Wind friction parametrisation used in emission models for wastewater treatment plants: A critical review

Emission models are widely applied tools for estimating atmospheric emissions from wastewater treatment plants (WWTPs). The friction velocity u_∗ is a key variable for the modelling of emissions from passive liquid surfaces in WWTPs. This work evaluated different parametrisations of u_∗ for passive liquid surfaces at the scale of WWTP units, which present relatively small fetches, based on available wind friction and wave data measured at wind-wave tanks (fetches spanning from approximately 3 to 100 m, and wind speeds from 2 to 17 m s^-1). The empirical correlation by Smith (1980; J. Phys. Oceanogr. 10, 709-726), which has been frequently adopted in air emission models (despite the fact that it was originally derived for the ocean) presented a general tendency to overestimate u_∗, with significant (although not extreme) relative errors (mean and maximum errors of 13.5% and 36.6%, respectively); the use of Charnock's relation, with Charnock constant 0.010, performed in a very similar manner (mean and maximum errors of 13.3% and 37.8%, respectively). Better estimates of u_∗ were achieved by parametrisations based on the significant wave steepness. Simplified correlations between the wind drag and the non-dimensional fetch were obtained. An approach was devised, comprising the use of Charnock's relation (with Charnock constant 0.010) and of these simplified correlations, depending on the ranges of frequency of the peak waves, fetch and wind speed. The proposed approach predicted u_∗ with improved accuracy (mean, maximum and 95%-percentile relative errors of 6.6%, 16.7% and 13.9%, respectively), besides being able to incorporate the influence of the fetch in the wind drag, thus taking into account the size of the tanks in the WWTPs.