Theoretical and experimental results for the distribution of molecular orientations at the liquid/vapour interface of water are compared. The present calculations are based on an extended mean-field density functional theory applied to an intermolecular potential model containing dipolar and quadrupolar interactions, with parameters chosen to agree with the TIP4P model of water. The results for the orientational order parameters at the interface are used to calculate several observable quantities as functions of temperature, namely: (i) the surface electrostatic potential, (ii) the coefficient of ellipticity; (iii) the nonlinear susceptibility measured by second-harmonic generation. Comparisons are made with both the experimental and computer simulation data for water. The limitations of current methods for revealing the preferred molecular orientations at an interface are discussed.