热带气旋登陆概率的Logistic模拟

本研究采用1949--2008年近60年的热带气旋资料,对热带气旋源地分布与登陆概率进行了描述统计以及相关分析;并在此基础上建立Logistic模型,模拟热带气旋的登陆概率。结果显示:(1)西北太平洋热带气旋源地分布和登陆气旋的源地分布存在显著差异。0°-10°N纬度带登陆频数与生成频数比偏低,纬度带10°-15°N则两者具有一致性,而15°N以北登陆频数比偏高。经度的分布上135°E以西偏高,135°E以东偏低。(2)热带气旋登陆概率与源地存在显著相关关系。以西北太平洋热带气旋源地做5°×5°的经纬度分类,源地愈偏东登陆概率愈小,而TC源地纬度变化对其登陆概率的影响不如经度变化显著,但是随纬度偏北略为增加。(3)Logistic模型对影响和登陆我国的热带气旋拟合表明,经度带由西向东4个生成TC频数较多的典型海区,即南海中北部海面、菲律宾群岛以东和琉球群岛附近海面、马里亚纳群岛附近海面、马绍尔群岛附近海面的登陆概率逐渐减低。本文首次将非参数检验、Logistic概率回归模型等统计方法应用于热带气旋气候特征研究,提高了对西北太平洋热带气旋源地与其登陆关联性的统计规律性认识。     

武汉和北京相距多远

武汉位于东经 114°,北纬 31° ,而北京位于东经116°,北纬 4 0° ,那么 ,武汉和北京的球面距离有多远 ?(以上称问题 )为了解决这个问题 ,先介绍了一个定理 .为方便叙述 ,本文采用有向角 ,规定东经为正 ,西经为负 .北纬为正 ,南纬为负 .例如西经 12 0°记为- 12 0° ,南纬 30°记为 - 30°.定理　设A ,B是地球表面上的任意两地 ,A地的经度为θ1,纬度为 φ1,B地的经度为θ2 ,纬度为φ2 ,地球中心为O ,球心角∠AOB =α(α∈ (0 ,π]) ,则有三角关系式cosα=sinφ1sinφ2 +cosφ1cosφ2 cos(θ1-θ2 ) .证明　设地球半径为R ,A ,B两地分别…     

关于耀斑-激波非对称传播的统计研究

本文根据耀斑活动所引起的地球物理效应(地磁扰动和宇宙线Forbush下降)、空间飞船的直接观测和射电源的行星际闪烁(IPS)观测的综合研究,得到了有关耀斑-激波在行星际空间传播的一些新认识.要点是:耀斑-激波相对耀斑法线常表现为非对称传播,最快的传播方向于经度上趋向行星际螺旋形磁场一边,纬度上接近太阳电流片方向;激波的东南部是高动力学参数(V,P,N,T)和高等离子体β参数区,其西北部则相反;磁场则是激波东南部较弱而西北部最强,与动力学参数的分布截然相反;激波东南部的能量高于西北部.在上述结果的基础上提出了关于耀斑-激波非对称传播的三维物理模型.该模型和新近根据大量飞船观测所进行的统计研究结果一致,能统一而自然地解释耀斑-地球物理效应随源耀斑分布的非对称性.耀斑-激波的三维非对称性传播和结构可能是其“效应”的非对称性分布的基本起源.     

三倍角公式一用

平面三角中三倍角公式是 sin3α=3sinα-4sin~3α。 cos3α=4cos~3α-3cosα。三倍角公式应用较广,它可以解决一些证明、求值、三角方程、应用题等问题。三倍角公式可以变化成如下形式: sin3α=4sinαsin(60°-α)sin(60°+α) 〈S〉 cos3α=4cosαcos(60°-α)cos(60°+α) 〈C〉 tg3α=tgα·tg(60°-α)tg(60°+α) 〈T〉证明:sin3α=3sin-4sin~3α=4sinα(3/4-sin~2α)=4sinα(sin60°-sina)(sin60°+sinα)=4sinαsin(60°-α)sin(60°+α)。     

基于空间统计模型的热带气旋路径模拟及其风险评估

该研究致力于建立台风路径模拟模型,目的在于提高风险评估的稳健性和实用性。首先,采用中国台风网提供的CMA-STI热带气旋最佳路径数据集,以广东省为研究区域,通过引入空间统计模型,结合马尔可夫—蒙特卡罗方法模拟了西北太平洋的热带气旋路径。进一步,参数和非参数假设检验结果表明模拟结果是合理的,可以作为风险评估的数据来源。在此基础上,本研究模拟出620年的台风路径,给出了以地级市为基础的重现期估计和风险图绘制方法。研究发现,模拟数据克服了历史数据的时空局限性,与历史数据相比较,基于模拟数据估计的重现水平更具准确性和稳定性;其次,采用模拟方法还可以绘制出历史数据无法实现的大比例风险图,很大程度上提高了风险评估的实用性.研究结果可以作为保险行业开展巨灾保险业务,政府部门制定防灾减灾规划的科学依据.     

随机估计和VDR检验

众所周知统计推断有三种理论:普遍承认的Neyman理论(频率学派),Bayes推断和信仰推断(Fiducial)。Bayes推断基于后验分布,由先验分布和样本分布求得。信仰推断是基于信仰分布(Confidence Distribution,简称CD),直接利用样本求得。两者推断方式一致,都是用分布函数作推断,称为分布推断。从分析传统的参数估计、假设检验特性来看,经典统计推断也可以视为分布推断。通常将置信上限看做置信度的函数。其反函数,即置信度是置信上界的函数,恰是分布函数,该分布恰是近年来引起许多学者兴趣的CD。在本文中,基于随机化估计(其分布是一CD)的概率密度函数,提出VDR检验。常见正态分布期望或方差的检验,多元正态分布期望的Hoteling检验等是其特例。VDR(vertical density representation)检验适合于多元分布参数检验,实现了非正态的多元线性变换分布族的参数检验。VDR构造的参数的置信域有最小Lebesgue测度。     

名校基础知识自测

★高一年级北京师大二附中 (10 0 0 88)　汪燕铭一、选择题1.ｓｉｎ15°·ｓｉｎ3 0°·ｓｉｎ75°的值等于 (　　 ) .(Ａ) 34 　 (Ｂ) 38　 (Ｃ) 18　 (Ｄ) 142 .ｃｏｓ2 75° +ｃｏｓ2 15° +ｃｏｓ75°·ｃｏｓ15°的值等于 (　　 ) .(Ａ) 62 　 (Ｂ) 32 　 (Ｃ) 54 　 (Ｄ) 1+343 .ｃｏｓ(α +β)·ｃｏｓ(α- β) =13 ,则ｃｏｓ2 α -ｓｉｎ2 β的值是(　　 ) .(Ａ) - 23 　 (Ｂ) - 13 　 (Ｃ) 23 　 (Ｄ) 134 .ｃｏｓ4 0° +ｃｏｓ60°+ｃｏｓ80°+ｃｏｓ160°等于 (　　 ) .(Ａ) 0　 (Ｂ) 12 　 (Ｃ) - 1　 (Ｄ) 15.ｃｏｓ π12 -ｃ…     

大气、地表水和海洋对地球自转极移季节变化的综合贡献

极移季节变化的地球物理定量激发迄今未得到圆满的解释. 基于大气海洋耦合数值环流模式, 计算了大气和地表水及海洋角动量变化. 与日本气象局(JMA)客观分析资料计算的大气角动量比较, 模式模拟的大气角动量东经90°分量要优于0°分量. 地表水和海洋激发有效地减少了极移与JMA大气角动量之间季节尺度上的差异, 并且结合JMA和美国环境预测中心(NCEP)的大气角动量对极移周年变化的综合激发都优于NCAR-CSM1气候模式的结果.     

地球纬度的测量

经纬度大家都知道是地理坐标 ,纬度是指地球表面上一点的球半径与赤道平面所成的角 ,并规定赤道的纬度为 0°,然后分南、北纬各90°.历史上因航海的需要而测量与计算当地纬度曾引发了很多争论与测量方法 ,其中有以测量北极星的仰角确定纬度的 ;有通过测量一年中各个日期下的各条纬线上的太阳高度 (仰角 )绘制成表 ,然后根据当地测出的太阳高度 ,按相应的测量日期查表得到相应的纬度 .本文介绍一种适合中学生测量计算当地纬度的方法 .一、测量数据当日影指向正北 (南 )时 ,用测角器测出此时太阳仰角的余角α .(规定 :日影指向正北(南 )时 ,α…     

从几道北京高考题看数学思想的解题威力

问题是数学的核心 ,思想 (数学思想 )是数学的灵魂 .数学思想在数学解题中的自觉应用正在引起广大中学生的高度重视 .2 0 0 2年高考第一次北京市自主命题 ,现撷取其中题目加以评析 ,供读者欣赏 .一、( 2 )在平面直角坐标系中 ,已知两点Ａ(ｃｏｓ80° ,ｓｉｎ80°) ,Ｂ(ｃｏｓ2 0°,ｓｉｎ2 0°) ,则 |ＡＢ|的值是(　　 ) .(Ａ) 12 　 (Ｂ) 22 　 (Ｃ) 32 　 (Ｄ) 1解　 |ＡＢ|=(ｃｏｓ80° -ｃｏｓ2 0°) 2 +(ｓｉｎ80° -ｓｉｎ2 0°) 2=ｃｏｓ2 80° +ｓｉｎ2 80° +ｃｏｓ2 2 0°+ｓｉｎ2 2 0° - 2 (ｃｏｓ80°ｃｏｓ2 0° +ｓｉｎ80°…     

Molecular lines and continuum from W51A (I) —CO and NH3 spectra and 3 mm continuum

As for the 5′ × 4′(～llpc × 9pc) region centered at W51 lRSl the observations of the 3.4 mm continuum, CO (J = 1-0) line and simultaneous NH₃(1,1), (2,2), (3,3), (4,4) inverse lines were made for studying the massive star formation region located in the main spiral arms of the Galaxy. In the directions of W51 IRS1, IRS2 and el/e2 in 3.4 mm continuum, analyses of the line profiles show that the absorption lines of ammonia, which arise from the gas in front of the HII region, are red-shifted with respect to the emission lines, which arise from the surrounding cloud. Furthermore, a radiation transfer and statistical equilibrium calculation of ammonia molecules show that the densities increase by 3–10 times from the eastern border to the center. These points hint that the collapse is happening in the molecular cloud core obscured in optical wavelengths. The effects of the radiation fields from radio, infrared and UCHII sources is non-negligible on the excitation of various molecules (e.g. NH₃) within the circle of radius 40″ centered at IRS1. The profiles of the COJ = 1–0 line in the circle change from double peaks ( ～ 60, ～ 68 km. s^-1) to triple peaks, i.e. the component ～53 km·s^?1, which associates with UCHII, also appears in the spectra. There are indications that the circle of radius 40″ centered at IRSI is a region of massive star forming activity     

A mathematical framework for stochastic climate models

There has been a recent burst of activity in the atmosphere‐ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degrees of freedom in stochastic climate prediction. Here a systematic mathematical strategy for stochastic climate modeling is developed, and some of the new phenomena in the resulting equations for the climate variables alone are explored. The new phenomena include the emergence of both unstable linear Langevin stochastic models for the climate mean variables and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances. All of these phenomena are derived from a systematic self‐consistent mathematical framework for eliminating the unresolved stochastic modes that is mathematically rigorous in a suitable asymptotic limit. The theory is illustrated for general quadratically nonlinear equations where the explicit nature of the stochastic climate modeling procedure can be elucidated. The feasibility of the approach is demonstrated for the truncated equations for barotropic flow with topography. Explicit concrete examples with the new phenomena are presented for the stochastically forced three‐mode interaction equations. The conjecture of Smith and Waleffe [Phys. Fluids 11 (1999), 1608–1622] for stochastically forced three‐wave resonant equations in a suitable regime of damping and forcing is solved as a byproduct of the approach. Examples of idealized climate models arising from the highly inhomogeneous equilibrium statistical mechanics for geophysical flows are also utilized to demonstrate self‐consistency of the mathematical approach with the predictions of equilibrium statistical mechanics. In particular, for these examples, the reduced stochastic modeling procedure for the climate variables alone is designed to reproduce both the climate mean and the energy spectrum of the climate variables. © 2001 John Wiley & Sons, Inc.     

Some studies on wave refraction in relation to beach erosion along the kerala coast

Using the British Admiralty bathymetric charts off the West Coast of India and employing the graphical method of constructing wave refraction diagrams, an attempt is made to study the behaviour of the shortperiod waves (4, 5 and 6 seconds) which are found to affect the coast generally in the neighbourhood of Cochin Port entrance. Nineteen stations, at intervals of roughly one mile, are chosen around the three-fathom line in this area. Considering a probable field of approach of deep-water waves, limited to a cone of 90°, five directions of approach are chosen at intervals of 22 1/2;° in the range of 202 1/2° to 292 1/2°. Refraction diagrams are prepared for these directions and periods, and from these, the refraction functions and directional parameters are evaluated for each station. The possible directions of flow of long-shore current and the areas vulnerable to erosion and sedimentation are investigated.     

Bayesian Hierarchical Space–time Modeling of Earthquake Data

Stochastic earthquake models are often based on a marked point process approach as for instance presented in Vere-Jones (Int. J. Forecast., 11:503–538, 1995). This gives a fine resolution both in space and time making it possible to represent each earthquake. However, it is not obvious that this approach is advantageous when aiming at earthquake predictions. In the present paper we take a coarse point of view considering grid cells of 0.5 × 0.5°, or about 50 × 50 km, and time periods of 4 months, which seems suitable for predictions. More specifically, we will discuss different alternatives of a Bayesian hierarchical space–time model in the spirit of Wikle et al. (Environ. Ecol. Stat., 5:117–154, 1998). For each time period the observations are the magnitudes of the largest observed earthquake within each grid cell. As data we apply parts of an earthquake catalogue provided by The Northern California Earthquake Data Center where we limit ourselves to the area 32–37° N, 115–120° W for the time period January 1981 through December 1999 containing the Landers and Hector Mine earthquakes of magnitudes, respectively, 7.3 and 7.1 on the Richter scale. Based on space-time model alternatives one step earthquake predictions for the time periods containing these two events for all grid cells are arrived at. The model alternatives are implemented within an MCMC framework in Matlab. The model alternative that gives the overall best predictions based on a standard loss is claimed to give new knowledge on the spatial and time related dependencies between earthquakes. Also considering a specially designed loss using spatially averages of the 90th percentiles of the predicted values distribution of each cell it is clear that the best model predicts the high risk areas rather well. By using these percentiles we believe that one has a valuable tool for defining high and low risk areas in a region in short term predictions.      

Comparison between experimental data and theoretical calculations of free convection in water near its density maximum

Experimental data on free convection of water in the region of maximum density are interpreted by a theoretical model. The agreement between our theory and experimental data is excellent.Typical arrests in the temperature versus time curves and loops in warming-cooling cycles indicate large effects on convection generated by small changes in the space-time density profiles. These observations are fully explained by an extended theoretical approach which takes into account complex phenomena occurring in the boundary layer region. The comparison between theory and experiments indicates how the convective motion propagates from the boundary layer to the internal region of the fluid (central nucleus). Thanks to the extreme sensitivity of the temperature behaviour to relatively small density variations, a complete information about density profile around 4°C can be obtained by a quite simple experimental apparatus. Experimental data at temperature ranges between 0°C and 8°C can “feel” the asymmetry in the density curve around 4°C which is of about 8 parts per million. Our results can bring some light on the experiments performed by Azouni about the water hysteresis loop around 4°C.     

The chemical composition and original nature of the Dharwar phyllites of the Shivrajpur-Bamankua area,district Panch Mahals,Gujarat state

The chemical composition of the two most common varieties of non-manganiferous Dharwar phyllites of the Shivrajpur-Bamankua area was examined in an attempt to ascertain their original nature. The lithological and petrographical characteristics of these phyllites, studied in some detail by the author in connection with the main problem of genesis of the workable manganese ore deposits occurring in these phyllites near Shivrajpur (22° 26′ : 73° 37′) and Bamankua (22° 27′ : 73° 37′), indicate that their grade of metamorphism in this part of the country is low and comparable to the green-schist facies. Occasionally, the phyllites are intermixed with soft slate, shale and lithomarge. The phyllites have a very high silica content, excess of alumina over the amount necessary for feldspar, dominance of magnesia over lime, potash over soda and ferric oxide over ferrous oxide and possess a composition fairly compatible with average pre-Cambrian phyllites and slates of sedimentary origin. The comparative study also suggests that nearly all the important chemical constituents of the phyllites are in normal order except silica, which is exceptionally high and the ferric/ferrous oxide ratio in this case, is in reverse order. However, the unusual order of these two constituents has not affected the conclusions seriously, as may be seen in the justifications given in support of it. The percentage by weight of combined water is unusually low and it might probably be due to progressive dehydration during metamorphism and intense folding of the pre-existing metasediments. From the present investigation, the phyllites of the Shivrajpur-Bamankua area have been assigned to a sedimentary source consisting of somewhat highly siliceous pelites, which were partially metamorphosed into phyllites.     

Geomagnetic responses in high latitudes during the storm of july 15—16, 2000

The ionospheric equivalent currents in the high latitudes and the auroral electrojet system during the geomagnetic storm on July 15–16, 2000 are analyzed by using geomagnetic data from IMAGE chain. The large-scale vortices of equivalent currents are observed in the storm. The vortices on the dusk side of ionosphere correspond to four-celled pattern of plasma convection associated with NBZ, region I and region II field-aligned currents. Only one vortex can be found on the dawn side of ionosphere after interplanetary magnetic field (IMF) turns southward. In the initial phase of the storm, the center of eastward electrojets tends to shift equatorward. It arrives at 58.62° latitude of corrected geomagnetic coordinates (CGM). The westward electrojets are strong in the main phase. The center of westward electrojets in this period moves equatorward and may be beyond the southernmost station (56.45°) of the chain.

     

Hierarchical Low Rank Approximation of Likelihoods for Large Spatial Datasets

Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statistics face tremendous challenges due to the prohibitive computational burden. Various approximation methods have been introduced to reduce the computational cost. However, most of them rely on unrealistic assumptions for the underlying process and retaining statistical efficiency remains an issue. We develop a new approximation scheme for maximum likelihood estimation. We show how the composite likelihood method can be adapted to provide different types of hierarchical low rank approximations that are both computationally and statistically efficient. The improvement of the proposed method is explored theoretically; the performance is investigated by numerical and simulation studies; and the practicality is illustrated through applying our methods to two million measurements of soil moisture in the area of the Mississippi River basin, which facilitates a better understanding of the climate variability. Supplementary material for this article is available online.