Surface Energy Balance Notes

Potential Evapotranspiration, Priestley-Taylor Model and the Decoupling Coefficient
As shown by Priestley and Taylor (1972), the Priestley-Taylor equation provides robust estimates of potential evapotranspiration in the absence of advection from a dense well-watered canopy or a free-water surface in the absence of advection. Evaporation from such a wet surface is representative of the condition when the surface resistance rs=0. Defining this rate as LE0, it follows that the Priestley-Taylor rate

LEPTLE0                                                                                                                                                            Eqn 1

If this were not true, the Priestley-Taylor model would not perform as well as it did for free-water or ocean surfaces (in the absences of advection), as shown by Priestley and Taylor (1972). Further, since the surface-atmosphere decoupling coefficient

Ω=LE/LE0                                                                                                                                                           Eqn 2       

(Monteith 1965), it follows that

Ω=LE/LEPT                                                                                                                                                         Eqn 3

This should be valid for non-advective conditions, and/or when the influence of air dryness (i.e. VPD) varies in proportion to net radiation. The Penman equation or the Penman-Monteith equation with
rs=0 should provide a more accurate estimate of LE0 we=hen such conditions are not met. Considering that the Priestley-Taylor model is given by

LEPT=αPTLEeq                                                                                                                                                    Eqn 4

it follows from Eqn 3 and 4 that
 

Ω=1/αPT*LE/LEeq                                                                                                                                                Eqn 5

Therefore, Ω and αPT are inversely related, and when LE=LEeq

Ωeq=αPT-1                                                                                                                                                           Eqn 6

as shown by Pereira (2004). 

References
Monteith, J.L., 1965. Evaporation and environment. Symp. Soc. Exptl. Biol. 19, 205–234.
Pereira, A.R., 2004. The Priestley-Taylor parameter and the decoupling factor for estimating reference evapotranspiration. Agric. For. Meteorol. 125 (3-4),
305-313.
Priestley, C.H.B., Taylor, R.J., 1972. On the assessment of surface heat flux and evaporation using large-scale parameters. Mon.Weather Rev. 100 (2), 81–92.