Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part I: Theory and Integral Formulae

The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic treatments.Classic integral formulas and their variants are used to formulate solutions for the coupled problems.In the absence of data holes,the total solution is the sum of two integral solutions.One is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity,and its two components(velocity potential and streamfunction) can be constructed by applying Green’s function for Poisson equation in unbounded domain to the divergence and vorticity inside the domain.The other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity,and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the domain.By setting either the velocity potential(or streamfunction) component to zero,the other component of the externally induced solution can be expressed by the imaginary(or real) part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced solution.The streamfunction(or velocity potential) for the externally induced solution can also be expressed by the boundary integral of a double-layer(or singlelayer) density function.In the presence of data holes,the total solution includes a data-hole-induced solution in addition to the above internally and externally induced solutions.     

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part II: Numerical Methods and Test Experiments

Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary(around a data hole) inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes(grid-staggering,local-nesting and piecewise continuous integration) are designed to deal with the singularity of the Green’s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential(or streamfunction) component to zero,the other component of the solution can be computed in two ways:(1) Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.(2) Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting(or piecewise continuous integration),the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point(or along the entire boundary).When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.     

有限区域风速场求解流函数和速度势场的有效方案

流函数和速度势是表示风场的一种变量, 在数值天气预报模式和分析、同化方案中经常使用, 通常可以用风速分量场求解Poisson方程得到。对于有限区域系统, 往往采用差分方法, 但由于存在边界问题, 用计算所得到的流函数和速度势场重建风速场, 在边界附近经常出现明显的偏差。基于差分方法、利用有限区域风速场求解流函数和速度势场的基本方法和特点的分析, 在Arakawa A网格分布的有限区域, 设计了一种用差分方法求解流函数和速度势场的有效方案。在该有效方案中, 通过将有限区域向外扩展二圈, 风速场线性外推, 改进计算边界风速值和边界定解条件的效果; 尽可能使用协调、一致的差分格式, 提高求解精度; 最后利用一种增量订正迭代方法, 迭代2~3次就可以获得令人满意的结果。实例试验的对比、检验显示, 用该方案计算求得的流函数和速度势场重建风速场, 具有非常高的精度。     

Hybrid Methods for Computing the Streamfunction and Velocity Potential for Complex Flow Fields over Mesoscale Domains

Three types of previously used numerical methods are revisited for computing the streamfunction ψ and velocity potential χ from the horizontal velocity v in limited domains. The first type, called the SOR-based method, uses a classical successive over-relaxation(SOR) scheme to compute ψ(or χ) first with an arbitrary boundary condition(BC) and then χ(orψ) with the BC derived from v. The second type, called the spectral method, uses spectral formulations to construct the inner part of(ψ, χ)—the in...     

有限区域流函数和速度势的3种求解方法在分析台风Bilis暴雨增幅中的比较研究

将有限区域流函数、速度势求解中常用的两种张驰法(即理查逊法和加速利布曼法)与调和—余弦谱展开法(H-C法)进行了比较,理论研究表明:H-C法单独考虑边界影响分量,物理意义明确,且不会丢失边界上的天气系统;从计算上看,H-C法重建的风场能精确还原原始风场,且计算效率明显高于两种张驰法,即收敛更快。通过在台风Bilis(0604)暴雨增幅过程诊断中的应用发现,常用的两种张驰迭代方法在求解有限区域流函数和速度势的问题上效果都不是很好,即:用理查逊法和加速利布曼法计算的流函数和速度势重建的风场与原始风场差别较大,不能准确还原原始风场;用H-C法不仅计算效率高,还原的风场与原始风场差异极小,且不受南边界较强的西南季风涌影响,在暴雨增幅前期能较好地反映与暴雨增幅相关的强辐合信号。因此,可用H-C法计算得到的无辐散风和无旋风对有限区域的天气系统进行更深入的动力结构分析。     

用有限区域风速场准确求解流函数和速度势场的方法

流函数和速度势是气象业务和研究中常用于表述风速的一组变量。用有限区域风速场, 使用有限差分方法求解得到的流函数和速度势场重建初始风速场, 由于受区域边界的限制往往有明显的偏差。虽然有许多求解方法的研究, 但是, 至今仍尚未见到一种真正准确的求解计算方案。首先, 介绍用Arakawa A网格和D网格分布的有限区域风速场求解流函数和速度势场的一般有限差分计算方法, 探讨用它们的解重建风速场产生误差的原因。然后, 针对这些原因, 对给定的有限区域, 通过线性外推初始风速场, 扩展求解计算区域, 使用协调、一致的有限差分格式方案, 准确计算求解区域的边界有旋风速、散度风速和速度势的定解边界条件, 以及恰当选择流函数、速度势、涡度和散度等变量的分布网格, 设计了用上述两种网格分布的风速场准确求解流函数、速度势场的方案, 并对其正确性加以证明, 它们可以推广应用于其他Arakawa网格。用实际资料试验同样显示, 方案避免了重建风速场误差的出现, 与初始风速场相比, 全场风速最大偏差精度达到10-12m/s或以上, 在计算机精度造成的计算误差影响范围内。本文的研究很好解决了长期以来用有限区域风速场、 使用有限差分方法无法准确求解流函数和速度势场的问题。     

近40年那曲地区日照时数和风速变化特征

利用那曲地区6个气象站1961—2000年逐日日照时数和风速资料,采用常规统计方法和墨西哥帽小波变换分析那曲地区近40年日照时数和风速的地理分布以及年内、年际、年代际变化规律。主要结果是:那曲大部分地区,年总日照时数大于2550小时,年平均风速大于4m·s-1;近40年那曲地区春季、夏季、秋季、冬季、生长季(5—9月)和年6个时段的日照时数均呈减少趋势;风速冬季呈减少趋势,其它时段呈增加趋势;6个时段的90年代日照和风速都小于80年代;2000—2005年日照时数和风速继续减小的可能性比较大。     

暴雨的多普勒天气雷达速度辐合风场特征

多普勒天气雷达探测大范围强降水时,其多普勒速度回波特征既不同于单纯的暖(冷)平流的特征(S或反S形)也不同于纯粹的大尺度辐合(散)运动特征(弓状), 而是暖(冷)平流和辐合(散) 两种运动相结合的风场(称之为复合风场)所产生的多普勒速度特征.应用天津塘沽新一代天气雷达资料,并结合自动气象站资料和改进的EVAD 技术,分析2005年8月16日发生在海河流域的一次大范围、长时间的强降雨天气过程的多普勒天气雷达资料.结果表明:(1)当低层出现暖平流和辐合运动相结合的复合风场特征时,即多普勒天气雷达速度场产品表现为自雷达中心开始,在同一距离圈上,一侧的零速度线弯向正速度区的顺转程度明显大于另一侧的零速度线弯向负速度区的顺转程度,即负速度区面积大于正速度区的面积时,降水就增强或维持.(2)当低层出现暖平流和辐散运动相结合的复合风场特征时,对应降水减弱或停止.这种对雷达速度场的辐合辐散分析将对大范围强降水的形成、发展、维持和消散具有很好的临近预报指示作用.     

Computing solar heating in a fog layer: a new parameterization

Computation of solar radiation flux within a fog layer is essential during the dissipation stage. A new parameterization of the asymmetry factor g and of the single scattering albedo ω allows the use of a monospectral model (FB), already designed for cloudy layer by Fouquart and Bonnel (1980). This new parameterization is necessary because of the different droplet size distributions existing in clouds and fogs. A calculation method of new g and ω values, in function of the optical thickness δ and of the effective radius r_e of droplet size distribution is proposed.     

最大风速变化特征及再现期极值估算

利用枣庄市1971~2008年各月10 min最大风速资料,对枣庄最大风速统计分析。发现38年中枣庄春季、夏季、秋季、冬季和全年的最大风速都呈下降趋势,年最大风速以每10年1.47 m/s的幅度下降,冬季下降最快,达到每10年降低1.67 m/s,夏季、秋季降低幅度很接近,都小于年平均最大风速降幅,春季最大风速下降最慢,且最大风速极值主要出现在春季。枣庄各月最大风速变化曲线呈递减的"两峰两谷"形。用柯尔莫哥洛夫方法对耿贝尔分布函数进行拟合优度的检验,其显著水平达到0.05,因此利用耿贝尔分布函数估算出枣庄未来若干年的最大风速极值,以满足生产建设规划与设计中对最大风速极值的要求。     

有限区域内球谐展开的误差分析

以500 hPa高度场为例在有限区域内进行球谐函数的展开。结果表明：当纬向截点数L为64,且经圈截点为32时,对应于波数M=L/2=32的球谐展开误差最小。这时对4种有限区域计算的谱展前后的均方根误差都小于2.5位势米（0.04%）,最大绝对误差都小于14位势米（0.23%）。有限区域谱展前后的均方根误差比全球范围的相应值要小2—3位势米,这主要是由于有限区域内纬向格距较小的缘故。     

近53a来祁连山南北坡潜在蒸散量及地表湿润度变化趋势分析

利用祁连山地区15个气象台站1961~2013年月气象资料,计算和分析该地区潜在蒸散量和湿润指数的变化趋势。研究表明:(1)祁连山南北坡潜在蒸散量的年变化表现为单峰型,较大值出现在5~8月,较小值出现在12月至翌年2月。湿润指数从5月开始逐渐增大,南坡7月最大,北坡9月最大,10月开始逐步减小。湿润指数与潜在蒸散量在祁连山地区存在明显的位相差。季节表现均为夏季最大、春秋季次之、冬季最小,潜在蒸散量相邻季节间的波动北坡明显大于南坡,湿润指数则相反;(2)祁连山地区南北坡潜在蒸散量均在波动中呈显著增加趋势,而湿润指数波动中缓慢增加,但变化趋势不明显。潜在蒸散量和湿润指数增加速率均是北坡大于南坡。南北坡潜在蒸散量和湿润指数未来变化趋势总体上将同过去保持一致,且北坡年潜在蒸散量变化趋势强度强于南坡;(3)通过与各气候因子的多元回归分析表明,影响祁连山南北坡湿润指数(潜在蒸散量)的主要因子是降水量(气温),其他气候因子的变化对地表干湿状况起增强或削弱作用。     

多普勒雷达的速度图像特征及其在一次降雪过程中的应用

该文首先介绍了大面积降水的多普勒天气雷达径向速度PPI图像识别技术, 包括:①冷暖平流与大尺度辐合辐散运动叠加的图像特征; ②由零线的朝向和正负速度面积、径向速度值的大小判断风向风速辐合辐散的图像特征, 然后介绍了利用EVAD技术由雷达基数据定量计算大气平均散度和平均垂直速度的方法, 最后应用图像识别技术和EVAD方法对石家庄2004年冬季的一次大面积降雪过程进行了详细分析, 发现:此次大面积降雪过程有明显的辐合辐散图像特征, 径向速度值小, 辐合辐散弱, 始终存在暖平流。另外, 降雪强度和散度、垂直速度关系密切:辐合层厚度加大, 辐散抬高, 则降雪加强; 辐合、辐散层高度降低, 则降雪减弱。同时, 由EVAD技术定量计算的散度和相同时刻由径向速度图像产品定性分析的辐合、辐散基本一致。     

网格计算及其在气象中的应用

网格是近年来最新发展起来的一种计算技术。通过使用一组开放标准与协议,各机构能够通过互联网或内部网访问数据、存储介质和其它异构计算资源,最终将分布在不同地理位置上的网络、数据、计算资源、存储、应用等在内的资源整合成为一个无缝的计算环境。气象以其高计算量、高吞吐量和密集型服务在美国、欧洲、日本等网格应用计划中占有重要的地位。如ECMWF的EcAccess,美国超级计算应用中心的MEAD等。这些计划的实施将有效地聚合分布在不同地理位置上的高性能计算资源与人力资源,实现计算资源和气象数据的共享,为数值预报乃至地球系统模拟提供一个远程的协同攻关环境。     

Developments in national climate change mitigation legislation and strategy

The results are presented from a survey of national legislation and strategies to mitigate climate change covering almost all United Nations member states between 2007 and 2012. This data set is distinguished from the existing literature in its breadth of coverage, its focus on national policies (rather than international pledges), and on the use of objective metrics rather than normative criteria. The focus of the data is limited to national climate legislation and strategies and does not cover subnational or sectoral measures. Climate legislation and strategies are important because they can: enhance incentives for climate mitigation; provide mechanisms for mainstreaming; and provide a focal point for actors. Three broad findings emerge. First, there has been a substantial increase in climate legislation and strategies between 2007 and 2012: 67% of global GHG emissions are now under national climate legislation or strategy compared to 45% in 2007. Second, there are substantial regional effects to the patterns, with most increases in non-Annex I countries, particularly in Asia and Latin America. Third, many more countries have adopted climate strategies than have adopted climate legislation between 2007 and 2012. The article concludes with recommendations for future research.

Policy relevance The increase in climate legislation and strategy is significant. This spread suggests that, at the national level, there is some movement in reshaping climate governance despite the relatively slow pace of global negotiations, although the exact implications of this spread require further research on stringency of actions and their implementation. Asia and Latin America represent the biggest improvements, while OECD countries, which start from a high base, remain relatively stagnant. Implications of regional patterns are further refined by an analysis by emissions, which shows that some areas of low levels of legislation and strategy are also areas of relatively low emissions. A broad trend toward an emphasis on strategies rather than legislation, with the significant exception of China, calls for enhanced research into the practical impact of national non-binding climate strategies versus binding legislation on countries’ actual emissions over time.     

近28a河南主要农业气象灾害及其影响

利用河南1978-2005年农作物受灾面积资料和新中国成立以来的产量资料,分析了河南主要农业气象灾害的变化特征和对农业生产的影响,结果表明,28 a来河南农作物受灾面积呈上升趋势,其阶段性变化为20世纪70年代后期至80年代前期较少,80年代中后期至21世纪初明显增多,最近几年又明显减少。气候条件对农业生产的影响以50年代最有利,80年代次之,70年代较差,60年代最差。     

近28a河南主要农业气象灾害及其影响

利用河南1978-2005年农作物受灾面积资料和新中国成立以来的产量资料，分析了河南主要农业气象灾害的变化特征和对农业生产的影响，结果表明，28a来河南农作物受灾面积呈上升趋势，其阶段性变化为20世纪70年代后期至80年代前期较少，80年代中后期至21世纪初明显增多，最近几年又明显减少。气候条件对农业生产的影响以50年代最有利，80年代次之，70年代较差，60年代最差。     

Coherence and Scale of Vertical Velocity in the Convective Boundary Layer from a Doppler Lidar

We utilized a Doppler lidar to measure integral scale and coherence of vertical velocity w in the daytime convective boundary layer (CBL). The high resolution 2 μm wavelength Doppler lidar developed by the NOAA Environmental Technology Laboratory was used to detect the mean radial velocity of aerosol particles. It operated continuously in the zenith-pointing mode for several days in the summer 1996 during the “Lidars in Flat Terrain” experiment over level farmland in central Illinois. We calculated profiles of w integral scales in both the alongwind and vertical directions from about 390 m height to the CBL top. In the middle of the mixed layer we found, from the ratio of the w integral scale in the vertical to that in the horizontal direction, that the w eddies are squashed by a factor of about 0.65 as compared to what would be the case for isotropic turbulence. Furthermore, there is a significant decrease of the vertical integral scale with height. The integral scale profiles and vertical coherence show that vertical velocity fluctuations in the CBL have a predictable anisotropic structure. We found no significant tilt of the thermal structures with height in the middle part of the CBL.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

一种新型雷电潜势预报指数的构建与试验

利用WRF模式输出的0~-20℃层5种水成物粒子质量混合比及垂直上升速度变量,结合雷暴云碰撞非感应起电机制,构建了一种新型的雷电潜势指数(lightning potential index,简称LPI)。量纲分析结果表明,LPI指数本质上是一种能量指数,能够用来定量衡量雷暴云中的起电放电潜势。利用北京地区2007年9月2日和2015年7月16~17日的2次典型雷电天气过程对LPI指数的应用情况进行实例验证,结果表明:LPI指数与闪电活动在时间演变上具有较好的一致性,在空间分布上也具有较好的对应关系,它能够模拟出闪电活动的变化情况及峰值特征,其时间序列与闪电活动具有显著的正相关性。LPI指数计算方案简洁,物理意义明确,在精细化雷电潜势客观预报中具有一定的应用价值和前景。