1 Theoretical research works in Institute of Heavy Rain 2 Evolution and propagation of MCSs over Meiyu fronts and inertia-gravitational wave-CISK 1 Theoretical research works in Institute of Heavy Rain 2 Evolution and propagation of MCSs over Meiyu fronts and inertia-gravitational wave-CISK Hu Bowei （胡伯威） Wang Xiaofang （王晓芳） Cui Chunguang( 崔春光 ) (Institute of heavy rain,China Meteorological Administration,Wuhan ,China)

1 The theoretical research works in Institute of Heavy Rain 1 The meso-scale dynamically balance mechanisms of the heavy rain systems over the Mid-and-Lower reaches of Yangtze river. 2 The chance of the temporary meeting between two of the meso-scale conditions or among further more conditions in space and time is particularly important to whether or not the rain storm events can occur and what time what location the events occur. 3 The influence of the complicated “meso-scale” terrain in the Mid-and-Lower Reaches of Yangtze River on the heavy rain occurrence and its mechanism. 4 What / s the role of the so called “low-level moisture front” in the initiation and evolution of the heavy rain weather systems over the equivalent-barotropic-characterized Meiyu front. 5 The effects of the meso-scale inertia-gravitational waves on the initiation and propagation of severe convective rain storm.

（ UTC ） （ UTC) 2 Evolution and propagation of MCSs over Meiyu fronts and inertia-gravitational wave-CISK

（ Beijing Time ） （ Beijing Time ） Such MCSs usually appear the “up and down—stream development” phenomena and hence a “cloud clusters wave train” along the Meiyu fronts. This often cause the locally outburst heavy rain, which the forecasters can not track before.

2.1 “Low-level moisture front” CISK is not only related to the atmospheric humidity condition and the convective instability energy but also related to their horizontally non- homogeneous distribution. So the effect of “Low-level moisture front”, which is adhering to the Meiyu front, is the important factor that must be considered.

2.2 The basic equations and the parameterized expression of the cumulus heating (1)

(2) (3) (4) (5) Here the terms containing ( ) are omitted, and ( ) is in direct proportion to the weighted vertically integration of moisture in the lower troposphere. The equations system is reduce to:

2.3 W—equation: （7） （7） （6）（6） Wherein Taking (7) (8)

Fig1 the variation of (solid line)and (dashed line) with the pressure

2.4 Frequency equation: wherein

In the common situation the convective stability of second kind is determined by the value of ( ), but around the “ moisture front ”, the stability is also influenced by the -ward second order derivative of the humidity field M 2 ( ), The contribution of M 2 is maximal where its negative value takes the maximum,and this place is just near the south border of the “ moisture frontal zone ”. So here the largest increase rate occurs.

2.5 The energy dispersion and the up and down-stream development

The wave speed: The envelop velocity:

The condition permitting the “ up and down-stream development ” to occur: In stable range: 1.6*10 m 2 ·s -2 <M< 0.87*10 3 m 2 ·s -2 In instable range: 0.87*10 3 m 2 ·s -2 <M<1.31*10 3 m 2 ·s -2

Theoretically, the possibility of the occurrence of “ up and down-stream development ” along Meiyu front is hopeful. The situation which is most favorable to the occurrence of the up and down- stream development is that the disturbances take place near the south border of the “ low-level moisture front ” and propagate along the frontal zone. And the most favorable condition of stability is nearly neutral.

2.6 The effect of horizontal-wind shear In the “dry” stratified atmosphere without cumulus heating, practically in any case the effect of horizontal wind sear can not make the inertia-gravitational waves become instable. And only in the nearly “CISK” situation the strong horizontal wind shear has a positive contribution to the instability of the wave disturbances. And such additional instability is mainly attributing to the meridional second order derivative of the velocity of basic flow. So the most favorable location is around the low-level jet stream on the south of the Meiyu front.

Thank you !