Topographic generation of intermediate-scale motions by wind-driven currents — A model for the circulation in the vicinity of the Indian-Antarctic ridge

When a broad ocean current encounters a large-scale topographic feature, standing Rossby wave patterns can be generated. Short Rossby waves with a scale L_i = √ Q/β (Q is the speed of the approaching flow; β is the meridional gradient of f) are generated east of the topography. If the zonal scale of the topography, L, is planetary, long standing Rossby waves can be generated west of the topography, when the current has a meridional component. The long waves focus the disturbance zonally and produce alternating regions of intensified or reduced zonal flow. The meridional scale that characterizes these zonal bands is the intermediate scales, L = L_i^2/3L^1/3. When the meridional topographic scale is comparable to L, the amplitude of the long-wave disturbance is dominant. Using multiple-scale methods to exploit the scale gap between the planetary, intermediate and Rossby wave scales, the topographically induced pressure and velocity fields due to a zonal ridge are obtained. When the planetary-scale flow field is directed poleward, a westward counterflow can occur along the poleward flank of the ridge. The meridional scales of these topographically induced flows are comparable to those observed along the Indian-Antarctic Ridge by Callahan (1971).     

ON THE OPTIMAL BACKGROUND ERROR COVARIANCES: DIFFERENT SCALE ERRORS’ CONTRIBUTION

The large-scale and small-scale errors could affect background error covariances for a regional numerical model with the specified grid resolution.Based on the different background error covariances influenced by different scale errors,this study tries to construct a so-called"optimal background error covariances"to consider the interactions among different scale errors.For this purpose,a linear combination of the forecast differences influenced by information of errors at different scales is used to construct the new forecast differences for estimating optimal background error covariances.By adjusting the relative weight of the forecast differences influenced by information of smaller-scale errors,the relative influence of different scale errors on optimal background error covariances can be changed.For a heavy rainfall case,the corresponding optimal background error covariances can be estimated through choosing proper weighting factor for forecast differences influenced by information of smaller-scale errors.The data assimilation and forecast with these optimal covariances show that,the corresponding analyses and forecasts can lead to superior quality,compared with those using covariances that just introduce influences of larger-or smallerscale errors.Due to the interactions among different scale errors included in optimal background error covariances,relevant analysis increments can properly describe weather systems(processes)at different scales,such as dynamic lifting,thermodynamic instability and advection of moisture at large scale,high-level and low-level jet at synoptic scale,and convective systems at mesoscale and small scale,as well as their interactions.As a result,the corresponding forecasts can be improved.     

Influence of bottom topography roughness on the jet and inertial recirculation of a mid-latitude gyre

Several numerical experiments are conducted to examine the influence of mesoscale, bottom topography roughness on the inertial circulation of a wind-driven, mid-latitude ocean gyre. The ocean model is based on the quasi-geostrophic formulation, and is eddy-resolving as it features high vertical and horizontal resolutions (six layers and a 10 km grid). An antisymmetrical double-gyre wind stress curl forces the baroclinic modes and generates a strong surface jet. In the case of a flat bottom, inertia and inverse energy cascade force the barotropic mode, and the resulting circulation features strong, barotropic, inertial gyres. The sea-floor roughness inhibits the inertial circulation in the deep layers; the barotropic component of the flow is then forced by eddy-topography interactions, and its energy concentrates at the scales of the topography. As a result, the baroclinicity of the flow is intesified: the barotropic mode is reduced with regard to the baroclinic modes, and the bottom flow (constrained by the mesoscale sea-floor roughness) is decoupled from the surface flow (forced by the gyre-scale wind). Rectified, mesoscale bottom circulation induces an interfacial form stress at the thermocline, which enhances horizontal shear instability and opposes the eastward penetration of the jet. The mean jet is consequently shortened, but the instantaneous jet remains very turbulent, with meanders of large meridional extent. The sea-floor roughness modifies the energy pathways, and the eddies have an even more important role in the establishment of the mean circulation: below the thermocline, rectification processes are dominant, and eddies transfer energy toward permanent mesoscale circulations strongly correlated with topography, whereas above the thermocline mean flow and eddy generation are influenced by the mean bottom circulation through interfacial stress. The topography modifies the vorticity of the barotropic and highest baroclinic modes. Vorticity accumulates at the small topographic scales, and the vorticity content of the highest modes, which is very weak in the flat-bottom case, increases significantly. Few changes occur in surface-intensified modes. In the deep layers of the model, the inverse correlation between relative vorticity and topography at small scales ensures the homogenization of the potential vorticity, which mainly retains the largest scales of the bottom flow and the scale of β.     

The exchange of fluid mass between quasi-geostrophic and ageostrophic motions during the reflection of Rossby waves from a coast. I. The case of an infinite rectilinear coast

When the problem of the reflection of spatially localized Rossby waves from a coast is treated using the quasigeostrophic (QG) approximation, the total fluid mass and the along-shore circulation calculated from the geostrophic height field are not conserved. To understand the correct mass balance and the degree to which the QG equations and boundary conditions may be in error, we analyze an initial-value problem for the Laplace tidal equations on a β-plane in the asymptotic limit 1, where is the ratio of the spatial scale of the motion to the Earth's radius.It is shown that there is a coupling between QG and O() fields. Physically, the coupling occurs by a peculiar adjustment process in the O() approximation in which fast gravity waves are permanently generated to build up a quasi-stationary edge Kelvin wave. Different temporal scales (large for O(1) Rossby waves and small for the O() gravity waves make comparable the contributions of the waves to the mass and circulation balance equations. However, QG analysis itself describes the reflection of Rossby waves correctly, but is incomplete, and for satisfactory balances one has to take into account the fields of both orders of the approximation.Applications of the results to closed basins, baroclinicity, and variable bottom topography are discussed. It is conjectured that an interaction of strong oceanic eddies with a coast (continental slope) may give rise to noticeable along-shore jet currents.     

正压准地转模式中大地形作用下的低频波

利用包含大地形和常速纬向基本气流的正压准地转位涡度方程,研究了大地形对低频波激发的作用,结果表明,起作用的地形因子主要是地形的最大高度和地形坡度。地形最大高度的作用主要是使Rossby波趋向低频,而地形坡度的作用主要是对Rossby波的稳定性起决定作用,同时适当的地形坡度也可导致低频波的形成。而常速纬向基流在总体上的作用是使波动变得趋向低频,且西风基流更有利于低频（30～60天）波的形成。从纬向波数上看,纬向3波以上的波动更容易出现低频（30～60天）。     

Planetary geostrophic equations for the atmosphere with evolution of the barotropic flow

Atmospheric phenomena such as the quasi-stationary Rossby waves, teleconnection patterns, ultralong persistent blockings and the polar/subtropical jet are characterized by planetary spatial scales, i.e. scales of the order of the earth’s radius. This motivates our interest in the relevant physical processes acting on the planetary scales. Using an asymptotic approach, we systematically derive reduced model equations valid for atmospheric motions with planetary spatial scales and a temporal scale of the order of about 1 week. We assume variations of the background potential temperature comparable in magnitude with those adopted in the classical quasi-geostrophic theory. At leading order, the resulting equations include the planetary geostrophic balance. In order to apply these equations to the atmosphere, one has to prescribe a closure for the vertically averaged pressure. We present an evolution equation for this component of the pressure which was derived in a systematic way from the asymptotic analysis. Relative to the prognostic closures adopted in existing reduced-complexity planetary models, this new dynamical closure may provide for more realistic increased large-scale, long-time variability in future implementations.     

Solitary Rossby waves over variable relief and their stability. Part I: The analytical theory

Nonlinear permanent form solutions have been found for the barotropic, quasi-geostrophic divergenceless vorticity equation describing large scale, rotating flows over zonal relief. In the linear limit these solutions are topographic Rossby waves. The analytical procedure is an expansion in two small dimensionless parameters, an amplitude parameter (the Rossby number) and the aspect ratio between North-South (cross-relief) and East-West length scales. Permanent form solutions exist when these two parameters, and the related effects of dispersion and nonlinearity, mutually balance. By the same expansion procedure, an analytical linearized stability theory has been formulated which proves the neutral stability of these solutions to infinitesimal, two-dimensional perturbations.     

小尺度地形引起的切变重力波

在大气边界层中,特别是山区的边界层中,经常可以观测到重力波的活动。例如Bull和Neisser分析了1974年4月至7月的2300时的微气压计记录。他们发现约38％的观测时间里都存在振幅至少为10—20 dPa的重力波活动,其中大多数重力波的振幅为25—70 dPa。由于风速切变和温度层结的不同,重力波引起的垂直位移的大小可能为百米,也可能达到整个夜间边界层厚度的量级。 很多大气活动都可能引起重力波,例如锋面、低空急流、局地风切变、逆温及强对流等等。地形特别是在夜间也是产生重力波的重要来源。当稳定度随高度急剧减少或风速随高度急剧增加时,在山脊的背风坡经常可以发现一系列的波动活动。     

An invariant theory of the linearized shallow water equations with rotation and its application to a sphere and a plane

The system of linearized shallow water equations is formulated in this paper on any rotating and smooth surface M in terms of differential geometry. The system decouples into two separate equations: a scalar one for the height deviation and a vector one for the velocity field. For low and high frequencies these equations yield asymptotic equations whose solutions are the generalizations of the Poincare and Rossby waves to smooth surface. The application of these equations to the β-plane yields both new and previously known equations for the height deviation and for the velocity components. The application of the equations to the rotating spherical Earth shows that the meridional amplitudes of Poincare and Rossby waves are both described by the prolate angular spheroidal wave functions. The asymptotic and the power series expansions of the eigenvalues of these functions yield new approximations for the dispersion relations of these waves on a sphere. The new dispersion relations are very accurate in the physically relevant range of the single nondimensional model parameter – the square of the nondimensional gravity waves’ phase speed. The invariant formulation can also be applied to other surfaces that are of geophysical interest such as an oblate ellipsoid of revolution.     

一种快速预处理算法及其在浅水波方程中的应用

为了提高数值求解大气方程的计算速度,我们研究了稀疏逼近逆预处理方法及其在数值求解浅水波方程中的应用,这是一种求解大型线性方程组的快速算法,该算法的核心内容是稀疏逼近逆非零元模式的选取。首先导出了一种稀疏逼近逆的非零元模式及其确定方法,然后以浅水方程的差分格式为例,借助于GMRES迭代算法,对这种预处理快速算法应用前后的计算速度进行了比较,发现该快速算法能大幅度提高运算速度。另外,该预处理快速算法简单、易于并行,是一种值得在大气方程中推广应用的方法。     

地形非均匀性对网格区地面长波辐射通量计算的影响

从理论和数值试验两个方面证明地形的非均匀性(如海拔高度)对网格区地面长波辐射通量的计算有重要影响,海拔高度场的区域平均值及其变差系数是影响网格区地面长波辐射通量的主要因素,仅仅用地表均匀假定下的区域平均参量(如平均海拔高度和平均温度)所计算的网格区地表有效辐射通量值与其真实值之间存在着一定的误差。由于地表有效辐射通量是海拔高度的非线性函数,在特定情况下,其影响相当大,可产生不容忽略的误差。相对而言,海拔高度自身非均匀性对误差的影响远大于地表温度非均匀性项及其混合扰动项所产生的误差。对于不同的地形平均高度,地形非均匀性影响的程度并不相同。平均高度较小时,非均匀性的影响几乎可以忽略,但随着地形平均高度的增加,地形非均匀性的影响程度呈非线性增长趋势。因而,在复杂地形区域,考虑次网格地形的热力作用非常必要。     

The physical effects of topography and heat sources on the formation and maintenance of the summer monsoon over Asia

The physical effects of topography and heat sources on the formation and maintenance of the summer mon-soon over Asia we discussed in this paper by using the transformed Eularian-mean equations and a quasigeostrophic 34-level spherical coordinate model.The computed results of the divergence of the E-P flux, the induced meridional circulation and the pertur-bation geostrophic wind speed induced by the forcing of topography and heat sources show that the diabatic heating effect over the Tibetan Plateau may play an important role for the formation and maintenance of the summer monsoon over Asia, which is much greater than the dynamical effect of topography.The computed results also show that, of the physical effects of topography and heat sources on the formation and maintenance of the summer monsoon over Asia, the effect of forced meridional circulation is larger than that of the divergence of E-P flux of the induced waves.     

四川地形扰动对降水分布影响

引入一维加权平均的谱分析方法定量研究四川地形强迫对该区域降水分布的影响。结果表明:纬向地形和冬季降水谱峰锁相于同一波长（475.8 km）,呈共振关系,地形与其他季节降水呈漂移关系,这与经向和纬向上环流变动有关,即冬季纬向环流占主导,纬向地形触发的大气波动对冬季降水策动作用大;夏季降水是各种不同尺度系统相互作用的结果,地形是重要因素之一。经向和纬向地形特征尺度分别为296.8 km和475.8 km,反映了地形强迫的中尺度特征,且纬向地形谱峰比经向大1个数量级,纬向强迫更明显。夏季降水谱峰比冬季大2个数量级,降水系统纬向特征尺度比冬季小约150 km,说明夏季在纬向地形强迫下,降水系统尺度减小的同时其强度大大增加,这在一定程度上可以解释中尺度对流性降水在夏季偏多。四川夏季最大降水位于雅安地区,其地形扰动比四川整体扰动更明显,故产生的降水也更大。夏季降水和经向地形锁相于同一波长（37.1 km）,经向地形对雅安夏季强降水起关键作用。     

数值积分过程中截断误差和舍入误差的分离方法及其效果检验

本文讨论数值积分过程中截断误差和舍入误差的分离方法和理论,解析地给出某些数值计算方法的理论截断误差,并以此来分离计算结果中的误差.然后引入参考解的办法,用来分离更为一般的微分方程求解过程中的截断误差和舍入误差.以参考解算法为基础,对一个偏微分方程的数值解进行计算,所得结果与采用理论截断误差得到的结果进行了对比,发现:(...     

The effects of topography on the summer atmospheric energetics of the Northern Hemisphere in a low-resolution global spectral model

An analysis is made of the effects of topography on the summer atmospheric energetics of the Northern Hemisphere in a low-resolution global spectral model. The numerical mode! is a global, spectral, primitive equation model with five equally spaced sigma levels in the vertical and triangular truncation at wavenumber 10 in the horizontal. The model includes comparatively full physical processes. Each term of the energy budget equations is calculated in four specific latitudinal belts (81.11°S–11.53°S; 11.53°S–11.53°N; 11.53°N–46.24°N; 46.24°N–81.11°N) from a five-year simulation with mountains and a one-year simulation without mountains, respectively. Differences between them are compared and statistically tested. The results show that synoptical scale waves transport available potential energy and kinetic energy to long waves and increase conversion from available potential energy of the zonal flow to eddy's and from the eddy kinetic energy to the zonal kinetic energy in region 3 (11.53°N-46.24°N) due to mountains; topography intensifies the atmospheric baroclinity in region 3, consequently the baroclinic conversion of atmosphere energy is increased. The seasonal characteristics associated with the summer atmospheric energy source in region 3 are caused by seasonal variation of the solar radiation and the land-ocean contrasts and independent of topographic effects. The mechanism of topographic effects on the increase of long wave kinetic energy is also discussed.     

The effect of topography on the stability of a barotropic coastal current

We consider small non-divergent perturbations to a barotropic current flowing parallel to a straight coastline. Sufficient conditions for stability and a semi-circle theorem are established for general current profiles and topography. An asymptotic expansion for long waves is described. Some analytic solutions are obtained when the topography is piece-wise constant and the current is piece-wise linear. Two kinds of instability, a shear instability and a topographic instability, are identified. Our results are applied to a model of the East Australian current.     

尺度分解技术在定量降水临近预报检验中的应用

采用2004年Casati提出的强度-尺度检验技术,选取2008年汛期代表不同类型降水(对流云降水、层状云降水、混合云降水)的4个降水过程,从尺度分解角度入手,对"世界气象组织天气研究计划——北京奥运会预报示范项目"(WWRP B08FDP)项目中4个I临近预报参加系统(BJANC,GRAPES-SWIFT,STEPS,CARDS)的1h定量降水预报进行时空尺度分解检验,研究降水预报技巧与降水时空尺度和强度之间的关系。结果表明:尽管目前国际先进的临近预报系统的水平分辨率已高达1～2km,但其有技巧的临近预报能力主要集中于空间尺度大于32km、时间尺度大于1h的降水系统,而对小于这些尺度的降水系统预报能力仍非常有限;在不同时空尺度的临近预报降水误差中,60%以上的误差来自于空间尺度小于8km的降水,85%以上的误差来自于时间尺度小于1h的降水,传统的外推技术不能满足这些较小时空尺度降水预报的需求,要发展有效的预报方法来提高较小时空尺度降水的预报能力。将基于外推的临近预报和基于稠密观测资料、快速更新的数值预报的潜势预报相结合可能是一条有效的解决途径。     

Analysis and application of multiple-precision computation and round-off error for nonlinear dynamical systems

This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.     

Effects of Topographic Slopes on Hydrological Proecsses and Climate

Based on previous research results on river re-distribution models, a modification on the effects of topographic slopes for a runoff parameterization was proposed and implemented to the NCAR＇s land sur face model (LSM). This modification has two aspects: firstly, the topographic slopes cause outflows from higher topography and inflows into the lower topography points; secondly, topographic slopes also cause decrease of infiltration at higher topography and increases of infiltration at lower topography. Then changes in infiltration result in changes in soil moisture, surface fluxes and then in surface temperature, and eventual ly in the upper atmosphere and the climate. This mechanism is very clearly demonstrated in the point bud gets analysis at the Andes Mountains vicinities. Analysis from a regional scale perspective in the Mackenzie GEWEX Study (MAGS) area, the focus of the ongoing Canadian GEWEX program, shows that the modi fied runoff parameterization does bring significant changes in the regional surface climate. More important ly, detailed analysis from a global perspective shows many encouraging improvements introduced by the modified LSM over the original model in simulating basic atmospheric climate properties such as thermodynamic features (temperature and humidity). All of these improvements in the atmospheric climate simulation illustrate that the inclusion of topographic effects in the LSM can force the AGCM to produce a more realistic model climate.