一种改进的平缓-混合地形追随坐标在GRAPES中尺度模式中的应用研究

平缓-混合地形追随坐标（T-F坐标）可以减小坐标面上的地形影响带来的各种计算误差。以余弦三角函数为基函数的平缓-混合坐标（COS坐标）高层坐标面水平,计算误差较小,但是低层坐标面之间的厚度较薄,增大了计算误差,给模式稳定性及模拟效果带来较大的影响。设计一种改进的COS坐标,使低层坐标面垂直分布更加均匀,应用于GRAPES-Meso模式进行理想试验和实际模拟试验。结果表明,改进的COS坐标相对COS坐标,中高层计算误差相当,低层地形作用衰减的垂直变化更加均匀,减小了计算误差,提高了计算稳定性;地形重力波试验结果显示,改进的COS坐标重力波破碎相对COS坐标有一定缓解,更接近解析值;批量模拟试验结果显示,改进的COS坐标各个层次上的月平均模拟偏差比单尺度双曲函数平缓-混合坐标（简称SLEVE1坐标）更小,均方根误差减小,距平相关系数增大。改进的COS坐标有效地解决了COS坐标的计算问题,提高了模式预报效果。      

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。      

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。     

不同平缓-混合坐标对一次高原准静止锋降水过程模拟影响对比分析

GRAPES_Meso模式预报存在南风偏大、虚假降水偏多等问题,且在大地形下游地区异常明显。平缓-混合坐标可以有效减小气压梯度力计算误差以及平流输送误差,而这两种误差与风场和水汽场预报密切相关。基于GRAPES_Meso模式选择四种平缓-混合坐标对一次典型的高原东部准静止锋降水过程进行模拟分析。模拟结果表明,较弱的天气形势演变下,平缓-混合坐标的改进效果比较明显,可以有效缓解风场预报偏差、虚假降水、虚假天气系统等问题,个例模拟的结果与实况更接近。     

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.     

地形追随坐标系下埃特尔位涡的计算

随着数值天气预报模式的日益普及以及位涡在不同天气、气候时、空尺度上的广泛应用,对采用模式输出资料计算的埃特尔（Ertel）位涡的精度提出了更高要求。将气象要素从中尺度模式普遍采用的地形追随坐标系向定义位涡的z或p坐标系的插值过程（插值法）,是导致埃特尔位涡计算误差的主要原因。文中利用地形追随坐标系与z（p）坐标系的变换关系,导出了z坐标系定义的埃特尔位涡在地形追随坐标系中的表达形式,实现了直接在模式格点上计算埃特尔位涡（直接法）,在提高计算精度的同时,保留了其在z坐标系中的物理意义,方便了分析与应用。为了进一步分析直接法在减少计算误差方面的作用,使用WRF模式对2016年7月发生在华北地区复杂地形背景下的一次黄淮气旋爆发过程进行了模拟,利用模式输出资料对此次天气过程中强降水时段插值法计算误差的分布进行了分析。结果表明,利用直接法计算位涡可有效减少插值法引入的计算误差,中低层均方根误差可达0.5 PVU,中高层可达0.3 PVU。将其应用到中小尺度对流性天气精细化结构的分析及气候统计研究中,可以有效减少插值法误差对结果产生的不良影响,提高计算和分析准确度。      

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.     

用线性化全球原始方程谱模式研究地形强迫行星波垂直传播特征

本文用线性化全球原始方程谱模式来研究地形强迫行星波的垂直传播过程及演变特征.模式的积分结果表明:行星波的能量沿两支波导进行传播,在波从对流层向平流层传播中,极地波导起着主要作用.由于重力波破碎的阻尼作用,地形强迫的行星波无论它的波作用量或振幅都呈现振荡状态.     

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。     

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。     

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]…     

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。     

Large-Eddy Simulations of Atmospheric Flows Over Complex Terrain Using the Immersed-Boundary Method in the Weather Research and Forecasting Model

Atmospheric flow over complex terrain, particularly recirculation flows, greatly influences wind-turbine siting, forest-fire behaviour, and trace-gas and pollutant dispersion. However, there is a large uncertainty in the simulation of flow over complex topography, which is attributable to the type of turbulence model, the subgrid-scale (SGS) turbulence parametrization, terrain-following coordinates, and numerical errors in finite-difference methods. Here, we upgrade the large-eddy simulation module within the Weather Research and Forecasting model by incorporating the immersed-boundary method into the module to improve simulations of the flow and recirculation over complex terrain. Simulations over the Bolund Hill indicate improved mean absolute speed-up errors with respect to previous studies, as well an improved simulation of the recirculation zone behind the escarpment of the hill. With regard to the SGS parametrization, the Lagrangian-averaged scale-dependent Smagorinsky model performs better than the classic Smagorinsky model in reproducing both velocity and turbulent kinetic energy. A finer grid resolution also improves the strength of the recirculation in flow simulations, with a higher horizontal grid resolution improving simulations just behind the escarpment, and a higher vertical grid resolution improving results on the lee side of the hill. Our modelling approach has broad applications for the simulation of atmospheric flows over complex topography.     

A unified linear theory of wavelike perturbations under general ocean conditions

A linearized instability analysis model with five unknowns was proposed to describe disturbance motions under general oceanic background conditions, including large-scale current shear, density stratification, frontal zone, and arbitrary topography. A unified linear theory of wavelike perturbations for surface gravity waves, internal gravity waves and inertial gravity waves was derived for the adiabatic case, and the solution was then found using Fourier integrals. In this theory, we discarded the assumptions widely accepted in the literature concerning derivations of wave motions such as the irrotationality assumption for surface gravity waves, the rigid-lid approximation for internal gravity waves, and the long-wave approximation for inertial gravity waves. Analytical solutions based on this theory indicate that the complex dispersion relationships between frequency and wave-number describing the propagation and development of the three types of wavelike perturbation motions include three components: complex dispersion relationships at the sea surface; vertical invariance of the complex frequency; and expressions of the vertical wave-number (phase). Classical results of both surface waves and internal waves were reproduced from the unified theory under idealized conditions. The unified wave theory can be applied in the dynamical explanation of the generation and propagation properties of internal waves that are visible in the satellite SAR images in the southern part of the China Seas. It can also serve as the theoretical basis for both a numerical internal-wave model and analytical estimation of the ocean fluxes transported by wavelike perturbations.     

一个包含土壤和植被的区域气候模式及其性能检验

本文研制了一个三维地气耦合的区域气候模式，该模式由大气、土壤和植被三个子模式组成，各子模式间通过动量、能量和水份交换过程进行相互作用。在大气子模式中提出用z-z*混合坐标系处理地形的新方法，并把诊断分析中的散度修订方案引入数值模式，使其在物理依据上更加合理。此外，模式中较为详细地考虑了影响区域气候形成和变化的物理过程。简单的数值试验表明，区域气候模式比较真实地模拟了土壤和植被冠层的温度日变化，对区域气候平均态也有一定的模拟能力，可较好地处理大地形，具有良好的稳定性能，并对下垫面热力非均匀性的响应也是敏感的。     

一次暴雪过程地形方案的敏感性试验研究

利用WRF模式中提供的包络地形、轮廓地形和平均地形方案对2005年12月20-21日的山东暴雪过程进行数值模拟.结果表明:地形方案与降雪的时空分布有很大的相关性,地形越接近实际地形,降雪的时空分布越接近实况;降雪过程中有明显的中尺度重力波活动,降雪的峰值滞后于重力波的波峰;重力波受地形影响很大,地形越不平滑,重力波的强度越强、移速越慢;当重力波的强度较强时,降雪峰值滞后于波峰的时间差也较长.     

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.     

A Method of Analysis for Turbulent Flows Using the Streamline Coordinate System

A procedure is described for analysing the transport equations for Reynolds stresses written in a streamline coordinate system, starting from the fields of first- and second-order moments of wind velocity measured in a terrain-following system over topography. In the analysis, the equations are split into two parts: the first contains the terms that can be calculated directly from measurements; the second contains third-order moments that are parameterized using suitable models. To evaluate the error associated with both parts, a Monte-Carlo technique that takes into account the experimental errors is proposed. An example of the application of this method for the Reynolds shear stress equation, using wind-tunnel data for non-separating flow over a two-dimensional valley, is reported. The comparison between the measured and modelled parts is fair near the surface, while at higher levels, the modelled part can be shown to miss a correct treatment of the third-order moments. In the frame of this analysis, the use of the correct derivative transformation has been found to be significant even for moderately sloping topography.     

Energy- and Flux-Budget Turbulence Closure Model for Stably Stratified Flows. Part II: The Role of Internal Gravity Waves

We advance our prior energy- and flux-budget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.2–0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.