With the definition of generalized potential temperature, a new generalized frontogenesis function, which is expressed as the Lagrangian change rate of the magnitude of the horizontal generalized potential temperature gradient, is derived. Such a frontogenesis function is more appropriate for a real moist atmosphere because it can reflect frontogenesis processes, in which the atmosphere in a frontal zone is typically characterized by neither completely dry nor uniform saturation. Furthermore, by derivation, the expression of generalized frontogenesis function includes both temperature and humidity gradients, which is different from and superior to the traditional frontogenesis function in moist processes, which also uses equivalent potential temperature. Diagnostic studies of real cases are performed and show that the generalized frontogenesis function in non- uniformly saturated moist atmosphere indeed provides a useful tool for frontogenesis, compared to using the traditional frontogenesis function. The new frontogenesis function can be used in situations involving either a strong temperature or moisture gradient and is closely correlated with precipitation.
A new frontogenesis function is developed and analyzed on the basis of a local change rate of the absolute horizontal gradient of the resultant deformation. Different from the traditional frontogenesis function, the newly defined deformation frontogenesis is derived from the viewpoint of dynamics rather than thermodynamics. Thus, it is more intuitive for the study of frontogenesis because the compaction of isolines of both temperature and moisture can be directly induced by the change of a flow field. This new frontogenesis function is particularly useful for studying the mei-yu front in China because mei-yu rainbands typically consist of a much stronger moisture gradient than temperature gradient, and involve large deformation flow. An analysis of real mei-yu frontal rainfall events indicates that the deformation frontogenesis function works remarkably well, producing a clearer mei-yu front than the traditional frontogenesis function based on a measure of the potential temperature gradient. More importantly, the deformation frontogenesis shows close correlation with the subsequent（6 h later） precipitation pattern and covers the rainband well, bearing significance for the prognosis or even prediction of future precipitation.
