AN IMPROVED SEMI-IMPLICIT TIME DIFFERENCE SCHEME OF SPECTRAL MODEL AND NUMERICAL APPLICATIONS

In fact,the popular semi-implicit time difference scheme of spectral model still includes someimportant linear terms using time explicit difference scheme,and the major terms are directlyrelated to fast internal-and external-gravity waves in the atmospheric forecasting equation.Additionally,due to using time difference on two terms at different time.the popular schemeartificially introduces unbalance between pressure gradient force and Coriolis force terms whilenumerically computing their small difference between large quantities.According to thecomputational stability analysis conducted to the linear term time difference scheme in simpleharmonic motion equation,one improved semi-implicit time difference scheme is also designed inour study.By adopting a kind of revised time-explicit-difference scheme to these linear terms thatstill included in spectral model governing equations,the defect of spectral model which only partlyusing semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectralcoefficients of prognostic equations,especially of Helmholtz divergence equation,can be workedout without any numerical iteration,the time-step (computation stability) can also be enlarged(enhanced) by properly introducing an adjustable coefficient.     

AN IMPROVED SEMI-IMPLICIT TIME DIFFERENCE SCHEME OF SPECTRAL MODEL AND NUMERICAL APPLICATIONS*

In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and external-gravity waves in the atmospheric forecasting equation.Additionally,due to using time difference on two terms at different time.the popular schemear tificially introduces unbalance between pressure gradient force and Coriolis force terms while numerically computing their small difference between large quantities.According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation,one improved semi-implicit time difference scheme is also designed in our study.By adopting a kind of revised time-explicit-difference scheme to these linear terms that still included in spectral model governing equations,the defect of spectral model which only partlyusing semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectral coefficients of prognostic equations,especially of Helmholtz divergence equation,can be worked out without any numerical iteration,the time-step (computation stability) can also be enlarged (enhanced) by properly introducing an adjustable coefficient.     

The wavenumber-frequency characteristics of the tropical waves in an aqua-planet GCM

Based on the aqua-planet experiments, the wavenumber-frequency characteristics of tropical waves and their influencing factors in SST distribution and the convective parameterization scheme are investigated using the spectral atmospheric general circulation model （SAMIL）. Space-time spectral analysis is used to obtain the variance of convectively coupled tropical waves. In the Control experiment with maximum SST located at the equator the simulated tropical-wave behaviors are in agreement with those in observations and theoretical solutions. When the maximum SST is located at 5°N, the symmetric and antisymmetric waves are much weaker than those in the control experiment, suggesting that tropical wave activities are very sensitive to the SST distributions. Importantly, the variance maximum of Madden-Julian oscillation （MJO） is found to occur around 5°N, which suggests that the development of the MJO depends largely on the latitude of maximum SST. Furthermore, the seasonal variations of MJO may be mainly caused by the seasonal variations of the maximum SST. The experiment results with two different cumulus schemes the Manabe moist convective adjustment and Zhang-McFarlane （ZM） convective scheme, were also compared to examine the impacts of convective parameterization. Weakened variances of each individual tropical wave when the ZM scheme is used suggest that the ZM scheme is not favorable for the tropical wave activities. However, the wave characteristics are different when the ZM scheme is used in different models, which may imply that the simulated basic state is important to the meridional distributions of the waves. The MJO signals suggest that the parameterization scheme may have great influence on the strength, but have less direct impact on the MJO distribution. The frequency of the tropical waves may be associated with the moisture control of convection and the large-scale condensation scheme used in the model.     

THE SENSITIVITY OF THE NUMERICAL SIMULATION TO OROGRAPHY SPECIFICATION IN THE LOWRESOLUTION SPECTRAL MODEL－PART II: IMPACT OF THE SMOOTHED OROGRAPHY AND RIPPLES ON SIMULATIONS

In order to investigate the impact of the smoothed orography and the spurious orographic ripples on simu-lations in the low-resolution spectral model, three different numerical tests, that is, the unsmoothed orography scheme, the smoothed orography scheme and non-ripples scheme are performed. In this paper, the model used by us is the same as Part I except for orographic specification.The results from simulations indicate that, as far as the climatic simulation is concerned, some aspects of the simulated stationary disturbances, zonal and meridional wind, temperature and precipitation in the low-resolu-tion spectral model with properly smoothed mountains are significantly improved, especially in winter hemis-phere.The deep ripples in the model with the unsmoothed orography produce spurious high pressure regions at the surface with subsidence, and suppress rainfall, causing an unrealistic splitting of the precipitation area in northern winter and summer. Removal of tbe deep ripples by using the special procedure for smoothing topog-raphy allows a strong upward motion in the ripple area with heavy rainfall, eliminating the unrelistic split in the precipitation area.     

Intraseasonal tropical variability in an intermediate complexity atmospheric model

The convective equatorial waves in the NCEP/NCAR reanalysis and intermediate complexity atmospheric model QTCM are studied on the base of double space-time spectral analysis. The frequency-wavenumber spectra of outgoing longwave radiation, precipitation, zonal wind stress and net heat flux are obtained. Further, the propagation characteristics, amplitude and seasonal variability of filtered waves are analyzed. It is shown that QTCM simulates a wide variety of equatorial waves that share many characteristics with the observations. It is suggested that convective scheme applied in the model allows for simulation of interaction at interannual-intraseasonal time scales. The role of interannual SST forcing and extratropical excitation is elucidated using the model’s experiments with specific boundary conditions.     

Fundamental Framework and Experiments of the Third Generation of IAP/LASG World Ocean General Circulation Model

1.IntroductionThefirstbaroclinicoceanicgeneralcirculationmodel(OGCM)developedattheStateKeyLaboratoryofNumericalModelingforAtmosphericSciencesandGeophysicalFluidDynamics(LASG),InstituteofAtmosphericPhysics(IAP)isafour--layermodelwithitshorizontalresol...     

参考大气和大气质量守恒格式对气候模式月预报效果的改进试验

为了考查参考大气和大气质量守恒格式对气候谱模式月预报的改进能力,我们在国家气候中心气候谱模式中引入了这两个方案,选取了两个个例进行验证。对不同方案的月平均预报结果与实况进行了比较,并讨论了不同方案对高度场距平相关系数和均方根误差的影响。本文个例试验结果表明,这两个方案对月平均预报结果均有改进,参考大气方案的改进比大气质量守恒方案更为明显。     

GRAPES的新初始化方案

四维变分同化由于引入预报模式作为一项约束,理论上它的分析场已经具有较好的平衡性,但实施时还会有诸多因重力波导致的高频振荡过程,因此,四维变分同化(4DVar)分析仍需要初始化。文中描述了GRAPES全球四维变分同化系统(GRAPES-4DVar)的新初始化方案的科学设计、公式演绎以及试验结果。GRAPES-4DVar的新初始化方案采用数字滤波方案作为代价函数的一项约束控制重力波引发的不平衡结构,约束强加在分析增量上与极小化迭代过程同步进行。新的初始化方案是变分同化系统的一部分,数字滤波的积分时间与4DVar的同化时间窗一致,不会对4DVar产生额外的计算资源消耗;并能适应长时间窗的同化,不会因为时间窗的延长而削弱慢波过程。新初始化方案中,模式轨迹的光滑程度可在变分同化中通过重力波控制项的权重系数方便控制。GRAPES全球四维变分同化的理想和循环同化批量试验都表明,在四维变分同化中,重力波的控制依然非常重要,具有初始化的GRAPES试验,无论分析还是预报技巧都较无初始化的有明显优势。与以前分析和滤波独立实施的旧初始化方案相比,新方案的分析和预报效果略优,同时有效地节省循环同化系统的运行时间,这对四维变分同化来说非常重要。     

Convectively coupled Kelvin and easterly waves in a regional climate simulation of the tropics

This study evaluates the performance of a regional climate model in simulating two types of synoptic tropical weather disturbances: convectively-coupled Kelvin and easterly waves. Interest in these two wave modes stems from their potential predictability out to several weeks in advance, as well as a strong observed linkage between easterly waves and tropical cyclogenesis. The model is a recent version of the weather research and forecast (WRF) system with 36-km horizontal grid spacing and convection parameterized using a scheme that accounts for key convective triggering and inhibition processes. The domain spans the entire tropical belt between 45°S and 45°N with periodic boundary conditions in the east–west direction, and conditions at the meridional/lower boundaries specified based on observations. The simulation covers 6 years from 2000 to 2005, which is long enough to establish a statistical depiction of the waves through space-time spectral filtering of rainfall data, together with simple lagged-linear regression. Results show that both the horizontal phase speeds and three-dimensional structures of the waves are qualitatively well captured by the model in comparison to observations. However, significant biases in wave activity are seen, with generally overactive easterly waves and underactive Kelvin waves. Evidence is presented to suggest that these biases in wave activity (which are also correlated with biases in time–mean rainfall, as well as biases in the model’s tropical cyclone climatology) stem in part from convection in the model coupling too strongly to rotational circulation anomalies. Nevertheless, the model is seen to do a reasonable job at capturing the genesis of tropical cyclones from easterly waves, with evidence for both wave accumulation and critical layer processes being importantly involved.     

北京MST雷达功率谱密度处理算法改进

北京MST（mesosphere-stratosphere-troposphere,中间层-平流层-对流层）雷达是我国“子午工程”一期中探测大气动力结构的独特大型设备。雷达自2011年建成以来,已获取较好的大气风场数据,但在其他要素提取方面仍有改进需求。从噪声电平估算与目标回波识别这两个关键步骤改进雷达原始功率谱密度处理算法,以期得到更准确的大气要素信息。在噪声电平估算方面,提出应用对数-线性拟合方案快速实现客观分析法,与二分法方案差值的标准差为0.43 dB,表明对数-线性拟合方案能兼顾时效性与准确性。改进后的数据处理算法能够精确识别目标回波。利用改进算法处理2012年1—12月数据结果与雷达、探空以及ERA5再分析数据进行比较,各高度纬向风与探空测值的均方根误差均为2~3 m·s-1,优于雷达产品和探空测值均方根误差（3~4 m·s-1）,信噪比、谱宽和垂直速度质量也有明显提高,表明改进算法可靠、有效且相对易于实现。     

An Impact of Hydrostatic Extraction Scheme on BMRC’s Global Spectral Model

There are two important features in geophysical fluid dynamics. One is that the atmospheric and oceanic equa-tions of motion include the Coriolis force; another is that they describe a stratified fluid. The hydrostatic extraction scheme, or standard stratification approximation, posed by Zeng (1979), reflects the second aspect of geophysical flu-id dynamics. There exist two major advantages in this scheme; accurate computation of the pressure gradient force can be obtained over steep mountain slopes, and the accumulation error in vertical finite differencing can be reduced, especially near the tropopause.Chen et al (1987) introduced the hydrostatic extraction scheme into a global spectral model, which attained pre-liminary success at low resolution. Zhang and Sheng et al (1990) developed and improved the hydrostatic extraction scheme in a global spectral model, in which C0, the parameter that represents the stratification of the reference at-mosphere, changes not only with height, but also with latitude. The scheme has been incorporated BMRC’s global spectral model (IAPB). Four 5-day forecasts have been performed to test the IAPB with the hydrostatic extraction scheme. Objective verifications demonstrate a positive effect of the hydrostatic extration scheme on BMRC’s model, particularly at upper levels, over the tropics and the Antartic region.     

Fundamental framework and experiments of the third generation of IAP / LASG world ocean general circulation model

A new generation of the IAP / LASG world ocean general circulation model is designed and presented based on the previous 20-layer model, with enhanced spatial resolutions and improved parameterizations. The model uses a triangular-truncated spectral horizontal grid system with its zonal wave number of 63 (T63) to match its atmospheric counterpart of a T63 spectral atmosphere general circulation model in a planned coupled ocean-atmosphere system. There are 30 layers in vertical direction, of which 20 layers are located above 1000 m for better depicting the permanent thermocline. As previous ocean models developed in IAP / LASG, a free surface (rather than “rigid-lid” approximation) is included in this model. Compared with the 20-layer model, some more detailed physical parameterizations are considered, including the along / cross isopycnal mixing scheme adapted from the Gent-MacWilliams scheme. The model is spun up from a motionless state. Initial conditions for temperature and salinity are taken from the three-dimensional distributions of Levitus’ annual mean observation. A preliminary analysis of the first 1000-year integration of a control experiment shows some encouraging improvements compared with the twenty-layer model, particularly in the simulations of permanent thermocline, thermohaline circu?lation, meridional heat transport, etc. resulted mainly from using the isopycnal mixing scheme. However, the use of isopycnal mixing scheme does not significantly improve the simulated equatorial thermocline. A series of numerical experiments show that the most important contribution to the improvement of equatori?al thermocline and the associated equatorial under current comes from reducing horizontal viscosity in the equatorial regions. It is found that reducing the horizontal viscosity in the equatorial Atlantic Ocean may slightly weaken the overturning rate of North Atlantic Deep Water.     

Development and Test of Hydrostatic Extraction Scheme in Spectral Model

The introduction of “hydrostatic extraction” scheme, or “standard stratification approximation”, into spectral model gained some advantages compared with commonly used schemes. However, computational instability may oc-cur for high vertical resolution versions if the stratification parameter C0 taken as a constant. In this paper, the pos-sible cause leading to the instability is discussed and an improved scheme presented where C0 is generalized to be a function of both height and latitudes. Hence the reference atmosphere gets closer to the real atmosphere and the tem-perature deviation field to be expanded becomes smoother everywhere. Test by real case forecasts shows good computational stability of the new scheme and better prediction performance than usual schemes of spectral model.     

平均环流的诊断与预报

本文采用实际的大气资料分析了一个正压平均环流距平模式各项的相对重要性.结果表明,单纯考虑初始场的惯性预报的准确率随所取平均时间的增加而迅速下降,并以长波和超长波段最为显著. 加上气候平均风场及地球球面效应等动力因子后的修正的惯性预报,其结果不如纯惯性预报好.而且,所取的平均时间越长,效果越差.加进散度订正因子后,对长波和超长波的预报起明显改进作用, 对平均环流的预报起重要作用的因子是未知的强迫作用项.根据分析,本文提出了提高平均环流预报准确率的可能途径.     

一种渐变网格方案及其与嵌套网格方案的比较

本文给出了一种渐变网格及其相应的数值积分方案，并利用线性平流方程，分别采用该渐变网格、不等距网格和3种嵌套网格共5种方案进行数值试验。结果表明，在套网格方案中，采用精度较高且截断误差相近的不同格式进行嵌套计算误差较小；而变网格(包括渐变网格和不等距网格)方案既能简化积分过程，又能避免反射波，从而明显地提高了计算精度。     

Peculiarities of the Approach to Calculation of Wind Waves in the Caspian Sea

A high-precision digital elevation model of the Caspian Sea with the spatial resolution of 0.001° x 0.001° is constructed and used as a basis for computation grids of various scales. A three-level scheme for calculating wind waves with the sequence of nested grids (Caspian Sea-Northern Caspian, Absheron Peninsula, Turkmenbashy city-the Northern Caspian key areas) is developed. A scenario designer is implemented which considers in calculations the ice edge position and the coastline dynamics. The SWAN spectral wave model is adapted to the Caspian Sea conditions. The series of calculations and the comparison of the obtained results with observational data are provided. It is found that the best result is obtained when corrected reanalysis data are used for calculations.     

The Application of Flux-Form Semi-Lagrangian Transport Scheme in a Spectral Atmosphere Model

A flux-form semi-Lagrangian transport scheme(FFSL) was implemented in a spectral atmospheric GCM developed and used at IAP/LASG.Idealized numerical experiments show that the scheme is good at shape preserving with less dissipation and dispersion,in comparison with other conventional schemes.Importantly,FFSL can automatically maintain the positive definition of the transported tracers,which was an underlying problem in the previous spectral composite method(SCM).To comprehensively investigate the impact of FFSL on GCM results,we conducted sensitive experiments.Three main improvements resulted:first,rainfall simulation in both distribution and intensity was notably improved,which led to an improvement in precipitation frequency.Second,the dry bias in the lower troposphere was significantly reduced compared with SCM simulations.Third,according to the Taylor diagram,the FFSL scheme yields simulations that are superior to those using the SCM:a higher correlation between model output and observation data was achieved with the FFSL scheme,especially for humidity in lower troposphere.However,the moist bias in the middle and upper troposphere was more pronounced with the FFSL scheme.This bias led to an over-simulation of precipitable water in comparison with reanalysis data.Possible explanations,as well as solutions,are discussed herein.     

Circulations caused by interaction of underwater currents and surface waves

The interaction between non-uniform near-surface currents and long surface waves is shown to produce large-scale secondary circulations. The circulations are caused by the Craik–Leibovich vortex force imposed on the existing non-uniform current by the surface waves. The current could be produced by different types of sources, such as by ship wakes or by river and sewer outflows. In this paper the circulations are considered for three representative types of currents: a near-surface jet, a shear current, and an underwater jet. A model similar to the model of Langmuir circulations is formulated and studied numerically. The general model takes into account the effect of viscosity on the main current as well as the effect of the circulation-related advection on the main current and secondary flow itself. A simplified model that describes the initial stage of the development of circulations was used in order to demonstrate the strength of the phenomenon and its dependence on some parameters of the problem. At this initial stage, the effect of viscosity on the main current as well as the effect of advection caused by the circulations was neglected (under assumption that the perturbation velocity is small). The effect of the viscosity on the circulations was included in the solution, and it was shown that initial development of the circulations is practically independent of the viscosity. This fact simplifies the solution of the problem and removes the uncertainty related to the value of the turbulent viscosity at the initial stage of the circulations. The results obtained demonstrate that strong circulations are generated under very realistic assumptions regarding the parameters of the current and the surface waves. The maximum velocity at the surface produced by such circulations can easily reach several centimeters per second. A circulatory flow with this magnitude of velocity at the surface can significantly affect short surface waves and, correspondingly, radar and optical signatures produced by the initial currents on the sea surface. Some important conclusions about the nature of these signatures are made based on numerical results and simple qualitative arguments. Theoretical predictions include, for example, the asymmetry of centerline ship wakes and the difference in the width and length between images of two wakes of similar ships moving in opposite directions when ambient surface waves are present.     

Parametrization and influence of subgridscale orography in general circulation and numerical weather prediction models

Summary The problem of representing the drag due to subgridscale orography is examined. Results from model simulations are used to illustrate clear deficiencies in the global angular momentum budgets and possible ways of correcting for these deficiencies are considered. It is argued that a formulation for the stress due to subgridscale gravity waves is required, as was first recognized by Boer et al. (1984a, b), and the impact of a scheme based on Palmer et al. (1986) is presented. The scheme is improved by using directionally-dependent subgridscale orographic variances. Results from 90-day integrations using the ECMWF and UKMO models with similar resolutions are very much in accord both with and without a wave drag parametrization scheme; showing much improved wintertime circulations.The relationship between the wave drag and the model orography is examined with the use of idealized stress profiles whereby the wave drag is limited to either near the surface or in the stratosphere. A combination of parametrized wave drag with an envelope orography performs best at this stage of development.Results are presented from a substantial series of ten-day forecast experiments with the ECMWF operational model using mean and (1 ) envelope orographies, these show significant improvements in forecast skill.With 26 Figures