Geoscience Reference
In-Depth Information
The Penman-Monteith equation is very similar to the Penman equation, except for
the factor 1+ r
r
c
in the denominator. 3 This modiication has the following effects:
a
The canopy resistance is the main determining factor for the partitioning of available
energy between latent heat lux and sensible heat lux ( Figure 7.3a ). For small values
of the canopy resistance most (but not all) available energy is used for transpiration,
whereas when the canopy resistance is large, transpiration will be reduced (because the
denominator of both the radiation term and the aerodynamic term will increase). But,
whereas r c = 0 s m -1 does not imply that all energy is used for transpiration, r c does
imply the absence of transpiration.
The partitioning of available energy also depends on the aerodynamic resistance (
Fig-
ure 7.3b ). But this inluence is modiied by the canopy resistance in peculiar way. If the
canopy resistance is zero or low, a reduced r a (e.g., due to higher wind speed) always
leads to a higher evapotranspiration. This seems trivial, as a more eficient exchange
of water vapour between the surface and the air should favour evapotranspiration. But
the same argument could hold for the sensible heat lux. However, for a ixed available
energy, only one of the two luxes can increase and the other has to decrease accordingly.
So why does the evapotranspiration 'beneit' from a lower aerodynamic resistance if the
canopy resistance is low? And why does the reverse happen when the canopy resistance
is high: the sensible heat lux increases with decreasing r a ?
The key to this problem is the surface temperature, which inluences both H and L v E
(through e sat ( T s ); see Eq. ( 7.14 )). A lower r a leads to a stronger coupling between surface
and atmosphere. Hence, a smaller contrast in temperature and humidity between the sur-
face and the atmosphere is suficient to yield the same luxes of sensible and latent heat:
the surface temperature will be closer to the air temperature.
If
r c is small, the change in total resistances for heat ( r a ) and moisture ( r a + r c ) will be
nearly identical. Then the impact of a change in r a on H and L v E depends solely on
the related changes in T a - T s and e a - e sat ( T s ), respectively (see Eqs. ( 7.8 ) and ( 7.14 )).
Because the latter can approximated as VPD + s ( T a - T s ), we can see that the relative
change in the contrast in moisture between atmosphere and surface will always be less
than the relative change in temperature contrast. Hence L v E beneits most from the
decreased aerodynamic resistance.
In the case of a large
r c , the changes in the total resistances for heat ( r a ) and moisture
( r a + r c ) will no longer be identical. The relative decrease in r a + r c will be much less
than that in r a . If we assume r a + r c to be nearly constant, while the surface-to-atmo-
sphere moisture contrast decreases due to the decrease in surface temperature, the
evapotranspiration will decrease with decreasing aerodynamic resistance (in favour
of an increase of the sensible heat lux).
r
r
3 Often γ 1+
c
a
is denoted by γ* , a psychrometric constant that takes into account that the resistances for moisture
and heat transfer differ.
 
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