Variational Principle of Instability of Atmospheric Motions

Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is universal for obtaining criteria of instability in all models with all possible basic flows. For example, the model can be barotropic or baroclinic, layer or continuous, quasi-geostrophic or primitive equations; the basic flow can be zonal or nonzonal, steady or unsteady.Although the basic flows possess a great deal of variety, they all are the stationary points in the functional space determined by an appropriate invariant functional. The basic flow is an unsteady one if the conservation of angular momentum is included in the associated functional.The second variation, linear or nonlinear, gives the criteria of instability. Especially, the general criteria of instability for unsteady basic flow, orographically disturbed flow as well as nongeostrophic flow are first obtained by the method described in this paper.It is also shown that the difference between the criteria of instability obtained by the linear theory and our variational principle clearly indicates the importance of using nonlinear governing equations.In the appendix the theory is extended to cases such as in a β-plane where the fluid does not possess finite total energy, hence the variational principle can not be directly applied. However, a generalized Liapbunoff norm can still be obtained on the basis of variational consideration.

Comments on Zeng's Paper “Variational Principle of Instability of Atmospheric Motions”

After my paper (Zeng, 1986b) was published and another (Zeng, 1989) was submitted to the journal, I found two papers written by Arnold (1966) and McIntyre et al. (1987) and received some reprints of Ripa’s papers (1983; 1984; 1987; 1988) in the same field. I thank Drs. Mu Mu and Pedro Ripa very much for showing and sending me these interesting papers.

Topographically Forced Rossby Wave Instability and the Development of Blocking in the Atmosphere

In this paper, the linear stability of disturbance superimposed on basic state Rossby wave forced by topography is investigated, and pointed out that when a certain criterion is satisfied by the basic flow and the height of topography for the subresonance, the small disturbance may be unstable. Furthermore, we also compare the evolution of the instability disturbance with the development of blocking in the Pacific, and we suggested that the topographically forced Rossby wave instability may provide a possible mechanism for the development of blocking in the Pacific.

The Possibilities of Using the Minimax Method to Diagnose the State of the Atmosphere

The article is devoted to the discussion of the possibilities of approbation of one of the probabilistic methods of verification of evaluation works-the minimax method or the method of establishing the minimum risk of making erroneous diagnoses of the instability of the planetary boundary layer of air.Within the framework of this study,the task of probabilistic forecasting of diagnostic parameters and their combinations,leading in their totality to the formation of an unstable state of the planetary boundary layer of the atmosphere,was carried out.It is this state that,as shown by previous studies,a priori contribution to the development of a number of weather phenomena dangerous for society(squalls,hail,heavy rains,etc.).The results of applying the minimax method made it possible to identify a number of parameters,such as the intensity of circulation,the activity of the Earth’s magnetosphere,and the components of the geostrophic wind velocity,the combination of which led to the development of instability.In the future,it is possible to further expand the number of diagnosed parameters to identify more sensitive elements.In this sense,the minimax method,the usefulness of which is shown in this study,can be considered as one of the preparatory steps for the subsequent more detailed method for forecasting individual hazardous weather phenomena.

An evaluation of input/dissipation terms in WAVEWATCH Ⅲ using in situ and satellite significant wave height data in the South China Sea

A WAVEWATCH III version 3.14（WW3） wave model is used to evaluate input/dissipation source term packages WAM3, WAM4 and TC96 considering the effect of atmospheric instability. The comparisons of a significant wave height acquired from the model with different packages have been performed based on wave observation radar and HY-2 altimetry significant wave height data through five experiments in the South China Sea domain spanning latitudes of 0°–35°N and longitudes of 100°–135°E. The sensitivity of the wind speed correction parameter in the TC96 package also has been analyzed. From the results, the model is unable to dissipate the wave energy efficiently during a swell propagation with either source packages. It is found that TC96 formulation with the ＂effective wind speed＂ strategy performs better than WAM3 and WAM4 formulations. The wind speed correction parameter in the TC96 source package is very sensitive and needs to be calibrated and selected before the WW3 model can be applied to a specific region.

Simulation Study About the Influence of Atmospheric Stratification on Lightning Activities

A 2D model about charging and discharging processes in thundercloud is used to simulate three differential atmospheric stratifications resulting in discrepant thunderstorm processes in Beijing region. The dynamic and microphysical processes in thunderstorm and their influence on lightning activities are also discussed. The results indicate that ascending velocity and water vapor are the most important factors to influence lightning activities. At the same time, they affect each other and are together controlled by atmospheric stratification. The magnitude of the ascending velocity determines the intensity of storm and the time when the thunderstorm matured. The thunderstorm with strong updrafts can reach a large height in a short time. Strong persistent updrafts and sufficient water vapor which help to generate more ice phase hydrometeors that directly influence charging and discharging process will prolong the mature stage of the thunderstorm and thereby enhance lightning activities. Though the big density of ice phase hydrometeors can be formed, it is difficult to sustain a long time in the condition of strong updrafts and scant water vapor. Under the condition of weak updrafts and sufficient water vapor in the whole levels, it is easy to form warm cloud process in which the ice phase process and lightning activities are weak. The favorable stratification conditions for strong lightning activities are the sufficient vapor in the lower atmosphere, moderate humidity in the mid troposphere. big instability energy and some suitable convective inhibition. Through calculating some atmospheric instability parameters, it is indicated that convective instability index smaller than -10℃ （negative means instable）, convective available potential energy larger than 1000 J kg-1, convective inhibition larger than 40 J kg-1 the 700-hPa potential equivalent temperature larger than 340 K and the 35%-85% humidity in the mid troposphere （700-400 hPa） are the advantageous conditions for strong lightning activities.

Increasing Trend of Summertime Synoptic Wave Train Activity over the Western North Pacific since 1950

The change of summertime synoptic-scale wave train(SWT) activity over the western North Pacific(WNP) since1950 was investigated based on the NCEP–NCAR reanalysis data. It is found that the intensity of SWT has a rising trend, while its structure and phase propagation characteristics remain unchanged. Environmental factors responsible for the rising trend are investigated. By separating the whole period into three warming phases(P1: 1950–1958, P2:1978–1986, and P3: 2006–2014), we found that even though the vertical velocity shows a rising trend, the background low-level vorticity over the monsoon trough region increases from P1 to P2 but decreases from P2 to P3, and so is the low-level barotropic energy conversion(CK). Thus, just the environmental dynamic factor could not explain the continuous rising SWT trend. On the other hand, thermodynamic factor, such as the sea surface temperature(SST), moisture, and atmospheric instability, shows a clear step-by-step increasing trend. A non-dimensional synoptic activity index(SAI) that combines the dynamic and thermodynamic factors is then proposed. This index well captures the observed long-term trend of the SWT intensity.