A generalized frontogenesis function and its application

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.