Influence of cloud temperature on brightness temperature and consequences for water retrieval

In this paper we show that to improve existing radiometric methods to estimate path-integrated cloud liquid water, the physical approximations commonly used concerning the direct model have to be reconsidered. In fact, even if the problem that consists in deducing the brightness temperatures from atmospheric quantities is rigorously solved (for a nonscattering atmosphere) by means of the radiative transfer equation, the relation between radiometric temperatures and one physical global quantity integrated content is not always determined from theoretical considerations. In all the dual-frequency retrieval models commonly used, the method always consists in the separation of the two water phases based on two radiometric measurements: one at a vapor-sensitive frequency and one at a cloud-sensitive frequency. The variations in the vertical absorption profile are neglected, in particular the temperature one, thus leading to linear expressions that allow an easier resolution of the inverse problem. Through an important set of simulated data, the authors have proved that a new global variable, which allows us to take the temperature profile into account, can greatly improve the modelization of the direct problem. The introduction of this quantity helped the authors to show that the relationship between brightness temperature and liquid water content is a nonlinear one. Even if the analytical inversion of the direct model allows only a relatively small improvement in water vapor and liquid water prediction, the consequences for the inverse problem are also discussed. To improve the existing dual-frequency algorithm, additional information sensitive to temperature profile is needed. For example, a third radiometer frequency can improve the inverse algorithm, but it should be used in a nonlinear expression