The Priestley and Taylor <1972> method (PT) and the complementary relationship (CR) introduced by Bouchet <1963> for the estimation of extended area or regional evapotranspiration are examined using a model of the coupled interactions between the mixed layer and the land surface. The model is shown to be in good agreement with observations from the First International Satellite Land Surface. Climatology Project Field Experiment. It appears that the parameter &agr; in the PT is slightly lower than the suggested constant value 1.26 and is quite insensitive to the growth of the boundary layer. We find some support for the CR but do not resolve the problem of estimating the potential evaporation under unstressed conditions.¿ 1997 American Geophysical Union