From data obtained in field studies of growth and water-use characteristics of cotton at Kimberley Research Station, Kununurra, Western Australia, a method is developed for obtaining an approximation of Penman's potential evaporation. The predictor used for this approximation is an adjusted version of a weighted vapour pressure deficit based on mean maximum screen temperature and found previously to provide an efficient basis for estimating evaporation from the standard (sunken) Australian evaporation tank. Using daily data, a distinctive linear relationship between the weighted vapour pressure deficit and Penman evaporation was identified for periods with low advection. An adjustment factor, based upon either the wet bulb depression or relative humidity, was then derived empirically to make this relationship applicable over a range of dryness conditions. When applied with mean data over ten-day intervals, the method was found to give close agreement with Penman evaporation at four Australian stations having differing climatic environments. At all of these stations the approximated value is more highly correlated with the Penman evaporation than are the estimates of tank evaporation obtained from empirical relationships having either the unadjusted weighted vapour pressure deficit or the simple saturation deficit as the independent variable. At two extra-tropical stations, the correlation between Penman evaporation and the approximated value exceeds that between Penman and observed tank evaporation, but at tropical stations the latter correlation is slightly higher. A broad regional application of the method is carried out, using published mean monthly climatic data for a network of 143 Australian stations. An index of advective strength derived as the ratio of the estimated tank evaporation (from the unadjusted weighted vapour pressure deficit) to the approximated Penman evaporation is also calculated. These parameters are mapped and discussed for summer and winter situations.