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Table of Contents

  1. WATFLOOD USER’S MANUAL
  2. HYDROLOGICAL MODEL
  3. WATERSHED DATA REQUIREMENTS
  4. MODEL PARAMETERS AND OPTIMIZATION
  5. RAINFALL DATA PROCESSING
  6. FLOW DATA
  7. SNOW DATA PREPARATION
  8. TEMPERATURE DATA
  9. RADIATION DATA
  10. OUTPUT FILES
  11. PROGRAM REVISIONS
  12. BIBLIOGRAPHY

2.3.1   Priestley-Taylor Equation

The Priestley-Taylor model (Priestley and Taylor, 1972) is a modification of Penman’s more theoretical equation. Used in areas of low moisture stress, the two equations have produced estimates within approximately 5% of each other (Shuttleworth and Calder, 1979). An empirical approximation of the Penman combination equation is made by the Priestley-Taylor to eliminate the need for input data other than radiation. The adequacy of the assumptions made in the Priestley-Taylor equation has been validated by a review of 30 water balance studies in which it was commonly found that, in vegetated areas with no water deficit or very small deficits, approximately 95% of the annual evaporative demand was supplied by radiation (Stagnitti et al., 1989).

It is reasoned that under ideal conditions evapotranspiration would eventually attain a rate of equilibrium for an air mass moving across a vegetation layer with an abundant supply of water, the air mass would become saturated and the actual rate of evapotranspiration (AET) would be equal to the Penman rate of potential evapotranspiration. Under these conditions evapotrans-piration is referred to as equilibrium potential evapotranspiration (PETeq). The mass transfer term in the Penman combination equation approaches zero and the radiation terms dominate. Priestley and Taylor (1972) found that the AET from well watered vegetation was generally higher than the equilibrium potential rate and could be estimated by multiplying the PETeq by a factor (a) equal to 1.26:

          (2.7)

where Kn is the short-wave radiation, Ln is the long-wave radiation, s(Ta) is the slope of the saturation-vapour pressure versus temperature curve, g is the psychrometric constant, rw is the mass density of water, and lv is the latent heat of vaporization. Although the value of a may vary throughout the day (Munro, 1979), there is general agreement that a daily average value of 1.26 is applicable in humid climates (De Bruin and Keijman, 1979; Stewart and Rouse, 1976; Shuttleworth and Calder, 1979), and temperate hardwood swamps (Munro, 1979). Morton (1983) notes that the value of 1.26, estimated by Priestley and Taylor, was developed using data from both moist vegetated and water surfaces. Morton has recommended that the value be increased slightly to 1.32 for estimates from vegetated areas as a result of the increase in surface roughness (Morton, 1983; Brutsaert and Stricker, 1979). Generally, the coefficient a for an expansive saturated surface is usually greater than 1.0. This means that true equilibrium potential evapotranspiration rarely occurs; there is always some component of advection energy that increases the actual evapotranspiration. Higher values of a, ranging up to 1.74, have been recommended for estimating potential evapotranspiration in more arid regions (ASCE, 1990).

The a coefficient may also have a seasonal variation (De Bruin and Keijman, 1979), depending on the climate being modeled. The study by DeBruin and Keijman (1979) indicated a variation in a with minimum values occurring during the mid-summer when radiation inputs were at their peak, and maxima during the spring and autumn (winter values were not determined) when in relation to advective effects, radiation inputs were large. The equation has performed very well, not only for open water bodies, but also for vegetated regions. The satisfactory performance of the equation is probably because the incoming solar radiation has some influence on both the physiological and the meteorological controls of evapotranspiration. A value of 1.26 has been used for alpha throughout. Temporal variations in a as suggested by researchers are emulated by the conversion factors used in the calculation of AET from the PET which is described below.

Estimates of PET using the Priestley-Taylor equation have been adjusted as a function of the difference in albedo at the site where measurements of radiation have been made (albe), and the land classes with differing albedo (alb). In the adjustment, it is assumed that the ground heat flux (which should be included in the net all-wave radiation data if it is available) contributes 5% of the overall energy. The remaining 95% of the potential evapotranspiration estimate is scaled as a function of the difference in albedo:

          (2.8)

Potential Evapotranspirationarrowleft.jpg (828 bytes) arrowright.jpg (541 bytes)Hargreaves Equation
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