A theory for the retrieval of virtual temperature from winds, radiances and the equations of fluid dynamics

A technique to deduce the virtual temperature from the combined use of the equations of fluid dynamics, observed wind and observed radiances is described. The wind information could come from ground-based sensitivity very high frequency (VHF) Doppler radars and/or from space-borne Doppler lidars. The radiometers are also assumed to be either space-borne and/or ground-based. From traditional radiometric techniques the vertical structure of the temperature can be estimated only crudely. While it has been known for quite some time that the virtual temperature could be deduced from wind information only, such techniques had to assume the infallibility of certain diagnostic relations. The proposed technique is an extension of the Gal-Chen technique. It is assumed that due to modeling uncertainties the equations of fluid dynamics are satisfied only in the least square sense. The retrieved temperature, however, is constrained to reproduce the observed radiances. It is shown that the combined use of the three sources of information (wind, radiances and fluid dynamical equations) can result in a unique determination of the vertical temperature structure with spatial and temporal resolution comparable to that of the observed wind.