| First using analytical method, we obtained the nonlinear baroclinic subcritical instability criterion and symmetric subcritical instability criterion. Second usingnumerical experiments, we analyzed the influenced fact on the baroclinicsubcritical instability, and we also analyzed what the nonlinear subcritical symmetric instability effects on a rainstorm, and advanced a new mechanism produced the rainstorm. The main conclusions are as follows:1. Starting from a two-layer nonlinear quasi-geostrophic baroclinic vorticity equation containing Ekman friction, a new generalized energy is proposed to act as Lyapunov function and thus a new criterion of nonlinear baroclinic subcritical instability containing two inequalities is obtained. One of the inequalities is that the initial disturbance amplitude is more than a critical value, and the other is that the frictional coefficient is more than another critical value. The former adds a strong restriction to the latter, thus denoting that the subcritical instability easily occurs for a finite-amplitude disturbance in the real atmosphere. The new criterion has greatly improved the previous results. The result also shows, for the waves of 0.5 k<6, the nonlinear baroclinic subcritical instability easily occurs than the barotropic one.2. A two-layer quasi-geostrophic model forced by surface friction and radiative relaxation is used to study numerically the phenomenon of subcritical instability in baroclinic atmosphere. The numerical experiments show that when nondimensionparameter 0.35 <0.65, the phenomenon of subcritical instability can exist in two-layer baroclinic atmosphere. The occurrence of subcritical instability is relative to The latitudinal gradient of Coriolis parameter . The latitudinal gradient of Coriolisparameter is also an important factor that affects the strength of baroclinic stability, the larger its value is, the smaller strength of the baroclinic stability is. i.e., the higher the latitude is, the more strength of the baroclinic stability is.when the atmosphere system occurs nonlinear instability in the subcritical instability region, it will split more wave resolutions than in the supercritical instability region and need more time to occur the subcritical instability, therefore it may have effect on the form and development of some synoptic system.3. Starting from nonlinear equations on the f-plane containing frictional dissipation under the Boussinesq approximation. A new kind of generalized energy is proposed as the Lyapunov function, and thereby resulting in a new criterion ofgeneralized nonlinear symmetric stability. It shows that not only must the dissipative coefficient be greater than a certain critical value but the initial disturbance amplitude must be synchronously smaller than another marginal value as well. It follows that the latter imposes a crucial constraint on the former, thus leading to the fact that when the amplitude is bigger compared to another critical value, generalized nonlinear subcritical symmetric instability may occur.4. Having experiment of the rainfall from 12UT of 4th to 12UT 5th Jul in 2003 with the mesoscale model MM5V3, the result shows that (1)the nonlinear subcritical symmetric instability is probably one of the main mechanism of this rainfall. (2) the increase of rainfall is closely associated with the increase of the disturbance wind which often can be found before the increase of rainfall, so the increase of the nonlinear subcritical symmetric instability can make the rainfall increase. (3) Heavy precipitation often occurs between the south of axis of upper jet at 200hPa and the north of axis of low jet at 850hPa. the nonlinear subcritical symmetric instability has closely effect on the upper jet and may trigger the nucleus of upper jet to form, it also has closely effect on the low jet in such a way that it appears before the low jet occurs.(4)the nonlinear subcritical symmetric instability mainly occurs at middle or high level which makes the atmosphere from linear sym...
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