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。      

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。      

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。     

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.     

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.     

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。     

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。     

Directional Shear in the Nocturnal Atmospheric Surface Layer

Stratified nocturnal flow above and within a small valley of approximately 12-m depth and a few hundred metres width is examined as a case study, based on a network of 20 sonic anemometers and a central 20-m tower with eight levels of sonic anemometers. Several regimes of stratified flow over gentle topography are conceptually defined for organizing the data analysis and comparing with the existing literature. In our case study, a marginal cold pool forms within the shallow valley in the early evening but yields to larger ambient wind speeds after a few hours, corresponding to stratified terrain-following flow where the flow outside the valley descends to the valley floor. The terrain-following flow lasts about 10 h and then undergoes transition to an intermittent marginal cold pool towards the end of the night when the larger-scale flow collapses. During this 10-h period, the stratified terrain-following flow is characterized by a three-layer structure, consisting of a thin surface boundary layer of a few metres depth on the valley floor, a deeper boundary layer corresponding to the larger-scale flow, and an intermediate transition layer with significant wind-directional shear and possible advection of lee turbulence that is generated even for the gentle topography of our study. The flow in the valley is often modulated by oscillations with a typical period of 10 min. Cold events with smaller turbulent intensity and duration of tens of minutes move through the observational domain throughout the terrain-following period. One of these events is examined in detail.     

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。     

Numerical simulations of stratiform boundary-layer clouds on the meso-γ-scale. Part II: The influence of a step change in surface roughness and surface temperature

A higher order closure mesoscale model is used to study the influence of different surface properties on stratiform boundary-layer clouds. The model is hydrostatic, has a terrain-following coordinate system and a sub-grid scale condensation scheme. It also has a radiation parameterisation for shortwave and longwave radiation in order to calculate radiative cooling/heating. The simulations show the effects on a cloud field when cool or cold air is advected over warm water, the possible influence of local circulation systems on cloud fields in situations with weak synoptic forcing and the influence on a cloud field by growing internal boundary layers. Some of the results are compared with simpler physical models, and limitations in those are demonstrated.     

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。     

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.     

环境风场对地形对流云发展的影响

通过一个带地形处理的二维弹性对流云数值模式，模拟了斜坡地形上不同的环境风对地形对流云发展的影响。模拟结果表明，环境风场对于地形抬升产生的对流云的发展强度、云体结构以及地面降水等具有重大的影响。当中上层风与爬坡风的方向相反时，环境风切变和中上层风速越大，对流的强度越大；当中上层风和爬坡风方向一致时，环境风切变削弱对流云的最大强度。     

Wind energy estimates by use of a diagnostic model

A diagnostic model is a relatively simple and practical tool for modeling the wind flow of the boundary layer in complex terrain. The model begins with a wind analysis based on available surface wind reports and geostrophic winds (computed from pressure data). The height of the boundary layer top (upper surface of the computational domain) is prescribed to fit local conditions. Using the continuity equation in terrain-following coordinates, the winds at mesh points are adjusted to produce nondivergence while maintaining the original vertical component of vorticity. The method of computing the nondivergent winds uses direct alterations. This method may be useful for other modeling purposes and will be described. Data for a long period (usually a year) are analyzed to obtain eigenvectors and the associated time series of their coefficients at each observation time. The model is run only for the five or six eigenvectors that explain most of the variance. The wind field at any particular time is reconstructed from the eigenvector solutions and their appropriate coefficients. Comparisons of model results with measured winds at sites representing different types of terrain will be shown. The accuracy and economy of the model make it a useful tool for estimating wind energy and also for giving wind fields for low-level diffusion models.     

Numerical simulations of stratiform boundary-layer clouds on the meso-γ-scale. Part I: The influence of terrain height differences

A higher order closure mesoscale model is used to study the influence of terrain height differences on the meso--scale on stratiform boundary-layer clouds. The model is hydrostatic, has a terrain-following coordinate system and a sub-grid scale condensation scheme. It also has a radiation parameterisation for shortwave and longwave radiation in order to calculate radiative cooling/heating. The simulations show that the cloud base height variations induced by the terrain can be much larger than motivated by terrain height variations alone. It is also shown how this behavior is dependent on upstream boundary-layer conditions and/or changes in the turbulence field. Other features studied include the wave in the lee of a ridge/hill and the associated lifting of the cloud base. The results are compared with some simpler physical models, and limitations in those models are demonstrated.