A stochastic model of temporal variations in monthly temperature, precipitation, snowfall, and resulting snowpack

We report a Monte Carlo representation of the long-term inter-annual variability of monthly snowfall on a detailed (1 km) grid of points throughout the southwest. An extension of the local climate model of the southwestern United States (Stamm and Craig 1992) provides spatially based estimates of mean and variance of monthly temperature and precipitation. The mean is the expected value from a canonical regression using independent variables that represent controls on climate in this area, including orography. Variance is computed as the standard error of the prediction and provides site-specific measures of (1) natural sources of variation and (2) errors due to limitations of the data and poor distribution of climate stations. Simulation of monthly temperature and precipitation over a sequence of years is achieved by drawing from a bivariate normal distribution. The conditional expectation of precipitation. given temperature in each month, is the basis of a numerical integration of the normal probability distribution of log precipitation below a threshold temperature (3°C) to determine snowfall as a percent of total precipitation. Snowfall predictions are tested at stations for which long-term records are available. At Donner Memorial State Park (elevation 1811 meters) a 34-year simulation - matching the length of instrumental record - is within 15 percent of observed for mean annual snowfall. We also compute resulting snowpack using a variation of the model of Martinec et al. (1983). This allows additional tests by examining spatial patterns of predicted snowfall and snowpack and their hydrologic implications.

意大利威尼托（Veneto）的刺叶栎林-植物社会学生物多样性研究

刺叶栎( Quercus ilex L．)是地中海的常绿树种，属于古老的第三纪植物区系成份。本文根据苏黎世——蒙特利尔学派的植被学基本原理，全面地研究了分布在整个威尼托(Veneto)大区的剌叶栎林，详细研究刺叶栎林的群落组成、结构及类型划分。同时，对威尼托的刺叶栎林同北京山区的栎林进行了比较研究。最后，着重研究了威尼托刺叶栎林的生物多样性。 威尼托的刺叶栎林主要分布在亚得里亚海沿岸（包括Foci del Tagtiamento和Bosco Nordio e Rosolina Mare两地）、Lago di Garda和Colli Euganei。 在气候上，亚得里亚海沿岸属于半地中海气候。加尔达湖区域(Laqo di Garda)则是接近欧洲中部的大陆性气候，且维持半地中海的气候特点。Co t l i Euganei是这两地气候的过渡类型，且更接近亚得里亚海沿岸的类型。 在亚得里亚海沿岸的刺叶栎林可以分为三类，第一类(I)是一些矮树丛，这是Fraxinus ornus和Quercus ilex混交林的前身，较干旱。第二类群落(II)缺少乔木层，灌木层是由一些盖度不大的刺叶栎代替，更干旱。第三类群落(Ⅲ)是一群在外貌上相同的成熟群落．Fraxinus ornus和Quercus ilex得到充分发展，较中生。 在加尔达湖区的刺叶栎林可划分为三类。第一类群落(I)代表一组耐旱、开敞的矮树丛，含有Sesterio Variae-Ostryelum群丛的特征种，这一类可划分为SesLerio Variae-Ostryetum群 丛，土壤贫脊和干旱。第二类群落(Ⅱ)代表一类较郁闭的矮树丛，含有较多的Prunetalia群落目的成份，土壤较贫脊。第三类群(Ⅲ)代表一类郁闭的群落，乔木具有很大的密度因而林下灌木不能充分发展。SesLerio Variae-Ostryetum群丛和Prunetalia群落目的成份均不多。 在Colli Euganei的刺叶栎林可划分为二类。第一类群落(I)是一些不郁闲的矮树林组成。大体上分为地中海旱生栎林和地中海假灌丛。第二类群落(II)代表了较中生状态的植被，刺叶标种群绝对郁闭。 北京地处华北大平原的西北部。北京山地的气候为温带陆地性季风气候，其地带性的落叶阔叶林是以栎林为典型。虽然这些栎林同意大利威尼托刺叶栎林是两种不同的森林类型，但两者之间是存在着一定的联系。其共有的科有20个，共有属有11个。他们在植物组成中，以禾本科，蔷薇科和豆科的植物种类为最多。在乔木层中，他们都是以壳斗科的栎属(Quercus)为优势，其中木犀科的白蜡属(Fraxinus)和槭树属(Acer)较多。 本文对威尼托大区刺叶栎林的物种多度分布格局进行了全面探讨，计算出刺叶栎林的几何分布模型、Broken-stick分布模型、Log分布模型、Log-normat分布模型等四种物种多度分布的理论模型，并将这些理论分布模型用“序列／多度”图解和“多度／频度”图解表示出来。其中，几何分布模型．Broken-stick1分布模型用“序列／多度”图解表示。Broken-stick2分布模型、Log分布模型、Log-normal分布模型用“多度／频度”图解表示。 对上述四个物种多度的理论分布同实际现察的物种多度分布进行X2分析，在5％的显著性水平上，对整个威托大区的刺叶 栎林，几何分布模型最能代表其物种多度分布，显著性最大;Log-normal分布模型也可以用来代表威尼托刺叶标妹的物种多度分布，其显著性次于几何分布模型的显著性。这表明威尼托的刺叶栎林尚处于演替的早期阶段，这些刺叶栎林曾受到严重破坏，现正在恢复。 通过比较Foci del Tagtiamento和Bosco Nordio加尔达湖区、Colli Euganei四个地方刺叶栎林的物种多度的几何分布模型和Log-normal分布模型，显示出Lago di Garda（加尔达湖区）的刺叶栎林生物多样性最好、Foci del Tagtiamento刺叶栎林生物多样性较好．Bosco Nordio的剌叶栎林生物多样性较差．Colli Euganei的刺叶栎林生物多样性最差。 再利用多样性指数计算全部威尼托大区剌叶栎林的生物多样性。计算的多样性指数有丰富度指数（包括Margalef指数、Men-hinick指数、Monk指数）、多样性指数(Shannon信息指数、Bri llouin个息指数、Gini指数、PIE指数、Mcintosh指数)、优势度指数(Berger-Parker指数、Simpson指数)、均一度指数(Pielou均一度指数、Brillouin均一度指数，PIE的V’均一度指数．PIE的V均一度指数，N2的V’均一度指数，N2的V均一度指数，Mclntosh均一度指数，Hill的F10均一度指数，Hill的E21均一度指数，Hill的F21的一度指数）。通过比较丰富度指数，多样性指数、均一度指数与优势度之间的关系，结果，Simpson优势度指数同Men-hinick物种丰富度指数、Shannon信息指数、Bril-louin信息指数、Pielou均一度指数，Brillouin均一度指数，Mcintosh均一度指数、PIE的V’均一度指数呈负相关关系，因此，上述生物多样性指数可以较好地反映威尼托大区刺叶栎林的生物多样性。反映出的结果是：加尔达湖区刺叶栎林生物多样性最好，Foci del Tagtiamento刺叶栎林生物多样性较好，Bosco Nordio的剌叶栎林生物多样性较差．Colli Euganei的刺叶栎林生物多样性最差。 生物多样性的研究显示出生物多样性同生境状况的密切联系。往往受人为干扰严重的群落生物多样性低、如Coli Euganei和亚得里亚海岸刺叶栋林;而受人为破坏较轻的群落其生物多样性高，如加尔达湖区刺叶栎。 生物多样性的研究还显示出生物多样性同群落演替的发展阶段密切相关，在群落演替初期，由于缺乏优势种，而又有大量物种侵入，物多样性相对较高。在群落演替中期，由于形成了一个或几个优势种，优势度的增加导致了生物多样性相对减低。如Foci del Tagtiamento刺叶栎林生物多样性高于Bosco Nordio刺叶栎林的生物多样性。到演替后期，随着更多物种的侵入，群落结构的复杂化、生物多样性又将逐步提高。

FIRST PASSAGE APPROXIMATION FOR NORMAL STATIONARY RANDOM PROCESSES.

A new approximate solution for the first passage probability of a stationary Gaussian random process is presented which is based on the estimation of the mean clump size. A simple expression for the mean clump size is derived in terms of the cumulative normal distribution function, which avoids the lengthy numerical integrations which are required by similar existing techniques. The method is applied to a linear oscillator and an ideal bandpass process and good agreement with published results is obtained. By making a slight modification to an existing analysis it is shown that a widely used empirical result for the asymptotic form of the first passage probability can be deduced theoretically.

Numerical investigation of particle velocity distributions in aeolian sand transport

Particle velocity distribution in a blowing sand cloud is a reflection of saltation movement of many particles. Numerical analysis is performed for particle velocity distribution with a discrete particle model. The probability distributions of resultant particle velocity in the impact-entrainment process, particle horizontal and vertical velocities at different heights and the vertical velocity of ascending particles are analyzed. The probability distributions of resultant impact and lift-off velocities of saltating particles can be expressed by a log-normal function, and that of impact angle comply with an exponential function. The probability distribution of particle horizontal and vertical velocities at different heights shows a typical single-peak pattern. In the lower part of saltation layer, the particle horizontal velocity distribution is positively skewed. Further analysis shows that the probability density function of the vertical velocity of ascending particles is similar to the right-hand part of a normal distribution function, and a general equation is acquired for the probability density function of non-dimensional vertical velocity of ascending particles which is independent of diameter of saltating particles, wind strength and height. These distributions in the present numerical analysis are consistent with reported experimental results. The present investigation is important for understanding the saltation state in wind-blown sand movement. (C) 2009 Elsevier B.V. All rights reserved.

CFD-DEM simulation of three-dimensional aeolian sand movement

A three-dimensional CFD-DEM model is proposed to investigate the aeolian sand movement. The results show that the mean particle horizontal velocity can be expressed by a power function of heights. The probability distribution of the impact and lift-off velocities of particles can be described by a log-normal function, and that of the impact and lift-off angles can be expressed by an exponential function. The probability distribution of particle horizontal velocity at different heights can be described as a lognormal function, while the probability distribution of longitudinal and vertical velocity can be described as a normal function. The comparison with previous two-dimensional calculations shows that the variations of mean particle horizontal velocity along the heights in two-dimensional and three-dimensional models are similar. However, the mean particle density of the two-dimensional model is larger than that in reality, which will result in the overestimation of sand transportation rate in the two-dimensional calculation. The study also shows that the predicted probability distributions of particle velocities are in good agreement with the experimental results.

Tree diameter distribution modelling: introducing the logitlogistic distribution

Johnson's SB distribution is a four-parameter distribution that is transformed into a normal distribution by a logit transformation. By replacing the normal distribution of Johnson's SB with the logistic distribution, we obtain a new distributional model that approximates SB. It is analytically tractable, and we name it the "logitlogistic" (LL) distribution. A generalized four-parameter Weibull model and the Burr XII model are also introduced for comparison purposes. Using the distribution "shape plane" (with axes skew and kurtosis) we compare the "coverage" properties of the LL, the generalized Weibull, and the Burr XII with Johnson's SB, the beta, and the three-parameter Weibull, the main distributions used in forest modelling. The LL is found to have the largest range of shapes. An empirical case study of the distributional models is conducted on 107 sample plots of Chinese fir. The LL performs best among the four-parameter models.

Dimethylsulfide gas transfer coefficients from algal blooms in the Southern Ocean

Air–sea dimethylsulfide (DMS) fluxes and bulk air–sea gradients were measured over the Southern Ocean in February–March 2012 during the Surface Ocean Aerosol Production (SOAP) study. The cruise encountered three distinct phytoplankton bloom regions, consisting of two blooms with moderate DMS levels, and a high biomass, dinoflagellate-dominated bloom with high seawater DMS levels (> 15 nM). Gas transfer coefficients were considerably scattered at wind speeds above 5 m/s. Bin averaging the data resulted in a linear relationship between wind speed and mean gas transfer velocity consistent with that previously observed. However, the wind-speed-binned gas transfer data distribution at all wind speeds is positively skewed. The flux and seawater DMS distributions were also positively skewed, which suggests that eddy covariance-derived gas transfer velocities are consistently influenced by additional, log-normal noise. A flux footprint analysis was conducted during a transect into the prevailing wind and through elevated DMS levels in the dinoflagellate bloom. Accounting for the temporal/spatial separation between flux and seawater concentration significantly reduces the scatter in computed transfer velocity. The SOAP gas transfer velocity data show no obvious modification of the gas transfer–wind speed relationship by biological activity or waves. This study highlights the challenges associated with eddy covariance gas transfer measurements in biologically active and heterogeneous bloom environments.

The Effect of Volume Shape Factor on the Crystal Size Distribution of Fragments due to Attrition

The effect of volume shape factor on crystal size distribution (CSD) is usually ignored to simplify the analysis of population balance equation. In the present work, the CSD of fragments generated from a mechanically stirred crystallizer as the result of attrition mechanism has been reported when the volume shape factor conforms to normal distribution. The physical model of GAHN and MERSMANN which relates the attrition resistance of a crystalline substances to its mechanical properties has been employed. The simulation of fragment size distribution was performed by Monte Carlo (MC) technique. The results are compared with those reported by GAHN and MERSMANN.

Response characteristics of optical sensors for oxygen: models based on a distribution in tau(o) or kappa(q)

The features of two popular models used to describe the observed response characteristics of typical oxygen optical sensors based on luminescence quenching are examined critically. The models are the 'two-site' and 'Gaussian distribution in natural lifetime, tau(o),' models. These models are used to characterise the response features of typical optical oxygen sensors; features which include: downward curving Stern-Volmer plots and increasingly non-first order luminescence decay kinetics with increasing partial pressures of oxygen, pO(2). Neither model appears able to unite these latter features, let alone the observed disparate array of response features exhibited by the myriad optical oxygen sensors reported in the literature, and still maintain any level of physical plausibility. A model based on a Gaussian distribution in quenching rate constant, k(q), is developed and, although flawed by a limited breadth in distribution, rho, does produce Stern-Volmer plots which would cover the range in curvature seen with real optical oxygen sensors. A new 'log-Gaussian distribution in tau(o) or k(q)' model is introduced which has the advantage over a Gaussian distribution model of placing no limitation on the value of rho. Work on a 'log-Gaussian distribution in tau(o)' model reveals that the Stern-Volmer quenching plots would show little degree in curvature, even at large rho values and the luminescence decays would become increasingly first order with increasing pO(2). In fact, with real optical oxygen sensors, the opposite is observed and thus the model appears of little value. In contrast, a 'log-Gaussian distribution in k(o)' model does produce the trends observed with real optical oxygen sensors; although it is technically restricted in use to those in which the kinetics of luminescence decay are good first order in the absence of oxygen. The latter model gives a good fit to the major response features of sensors which show the latter feature, most notably the [Ru(dpp)(3)(2+)(Ph4B-)(2)] in cellulose optical oxygen sensors. The scope of a log-Gaussian model for further expansion and, therefore, application to optical oxygen sensors, by combining both a log-Gaussian distribution in k(o) with one in tau(o) is briefly discussed.

Inverse Gaussian Modeling of Turbulence-Induced Fading in Free-Space Optical Systems

We propose the inverse Gaussian distribution, as a less complex alternative to the classical log-normal model, to describe turbulence-induced fading in free-space optical (FSO) systems operating in weak turbulence conditions and/or in the presence of aperture averaging effects. By conducting goodness of fit tests, we define the range of values of the scintillation index for various multiple-input multiple-output (MIMO) FSO configurations, where the two distributions approximate each other with a certain significance level. Furthermore, the bit error rate performance of two typical MIMO FSO systems is investigated over the new turbulence model; an intensity-modulation/direct detection MIMO FSO system with Q-ary pulse position modulation that employs repetition coding at the transmitter and equal gain combining at the receiver, and a heterodyne MIMO FSO system with differential phase-shift keying and maximal ratio combining at the receiver. Finally, numerical results are presented that validate the theoretical analysis and provide useful insights into the implications of the model parameters on the overall system performance. © 2011 IEEE.

Experimentelle und numerische Untersuchungen zur Dispersion von Dichteströmungen in einem stochastischen Modellaquifer

Es ist bekannt, dass die Dichte eines gelösten Stoffes die Richtung und die Stärke seiner Bewegung im Untergrund entscheidend bestimmen kann. Eine Vielzahl von Untersuchungen hat gezeigt, dass die Verteilung der Durchlässigkeiten eines porösen Mediums diese Dichteffekte verstärken oder abmindern kann. Wie sich dieser gekoppelte Effekt auf die Vermischung zweier Fluide auswirkt, wurde in dieser Arbeit untersucht und dabei das experimentelle sowohl mit dem numerischen als auch mit dem analytischen Modell gekoppelt. Die auf der Störungstheorie basierende stochastische Theorie der macrodispersion wurde in dieser Arbeit für den Fall der transversalen Makodispersion. Für den Fall einer stabilen Schichtung wurde in einem Modelltank (10m x 1.2m x 0.1m) der Universität Kassel eine Serie sorgfältig kontrollierter zweidimensionaler Experimente an einem stochastisch heterogenen Modellaquifer durchgeführt. Es wurden Versuchsreihen mit variierenden Konzentrationsdifferenzen (250 ppm bis 100 000 ppm) und Strömungsgeschwindigkeiten (u = 1 m/ d bis 8 m/d) an drei verschieden anisotrop gepackten porösen Medien mit variierender Varianzen und Korrelationen der lognormal verteilten Permeabilitäten durchgeführt. Die stationäre räumliche Konzentrationsausbreitung der sich ausbreitenden Salzwasserfahne wurde anhand der Leitfähigkeit gemessen und aus der Höhendifferenz des 84- und 16-prozentigen relativen Konzentrationsdurchgang die Dispersion berechnet. Parallel dazu wurde ein numerisches Modell mit dem dichteabhängigen Finite-Elemente-Strömungs- und Transport-Programm SUTRA aufgestellt. Mit dem kalibrierten numerischen Modell wurden Prognosen für mögliche Transportszenarien, Sensitivitätsanalysen und stochastische Simulationen nach der Monte-Carlo-Methode durchgeführt. Die Einstellung der Strömungsgeschwindigkeit erfolgte - sowohl im experimentellen als auch im numerischen Modell - über konstante Druckränder an den Ein- und Auslauftanks. Dabei zeigte sich eine starke Sensitivität der räumlichen Konzentrationsausbreitung hinsichtlich lokaler Druckvariationen. Die Untersuchungen ergaben, dass sich die Konzentrationsfahne mit steigendem Abstand von der Einströmkante wellenförmig einem effektiven Wert annähert, aus dem die Makrodispersivität ermittelt werden kann. Dabei zeigten sich sichtbare nichtergodische Effekte, d.h. starke Abweichungen in den zweiten räumlichen Momenten der Konzentrationsverteilung der deterministischen Experimente von den Erwartungswerten aus der stochastischen Theorie. Die transversale Makrodispersivität stieg proportional zur Varianz und Korrelation der lognormalen Permeabilitätsverteilung und umgekehrt proportional zur Strömungsgeschwindigkeit und Dichtedifferenz zweier Fluide. Aus dem von Welty et al. [2003] mittels Störungstheorie entwickelten dichteabhängigen Makrodispersionstensor konnte in dieser Arbeit die stochastische Formel für die transversale Makrodispersion weiter entwickelt und - sowohl experimentell als auch numerisch - verifiziert werden.

A generalization of Student’s t-distribution from the viewpoint of special functions

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

Searching for consensus in ahp-group decision making. A bayesian perspective

This paper sets out to identify the initial positions of the different decision makers who intervene in a group decision making process with a reduced number of actors, and to establish possible consensus paths between these actors. As a methodological support, it employs one of the most widely-known multicriteria decision techniques, namely, the Analytic Hierarchy Process (AHP). Assuming that the judgements elicited by the decision makers follow the so-called multiplicative model (Crawford and Williams, 1985; Altuzarra et al., 1997; Laininen and Hämäläinen, 2003) with log-normal errors and unknown variance, a Bayesian approach is used in the estimation of the relative priorities of the alternatives being compared. These priorities, estimated by way of the median of the posterior distribution and normalised in a distributive manner (priorities add up to one), are a clear example of compositional data that will be used in the search for consensus between the actors involved in the resolution of the problem through the use of Multidimensional Scaling tools

A new study on the power distribution of OFDMA, SC-FDMA and CP-CDMA signals

This paper explores a new technique to calculate and plot the distribution of instantaneous transmit envelope power of OFDMA and SC-FDMA signals from the equation of Probability Density Function (PDF) solved numerically. The Complementary Cumulative Distribution Function (CCDF) of Instantaneous Power to Average Power Ratio (IPAPR) is computed from the structure of the transmit system matrix. This helps intuitively understand the distribution of output signal power if the structure of the transmit system matrix and the constellation used are known. The distribution obtained for OFDMA signal matches complex normal distribution. The results indicate why the CCDF of IPAPR in case of SC-FDMA is better than OFDMA for a given constellation. Finally, with this method it is shown again that cyclic prefixed DS-CDMA system is one case with optimum IPAPR. The insight that this technique provides may be useful in designing area optimised digital and power efficient analogue modules.

Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned