Stable and Unstable Eigensolutions of Laplace''''s Tidal Equations for Zonal Wavenumber Zero

Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear. New results are presented for the inclusion of dissipative processes and the case of unstable conditions. In both instances the (nonzero) eigenfrequencies are complex. In the latter case, additional stable (i.e. real) eigenfrequencies appear in the numerical results for the absolute value of the Lambparameter ε being larger than a critical value εc. Further, it is shown that any degeneracies are removed through the inclusion of dissipation. Moreover, asymptotic relations are derived employing the relation of Laplace's tidal equations for m = 0 to the spheroidal differential equation. The implications of these findings to numerical techniques are demonstrated and results of computations are presented.     

ON THE GENERATION AND MAINTENANCE OF ATMOSPHERIC DISTURBANCES

Blocking is one of the intensive atmospheric disturbances which can maintain for a long time. In this paprer we investigate the general conditions favorable for the generation and maintenance of the intensive disturbances. First, the evolutional process of disturbances superimposed on a jet-like zonal flow is studied by using the wave-packet representation and the WKBJ method. Second, the mechanism for generation and maintenance of disturbances is investigated by using the nonlinear equations and the general physical laws. Finally, some numerical experiments are given for illustration, showing the rapid absorption of disturbances by the jet-like zonal flow in one case and the maintenance of disturbances for a long time in the other case.     

Topographically Forced Three-Wave Quasi-Resonant and Non-Resonant Interactions among Barotropic Rossby Waves on an Infinite Beta-Plane

In this paper, we first apply the assumption h=εh` of topographic variation (h is the nondimensional topographic height and is a small parameter) to obtain nonlinear equations describing three-wave quasi-resonant and non-resonant interactions among Rossby waves for zonal wavenumbers 1-3 over a wavenumber-two bottom topography (WTBT). Some numerical calculations are made with the fourth-order Rung-Kutta Scheme. It is found that for the case without topographic forcing, the period of three-wave quasi-resonance (TWQR) is found to be in-dependent of the zonal basic westerly wind, but dependent on the meridional wavenumber and the initial amplitudes. For the fixed initial data, when the frequency mismatch is smaller and the meridional wavelength is moderate, its pe-riod will belong to the 30-60-day period band. However, when the wavenumber-two topography is included, the pe-riods of the forced quasi-resonant Rossby waves are also found to be strongly dependent on the setting of the zonal basic westerly wind. Under the same conditions, only when the zonal basic westerly wind reaches a moderate extent, intraseasonal oscillations in the 30-60-day period band can be found for zonal wavenumbers 1-3. On the other hand, if three Rossby waves considered have the same meridional wavenumber, three-wave non-resonant interaction over a WTBT can occur in this case. When the WTBT vanishes, the amplitudes of these Rossby waves are conserved. But in the presence of a WTBT, the three Rossby waves oscillate with the identical period. The period, over a moder-ate range of the zonal basic westerly wind, is in the intraseasonal, 30-60-day range.     

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     

A global spectral element model for poisson equations and advective flow over a sphere

A global spherical Fourier–Legendre spectral element method is proposed to solve Poisson equations and advective flow over a sphere. In the meridional direction, Legendre polynomials are used and the region is divided into several elements. In order to avoid coordinate singularities at the north and south poles in the meridional direction, Legendre–Gauss–Radau points are chosen at the elements involving the two poles. Fourier polynomials are applied in the zonal direction for its periodicity,with only one element. Then, the partial differential equations are solved on the longitude–latitude meshes without coordinate transformation between spherical and Cartesian coordinates. For verification of the proposed method, a few Poisson equations and advective flows are tested. Firstly, the method is found to be valid for test cases with smooth solution. The results of the Poisson equations demonstrate that the present method exhibits high accuracy and exponential convergence. Highprecision solutions are also obtained with near negligible numerical diffusion during the time evolution for advective flow with smooth shape. Secondly, the results of advective flow with non-smooth shape and deformational flow are also shown to be reasonable and effective. As a result, the present method is proved to be capable of solving flow through different types of elements, and thereby a desirable method with reliability and high accuracy for solving partial differential equations over a sphere.     

The Development of a Nonhydrostatic Global Spectral Model

With the development of numerical weather prediction technology,the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general circulation have become more and more unfit for high-impact weather prediction.To address this,it is important to invest in the development of global nonhydrostatic models.Few existing nonhydrostatic global models use consistently the grid finite difference scheme for the primitive equations of dynamical cores,which can subsequently degrade the accuracy of the calculations.A new nonhydrostatic global spectral model,which utilizes the Eulerian spectral method,is developed here from NCAR Community Atmosphere Model 3.0(CAM3.0).Using Janjic's hydrostatic/nonhydrostatic method,a global nonhydrostatic spectral method for the primitive equations has been formulated and developed.In order to retain the integrity of the nonhydrostatic equations,the atmospheric curvature correction and eccentricity correction are considered. In this paper,the Held-Suarez idealized test and an idealized baroclinic wave test are first carried out,which shows that the nonhydrostatic global spectral model has similar climate states to the results of many other global models for long-term idealized integration,as well as better simulation ability for short-term idealized integration.Then,a real case experiment is conducted using the new dynamical core with the full physical parameterizations of subgrid-scale physical processes.The 10-day numerical integration indicates a decrease in systematic error and a better simulation of zonal wind,temperature,and 500-hPa height.     

Sensitivity of Nonlinearity on the ENSO Cycle in a Simple Air-sea Coupled Model

In this paper,the influence of the El NioSouthern Oscillation (ENSO) cycle on the sensitivity of nonlinear factors in the numerical simulation is investigated by conducting numerical experiments in a simple air-sea coupled model for ENSO prediction.Two sets of experiments are conducted in which zonal nonlinear factors,meridional nonlinear factors,or both are incorporated into the governing equations for the atmosphere or ocean.The results suggest that the ENSO cycle is very sensitive to the nonlinear factor of the governing equation for the atmosphere or ocean.Thus,incorporating nonlinearity into air-sea coupled models is of exclusive importance for improving ENSO simulation.     

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.     

The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations

The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.     

Some aspects of the diurnal and semidiurnal tidal wind field in meteor zone

The diurnal and semidiurnal tidal wind field variations in the altitudes between 80 and 100 km of the earth’s atmosphere over a mid-latitude station are studied by means of the phases of the zonal and meridional wind measurements made at Atlanta (34oN, 84oW). The rotation of diurnal tidal wind vector is seen to be clockwise at lower heights (80-86 km), swinging between clockwise and unti-clockwise at intermediate heights (88-96 km) and anti-clockwise at higher-heights (96- 100 km). The senses of rotation of diurnal and semidiurnal tidal wind vectors are compared between the stations located in the same and opposite hemispheres. The results are consistent with the tidal theory in the case of Atlanta and Adelaide (35oS, 139oE) whereas in the case of other stations considered in the present study, they showed marked variations.     

Diagnostic Study of Global Energy Cycle of the GRAPES Global Model in the Mixed Space-Time Domain

Some important diagnostic characteristics for a model’s physical background are reflected in the model’s energy transport, conversion, and cycle. Diagnosing the atmospheric energy cycle is a suitable way towards understanding and improving numerical models. In this study, formulations of the “Mixed Space-Time Domain”energy cycle are calculated and the roles of stationary and transient waves within the atmospheric energy cycle of the Global-Regional Assimilation and Prediction System （GRAPES） model are diagnosed and compared with the NCEP analysis data for July 2011. Contributions of the zonal-mean components of the energy cycle are investigated to explain the performance of numerical models. The results show that the GRAPES model has the capability to reproduce the main features of the global energy cycle as compared with the NCEP analysis. Zonal available potential energy （AZ） is converted into stationary eddy available potential energy （ASE） and transient eddy available potential energy （ATE）, and ASE and ATE have similar values. The nonlinear conversion between the two eddy energy terms is directed from the stationary to the transient. AZ becomes larger with increased forecast lead time, reflecting an enhancement of the meridional temperature gradient, which strengthens the zonal baroclinic processes and makes the conversion from AZ to eddy potential energy larger, especially for CAT （conversion from AZ to ATE）. The zonal kinetic energy （KZ） has a similar value to the sum of the stationary and transient eddy kinetic energy. Barotropic conversions are directed from eddy to zonal kinetic energy. The zonal conversion from AZ to KZ in GRAPES is around 1.5 times larger than in the NCEP analysis. The contributions of zonal energy cycle components show that transient eddy kinetic energy （KTE） is associated with the Southern Hemisphere subtropical jet and the conversion from KZ to KTE reduces in the upper tropopause near 30？S. The nonlinear barotropic conversion between stationary     

THE SENSITIVITY OF NUMERICAL SIMULATION TO OROGRAPHY SPECIFICATION IN THE LOW RESOLUTION SPECTRAL MODEL－PART I: THE EFFECTS OF OROGRAPHY ON THE ATMOSPHERIC GENERAL CIRCULATION

In order to identify the sensitivity of the numerical simulation to the orography specification in a low resolution spectral model, two sets of numerical experiments for full-mountain and no-mountain cases are performed. By comparing the results, it is possible to determine the eflects of mountains on the atmospheric general circulation.This is a global, spectral model incorporating the primitive equations sugmented by physical parameterization and mountains, with five equally-spaced sigma levels in the vertical ang a triangular truncation at wavenum-ber 10 in the horizontal.Analysis of results supports earlier work by demonstrating that the low resolution global spectral model is capable of simulating the major features of global general circulation and indicates that it is necessary to consider the effects of mountains on stationary disturbances in the numerical simulation. The simulations show that topography plays an important role in intensifying heat sources for maintenance of disturbances.All the     

Some Aspects of the Diurnal and Semidiurnal Tidal Wind Field in Meteor Zone

The diurnal and semidiurnal tidal wind field variations in the altitudes between 80 and 100 km of the earth's atmosphere over a mid-latitude station are studied by means of the phases of the zonal and meridional wind measurements made at Atlanta (34 ° N, 84 ° W). The rotation of diurnal tidal wind vector is seen to be clockwise at lower heights (80-86 km), swinging between clockwise and anti-clockwise at intermediate heights (88-96 km) and anti-clockwise at higher heights (96-100 km). The senses of rotation of diurnal and semidiurnal tidal wind vectors are compared between the stations located in the same and opposite hemispheres. The results are consistent with the tidal theory in the case of Atlanta and Adelaide (35°S, 139 ° E) whereas in the case of other stations considered in the present study, they showed marked variations.     

DISSIPATION EFFECT ON THE FLOW OVER MOUNTAINS

In the paper,the turbulent dissipation is considered in the model for studying the flow overmountains.The governing equation is a first order ordinary differential equation derived from analgebraic equation without dissipation case.The solution is sensitive to the upstream condition ofdissipation.The dissipation not only reduces the strength of discontinuity but also changes theproperties of the governing equation.In the paper,the qualitative characteristic features of thegoverning equation are discussed.The numerical results with super and sub-critical cases are alsodiscussed in detail.The results show that the turbulent dissipation is an important factor and is notnegligible.     

High resolution global modeling of the atmospheric circulation

An informal review is presented of recent developments in numerical simulation of the global atmospheric circulation with very fine numerical resolution models. The focus is on results obtained recently with versions of the GFDL SKYHI model and the Atmospheric Model for the Earth Simulator (AFES) global atmospheric models. These models have been run with effective horizontal grid resolution of 10–40 km and fine vertical resolution. The results presented demonstrate the utility of such models for the study of a diverse range of phenomena. Specifically the models are shown to simulate the development of tropical cyclones with peak winds and minimum central pressures comparable to those of the most intense hurricanes actually observed. More fundamentally, the spectrum of energy content in the mesoscale in the flow can be reproduced by these models down to near the smallest explicitly-resolved horizontal scales. In the middle atmosphere it is shown that increasing horizontal resolution can lead to significantly improved overall simulation of the global-scale circulation. The application of the models to two specific problems requiring very fine resolution global will be discussed. The spatial and temporal variability of the vertical eddy flux of zonal momentum associated with gravity waves near the tropopause is evaluated in the very fine resolution AFES model. This is a subject of great importance for understanding and modelling the flow in the middle atmosphere. Then the simulation of the small scale variations of the semidiurnal surface pressure oscillation is analyzed, and the signature of significant topographic modulation of the semidiurnal atmospheric tide is identified.     

Teleconnection Patterns along the Asian Jet Associated with Different Combinations of Convection Oscillations over the Indian Continent and Western North Pacific during Summer

A zonal teleconnection has been found along the Asian jet over the Eurasian continent during summer.In this study,the authors investigated circulation anomalies in the extratropics,in particular for the zonal teleconnection,under different combinations of subtropical convection anomalies over the northern Indian continent (IND) and the western North Pacific (WNP).The outof-phase configuration (i.e.,stronger (weaker) IND convection and weaker (stronger) WNP convection) was found to be more common than the in-phase configuration (i.e.,stronger (weaker) IND convection and stronger (weaker) WNP convection),which is consistent with previous results.Composite results indicated that circulation anomalies for out-of-phase configurations of 30-60-day convection oscillations are much stronger in the middle latitudes than those for in-phase configurations.In addition,zonal teleconnection patterns are predominant for the out-of-phase configurations,particularly for the configuration of strong IND convection and weak WNP convection;however,they are either weak or obscure for the in-phase configurations.These results suggest that the zonal teleconnection pattern along the Asian jet is dependent on different combinations of the IND and WNP subtropical convection anomalies.     

A comparison of the radar ray path equations and approximations for use in radar data assimilation

The radar ray path equations are used to determine the physical location of each radar measurement. These equations are necessary for mapping radar data to computational grids for diagnosis, display and numerical weather prediction (NWP). They are also used to determine the forward operators for assimilation of radar data into forecast models. In this paper, a stepwise ray tracing method is developed. The influence of the atmospheric refractive index on the ray path equations at different locations related to an intense cold front is examined against the ray path derived from the new tracing method. It is shown that the radar ray path is not very sensitive to sharp vertical gradients of refractive index caused by the strong temperature inversion and large moisture gradient in this case. In the paper, the errors caused by using the simplified straight ray path equations are also examined. It is found that there will be significant errors in the physical location of radar measurements if the earth’s curvature is not considered, especially at lower elevation angles. A reduced form of the equation for beam height calculation is derived using Taylor series expansion. It is computationally more efficient and also avoids the need to use double precision variables to mitigate the small difference between two large terms in the original form. The accuracy of this reduced form is found to be sufficient for modeling use.     

Developments of the Three-Dimensional Variational Data Assimilation System for the Nonhydrostatic GRAPES

Based on the original GRAPES (Global/Regional Assimilation and PrEdiction System) 3DVAR (p3DAR), which is defined on isobaric surface, a new three-dimensional variational data assimilation system (m3DVAR) is constructed and used exclusively with the nonhydrostatic GRAPES model in order to reduce the errors caused by spatial interpolation and variable transformation, and to improve the quality of the initial value for operational weather forecasts. Analytical variables of the m3DVAR are fully consistent with predictands of the GRADES model in terms of spatial staggering and physical definition. A different vertical coordinate and the nonhydrostatic condition are taken into account, and a new scheme for solving the dynamical constraint equations is designed for the m3DVAR. To deal with the difficulties in solving the nonlinear balance equation at σ levels, dynamical balance constraints between mass and wind fields are reformulated, and an effective mathematical scheme is implemented under the terrain-following coordinate. Meanwhile, new observation operators are developed for routine observational data, and the background error covariance is also obtained. Currently, the m3DVAR system can assimilate all routine observational data. Multi-variable idealized experiments with single point observations are performed to validate the m3DVAR system. The results show that the system can describe correctly the multi-variable analysis and the relationship of the physical constraints. The difference of innovation and the analysis residual for ∏ also show that the analysis error of the m3DVAR is smaller than that of the p3DVAR. The Ts scores of precipitation forecasts in August 2006 indicate that the m3DVAR system provides reduced errors in the model initial value than the p3DVAR system. Therefore, the m3DVAR system can improve the analysis quality and initial value for numerical weather predictions.     

ALGEBRAIC ROSSBY SOLITARY WAVE AND BLOCKING IN THE ATMOSPHERE

In this paper, the atmosphere is divided into two regions which are governed by different equations. Furthermore, multiple-scale method is used to obtain the Benjamin-Ono equation satisfied by the nonlinear Rossby wave in weak shear zonal flow. The equation has algebraic solitary wave solution, and the sta-tionary streamfunction fields in the atmosphere are calculated by using numerical method, and the results demonstrate that the stationary solution is antisymmetric dipoles with the anticyclone north of the cyclone, and the structure is similar to the equivalent modon obtained by Mcwilliains (1980), Because the modon obtained here is an algebraic solitary wave, the modon may be called “algebraic modon”, and the stationary algebraic modon is consistent with observations of blocking pattern in the atmosphere.