一种新水平网格的Rossby波计算特性

提出了一个新的水平跳点网格（LE网格）,这种网格将h放置在格点上,u,v同时放置在x方向和y方向格点中间.并采用一种推导频散关系的通用方法,研究在该LE网格上与Arakawa A E网格上描述Rossby波产生误差的情况,分可分辨和不可分辨两种情况.采用二阶中央差或四阶紧致差分格式从频率和群速度两个方面进行对比分析,结果表明不论在可分辨或不可分辨情况下,还是采用二阶中央差或四阶紧致差分格式,在频率和群速度两方面,LE网格在描述Rossby波产生的误差均较Arakawa A E网格要小,同时也表明不论在可分辨还是不可分辨的情况下,采用高精度的四阶紧致差分格式,LE网格和Arakawa A_E网格在描述Rossby波时产生的频率误差和x、y方向群速度误差并非必然减少.     

Relative role of subinertial and superinertial modes in the coastal long wave response forced by the landfall of a tropical cyclone

A set of numerical experiments has been performed in order to analyze the long-wave response of the coastal ocean to a translating mesoscale atmospheric cyclone approaching the coastline at a normal angle. An idealized two-slope shelf topography is chosen. The model is forced by a radially symmetric atmospheric pressure perturbation with a corresponding gradient wind field. The cyclone's translation speed, radius, and the continental shelf width are considered as parameters whose impact on the long wave period, modal structure, and amplitude is studied. Subinertial continental shelf waves (CSW) dominate the response under typical forcing conditions and on the narrower shelves. They propagate in the downstream (in the sense of Kelvin wave propagation) direction. Superinertial edge wave modes have higher free surface amplitudes and faster phase speeds than the CSW modes. While potentially more dangerous, edge waves are not as common as subinertial shelf waves because their generation requires a wide, gently sloping shelf and a storm system translating at a relatively high (∼10 m s⁻¹ or faster) speed. A relatively smaller size of an atmospheric cyclone also favors edge wave generation. Edge waves with the highest amplitude (up to 60% of the forced storm surge) propagate upstream. They are produced by a storm system with an Eulerian time scale equal to the period of a zero-mode edge wave with the wavelength of the storm spatial scale. Large amplitude edge waves were generated during Hurricane Wilma's landfall (2005) on the West Florida shelf with particularly severe flooding occurring upstream of the landfall site.     

Generation of baroclinic topographic waves by a tropical cyclone impacting a low-latitude continental shelf

Numerical model experiments have been performed to analyze the low-latitude baroclinic continental shelf response to a tropical cyclone. The theory of coastally trapped waves suggests that, provided appropriate slope, latitude, stratification and wind stress, bottom-intensified topographic Rossby waves can be generated by the storm. Based on a scale analysis, the Nicaragua Shelf is chosen to study propagating topographic waves excited by a storm, and a model domain is configured with simplified but similar geometry. The model is forced with wind stress representative of a hurricane translating slowly over the region at 6 km h⁻¹. Scale analysis leads to the assumption that baroclinic Kelvin wave modes have minimal effect on the low-frequency wave motions along the slope, and coastal-trapped waves are restricted to topographic Rossby waves. Analysis of the simulated motions suggests that the shallow part of the continental slope is under the influence of barotropic topographic wave motions and at the deeper part of the slope baroclinic topographic Rossby waves dominate the low-frequency motions. Numerical solutions are in a good agreement with theoretical scale analysis. Characteristics of the simulated baroclinic waves are calculated based on linear theory of bottom-intensified topographic Rossby waves. Simulated waves have periods ranging from 153 to 203 h. The length scale of the waves is from 59 to 87 km. Analysis of energy fluxes for a fixed volume on the slope reveals predominantly along-isobath energy propagation in the direction of the group velocity of a topographic Rossby wave. Another model experiment forced with a faster translating hurricane demonstrates that fast moving tropical cyclones do not excite energetic baroclinic topographic Rossby waves. Instead, robust inertial oscillations are identified over the slope.     

The mechanism of the effects of the upwelling mean on the ENSO event mature phase locking

The mechanism of the effects of the upwelling mean on the ENSO event mature phase locking is ex-amined by using a mixed-mode model. The results show that the positive feedback process of the ef-fects of the seasonal variation of the upwelling mean on the Kelvin wave is the mechanism of the locking of the event mature phase to the end of the calendar year. The memory of the Rossby waves for the sign-shifting of the sea surface temperature anomaly from positive to negative 6 months before the cold peak time is the other mechanism of the locking of the La Nia event mature phase to the end of the calendar year. The results here are different from previous ones which suggest that the balance between cold and warm trends of sea surface temperature anomaly is the mechanism involved. The cold trend is caused by the upwelling Kelvin wave from upwelling Rossby wave reflected at the western boundary, excited by the westerly anomaly stress over the central Pacific and amplified by the seasonal variation of the coupled strength in its way propagating westward. The warm trend is caused by the Kelvin wave forced by the western wind stress over the middle and eastern equatorial Pacific. The cause of the differences is due to the opposite phase of the seasonal variation of the upwelling mean to that in the observation and an improper parameterization scheme for the effects of the seasonal varia-tion of the upwelling mean on the ENSO cycle in previous studies.     

Interannual variability in the Biannual Rossby waves in the tropical Indian Ocean and its relation to Indian Ocean Dipole and El Nino forcing

The interannual variability of the tropical Indian Ocean is studied using Simple Ocean Data Assimilation (SODA) sea surface height anomalies (SSHA) and Hadley Centre Ice Sea Surface Temperature anomalies. Biannual Rossby waves (BRW) were observed along the 1.5° S and 10.5° S latitudes during the Indian Ocean Dipole (IOD) years. The SODA SSHA and its BRW components were comparable with those of Topex/Poseidon. The phase speed of BRW along 1.5° S is −28 cm/s, which is comparable with the theoretical speed of first mode baroclinic (equatorially trapped) Rossby waves. This is the first study to show that no such propagation is seen along 1.5° S during El Nino years in the absence of IOD. Thus the westward propagating downwelling BRW in the equatorial Indian Ocean is hypothesized as a potential predictor for IOD. These waves transport heat from the eastern equatorial Indian Ocean to west, long before the dipole formation. Along 10.5° S, the BRW formation mechanisms during the El Nino and IOD years were found to be different. The eastern boundary variations along 10.5° S, being localized, do not influence the ocean interior considerably. Major portion of the interannual variability of the thermocline, is caused by the Ekman pumping integrated along the characteristic lines of Rossby waves. The study provides evidence of internal dynamics in the IOD formation. The positive trend in the downwelling BRW (both in SODA and Topex/Poseidon) is of great concern, as it contributes to the Indian Ocean warming.     

On the generation of coastline-following grids for ocean models—trade-off between orthogonality and alignment to coastlines

Regional ocean models usually utilize orthogonal curvilinear grids that are fit to the coastline of the modeled regions. While the orthogonality of the grid is required from the perspective of the numerical algorithms, the alignment to the irregular coastlines improves the characterization of the land-sea distribution and the ocean simulation. In this article, we carry out fractal analysis of two representative coastal regions and discuss the trade-offs between the orthogonality and coastline alignment during the grid generation of these regions. A new grid generation method based on Schwarz-Christoffel conformal mappings is proposed, with automatic coastal boundary retrieval algorithm that generates resolution dependent boundary for grid generation and alleviates the human efforts involved in traditional methods. We show that for the southeastern Pacific region, the coastline is smooth with low fractal dimension and there exists effective trade-off with a coastline boundary that adjusts to the desired grid resolution. On the contrary, there is no effective trade-off for southeast China seas where the coastline is of higher fractal dimension, and a coarser coastline boundary is recommended for better orthogonality with little loss in coastline alignment. Further numerical study of coastal trapped Kelvin waves for the typical regions demonstrate that the new coastline-fitting grids achieve smaller error in numerical dispersion and higher accuracy. Through analysis, we conclude that for grid generation for regional ocean modeling, modelers should bring into consideration of the multi-scale fractal characteristics of the coastline.     

Global distribution and climatological features of the 5–6-day planetary waves seen in the SABER/TIMED temperatures (2002–2007)

The paper is focused on the global spatial structure, seasonal and interannual variability of the ～5-day Rossby (W1) and ～6-day Kelvin (E1) waves derived from the SABER/TIMED temperature measurements for 6 full years (January 2002–December 2007). The latitude structure of the ～5-day W1 wave is related to the gravest symmetric wave number 1 Rossby wave. The vertical structure of the ～5-day Rossby wave amplitude consists of double-peaked maxima centred at ～80–90 km and ～105–110 km. This wave has a vertically propagating phase structure from the stratosphere up to 120 km altitude with a mean vertical wavelength of ～50–60 km. The ～6-day E1 wave is an equatorially trapped wave symmetric about the equator and located between 20°N and 20°S. Its seasonal behaviour indicates some equinoctial and June solstice amplifications, while the vertical phase structure indicates that this is a vertically propagating wave between 20–100 km altitudes with a mean vertical wavelength of ～25 km.     

Stability and Grid Dispersion of the P-SV 4th-Order Staggered-Grid Finite-Difference Schemes

Stability and grid dispersion in the P-SV 4th-order in space, 2nd-order in time, displacement-stress staggered-grid finite-difference scheme is investigated in the case of a homogeneous unbounded medium. All results, however, also apply to the velocity-stress and displacement- velocity-stress finite-difference schemes. Independent stability conditions for the P and S waves are obtained by exact separation of equations for the two types of waves. Since the S-wave group velocity can differ from the actual velocity as much as 5% for the sampling ratio 1/5, commonly used in numerical modelling, the sampling of the minimum S wavelength by 6 grid spacings (with the velocity difference not larger than 2.5%) is recommended. Grid dispersion is strongest for a wave propagating in a direction of a coordinate axis and weakest for a wave propagating along a plane diagonal. Grid dispersion in the 4 ^th -order scheme for the sampling ratios s = 1/5 and s = 1/6 is smaller than grid dispersion in the 2 ^nd -order scheme for s = 1/10 and s = 1/12, respectively.     

空间分辨率和空间差分精度对水平网格性能的影响

为了说明在物理空间中空间差分精度和空间分辨率对Arakawa A-D网格性能的影响程度,将线性浅水方程组采用二阶中央差和四阶中央差格距分别取100 km、10 km和1 km在Arakawa A-D网格上进行离散和120 min的模拟预报,模拟结果和解析解进行比较,结果表明：当网格距是1 km时,不论采用二阶中央差分方案还是四阶中央差分方案,重力惯性波在4种网格上模拟的结果相同,即变量配置的影响是可以忽略的;当网格距增加到10 km或100 km时,不同的变量配置模拟的结果是不同的.但是,不论对二阶中央差还是四阶中央差,当网格距相同的情况下,在C网格上模拟得到的结果均方根误差最小,在D网格上模拟得到的结果均方根误差最大.同时也表明：当差分精度从二阶增加到四阶后,模拟结果的误差并非一致减少,并和群速相对误差的变化一致,因此对于初值为混合波的多变量方程组而言,增加差分精度不能改进模拟的结果.并且缩小网格距比增加差分精度对减少在Arakawa A-D 网格上离散产生的误差更明显.     

On isallobaric effect in a quasi-geostrophic topographic-drag problem

Abstract

Isallobaric effect of a slowly varying quasi-geostrophic flow represented by propagating waves may give rise to a mean steady topographic drag component which turns out to be the principal one when viscous effects are negligibly small. This drag component decreases, in contrast to the quasi-geostrophic component, when statistical properties of the topography become isotropic. When the phase velocity of the incident wave is much larger (smaller) than the phase speed of Rossby waves, the isallobaric drag becomes independent (dependent) on the sign of that velocity.     

简单热带海气耦合模型中不同扰动形式的作用

在局地热平衡情况下,将物理量先用韦伯函数展开,然后去掉相应分量的滤波方 法,讨论了简单热带海气耦合模型中不同形式扰动的作用和贡献,结果表明,在热带海气耦合 系统中,大气准定常 Ｒｏｓｓｂｙ波和海洋 Ｒｏｓｓｂｙ波对于耦合系统贡献较大,它们决定着耦合系统 与耦合扰动的性质,而大气准定常Ｋｅｌｖｉｎ波和海洋Ｋｅｌｖｉｎ波对于耦合系统贡献相对较小．     

Planetary wave coupling (5–6-day waves) in the low-latitude atmosphere–ionosphere system

Vertical coupling in the low-latitude atmosphere–ionosphere system driven by the 5-day Rossby W1 and 6-day Kelvin E1 waves in the low-latitude MLT region has been investigated. Three different types of data were analysed in order to detect and extract the ∼6-day wave signals. The National Centres for Environmental Prediction (NCEP) geopotential height and zonal wind data at two pressure levels, 30 and 10 hPa, were used to explore the features of the ∼6-day waves present in the stratosphere during the period from 1 July to 31 December 2004. The ∼6-day wave activity was identified in the neutral MLT winds by radar measurements located at four equatorial and three tropical stations. The ∼6-day variations in the ionospheric electric currents (registered by perturbations in the geomagnetic field) were detected in the data from 26 magnetometer stations situated at low latitudes. The analysis shows that the global ∼6-day Kelvin E1 and ∼6-day Rossby W1 waves observed in the low-latitude MLT region are most probably vertically propagating from the stratosphere. The global ∼6-day W1 and E1 waves seen in the ionospheric electric currents are caused by the simultaneous ∼6-day wave activity in the MLT region. The main forcing agent in the equatorial MLT region seems to be the waves themselves, whereas in the tropical MLT region the modulated tides are also of importance.     

Experimental study of long nonlinear internal waves in rotating fluid

Experiments were performed on the rotating platform 14 m in diameter equipped with a simple internal wave generator. Internal waves were generated for a wide range of Coriolis parameters. When the rotation is very weak, i.e., when the internal Rossby radius of deformation is much larger than the wavelength, then the stable nonlinear waves generated are solitary waves. These have a horizontal crest, as in the nonrotating case. When the rotation is strong, i.e., when the internal Rossby radius is at most comparable with the wavelength, then Sverdrup-like periodic waves can be generated, but no solitary wave can then propagate. For the intermediate case, Ostrovsky waves are generated. Their phase speed increases with increasing amplitude. Then, there are two characteristic wave lengths: one which varies with the inverse square root of the amplitude, as for the KdV wave, and the other, linked with the rotation, which varies as the square root of the amplitude. The experimental results are thus in agreement with most of the conclusions in recent analytical developments.     

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part II: Pacific and Atlantic Oceans

The effect of viscosity, non linearities, incident wave period and realistic eastern coastline geometry on energy fluxes are investigated using a shallow water model with a spatial resolution of 1/4 degree in both meridional and zonal directions. Equatorial and mid-latitude responses are considered. It is found that (1) the influence of the coastline geometry and the incident wave period is more important for the westward energy flux than for the poleward flux, and (2) the effect of the inclination of the eastern ocean boundary on the poleward energy flux, for the Pacific and Atlantic Oceans, decline as the period of the incident wave increases. Furthermore, the model simulations suggest that the poleward energy fluxes from meridional boundaries give plausible results for motions of seasonal and annual periods. For comparatively shorter periods, a realistic coastline geometry has to be included for more accurate results. It is recommended that any numerical model involving the reflection of baroclinic Rossby waves (of intraseasonal, seasonal or annual periods) on the eastern Pacific or Atlantic Oceans, should consider the effect of the coastline geometry in order to improve the accuracy of the results.     

Computational properties of a new horizontal staggered grid

On variable configuration in the horizontal direction, Winninghoff[1] had some discussions in the 1960s. Subsequently, according to the thoughts of Winning- hoff, Liu Yudi[2―9] has widely and deeply studied al- most all the existing horizontal grids from the fre- quency and group velocity of inertia gravity and Rossby waves. Results show that although Arakawa C grid is the best one among all existing horizontal grids, it also has some shortcomings. For example, there is still an “average…     

Long Wave Resonance in Tropical Oceans and Implications on Climate: the Atlantic Ocean

Based on the well established importance of long, non-dispersive baroclinic Kelvin and Rossby waves, a resonance of tropical planetary waves is demonstrated. Three main basin modes are highlighted through joint wavelet analyses of sea surface height (SSH) and surface current velocity (SCV), scale-averaged over relevant bands to address the co-variability of variables: (1) a 1-year period quasi-stationary wave (QSW) formed from gravest mode baroclinic planetary waves which consists of a northern, an equatorial and a southern antinode, and a major node off the South American coast that straddles the north equatorial current (NEC) and the north equatorial counter current (NECC), (2) a half-a-year period harmonic, (3) an 8-year sub-harmonic. Contrary to what is commonly accepted, the 1-year period QSW is not composed of wind-generated Kelvin and Rossby beams but results from the excitation of a tuned basin mode. Trade winds sustain a free tropical basin mode, the natural frequency of which is tuned to synchronize the excitation and the ridge of the QSWs. The functioning of the 1-year period basin mode is confirmed by solving the momentum equations, expanding in terms of Fourier series both the coefficients and the forcing terms. The terms of Fourier series have singularities, highlighting resonances and the relation between the resonance frequency and the wavenumbers. This ill-posed problem is regularized by considering Rayleigh friction. The waves are supposed to be semi-infinite, i.e. they do not reflect at the western and eastern boundaries of the basin, which would assume the waves vanish at these boundaries. At the western boundary the equatorial Rossby wave is deflected towards the northern antinode while forming the NECC that induces a positive Doppler-shifted wavenumber. At the eastern boundary, the Kelvin wave splits into coastal Kelvin waves that flow mainly southward to leave the Gulf of Guinea. In turn, off-tropical waves extend as an equatorially trapped Kelvin wave, being deflected off the western boundary. The succession of warm and cold waters transferred by baroclinic waves during a cycle leaves the tropical ocean by radiation and contributes to western boundary currents. The main manifestation of the basin modes concerns the variability of the NECC, of the branch of the South Equatorial Current (SEC) along the equator, of the western boundary currents as well as the formation of remote resonances, as will be presented in a future work. Remote resonances occur at midlatitudes, the role of which is suspected of being crucial in the functioning of subtropical gyres and in climate variability.     

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part I: hypothetical boundaries

A baroclinic shallow-water model is developed to investigate the effect of the orientation of the eastern ocean boundary on the behavior of equatorial Kelvin waves. The model is formulated in a spherical polar coordinate system and includes dissipation and non-linear terms, effects which have not been previously included in analytical approaches to the problem. Both equatorial and middle latitude response are considered given the large latitudinal extent used in the model. Baroclinic equatorial Kelvin waves of intraseasonal, seasonal and annual periods are introduced into the domain as pulses of finite width. Their subsequent reflection, transmission and dissipation are investigated. It is found that dissipation is very important for the transmission of wave energy along the boundary and for reflections from the boundary. The dissipation was found to be dependent not only on the presence of the coastal Kelvin waves in the domain, but also on the period of these coastal waves. In particular the dissipation increases with wave period. It is also shown that the equatorial β-plane approximation can allow an anomalous generation of Rossby waves at higher latitudes. Nonlinearities generally have a small effect on the solutions, within the confines of this model.     

The generation of baroclinic rossby waves by meridional oscillations of a zonal wind stress

Abstract

This paper investigates the generation of linear baroclinic Rossby waves by meridional oscillations of a climatological zonal wind stress in a reduced gravity ocean bounded by an eastern coastline. Using a power series technique an analytical solution is derived for the interfacial displacement. It is found that for a given period of oscillation of the zonal winds, a finite number of propagating Rossby waves will be generated with frequencies equal to a harmonic of the forcing frequency. The number of propagating modes increases with increasing period of the wind stress. In addition to the propagating waves the complete solution for the interfacial displacement consists of a rapidly convergent infinite sum of evanescent terms. The displacement field is calculated for atmospheric forcing parameters typical of those found at mid-latitudes. Further, it is shown that a near resonant response can be generated using atmospheric parameter values typical of those found over the North Pacific.     

Tube wave modeling by the finite-difference method with varying grid spacing

A finite-difference approach of aP-SV modeling scheme is applied to compute seismic wave propagation in heterogeneous isotropic media, including fluid-filled boreholes. The discrete formulation of the equation of motion requires the definition of the material parameters at the grid points of the numerical mesh. The grid spacing is chosen as coarse as possible with respect to the accurate representation of the shortest wavelength. If we assume frequencies lower than 250 Hz then the grid spacing is usually chosen in the range of a few meters. One encounters difficulties because of the large-scale difference between the grid spacing and the size of the borehole, usually several centimeters.These difficulties can be overcome by a grid refinement technique. This technique provides the construction of grids with varying grid spacing. The grid spacing in the vicinity of the borehole is chosen such that the borehole is properly represented. An example demonstrates the accuracy of this technique by comparisons with other methods. Unlike many analytical methods, the FD method can handle complex subsurface geometries. Further numerical examples of walk-awayVSP configurations show tube wave propagation within fluid-filled boreholes of realistic diameters.     

Imaging Offsets in the Moho: Synthetic Tests using Gaussian Beams with Teleseismic Waves

We carry out a sequence of numerical tests to understand conditions under which rapid changes in crustal thickness can be reliably imaged by teleseismic body waves. Using the finite-difference method over a 2-D grid, we compute synthetic seismograms resulting from a planar P-wavefield incident below the grid. We then image the Moho using a migration scheme based on the Gaussian beam representation of the wavefield. The use of Gaussian beams for the downward propagation of the wavefield is particularly advantageous in certain geologically critical cases such as overthrusting of continental lithosphere, resulting in the juxtaposition of high-velocity mantle material over crustal rocks. In contrast to ray-based methods, Gaussian beam migration requires no special treatment to handle such heterogeneities. Our results suggest that with adequate station spacing and signal-to-noise ratios, offsets of the Moho, on the order of 10 km in height, can be reliably imaged beneath thickened crust at depths of about 50 km. Furthermore, even sharp corners and edges are faithfully imaged when precise values of seismic wave speeds are available. Our tests also demonstrate that flexibility in choices of different types of seismic phases is important, because any single phase has trade-offs in issues such as spatial resolution, array aperture, and amplitude of signals.