POSSIBILITY TO USE SCHÖRDINGER EQUATION TO DESCRIBE LARGE-SCALE PROBABILITY WAVES AND ITS APPLICATION IN SEASONAL PREDICTION

Under the influence of a one-dimensional stationary outfield with the equilibrium between kinetic and potential energy produced by it,a modified Schördinger equation in the form i(∂ψ/∂t)t=a ∂²ψ/∂x²-ib∂,where b=b_o∂T/∂x,is used to describe the behavior of the probability wave on the six-month departure charts at the 500 hPa level.It is found that C=2πa/L-b_o∂T/ax and when L→∞,then C=-b_o∂T/∂x,where C is wave velocity,a and b are constants,and L is wavelength.The motion direction of probability waves is against the outfield temperature gradient,and their velocity is related to the absolute value of temperature gradient.The motion of waves shrinks in heat sinks and expands in heat sources,which have been verified in practice.Finally the six-month departure probability wave and the modified Schördinger equation are used in the MOS predictions of temperature and rainfall in spring-summer 1981-1985 in Jilin Province and the accuracy for trend predictions is equal to 80%.     

APPLICATION OF PROBABILITY WAVE IN LONG-RANGE SEASONAL PREDICTION

It is discussed that the anomaly in long-range weather is due to the stable sustained circulation.Waveson monthly or seasonal departure maps can essentially be regarded as probability waves which reflectthe anomaly distribution of heat sources and sinks on the earth's surface.The persistent stable circulationcreats these distributions which serve as persistent disturbance sources and in turn feedback the generalcirculation with persistent stability in later period.The departure probability waves on a six-month (September—February)chart reflect the anomalous dis-tribution of heat sources and sinks on the underlying surface.The waves north of 30°N move slowly andeastward on the Eurasian Continent against the temperature gradient,while they are stationary south of 30°N.A statistical model is developed to predict the spring—summer temperature and precipitation of next yearby using the six-month departure probability wave of last year.During 1982--1985 it was tested in severalprovinces of northern China with encousaging results.     

ON THE INFLUENCES OF LARGE-SCALE INHOMOGENEITY OF SEA TEMPERATURE UPON THE OCEANIC WAVES IN THE TROPICAL REGIONS——PART I : LINEAR THEORETICAL ANALYSIS

By using a linear oceanic mixed layer model, the influences of the horizontal gradients of sea surface temperature (SST) and the depth variations of the mixed layer upon tropical oceanic waves are investigated. The equatorial Rossby wave will be modified and a kind of slower thermal wave has been revealed under the influences of inhomogeneities of large-scale sea temperature field. An interesting result is that the propagating direction of the thermal wave is opposite to that of the classical Rossby wave. The result also shows that the thermal wave becomes dominant when the meridional gradient of sea temperature in the mixed layer exceeds a critical value. As a first approximation, it seems that both waves obtained by this study may be used to explain the observational facts that the SST anomalies can usually propagate in both directions, that is, eastward and westward, during the El Nino events.     

Power and Cross-Spectra for the Turbulent Atmospheric Motion and Transports in the Domain of Wave Number Frequency Space: Theoretical Aspects

The study of large-scale atmospheric turbulence and transport processes is of vital importance in the general circulation of the atmosphere. The governing equations of the power and cross-spectra for the atmospheric motion and transports in the domain of wave number frequency space have been derived. The contributions of the nonlinear interactions of the atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies and to the meridional transports of angular momentum and sensible heat in the atmosphere have been discussed.     

THE EFFECTS OF THE PLATEAU''S TOPOGRAPHIC GRADIENT ON ROSSBY WAVES AND ITS NUMERICAL SIMULATION

By using barotropic model equations, this article analyzed the characteristics of Rossby waves, the propagation features of wave energy and the influence of dynamic and thermal effects of the Tibetan Plateau on Rossby waves, and the focus is on discussing the plateau's topographic gradient effects on atmospheric Rossby waves. Then based on the WRF3.2 and the NCEP/NCAR FNL reanalysis data, we devised comparative tests of changing the plateau's topographic gradient and simulated a process of persistent heavy rain that happened in May 2010 in South China. The results are shown as follows. The Tibetan Plateau’s topography is conducive to the formation of atmospheric Rossby waves. while the plateau's terrain, its friction and heating effects can all make the atmospheric Rossby waves develop into the planetary waves; The effects of plateau's north and south slopes on the Rossby wave’ phase velocity is opposite, and when the slope reached a certain value can the quasi-steady normal fluctuations be generated; Simultaneously, due to the plateau's topographic gradient, descending motion appears at the west side of the plateau while ascending motion appears at the east side, and the vertical movement increased with the amplification of topographic gradients. The plateau's topographic gradient also obviously amplified the precipitation in South China, and the rainfall area increased with the amplification of topographic gradients and gradually moved from south to north and from west to east, which is conducive to the occurrence and development of convective activities in the downstream areas of the Tibetan Plateau; Moreover, for the plateau’s dynamic and thermal effects, the Rossby wave’ propagation shows upstream effects of energy dispersion, so the plateau can then affect the weather in downstream areas. Moreover, the wave group velocity increased with the degree of topographic slope.     

HEAT SOURCE-INFLUENCED FINITE AMPLITUDE ULTRALONG WAVE

Discussed in this paper is finite amplitude ultralong wave under the influence of heat sources.The conditions arefirst investigated for the existence of periodic and solitary ultralong waves of finite amplitude in the Burger model withthe aid of Hamilton function and variation of total energy and then the wave analytical expression is formulated bymeans of the functional approximation and the Hamilton function as the motion invariant in nature.Results show thatthe finite amplitude ultralong wave influenced by heat sources is unlikely to generate a solitary wave solution and im-poses no constraints on horizontal divergence as opposed to the case with the effect of heat sources available.     

Wintertime Stratospheric Anomalies-Part II: Sudden Warmings

The process of stratospheric sudden warmings from development of planetary waves to.the sudden cooling after reversal of mean zonal circulation will be studied with the primitive equations of heat and momentum balances. It will be explained that the sudden warmings may occur only in the polar regions of winter stratosphere where zonal mean temperature decreases poleward. The heating rate in the order of major warmings is produced by developed planetary waves in the stratospheric breaking layers. The particular perturbation structure characterized by large amplitude of wave 1 together with minimum of wave 2 discovered by Labitzke (1977) is crucial for initiation of major warmings. The cooling by the same mechanism can be produced in the regions with reversed mean temperature gradient.     

On the low-frequency,planetary-scale motion in the tropical atmosphere and oceans

Scale analyses for long wave, zonal ultralong wave (with zonal scale of disturbance L1~104 km and meridional scale L2~103 km) and meridional ultralong wave (L1~103 km, L2~104 km) are carried out and a set of approximate equations suitable for the study of these waves in a dry tropical atmosphere is obtained. Under the condition of sheared basic current, frequency analyses for the equations are carried out. It is found that Rossby waves and gravity waves may be separated for n ≥ l where n is the meridional wave number, whereas for n = 0 and L1~1000 km, the mixed Rossby-gravity wave will appear. Hence it is confirmed that the above results of scale analyses are correct. The consistency be-tween frequency analysis and scale analysis is established.The effect of shear of basic current on the equatorial waves is to change their frequencies and phase velocities and hence their group velocities. It increases the velocity of westward travelling Rossby waves and inertia-gravity and mixed waves, but decelerates the eastward inertia-gravity waves and the Kelvin wave. The recently observed low-frequency equatorial ocean wave may be interpreted as an eastward Kelvin wave in a basic current with shear.     

ON THE LOW-FREQUENCY, PLANETARY-SCALE MOTION IN THE TROPICAL ATMOSPHERE AND OCEANS

Scale analyses for long wave, zonal ultralong wave (with zonal scale of disturbance L,-104 km and meridional scale ?-103 km) and meridional ultralong wave (L,-103 km, L2-104 km) are carried out and a set of approximate equations suitable for the study of these waves in a dry tropical atmosphere is obtained. Under the condition of sheared basic current, frequency analyses for the equations are carried out. It is found that Rossby waves and gravity waves may be separated for n≥1 where n is the meridional wave number, whereas for n=0 and L1-1000 km, the mixed Rossby-gravity wave will appear. Hence it is confirmed that the above results of scale analyses are correct. The consistency between frequency analysis and scale analysis is established.The effect of shear of basic current on the equatorial waves is to change their frequencies and phase velocities and hence their group velocities. It increases the velocity of westward travelling Rossby waves and inertia-gravity and mixed waves, but decelerates the ea     

Tropical gravity-atmospheric long wave and the walker circulation

Orders of magnitude of terms related to earth’s rotation in linearized vorticity and divergence equations governing tropical large-scale motion are analysed. It is discovered that βyD and βyξ are smaller by one order than βv and βu respectively and then may be neglected. On this basis, tropical wave motions are discussed. It is found that there exists a kind of gravity-atmospheiic long waves which is non-vorticit atmospheric long wave, whereas the Kelvin wave is essentially the gravity-atmospheric long wave with its velocity being much lower than that of gravity. Computation shows that there also exists a kind of large-scale slow waves whose moving speed is lower by one order of magnitude than that of Kelvin wave. Such slow wave is likely to be the Walker Circulation.     

TROPICAL GRAVITY-ATMOSPHERIC LONG WAVE AND THE WALKER CIRCULATION

Orders of magnitude of terms related to earth's rotation in linearized vorticity and divergence equations governing tropical large-scale motion are analysed. It is discovered that βyD and βyζ are smaller by one order than βv and βu respectively and then may be neglected. On this basis, tropical wave motions are di s-cussed. It is found that there exists a kind of gravity-atmospheric long waves which is non-vorticit atmospheric long wave, whereas the Kelvin wave is essentially the gravity-atmospheric long wave with its velocity being much lower than that of gravity. Computation shows that there also exists a kind of large-scale slow waves whose moving speed is lower by one order of magnitude than that of Kelvin wave. Such slow wavs is likely to be the Walker Circulation.     

Principle of Cross Coupling Between Vertical Heat Turbulent Transport and Vertical Velocity and Determination of Cross Coupling Coefficient

It has been proved that there exists a cross coupling between vertical heat turbulent transport and vertical velocity by using linear thermodynamics. This result asserts that the vertical component of heat turbulent transport flux is composed of both the transport of the vertical potential temperature gradient and the coupling transport of the vertical velocity. In this paper, the coupling effect of vertical velocity on vertical heat turbulent transportation is validated by using observed data from the atmospheric boundary layer to determine cross coupling coefficients, and a series of significant properties of turbulent transportation are opened out. These properties indicate that the cross coupling coefficient is a logarithm function of the dimensionless vertical velocity and dimensionless height, and is not only related to the friction velocity u*, but also to the coupling roughness height zW0 and the coupling temperature TW0 of the vertical velocity. In addition, the function relations suggest that only when the vertical velocity magnitude conforms to the limitation |W/u*|≠1, and is above the level zW0, then the vertical velocity leads to the cross coupling effect on the vertical heat turbulent transport flux. The cross coupling theory and experimental results provide a challenge to the traditional turbulent K closure theory and the Monin-Obukhov similarity theory.     

THE SEMI-GEOSTROPHIC ADAPTATION PROCESS WITH TWO-LAYER BAROCLINIC MODEL IN LOW LATITUDE ATMOSPHERE

In this paper, the adaptation process in low latitude atmosphere is discussed by means of a two-layer baroclinic model on the equator β plane, showing that the adaptation process in low latitude is mainly dominated by the internal inertial gravity waves. The initial ageostrophic energy is dispersed by the internal inertial gravity waves, and as a result, the geostrophic motion is obtained in zonal direction while the ageostro-phic motion maintains in meridional direction, which can be called semi-geostrophic balance in barotropic model as well as semi-thermal-wind balance in baroclinic model. The vertical motion is determined both by the distribution of the initial vertical motion and that of the initial vertical motion tendency, but it is unrelated to the initial potential vorticity. Finally, the motion tends to be horizontal. The discussion of the physical mechanism of the semi-thermal-wind balance in low latitude atmosphere shows that the achievement of the semi-thermal-wind balance is due to the adjustment between the stream field and the temperature field through the horizontal convergence and divergence which is related to the vertical motion excited by the internal inertial gravity waves. The terminal adaptation state obtained shows that the adaptation direction between the mean temperature field and the shear flow field is determined by the ratio of the scale of the initial ageostrophic disturbance to the scale of one character scale related to the baroclinic Rossby radius of deformation. The shear stream field adapts to the mean temperature field when the ratio is greater than 1, and the mean temperature field adapts to the shear stream field when the ratio is smaller than 1.     

ON THE INFLUENCES OF LARGE-SCALE INHOMOGENEITY OF SEA TEMPERATURE UPON THE OCEANIC WAVES IN THE TROPICAL REGIONS-PART II: LINEAR NUMERICAL EXPERIMENTS

By using a linear oceanic mixed layer model, the long period waves in the tropical ocean are investigated numerically. Due to the inhomogeneity of the large-scale average sea temperature field of the ocean in tropical regions, besides the westward propagating equatorial Rossby wave to be modified, there will be a kind of long period thermal wave which propagates eastward under certain oceanic background conditions. Under the influences of these two kinds of waves, the propagating and evolving processes of the sea surface temperature anomalies (SSTA) are clearly shown by numerical experiments. The results of numerical experiments are consistent with the ones obtained by the theoretical analysis in Part I. The possible relationship between these two kinds of waves and El Nino events is also discussed indirectly.     

Group Velocity of Anisotropic Waves-Part Ⅰ: Mathematical Expression

The group velocity used in meteorology in the last 30 years was derived in terms of conservation of wave energy or crests in wave propagation. The conservation principle is a necessary but not a sufficient condition for deriving the mathematical form of group velocity, because it cannot specify a unique direction in which wave energy or crests propagate. The derived mathematical expression is available only for isotropic waves. But for anisotropic waves, the traditional group velocity may have no a definite direction, because it varies with rotation of coordinates. For these reasons, it cannot be considered as a general expression of group velocity. A ray defined by using this group velocity may not be the trajectory of a reference point in an anisotropic wave train. The more general and precise expression of group velocity which is applicable for both isotropic and anisotropic waves and is independent of coordinates will be derived following the displacement of not only a wave envelope phase but also a     

Group Velocity of Anisotropic Waves-Part Ⅱ: Conservative Properties

It has been argued in Part I that traditional expression of multidimensional group velocity used in meteorology is only applicable for isotropic waves. While for anisotropic waves, it cannot manifest propagation of waves group along the trajectory of a reference wave point, and varies with rotation of coordinates. The general mathematical expression of group velocity which may be used also for anisotropic waves has been derived in Part I. It will be proved that the mean wave energy, momentum and wave action density are all conserved as a wave group propagates at the general group velocity. Since general group velocity represents the movement of a reference point in either isotropic or anisotropic wave trains, it may be used to define wave rays. The variations of wave parameters along the rays in a slowly varying environment are represented by ray-tracing equations. Using the general group velocity, we may derive the anisotropic ray-tracing equations, which give the traditional ray-tracing equations for     

Evidence of Specific MJO Phase Occurrence with Summertime California Central Valley Extreme Hot Weather

This study examines associations between California Central Valley(CCV) heat waves and the Madden Julian Oscillation(MJO). These heat waves have major economic impact. Our prior work showed that CCV heat waves are frequently preceded by convection over the tropical Indian and eastern Pacific oceans, in patterns identifiable with MJO phases. The main analysis method is lagged composites(formed after each MJO phase pair) of CCV synoptic station temperature, outgoing longwave radiation(OLR), and velocity potential(VP). Over the CCV, positive temperature anomalies occur only after the Indian Ocean(phases 2-3) or eastern Pacific Ocean(phases 8-1) convection(implied by OLR and VP fields). The largest fractions of CCV hot days occur in the two weeks after onset of those two phase pairs. OLR and VP composites have significant subsidence and convergence above divergence over the CCV during heat waves, and these structures are each part of larger patterns having significant areas over the Indian and Pacific Oceans. Prior studies showed that CCV heat waves can be roughly grouped into two clusters: Cluster 2 is preceded by a heat wave over northwestern North America, while Cluster 1 is not. OLR and VP composite analyses are applied separately to these two clusters. However, for Cluster 2, the subsidence and VP over the CCV are not significant, and the large-scale VP pattern has low correlation with the MJO lagged composite field. Therefore, the association between the MJO convection and subsequent CCV heat wave is more evident in Cluster 1 than Cluster 2.     

A REGIONAL COUPLED AIR–SEA–WAVE MODEL: SIMULATION OF UPPER-OCEAN RESPONSES TO AN IDEALIZED TROPICAL CYCLONE

In this study a coupled air–sea–wave model system, containing the model components of GRAPES-TCM, ECOM-si and WAVEWATCH III, is established based on an air–sea coupled model. The changes of wave state and the effects of sea spray are both considered. Using the complex air–sea–wave model, a set of idealized simulations was applied to investigate the effects of air–sea–wave interaction in the upper ocean. Results show that air–wave coupling can strengthen tropical cyclones while air–sea coupling can weaken them; and air–sea–wave coupling is comparable to that of air–sea coupling, as the intensity is almost unchanged with the wave model coupled to the air–sea coupled model. The mixing by vertical advection is strengthened if the wave effect is considered, and causes much more obvious sea surface temperature (SST) decreases in the upper ocean in the air–sea coupled model. Air–wave coupling strengthens the air–sea heat exchange, while the thermodynamic coupling between the atmosphere and ocean weakens the air–sea heat exchange: the air–sea–wave coupling is the result of their balance. The wave field distribution characteristic is determined by the wind field. Experiments are also conducted to simulate ocean responses to different mixed layer depths. With increasing depth of the initial mixed layer, the decrease of SST weakens, but the temperature decrease of deeper layers is enhanced and the loss of heat in the upper ocean is increased. The significant wave height is larger when the initial mixed layer depth increases.     

SOME CATASTROPHE PROPERTIES OF TWO-LAYER SHEAR FLOW

In this paper a simple current system which consists of two stratified incompressible layers is examined. For the basic equations of the motion of fluid a lower order spectrum model is established by means of Galerkin method. Adopting the difference of wind velocity between the upper and lower layers, As =as a control parameter, the bifurcation and stability of the solution of the dynamical systemare discussed. It is found that the flow states in the lower layer will have a catastrophe, when where Cg is the phase velocity of the internal inertio-gravitational wave in a geostrophic current.These results may give a reasonable explanation for the mechanism of the catastrophe phenomena, including the "pressure-jump" in the atmosphere.     

Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves

The variations in the wave energy and the amplitude along the energy dispersion paths of the barotropic Rossby waves in zonally symmetric basic flow are studied by solving the wave energy equation,which expresses that the wave energy variability is determined by the divergence of the group velocity and the energy budget from the basic flow.The results suggest that both the wave energy and the amplitude of a leading wave increase significantly in the propagating region that is located south of the jet axis and enclosed by a southern critical line and a northern turning latitude.The leading wave gains the barotropic energy from the basic flow by eddy activities.The amplitude continuously climbs up a peak at the turning latitude due to increasing wave energy and enlarging horizontal scale(shrinking total wavenumber).Both the wave energy and the amplitude eventually decrease when the trailing wave continuously approaches southward to the critical line.The trailing wave decays and its energy is continuously absorbed by the basic flow.Furthermore,both the wave energy and the amplitude oscillate with a limited range in the propagating region that is located near the jet axis and enclosed by two turning latitudes.Both the leading and trailing waves neither develop nor decay significantly.The jet works as a waveguide to allow the waves to propagate a long distance.