A Global Spectral Model and Test of Its Performance

A brief introduction is given of a global spectral model, its dynamical framework and diabatic physical processes involved. A number of real forecasts are shown to illustrate the forecasting capability of the model for various weather processes. It can even manage to predict some of those typical weather processes in summer which used to be difficult to forecasters.

Dynamic corner frequency in source spectral model for stochastic synthesis of ground motion

The static comer frequency and dynamic comer frequency in stochastic synthesis of ground motion from fi- nite-fault modeling are introduced, and conceptual disadvantages of the two are discussed in this paper. Furthermore, the non-uniform radiation of seismic wave on the fault plane, as well as the trend of the larger rupture area, the lower comer frequency, can be described by the source spectral model developed by the authors. A new dynamic comer frequency can be developed directly from the model. The dependence of ground motion on the size of subfault can be eliminated if this source spectral model is adopted in the synthesis. Finally, the approach presented is validated from the comparison between the synthesized and observed ground motions at six rock stations during the Northridge earthquake in 1994.

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.

NEW METHOD FOR LOW ORDER SPECTRAL MODEL AND ITS APPLICATION

In order to overcome the deficiency in classical method of low order spectral model, a new method for low order spectral model was advanced. Through calculating the multiple correlation coefficients between combinations of different functions and the recorded data under the least square criterion, the truncated functions which can mostly reflect the studied physical phenomenon were objectively distilled from these data. The new method overcomes the deficiency of artificially selecting the truncated functions in the classical low order spectral model. The new method being applied to study the inter-annual variation of summer atmospheric circulation over Northern Hemisphere, the truncated functions were obtained with the atmospheric circulation data of June 1994 and June 1998. The mechanisms for the two-summer atmospheric circulation variations over Northern Hemisphere were obtained with two-layer quasi-geostrophic baroclinic equation.

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 occur for high vertical resolution versions if the stratification parameter C0 taken as a constant. In this paper, the possible 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 temperature 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.

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 equations 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 fluid 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 preliminary 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 atmosphere, 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.

A Study of Bispectra in Relation to the Adequacy of Wave Spectral Model

In this paper, the characteristics of laboratory wind waves under various wind speeds and water depths are studied. It is found that either the real or the imaginary part of the bispectrum can be related to the asymmetry of the wave profile, and the bicoherence is related to the ratio of nonlinear to linear wave component. Occasionally, these two categories of nonlinear index lead to opposite inferences, because each of them has its own significance and functions. The applicability of linear wave spectral model in ocean waves becomes questionable only when strong nonlinearity is indicated by both of these two indexes, The linear spectral representation of wave fields does not necessarily become inadequate as water depth decreases, and its appropriateness can be examined through the characteristics of the bispectrum.

ON THE MULTIPLE SOLUTIONS TO A THREE-COEFFICIENT SPECTRAL MODEL OF WIND-DRIVING OCEAN CURRENT EQUATION

In this paper,a research on the problem of multiple solutions of the three-coefficient low-spectrum model for the quasi-geostrophic ocean current equation with forcing and dissipation terms is carried out.The state of the ocean current under wind conditions such as those of typhoon is discussed carefully and the rela- tions between the multiple solutions and the coefficients R and ε are analyzed.It is seen that in an approxi- mate triangular region with the Rossby-coefficient R less than 0.5,and the friction-coefficient ε less than 0.22, there exist three equifibrium solutions,among which two are stable and one is unstable.For the former,the coefficient A or B in the expansion is rather large,while for the latter,A or B is relatively small.They respectively imply how much the ocean energy is fed back from the wind stress and the solution with a large A is much more stable than that with a larger B.

Seasonal Characteristics and Interannual Variability of Monthly Scale Low-Frequency Oscillation in a Low-Order Global Spectral Model

Analysis is done of five-year low-pass filtered data by a five-layer low-order global spectral model, indicating that although any non-seasonal external forcing is not considered in the model atmosphere,monthly-scale anomaly takes place which is of remarkable seasonality and interannual variability.Analysis also shows that for the same seasonal external forcing the model atmosphere can exhibit two climatic states,similar in the departure pattern but opposite in sign, indicating that the anomaly is but the manifestation of the adverse states, which supports the theory of multi-equilibria proposed by Charney and Devore(1979) once again.Finally, the source for the low-frequency oscillation of the global atmosphere is found to be the convective heat source / sink inside the tropical atmosphere as discussed before in our study.Therefore, the key approach to the exploration of atmospheric steady low-frequency oscillation and the associated climatic effect lies in the examination of the distribution of convective heat sources / sinks and the variation in the tropical atmosphere.

ON PROBLEMS OF HIGHLY TRUNCATED LOW-SPECTRAL MODEL IN STUDIES OF MULTIPLE EQUILIBRIA IN THE ATMOSPHERE

The multiple atmospheric equilibria are studied by using a barotropic vorticity equation with thermal forcing and dissipative effects. Different low-spectral models are used to discuss the variations of theequilibrium states, with the results that the multiple features of equilibrium states depend heavily on thetruncations of the spectra, and the low-spectral model has obvious shortcomings in solving non-linear equations,suggesting that one has to be very Careful to employ highly truncated low-spectral model in approximating partial differential equations.

Spectral Models for Improving Atmospheric Correction Results in Complex Oceanic Waters around India

Atmospheric correction over turbid and productive waters continues to be problematic and often results in excessive errors in retrieved water-leaving radiance and bio-geo-physical products. This may be likely due to overestimation of La + Lra (atmospheric signal due to aerosol and Rayleigh scattering) in the visible and thus reduction in Lw which appears as an elevated pigment concentration. Spectral models for reconstructing the atmospherically distorted data are developed and their results are thoroughly validated with in-situ data from a wide range of waters. Good agreement was found between the retrieved products and in-situ data. Our results indicate that the new spectral models have the potential to improve the accuracy of ocean colour retrievals in optically complex waters, and can become an important part of the processing of data from ocean colour sensors (e.g., Ocean colour monitor OCM2) with only two near-infrared bands (i.e., 765 and 865 nm).

THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SPECTRAL MODEL OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL PREDICTION

In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time- discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability. The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration. The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short)can contribute up to one-third of the total systematic root-mean-square(RMS)error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors, roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging.

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 scheme artificially 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 partly using 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.

A GLOBAL SPECTRAL MODEL WITH VARIABLE POLES AND ITS APPLICATION TO THE SHALLOW-WATER EQUATIONS

Since we find out that the global spectral model with trapezoidal truncation has higher resolution in high latitudes(polar cap)than in low latitudes,this paper presents a global spectral model with variable poles which can be located at the center of interested area.The transform methods from traditional global spectral model to the new model are given and applied to a shallow-water equation model.The control ex- periments for 72h predictions were carried out.The“northern pole”in the transformed model was located at 15°N,135°E.And the results showed that the predictions of weather systems in the area around the“new pole”(the polar cap,latitudes >60°)were better than those by the traditional model and the root mean square errors were improved.

THE INITIAL WIND SCHEME OF THE HEMISPHERIC SPECTRAL MODEL AND ITS EFFECT ON THE DATA ASSIMILATION

A series of data assimilation and forecast test have been carried out with a hemispheric spectral model(T42L9H).It is found that the numerical scheme for determining hemispheric initial wind is important to data assimilation and forecast.An inappropriate scheme may cause computational sources of divergence near the equator,which are responsible for the spurious strong precipitation and corresponding latent heat release.Obviously,this problem differs from either the hemispheric/global domain effect or the tropical data effect pointed by Dalley et al.(1981).Based on the previous studies,the new scheme of divergence and vorticity correction is presented,and the difference with other schemes and its effects on the data assimilation are discussed against the control test. Preliminary tests have shown that the new divergence correction scheme proposed in this paper may be a preferable choice to overcome the initial computational errors in the hemispheric data assimilation.

DESIGNATION AND APPLICATION OF A SPHERICAL LONG-WAVE SPECTRAL MODEL

A two-level,quasi-geostrophic long-wave model based on spherical coordinates was developed with the explicit part belonging to a low-order model.However,it includes not only diabatic heating,Ekman fric- tion and mountain distribution,but also parameterized forcing effects of transfer properties of transient eddies. Experiment results showed that,due to the introduction of the parameterization of transfer properties of transient eddies,remarkable improvements on characters of low-order model had been obtained.In addition to its economization in calculation and conciseness in physics as in a low-order model,the long- wave model was shown to describe the energetics and angular momentum balance of the atmosphere much more reasonably,and to present the features of zonal mean westerlies and stationary waves much more correctly than the corresponding low-order model.This kind of long-wave model was therefore regarded as suitable for theoretical research and numerical modelling of some aspects of the general circulation of the atmosphere.

SYSTEMATIC FORECAST ERROR IN U.S.NMC OPERATIONAL SPECTRAL MODEL

The distribution of monthly mean error of NMC model forecasts and its seasonal variation are investi- gated.The ratio of monthly mean error to standard deviation is used here to find out that the region where a correction of systematic error is needed and appropriate is mainly in low latitudes.The improvement,after the model's vertical resolution and some physical parameters were changed from April 1985,is investigated,and the NMC operational model forecasts have also compared with those of ECMWF.

Parallel Computing of the Global Spectral Atmospheric Model on the YH－2 Supercomputer

A global spectral atmospheric model has been vectorized and multitasked on the YH-2 supercomputer. The model is used for the operational system of medium--range numerical weather prediction in National Meteorological Center(NMC), China. In this paper the vectorization algorithms of the spectral-grid transformation and multitasking schemes of the model are discussed in detail. The results show that high speed-up for tile model can be obtained.

A spectral model based on atmospheric self-memorization principle

Based on the atmospheric self_memorization principle, a complex memory function was introduced and the spectral form of atmospheric self_memorial equation was derived. Setting up and solving the equation constitute a new approach of the numerical weather prediction. Using the spectral model T42L9 as a dynamic kernel, a global self_memorial T42 model (SMT42) was established, with which twelve cases of 30_d integration experiments were carried out. Compared with the T42L9, the SMT42 is much better in 500 hPa forecast not only for daily circulation but also for monthly mean circulation. The anomaly correlation coefficient (ACC) of forecast for monthly mean circulation has been improved to 0.42, increased by 0.05, and the root_mean_square error (RMSE) has been reduced from 6.09 to 4.03 dagpm.

A spectral mixture model analysis of the Kuroshio variability and the water exchange between the Kuroshio and the East China Sea

For understanding more about the water exchange between the Kuroshio and the East China Sea,We studied the variability of the Kuroshio in the East China Sea(ECS) in the period of 1991 to 2008 using a three-dimensional circulation model,and calculated Kuroshio onshore volume transport in the ECS at the minimum of 0.48 Sv(1 Sv ;106 m3/s) in summer and the maximum of 1.69 Sv in winter.Based on the data of WOA05 and NCEP,The modeled result indicates that the Kuroshio transport east of Taiwan Island decreased since 2000.Lateral movements tended to be stronger at two ends of the Kuroshio in the ECS than that of the middle segment.In addition,we applied a spectral mixture model(SMM) to determine the exchange zone between the Kuroshio and the shelf water of the ECS.The result reveals a significantly negative correlation(coefficient of-0.78) between the area of exchange zone and the Kuroshio onshore transport at 200 m isobath in the ECS.This conclusion brings a new view for the water exchange between the Kuroshio and the East China Sea.Additional to annual and semi-annual signals,intra-seasonal signal of probably the Pacific origin may trigger the events of Kuroshio intrusion and exchange in the ECS.