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1.
基于2 km分辨率的ARW-WRF数值模拟资料,讨论了台风"珍珠"(2006)螺旋雨带中对流单体及内雨带的发展机制。结果表明:模式很好地再现了台风的路径和强度。作为雨带中仅仅存在于眼壁外侧的内雨带,其传播机制与重力波、涡旋Rossby波及混合波没有联系,其可能发展机制仅与低层出流、水平风场和变形场有关。低层出流使得内雨带径向向外运动,而低层的水平风场和变形场使其形成螺旋结构。同时,就螺旋雨带中精细对流单体的发展而言,涡度收支方程定量分析表明,其主要通过两种方式获得垂直涡度:水平涡度倾斜为垂直涡度;上升运动拉伸垂直涡度。随着平流输送,对流单体在眼壁附近合并和汇聚。  相似文献   

2.
Finescale spiral rainbands associated with Typhoon Rananim(2004)with the band length ranging from 10 to nearly 100 km and band width varying from 5 to 15 km are simulated using the Fifth-Generation NCAR/Penn State Mesoscale Model(MM5).The finescale rainbands have two types:one intersecting the eyewall and causing damaging wind streaks,and the other distributed azimuthally along the inner edge of the eyewall with a relatively short lifetime.The formation of the high-velocity wind streaks results from the interaction of the azimuthal flow with the banded vertical vorticity structure triggered by tilting of the horizontal vorticity.The vertical advection of azimuthal momentum also leads to acceleration of tangential flow at a relatively high altitude.The evolution and structures of the bands are also examined in this study. Further investigation suggests that the boundary inflection points are related tightly to the development of the finescale rainbands,consistent with previous findings using simple symmetric models.In particular,the presence of the level of inflow reversal in the boundary layer is a crucial factor controlling the formation of these bands.The near-surface wavy peaks of vertical vorticity always follow the inflection points in radial flow.The mesoscale vortices and associated convective updrafts in the eyewall are considered to strengthen the activity of finescale bands,and the updrafts can trigger the formation of the bands as they reside in the environment with inflow reversal in the boundary layer.  相似文献   

3.
Multisatellite data is used to analyze the characteristics of three eyewall replacement cycles (ERCs) during the lifetime of Typhoon Muifa (1109). Spiral rainbands evolutions, concentric eyewall (CE) structure modes, CE durations, and intensity changes are discussed in detail. In addition, an ERC evolution model of Typhoon Muifa is given. There are four main findings. (1) The outer spiral rainband joins end to end to form the outer eyewall after it disconnects from the original (inner) eyewall. The inner eyewall weakens as the outer eyewall becomes axisymmetric and is intensified. The contraction of the outer eyewall causes the inner eyewall to dissipate rapidly. Finally, the ERC ends with an annular eyewall or spiral rainbands. (2) Although the CE duration times of Typhoon Muifa’s three ERCs covered a large range, the CE structures were all maintained for approximately 5 h from the formation of the axisymmetric outer eyewall to the end of the cycle. (3) There is no obvious precipitation reflectivity in the eye or moat region for the subsidence flow. The convection within the two eyewalls is organized as a radially outward slope with increasing height. (4) Typhoon intensity estimation results based on ADT may not explain the intensity variations associated with ERC correctly, while the typhoon’s warm core data retrieved from AMSU-A works well.  相似文献   

4.
超强台风"韦帕"(Wipha)是2007年登陆中国大陆最强的台风,在浙江省造成了特大暴雨。利用宁波和舟山双多普勒天气雷达同步观测资料,对"韦帕"的两条螺旋雨带进行了双雷达三维风场反演;并综合利用组网雷达拼图数据等资料,对螺旋雨带的三维精细结构进行了分析。研究表明:(1)两条螺旋雨带的三维结构有很多相似之处。螺旋雨带内部低层有多个强回波区,水平速度大值区主要分布在强回波带上;强回波带的低层有较强的上升气流,最强上升气流超过4 m/s。在螺旋雨带中存在多个辐合辐散对、上升下沉气流对,这对于螺旋雨带的维持和进一步发展具有重要作用。在沿着台风中心的垂直剖面内,螺旋雨带内部的强回波区向雨带外侧倾斜。雨带外侧2 km高度以下的低层有较强的内流,最大值为5 m/s;雨带内侧有较强的外流,2 km高度以上均受外流控制;内流和外流在雨带中部低层汇合抬升。切向速度的强中心出现在3 km高度,速度值随高度增加而逐渐减小。(2)两个时段的螺旋雨带也存在差异。前一个时段的螺旋雨带对流发展更旺盛,45 dBZ的回波高度为4.8 km,而后一个时段的螺旋雨带45 dBZ的回波高度仅3.2 km。垂直剖面内,前一个时刻螺旋雨带低层辐合更强,最强辐合值超过-15×10^-4s^-1,正是由于低层的强辐合和充足的水汽供应,才使得雨带内部中低层的回波发展旺盛。  相似文献   

5.
Based on the data(including radius of maximum winds) from the JTWC(Joint Typhoon Warning Center),the tropical cyclones(TCs) radii of the outermost closed isobar, TCs best tracks from Shanghai Typhoon Institute and the Black Body Temperature(TBB) of the Japanese geostationary meteorological satellite M1 TR IR1, and combining13 tropical cyclones which landed in China again after visiting the island of Taiwan during the period from 2001 to2010, we analyzed the relationship between the number of convective cores within TC circulation and the intensity of TC with the method of convective-stratiform technique(CST) and statistical and composite analysis. The results are shown as follows:(1) The number of convective cores in the entire TC circulation is well corresponding with the outer spiral rainbands and the density of convective cores in the inner core area increases(decreases) generally with increasing(decreasing) TC intensity. At the same time, the number of convective cores within the outer spiral rainbands is more than that within the inner core and does not change much with the TC intensity. However, the density of convective cores within the outer spiral rainbands is lower than that within the inner core.(2) The relationship described above is sensitive to landing location to some extent but not sensitive to the structure of TC.(3) The average value of TBB in the inner core area increases(decreases) generally with increasing(decreasing) of TC intensity, which is also sensitive to landing situation to some extent. At the same time, the average value of TBB within the outer spiral rainbands is close to that within the entire TC circulation, and both of them are more than that within the inner core. However, they do not reflect TC intensity change significantly.(4) The results of statistical composite based on convective cores and TBB are complementary with each other, so a combination of both can reflect the relationship between TC rainbands and TC intensity much better.  相似文献   

6.
The impact of cloud microphysical processes on the simulated intensity and track of Typhoon Rananim is discussed and analyzed in the second part of this study.The results indicate that when the cooling effect due to evaporation of rain water is excluded,the simulated 36-h maximum surface wind speed of Typhoon Rananim is about 7 m s-1 greater than that from all other experiments; however,the typhoon landfall location has the biggest bias of about 150 km against the control experiment.The simulated strong outer rainbands and the vertical shear of the environmental flow are unfavorable for the deepening and maintenance of the typhoon and result in its intensity loss near the landfall.It is the cloud microphysical processes that strengthen and create the outer spiral rainbands,which then increase the local convergence away from the typhoon center and prevent more moisture and energy transport to the inner core of the typhoon.The developed outer rainbands are supposed to bring dry and cold air mass from the middle troposphere to the planetary boundary layer (PBL).The other branch of the cold airflow comes from the evaporation of rain water itself in the PBL while the droplets are falling.Thus,the cut-off of the warm and moist air to the inner core and the invasion of cold and dry air to the eyewall region are expected to bring about the intensity reduction of the modeled typhoon.Therefore,the deepening and maintenance of Typhoon Rananim during its landing are better simulated through the reduction of these two kinds of model errors.  相似文献   

7.
Typhoon Rananim (2004) was one of the severest typhoons landfalling the Chinese mainland from 1996 to 2004. It brought serious damage and induced prodigious economical loss. Using a new generation of mesoscale model, named the Weather Research and Forecasting (WRF) modeling system, with 1.667 km grid horizontal spacing on the finest nested mesh, Rananim was successfully simulated in terms of track, intensity, eye, eyewall, and spiral rainbands. We compared the structures of Rananim to those of hurricanes in previous studies and observations to assess the validity of simulation. The three-dimensional (3D) dynamic and thermal structures of eye and eyewall were studied based on the simulated results. The focus was investigation of the characteristics of the vortex Rossby waves in the inner-core region. We found that the Rossby vortex waves propagate azimuthally upwind against the azimuthal mean tangential flow around the eyewall, and their period was longer than that of an air parcel moving within the azimuthal mean tangential flow. They also propagated outward against the boundary layer inflow of the azimuthal mean vortex. Futhermore, we studied the connection between the spiral potential vorticity (PV) bands and spiral rainbands, and found that the vortex Rossby waves played an important role in the formation process of spiral rainbands.  相似文献   

8.
The impact of cloud microphysical processes on the simulated intensity and track of Typhoon Rananim is discussed and analyzed in the second part of this study. The results indicate that when the cooling effect due to evaporation of rain water is excluded, the simulated 36-h maximum surface wind speed of Typhoon Rananim is about 7 m s−1 greater than that from all other experiments; however, the typhoon landfall location has the biggest bias of about 150 km against the control experiment. The simulated strong outer rainbands and the vertical shear of the environmental flow are unfavorable for the deepening and maintenance of the typhoon and result in its intensity loss near the landfall. It is the cloud microphysical processes that strengthen and create the outer spiral rainbands, which then increase the local convergence away from the typhoon center and prevent more moisture and energy transport to the inner core of the typhoon. The developed outer rainbands are supposed to bring dry and cold air mass from the middle troposphere to the planetary boundary layer (PBL). The other branch of the cold airflow comes from the evaporation of rain water itself in the PBL while the droplets are falling. Thus, the cut-off of the warm and moist air to the inner core and the invasion of cold and dry air to the eyewall region are expected to bring about the intensity reduction of the modeled typhoon. Therefore, the deepening and maintenance of Typhoon Rananim during its landing are better simulated through the reduction of these two kinds of model errors.  相似文献   

9.
The evolution of spiral-band-like structures triggered by asymmetric heating in three tropical-cyclone-like vortices of different intensities is examined using the Three-Dimensional Vortex Perturbation Analyzer and Simulator (3DVPAS) model. To simulate the spiral bands, asymmetric thermal perturbations are imposed on the radius of maximum wind (RMW) of vortices, which can be considered as the location near the eyewall of real tropical cyclones (TCs). All the three vortices experience a hydrostatic adjustment after the introduction of thermal asymmetries. It takes more time for weaker and stable vortices to finish such a process. The spiral-band-like structures, especially those distant from the vortex centers, form and evolve accompanying this process. In the quasi-balance state, the spiral bands are gradually concentrated to the inner core, the wave behavior of which resembles the features of classic vortex Rossby (VR) waves. The unstable vortices regain nonhydrostatic features after the quasi-balance stage. The spiral bands further from the vortex center, similar to distant spiral bands in real TCs, form and maintain more easily in the moderate basic-state vortex, satisfying the conditions of barotropic instability. The widest radial extent and longest-lived distant bands always exist in weak and stable vortices. This study represents an attempt to determine the role of TC intensity and stability in the formation and evolution of spiral bands via hydrostatic balance adjustment, and provides some valuable insights into the formation of distant spiral rainbands.  相似文献   

10.
云微物理过程是影响台风降水数值模拟的关键过程。利用华东中尺度模式系统,选取Thompson与CLR两种微物理参数化方案对台风“利奇马”进行数值模拟,对比观测、卫星资料,评估两个微物理参数化方案对台风模拟的影响,结果表明:相比于Thompson方案,CLR方案对台风“利奇马”的模拟在登陆后的路径、强度、降水明显更接近观测;Thompson方案在距离台风中心约100 km形成较强的螺旋雨带,而CLR方案在距离台风中心150 km左右的位置形成了较弱的螺旋雨带。进一步的分析表明,CLR方案模拟出的外围雨带距离台风中心的距离更远,是由于CLR方案中冰、霰等冰相态水凝物下落速度更小,更有可能被推送到距离台风中心更远的位置,从而形成不同的雨带分布。   相似文献   

11.
The vertical structure and microphysics of Typhoon Kompasu that caused a lot of damage associated with strong winds and heavy rainfall over the Seoul metropolitan area on 1~2 September 2010 were examined primarily from wind profiler measurements. Four different periods that represent a stratiform, outer rainband, inner rainband, and eyewall region during passage of Typhoon Kompasu from 1200 to 2300 UTC 1 September were selected based on bright band intensities and vertical profiles of radar reflectivities and Doppler velocities. The bright band signatures observed in all of these periods indicated that the structure of Kompasu was basically stratiform in a weakening phase. Maximum rainfall rates up to 50 mm hr?1 at the surface and mean wind speeds greater than 30 m s?1 in the 2–4 km layer were observed in the eyewall region. Unlike the other regions that showed nearly zero vertical air motions or weak downdrafts below a melting layer, a mean updraft of ~1 m s?1 was analyzed only in the eyewall region, which suggests that the updrafts may have enhanced drop growth that led to increasing surface rainfall rates. For each region, the vertical mean characteristics of rainfall parameters retrieved from wind profiler spectra below the melting layer were also examined. The rain properties between the inner and outer rainband were similar although they were apart with a distance of more than 100 km (> 2 hrs in time). The averaged mass-weighted mean diameters within the rainbands were larger than those in the stratiform and eyewall regions. A weaker bright band in the eyewall region suggests the presence of a relatively larger number of rimed particles associated with the updrafts around the melting layer. A stronger bright band was present in the rainbands, which indicates more active aggregation right above the melting layer.  相似文献   

12.
Forecasting the rapid intensification of tropical cyclones over offshore areas remains difficult. In this article, the Weather Research and Forecast (WRF) model was used to study the rapid intensification of Typhoon Haikui (1211) off the shore of China. After successful simulation of the intensity change and track of the typhoon, the model output was further analyzed to determine the mechanism of the rapid change in intensity. The results indicated that a remarkable increase in low-level moisture transportation toward the inner core, favorable large-scale background field with low-level convergence, and high-level divergence played key roles in the rapid intensification of Typhoon Haikui in which high-level divergence could be used as an indicator for the rapid intensity change of Typhoon Haikui approximately 6 h in advance. An analysis of the typhoon structure revealed that Typhoon Haikui was structurally symmetric during the rapid intensification and the range of the eyewall was small in the low level but extended outward in the high level. In addition, the vertically ascending motion, the radial and tangential along wind speeds increased with increasing typhoon intensity, especially during the process of rapid intensification. Furthermore, the intensity of the warm core of the typhoon increased during the intensification process with the warm core extending outward and toward the lower layer. All of the above structural changes contributed to the maintenance and development of typhoon intensity.  相似文献   

13.
Idealized numerical simulations are conducted in this study to comparatively investigate the characteristics of the stratiform sector in the outer rainbands of tropical cyclones(TCs)in lower-and upper-layer vertical wind shear(VWS)with moderate magnitude.Consistent with the results in previous studies,the outer rainband stratiform sector of the TCs simulated in both experiments is generally located downshear left.Upper-layer VWS tends to produce stronger asymmetric outflow at upper levels in the downshear-left quadrant than lower-layer shear.This stronger asymmetric outflow transports more water vapor radially outward from the inner core to the outer core at upper levels in the downshear-left quadrant in the upper-layer shear experiment.More depositional growth of both graupel and cloud ice thus occurs downshear left in upper layers in the outer core,yielding more diabatic heating and stronger upward motions,particularly in the stratiformdominated part of the stratiform sector in the upper-layer shear experiment.Resultingly,a better-organized stratiform sector in the outer rainbands is found in the upper-layer VWS experiment than in the lower-layer VWS experiment.The diabatic heating associated with the stratiform sector produces strong midlevel outflow on the radially inward side of,and weak midlevel inflow on the radially outward side of,the heating core,with lower-level inflow beneath the midlevel outflow and upper-level inflow above.The upper-layer VWS tends to produce a deeper asymmetric inflow layer in the outer rainband stratiform sector,with more significant lower-level inflow and tangential jets in the upper-layer VWS experiment.  相似文献   

14.
Radar observations of the strong Typhoon Bilis (2000) are unique for investigating the effect of Taiwan high orography on the mesoscale structures of storm system in the vicinity of southeastern Taiwan. Typhoon Bilis was the first tropical storm, which possessed the double eyewall feature observed by Doppler radar over the Taiwan area. The inner eyewall exhibited an approximately circular shape with a diameter of 20?km. Convections associated with the storm were cyclonically and radially outward propagated, with the linear aspect in the right flank of the system and counterclockwise and spiral migration in the left flank, maintaining the development of the outer eyewall. The low-level maximum Doppler winds in the left and right flanks relative to the typhoon movement were comparable, owing to a prominent confluence in the left flank. The prominent confluent zone was constructed by two wind fields, the northwesterly from the inner circulation of the typhoon and the outer circulation in the streamline analysis. The replacement of maximum wind between the inner and outer eyewalls, extending from low levels to middle levels in the left flank of the storm, was a clear model for the examination of the significance of the orographic effect on a severe typhoon. A conceptual model for a case of super typhoon under the influence of Taiwan high terrain was constructed.  相似文献   

15.
在分析云微物理参数化对云结构和降水特征的影响的基础上,研究云微物理参数化过程对台风"云娜"强度与路径的影响.结果表明:云微物理过程对台风强度和路径有一定影响,其中不考虑雨水蒸发冷却效应后,比其他试验最终地面最大风速强7 m/s以上,但此时登陆地点误差最大,与对照试验偏离150 km左右.我们还从螺旋雨带结构变化及环境风切变影响角度分析台风临近登陆时强度模拟减弱的原因,发现过强的外围螺旋雨带以及环境风场垂直切变对于台风的加深、维持是不利的,他们可能会造成"云娜"临近登陆时强度的下降.不难看出,云微物理过程可以加强甚至产生外螺旋雨带,当外围雨带发展加强之后,可以引起局地辐合强度增强,从而限制了大量水汽和能量向台风内核输送,从而会导致台风强度下降.此外,外围螺旋雨带的发展,还可以从对流层中层带来干冷空气入侵行星边界层;而当入流边界层中雨水下落时,其自身的蒸发也会使周围气块温度下降;这些干冷气团在入流气流的输送下进入台风内核,从而对云墙产生了"冷侵蚀",最终引起台风强度下降.因此,减小上述两方面的模拟误差,应能改进台风"云娜"登陆过程中强度的模拟效果.  相似文献   

16.
By using the Advanced Regional Eta-coordinate Model (AREM),the basic structure and cloud features of Typhoon Rananim are simulated and verified against observations.Five sets of experiments are designed to investigate the effects of the cloud microphysical processes on the model cloud structure and precipitation features.The importance of the ice-phase microphysics,the cooling effect related to microphysical characteristics change,and the influence of terminal velocity of graupel are examined.The results indicate that the cloud microphysical processes impact more on the cloud development and precipitation features of the typhoon than on its intensity and track.Big differences in the distribution pattern and content of hydrometeors,and types and amount of rainfall occur in the five experiments,resulting in different heating and cooling effects.The largest difference of 24-h rain rate reaches 52.5 mm h-1.The results are summarized as follows:1) when the cooling effect due to the evaporation of rain water is excluded,updrafts in the typhoon's inner core are the strongest with the maximum vertical velocity of-19 Pa s-1 and rain water and graupel grow most dominantly with their mixing ratios increased by 1.8 and 2.5 g kg-1,respectively,compared with the control experiment; 2) the melting of snow and graupel affects the growth of rain water mainly in the spiral rainbands,but much less significantly in the eyewall area; 3) the warm cloud microphysical process produces the smallest rainfall area and the largest percentage of convective precipitation (63.19%),while the largest rainfall area and the smallest percentage of convective precipitation (48.85%) are generated when the terminal velocity of graupel is weakened by half.  相似文献   

17.
The Advanced Weather Research and Forecasting Model (ARW) is used to simulate the local heavy rainstorm process caused by Typhoon Matsa over the northeastern coast of Zhejiang Province in 2005. The results show that the rainstorm was caused mainly by the secondary spiral rainband of the Stationary Band Complex (SBC) structure. Within the secondary spiral rainband there was a strong meso-β-scale convergence line generated in the boundary layer, corresponding very well to the Doppler radar echo band. The convergence line comprised several smaller convergence centers, and all of these convergence columns inclined outward. Along the convergence line there was precipitation greater than 20 mm occurring during the following one hour. During the heavy rainstorm process, the Doppler radar echo band, convergence line, and the precipitation amount during the following one hour, moved and evolved synchronously. Further study reveals that the vertical shear of radial wind and the low-level jet of tangential wind contributed to the genesis and development of the convergence columns. The combined effect of the ascending leg of the clockwise secondary circulation of radial wind and the favorable environment of the entrance region of the low-level jet of tangential wind further strengthened the convergence. The warm, moist inflow in the lower levels was brought in by the inflows of the clockwise secondary circulation and uplifted intensely at the effect of convergence. In the convectively instable environment, strong convection was triggered to produce the heavy rainstorm.  相似文献   

18.
The three-dimensional structures and ingredients leading to extremely heavy precipitation associated with the passage of Typhoon Morakot (2009) over the Central Mountain Range (CMR) of Taiwan are investigated. Using a numerical model, the track, track deflection, characteristic rainbands, and precipitation patterns and maxima are successfully reproduced after verification against observational data. The high-level outward flow of the secondary circulation around the eyewall is not very clear even during Morakot’s strongest stage. In the control case, the eyewall collapses within 5 h after landfall that is closely associated with limited precipitation along the track after landfall. During the early stage of landfall, the deep convection on the windward (west) side of the CMR helps strengthening the secondary circulation. A quantitative comparison of total precipitable water, translation speed, and orographic lifting among 12 typhoons in recent years causing large accumulated rainfall in Taiwan shows that the abundant water vapor around Taiwan outweighs translation speed and orographic lifting in resulting in the record-breaking precipitation. It is found that the major processes leading to strong upward motion in the extremely heavy precipitation during 0000 UTC 8 August–0000 UTC 9 August are initiated by orographic lifting by CMR.  相似文献   

19.
To better understand how severe storms form and evolve in the outer rainbands of typhoons, in this study, we investigate the evolutionary characteristics and possible formation mechanisms for severe storms in the rainbands of Typhoon Mujigae, which occurred during 2–5 October 2015, based on the NCEP–NCAR reanalysis data, conventional observations, and Doppler radar data. For the rainbands far from the inner core (eye and eyewall) of Mujigae (distance of approximately 70–800 km), wind speed first increased with the radius expanding from the inner core, and then decreased as the radius continued to expand. The Rankine Vortex Model was used to explore such variations in wind speed. The areas of strong stormy rainbands were mainly located in the northeast quadrant of Mujigae, and overlapped with the areas of high winds within approximately 300–550 km away from the inner core, where the strong winds were conducive to the development of strong storms. A severe convective cell in the rainbands developed into waterspout at approximately 500 km to the northeast of the inner core, when Mujigae was strengthening before it made landfall. Two severe convective cells in the rainbands developed into two tornadoes at approximately 350 km to the northeast of the inner core after Mujigae made landfall. The radar echo bands enhanced to 60 dBZ when mesocyclones occurred in the rainbands and induced tornadoes. The radar echoes gradually weakened after the mesocyclones weakened. The tops of parent clouds of the mesocyclones elevated at first, and then suddenly dropped about 20 min before the tornadoes appeared. Thereby, the cloud top variation has the potential to be used as an early warning of tornado occurrence.  相似文献   

20.
The impact of different cloud microphysics parameterization schemes on the intensity and structure of the Super-strong Typhoon Rammasun (1409) in 2014 is investigated using the Weather Research and Forecasting model version 3.4 with eight cloud microphysics parameterization schemes. Results indicate that the uncertainty of cloud microphysics schemes results in typhoon forecast uncertainties, which increase with forecast time. Typhoon forecast uncertainty primarily affects intensity predictions, with significant differences in predicted typhoon intensity using the various cloud microphysics schemes. Typhoon forecast uncertainty also affects the predicted typhoon structure. Greater typhoon intensity is accompanied by smaller vortex width, tighter vortex structure, stronger wind in the middle and lower troposphere, greater height of the strong wind region, smaller thickness of the eyewall and the outward extension of the eyewall, and a warmer warm core at upper levels of the eye. The differences among the various cloud microphysics schemes lead to the different amounts and distributions of water vapor and hydrometeors in clouds. Different hydrometeors have different vertical distributions. In the radial direction, the maxima for the various hydrometeors forecast by a single cloud microphysics scheme are collocated with each other and with the center of maximum precipitation. When the hydrometeor concentration is high and hydrometeors exist at lower altitudes, more precipitation often occurs. Both the vertical and horizontal winds are the strongest at the location of maximum precipitation. Results also indicate that typhoon intensities forecast by cloud microphysics schemes containing graupel processes are noticeably greater than those forecast by schemes without graupel processes. Among the eight cloud microphysics schemes investigated, typhoon intensity forecasts using the WRF Single-Moment 6-class and Thompson schemes are the most accurate.  相似文献   

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