Simulations are widely used to predict noise emissions from traffic, railroad, aircraft, and wind farms and for sound field control. The latter employs multiple sources interacting and it requires accurate phase information. Acoustic models require precise characterization of the medium properties. The logarithmic profile is one of the most commonly used forms to model the wind speed. However, this profile is accurate only in neutral conditions, i.e., when there is not heat flux at the surface. The conventionally neutral boundary layer (CNBL) is the most frequently occurring neutral regime. In this case, the logarithmic profile underestimates the wind speed. This paper analyses the effect that this modelling error has on the sound field close to the ground, for near-ground sources. The first section introduces an approximation of the wind and temperature profiles in such a regime. Afterwards, the sound fields corresponding to the logarithmic profile, a representative CNBL profile, and three more test cases are simulated using the Crank-Nicholson parabolic equation; these are compared employing different metrics. The difference in wind speed introduces a phase error that increases with distance. Moreover, wind speed underestimations also lead to underpredictions of the energy refracted downward.