Kinetic Energy Budget Equations of Rotational and Divergent Flow in Terrain-following Coordinates

In this study, kinetic energy budget equations of rotational and divergent flow in pressure coordinates are derived on terrain-following coordinates. The new formulation explicitly shows the terrain effects and can be applied directly to model-simulated dynamic and thermodynamic fields on the model’s original vertical grid. Such application eliminates interpolation error and avoids errors in virtual weather systems in mountainous areas. These advantages and their significance are demonstrated by a numerical study in terrain-following coordinates of a developing vortex after it moves over the Tibetan Plateau in China.     

Effects of terrain-following vertical coordinates on high-resolution NWP simulations

With increasing resolution in numerical weather prediction(NWP)models,the model topography can be described with finer resolution and includes steeper slopes.Consequently,negative effects of the traditional terrain-following vertical coordinate on high-resolution numerical simulations become more distinct due to larger errors in the pressure gradient force(PGF)calculation and associated distortions of the gravity wave along the coordinate surface.A series of numerical experiments have been conducted in this study,including idealized test cases of gravity wave simulation over a complex mountain,error analysis of the PGP estimation over a real topography,and a suite of real-data test cases.The GRAPES-Meso model is utilized with four different coordinates,i.e.,the traditional terrain-following vertical coordinate proposed by Gal-Chen and Somerville(hereinafter referred to as the Gal.C.S coordinate),the one-scale smoothed level(SLEVE1),the two-scale smoothed level(SLEVE2),and the COSINE(COS)coordinates.The results of the gravity wave simulation indicate that the GRAPES-Meso model generally can reproduce the mountain-induced gravity waves,which are consistent with the analytic solution.However,the shapes,vertical structures,and intensities of the waves are better simulated with the SLEVE2 coordinate than with the other three coordinates.The model with the COS coordinate also performs well,except at lower levels where it is not as effective as the SLEVE2 coordinate in suppressing the PGF errors.In contrast,the gravity waves simulated in both the Gal.C.S and SLEVE1 coordinates are relatively distorted.The estimated PGF errors in a rest atmosphere over the real complex topography are much smaller(even disappear at the middle and upper levels)in the GRAPES-Meso model using the SLEVE2 and COS coordinates than those using the Gal.C.S and SLEVE1 coordinates.The results of the real-data test cases conducted over a one-month period suggest that the three modified vertical coordinates(SLEVE1,SLEVE2,and COS coordinates)give better results than the traditional Gal.C.S coordinate in terms of forecasting bias and root mean square error,and forecasting anomaly correlation coefficients.In conclusion,the SLEVE2 coordinate is proved to be the best option for the GRAPES-Meso model.     

An Impact Study of the Vertical Coordinate on a Non-hydrostatic Mesoscale High-Resolution Model

With the high-speed development of high-powered computer techniques, it is possible that a high-resolution and multi-scale unified numerical model is applied to the operational weather prediction. Some techniques about mesoscale non-hydrostatic numerical weather prediction are addressed, and the impact of the vertical coordinate system is one of them. Based on WRF (Weather Research and Forecasting) model, the influence of vertical coordinates on the non-hydrostatic mesoscale high-resolution model is compared. The results show that the error of various coordinates in lower levels is almost same when we use the geometry height (z) and the pressure (p) to set up a terrain-following coordinate; but the error of the height terrain-following coordinate in higher levels is smaller than that of the pressure terrain-following coordinate. The higher the resolution is, the bigger the error will be. The results of the high-resolution simulation exhibited that the trend of the difference in the two coordinates existed. In addition, the correlative coefficient and standard error are also analysed by the comparison between the forecast fields and the corresponding analysis fields.     

Testing the Ability of Numerical Model to Simulate Climate and Its Change With 4D-EOF Analysis

The four-dimensional empirical orthogonal function (4D-EOF), which in reality is a simple combination of three-dimensional EOF (3D-EOF) and extended EOF (EEOF), is put forward in this paper to test the ability of numerical model to simulate climate and its change. The 4D-E0F analysis is able to reveal not only the horizontal characteristic pattern of analyzed variable, and its corresponding annual and inter-annual variations, but also the vertical structural characteristics. The method suggested is then used to analyze the monthly mean 100-, 500-, 70G-, and 1000-hPa geopotential height fields (4941 grids and grid spacing 60 km) and their anomaly fields in 1989-1998 simulated by the MM5V3 from the RMIP (Regional Climate Model Inter-comparison Project for East Asia)-II, as well as their counterparts (used as the observed fields) from the NCEP/NCAR re-analysis dataset in the same period. The ability of MM5V3 in simulating East Asian climate and its change is tested by comparing the 4D-EOF analysis results of the simulated and observed datasets. The comparative analyzed results show that the horizontal pattern of the first eigenvector of the observed monthly mean geopotential height fields and its vertical equivalent barotropic feature were well simulated; the simulations of the first two eigenvectors of the observed monthly mean geopotential height anomaly fields were also successful for their horizontal abnormal distributions and significant equivalent barotropic features in the vertical were well reproduced; and furthermore, the observed characteristics, such as the variation with height, the annual and inter-annual variations of the monthly mean geopotential height/anomaly fields were also well reflected in the simulation. Therefore, the 4D-EOF is able to comprehensively test numerical model's ability of simulating the climate and its change, and the simulation ability of MM5V3 for the climate and its change in East Asia in the 1990s was satisfactory.     

GENERAL FORMS OF DYNAMIC EQUATIONS FOR ATMOSPHERE IN NUMERICAL MODELS WITH TOPOGRAPHY

The atmospheric dynamic equations have been transformed from the z-coordinate system into a generalized vertical coordinate system by using a sc-called DDD transformation method. Then the generalized system is assumed being pressure, sigma or incorporated pressure-sigma coordinate system and corresponding equations are obtained with the second-order accuracy. It is pointed out that the usual equations are only of the first-order accuracy when their space-differential terms are approximated by central finite differences. Therefore the usual forms of the equations may result in quite large errors on steep slopes of mountains included in a model.     

VORTEX MOTIONS IN THE ATMOSPHERIC CONVECTIVE BOUNDARY LAYER

Large vortices with scales ranging from hundreds meters to tens of kilometers are generallyfound in the atmospheric convective boundary layer(CBL).These vortices play important roles in the vertical transport of momentum,heat,water vaporand other tracers in the boundary layer.On the basis of the view of interaction between theconvection in CBL and the gravity waves in the upper stable layer the authors developed aconvection-wave theory on the formation of large vortices.According to the theory thewavenumber spectrum of the large vortices mainly depends on the atmospheric conditions in bothof the upper and lower layers,such as wind speed,wind direction shear,stratification as well astemperature jump.In the present paper satellite image and weather data in a case of cold air outbreak over warmocean are analyzed to study every stage of the convective processes,such as cloud street,convective cell as well as their transformation.According to the theory the wavenumbercompositions for cloud street and convective cell are calculated,respectively,on the basis of theatmospheric conditions at every stage.The distributions of vertical motions,convergent band anddisturbed interface are obtained and compared with the cloud patterns in the convective processes.Thus the study seems to offer a likely explanation for the origin of large vortices in CBL.     

Statistical Relationship Between UVB(280-320nm) and Broadband Solar Radiation(295-2800nm) at a Subtropical Location(Qena,Egypt)

The present study quantifies the relationship between ultraviolet-B(UVB) and broadband solar radiation(G) at Qena,Egypt.Data from 10-year hourly integrated totals for both UVB and G on a horizontal surface were used to determine the best fit between the two radiation types.On the basis of the correlation of determination(r2),a second-order polynomial was determined to provide the best fit.For the purpose of developing an empirical model to estimate UVB,all of the cases of UVB and G from a nine-year study from 2001 to 2009 were introduced.Monthly and seasonal empirical models,as well as a general expression,were established for UVB as a function of G.The values of r2 ranged from 0.90 to 0.97.By using a new dataset of G,the estimated and the corresponding measured values of UVB were determined to be in good agreement whereby the values of r2 between the two ranged from 0.91 to 0.98.In addition,the significance and performance of the regression forms were evaluated with the aid of several statistical analysis procedures.The values of the index of modeling(d) and coefficient of modeling efficiency(ME) were close to one.Moreover,the values of RMSE,mean bias error(MBE),and mean absolute error(MAE) were lower than the experimental errors.On the basis of this analysis,it has been determined that the suggested regression forms can be used to estimate UVB when it difficult to obtain measurements or when measurements are available only for limited periods at the studied region.     

A modified moist ageostrophic <Emphasis Type="Italic">Q</Emphasis> vector

The quasi-geostrophic Q vector is an important rainfall associated with large-scale weather systems diagnostic tool for studying development of surface and is calculated using data at single vertical level. When ageostrophic Q vector was introduced, it required data at two vertical levels. In this study, moist ageostrophic Q vector is modified so that it can be calculated using data at a single vertical level. The comparison study between the original and modified moist ageostrophic Q vectors is conducted using the data from 5 to 6 July 1991 during the torrential rainfall event associated with the Changjiang-Huaihe mei-yu front in China. The results reveal that divergences of original and modified moist ageostrophic Q vectors have similar horizontal distributions and their centers are almost located in the precipitation centers. This indicates that modified moist ageostrophic Q vector can be used to diagnose convective development with reasonable accuracy.     

The mesoscale balance and imbalance and the corresponding potential vorticity inversion from the view of helicity

The static balance and the geostrophic balance are the common balances in meteorology.All the synoptic systems and most of the mesoscale systems satisfy the above two balances.However,due to the strong convection and non-geostrophic feature,many mesoscale systems usually present as static imbalance,and the quasi-geostrophic approximation is no longer attainable.This paper tried to find out a kind of balance that exists for mesoscale convective system.To do this,the concrete mathematics definitions for balance and imbalance equations were defined.Then,it is proposed that the new balance equation should include the divergence,vorticity,and vertical motion simultaneously,and the helicity equation was a good choice for the basis.Finally,the mesoscale balance and imbalance equations were constructed,as well as a new balance model that was based on the helicity,horizontal divergence,vertical vorticity,continuity,and thermal dynamic equations under same approximations.Moreover,the corresponding potential vorticity(PV)inversion technique was introduced.It was pointed out that by using the PV conservation and the potential temperature conservation,the flows of the mesoscale balance model can be deduced,and their comparison with the real fields would give the degree of the imbalance.     

THE LOW-PRESSURE SYSTEM IN THE VERTICAL VELOCITY OMEGA ON THE SCALE OF SYSTEM SENSITIVITY

In this study, the relationship between scale and vertical velocity in a low-pressure system is explored using the wave characteristics of atmospheric disturbances and the structural characteristics of low-pressure systems. The ω differential equation, as determined by the transient geopotential height field Φ, is solved to obtain an analytical solution composed only of wavelength, horizontal speed, and atmospheric stability, i.e., the ω diagnostic equation of a low-pressure system. This equation also shows that vertical velocity in the low-pressure system is very sensitive to the horizontal scale, i.e., a smaller horizontal scale means a larger vertical velocity.     

逐层平滑地形的平缓地形追随坐标在高分辨率GRAPES模式中的应用研究

高分辨率GRAPES模式如3 km模式对地形的识别程度更高,模式中各高度坐标面可识别的地形坡度也更大,地形作用带来的气压梯度力计算误差和平流输送误差更突出。平缓地形追随坐标可以通过多种方式衰减坐标面上的地形影响进而减小这些计算误差。选择一种逐层平滑地形的平缓地形追随坐标,基于GRAPES-3km模式进行理想试验和批量模拟试验。试验结果显示:逐层平滑地形的平缓地形追随坐标相对其他平缓地形追随坐标对地形重力波模拟更接近解析值;24 h滚动预报月连续模拟试验中逐层平滑地形的平缓地形追随坐标一定程度上能降低高层月平均的温度场、风场的模拟误差,月平均的降水评分也有所提高。逐层平滑地形的平缓地形追随坐标应用于GRAPES-3km模式有较好的模拟效果。      

地形追随垂直运动方程在南疆极端暴雨中的诊断分析

针对2021年6月15～17日发生在昆仑山脉北坡的南疆极端暴雨过程,本文综合考虑地形对暴雨发生、发展的作用后,利用地形追随坐标控制方程并采用Boussinesq近似推导建立了地形追随坐标的非静力平衡广义垂直运动方程。诊断结果表明,经向气压梯度力耦合经向散度项（项一）、垂直气压梯度力耦合纬向散度项（项二）和非绝热加热经向梯度项（项三）是激发暴雨垂直运动发展演变的三个主要强迫项。项一体现了偏北风逐渐增强,在昆仑山脉的阻挡下导致经向辐合增强,触发了垂直上升运动。经向气流辐合始终是对流活动最主要的强迫过程,其次为纬向气流辐合。在地形追随坐标形式下,经向和垂直气压梯度能够增强项一和项二。对流发展阶段,水汽辐合与非绝热加热过程增强了非绝热加热经向梯度,促进了垂直上升运动发展。在地形的影响下,对流层中高层西风过山气流波动特征明显。重力波活动导致的高层辐散进一步促进了山脉迎风坡对流活动。经向和纬向气流辐合、非绝热加热过程以及重力波活动等多个因素共同造成了此次南疆极端暴雨。     

三维海陆风的数值模拟

本文利用地形坐标,建立了一个模拟用的三维海陆风模式,来模拟城市、斜坡和海岸形状等对海陆风的影响。结果表明,海陆风主要受海陆温差影响,海岸线附近的坡地和城市的存在,对海风发展有利。     

IMPACT STUDY ON THE CALCULATION OF VERTICAL VELOCITY IN DIFFERENT VERTICAL COORDINATE SYSTEMS

1 INTRODUCTION First, let’s have a review of various vertical coordinate systems used in numerical weather prediction (NWP). Richardson[1] (1922) first attempted to use the geometrical height z as the vertical coordinate system. Though geometrical height is easy to understand as a concept, it had not been applied in NWP until Kasahara and Washington (1967) rewrote his predictive equations and used state-of-the-art high-speed computers to conduct NWP in height coordinates. Eliassen[2]…     

一种新型高度地形追随坐标在GRAPES区域模式中的实现:理想试验与比较研究

将一种新的高度地形追随坐标(Klemp坐标)引入了GRAPES区域模式,并与传统追随坐标(Gal-Chen坐标)和平缓地形追随坐标(SLEVE,Smooth Level Vertical coordinate)进行了比较。对不同坐标下气压梯度力的计算误差通过理想静止大气试验进行了评估,结果表明:与Gal-Chen坐标和SLEVE坐标相比,Klemp坐标有效地减小了气压梯度力的计算误差。理想重力波模拟试验表明,Klemp坐标下对重力波的模拟相比其他两种坐标也更接近于解析解。模式进一步采用了Mahrer气压梯度计算方案减少了计算误差,并提高了模式的精度和稳定性。实际个例试验与理想试验的结论相似。     

非静力中尺度高分辨率模式模拟中的垂直坐标影响研究

近几年来,随着高性能计算机技术的高速发展,甚高分辨率的中尺度数值预报模式业务应用已成为可能,与之相关的一系列模式技术的新问题也随之提了出来,垂直坐标系的影响就是其中之一。文中借助于美国新一代数值预报模式WRF(WeatherReseachandForecast),比较了非静力中尺度模式高分辨率模拟应用的垂直坐标影响问题。研究表明,当选用几何高度(z)和气压(p)来构造地形追随坐标时,低层两坐标引起的误差基本一样,中高层高度地形追随坐标引起的误差小于气压地形追随坐标;而且分辨率越高差异愈大。高分辨率模拟结果也表明,这种差异趋势是存在的;此外,本文对天气过程的预报要素场进行了相关的分析。     

不同垂直坐标系对垂直速度计算的影响

近年来,随着高精度中尺度数值预报模式和多尺度统一模式的发展,与之相关的一些非静力中尺度模式技术也随之提了出来,垂直坐标系的影响问题就是其中之一。本文借助于高精度美国新一代数值预报模式WRF(Weather Reseach and Forecast),模拟分析了两种不同的坐标系对模式大气中垂直速度计算的影响。试验结果表明,不同的坐标系对大气垂直速度大小计算存在着差异,特别是当分辨率提高时,不同垂直坐标系对大气垂直结构的刻画的差别更加明显。由于垂直速度与降雨过程密切相关,垂直速度的计算差异必然影响模式对降雨过程的描述。理想试验结果表明,在气压地形追随坐标中气压梯度力的计算对地表气压计算很敏感。     

TRAJECTORY ANALYSES OF THE DUSTSTORMS OVER EAST ASIA*

The transports of dust are calculated using 3-dimensional(3-D) trajectory method for three cases of duststorms in the terrain-following coordinate system,and the synoptic processes are also discussed for each case.The case of 17-20 April 1980,a severe duststorm was associated with the rapid development of a cyclone over the Mongolia Plateau.The dust moved from west to east across several deserts,formed a typical dust path in spring.The other two were weaker and the dust was triggered by the strong wind behind the cold front from northwest or north.Because the vertical velocity is considered in 3-D trajectory analysis,trajectories calculated should better reveal the transport rule of the dust particles and the results seem to be more consistent with the synoptic processes.The trajectory analysis on the 2-D isobaric surfaces is simpler but can be used only in the conditions with weak vertical wind shear and weak vertical velocity.The difference of trajectories at lower levels between two methods may be caused by the different treatment of orography.     

Model evaluation experiments in the North Atlantic Basin: simulations in nonlinear terrain-following coordinates

A primitive equation ocean circulation model in nonlinear terrain-following coordinates is applied to a decadal-length simulation of the circulation in the North Atlantic Ocean. In addition to the stretched sigma coordinate, novel features of the model include the utilization of a weakly dissipative, third-order scheme for tracer advection, and a conservative and constancy-preserving time-stepping algorithm. The objectives of the study are to assess the quality of the new terrain-following model in the limit of realistic basin-scale simulations, and to compare the results obtained with it against those of other North Atlantic models used in recent multi-model comparison studies.The new model is able to reproduce many features of both the wind-driven and thermohaline circulation, and to do so within error bounds comparable with prior model simulations (e.g., CME and DYNAMO). Quantitative comparison with comparable results obtained with the Miami Isopycnic Coordinate Model (MICOM) show our terrain-following solutions are of similar overall quality when viewed against known measures of merit including meridional overturning and heat flux, Florida Straits and Gulf Stream transport, seasonal cycling of temperature and salinity, and upper ocean currents and tracer fields in the eastern North Atlantic Basin. Sensitivity studies confirm that the nonlinear vertical coordinate contributes significantly to model fidelity, and that the global inventories and spatial structure of the tracer fields are affected in important ways by the choice of lateral advection scheme.