GRAPES-3DVar高阶递归滤波方案及其初步试验

背景误差协方差矩阵B及其逆的求解是三维变分同化研究的核心问题之一.在GRAPES区域三维变分同化系统(GRAPES-3Dvar)中背景误差协方差矩阵的水平变换部分,假定各向同性并进行递归滤波运算.原有方案中采用一阶递归滤波器,但收敛不够迅速,每次循环同化时需滤波10次才能使目标函数收敛.根据Purser等2003年的研...     

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.     

HEAT SOURCE-INFLUENCED FINITE AMPLITUDE ULTRALONG WAVE*

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

A Refinement of the McMillen (1988) Recursive Digital Filter for the Analysis of Atmospheric Turbulence

We present a refinement of the recursive digital filter proposed by McMillen (Boundary-Layer Meteorol 43:231–245, 1988), for separating surface-layer turbulence from low-frequency fluctuations affecting the mean flow, especially over complex terrain. In fact, a straightforward application of the filter causes both an amplitude attenuation and a forward phase shift in the filtered signal. As a consequence turbulence fluctuations, evaluated as the difference between the original series and the filtered one, as well as higher-order moments calculated from them, may be affected by serious inaccuracies. The new algorithm (i) produces a rigorous zero-phase filter, (ii) restores the amplitude of the low-frequency signal, and (iii) corrects all filter-induced signal distortions.     

一阶Buterworth递归式带通滤波器技术改进方案

把一阶Ｂｕｔｔｅｒｗｏｒｔｈ递归带通滤波器应用于滑动样本,输出序列出现了振幅和位相的相对误差,为了克服这种现象给制作中长期预报带来的困难,作者通过数值试验,分析了该滤波器的误差传递特性,并设计了“拟定初值的三步滤波方案”。大量试验表明,该方案可较为有效地抑制输出序列的误差和位相飘移。     

一阶Buterworth递归式带通滤波器技术改进方案

把一阶Ｂｕｔｔｅｒｗｏｒｔｈ递归式（ＦＢＲ）带通滤波器应用于滑动样本,输出序列出现了振幅和位相的相对误差。为了克服这种现象给制作中长期预报带来的困难,作者通过数值试验,分析了该滤波器的误差传递特性,并设计了“拟定初值的三步滤波方案”。大量试验表明,该方案可较为有效地抑制输出序列的误差和位相飘移     

论小尺度过程动力学的一些基本问题

本文对层结大气中小尺度过程动力学的一些基本问题作了研究。 首先用频率法对线性化后的小尺度运动方程作了分析。分析指出,线性化后的运动方程中包含了两种不同类型的波动,即快速传播的声波和相对声波而言的慢波——重力内波。 对于有气象意义的运动而言,声波是一种“噪音”,必须从运动方程中把它滤掉。文中指出,由于静力偏差(非静力平衡)对小尺度运动的发展具有重要的意义,一般用静力平衡来消除声波的方法对小尺度运动并不适用。文中提出了三种不同的消除声波的方法,即1)不可压缩条件的应用;2)将解按参数ε’(=V~2/gL)的冪次展开; 3)平衡方程的应用。同时分析了这三种不同滤波方法所带来的误差程度。 作为初值问题,研究了当在某一时刻在大气有限区域内的扰动破坏了静力平衡后所激发出的声波的频散性质,指出,从静力平衡的破坏到其种平衡状态的建立,场的这一适应过程完成得极其迅速。 最后,利用所提出的滤波方法,建立了滤掉声波后的二维非线性运动方程组。     

卡尔曼滤波方法在天气预报中的应用

从气象应用角度介绍了卡尔曼滤波的基本原理及其递推算法。为了说明卡尔曼滤波递推算法的应用方法，制作了北京１９９３年１月份逐日最低气温３６小时预报。预报结果令人满意，表明该方法很有实用价值，与ＭＯＳ方法相比，它的优点是不需要收集大样本历史资料，因此，它容易适应数值预报模式的变化。     

A study of the environmental influence on the amplitude of lee waves

A three-layer theoretical model is used to calculate the lee wave of a real example occurring over Blue Ridge in Pittsburgh, in which the maximum vertical velocity is 0.11 m s^-1. Based on this, the influence of changes in the thickness and values of the Scorer parameter in each layer are analyzed. It is shown that the influence of each layer parameters on the lee-wave amplitude is different, and the amplitude is more sensitive to the changes in the lower layer. Since the environment changes can affect the Scorer parameter profile, the influence of the environment on the amplitude is studied. The results show that the amplitude will decrease in the daytime because of solar heating, and increase at night because of radiational cooling, according to observational data. The case is also simulated by the Advanced Regional Prediction System （ARPS） model. The simulated amplitude is 0.089 m s^-1, which is close to the calculated result. Numerical sensitivity experiments are performed to test the former calculated experiments. The simulated results are consistent with the analytically calculated results.     

Characteristics of annulus baroclinic flow structure during amplitude vacillation

An investigation is made of the mechanics of amplitude vacillation in a numerically simulated rotating annulus flow system. Amplitude vacillation is characterized by a periodic change of vertical wave structure in concert with growth and decay of wave amplitude and phase speed. The temperature wave amplitude profile for the dominant component consists of three local maxima: (1) lower boundary layer, (2) upper half layer and (3) lower half layer. The lower layer waves lead the time-dependent structural variation during vacillation. Two types of amplitude vacillation found in the experimental measurements (Buzyna et al., 1989: J. Atmos. Sci. 46, 2716–2729) can be distinguished in the temperature wave by whether the lower layer waves split from and travel behind the upper layer waves by one wave period in each cycle of vacillation. Linear eigenvalue analyses with respect to the instantaneous axisymmetric state at various points in time are performed to elucidate the simple interaction between the dominant wave and the zonal mean state. During the vacillation cycle, the zonal mean state is modified by the wave, which causes a change in growth rate and vertical structure of the linearly most unstable eigenmode. This, in turn, forces the actual changes of the nonlinear solutions.     

A one-dimensional model for the interaction between continental-scale ice sheets and atmospheric stationary waves

 The great continental ice sheets of the Pleistocene represented a significant topographic obstacle to the westerly winds in northern midlatitudes. This work explores how consequent changes in the atmospheric stationary wave pattern might have affected the shape and growth of the ice sheets themselves. A one dimensional (1-D) model is developed which permits an examination of the types and magnitudes of the feedbacks that might be expected. When plausible temperature perturbations are introduced at the ice-sheet margin which are proportional to the stationary wave amplitude, the equilibrium shape of the ice sheet is significantly altered, and depends on the sign of the perturbation. The proposed feedback also affects the response of the ice sheet to time-varying climate forcing. The results suggest that the evolution of a continental-scale ice sheet with a land-based margin may be significantly determined by the changes it induces in the atmospheric circulation. Received: 1 October 1999 / Accepted: 17 July 2000     

Application of a Recursive Filter to a Three-Dimensional Variational Ocean Data Assimilation System

In order to improve the efficiency of the Ocean Variational Assimilation System (OVALS), which has been widely used in various applications, an improved OVALS (OVALS2) is developed based on the recursive filter (RF) algorithm. The first advantage of OVALS2 is that memory storage can be substantially reduced in practice because it implicitly computes the background error covariance matrix; the second advantage is that there is no inversion of the background error covariance by preconditioning the control var...     

Process, Forcing, and Signal Analysis of Global Mean TemperatureVariations by Means of a Three-Box Energy Balance Model

An analytic solution of an energy balance model (EBM) is presented which can beused as a recursive filter for time series analysis. It is shown that the EBM can reproduce the solution of a coupled atmosphere-ocean general circulation model (AOGCM) experiment. Contrary to the AOGCM, the EBM easily allows for variations in climate sensitivity to satisfy the full range of uncertainty concerned with this parameter. The recursive filter is applied to two natural and two anthropogenic forcing mechanisms which are expressed in terms of heating rate anomaly time series: volcanism, solar activity, greenhouse gases (GHG), and anthropogenic tropospheric aerosols. Thus, we obtain modelled global mean temperature variations as a response to the different forcings and with respect to the uncertainty in the forcing approximations and climate sensitivity. In addition, it is shown that the observed (ENSO-corrected) global mean temperature time series within the period from 1866 to 1997 can be explained by the external forcings which have been considered and an additional white noise forcing. In this way we are able to separate different signals and compare them. As a result, global anthropogenic climate change due to GHG forcing can be detected at a high level of significance without considering spatial patterns of climate change but including natural forcing, which is usually not done. Furthermore, it is shown that solar forcing alone does not lead to significantclimate change, whereas solar and volcanic forcing together lead to a significant natural climate change signal. Anthropogenic climate change due to GHG forcing may partly be masked by anthropogenic aerosol cooling.     

有地形坡度的非线性Kelvin行波

提出了一个考虑地形坡度的非线性Kelvin行波解的模型，在假定了地形坡度沿山脉走向不变而仅在垂直于山脉走向的方向有改变的情况下，求得了该模型的解析解，这有助于加深对沿海山地捕获波的认识。文中还将该解与经典情形(即侧边界取为垂直刚壁而底面为水平)的解作了比较，发现前者的波速与扰动振幅均较后者要小，这与我国东南沿海武夷山区的沿海山地捕获波的情况相一致。     

Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

Variations in wave energy and amplitude for Rossby waves are investigated by solving the wave energy equation for the quasigeostrophic barotropic potential vorticity model.The results suggest that compared with rays in the nondivergent barotropic model,rays in the divergent model can have enhanced meridional and zonal propagation,accompanied by a more dramatic variability in both wave energy and amplitude,which is caused by introducing the divergence effect of the free surface in the quasigeostrophic model.For rays propagating in a region enclosed by a turning latitude and a critical latitude,the wave energy approaches the maximum value inside the region,while the amplitude approaches the maximum at the turning latitude.Waves can develop when both the wave energy and amplitude increase.For rays propagating in a region enclosed by two turning latitudes,the wave energy approaches the minimum value at one turning latitude and the maximum value at the other latitude,while the total wavenumber approaches the maximum value inside the region.The resulting amplitude increases if the total wavenumber decreases or the wave energy increases more significantly and decreases if the total wavenumber increases or the wave energy decreases more significantly.The matched roles of the energy from the basic flow and the divergence of the group velocity contribute to the slightly oscillating wave energy,which causes a slightly oscillating amplitude as well as the slightly oscillating total wavenumber.     

Influences of vorticity source and momentum source on atmospheric circulation

A simplified one-dimensional barotropic vorticity equation is used to study the influences of the vorticity and the momentum source on the large scale wave. Both vorticity source and momentum source can cause the formation of the large scale wave, but the former can produce large scale wave only under the condition that there is apparent basic flow acting on it, while the latter can produce the large scale wave even when ū tends to be zero. Furthermore, the amplitude of steady wave caused by the former is proportional to √ū, while the amplitude caused by the latter has no relation to ū, instead it depends only on the magnitude of the perturbation of momentum.     

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.     

An attempt to deconstruct the Atlantic Multidecadal Oscillation

The link between the Atlantic Multidecadal Oscillation (AMO) and low-frequency changes of the Atlantic Meridional Overturning Circulation (AMOC) is investigated in three historical and five control simulations with different climate models. An AMOC intensification is followed by a positive AMO phase in each case, but the time lag and the strength of the AMO–AMOC link depend on the model and the type of simulation. In historical simulations, the link is sensitive to the method used to remove the influence of external and anthropogenic forcing from the sea surface temperature (SST) before defining the AMO. Subtracting the regression onto the global mean SST leads to better correlations between the AMO and the AMOC than linear or quadratic detrending, or removing the global mean SST, but a dynamical filter based on linear inverse modeling (LIM) yields even slightly higher correlations. The LIM filter, which decomposes the SST field into non-orthogonal normal modes that may have a physical interpretation, allows investigating whether removing Pacific links from SST improves the AMOC–AMO correlation. In several cases, there is a small improvement when removing the links to the El Niño Southern Oscillation, but the correlation becomes weaker in one historical simulation, so no firm conclusion can be drawn. Additionally removing the modes associated with the Pacific decadal variability strongly degrades the representation of AMOC changes by the AMO in one model, and it tends to reduce the AMOC–AMO correlation in most others, reflecting the strong relation between the Pacific and the Atlantic at decadal scales. The LIM-based filter is finally applied to observed SSTs, confirming that the AMO amplitude is smaller and its recent positive phase weaker than when the global effects are represented by a linear trend. When the global signal is removed, the observed AMO leads the Pacific Decadal Oscillation, but does not significantly lag it, as suggested earlier, stressing the need to carefully remove global changes when investigating low-frequency interbasin connections.     

分层气流条件下地形降水的二维理想数值试验

利用WRF v3.5中尺度数值模式,在条件不稳定层结下,针对分层气流(基本气流风速和大气湿浮力频率呈二层均匀分布)过山时,地形对降水的影响进行了多组二维理想数值试验,以研究不同高度、尺度山脉和不同方向基本气流对降水形态和分布的影响。模拟结果表明,地形重力波触发对流是地形降水的主要机制之一,地形波的特征(波长、振幅)和传播均受到地形和基本气流的影响,其中,强基本气流流经高而陡峭的山脉时,更容易在其背风坡捕捉到重力波,地形降水呈现多种模态,反之亦然;当改变基本气流与山脉交角时,主要通过影响地形强迫抬升速度、基流对波动稳定性发展来进一步影响地形降水的强度和分布。     

地形强迫对大气长波调整的可能影响

地形作为大气的外部强迫,其动力和热力作用对波动结构演变及极端天气出现都有不能忽视的作用。本文通过数值求解考虑地形强迫的β平面正压准地转位势涡度方程,探讨了地形强迫作用对大气长波调整的可能影响,结果表明:同非线性作用和纬向非均匀基流作用一样,无基流情形下具有纬向差异的地形分布影响了大气长波结构的演变,也能强迫出大气长波调整现象。大气长波调整依赖于地形的高度和地形分布,地形越高,长波越容易出现波数的调整;地形波数越大,即地形结构复杂,越不易出现波数变化。大气长波调整还与纬度有关,纬度越高,β越小,地形强迫作用越突出,长波调整容易出现;反之,低纬度以β效应为主的线性波动不易出现波数调整。大气长波调整对波动初始波动的振幅不敏感,但依赖于波动的初始结构。此外,有基流作用时,地形强迫还是诱发定常波的重要因素,且定常波流场结构依赖于地形高度分布,与波动初始结构无关。