Et P Q G [AS

where Et is the catchment average actual evapotranspiration flux, P is the estimated catchment average precipitation input, Q is the measured stream discharge, G is any groundwater discharge across the basin divides, and AS is the change in storage (in brackets because it is often assumed negligible over of long time period such as the water year).

This approach, however, assumes that accurate estimates of the precipitation inputs and discharge outputs are available, and that the change of storage can be either considered to be negligible or estimated. Unfortunately, estimating changes of storage at the catchment scale is equally fraught with difficulty. The result is that any errors in the terms on the right-hand side of the water balance equation will result in error in the estimate of actual evapotranspiration. Thus, in what follows, we will consider ways of estimating actual evapotranspiration more directly.

Water balance estimates of evapotranspiration can, however, be useful. In 1954, an engineer for the Fylde Water Board, Frank Law, started lysimeter and water balance experiments at the Stocks Reservoir site in the Forest of Bowland, Lancashire to investigate the hypothesis that tree-covered catchments lost more water to evapotranspiration than grassland catchments. His conclusion that planting forest on water supply reservoir catchment areas might greatly reduce water yield was controversial and led to the more detailed studies in the paired catchment experiments at Plynlimon, mid-Wales. These experiments, at least initially, showed that Frank Law was right, with up to 60 per cent greater evapotranspiration at Plynlimon in the early stages of forest growth on the forested River Severn catchment compared with the grassland River Wye (Fig. 10.1). This simple conclusion can, however, be complicated by other effects. At the small Coalburn catchment in the Kielder Forest in northern England, Robinson (1998) shows how forest-ditching associated with the planting of trees resulted in drier soils and initially caused a reduced actual evapotranspiration loss and that it was some 20 years before evapotranspiration rates returned to pre-plantation levels (Fig. 10.2).

To obtain more direct estimates of evapotranspiration, we need to consider the energy budget of a surface. In Fig. 10.3, we distinguish water and land surfaces. Over a water surface, water is always available, but energy from the Sun can penetrate the surface and act to heat the water body as well as evaporate water from the surface as latent heat. Sensible heat energy can also be supplied directly from (or lost to) the lower layer of the atmosphere, depending on the difference in temperature between the water and the air. The transfer of sensible heat will be much more efficient with a higher wind speed even though a water surface is relatively smooth (has a relatively high aerodynamic resistance to transport). Over a land surface, on the other hand,

Fig. 10.1 Annual water balance estimates of evapotranspiration (as precipitation-discharge) expressed as a ratio of totals from the 70 per cent forested River Severn to the grassland River Wye catchments at Plynlimon, mid-Wales. The dotted line is a 5-year moving average. Data taken from Hudson et at. (1997). Forest harvesting in parts of the River Severn started in 1985.

Fig. 10.1 Annual water balance estimates of evapotranspiration (as precipitation-discharge) expressed as a ratio of totals from the 70 per cent forested River Severn to the grassland River Wye catchments at Plynlimon, mid-Wales. The dotted line is a 5-year moving average. Data taken from Hudson et at. (1997). Forest harvesting in parts of the River Severn started in 1985.

Fig. 10.2 Changes in actual évapotranspiration (as precipitation-discharge in millimetres) in comparison with Penman potential evapotranspiration (see Section 10.2.3) at the Coalburn experiment catchment in northern England. Drainage and planting of conifer plantations started in this catchment in 1972. The solid line is a moving average (from Robinson, 1998).

Fig. 10.2 Changes in actual évapotranspiration (as precipitation-discharge in millimetres) in comparison with Penman potential evapotranspiration (see Section 10.2.3) at the Coalburn experiment catchment in northern England. Drainage and planting of conifer plantations started in this catchment in 1972. The solid line is a moving average (from Robinson, 1998).

Fig. 10.3 Energy budget components of vegetation and water surfaces. Rj is incoming clear-sky shortwave radiation; Ra is reflected short wave radiation; Ro is outgoing long-wave radiation; C is sensible heat flux; XEa is actual latent heat flux; V is storage of energy in vegetation or water body; G is energy exchange with ground; Ps is energy used in photosynthesis. Note that all terms are expected to vary in space and time.

Fig. 10.3 Energy budget components of vegetation and water surfaces. Rj is incoming clear-sky shortwave radiation; Ra is reflected short wave radiation; Ro is outgoing long-wave radiation; C is sensible heat flux; XEa is actual latent heat flux; V is storage of energy in vegetation or water body; G is energy exchange with ground; Ps is energy used in photosynthesis. Note that all terms are expected to vary in space and time.

such transport can be much more efficient over a rough tree canopy (which has a low aerodynamic resistance) but evaporation and transpiration may be limited by the availability of water, particularly after extended dry periods. The structure of a vegetated surface may also be much more complicated, with multiple leaf layers at different levels contributing to the use of energy in photosynthesis and loss of water by transpiration. A wet soil surface, if energy is available to provide the latent heat of vaporisation, might also contribute to the total latent heat flux through evaporation. The soil can also act as a heat store, generally heating up during the day and releasing heat during the night. Evaporation from a bare soil surface is somewhat simpler, but can still be limited by water availability once the surface starts to dry out.

In the diagram, R} is the incoming short-wave solar radiation, Ra is the reflected short-wave radiation, and Ro is the net outgoing long-wave radiation from the land or water surface. These terms can be measured by a net radiometer as net radiation RN. C is the sensible heat transfer to the air, V is the change in stored energy in the vegetation canopy or water body, and G is the energy transfer between canopy or water and the underlying soil or lake bed. Ps is the energy used in photosynthesis. This is normally small relative to the other terms and usually neglected. Then the energy balance equation can be written as follows:

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