 m of the atmosphere was approximately 0.25 g kg -1 per hour. Compute
the change with height of the latent heat lux in between the surface and a height of 20
m (assume reasonable values for the air density and the latent heat of vaporization).
c) Around 8 UTC the latent heat lux was approximately 150 W m -2 . How large is the change
of the latent heat lux with height as a percentage of the surface latent heat lux?

At the lower boundary of the surface layer Earth's surface is located, covered by
trees, grass, stones, ice, buildings, streets, etc. Nearly all natural and man-made sur-
faces can be considered to be aerodynamically rough. This means that the roughness
obstacles (with height h c , canopy height; see Figure 3.13 ) are much higher than the
thickness of the viscous sublayer which is adjacent to every interface between a luid
and a smooth surface (solid or luid). 12 The fact that the air has to low around the
roughness obstacles implies that between and just above those obstacles the mean tur-
bulent quantities (wind speed, luxes, etc.) vary horizontally. For example, the wind
speed just behind a tree is different from the wind speed between the trees. But even
well above the roughness obstacles, the effect of the surface on the proiles of mean
quantities (e.g., wind speed and temperature) is visible. The layer in which the spatial
variation of the rough surface inluences the shape of the proiles is called the rough-
ness sublayer . The thickness of this layer is of the order of 1.6 h c (Wieringa, 1993 ) but
also depends on the structure of the canopy (Graefe, 2004 ).

12 The thickness of this viscous sublayer is δν

≈ 5/ u where ν is the kinematic viscosity. Depending on u* , δ is of
the order of 1 mm (Garratt, 1992 ). In fact the combination of surface properties and the low determine whether a
surface is aerodynamically rough.