For the potential vorticity(PV) invariant, there is a PV-based complete-form vorticity equation, which we use heuristically in the present paper to answer the following question: for the Ertel–Rossby invariant(ERI), is there a corresponding vorticity tendency equation? Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors' influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.
NCEP-NCAR reanalysis data were used to analyze the characteristics and evolution mechanism of convective and symmetric instability before and during a heavy rainfall event that occurred in Beijing on 21 July 2012.Approximately twelve hours before the rainstorm,the atmosphere was mainly dominated by convective instability in the lower level of 900-800 hPa.The strong southwesterly low-level jet conveyed the moist and warm airflow continuously to the area of torrential rain,maintaining and enhancing the unstable energy.When the precipitation occurred,unstable energy was released and the convective instability weakened.Meanwhile,due to the baroclinicity enhancement in the atmosphere,the symmetric instability strengthened,maintaining and promoting the subsequent torrential rain.Deriving the convective instability tendency equation demonstrated that the barotropic component of potential divergence and the advection term played a major role in enhancing the convective instability before the rainstorm.Analysis of the tendency equation of moist potential vorticity showed that the coupled term of vertical vorticity and the baroclinic component of potential divergence was the primary factor influencing the development of symmetric instability during the precipitation.Comparing the effects of these factors on convective instability and symmetric instability showed some correlation.
Drought is one of the complex meteorological disasters affecting water resources,agriculture,livestock,and socioeconomic patterns of a region.Although drought prediction is difficult,it can be monitored based on climatological information.In this study,we provide high spatiotemporal resolution drought climatology,using observational,gridded precipitation data(0.5°×0.5°) from the Global Precipitation Climatological Center and soil moisture data from the Climate Prediction Center for the 60-yr period 1951-2010.The standardized precipitation index(SPI) based on a fitted Gamma distribution and Run method has been calculated from the regional drought identification model(ReDIM) for 3,6,9,12,and 24 months.The results show strong temporal correlations among anomalies of precipitation,soil moisture,and SPI.Analysis of long-term precipitation data reveals that the drought vulnerability concentrates on monsoon season(JulySeptember),which contributes 72.4%and 82.1%of the annual precipitation in northern and southern Sindh,respectively.Annual and seasonal analyses show no significant changes in the observed precipitation.The category classification criteria are defined to monitor/forecast drought in the selected area.Further analysis identifies two longest episodes of drought,i.e.,1972-1974 and 2000-2002,while 1969,1974,1987,and 2002 are found to be the most severe historical drought years.A drought hazard map of Sindh was developed,in which 10 districts are recognized as highly vulnerable to drought.This study helps to explain the time,duration,intensity,and frequency of meteorological droughts over Sindh as well as its neighboring regions,and provides useful information to disaster management agencies and forecasters for assessing both the regional vulnerability of drought and its seasonal predictability in Pakistan.
Progress over the past decade in understanding moisture-driven dynamics and torrential rain storms in China is reviewed in this paper. First, advances in incorporating moisture effects more realistically into theory are described, including the development of a new parameter, generalized moist potential vorticity(GMPV) and an improved moist ageostrophic Q vector(Qum). Advances in vorticity dynamics are also described, including the adoption of a "parcel dynamic" approach to investigate the development of the vertical vorticity of an air parcel; a novel theory of slantwise vorticity development, proposed because vorticity develops easily near steep isentropic surfaces; and the development of the convective vorticity vector(CVV)as an effective new tool. The significant progress in both frontal dynamics and wave dynamics is also summarized, including the geostrophic adjustment of initial unbalanced flow and the dual role of boundary layer friction in frontogenesis, as well as the interaction between topography and fronts, which indicate that topographic perturbations alter both frontogenesis and frontal structure. For atmospheric vortices, mixed wave/vortex dynamics has been extended to explain the propagation of spiral rainbands and the development of dynamical instability in tropical cyclones. Finally, we review wave and basic flow interaction in torrential rainfall, for which it was necessary to extend existing theory from large-scale flows to mesoscale fields, enriching our knowledge of mesoscale atmospheric dynamics.
Terrain characteristics can be accurately represented in spectrum space. Terrain spectra can quantitatively reflect the effect of topographic dynamic forcing on the atmosphere. In wavelength space, topographic spectral energy decreases with decreasing wavelength, in spite of several departures. This relationship is approximated by an exponential function. A power law relationship between the terrain height spectra and wavelength is fitted by the least-squares method, and the fitting slope is associated with grid-size selection for mesoscale models. The monotonicity of grid size is investigated, and it is strictly proved that grid size increases with increasing fitting exponent, indicating that the universal grid size is determined by the minimum fitting exponent. An example of landslide-prone areas in western Sichuan is given, and the universal grid spacing of 4.1 km is shown to be a requirement to resolve 90% of terrain height variance for mesoscale models, without resorting to the parameterization of subgrid-scale terrain variance. Comparison among results of different simulations shows that the simulations estimate the observed precipitation well when using a resolution of 4.1 km or finer. Although the main flow patterns are similar, finer grids produce more complex patterns that show divergence zones, convergence zones and vortices.Horizontal grid size significantly affects the vertical structure of the convective boundary layer. Stronger vertical wind components are simulated for finer grid resolutions. In particular, noticeable sinking airflows over mountains are captured for those model configurations.
Considering some simple topological properties of vorticity vector, the frozen-in property of vorticity herein is revisited. A vortex line, as is analogous to velocity vector along a streamline, is defined as such a coincident material(curve) line that connects many material fluid elements, on which the local vorticity vector for each fluid element is also tangent to the vortex line. The vortex line evolves in the same manner as the material line that it is initially associated with. The vortex line and the material line are both oriented to the same directions, and evolve with the proportional magnitude, just like being ‘frozen' or ‘glued' to the material elements of the fluid under the barotropic assumption. To relax the limits of incompressible and barotropic atmosphere, the frozen-in property is further derived and proved in the baroclinic case. Then two effective usages are given as examples. One is the derivation of potential vorticity conservation from the frozen-in property in both barotropic and baroclinic atmospheres, as a theory application, and the other is used to illuminate the vorticity generation and growth in ideal cases and real severe weather process, e.g., in squall line, tornado, and other severe convection weather with vortex. There is no necessity to derive vorticity equation, and this method is very intuitive to explain vorticity development qualitatively, especially for fast analysis for forecasters. Certainly, by investigating the evolution of vortex line, it is possible to locate the associated line element vector and its development on the basis of the frozen-in property of vorticity. Because it is simple and visualized, it manifests broad application prospects.
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 nonuniformly 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.
