A Numerical Study of Geostrophic Adjustment and Frontogenesis

Using the PSU/NCAR Mesoscale Model version four(MM4), the frontogenesis and geostrophic adjustment problem in atmosphere with imbalance initial ideal data and conditions are studied. Based on results of experiments, it is found that the objective analysis and initialization procedure of the Model are not sensitive to the initial conditions used in this study. The final state of atmosphere, through process of adjustment, depends on the temperature gradient intensity of initial imbalance conditions. The front can be formed with appropriate condition. The processes of the frontogenesis are studied. It is also found that the response of the model to the ideal initial data used in this investigation is sensitive to the selected lateral boundary condition. The time-dependent inflow/outflow lateral boundary condition is the best implemented option for this numerical study. Energetic study of the experiments shows that the front is formed after the initial transient stage when there is no exchange of energy between the kinetic and potential energy. The time needed for the formation of the front is longer than that predicted theoretically. The ratio of kinetic energy to the released potential energy is considered. This ratio varies with the temperature gradient intensity and the type of used wind for computing kinetic energy (geostrophic or geostrophic plus ageostrophic wind). The larger temperature gradient, the larger magnitude of this ratio. A maximum value of energy in either type of computed kinetic energies (geostrophic wind kinetic energy and actual wind kinetic energy) for cases that the fronts are observed whereby, and its magnitude and occurrence time depend on initial data distribution. The variation of the computed kinetic energies with time, after transition time, is reasonable and no significant conversion of the energy between kinetic and potential energy goes on, however, stability within variables is not achieved.

Topographic Effect on Geostrophic Adjustment and Frontogenesis

Three conservative principles: potential vorticity, absolute momentum and potential temperature are used to study the influence of topography on the local frontogenesis and geostrophic adjustment, which are induced by the inhomogeneous thermal fields. It is found that the horizontal distribution of the initial potential temperature and its position relative to the mountain play important roles during the geostrophic adjustment and local frontogenesis. The frontogenesis is weakened by the mountain when the initial thermal perturbation is located at the base of the upwind slope. The frontal discontinuity cannot occur unless the horizontal contrast of the initial potential temperature is great enough. Whereas, the situation is opposite when the initial thermal disturbance is main-ly situated near the peak of the mountain. Complementary to the aforementioned cases, the effect of topog-raphy on the frontogenesis depends on the stratification of the flow when the initial thermal disturbance lies at the foot of lee slope. For weak stratification, topography is favorable to the formation of frontal discontinuity, vice versa. This discrepancy is attributed to the difference of subsidence warming, caused by the mountain, when the stratification is either strong or weak. Furthermore, the energy conversion ratio between the kinetic and potential energy during the geostrophic adjustment process is also affected by the topography. In contrast to the flat bottom case, the ratio is reduced (increased) when the initial thermal perturbation lies in the up-wind slope (lee slope). The reason is that the gravity force does negative work in the former case while does positive work in the latter case. Key words Topography - Geostrophic adjustment - Frontogenesis This work was supported by the National Natural Science Foundation of China under Grant 49735180, and by the State Key Basic Program: CHERES.

Geostrophic meridional transport in tropical Northwest Pacific based on Argo profiles

Absolute geostrophic currents in the North Pacific Ocean were calculated using P-vector method from newly gridded Argo profiling float data collected during 2004-2009. The meridional volume transport of geostrophic currents differed significantly from the classical Sverdrup balance, with differences of 10×106 -20×106 m3 /s in the interior tropical Northwest Pacific Ocean. Analyses showed that errors of wind stress estimation could not explain all of the differences. The largest differences were found in the areas immediately north and south of the bifurcation latitude of the North Equatorial Current west of the dateline, and in the recirculation area of the Kuroshio and its extension, where nonlinear eddy activities were robust. Comparison of the geostrophic meridional transport and the wind-driven Sverdrup meridional transport in a high-resolution OFES simulation showed that nonlinear effects of the ocean circulation were the most likely reason for the differences. It is therefore suggested that the linear, steady wind-driven dynamics of the Sverdrup theory cannot completely explain the meridional transport of the interior circulation of the tropical Northwest Pacific Ocean.

Fronts and surface zonal geostrophic current along 115°E in the southern Indian Ocean

Altimeter and in situ data are used to estimate the mean surface zonal geostrophic current in the section along 115°E in the southern Indian Ocean,and the variation of strong currents in relation to the major fronts is studied.The results show that,in average,the flow in the core of Antarctic Circumpolar Current（ACC） along the section is composed of two parts,one corresponds to the jet of Subantarctic Front（SAF） and the other is the flow in the Polar Front Zone（PFZ）,with a westward flow between them.The mean surface zonal geostrophic current corresponding to the SAF is up to 49 cm · s^-1 at 46°S,which is the maximal velocity in the section.The eastward flow in the PFZ has a width of about 4.3 degrees in latitudes.The mean surface zonal geostrophic current corresponding to the Southern Antarctic Circumpolar Current Front（SACCF） is located at 59.7 °S with velocity less than 20 cm · s^-1.The location of zonal geostrophic jet corresponding to the SAF is quite stable during the study period.In contrast,the eastward jets in the PFZ exhibit various patterns,i.e.,the primary Polar Front（PF1） shows its strong meridional shift and the secondary Polar Front（PF2） does not always coincide with jet.The surface zonal geostrophic current corresponding to SAF has the significant periods of annual,semi-annual and four-month.The geostrophic current of the PFZ also shows significant periods of semi-annual and four-month,but is out of phase with the periods of the SAF,which results in no notable semi-annual and fourmonth periods in the surface zonal geostrophic current in the core of the ACC.In terms of annual cycle,the mean surface zonal geostrophic current in the core of the ACC shows its maximal velocity in June.

Energetics of Geostrophic Adjustment in Rotating Flow

Energetics of geostrophic adjustment in rotating flow is examined in detail with a linear shallow water model. The initial unbalanced flow considered first falls tinder two classes. The first is similar to that adopted by Gill and is here referred to as a mass imbalance model, for the flow is initially motionless but with a sea surface displacement. The other is the same as that considered by Rossby and is referred to as a momentum imbalance model since there is only a velocity perturbation in the initial field. The significant feature of the energetics of geostrophic adjustment for the above two extreme models is that although the energy conversion ratio has a large case-to-case variability for different initial conditions, its value is bounded below by 0 and above by 1 / 2. Based on the discussion of the above extreme models, the energetics of adjustment for an arbitrary initial condition is investigated. It is found that the characteristics of the energetics of geostrophic adjustment mentioned above are also applicable to adjustment of the general unbalanced flow under the condition that the energy conversion ratio is redefined as the conversion ratio between the change of kinetic energy and potential energy of the deviational fields.

Large Scale Perturbations in Extratropical Atmosphere-Part Ⅱ: On Geostrophic Waves

We have examined, in Part Ⅰ, the propagation mechanism and geostrophic property of classical Rossby waves in a non-divergent barotropic atmosphere. As we found that the non-divergent Rossby waves do not propagate in a hydrostatically equilibrium atmosphere, and do not manifest a good geostrophic property, an alternative large scale circulation pattern of geostrophic waves has been proposed (McHall, 1991a). The propagation mechanism and geostrophic property of these waves are examined in the present study.

Quasi-Geostrophic方程经典解的爆破准则

考虑Quasi-Geostrophic方程,以经典解沿流线小时间的表现,给出Quasi-Geostrophic方程经典解沿流线爆破的一个充分条件.方法是从Quasi-Geostrophic方程推出一个解的梯度长度的倒数沿流线的微分不等式,从而推出结论.手法与结果都类似于Chae关于3维不可压Euler方程组经典解的爆破工作.该结果对进一步研究Quasi-Geostrophic方程相关问题,有一定的启示作用.

Absolute geostrophic currents in global tropical oceans

A set of absolute geostrophic current(AGC) data for the period January 2004 to December 2012 are calculated using the P-vector method based on monthly gridded Argo profi les in the world tropical oceans. The AGCs agree well with altimeter geostrophic currents, Ocean Surface Current Analysis-Real time currents, and moored current-meter measurements at 10-m depth, based on which the classical Sverdrup circulation theory is evaluated. Calculations have shown that errors of wind stress calculation, AGC transport, and depth ranges of vertical integration cannot explain non-Sverdrup transport, which is mainly in the subtropical western ocean basins and equatorial currents near the Equator in each ocean basin(except the North Indian Ocean, where the circulation is dominated by monsoons). The identifi ed nonSverdrup transport is thereby robust and attributed to the joint effect of baroclinicity and relief of the bottom(JEBAR) and mesoscale eddy nonlinearity.

Geostrophic Spirals Generated by the Horizontal Diffusion of Vortex Stretching in the Yellow Sea

Horizontal velocity spirals with a clockwise rotation(downward looking) rate of 1.7?m^(-1), on average, were observed in the western and northern Yellow Sea from December 2006 to February 2007. With the observed thermal wind relation,the beta-spiral theory was used to explain the dynamics of spirals. It was found that the horizontal diffusion of geostrophic vortex stretching is likely to be a major mechanism for generating geostrophic spirals. Vertical advection associated with surface/bottom Ekman pumping and topography-induced upwelling is too weak to support these spirals. Strong wind stirring and large heat loss in wintertime lead to weak stratification and diminish the effects of vertical advection. The cooling effect and vertical diffusion are offset by an overwhelming contribution of horizontal diffusion in connection with vortex stretching. The Richardson number-dependent vertical eddy diffusivity reaches a magnitude of 10^(-4) m^2 s^(-1) on average. An eddy diffusivity of 2870 m^2 s^(-1) is required for dynamic balance by estimating the residual term. This obtained value of 10-4 m^2 s^(-1) is in good agreement with the estimation in terms of observed eddy activities. The suppressed and unsuppressed diffusivities in the observation region are 2752 and 2881 m^2 s^(-1), respectively, which supports a closed budget for velocity rotation.

A METHOD TO ESTIMATE DYNAMIC HEIGHT AND GEOSTROPHIC TRANSPORT RELATIVE TO DEEPER LEVELS FROM 400M EXPENDABLE BATHYTHERMOGRAPH IN THE INDONESIAN THROUGHFLOW

The Expendable Bathythermograph (XBT) Programme used a mix of T4 (450m) and T7(750 m) XBT’s during the pre-TOGA periods. Studies are needed to determine how to use the T4/T7 datatogether, in particular with regard to a reference level for calculation of dynamic height and geostrophiccurrents. Temperature profiles to 750 m collected from 1986 through 1989 on the trackline across theIndonesian throughflow between NW Australia and Java are used to show the relations between dynamicbeight and geostriohic flow using reference levels at 400 db and 750 db. A very high temporalcorrelation between vertically averaged temperture in the upper 400 m and dynamic height at 50 m rela-tive to 750 db was found. The corresponding regression relationships are presented for all one degree lati-tude bins along the section and can be used for dynamical calculation of currents in the upper 400 m rel-ative to 750 db .An attempt is made to estimate volume transport relative to 750 db from 400 m pro-files. Problems which make

The Relationship between the Meridional Profile of Zonal- mean Geostrophic Wind and Station Wave at 500 hPa

The sea-level pressure (SLP), 500 hPa height, zonal-mean 500 hPa height ([Z(500)]), stationary wave eddy component of the 500 hPa height (Z(500)*) and zonal-mean 500 hPa geostrophic wind [U-g] fields poleward of 20 degreesN are examined for the period 1958-1997, with emphasis on the winter season. The relationships between the Arctic Oscillation (AO)index and algebraic difference of the zonal-mean wind in 55 degreesN and 35 degreesN (Ut) index were investigated, making use the Monte Carlo procedure, Singular Value Decomposition (SVD), Empirical orthogonal function (EOF) and regression method. The leading modes of empirical orthogonal function (EOF's) of SLP are more robust than the 500 hPa height EOF's. not only in the ratio of the two largest eigenvalues, but in more zonally symmetric. Comparing the meridional profiles of zonal-mean wind amplitude associated with the AO and Ut index, the profiles for the two indexes are very similar, both with respect to amplitude and the placement of the maximum and minimum. Comparing the station wave component of 500 hPa height field regressed upon the AO and Ut index. there is one-to-one correspondence between all the major centers of action in the two maps, especially in the North Atlantic and Eurasian continent. The pattern is unlike the prominent teleconnection patterns, they have hemispheric extent and cannot be interpreted in term of the individual wavetrains.

CALCULATION OF BASIC ENVIRONMENTAL GEOSTROPHIC FLOW AND STATISTICAL STUDY ON TC TRACK AND ITS DEVIATION

Using the T63L16 analysis data with the resolution of 1.875╳1.875 degree of latitude and lon-gitude obtained from National Meteorological Center (NMC) and the real central position information of tropi-cal cyclone (referred to as TC hereafter) numbered by NMC, the basic environmental geostrophic flow at 126 time levels of 25 TCs in 1996 are calculated. The vertical distribution features of the flows are analyzed. Be-sides, the deviation of real TC tracks from the flows (referred as steering deviation hereafter, namely, the de-viation between the real central position of TC and the position calculated according to the steering flow) is also investigated. The result shows that the steering deviation would be different if the domain used to calculate the steering flow is different. The present paper obtains the optimum domain size to calculate the steering flow. It is found that the steering deviation is related to the velocity of steering flow and the initial latitude and intensity of TC itself, and that TC motion has relationship with the vertical shear structure of environmental geostrophic flow. The result also shows that the optimum steering flow is the deep-layer averaged basic flow from 1000 hPa to 200 hPa. Having the knowledge of these principle and features would help make accurate forecast of TC motion.

The construction of high precision geostrophic currents based on new gravity models of GOCE and satellite altimetry data

The new gravity field models of gravity field and steady-state ocean circulation explorer(GOCE),TIM_R6 and DIR_R6,were released by the European Space Agency(ESA)in June 2019.The sixth generation of gravity models have the highest possible signal and lowest error levels compared with other GOCE-only gravity models,and the accuracy is significantly improved.This is an opportunity to build high precision geostrophic currents.The mean dynamic topography and geostrophic currents have been calculated by the 5th(TIM_R5 and DIR_R5),6th(TIM_R6 and DIR_R6)release of GOCE gravity field models and ITSG-Grace2018 of GRACE gravity field model in this study.By comparison with the drifter results,the optimal filtering lengths of them have been obtained(for DIR_R5,DIR_R6,TIM_R5 and TIM_R6 models are 1°and for ITSG-Grace2018 model is 1.1°).The filtered results show that the geostrophic currents obtained by the GOCE gravity field models can better reflect detailed characteristics of ocean currents.The total geostrophic speed based on the TIM_R6 model is similar to the result of the DIR_R6 model with standard deviation(STD)of 0.320 m/s and 0.321 m/s,respectively.The STD of the total velocities are 0.333 m/s and 0.325 m/s for DIR_R5 and TIM_R5.When compared with ITSG-Grace2018 results,the STD(0.344 m/s)of total geostrophic speeds is larger than GOCE results,and the accuracy of geostrophic currents obtained by ITSG-Grace2018 is lower.And the absolute errors are mainly distributed in the areas with faster speeds,such as the Antarctic circumpolar circulation,equatorial region,Kuroshio and Gulf Stream areas.After the remove-restore technique was applied to TIM_R6 MDT,the STD of total geostrophic speeds dropped to 0.162 m/s.

An assessment of the CMIP5 models in simulating the Argo geostrophic meridional transport in the North Pacifi c Ocean

Eleven climate system models that participate in the Coupled Model Intercomparison Project phase 5(CMIP5)were evaluated based on an assessment of their simulated meridional transports in comparison with the Sverdrup transports.The analyses show that the simulated North Pacifi c Ocean circulation is essentially in Sverdrup balance in most of the 11 models while the Argo geostrophic meridional transports indicate signifi cant non-Sverdrup gyre circulation in the tropical North Pacifi c Ocean.The climate models overestimated the observed tropical and subtropical volume transports signifi cantly.The non-Sverdrup gyre circulation leads to non-Sverdrup heat and salt transports,the absence of which in the CMIP5 simulations suggests defi ciencies of the CMIP5 model dynamics in simulating the realistic meridional volume,heat,and salt transports of the ocean.

Geostrophic Wave Circulations(English edition)

Abstract

Identification and Interpretation of Earth’s Atmosphere Dynamics’ and Thermodynamics’ Similarities between Rogue Waves and Oceans’ Surface Geostrophic Wind

In their daily practices, meteorologists make extensive use of the geostrophic wind properties to explain many weather phenomena such as the meaning and direction of the horizontal winds that take place around the low atmospheric pressures. The biggest challenge that faces the public who is interested in information disseminated by meteorologists is to know exactly what means the geostrophic wind. Besides the literal definitions scattered in very little scientific work, there is unfortunately no book which gives importance to the algebraic definition of the geostrophic wind. Our work shows that to better understand the behavior of natural phenomena, it is essential to combine the theories with based observations. Obviously, observations cannot be relevant without a theory that guides the observers. Conversely, no theory can be validated without experimental verification. Synoptic observations show that in the “free atmosphere!” the wind vectors are very nearly parallel to isobars, and the flow is perpendicular to the horizontal pressure gradient force, at least at any given instant. This kind of information recommends great caution when making geostrophic approximations. Our work also shows that for tornadoes, there is no need to move away from the surface of the oceans to observe the geostrophic balance. Undoubtedly, identification and interpretation of earth’s atmosphere dynamics’ and thermodynamics’ similarities between rogue waves and oceans’ surface geostrophic wind will be an easy exercise to researchers who will give importance to result provided by this paper.

Flows’ Similarities between Tornadoes or Cyclones Kinematics and Motions Resulting from Weather Phenomena Coupling Geostrophic Wind with Passive Convection

Tornadoes and cyclones, as is stated in numerous literary and audiovisual works dedicated to these out of balance physical systems, are two powerful and spectacular atmospheric phenomena whose vertical and horizontal profiles of winds and temperatures are not yet well known. Indeed, data and routine observations accumulated in the World Meteorological Organization (WMO) databases, regardless of their diversity and perfection of the instruments used to achieve these data (e.g. satellites, onboard cameras, wind profilers, ultra modern calculators, etc.), offer mind-blowing performances on the extent of damage caused by these disturbances, but information provided by these ground and space based observations will never allow access to real profiles of winds associated with tornadoes and cyclones both at the ground’s surface and aloft. The works recently carried out by C. Mbane Biouele allow us to discover that winds associated with tornadoes and hurricanes result from vectors addition of troposphere’s horizontal geostrophic winds and vertical movements associated with passive convection. Unfortunately, geostrophic wind and passive convection are two familiar meteorological phenomena described with much awkwardness and monumental mistakes by all scientific books written by authors who have remained loyal to Hadley principle which states (for centuries) that hot air is lighter than cold air. It is very important to know that C. Mbane Biouele’s very recent publications demonstrate that Hadley principle is not valid in the troposphere’s regions occupied by Ferrell cells. Indeed, it is urgent for the development of meteorology to highlight with great insistence to everyone that there is a Physics principle diametrically opposed to popular Hadley one which provides thermodynamic reasons of the formation of Ferrell cells. This Principle will be named Mbane Biouele Principe and be clearly stated in this paper.

Detecting surface geostrophic currents using wavelet filter from satellite geodesy

According to the features of spatial spectrum of the dynamic ocean topography (DOT),wavelet filter is proposed to reduce short-wavelength and noise signals in DOT. The surface geostrophic currents calculated from the DOT models filtered by wavelet filter in global and Kuroshio regions show more detailed information than those from the DOT models filtered by Gaussian filter. Based on a satellite gravity field model (CG01C) and a gravity field model (EGM96),combining an altimetry-derived mean sea surface height model (KMSS04),two mean DOT models are estimated. The short-wavelength and noise signals of these two DOT models are removed by using wavelet filter,and the DOT models asso-ciated global mean surface geostrophic current fields are calculated separately. Comparison of the surface geostrophic currents from CG01C and EGM96 model in global,Kuroshio and equatorial Pacific regions with that from oceanography,and comparison of influences of the two gravity models errors on the precision of the surface geostrophic currents velocity show that the accuracy of CG01C model has been greatly improved over pre-existing models at long wavelengths. At large and middle scale,the surface geostrophic current from satellite gravity and satellite altimetry agrees well with that from oceanography,which indicates that ocean currents detected by satellite measurement have reached relatively high precision.

Variability of the currents in the Luzon Strait during spring of 2002 obtained from observations and satellite geostrophic currents and spectral analyses

The structure and variability of the currents in the Luzon Strait during spring of 2002 are studied, based on the current measurements at the average position of the mooring station (20°49′57"N, 120°48′12"E) from March 17 to April 15, 2002, satellite geostrophic currents in the Luzon Strait, and the spectral analyses, using the maximum entropy method. The subtidal currents at the mooring station show de-creased amplitudes downward with an anti-cyclonic rotation, suggesting that the currents enter and exit the South China Sea in the upper and intermediate layers, respectively. The vertical structure of the currents in the Luzon Strait suggests strongly the sandwiched structure of the LST, even though the bottom part of the profile is not resolved by the observational grid. The spectral analyses show the following periods of significant spectral peaks: (1) the tidal currents variability in the vertical direction; (2) the period about 4-6 d for the two cases of frequency f >0 and f<0 at the 200 and 500 m levels, but at the 800 m level only for the case of f >0; (3) The fluctuation in the period range is about 2-3 days for the two cases of f >0 and f<0 at the 200, 500 and 800 m levels, namely the Luzon Strait currents exhibit significant synoptical variability throughout the water column up to 800 m deep. Both direct current measurements and in situ hydrographic and satellite survey suggest no Kuroshio loop current in the Luzon Strait during the spring of 2002.

INVESTIGATION ON GEOSTROPHIC ADJUSTMENT,FRONTOGENESIS AND OSCILLATIONS

Geostrophic adjustment and frontogenesis are examined by means of the 2-D ARPS model. The simulation shows that.without the large-scale forcing,both the frontogenesis and frontolysis are observed during the geostrophic adjustment process and the intensity of the front oscillates in the case of no discontinuity.The convergence (divergence) induced by the secondary circulation is the most important factor for frontogenesis (frontolysis) at the top and bottom boundaries.The amplitude and period of oscillation are dependent on the initial atmospheric stratification and the Coriolis frequency,and they are related to the inertio-gravity wave.