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e sat ( T )
e sat ( T )
e a
e a
x
x
E > E eq
E = E eq
Figure 7.6 The concept of equilibrium evaporation for a closed box (left) and an
atmospheric boundary layer that exchanges water vapour with the free troposphere
through entrainment of dry air (right). The air lows in the direction of the black
arrow. The grey arrows signify evaporation from the surface or loss of water vapour
through entrainment (only at the right). The saturated vapour pressure (top) increases
as air lows over the surface because heat is added to the air as well.
Question 7.9: Compute the Bowen ratio for a situation where equilibrium evaporation
takes place for two conditions assume γ = 0.66 hPa K -1 :
a) Air temperatures is 5 ºC.
b) Air temperature is 25 ºC.
c) Which of the two cases has the highest evaporation?
Question 7.10: Show that for the closed box in Figure 7.6 (left) indeed the VPD
( e a - e sat ( T a )) does not change in time if the evaporation is equal to the equilibrium
evaporation.
An indirect effect of the entrainment of dry air is that a negative feedback will
occur with the surface evapotranspiration: more dry air entrainment leads to a drier
boundary layer, which leads to an increase of surface evapotranspiration (through
the aerodynamic term). This increase in evapotranspiration in turn counteracts -
partly - the effect of the dry air entrainment by moistening the boundary layer (see
feedback loop 3 in Figure 7.7 and van Heerwaarden et al., 2009 ). Other negative
feedbacks that limit the variation in the aerodynamic term are the following. If
evapotranspiration becomes limited, the sensible heat lux increases, which leads to
direct heating of the ABL, a subsequent increase of the VPD and hence an increase
of evapotranspiration (loop 1.1). The ABL is also heated by the entrainment of
warm air from the free troposphere, which leads to an increase of evapotranspi-
ration through increased VPD as well (loop 1.2). Finally, direct moistening of the
 
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