共查询到20条相似文献，搜索用时 15 毫秒
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Second-order exact ensemble averaged equation for linear stochastic differential equations with multiplicative randomness and random forcing is obtained by using the cumulant expansion ensemble averaging method and by taking the time dependent sure part of the multiplicative operator into account. It is shown that the satisfaction of the commutativity and the reversibility requirements proposed earlier for linear stochastic differential equations without forcing are necessary for the linear stochastic differential equations with forcing when the cumulant expansion ensemble averaging method is used. It is shown that the applicability of the operator equality, which is used for the separation of operators in the literature, is also subjected to the satisfaction of the commutativity and the reversibility requirements. The van Kampen’s lemma, which is proposed for the analysis of nonlinear stochastic differential equations, is modified in order to make the probability density function obtained through the lemma depend on the forcing terms too. The second-order exact ensemble averaged equation for linear stochastic differential equations with multiplicative randomness and random forcing is also obtained by using the modified van Kampen’s lemma in order to validate the correctness of the modified lemma. Second-order exact ensemble averaged equation for one dimensional convection diffusion equation with reaction and source is obtained by using the cumulant expansion ensemble averaging method. It is shown that the van Kampen’s lemma can yield the cumulant expansion ensemble averaging result for linear stochastic differential equations when the lemma is applied to the interaction representation of the governing differential equation. It is found that the ensemble averaged equations given for one the dimensional convection diffusion equation with reaction and source in the literature obtained by applying the lemma to the original differential equation are restricted with small sure part of multiplicative operator. Second-order exact differential equations for the evolution of the probability density function for the one dimensional convection diffusion equation with reaction and source and one dimensional nonlinear overland flow equation with source are obtained by using the modified van Kampen’s lemma. The equation for the evolution of the probability density function for one dimensional nonlinear overland flow equation with source given in the literature is found to be not second-order exact. It is found that the differential equations for the evolution of the probability density functions for various hydrological processes given in the literature are not second-order exact. The significance of the new terms found due to the second-order exact ensemble averaging performed on the one dimensional convection diffusion equation with reaction and source and during the application of the van Kampen’s lemma to the one dimensional nonlinear overland flow equation with source is investigated. 相似文献
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The balance equation for a substance washed out in a river basin is analyzed under the assumption that the runoff of this substance and its reserves in the watershed are directly proportional. The proportionality factor is perturbed by a random component, which accounts for the effect of atmospheric precipitation. The balance equation is transformed into a stochastic differential equation with a multiplicative white noise, which is used to construct a Fokker-Plank equation for the probability density of chemical flow. A stationary solution containing a power function is found for this equation. Because of the proportionality of the concentration and chemical flow, the concentration distribution also obeys the power law. Statistical treatment of empirical data on some water quality characteristics and water flow showed that the power law adequately describes the probability of unfavorable hydrochemical events. The parameters of this law for turbidity, color index, permanganate oxidability, and ammonia concentration are evaluated.__________Translated from Vodnye Resursy, Vol. 32, No. 4, 2005, pp. 452–458.Original Russian Text Copyright © 2005 by Dolgonosov, Korchagin. 相似文献
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Koichi Unami Macarius Yangyuoru Abul Hasan Md. Badiul Alam Gordana Kranjac-Berisavljevic 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(1):77-89
Micro-dams are expected to be feasible options for water resources development in semi-arid regions such as the Guinea savanna agro-ecological zone of West Africa. An optimal water management strategy in a micro-dam irrigation scheme supplying water from an existing reservoir to a potential command area is discussed in this paper based on the framework of stochastic control. Water intake facilities are assumed to consist of photovoltaic pumping system units and hoses. The knowledge of current states of the storage volume of the reservoir and the soil moisture in the command area is fed-back to the intake flow rate. A system of two stochastic differential equations is proposed as a model for the dynamics of the micro-dam irrigation scheme, so that temporally backward solution of the Hamilton–Jacobi–Bellman equation determines an optimal control, which represents the optimal water management strategy. A computational procedure using the finite element method is successfully implemented to provide comprehensive information on the optimal control. The results indicate that the water initially stored in the reservoir can support full irrigation for about 80 days under the optimal water management strategy, which is predominantly based on the demand-side principle. However, the volatility of the soil moisture in the command area must be reasonably small. 相似文献
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R. S. govindaraju M. L. Kavvas 《Stochastic Environmental Research and Risk Assessment (SERRA)》1991,5(2):89-104
A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths. 相似文献
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《Advances in water resources》2002,25(7):733-746
Backward location and travel time probabilities, which provide information about the former location of contamination in an aquifer, can be used to identify unknown contamination sources. Backward location probability describes the possible upgradient positions of contamination at a known time in the past, and backward travel time probability describes the time required for contamination to travel from a known upgradient location to an observation point. These probabilities are related to adjoint states of resident concentration, and their governing equation is the adjoint of a forward contaminant transport model. Using adjoint theory to obtain the appropriate governing equation, we extend the backward probability model for conservative solutes to more general non-uniform and transient flow fields. In particular, we address three important extensions, spatially-varying porosity, transient flow and temporally-varying porosity, and internal distributed sources and sinks of solute and water. For the first time we learn that forward and backward location and travel time probabilities are not necessarily equivalent to adjoint states, but are related to them. The extensions are illustrated using a vertically-integrated groundwater model, creating transient flow by a step change in pumping and using areal recharge as an internal distributed source. Both the movement and spread of probabilities are affected. With internal sources of water, there are two interpretations of backward probability, depending on whether or not the source of water is also a source of solute. The results demonstrate how the backward probability model can be applied to other, perhaps more important, non-uniform and transient flow conditions, with time- and space-varying water storage, such as time-varying pumping or unsaturated (or saturated–unsaturated) flow and transport with spatially- and temporally-varying moisture content. 相似文献
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A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths. 相似文献
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Bubble coalescence in basalt flows: comparison of a numerical model with natural examples 总被引：1，自引：0，他引：1
Gas accumulation in magma may be aided by coalescence of bubbles because large coalesced bubbles rise faster than small bubbles. The observed size distribution of gas bubbles (vesicles) in lava flows supports the concept of post-eruptive coalescence. A numerical model predicts the effects of rise and coalescence consistent with observed features. The model uses given values for flow thickness, viscosity, volume percentage of gas bubbles, and an initial size distribution of bubbles together with a gravitational collection kernel to numerically integrate the stochastic collection equation and thereby compute a new size spectrum of bubbles after each time increment of conductive cooling of the flow. Bubbles rise and coalesce within a fluid interior sandwiched between fronts of solidification that advance inward with time from top and bottom. Bubbles that are overtaken by the solidification fronts cease to migrate. The model predicts the formation of upper and lower vesicle-rich zones separated by a vesicle-poor interior. The upper zone is broader, more vesicular, and has larger bubbles than the lower zone. Basaltic lava flows in northern California exhibit the predicted zonation of vesicularity and size distribution of vesicles as determined by an impregnation technique. In particular, the size distribution at the tops and bottoms of flows is essentially the same as the initial distribution, reflecting the rapid initial solidification at the bases and tops of the flows. Many large vesicles are present in the upper vesicular zones, consistent with expected formation as a result of bubble coalescence during solidification of the lava flows. Both the rocks and model show a bimodal or trimodal size distribution for the upper vesicular zone. This polymodality is explained by preferential coalescence of larger bubbles with subequal sizes. Vesicularity and vesicle size distribution are sensitive to atmospheric pressure because bubbles expand as they decompress during rise through the flow. The ratio of vesicularity in the upper to that in the lower part of a flow therefore depends not only on bubble rise and coalescence, but also on flow thickness and atmospheric pressure. Application of simple theory to the natural basalts suggests solidification of the basalts at 1.0±0.2 atm, consistent with the present atmospheric pressure. Paleobathymetry and paleoaltimetry are possible in view of the sensitivity of vesicle size distributions to atmospheric pressure. Thus, vesicular lava flows can be used to crudely estimate ancient elevations and/or sea level air pressure. 相似文献
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Uncertainty in bed roughness is a dominant factor in providing a sufficiently accurate simulation of floodplain flows. This study describes a method to compute the transition probability density distribution of time-varying water elevations where the evolutionary process is based on a conventional one-dimensional storage cell model with governing stochastic differential equation. By including the random inputs (or noise terms) of bed roughness and initial water depth, time-dependent and spatially varying probability density function of the water surface leads to a Fokker–Planck equation. The model’s performance is evaluated by applying it to shallow water flow with a horizontal bed. Sensitivity of model predictions to variations in the bed friction parameters is shown. By comparing the result of the proposed method with that of conventional Monte Carlo simulation, the advantage of the former as a method for density function prediction is confirmed. 相似文献
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《Advances in water resources》1998,22(3):257-272
This work presents a rigorous numerical validation of analytical stochastic models of steady state unsaturated flow in heterogeneous porous media. It also provides a crucial link between stochastic theory based on simplifying assumptions and empirical field and simulation evidence of variably saturated flow in actual or realistic hypothetical heterogeneous porous media. Statistical properties of unsaturated hydraulic conductivity, soil water tension, and soil water flux in heterogeneous soils are investigated through high resolution Monte Carlo simulations of a wide range of steady state flow problems in a quasi-unbounded domain. In agreement with assumptions in analytical stochastic models of unsaturated flow, hydraulic conductivity and soil water tension are found to be lognormally and normally distributed, respectively. In contrast, simulations indicate that in moderate to strong variable conductivity fields, longitudinal flux is highly skewed. Transverse flux distributions are leptokurtic. the moments of the probability distributions obtained from Monte Carlo simulations are compared to modified first-order analytical models. Under moderate to strong heterogeneous soil flux conditions (σ2y≥1), analytical solutions overestimate variability in soil water tension by up to 40% as soil heterogeneity increases, and underestimate variability of both flux components by up to a factor 5. Theoretically predicted model (cross-)covariance agree well with the numerical sample (cross-)covarianaces. Statistical moments are shown to be consistent with observed physical characteristics of unsaturated flow in heterogeneous soils.©1998 Elsevier Science Limited. All rights reserved 相似文献
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Wilhelm BECHTELER Davood FARSHI Institute of Hydroscience Federal Armed Forces University Munich Neubiberg Germany 《国际泥沙研究》2001,16(2)
1 INTRODUCTIONFor many hydraulic engineering problems, the analysis of flow and bed level variations in openchannels is a fundamental prerequisite. forcal methOds fOr alluvial rivers are well develoPednowadays as far as onediInensional descriPtions are concemed. A cOmPrhensive analysis of Ihe wellknown models is Presented by Habersack(l998). HOwever, for a number of Problems such as channelwidening, flow pattem close to sPuds and etc. a more deailed knowledge of the bed level behavio… 相似文献
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It is generally known that the variability of earthquake ground motion is mainly in time and space. To investigate the impact of this variability on the seismic performance of a long-span flexible structure, we discuss the seismic dynamic responses of a real bridge subjected to stochastic seismic ground motion. We incorporate the effect of wave passage by means of the method of probability density evolution based on dynamic time-history analysis from the perspective of stochastic dynamics. First, we introduce the theory of probability density evolution and a category of stochastic seismic model. We then conduct a series of deterministic seismic dynamic analyses of the bridge to establish the probability density equation. Eventually, we obtain the probability information at the level of the probability density function of the seismic response by solving the probability-density evolution equation. The results show that the impact of travelling waves on a long-span structure is related to the characteristics of the earthquake ground motion and the structure, and that travelling waves increase the variability of the seismic response. 相似文献
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引入两个负指数型差值函数,估计降雨量的概率分布,以此描述流域降雨空间变异性问题.将降雨量空间统计分布与垂向混合产流模型耦合进行产流量计算,即对地表径流,采用超渗产流模式,根据降雨与土壤下渗能力的联合分布推求其空间分布;对地面以下径流,采用蓄满产流模式,以地表渗入量的均值作为输入,进行简化处理以提高其实用性;最终推导出总产流量概率分布函数计算公式.将流域概化成一个线性水库,并根据随机微分方程理论,推导任一计算时段洪水流量的概率分布,从而构建了一个完整的随机产汇流模型.以淮河支流黄泥庄流域为例进行应用研究,结果表明,该模型可提供洪水过程的概率预报,可用于防洪风险分析,若以概率分布的期望值作为确定性预报,亦具有较高精度. 相似文献
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Aleksey Sidorchuk 《水文研究》2005,19(7):1399-1417
A new stochastic method of detachment rate estimation was used in erosion modelling. This method was based on calculating the probability of driving forces exceeding resistance forces in the interaction of oscillating flow and structured soil. Knowledge of the probability density functions for flow velocity, soil cohesion, aggregate size and soil integrity makes it possible to calculate theoretically the erosion rate of cohesive soil for any combination of these stochastic variables. The proposed theory explains the variability in relationships between rate of detachment and flow velocity. With flow velocity, detachment rate increases more rapidly for more integrated soil with higher cohesion and larger aggregates. This theory also shows the great difference between soil erosion type for relatively high and relatively low flow velocities, and explains rather high errors, even with detailed models, in the calculation of low soil erosion rate. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Fuzzy-probabilistic calculations of water-balance uncertainty 总被引：1，自引：0，他引：1
Hydrogeological systems are often characterized by imprecise, vague, inconsistent, incomplete, or subjective information, which may limit the application of conventional stochastic methods in predicting hydrogeologic conditions and associated uncertainty. Instead, predictions and uncertainty analysis can be made using uncertain input parameters expressed as probability boxes, intervals, and fuzzy numbers. The objective of this paper is to present the theory for, and a case study as an application of, the fuzzy-probabilistic approach, combining probability and possibility theory for simulating soil water balance and assessing associated uncertainty in the components of a simple water-balance equation. The application of this approach is demonstrated using calculations with the RAMAS Risk Calc code, to assess the propagation of uncertainty in calculating potential evapotranspiration, actual evapotranspiration, and infiltration—in a case study at the Hanford site, Washington, USA. Propagation of uncertainty into the results of water-balance calculations was evaluated by changing the types of models of uncertainty incorporated into various input parameters. The results of these fuzzy-probabilistic calculations are compared to the conventional Monte Carlo simulation approach and estimates from field observations at the Hanford site. 相似文献
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1 INTRODUCTIONThe prediction of future impacts on terrestrial ecosystems by atmospheric, climatic and land-usechanges is the aim of watershed management. Meeting these requirements scientists, managers and policymakers try to achieve the sustainable management of the vitally important resources of watersheds due toan integrated ecosystem approach at the catchment scale. As composite landscapes often have a highdegree of contingency between its elements, the transport over these landscape s… 相似文献
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随机动力系统最优控制准则研究 总被引：2，自引：0，他引：2
根据线性二次最优控制理论,给出了系统随机最优控制的控制律一般形式。从目标控制量的物理意义出发,提出了基于系统概率密度演化分析的最优控制准则,建立了递阶层次的演化过程控制准则类。以线性单自由度体系随机地震反应最优控制为例,分析了各控制准则类的权矩阵参数优化结果,并根据最优控制律进行了系统随机最优控制研究。结果表明,本文提出的系统随机最优控制的控制律确定方法可以对系统性态进行有效的控制。 相似文献
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Nonlinear mechanisms of long-term variations in the Caspian Sea level are described. It is shown that with account taken of the dependence of the evaporation depth from the Volga basin surface on soil moisture content and the dependence of the evaporation depth from the sea surface on its level, we obtain a fundamentally new (chaotic) oscillation mechanism with several attraction levels. The stochastic differential equations describing the water budget of the sea basin and the sea proper and the respective solutions of the Fokker–Planck–Kolmogorov equation are shown to have stationary bimodal density of the level probability. The random process, characterizing the sea level variations at a nonlinear dependence between the evaporation rate and the level is found to be non-Gaussian. Noise-induced transitions, caused by nonlinear evaporation processes are described. A new nonlinear stochastic theory describing the Caspian Sea level variations and based on predicted physical effects is suggested. 相似文献
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Hakan Sirin 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,20(6):381-390
Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field. 相似文献