A simple gravity wave drag parametrization for use in medium‐range weather forecast models

Abstract

A simple gravity wave drag parametriiation over mountainous terrain is tested for its ability to reduce the systematic errors of medium‐range weather forecasts. Following Boer et al. (1984), this parametrization is a function of the low‐level wind speed and stability, the local Froude number, and the variance of the subgrid‐scale orographie features.

A comparison study of ten 7‐day forecasts obtained with envelope orography, wave drag or standard orography, shows that wave drag is as effective as envelope orography in reducing the systematic errors. A further comparison where the combined effects of the wave drag and that of a complementary enhanced orography (that is one that includes only the subgrid‐scale elements not treated separately by wave drag) are taken into account shows this latter approach to be the most promising in reducing orographically‐related systematic errors.     

GRAPES中地形重力波拖曳物理过程的引进和应用试验

在中国新一代全球中期/区域中尺度同化与预报系统(GRAPES)模式中引进了ECMWF地形重力波拖曳物理过程,填补了GRAPES全球中期数值预报系统中物理过程的空白。重新计算了地形重力波过程需要的地形静态资料数据,并与原ECMWF模式的地形静态参数进行了对比分析,验证了模式地形参数的正确性。利用GRAPES模式,进行了地形重力波拖曳物理过程影响的敏感性数值试验;结果表明:引进地形重力波拖曳过程以后,在存在大地形的区域,风场会发生变化,当纬向风遇到青藏高原时,一部分气流会产生爬坡效应而越过高原,使高原上空的西风气流减弱;另一部分气流会绕过高原,在高原的南侧产生绕流;随着模式积分时间的延长,风场变化会越来越明显,地形越复杂,风场的变化也越复杂;连续的模式积分试验结果显示,引进地形重力波过程,可以延长GRAPES模式的可用预报时效,提高了全球形势预报的准确率。通过对一次降水过程的模拟,对地形重力波过程影响降水预报的原因进行了简单分析。结果显示:引进地形重力波拖曳过程后,改变了大气流场的分布,使预报的流场更接近于大气真实状态,从而提高了降水预报的准确率。     

青藏高原地形重力波拖曳的初步分析及数值模拟研究

针对目前对青藏高原大地形激发的重力波拖曳相关问题还不十分清楚,在GRAPES_Meso模式中引入次网格地形重力波拖曳参数化方案,通过数值试验初步研究了青藏高原地区次网格地形重力波拖曳的一些相关参数,结果指出:(1)沿30°N地形重力波拖曳的垂直分布显示,阻塞拖曳主要存在于模式的低层(第1—5层),重力波拖曳主要存在于模式的第5—10层;从水平分布看,模式第3层以阻塞拖曳为主,主要位于青藏高原边缘地区,阻塞拖曳大值区沿喜马拉雅山脉走向和青藏高原东坡;模式第5层以重力波拖曳为主,主要位于青藏高原东部地区和云贵高原的北部边缘。(2)弗劳德数和气流绕流高度分析表明,在青藏高原喜马拉雅山脉一带和高原东部边缘地区,气流爬坡能力强,同时在这一地区绕流高度最高;弗劳德数越大的地区绕流高度距离地表越高。(3)采用次网格地形重力波拖曳参数化方案后,对于低层和高层地形重力波破碎的发生有更准确的描述,地形重力波是向上垂直传播的。(4)个例和批量试验检验结果表明,采用次网格地形重力波拖曳参数化方案对于风场和降水模拟有正效果,提高了模式预报的准确率。     

Surface pressure distribution and pressure drag on mountains

Summary A mesoscale numerical model is used to compute the different components of the pressure drag on mountains, i.e.: form drag, wave drag, hydrostatic drag, and total pressure drag, for stable stratification. The Froude number is chosen so that non-breaking lee-waves evolve.The paper explains how the different parts of the drag are computed from the numerical results and how they form part of the horizontal momentum budget.For a single mountain the drag from the evolving stationary solution is compared to the wave drag from linear inviscid theory. Wave drag turns out to be about one third of the value expected from linear theory, and nonlinear interaction between wave and form drag is found. Wave drag is responsible for about 75% of the total drag if blocking is negligible.For two obstacles with varying distance the wave drag in the stationary solution varies between 5% and 30% of the value from linear theory due to partial cancellation between the lee-waves from the two mountains.Finally in an instationary simulation the passage of a cold air mass over a mountain and the respective drag components have been computed. 1500 m above the crestline of the obstacle wave drag is only 10% to 30% of the total drag.From the present results it seems realistic that wave drag from ALPEX experimental data was only a few percent of the value expected from the surface pressure distribution and from linear theory.With 7 Figures     

一个双波地形重力波拖曳参数化方案

当地形次尺度强迫的作用与显式的经典动力作用效应相当时,地形重力波拖曳力对于环流的维持,以及动量和热量通量输送的动力效应变得十分显著。这种地形次尺度拖曳作用项可通过参数化的方法,在动力方程中加入额外的小项而引入数值模式。目前成熟的地形重力波拖曳参数化方法,如第1代基于线性单波理论的参数化方案;以及侧重考虑了临界层作用等因素对拖曳力的额外贡献的第2代参数化方案,都无法有效表达风速垂直变化引起的波动应力随高度变化的特征。基于上述考虑,本文给出了一个双波参数化方案用于计算地形重力波拖曳中由线性自由传播重力波造成的波动应力的垂直分布。通过二阶WKB近似,它对由风速垂直变化引起的对波动应力的选择性临界层吸收过程和经典的临界层吸收过程做了显式处理;而在不发生临界层吸收现象的地区,则用两个单波同时在垂直方向上进行应力的传播,并利用波饱和标准进行应力耗散。进一步地在真实地形(以大别山地区为个例)条件下的测试结果表明,通过在不同理想风速廓线以及北半球冬季中纬度纬向平均风廓线下对波动应力垂直分布的计算,证明该方案确实能有效地给出应力随高度变化的特征。     

A Two-Wave Scheme for Orographic Gravity Wave Drag Parameterization

When the magnitude of sub-scale ographic forcing is comparable with explicitly ordinary dynamic forcing, the drag effect reduced by ographic gravity wave is to be significant for maintaining dynamic balance of atmospheric circulation, as well as the momentum and energy transport. Such sub-scale ographic forcing should be introduced into numerically atmospheric model by means of drag being parameterized. Furthermore, the currently mature ographic gravity wave drag （OGWD） parameterization, i.e., the so-called first-generation （based on lineal single-wave theoretical framework） or the second-generation drag parameterization （including an important extra forcing by the contribution of critical level absorption）, cannot correctly and effectly describe the vertical profile of wave stress under the influence of ambient wind shearing. Based on aforementioned consideration, a new two-wave scheme was proposed to parameterize the ographic gravity wave drag by means of freely propagating gravity waves. It starts with a second order WKB approximation, and treats the wave stress attenuations caused by either the selective critical level absorption or the classical critical level absorption explicitly; while in the regions where critical levels are absent, it transports the wave stress vertically by two sinusoidal waves and deposits them and then damps them according to the wave saturation criteria. This scheme is thus used to conduct some sample computations over the Dabie Mountain region of East China, as an example. The results showed that the new two-wave scheme is able to model the vertical distribution of the wave stress more realistically.     

Fetch Limited Drag Coefficients

Measurements made at a tower located 2 km off the coast of Denmark inshallow water during the Risø Air Sea Experiment (RASEX) are analyzedto investigate the behaviour of the drag coefficient in the coastal zone.For a given wind speed, the drag coefficient is larger during conditions ofshort fetch (2-5 km) off-shore flow with younger growing waves than it isfor longer fetch (15-25 km) on-shore flow. For the strongest on-shorewinds, wave breaking enhances the drag coefficient. Variation of the neutral drag coefficient in RASEX is dominated byvariation of wave age, frequency bandwidth of the wave spectra and windspeed. The frequency bandwidth is proportional to the broadness of the waveheight spectra and is largest during conditions of light wind speeds. Usingthe RASEX data, simple models of the drag coefficient and roughness length are developed in terms of wind speed, wave age and bandwidth. An off-shoreflow model of the drag coefficient in terms of nondimensional fetch isdeveloped for situations when the wave state is not known.     

1979—2013年ERA-Interim资料的青藏高原低涡活动特征分析

为了更好地了解青藏高原多尺度地形的动力作用,并为改良数值模式中地形的表示方法奠定基础,通过采用2010年青藏高原西南部6个地面台站的观测资料以及4种不同分辨率的分析(再分析)资料,分别估算了冈底斯山及整个青藏高原主体范围内的地表气压拖曳,得出了青藏高原可能存在的拖曳类型,并且分析了青藏高原气压拖曳的一些特征。得出如下主要结论:由罗斯贝波产生的波动拖曳作为行星尺度的拖曳对青藏高原地区总拖曳的贡献最大;同时,青藏高原范围内存在着大量与天气过程密切相关的天气尺度的拖曳;对于冈底斯山对气流的中尺度动力作用的进一步分析可知,夏季基本全为气流分离,冬季500 hPa以下为气流分离,500—200 hPa为气流分离和波动破碎的混合区,而200 hPa以上的平流层则为重力波的产生及其破碎区域;冈底斯山地区的地表气压拖曳主要集中在3000—5000 m高度,并且,冈底斯山总拖曳的方向近乎与山脊垂直;地表气压和地形高度资料的分辨率越高,所能分辨出的更小波长的气压拖曳也越多,估算出的高原主体范围内的拖曳值也越大;变压梯度和地形梯度是影响气压拖曳的基本因子,但地形梯度对拖曳的影响最终是通过气压梯度来实现的。     

Impact of waves on the sea drag: measurements in the Baltic sea and a model interpretation

Measurements from the Baltic Sea and a wind-over-wave coupled model are used to study the wave impact on the sea drag. The study has been carried out for different wave conditions, namely a pure wind-sea, following-swell/ mixed sea and cross-swell/ mixed sea. Measurements reveal the fact that the sea drag is dependent on the sea-state. In stationary conditions and in the absence of severe cross-swell, swell reduces drag compared to wind-sea at the same wind speed. The cross-swell enhances the drag as compared to the following-swell case and the magnitude of the drag coefficient is increased with increasing the angle of swell propagation to the wind. It is shown that the agreement between the model results and measurements is good for pure wind-sea and stationary mixed-sea cases. Discrepancies occur at light winds, where most of the data represent pure swell conditions. During these pure swell conditions the data are characterized by a large variation of the drag coefficient. The variation is caused by mesoscale variability in the stress co-spectra, wind-cross-swell effects and nonstationarity in the wave and wind fields not represented in the model.     

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     

One-dimensional theory of the wave boundary layer

Results obtained in a 2-D modeling of the statistical structure of the wave boundary layer (WBL) are used for elaboration of the general approach to 1-D modeling taking into account the spectral properties of wave drag for an arbitrary wave field. In the case of the wave field described by the JONSWAP spectrum, the momentum and energy spectral density exchange, vertical profiles of the wave-induced momentum flux and dependence of total roughness parameter and drag coefficient on peak frequency are given. The reasons that the total roughness parameter increases with decreasing fetch are explained. The role of wind waves as an active element of the ocean-atmosphere dynamic system is also discussed.     

青藏高原边坡地形重力波拖曳方案应用的个例研究

本文针对我国西南地区的一次持续性暴雨过程,利用WRF模式引入地形重力波拖曳方案进行120h的模拟,对比结果认为引入地形重力波拖曳的模拟效果总体看来略有优势,并详细分析了不同模拟时段的位势高度场,风场,海平面气压场与降水,其结果认为,引入与未引入地形重力波模拟的差异主要出现在48~72h之后,位势高度场方面,72h之后,在青藏高原主体上引入拖曳方案后的模拟结果相对未引入拖曳方案的结果是正偏差,高原下游地区为负偏差,引入后的模拟相对准确;风场模拟方面同样72h以内的模拟差距较小,72h之后高原上出现一处气旋性涡旋,其中心位置的模拟,引入拖曳方案后的结果相对准确,本次个例中出现的一例西南低涡,两实验都能够较好的模拟出700h Pa的气旋性涡旋;降水模拟的结果表明,在72h之后,对于四川地区降水中心位置的模拟,引入拖曳方案的模拟有所提高,但中心依然过强。这方面主要考虑降水的模拟牵涉模式内部更为复杂的处理过程和其他因素,地形重力波拖曳只是其中一个影响因素而不是核心因素。另外此方案对温度场及海平面气压场模拟的影响不明显。理论上讲引入地形重力波拖曳效应的模拟是物理过程相对更为完善的,在本次个例中模拟效果也略优,但在高原下坡复杂地形处长期应用的模拟效果仍需要更多的测试,将在后续工作中加以完善。      

TESTING DRAG COEFFICIENT APPROACHES BY USING THE BUOY DATA COLLECTED IN MODERATE TO HIGH WIND UNDER FOLLOWING, CROSSING AND OPPOSING SWELL CONDITIONS

Hurricane intensity and track are strongly affected by air-sea interactions. Classified as following swells, crossing swells, and opposing swells, the observed wave height was parameterized by using the 10-m wind speed collected on 5 buoys by the National Buoy Data Center during 13 hurricane events. The path information of these 13 hurricanes was obtained from the National Hurricane Center Best Track (NHC-BT). Results show that the wave height increases exponentially with the 10-m wind speed, and the wave height reaches the maximum value, 11.2 m (8.1 m), when 10-m wind speed is 40 m s-1 under the following and crossing (opposing) swell conditions. We find that the wave steepness (the ratio of wave height to wave length) is proportional to the -2/3 power of the wave age (the ratio of wave phase velocity to 10-m wind speed). The parameterizations of friction velocity and drag coefficient are tested using the buoy data collected in moderate to high wind under following, crossing and opposing swell conditions. A wave age dependent equation for drag coefficient is found more accurate and suggested for future usage in numerical models. Further, these algorithms also suggest that wind-swell orientation needs to be considered to retrieve accurate surface drag under high winds and strong swells.     

Numerical Simulation of Wave Drag during Downslope Windstorms in Different Regions of Russia

The wave drag is considered for downslope windstorms in Novorossiysk, on Novaya Zemlya, and in Pevek. The research is based on the results of numerical simulation with the WRF-ARW model. Special attention is paid to the evaluation of the contribution that wave processes make to the overall dynamics of the phenomenon (based on the ratio of wave and orographic drag) and to the specific features of wave drag for different downslope windstorms.     

ANALYSIS OF SEA-SURFACE DRAG PARAMETERIZATIONS IN OPEN OCEAN CONDITIONS

Data from the Surface Waves and Processes Program (SWAPP) are employed to test current sea-surface drag parameterizations in open ocean conditions. General trends in the data indicate that drag increases with increasing wind speed and wave height, and decreases with wave age. However, scatter in the data limits the use of these parameters and other wave dependent parameterizations for modelling efforts. Upon close inspection, it is found that during the onset of three wind events analyzed separately, each of these parameters correlate well with the drag coefficient. However, the dependence of the drag coefficient on each of these parameters varies markedly from event to event. The disparity appears most closely linked to the turning rate of the wind, indicating that temporal and directional effects may play an important role. A temporal lag of O(4) hours between the rise of the wind and subsequent rise in the drag coefficient is also noticed, further pointing out the complexity of the wind-stress system.     

Drag of the sea surface

It is shown how the drag of the sea surface can be computed from the wind speed and the sea state. The approach, applicable both for fully developed and for developing seas, is based on conservation of momentum in the boundary layer above the sea, which allows one to relate the drag to the properties of the momentum exchange between the sea waves and the atmosphere.The total stress is split into two parts: a turbulent part and a wave-induced part. The former is parameterized in terms of mixing-length theory. The latter is calculated by integration of the wave-induced stress over all wave numbers. Usually, the effective roughness is given in terms of the empirical Charnock relation. Here, it is shown how this relation can be derived from the dynamical balance between turbulent and wave-induced stress. To this end, the non-slip boundary conditions is assigned to the wave surface, and the local roughness parameter is determined by the scale of the molecular sublayer.The formation of the sea drag is then described for fully developed and developing seas and for light to high winds.For the Charnock constant, a value of about 0.018–0.030 is obtained, depending on the wind input, which is well within the range of experimental data.It is shown that gravity-capillary waves with a wavelength less than 5 cm play a minor role in the momentum transfer from wind to waves. Most of the momentum is transferred to decimeter and meter waves, so that the drag of developing seas depends crucially on the form of the wave spectrum in the corresponding high wavenumber range.The dependence of the drag on wave age depends sensitively on the dependence of this high wavenumbertail on wave age. If the tail is wave-age independent, the sea drag appears to be virtually independent of wave age. If the tail depends on wave age, the drag also does. There is contradictory evidence as to the actual dependence. Therefore, additional experiments are needed.The investigation was in part supported by the Netherlands Geosciences Foundation (GOA) with financial aid from the Netherlands Organization for Scientific Research (NWO).     

包络地形和重力波拖曳对区域气候模拟效果的影响

用NCAR区域气候模式(RegCM2)的数值试验，研究了包络地形和地形重力波拖曳作用对1991年5、6月份中国区域内气候模拟效果的影响。通过试验结果的对比分析发现，在模式中引入地形重力波拖曳作用可在一定程度上改善模式对气候系统和要素的模拟效果，使模拟结果更符合气候实况。包络地形对模拟结果也有一定的改善，但对于细网格的区域气候模式(RCM)来说，其效果不如重力波拖曳明显。不论是地形重力波拖曳还是包络地形，在模式积分的初期，它们的作用并不明显，随着积分时间的增长，它们对模拟结果的影响程度增大。     

对流云街激发的重力波和波动阻力

大气边界层中的对流活动,可以在其上部稳定层中激发出重力波,并引起垂直动量输送,影响到对流层和平流层中的动量平衡过程.从二层模式中大气波动方程的线性解出发,得出了对流云街激发的重力波波阻解析表达式,并讨论了大气条件对波阻的影响.这些分析可有助于大气环流模式(GCM)中此类重力波波阻参数化表达式的建立和改进.     

包络地形和重力波拖曳对气候模拟效果的影响

该文用Nju-PσM的数值试验, 研究了包络地形和地形重力波拖曳作用对7月气候模拟效果的影响.通过试验结果的对比分析, 发现包络地形和重力波拖曳作用都可在一定程度上改善模式的模拟性能, 使模拟结果更符合气候实况.