Estimating Et over a landscape area or catchment

One of the problems of estimating Et is that of estimating the total flux over an area, including the combined effects of evaporation from water surfaces and the soil, evaporation of intercepted water on the vegetation canopy and transpiration from leaf surfaces. This is similar to the problem of estimating precipitation over an area based on point rain-gauge measurements, but with the difference that the number of sites with the measurements necessary to estimate evapotranspiration will in general be much smaller. Thus, de facto, hydrologists will often assume that actual evapotranspiration is relatively conservative over an area, so that a measurement at one site will provide a good estimate of the flux over a larger area. This is probably not a bad assumption when rates of actual evapotranspiration are limited by the energy inputs; it can be a very bad assumption when rates of actual evapotranspiration are limited by water availability.

A very obvious example occurs in areas that are seasonally dry, e.g. in summer in regions with a Mediterranean climate. As the soils dry out, progressively more and more of the landscape will be subject to water limitations (something that might also depend on the flow of water downslope and depths of soil and rooting in the landscape). An extreme case is where there is a landscape of dry hillslopes where evapotranspiration is small and wet valley bottoms that are still transpiring freely (see example calculation).

Example: Evapotranspiration over a catchment area with wet and dry surfaces Consider a situation where, at the end of a dry period, 80 per cent of a catchment is effectively water limited with actual evapotranspiration close to zero, while the remaining 20 per cent in the valley bottoms or irrigated agricultural fields are still transpiring freely at, say 5 mm day-1. Thus the actual average flux rate from the catchment would be:

Note that in this case, the air moving over the landscape would be warmed, and its specific humidity reduced, by the specific heat flux from the dry hillslopes where we would expect the Bowen ratio of C/lEt to be very high. Thus evapotranspiration over the valley bottoms would be expected to be enhanced as a result of advection of energy in the air moving from the upwind slopes.

However, if the average over the area was based only on the measurements in the dry area, then it would be estimated as zero; if it was based on measurements over the wet area, then it would be estimated as 5 mm day-1. Both would be quite wrong.

Thus the pattern of actual evapotranspiration over a landscape will have an important effect on catchment average actual evapotranspiration rates and therefore closure of the water balance for a catchment. In this case, the estimate could be improved by having two tiles with different characteristics (an approach now often used in the land surface parameterisations of atmospheric circulation models; see Section 10.6) but the mix of different rates of Et over different parts of the landscape will usually be more complex. As noted earlier, latent heat losses over one part of the landscape will affect the humidity of the air downwind. This is, in fact, the basis for a quite different approach to estimating Et based on a concept of complementarity.

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