含有Bernoulli数和Euler数的恒等式

Bernoulli数和Euler数是重要的经典组合数,它们在数学和理论物理中具有广泛的应用.利用基本三角函数的幂级数展开式结合发生函数方法,建立若干含有Bernoulli数和Euler数的算术恒等式.     

图的圈和路剖分问题

设G是一个顶点数为n的图，k为任意正整数且k≤n，证明了如果图G中任何一对不相邻顶点的最大度至少为n-k＋1/2，则G能剖分成k个子图Hi,1≤i≤k，其中Hi是圈或路；如果G是2-连通图，σ2（G）=min{dG（x）＋dG（y）x，Y∈y（G），x≠y，d（x，y）=2}≥n-k，G也能剖分成k个子图Hi，1≤i≤k，其中Hi是圈或路。     

常规气象资料雷暴日数使用中应注意的问题

雷电防御安全工作越来越受到各级政府重视和社会公众的关注,防雷技术服务部门要加快适应市场,满足日益增长的防雷安全的社会需求,在防雷设计评价、雷击灾害评估、雷电风险评估等服务上提升能力、提高质量.因此,正确分析应用常规气象资料中雷暴日数,对开展防雷技术服务十分重要.根据1957-2007年湖州气象观测站雷暴、闪电的变化资料,探讨分析影响雷暴闪电日数减少可能存在的几个因子,提出雷暴日数资料在防雷技术服务应用中应当关注的几个问题.     

简析雷击风险评估中雷暴日数的应用

以聊城2007—2010年雷击密度和雷击频度为研究对象,依据现行的雷击风险评估相关规范分析了确定被评估地区的年平均雷击次数和年平均允许雷击次数的重要性,从雷电的空间差异分布和时间差异分布两方面分析总结出采用人工观测雷暴日来计算雷击密度的局限性,并提出现阶段可采用雷暴日数极端值代替人工观测雷暴日进行计算。     

辽宁省雷暴日数的时空变化特征

利用1978—2007年辽宁59个站常规地面观测资料,对雷暴日数的时空变化进行分析。结果表明：辽宁省年平均雷暴日数为28.1 d,在空间分布上呈现从东、西部山区向中部丘陵、平原及沿海地区逐渐递减的特征。1978—2007年雷暴日数总体呈逐渐下降趋势,平均每10 a下降1.2 d;并且有明显的季、月变化,夏季最多,秋季次之,冬季几乎没有发生;3—5月迅速增多,6—8月变化趋于平稳,9—12月迅速减少。雷暴在14—20时发生频率最高,20—02时次之,02—08时最少。雷暴初终间日数平均为175.8 d,最长为295 d,最短为102 d。雷暴初日4月最多,5月次之,3月最少。雷暴终日10月最多,9月次之,12月最少。并呈开始早,结束晚的趋势。     

热带气旋复杂程度的分形维数表征

应用2006-2010年69个热带气旋1 295个时次的红外云图等资料,提取了1 295个TC的外缘线,用圆规法计算了这些外缘线的分形维数。将这1 295个分形维数自小到大排列,按等频数规则,将1 295个数分为5类,分别记为A、B、C、D、E类。A、B、C、D、E类分形维数的均值分别为1.21、1.26、1.29、1.33、1.40。然后寻找与这5个均值最接近的样本。这5个样本的红外云图和TBB等值线分布图显示:随着分形维数的加大,边缘线的非光滑程度逐渐加大,图形与准圆形的偏离程度逐渐加大,TC空间结构的复杂程度也逐渐加大。说明外缘线的分形维数可以在一定程度上定量表征TC的复杂程度。     

气象因子对小麦穗粒数的影响

本文比较系统的分析了小麦各生育阶段气象因子对小麦穗粒数的影响规律,建立了穗粒数的气候生态模型。     

呼和浩特市雷暴日数变化特征与气象要素关系的分析

利用内蒙古呼和浩特市6个气象观测站1960—2013年常规地面观测资料,对该市雷暴日数的时、空分布特征与气象因子的相关关系进行了统计分析。结果表明:呼和浩特市年平均雷暴日数为36.6d,呈南北多中部少纬向型特征;54a来雷暴日数呈显著减少趋势,平均减少幅度为1.9d/10a;该地区雷暴出现有很强的季节性特点,主要集中在5—9月之间,而夏季(6、7、8月)出现次数占全年的73.5%;雷暴日数与气温存在显著的负相关关系,与降水量、气压和水汽压间存在正相关关系,其中与水汽压存在较显著的关系。     

西太平洋副高活动指数的吸引子维数计算

基于NCEP／NCAR再分析资料计算出的西太平洋副高活动的三种特征指数,利用相空间重构方法对副高活动的三种特征指数的混沌特性和分数维进行了计算。计算结果表明,副高的短期活动存在混沌吸引子,副高脊线指数和面积指数动力系统的独立变量数目的上、下限分别为3和6,分析结果为副高动力系统的重构研究奠定了基础。     

On the turbulent Prandtl number in the stable atmospheric boundary layer

This study focuses on the behaviour of the turbulent Prandtl number, Pr _t , in the stable atmospheric boundary layer (SBL) based on measurements made during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA). It is found that Pr _t increases with increasing stability if Pr _t is plotted vs. gradient Richardson number, Ri; but at the same time, Pr _t decreases with increasing stability if Pr _t is plotted vs. flux Richardson number, Rf, or vs. ζ = z/L. This paradoxical behaviour of the turbulent Prandtl number in the SBL derives from the fact that plots of Pr _t vs. Ri (as well as vs. Rf and ζ) for individual 1-h observations and conventional bin-averaged values of the individual quantities have built-in correlation (or self-correlation) because of the shared variables. For independent estimates of how Pr _t behaves in very stable stratification, Pr _t is plotted against the bulk Richardson number; such plots have no built-in correlation. These plots based on the SHEBA data show that, on the average, Pr _t decreases with increasing stability and Pr _t < 1 in the very stable case. For specific heights and stabilities, though, the turbulent Prandtl number has more complicated behaviour in the SBL.     

Comparative energetics of ERA-40, JRA-25 and NCEP-R2 reanalysis, in the wave number domain

The European Centre for Medium-Range Weather Forecasts 40-year Reanalysis (ERA-40), the Japan Meteorological Agency and Central Research Institute of Electric Power Industry 25-year Reanalysis (JRA-25), and the National Centers for Environmental Prediction and Department of Energy AMIP-II Reanalysis (NCEP-R2) are intercompared through a global energetics analysis for all seasons.Overall, the Lorenz energy cycle is consistent among the three datasets. The flow of energy and the peaks and slopes in the spectra of the various components agree between the three reanalysis. Additionally, the temporal variability of the energy cycle terms shows consistency between the three reanalysis. Most differences between the three reanalysis are related to the magnitudes of energy forms and energy conversion/transfer rates at each wave number, generally following the relation ERA−40>JRA−25>NCEP−R2, and mainly located in the Southern Hemisphere. The best agreement between the three datasets is found for northern winter. Differences between the three datasets are greater for the other seasons, being greatest for northern summer. In general, these discrepancies are fairly modest, being likely due to the different model biases and resolutions, and the different data assimilation methods used by the respective reanalysis systems. The energetics of the three reanalysis become closer to each other in more recent years, which is likely due to the increase in the number of observations assimilated in the reanalysis.The NCEP-R2 reanalysis spectrum is smoother than those of ERA-40 and JRA-25, likely due to filtering and to its lower resolution model. The spectra show a rapid decrease for short waves in NCEP-R2 (n=36) and ERA-40 (n=63), as a consequence of filtering. The energy source in the nonlinear wave–wave interactions of kinetic energy, L(n), has a narrower spectral range in NCEP-R2 than in the other datasets. Energetics from the newer JRA-25 reanalysis is generally closer to that of ERA-40, with some exceptions as is the case of zonal–wave interactions of kinetic energy, M(n), for synoptic waves, or for eddy available potential energy, A_E, in the lower troposphere, for which JRA-25 is closer to NCEP-R2.     

On the number concentration of aerosols in towns

A simple model of the aerosol plume generated by a town is developed under the assumption that the generation rate of particles is proportional to the town population. Thus the volume concentration of aerosols in towns is predicted for various meteorological conditions. The effects of localized sources of aerosols, such as industrial chimney stacks, are considered.     

黔东南相当暴雨日数与雨日数的气候变化

利用1961—2015年共55 a黔东南地区16个气象观测站实时降水量观测资料,建立相当暴雨日数和雨日数的时间序列,分析黔东南地区相当暴雨日数与雨日数的时空变化特征。结果表明:黔东南相当暴雨日数的分布是以西南侧的雷公山脉为中心沿东北方向递减,雨日数则以东部和西部为大值区,南部和北部为小值区;相当暴雨日数主模态分别为西北—东南向递减的同位相型、西南—东北向为反位相型;雨日数主模态以西北至东部一线为中心,向两边递减的同位相分布,这与地形对降水机制影响有很大关系。相当暴雨日数呈上升趋势,雨日数在上世纪60年代中期至21世纪初相对稳定变化,之后呈下降趋势;相当暴雨日数和雨日数均具有2 a左右的主周期变化,雨日数还具有11 a左右的长周期变化。     

On the structure of supercritical western boundary currents

The structure of supercritical western boundary currents is investigated using a quasi-geostrophic numerical model. The basic flow is of meridional Munk balance, and the input boundary is perturbed by the most unstable wave solution obtained from linear spatial instability calculations. Self-preserving (or equilibrium) solutions are obtained for the model runs at Re=30, 60, 90, and 120, and their energy and vorticity budgets are analyzed. In an analogy with the laboratory turbulence of wall boundary layers, the western boundary layer is divided into inner and outer layers. In the inner layer, the mean energy is dissipated via direct viscous dissipation, while in the outer layer it is converted to the eddy energy via turbulence production. The main scenario is that the mean energy is produced in the inner layer via ageostrophic pressure work divergence, and it is partly removed due to viscous action within a narrow region near the wall, defined here as viscous sub-layer. The remaining portion is converted to the eddy energy via turbulence production in the outer layer, which is in turn transported to the inner layer, then again to the viscous sub-layer where it is ultimately dissipated. In the near-wall side, the vorticity balance of the mean flow is maintained by viscous effect and Reynolds flux divergence, while in the offshore side it is maintained by beta effect and Reynolds flux divergence. The length scale of the supercritical boundary current is roughly , where L_M is the Munk length, as observed from a dimensional analysis.     

Simulation of marine stratocumulus: effect of precipitation parameterization and sensitivity to droplet number concentration

Marine stratocumulus observations show a large variability in cloud droplet number concentration (CDNC) related to variability in aerosol concentration. Changes in CDNC modify the cloud reflectivity, but also affect cloud water content, cloud lifetime, and cloudiness, through changes in precipitation. In mesoscale models and general circulation models (GCMs), precipitation mechanisms are parameterized. Here we examine how the precipitation parameterization can affect the simulated cloud. Simulations are carried out with the one-dimensional version of the hydrostatic primitive equation model MAR (Modéle Atmosphérique Régional) developed at the Université catholique de Louvain. It includes a E- turbulence closure, a wide-band formulation of the radiative transfer, and a parameterized microphysics including prognostic equations for water vapour, cloud droplets and rain drops concentrations. In a first step, the model is used to simulate a horizontally homogeneous stratocumulus deck observed during the Atlantic Stratocumulus Transition Experiment (ASTEX) on the night of 12–13 June 1992. The observations show that the model is able to realistically reproduce the vertical structure of the cloud-topped boundary layer. In a second step, several precipitation parameterizations commonly used in mesoscale models and GCMs are tested. It is found that most parameterizations tend to overestimate the precipitation, which results in an underestimation of the vertically integrated liquid water content. Afterwards, using those parameterizations that are sensitive to CDNC, several simulations are performed to estimate the effect of CDNC variations on the simulated cloud. Based upon the simulation results, we argue that currently used parameterizations do not enable assessment of such a sensitivity.     

云滴数浓度影响混合型层状云降水的数值模拟

使用耦合了Morrison双参数微物理方案的中尺度WRF模式V2．2,对2008年1月25-29日发生在我国南方的冰雪天气过程进行了数值试验。在模式准确再现了此次天气过程形势演变特点的基础上,对模式微物理方案中云滴数浓度影响累积降水量的情况进行了敏感性试验,发现云滴数浓度对降水量的影响是复杂和非线性的。对此次天气过程中的微物理量进行了详细的分析,并从各种水成物粒子的发展演变上,讨论了云滴数浓度的增加在暖云和冷云两种降水机制上对降水产生的不同影响。结果表明,云滴数浓度越大,云水混合比就越大,云滴的尺度越小。雨滴对不同云滴数浓度的响应与云滴的情况相反,随着云滴数浓度的增加,雨滴数浓度减小,雨水也减少,暖云降水过程受到了抑制;冰晶和雪晶的数浓度的演变过程没有明显变化,而冰晶和雪晶的混合比是相应增加的,冷云降水过程得到了一定程度的增强。从本文模拟的个例来看,设置不同云滴数浓度所得到的总累计降水量的差异在1％以内。总的来说,增加云滴数浓度,降水量会减少。从比例上来看,增加云滴数浓度对暖云降水过程的抑制作用比对冷云降水过程的增强作用更为显著,但是在本文模拟的个例中,冷云降水过程占主导地位,减少的降水和增加的降水的绝对值在同一个量级上并且数值相近,它们相互抵消后得到的结果是降水量变化的绝对值大大减小了,这解释了增加云滴数浓度后模拟的总累积降水量变化不明显的原因。     

Seasonal variations of number size distributions and mass concentrations of atmospheric particles in Beijing

Particle number and mass concentrations were measured in Beijing during the winter and summer periods in 2003, together with some other parameters including black carbon (BC) and meteorological conditions. Particle mass concentrations exhibited low seasonality, and the ratio of PM2.5/PM10 in winter was higher than that in summer. Particle number size distribution (PSD) was characterized by four modes and exhibited low seasonality. BC was well correlated with the number and mass concentrations of accumulation and coarse particles, indicating these size particles are related to anthropogenic activities.Particle mass and number concentrations (except ultra-fine and nucleation particles) followed well the trends of 13C concentration for the majority of the day, indicating that most particles were associated with primary emissions. The diurnal number distributions of accumulation and coarse mode particles were characterized by two peaks.     

On the instability of a planetary boundary layer with Rossby number similarity

In Part I (1975), a linear stability analysis with respect to the formation of longitudinal vortex rolls was given for aturbulent boundary layer of the atmosphere. However, that analysis investigated the effect of inflection point instability only; therefore it is applicable only to the case of neutral stratification. In Part II presented here, the analysis is extended to include the combined effect of inflection point instability and instability due to heating from below. In contrast with the result in Part I, the main result is that in considering both these effects, longitudinal vortex rolls can develop only if the boundary layer has an unstable stratification. Another important result is that the structure of developing vortex rolls and their growth-rates are universal in a boundary layer with Rossby-number similarity, i.e., they are independent of any external parameter. The same is true for the orientation of the vortex rolls: the angle between the axis of the rolls and the surface stress is independent of external parameters. The only quantity which is not universal is the phase speed, which indicates the speed with which the rolls move in a direction perpendicular to the vortex axis; this phase speed depends on the geostrophic wind and on the roughness-length. Paper presented at the XIIIth Biennual Fluid Dynamics Symposium 5–10 September, 1977, Olsztyn, Poland.     

On the Scale-dependence of the Gradient Richardson Number in the Residual Layer

We present results of a technique for examining the scale-dependence of the gradient Richardson number, Ri, in the nighttime residual layer. The technique makes use of a series of high-resolution, in situ, vertical profiles of wind speed and potential temperature obtained during CASES-99 in south-eastern Kansas, U.S.A. in October 1999. These profiles extended from the surface, through the nighttime stable boundary layer, and well into the residual layer. Analyses of the vertical gradients of both wind speed, potential temperature and turbulence profiles over a wide range of vertical scale sizes are used to estimate profiles of the local Ri and turbulence structure as a function of scale size. The utility of the technique lies both with the extensive height range of the residual layer as well as with the fact that the sub-metre resolution of the raw profiles enables a metre-by-metre ‘sliding’ average of the scale-dependent Richardson number values over hundreds of metres vertically. The results presented here show that small-scale turbulence is a ubiquitous and omnipresent feature of the residual layer, and that the region is dynamic and highly variable, exhibiting persistent turbulent structure on vertical scales of a few tens of metres or less. Furthermore, these scales are comparable to the scales over which the Ri is less than or equal to the critical value of Ri _c of 0.25, although turbulence is also shown to exist in regions with significantly larger Ri values, an observation at least consistent with the concept of hysteresis in turbulence generation and maintenance. Insofar as the important scale sizes are comparable to or smaller than the resolution of current models, it follows that, in order to resolve the observed details of small Ri values and the concomitant turbulence generation, future models need to be capable of significantly higher resolutions.