Comparative Analysis of the Generalized Omega Equation and Generalized Vertical Motion Equation

Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.

A NOVEL METHOD FOR CALCULATING VERTICAL VELOCITY:A RELATIONSHIP BETWEEN HORIZONTAL VORTICITY AND VERTICAL MOVEMENT

The present work provides a novel method for calculating vertical velocity based on continuity equations in a pressure coordinate system.The method overcomes the disadvantage of accumulation of calculating errors of horizontal divergence in current kinematics methods during the integration for calculating vertical velocity,and consequently avoids its subsequent correction.In addition,through modifications of the continuity equations,it shows that the vorticity of the vertical shear vector(VVSV) is proportional to-ω,the vertical velocity in p coordinates.Furthermore,if the change of ω in the horizontal direction is neglected,the vorticity of the horizontal vorticity vector is proportional to-ω.When ω is under a fluctuating state in the vertical direction,the updraft occurs when the vector of horizontal vorticity rotates counterclockwise;the downdraft occurs when rotating clockwise.The validation result indicates that the present method is generally better than the vertical velocity calculated by the ω equation using the wet Q-vector divergence as a forcing term,and the vertical velocity calculated by utilizing the kinematics method is followed by the O'Brien method for correction.The plus-minus sign of the vertical velocity obtained with this method is not correlated with the intensity of d BZ,but the absolute error increases when d BZ is >=40.This method demonstrates that it is a good reflection of the direction of the vertical velocity.

Estimation of vertical diffusion coefficient based on a onedimensional temperature diffusion equation with an inverse method

Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.

The Genesis of Tropical Cyclone Bilis(2000) Associated with Cross-equatorial Surges

The purpose of this paper is to explore how a tropical cyclone forms from a pre-existing large-scale depression which has been observed and associated with cross-equatorial surges in the western North Pacific. Tropical cyclone Bilis(2000) was selected as the case to study.The research data used are from the results of the non-hydrostatic mesoscale model(MM5),which has successfully simulated the transformation of a pre-existing weak large-scale tropical depression into a strong tropical storm.The scale separation technique is used to separate the synoptic-scale and sub-synoptic-scale fields from the model output fields. The scale-separated fields show that the pre-existing synoptic-scale tropical depression and the subsynoptic scale tropical cyclone formed later were different scale systems from beginning to end.It is also shown that the pre-existing synoptic-scale tropical depression did not contract to become the tropical cyclone. A series of weak,sub-synoptic-scale low and high pressure systems appeared and disappeared in the synopticscale depression,with one of the low systems near the center of the synoptic-scale depression having deepened to become the tropical cyclone. The roles of the synoptic-scale flow and the sub-synoptic scale disturbances in the formation of the tropical cyclone are investigated by diagnoses of the scale-separated vertical vorticity equation.The results show that the early development of the sub-synoptic scale vortex was fundamentally dependent on the strengthening synoptic-scale environmental depression.The depression was strengthened by cross-equatorial surges,which increased the convergence of the synoptic-scale depression at low levels and triggered the formation of the tropical cyclone.

Investigating the initiation and propagation processes of convection in heavy precipitation over the western Sichuan Basin

Heavy precipitation events occur often over the western Sichuan Basin in summer, near the transition zone between the Sichuan Basin and the steep terrain of the Tibetan Plateau. One such event -- a heavy precipitation process that occurred on 18-20 August 2010, with clear nocturnal peaks -- is chosen as a case to tentatively explore how the convection associated with convectivescale precipitation is initiated and propagated. By utilizing the vertical momentum equation from the viewpoint of separating perturbation pressure into dynamic and thermal parts, it is demonstrated that the vertical momentum is induced by the imbalance of several forces, including the dynamic/buoyant part of the perturbation pressure gradient force and the buoyancy force, with the latter dominating during the nocturnal-peak period. Although a negative value of the dynamic perturbation pressure gradient force partly offsets the positive buoyant forcing inside the strong updraft, the pattern of vertical motion tendency is largely attributable to its buoyancy because of its larger magnitude. Relative to the buoyancy component, the dynamic part of the vertical perturbation pressure gradient is also examined, revealing a smaller order of magnitude. Thus, it is the thermal effect that should be responsible for the initiation and propagation of convection. As for the convective-scale precipitation, it always presents a trailing morphology relative to the strong leading-side updraft. Furthermore, overlapping strong signals of vertical motion and its tendency point towards strong precipitation in the future.

RELATIONSHIPS BETWEEN THE POSITION VARIATION OF THE WEST PACIFIC SUBTROPICAL HIGH AND THE DIABATIC HEATING DURING PERSISTENT INTENSE RAIN EVENTS IN YANGTZE-HUAIHE RIVERS BASIN

By using NCEP/NCAR daily reanalysis data and daily precipitation data of 740 stations in China, relationships between the position variation of the West Pacific subtropical high (WPSH) and the diabatic heating during persistent and intense rains in the Yangtze-Huaihe Rivers basin are studied. The results show that the position variation of WPSH is closely associated with the diabatic heating. There are strong apparent heating sources and moisture sinks in both the basin (to the north of WPSH) and the north of Bay of Bengal (to the west of WPSH) during persistent and intense rain events. In the basin, Q 1z begins to increase 3 days ahead of intense rainfall, maximizes 2 days later and then reduces gradually, but it changes little after precipitation ends, thus preventing the WPSH from moving northward. In the north of Bay of Bengal, 2 days ahead of strong rainfall over the basin, Q 1z starts to increase and peaks 1 day after the rain occurs, leading to the westward extension of WPSH. Afterwards, Q 1z begins declining and the WPSH makes its eastward retreat accordingly. Based on the complete vertical vorticity equation, in mid-troposphere, the vertical variation of heating in the basin is favorable to the increase of cyclonic vorticity north of WPSH, which counteracts the northward movement of WPSH and favors the persistence of rainbands over the basin. The vertical variation of heating in the north of Bay of Bengal is in favor of the increase of anti-cyclonic vorticity to the west of WPSH, which induces the westward extension of WPSH.

Intra-seasonal Features of an Extreme High Temperature Event in 2011 in Eastern China and Its Atmospheric Circulation

Based on the daily maximum air temperature(T_(max))data from the China Meteorological Data Network and the NCEP/DOE reanalysis data,the intra-seasonal circulation and evolution of an extreme high temperature event(EHTE)in the middle reaches of the Yangtze River(MYR)from August 9-21,2011 were explored,as well as the influence of diabatic heating on the position variation of the Western Pacific subtropical high(WPSH).Results show that the daily T_(max) in the MYR exhibits a vigorous intraseasonal oscillation(ISO)of 10-25 days in the extended summer of 1980-2018.The main factors affecting the EHTE in the summer of 2011 are the low-frequency wave train propagating southeastward in the mid-latitude of the upper troposphere and the low-frequency anticyclone moving northwestward in the lowlatitude of the mid-lower troposphere.The diagnosis of 925hPa thermodynamic equation indicates that the ISO features of the T_(max) in the core region is determined by the intra-seasonal variation of the adiabatic variation.In addition,the variations of the WPSH correspond well to the distribution of apparent heat source.In the early stage of the high temperature process,the apparent heat source in the north of the Bay of Bengal is a certain indicator for the westward extension of the WPSH.

Effect of condensation latent heat release on the relative vorticity tendency in extratropical cyclones:a case study

Taking an extratropical cyclone that produced extreme precipitation as the research object,this paper calculates the contribution of condensation latent heat release(LHR)to relative vorticity tendency based on the complete-form vertical vorticity tendency equation.The results show that the heating rate of convectional condensation LHR can reach up to about 40 times that of stable condensation LHR.Both the stable and convectional heating centers are higher than 700 hPa,which would cause∂Q/∂z>0 and a positive vorticity source in the lower troposphere.The vertical gradient of stable condensation LHR contributes little to the growth of relative vorticity,while the relative vorticity tendency associated with the vertical gradient of convectional condensation LHR can be an order of magnitude higher than the former.The positive vorticity source is always located right below the latent heating center,and its maximum value can always be found in the lower troposphere.Convectional LHR is the primary factor for cyclone development from the perspective of diabatic heating.The horizontal gradient of total condensation LHR can contribute about 65%of the actual vorticity growth,but the effect of the vertical gradient of convectional condensation(LHR)can reach twice as much.The adiabatic heating from LHR can cause vorticity tendency directly.However,it can also change the vertical and horizontal gradient of potential temperature,which can further induce vorticity tendency.

Climatology Characteristics of Walker Circulation in East-west Direction in the Equatorial Tropical Pacific Ocean

By using OLR monthly average data which was observed by American NOAA satellite and 500 hPa ω monthly average data of NCEP reanalysis,the indexes which represented the equatorial longitudinal circulation characteristics were defined. According to the intensity,scope and distribution characteristics of longitudinal circulation in the tropical equator area,the indexes which represented the intensity,position and scope climate characteristics of longitudinal circulation in the equatorial Pacific Ocean were diagnosed and studied. The results showed that the annual variation and interannual variation characteristics of Walker circulation in east-west direction in the equatorial Pacific Ocean were that the intensity and scope existed 5 and 15-16 years oscillatory periods,and the position had 4,12 years oscillatory periods.

A Synthetic Study of the Position Difference of the Southern Branch Trough of the Qinghai-Tibet Plateau Based on Objective Identification

The southern branch trough (SBT) mainly appears in the winter half year (November to May of the following year), using the 4 times daily NCEP/NCAR re-analysis data nearly 41 years (1979-2019) to analyze the differences of the SBT distribution of spatial location, frequency in winter and spring, then selects the “eastern type” and “western type” of the 10 most typical SBT, using simplified vertical vorticity tendency equation, using simplified vertical vorticity tendency equation to diagnosis of the SBT in power, heat, water vapor and wave energy in different positions. The results show that: 1) The location of the SBT is more eastward in winter, and more westward in spring. 2) The diagnosis results of the vorticity equation show that the vorticity of the southern branch of the “western type” is mainly contributed by advection term;the vorticity of the “eastern type” south branch is mainly contributed by the non-adiabatic heating term. 3) The SBT of the “eastern type” has more obvious vorticity advection than the southern branch of the “western type”, and the dynamic action is stronger. The “western type” SBT has stronger Q1, specific humidity advection and water vapor flux than the “eastern type” SBT, which is greatly affected by thermal action and water vapor. When the “eastern type” and “western type” SBT occur, the T-N wave activity flux appears obvious abnormal energy fluctuation propagation.

Case Study on the Impact of the Vortex in the Easterlies in the Tropical Upper Troposphere on the Western Pacific Subtropical Anticyclone

By employing the NCEP/NCAR reanalysis data （1000-10 hPa, 2.5°×2.5°）, the impact of the vortex in the easterlies （EV） over the tropical upper troposphere on the zonal movement of the western Pacific subtropical anticyclone （WPSA） during 19-25 June 2003 is analyzed in this paper. It is shown that the EV can extend from middle troposphere to the height of 50 hPa, reaching a maximum at 200 hPa. The vertical thermal distribution appears to be ＂warmer in the upper layer and colder in the lower layer＂. The WPSA retreats eastward abnormally when the EV and the vortex in the westerlies （WV） encounter around the same longitude while they move toward each other. It is also shown that the vorticity variation extends from the troposphere to the height of 50 hPa, with the most prominent change occurring at 200 hPa by the diagnostic analyses of the vertical vorticity equation. The WPSA appears to retreat abnormally eastward while the negative/positive vorticity change becomes stronger near the east/west side of the EV, and the areas with positive vorticity tendency both in the EV and WV join together into one belt along 130°E during the process of the EV and the WV moving toward each other. In the vorticity equation, the positive contribution caused by the horizontal advection term is the maximum, and the minimum is caused by theβ effect. It is also found that enhanced horizontal vorticity advection andβ effect, as well as the ＂barotropic development＂ resulted from the in-phase superposition of the southerly and the northerly winds in the easterlies and westerlies near 130~E, are in agreement with the WPSA eastward retreat.

Relationship Between the Western Pacific Subtropical High and the Subtropical East Asian Diabatic Heating During South China Heavy Rains in June 2005

Based on the daily NCEP/NCAR reanalysis data,the position variation of the western Pacific subtropical high（WPSH） in June 2005 and its relation to the diabatic heating in the subtropical East Asia are analyzed using the complete vertical vorticity equation.The results show that the position variation of the WPSH is indeed associated with the diabatic heating in the subtropical East Asian areas.In comparison with June climatology,stronger heating on the north side of the WPSH and relatively weak ITCZ（intertropical convergence zone） convection on the south side of the WPSH occurred in June 2005.Along with the northward movement of the WPSH,the convective latent heating extended northward from the south side of the WPSH.The heating to the west of the WPSH was generally greater than that inside the WPSH,and each significant enhancement of the heating field corresponded to a subsequent westward extension of the WPSH.In the mid troposphere,the vertical variation of heating on the north of the WPSH was greater than the climatology,which is unfavorable for the northward movement of the WPSH.On the other hand,the vertical variation of heating south of the WPSH was largely smaller than the climatology,which is favorable for the anomalous increase of anticyclonic vorticity,leading to the southward retreat of the WPSH.Before the westward extension of the WPSH in late June 2005,the vertical variation of heating rates to（in） the west（east） of the WPSH was largely higher（lower） than the climatology,which is in favor of the increase of anticyclonic（cyclonic） vorticity to（in） the west（east） of the WPSH,inducing the subsequent westward extension of the WPSH.Similar features appeared in the lower troposphere.In a word,the heating on the north-south,east-west of the WPSH worked together,resulting in the WPSH extending more southward and westward in June 2005,which is favorable to the maintenance of the rainbelt in South China.