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Figure B3.1.2 Sensitivity of actual evapotranspiration rates estimated using the Penman-Monteith equa-
tion for different values of aerodynamic and canopy resistance coefficients (after Beven, 1979a, with kind
permission of Elsevier).
The effects of drying of the soil on evapotranspiration rates can be reflected in an increase in r c
with decreasing soil moisture, although it is known that other factors, such as leaf temperature,
carbon dioxide concentration, insolation and even chemical signalling in the plant can play
a role in determining the effective canopy resistance. Calder (1977) suggested an empirical
relationship for the change in canopy resistance for transpiration that was a product of a
seasonal sinusoid and a function of vapour pressure deficit. Other, more complex, relationships
have been proposed by Jarvis (1976), Sellers (1985) and Tardieu and Davies (1993). These types
of relationship, and their links to carbon dioxide exchanges, are included in many SVAT or
LSP models linked to atmospheric circulation models. Such models, however, require many
more parameter values and there has also been a move, led by John Monteith, to investigate
the possiblity of using simple models with fewer parameters (Monteith, 1995a, 1995b).
More recently, it has been suggested that it might be possible to introduce additional con-
straints on rates of evapotranspiration by coupling carbon to the water budget of the plant
canopy. Evapotranspiration losses from plants are, after all, really only a biproduct of the need
for plants to exchange carbon dioxide with the atmosphere through their stomata for the pur-
poses of photosynthesis. Thus, if the net productivity of carbon and its use could be predicted,
then this would provide an important constraint on actual evapotranspiration. There are a
number of vegetation growth models available in the literature, with many parameters to be
specified. These do not always produce good predictions of productivity (e.g. Mitchell et al. ,
2009). It has been suggested, however, that it might be possible to simplify this approach by
invoking an optimality principle whereby a plant optimises its carbon production given the
prevailing boundary conditions of energy and water availability (Schymanski et al. , 2007).
Schymanski et al. (2008) have implemented a model that optimises the carbon cost of main-
taining its root system in the face of changes in the profile soil water content and have shown
that the resulting time evolution of the rooting profile provides a better prediction of evapotran-
spiration than a model using a fixed rooting profile. They have also shown that invoking the
optimality principle in constraining actual evapotranspiration can help guide the calibration
of catchment scale models (Schymanski et al. , 2009; see also Section 9.7).
The assumptions of the Penman-Monteith model for evapotranspiration can be summarised
as follows:
 
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