Nocturnal boundary layer profiles and measured frequency dependent influence on sound propagation

The stability of the nocturnal layer is expressed with the Obukhov length L which includes (in the bulk definition) a relation of the wind speed gradient to the temperature gradient. The effective sound speed gradient includes the sum of the wind speed gradient and temperature gradient. The main result is that the description of sound propagation should be improved by use of the Obukhov length to include the stability effects of the atmosphere which is especially necessary in the case of upwind sound propagation during the nocturnal boundary layer.