In 1963 Bouchet suggested a complementary concept for estimating large-scale evapotranspiration rates. His idea, since developed by Fred Morton and others, was that advection of air over a surface would mean that the humidity of the air would come into a dynamic equilibrium with the latent heat fluxes from the surface. What is measured as local evaporation and transpiration locally will therefore depend on what is happening up-wind. Thus, if the surface was dry, the humidity of the air would be relatively low, and the apparent potential evapotranspiration would be very high. If, on the other hand, the air mass was already humid and moving with low velocity, such that the vapour pressure deficit was low and the aerodynamic resistance was high, the apparent potential evapotranspiration would be low, even if energy and water were available. Based on this idea, both theoretical and practical studies have developed a relationship between actual evapotranspiration over an area, Et , to potential evapotranspiration, Ep, resulting in acceptable operational estimates of areal evapotranspiration. A full account of the development of the method is given in Morton (1983).
Potential evapotranspiration is generally defined as the local evapotranspiration under given atmospheric conditions when water supply is non-limiting. The use of evaporation pans as a way of estimating potential evapotranspiration (see Section 4.2.2) is essentially based on this idea. However, when considering a larger catchment or landscape scale, the complementary concept recognises that there is a feedback mechanism whereby changes in Et alter the temperature and humidity of the over-passing air which in turn changes Ep.
Thus instead of using Ep as a causal agent for estimating Et ,, Morton treats Ep as an effect of changes in Et caused by changes in the availability of water for evaporation from a larger area. This is demonstrated, under conditions of constant energy supply, in Fig. 10.9. Et increases from zero when there is no water available for evaporation from the surrounding area to a constant rate of Ew when there are no limitations on the availability of water. In contrast, Ep decreases from 2Ew, when Et = 0 and the air is hot and dry, down to a constant rate of Ew, when Et = 0 and the air is cool
and humid. Thus Morton postulates that, where conditions give near-steady fluxes, Ep and Et are complementary such that:
where the actual values of Ew and Ep must reflect changes in energy supply.
This equation provides the basis for the complementary relationship areal evapotranspiration model (CRAE). In conjunction with the CRAE model, a complementary relationship lake evaporation model (CRLE) provides estimates of lake evaporation from routine measurements of temperature, humidity and sunshine duration in the land environment (Morton, 1986). While evidence suggests that such a complementary relationship cannot strictly hold (LeDrew, 1979; Lhomme and Giulioni, 2006), Morton's results and modifications of the method (Crago and Crawley, 2005; Szilagyi and Jozsa, 2008), suggest that this can be a simple and useful way of estimating catchment-scale actual evapotranspiration, given estimates of potential evapotranspiration. Nash (1989) and Szilagyi and Jozsa (2008) point out that the complementary concept was not incompatible with the Penman approach to estimating potential evapotranspiration. It has been used with remote sensing information to estimate spatial patterns of evapotranspiration (e.g. Venturini et al., 2008) and as the basis for estimating evapotranspiration in a number of hydrological models.
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