A Lagrangian stochastic model for the trajectories of particle pairs and its application to the prediction of concentration variance within plant canopies

A simple Lagrangian stochastic model for the trajectories of particle pairs in high Reynolds-number turbulent flows is presented. In this model, the velocities of particle pairs are initially correlated but subsequently each particle moves independently. The independent single-particle trajectories are simulated using Thomson's model [J. Fluid Mech. 180, 529–556, 1987]. This two-particle model exactly satisfies the well-mixed condition for Gaussian turbulence when length scales, characterizing the two-point Eulerian velocity correlation function, vanish. Temperature variances, due to heat released as a passive scalar from an elevated plane source, within a model plant canopy (Coppin et al. Boundary Layer Meteorol. 35, 167–191, 1986) are shown to be well predicted by the model. It is suggested that for strongly inhomogeneous flows, the two-point Eulerian velocity function is of secondary importance in determining the simulated trajectories of particle pairs compared to the importance of ensuring satisfaction of the two-to-one constraint (Borgas and Sawford. J. Fluid Mech. 279, 69–99, 1994); i.e ensuring that one-particle statistics obtained from the two-particle model are the same as those obtained from the corresponding one-particle model. Limitations of this modelling approach are discussed.     

特殊建筑物雷击截收面积计算

从计算雷击截收面积的逻辑关系出发,以斜坡类建筑和圆顶形建筑两类特殊建筑为例,通过建立相关模型和数学公式,分析计算应从何位置按照何扩大宽度往外偏移能准确地求出截收面积。对于单檐斜坡类建筑、重檐建筑或古塔,根据房檐到屋脊（塔尖）的水平距离和垂直距离的关系,判断出应该按房檐还是屋脊（塔尖）偏移。对于圆顶形或椭圆顶形建筑,利用建筑屋顶的数学公式,建立了到圆心中轴线距离的数学公式,并对其求导数,得到了导数为0时点的横、纵坐标,此点即为偏移点位置,同时得到了对应的扩大宽度。利用AutoCAD偏移及求面积命令得到截收面积,为防雷设计及雷电灾害风险评估中雷击截收面积的准确计算提供参考。     

河南一次西南涡暴雨的大气排熵指数特征分析

应用耗散结构理论,基于广义相当位温构建大气排熵指数,利用常规观测资料、地面加密自动站雨量资料、NCEP/NCAR 1°×1°再分析资料等,对2008年7月21—23日一次西南低涡东移造成的河南省大范围暴雨过程的大气排熵指数进行诊断分析,结果表明:大气排熵指数的演变与此次西南涡暴雨落区和雨强关系密切,暴雨落在负排熵指数中心偏南一侧,大雨以上降水分布在排熵指数负值中心轴线附近及其偏南侧;强降水开始前,排熵指数明显减小,强降水持续时间与排熵指数低值维持时间联系紧密;雨强不仅与排熵指数低值有关,且与低值维持时间、6h变化量也有密切关系。排熵指数低值中心位置和中心值的强弱变化与该个例中西南低涡中心位置和其强弱变化具有较好一致性。     

金融领域的随机建模与基于软件R的Monte Carlo模拟(4):随机微分方程模型

主要研究线性随机微分方程模型,为此定义Itô随机微积分,建立Itô公式.鉴于研究的重点是利用R软件进行数值模拟,所以详细讨论了过去10多年来随机微分方程数值解的研究.     

纵向弥散作用与渗透介质非均质性定量关系的模拟研究

在地下水污染模拟预报中,弥散参数是很难确定的一个模型参数。因实验室小尺度弥散规律一般不能用于大尺度弥散过程,而野外示踪试验却耗资大、周期长,限制了其实用性。文中利用随机数值模拟手段、基于随机理论的蒙特卡罗方法及序贯高斯模拟技术来生成渗透系数随机场,并研究渗透系数对数场的方差、相关长度以及变异函数类型在不同尺度上对纵向弥散度的影响,进而建立纵向弥散度与随机分布渗透系数场的方差和相关长度的统计定量关系,并与Gelhar理论计算结果进行比较。数值模拟结果表明,经过一定迁移距离后纵向弥散度与随机分布渗透系数对数场的方差和相关长度具有良好的线性统计关系,与Gelhar理论公式表达的关系类型类似。但对于较大的方差,纵向弥散度模拟结果明显大于Gelhar理论计算值,而对于较大相关长度在迁移距离不很大时,纵向弥散度模拟结果明显小于Gelhar理论计算值。本研究可为野外大尺度地下水污染预报模型中水动力弥散参数的确定提供方法借鉴。     

海底双相随机介质声反射的SVM神经网络分类识别研究

考虑海底沉积介质为双相介质,为了更好地模拟实际海底底质的不均匀性,将随机介质理论引入双相介质理论。首先,通过基于随机-双相介质理论的高阶有限差分数值技术模拟计算海底底质分别为泥质砂、泥、泥质砾时的地震反射波信号。然后利用小波变换分别求取不同底质的一次反射波的包络作为其特征向量,最后利用基于粒子群智能算法优化的支持向量机神经网络对这些反射波信号进行分类识别。为了进一步考察所用方法的抗噪能力,对正演得到的海底底质反射波信号分别加入10%、30%、50%的高斯白噪音之后再进行分类,支持向量机仍然取得了较好的分类预测效果。基于上述正演模拟及分类识别方法的论证,提出了一套行之有效的微机软件模拟海底沉积物分类识别的一般化流程,这将有利于开展海底沉积物反射特征的进一步研究。     

云贵高原地区生态系统服务价值时空变化特征北大核心CSCD

针对云贵高原地区在开展生态恢复工程后的生态系统服务价值(ESVs)如何变化问题,本文基于当量因子和空间自相关分析等方法,研究了云贵高原地区ESVs的时空变化特征。结果表明:(1)土地利用类型转移主要是农田转为建设用地与水体。(2)在开展生态恢复工程后,生态系统得到了改善,ESVs在38年间呈先减少后增加的趋势,累计增加94.91亿元,森林的生态调节能力及产生的价值总量在2180亿元以上,最少的为荒漠,约为0.1亿元。(3)ESVs的空间分布格局表现为西南地区较高、中部较低。(4)1980—2018年ESVs表现为显著空间正相关,莫兰指数大于0.46,有明显的聚集特征。     

渗流井取水方式在大会坪水源地的应用

渗流井是一种结构较为复杂且有别于水平井及其他井孔的取水建筑物,利用河床砂砾石层的净化作用,将河水转化为地下水以获得水资源,该工程在干旱半干旱地区作用尤为显著。通过引入“等效渗透系数”,建立研究区的地下水流三维数值模型,分别模拟计算了平水期和枯水期渗流井的出水量,最终确定大会坪研究区的建议开采量为30600 m3/d。     

Approximate analytical and numerical solutions for radial non‐Darcian flow to a well in a leaky aquifer with wellbore storage and skin effect

This study investigated non‐Darcian flow to a well in a leaky aquifer considering wellbore storage and a finite‐thickness skin. The non‐Darcian flow is described by the Izbash equation. We have used a linearization procedure associated with the Laplace transform to solve such a non‐Darcian flow model. Besides, the Stehfest method has been used to invert the Laplace domain solutions for the drawdowns. We further analyzed the drawdowns inside the well for different cases. The results indicated that a smaller B_D results in a smaller drawdown at late times and the leakage has little effect on the drawdown inside the well at early times, where B_D is a dimensionless parameter reflecting the leakage. We have also found that the flow for the negative skin case approaches the steady‐state earlier than that for the positive skin. In addition, the drawdown inside the well with a positive skin is larger than that without skin effect at late times, and a larger thickness of the skin results in a greater drawdown inside the well at late times for the positive skin case. A reverse result has been found for the negative skin case. Finally, we have developed a finite‐difference solution for such a non‐Darcian flow model and compared the numerical solution with the approximate analytical solution. It has been shown that the linearization procedure works very well for such a non‐Darcian flow model at late times, and it underestimates the drawdowns at early times. Copyright © 2012 John Wiley & Sons, Ltd.     

Implementing quality control on a random number stream to improve a stochastic weather generator

For decades, stochastic modellers have used computerized random number generators to produce random numeric sequences fitting a specified statistical distribution. Unfortunately, none of the random number generators we tested satisfactorily produced the target distribution. The result is generated distributions whose mean even diverges from the mean used to generate them, regardless of the length of run. Non‐uniform distributions from short sequences of random numbers are a major problem in stochastic climate generation, because truly uniform distributions are required to produce the intended climate parameter distributions. In order to ensure generation of a representative climate with the stochastic weather generator CLIGEN within a 30‐year run, we tested the climate output resulting from various random number generators. The resulting distributions of climate parameters showed significant departures from the target distributions in all cases. We traced this failure back to the uniform random number generators themselves. This paper proposes a quality control approach to select only those numbers that conform to the expected distribution being retained for subsequent use. The approach is based on goodness‐of‐fit analysis applied to the random numbers generated. Normally distributed deviates are further tested with confidence interval tests on their means and standard deviations. The positive effect of the new approach on the climate characteristics generated and the subsequent deterministic process‐based hydrology and soil erosion modelling are illustrated for four climatologically diverse sites. Copyright © 2007 John Wiley & Sons, Ltd.