Observational Analyses of Baroclinic Boundary Layer Characteristics during One Frontal Winter Snowstorm

The evolution and characteristics of the baroclinic boundary layer for one frontal winter snowstorm were analyzed by using the well-documented dataset during Intensive Observation Period (IOP) 17 of STORM-FEST. It is found that when the warm moist air was lifted across the front, a great amount of latent heat release because of snowing increased the frontal temperature contrast to intensify frontogenesis. It is shown in the zig-zag section diagram of potential temperature that when the frontogenesis got stronger, a cold trough was formed and both low-level jet (LLJ) and upper-level jet (ULJ) emerged ahead of the front. In the strongest stage of frontogenesis, the frontal contrast of potential temperature of cold trough reached as high as 20 K. Hereafter the LLJ ahead of the front tended to weaken and the LLJ behind the front tended to strengthen. The frontal circulation system was dominated by the cold air advection behind the front, which transported the cold air behind the front forward to the warm area ahead of the front to weaken the cold trough and finally frontolysis occurred. It is shown by the analyses of turbulent characteristics of frontal baroclinic boundary-layer that the vertical shear (WV) above the boundary layer was very large, and the pumping of the strong wind shear in turbulent energy budget made the characteristic variables within the PBL well mixed. Sufficient moisture carried by southerly flow from the Mexico Gulf, and the strong baroclinity of the frontal boundary layer played key roles in this frontal winter snowstorm, and the large-scale ULJ behind the cold front is also advantageous to the development of the convective boundary layer.

Linear Momentum Approximation and Frontogenesis Caused by Baroclinic Ekman Momentum Flow

A method of linear momentum approximation is proposed that deals with weak nonlinear problems in an approximate manner. A motion of nonlinear nature is obtained in the system by assuming the motion to be in the form of linear momentum flow in the corresponding space introduced, followed by the transformation from the specified into a physical space. Significant results have been thereby derived in examining the effects of baroclinic Ekman momentum flow upon Eady-type baroclinic waves and frontogenesis. Also, this technique can be applied to investigate the dynamic characteristics of the weak nonlinear boundary layer including topography, stratification and non-Ekmantype friction for gaining further insight into the influence on the boundary layer inner parameters of terrain, baroclinicity and inhomogeneous process so that the classic theory is revised.

Analytical Solutions for Testing of Baroclinic and Wind-Driven Three-Dimensional Hydrodynamic Models

It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.

Conversion Characteristics between Barotropic and Baroclinic Circulations of the SAH in Its Seasonal Evolution

In the context of 1958–1997 NCEP/ NCAR re-analyses, the South Asia high (SAH) was divided into two components, barotropic and baroclinic, the former based on mass weighed vertical integration and the latter on the difference between the measured circulation and the barotropic component counterpart, whereupon the barotropic and baroclinic circulation conversion features were addressed of the research SAH during its seasonal variation. Evidence suggests that i) in summer (winter), the SAH is a thermal (dynamical) system, with dominant baroclinicity (barotropicity), either of the components accounting for approximately 70% of the total contribution; ii) as time progresses from winter to summer, accompanied by the barotropic SAH evolving into its baroclinic analog, the SAH is moving under the “ thermal guidance” of its baroclinic component circulation, suggesting that the component circulation precedes the system itself in variation; iii) the reversal happens when it goes from summer to winter, with the SAH displacement under the “ dynamic steering” of its barotropic component circulation. Key words SAH (South Asia high) - Barotropic circulation - Baroclinic circulation - Seasonal variation (1)This work is supported by the National Natural Sciences Foundation of China under Grant No.49735170.

Three Dimensional Baroclinic Numerical Model for Simulating Fresh and Salt Water Mixing in the Yangtze Estuary

For simulating fresh and salt water mixing in estuaries, a three dimensional nonlinear baroclinic numerical model is developed, in which the gradients of horizontal pressure contain die gradient of barotropic pressure arising from the gradient of tidal level and the gradient of baroclinic pressure due to the gradient of salinity. The Eulerian-Lagrangian method is employed to descretize both the momentum equations of tidal motion and the equation of salt water diffusion so as to improve the computational stability and accuracy. The methods to provide the boundary conditions and the initial conditions are proposed, and the criterion for computational stability of the salinity fields is presented. The present model is used for modeling fresh and salt water mixing in the Yangtze Estuary. Computations show that the salinity distribution has the characteristics of partial mixing pattern, and that the present model is suitable for simulation of fresh and salt water mixing in the Yangtze Estuary.

A Study of Formation and Development of One Kind of Cyclone on the Mei-yu (Baiu) Front

The paper presents one diagnosis of baroclinity and the coupling of jets during the developing process of a cyclone that occurred on the mei-yu (Baiu) front around the end of the second stage of the mei-yu (Baiu) in 1998. Results have shown that: (1) The advantageous changes of upper-level large-scale circulation caused the appearance and maintenance of the coupling between the upper-level jet (ULJ) and lower-level jet (LLJ) over the cyclone's area. The coupling of jets in this case possesses some different characteristics from previous cases. Moreover, the coupling between the ULJ and LLJ caused the intensification of both lower-level convergence and upper-level divergence, which was favorable for the development of this cyclone. (2) From the analysis of the voricity budget, the role of lower-level convergence in the development of the cyclone was emphasized. Divergent wind in the lower troposphere was a direct contributor to the development of the cyclone. (3) During the development of the cyclone, cold air and warm air were active over the cyclone's domain. Although this cyclone occurred at the mei-yu (Baiu) front, its development assumed baroclinity to a certain extent, which was just the main difference between this kind of cyclone and the first kind of low which is usually barotropic (or quasi-barotropic). (4) In recent years, studies on mei-yu front lows have paid more attention to the lower troposphere. In this paper, the analysis of the energy budget further supports this point: the certain effect of baroclinity forcing in the upper troposphere on mei-yu front lows cannot be ignored.

A survey of baroclinic tides in the Beibu Gulf in the South China Sea

The principal characteristics of the tides are investigated by a shipborne acoustic Doppler current Profiler at a fixed station located in the Beibu Gulf from 4 to 14 April 2003. Data analysis indicates that the diurnal tidal currents dominate local current variations at the observing site. Except the barotropic ME constituent, four principal tides comprise both back-and-forth barotropic and baroclinic tidal currents. The baroclinic tidal ellipse parameters vary with depth, showing complicate features, rather than monotonous features being figured. For baroclinic tidal constituents, vertical modes are different to each other. Similarly, the semi-major axes of the tidal constituents vary with depth. In the lower layer, a nonlinear regression approach is used to calculate and obtain the SEMA profiles of diurnal tidal constituents. Results show that in the thin bottom boundary layer, all of the parameters vary drastically with depth, totally distinguished from the vertical profiles above.

Energy Paths that Sustain the Warm-Sector Torrential Rainfall over South China and Their Contrasts to the Frontal Rainfall: A Case Study

Predicting warm-sector torrential rainfall over South China,which is famous for its destructive power,is one of the most challenging issues of the current numerical forecast field.Insufficient understanding of the key mechanisms underlying this type of event is the root cause.Since understanding the energetics is crucial to understanding the evolutions of various types of weather systems,a general methodology for investigating energetics of torrential rainfall is provided in this study.By applying this methodology to a persistent torrential rainfall event which had concurrent frontal and warm-sector precipitation,the first physical image on the energetics of the warm-sector torrential rainfall is established.This clarifies the energy sources for producing the warm-sector rainfall during this event.For the first time,fundamental similarities and differences between the warm-sector and frontal torrential rainfall are shown in terms of energetics.It is found that these two types of rainfall mainly differed from each other in the lower-tropospheric dynamical features,and their key differences lay in energy sources.Scale interactions(mainly through downscale energy cascade and transport)were a dominant factor for the warm-sector torrential rainfall during this event,whereas,for the frontal torrential rainfall,they were only of secondary importance.Three typical signals in the background environment are found to have supplied energy to the warm-sector torrential rainfall,with the quasi-biweekly oscillation having contributed the most.

Elimination of Computational Systematic Errors and Improvements of Weather and Climate System Models in Relation to Baroclinic Primitive Equations

The design of a total energy conserving semi-implicit scheme for the multiple-level baroclinic primitive equation has remained an unsolved problem for a long time. In this work, however, we follow an energy perfect conserving semi-implicit scheme of a European Centre for Medium-Range Weather Forecasts (ECMWF) type sigma-coordinate primitive equation which has recently successfully formulated. Some real-data contrast tests between the model of the new conserving scheme and that of the ECMWF-type of global spectral semi-implicit scheme show that the RMS error of the averaged forecast Height at 850 hPa can be clearly improved after the first integral week. The reduction also reaches 50 percent by the 30th day. Further contrast tests demonstrate that the RMS error of the monthly mean height in the middle and lower troposphere also be largely reduced, and some well-known systematical defects can be greatly improved. More detailed analysis reveals that part of the positive contributions comes from improvements of the extra-long wave components. This indicates that a remarkable improvement of the model climate drift level can be achieved by the actual realizing of a conserving time-difference scheme, which thereby eliminates a corresponding computational systematic error source/sink found in the currently-used traditional type of weather and climate system models in relation to the baroclinic primitive equations.

Nonlinear Saturation of Baroclinic Instability in the Phillips Model: The Case of Energy

A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case of energy—is studied within the context of Arnold’s second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd’s; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances Φ′ i at any time.

NUMERICAL STUDY ON THE FORMATION OF THE SOUTH CHINA SEA WARM CURRENT II. BAROCLINIC CASE

In this part, Levitus’ climatological temperature and salinity are incorporated in the numerical model developed in Part I. Diagnostic and prognostic experiment on the thermohaline circulation were conducted. The smooth Levitus’ data do not include any information on the South China Sea Warm Current (SCSWC), so it is not in the model produced diagnostic thermohaline circulation. Although the SCSWC does not appear in the wind driven circulation in the barotropic case, it appears in the prognostic wind driven circulation in the baroclinic case. This implies that the differing circulation patterns between barotropic case and baroclinic case are due to the stratification. The prognostic thermohaline circulation with wind stress and inflow/outflow transports at open boundaries are also discussed. Coupling of density and dynamic forces makes the circulation pattern more complicated. Even though the stratification is not always a direct cause of the formation of the SCSWC, it is at least an indirect cause.

Study on Instability in Baroclinic Vortex Symmetric Disturbance under Effect of Nonuniform Environmental Parameters

With the aid of the baroclinicity parameter M2,inertial instability parameter F2 and the stratification instability paramter N2 as the slowly varying function both spatially and temporally,an energetic equation is derived of symmetric perturbation waves in baroclinic vortices in the framework of progressively changing wavetrain theory,or WKB,alongside the examination of effects of these parameters upon the vortex disturbance.

A 3-DIMENSIONAL BAROCLINIC CIRCULATION MODEL OF THE TROPICAL AND NORTHERN PACIFIC

A primitive equation 3-dimensional baroclinic ocean model without the rigid-lid approximation is described.The horizontal resolution is 2.5°×2°and the vertical variations of the velocity components are resolved by 6 layers. In order to increase the allowable integration time step which is constrained by stability requirements, the vertically integrated continuity equation is linearized and both the pressure gradient terms and the Coriolis terms in the momentum equations are finite-differenced semi-implicitly.The model is applied to simulate the circulation as well as the free surface elevation and temperature patterns in the tropical and northern Pacific Ocean in both summer and winter using the wind and temperature data at the 1000 mb pressure level as input to the .model. The computed results are in general consistent with observed patterns. In particular, it is shown that the positions of the meandering axis of the Kuroshio in summer and winter are markedly different.

Charney’s Model—the Renowned Prototype of Baroclinic Instability—Is Barotropically Unstable As Well

The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic;when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.

Mesoscale Predictability of Moist Baroclinic Waves: Variable and Scale-dependent Error Growth

This study seeks to quantify the predictability of different forecast variables at various scales through spectral analysis of the difference between perturbed and unperturbed cloud-permitting simulations of idealized moist baroclinic waves amplify- ing in a conditionally unstable atmosphere. The error growth of a forecast variable is found to be strongly associated with its reference-state （unperturbed） power spectrum and slope, which differ significantly from variable to variable. The shallower the reference state spectrum, the more spectral energy resides at smaller scales, and thus the less predictable the variable since the error grows faster at smaller scales before it saturates. In general, the variables with more small-scale components （such as vertical velocity） are less predictable, and vice versa （such as pressure）. In higher-resolution simulations in which more rigorous small-scale instabilities become better resolved, the error grows faster at smaller scales and spreads to larger scales more quickly before the error saturates at those small scales during the first few hours of the forecast. Based on the reference power spectrum, an index on the degree of lack （or loss） of predictability （LPI） is further defined to quantify the predictive time scale of each forecast variable. Future studies are needed to investigate the scale- and variable-dependent predictability under different background reference flows, including real case studies through ensemble experiments.

Two Modes and Their Seasonal and Interannual Variation of the Baroclinic Waves/Storm Tracks over the Wintertime North Pacific

In this study,a newly developed method,termed moving empirical orthogonal function analysis（MEOF）,is applied to the study of midlatitude baroclinic waves over the wintertime North Pacific from 1979 to 2009.It is shown that when the daily,high-pass filtered（2–10 days） meridional wind at 250 h Pa is chosen as the variable of the MEOF analysis,typical features of baroclinic waves/storm tracks over the wintertime North Pacific can be well described by this method.It is found that the first two leading modes of the MEOF analysis,MEOF1 and MEOF2,assume quite different patterns.MEOF1 takes the form of a single wave train running in the east–west direction along 40°N,while MEOF2 is a double wave train pattern running in the east–west direction along 50°N and 30°N,respectively.The shift composites of various anomalous fields based on MEOF1 and MEOF2 assume typical baroclinic wave features.MEOF1 represents a primary storm track pulsing with an intrinsic time scale of two days.It shows significant ＂midwinter suppression＂ and apparent interannual variability.It is stronger after the mid-1990 s than before the mid-1990 s.MEOF2 represents a double-branch storm track,also with an intrinsic time scale of approximately two days,running along 50°N and 30°N,respectively.It shows no apparent seasonal variation,but its interannual and decadal variation is quite clear.It oscillates with larger amplitude and longer periods after the mid-1990 s than before the mid-1990 s,and is heavily modulated by El Ni n°o–Southern Oscillation（ENSO）.

Application of a self adaptive method to the simulation of the tidal front in the Huanghai Sea

A self adaptive three-dimensional baroclinic model is designed. A horizontal temperature gradient is used to control the grid size, which can improve computational precision in the fronts without inordinately increasing computation in the whole area. A simulation of the development and disappearance of the front in the Huanghai Sea is conducted with this model. Simulations of temperature distribution throughout the year are also conducted. The comoutational result agrees well with the observation.

The Role of the Halted Baroclinic Mode at the Central Equatorial Pacific in El Nifn Event

The role of halted ＂baroclinic modes＂ in the central equatorial Pacific is analyzed. It is found that dominant anomaly signals corresponding to ＂baroclinic modes＂ occur in the upper layer of the equatorial Pacific, in a two-and-a-half layer oceanic model, in assimilated results of a simple OGCM and in the ADCP observation of TAO. A second ＂baroclinic mode＂ is halted in the central equatorial Pacific corresponding to a positive SST anomaly while the first ＂baroclinic mode＂ propagates eastwards in the eastern equatorial Pacific. The role of the halted second ＂baroclinic mode＂ in the central equatorial Pacific is explained by a staged ocean-atmosphere interaction mechanism in the formation of El Nifio： the westerly bursts in boreal winter over the western equatorial Pacific generate the halted second ＂baroclinic mode＂ in the central equatorial Pacific, leading to the increase of heat content and temperature in the upper layer of the central Pacific which induces the shift of convection from over the western equatorial Pacific to the central equatorial Pacific; another wider, westerly anomaly burst is induced over the western region of convection above the central equatorial Pacific and the westerly anomaly burst generates the first ＂baroclinic mode＂ propagating to the eastern equatorial Pacific, resulting in a warm event in the eastern equatorial Pacific. The mechanism presented in this paper reveals that the central equatorial Pacific is a key region in detecting the possibility of ENSO and, by analyzing TAO observation data of ocean currents and temperature in the central equatorial Pacific, in predicting the coming of an El Nino several months ahead.

Propagation of Envelope Solitons in Baroclinic Atmosphere

The propagation of finns amplitude baroclinic wave packets in the two-layer model is investigated by using the multiple-scale method.It is shown that the propagation of the wave packets can be described by the so-called unstable nonlinear Schrodinger equation which possesses envelope soliton solutions.The speeds of the solitons are independent of their amplitudes,while the width of the solitons is directly proportional to their speeds but inversely proportional to their amplitudes.

A time-dependent baroclinic model on NEC bifurcation

As it is well-known, the North Equatorial Current (NEC) bifurcates into the Kuroshio flowing northward and the equatorward Mindanao Current, which is well depicted by Munk's theory in 1950 in terms of its climatology. However, Munk's theory is unable to tell the NEC bifurcation variability with time. In the present paper, a time-dependent baroclinic model forced by wind, in which temporal and baroclinic terms are added to Munk's equation, is proposed to examine the seasonal variability of the NEC bifurcation latitude. An analytical solution is obtained, with which the seasonal variability can be well described: NEC bifurcation reaches its northernmost position in December and its southernmost position in June with a range of about 1° in latitude, consistent with previous results with observations. The present solution will degenerate to Munk's one in the case of steady and barotropic state.