共查询到20条相似文献，搜索用时 664 毫秒
1.
Panayiotis Dimitriadis Demetris Koutsoyiannis 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(6):1649-1669
Three common stochastic tools, the climacogram i.e. variance of the time averaged process over averaging time scale, the autocovariance function and the power spectrum are compared to each other to assess each one’s advantages and disadvantages in stochastic modelling and statistical inference. Although in theory, all three are equivalent to each other (transformations one another expressing second order stochastic properties), in practical application their ability to characterize a geophysical process and their utility as statistical estimators may vary. In the analysis both Markovian and non Markovian stochastic processes, which have exponential and power-type autocovariances, respectively, are used. It is shown that, due to high bias in autocovariance estimation, as well as effects of process discretization and finite sample size, the power spectrum is also prone to bias and discretization errors as well as high uncertainty, which may misrepresent the process behaviour (e.g. Hurst phenomenon) if not taken into account. Moreover, it is shown that the classical climacogram estimator has small error as well as an expected value always positive, well-behaved and close to its mode (most probable value), all of which are important advantages in stochastic model building. In contrast, the power spectrum and the autocovariance do not have some of these properties. Therefore, when building a stochastic model, it seems beneficial to start from the climacogram, rather than the power spectrum or the autocovariance. The results are illustrated by a real world application based on the analysis of a long time series of high-frequency turbulent flow measurements. 相似文献
2.
Timothy Delsole 《Surveys in Geophysics》2004,25(2):107-149
Atmospheric and oceanic eddies are believed to be manifestations of quasigeostrophic turbulence — turbulence that occurs in
rapidly rotating, vertically stratified fluid systems. The heat, momentum, and water transport by these eddies constitute
a significant component of the climate balance, without which climate change cannot be understood. A major, unsolved problem
is whether the turbulent eddy fluxes can be parameterized in terms of the large-scale, background flow. In the past, stochastic
models have been used quite extensively to investigate quasigeostrophic turbulence in the case in which the eddy statistics
are isotropic and homogeneous. Unfortunately, these models ignore the background shear which is absolutely essential to maintaining
the eddies in the presence of dissipation. Recent attempts to extend stochastic models to shear flows have shown significant
skill in predicting the structure of the eddy fluxes in arbitrary, three-dimensionally varying flows. This paper provides
an accessible introduction to these models. The topics reviewed include quasigeostrophic turbulence and two-dimensional turbulence,
non-modal andoptimal perturbations, mathematical theory of stochastic models, stochastic model simulations with realistic
background states, and recent closure theories. A list of unsolved problems concludes this review. 相似文献
3.
《水文科学杂志》2013,58(1):142-150
Abstract Due to its great importance, the availability of long flow records, contemporary as well as older, and the additional historical information of its behaviour, the Nile is an ideal test case for identifying and understanding hydrological behaviours, and for model development. Such behaviours include the long-term persistence, which historically has motivated the discovery of the Hurst phenomenon and has put into question classical statistical results and typical stochastic models. Based on the empirical evidence from the exploration of the Nile flows and on the theoretical insights provided by the principle of maximum entropy, a concept newly employed in hydrological stochastic modelling, an advanced yet simple stochastic methodology is developed. The approach is focused on the prediction of the Nile flow a month ahead, but the methodology is general and can be applied to any type of stochastic prediction. The stochastic methodology is also compared with deterministic approaches, specifically an analogue (local nonlinear chaotic) model and a connectionist (artificial neural network) model based on the same flow record. All models have good performance with the stochastic model outperforming in prediction skills and the analogue model in simplicity. In addition, the stochastic model has other elements of superiority such as the ability to provide long-term simulations and to improve understanding of natural behaviours. 相似文献
4.
The Hurst phenomenon and fractional Gaussian noise made easy 总被引：1，自引：0，他引：1
DEMETRIS KOUTSOYIANNIS 《水文科学杂志》2013,58(4):573-595
Abstract The Hurst phenomenon, which characterizes hydrological and other geophysical time series, is formulated and studied in an easy manner in terms of the variance and autocorrelation of a stochastic process on multiple temporal scales. In addition, a simple explanation of the Hurst phenomenon based on the fluctuation of a hydrological process upon different temporal scales is presented. The stochastic process that was devised to represent the Hurst phenomenon, i.e. the fractional Gaussian noise, is also studied on the same grounds. Based on its studied properties, three simple and fast methods to generate fractional Gaussian noise, or good approximations of it, are proposed. 相似文献
5.
Huai-Hsien Huang Carlos E. Puente Andrea Cortis 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(4):955-968
Complex geometries often present in hydrologic data sets such as precipitation records have been difficult to model in their totality using classical stochastic methods. In recent years, we have developed extensions of a deterministic procedure, the fractal-multifractal (FM) method, whose patterns share fine details and textures of individual data sets in addition to the usual key statistical properties. This work discusses our latest efforts at encoding four geometrically distinct storms gathered in Iowa City with parameters found running a modified particle swarm optimization procedure. The results reaffirm the capabilities of the FM method as all storms are closely fitted within measurement errors. All sets may be encoded with a compression ratio exceeding 350:1, have a maximum error in cumulative distribution less than 2.5 %, and closely preserve the autocorrelation, power spectrum, and multifractal spectrum of the records. 相似文献
6.
Development of the instantaneous unit hydrograph using stochastic differential equations 总被引：1，自引：0，他引：1
Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement. 相似文献
7.
Sarino S. E. Serrano 《Stochastic Environmental Research and Risk Assessment (SERRA)》1990,4(2):151-160
Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement. 相似文献
8.
David Vere-Jones 《Pure and Applied Geophysics》2010,167(6-7):645-653
9.
《水文科学杂志》2013,58(6)
Abstract Abstract Characterization of heterogeneity at the field scale generally requires detailed aquifer properties such as transmissivity and hydraulic head. An accurate delineation of these properties is expensive and time consuming, and for many if not most groundwater systems, is not practical. As an alternative approach, stochastic representation of random fields is used and presented in this paper. Specifically, an iterative stochastic conditional simulation approach was applied to a hypothetical and highly heterogeneous pre-designed aquifer system. The approach is similar to the classical co-kriging technique; it uses a linear estimator that depends on the covariance functions of transmissivity (T), and hydraulic head (h), as well as their cross-covariances. A linearized flow equation along with a conditional random field generator constitutes the iterative process of the conditional simulation. One hundred equally likely realizations of transmissivity fields with pre-specified geostatistical parameters were generated, and conditioned to both limited transmissivity and head data. The successful implementation of the approach resulted in conditioned flow paths and travel-time distribution under different degrees of aquifer heterogeneity. This approach worked well for fields exhibiting small variances. However, for random fields exhibiting large variances (greater than 1.0), an iterative procedure was used. The results show that, as the variance of the ln[T] increases, the flow paths tend to diverge, resulting in a wide spectrum of flow conditions, with no direct discernable relationship between the degree of heterogeneity and travel time. The applied approach indicates that high errors may result when estimation of particle travel times in a heterogeneous medium is approximated by an equivalent homogeneous medium. 相似文献
10.
Abstract A model of a homogeneous isotropic turbulent flow is presented. The model provides different realizations of the random velocity field component with given correlation latitudinal and lateral functions and a spatial structure which obeys the Kolmogorov theory of homogeneous and isotropic turbulence. For the generation of the turbulent flow the structural function of the flow in the form suggested by Batchelor (Monin and Yaglom, 1975) was used. This function describes the spectrum of turbulence both in the viscous and inertial ranges. The isotropy and homogeneity of the velocity field of the model are demonstrated. The model is aimed at simulating the ‘‘fine'’ features of drop's (aerosol particles') motion, such as the deviations of drops’ velocity from the velocity of the flow, detailed structures of drops’ tracks, related to drops’ (particles') inertia. The model is intended also for the purpose of studying cloud drops’ and aerosol particles’ motion and their diffusional spreading utilizing the Monte Carlo methods. Some examples of drop tracks for drops of different size are presented. Drops’ tracks are very sophisticated, so that the relative position of drops falling initially from the same point can vary drastically. In some cases drops’ tracks diverge very quickly, in other cases all drops move within a turbulent eddy along nearly the same closed tracks, but with different speed. The concentration of drop tracks along isolated paths is found in spite of the existence of a large number of velocity harmonics. It is shown that drops (aerosol particles) tend to leave some areas of the turbulent flow apparently due to their inertia. These effects can possibly contribute to inhomogeneity of drops’ concentration in clouds at different spatial scales. 相似文献
11.
考虑土-结构相互作用和岩土参数不确定性的核电厂结构地震响应分析 总被引：2，自引：0，他引：2
针对核电厂结构,在考虑土-结构相互作用(SSI)的情况下进行随机地震反应分析,探讨地基岩土参数的不确定性对反应堆厂房楼层反应谱(FRS)的影响。运用ANSYS软件模块建立核电厂(NPP)结构有限元模型,通过设置边界弹簧单元和阻尼装置来考虑SSI效应;并且通过设置具有概率意义的弹簧刚度和阻尼系数,来模拟土特性参数的不确定性。随机响应分析与确定性分析的结果对比,揭示了岩性地基条件下SSI效应对核电厂FRS的影响以及地基岩土参数不确定性对FRS的影响程度。研究表明,在岩性地基条件下,亦不应忽略SSI效应;考虑SSI效应的随机分析模型同确定性模型相比,二者的分析结果较为接近,两方法都可用于NPP的FRS敏感性分析评估之中,并可进行相互比照。 相似文献
12.
Investigating long range dependence of river flows, especially in connection with various climate and storage related factors, is important in order to improve stochastic models for long range dependence and in order to understand deterministic and stochastic variability in long‐term behaviour of streamflow. Long range dependence expressed by the Hurst coefficient H is estimated for 39 (deseasonalized) mean daily runoff time series in Europe of at least 59 years using five estimators (rescaled range, regression on periodogram, Whittle, aggregated variances, and least squares based on variance). All methods yield estimates of H > 0.5 for all data sets. The results from the different estimators are significantly positively correlated for all pairs of methods indicating consistency of the methods used. Correlations between H and various catchment attributes are also analysed. H is strongly positively correlated with catchment area. Apparently, increasing storage with catchment area translates into increasing long range dependence. H is also positively correlated with mean discharge and air temperature and negatively correlated with the mean specific discharge and the seasonality index (maximum Pardé coefficient). No significant correlation is found between the Hurst coefficient and the length of the analyzed time series. The correlations are interpreted in terms of snow processes and catchment wetness. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
13.
14.
Demetris Koutsoyiannis 《水文科学杂志》2013,58(2):225-244
ABSTRACTThe old principle of parsimonious modelling of natural processes has regained its importance in the last few years. The inevitability of uncertainty and risk, and the value of stochastic modelling in dealing with them, are also again appreciated, after a period of growing hopes for radical reduction of uncertainty. Yet, in stochastic modelling of natural processes several families of models are used that are often non-parsimonious, unnatural or artificial, theoretically unjustified and, eventually, unnecessary. Here we develop a general methodology for more theoretically justified stochastic processes, which evolve in continuous time and stem from maximum entropy production considerations. The discrete-time properties thereof are theoretically derived from the continuous-time ones and a general simulation methodology in discrete time is built, which explicitly handles the effects of discretization and truncation. Some additional modelling issues are discussed with a focus on model identification and fitting, which are often made using inappropriate methods.
EDITOR Z.W. Kundzewicz ASSOCIATE EDITOR S. Grimaldi 相似文献
15.
P.E. O’Connell D. Koutsoyiannis H. F. Lins Y. Markonis A. Montanari T. Cohn 《水文科学杂志》2016,61(9):1571-1590
ABSTRACTEmanating from his remarkable characterization of long-term variability in geophysical records in the early 1950s, Hurst’s scientific legacy to hydrology and other disciplines is explored. A statistical explanation of the so-called “Hurst Phenomenon” did not emerge until 1968 when Mandelbrot and co-authors proposed fractional Gaussian noise based on the hypothesis of infinite memory. A vibrant hydrological literature ensued where alternative modelling representations were explored and debated, e.g. ARMA models, the Broken Line model, shifting mean models with no memory, FARIMA models, and Hurst-Kolmogorov dynamics, acknowledging a link with the work of Kolmogorov in 1940. The diffusion of Hurst’s work beyond hydrology is summarized by discipline and citations, showing that he arguably has the largest scientific footprint of any hydrologist in the last century. Its particular relevance to the modelling of long-term climatic variability in the era of climate change is discussed. Links to various long-term modes of variability in the climate system, driven by fluctuations in sea surface temperatures and ocean dynamics, are explored. Several issues related to the Hurst Phenomenon in hydrology remain as a challenge for future research.
Editor M. Acreman; Associate editor A. Carsteanu 相似文献
16.
Abstract Hydrological models are commonly used to perform real-time runoff forecasting for flood warning. Their application requires catchment characteristics and precipitation series that are not always available. An alternative approach is nonparametric modelling based only on runoff series. However, the following questions arise: Can nonparametric models show reliable forecasting? Can they perform as reliably as hydrological models? We performed probabilistic forecasting one, two and three hours ahead for a runoff series, with the aim of ascribing a probability density function to predicted discharge using time series analysis based on stochastic dynamics theory. The derived dynamic terms were compared to a hydrological model, LARSIM. Our procedure was able to forecast within 95% confidence interval 1-, 2- and 3-h ahead discharge probability functions with about 1.40 m3/s of range and relative errors (%) in the range [–30; 30]. The LARSIM model and the best nonparametric approaches gave similar results, but the range of relative errors was larger for the nonparametric approaches. Editor D. Koutsoyiannis; Associate editor K. Hamed Citation Costa, A.C., Bronstert, A. and Kneis, D., 2012. Probabilistic flood forecasting for a mountainous headwater catchment using a nonparametric stochastic dynamic approach. Hydrological Sciences Journal, 57 (1), 10–25. 相似文献
17.
This paper investigates the suitability of Sen's approach in modelling hydrologic time series and in particular the generation of synthetic flow series. It was found that several problems exist with the method as proposed. These include too many parameters in the model, difficulties in modelling skewed series, and finding a suitable stochastic model for the residuals between the original and the fitted cumulative departure curves. On the other hand, it has been found that Sen's method is effective in preserving the Hurst phenomenon and is especially suited for modelling time series with a relatively high Hurst coefficient but low lag-one serial correlation coefficient. Also, with some modifications to the suggested procedure some of the stated problems can be somewhat overcome. 相似文献
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19.
Mehdi Eshagh 《Geophysical Prospecting》2014,62(1):158-171
The idea of this paper is to present estimators for combining terrestrial gravity data with Earth gravity models and produce a high‐quality source of the Earth's gravity field data through all wavelengths. To do so, integral and point‐wise estimators are mathematically developed, based on the spectral combination theory, in such a way that they combine terrestrial data with one and/or two Earth gravity models. The integral estimators are developed so that they become biased or unbiased to a priori information. For testing the quality of the estimators, their global mean square errors are generated using an Earth gravity model08 model and one of the recent products of the gravity field and steady‐state ocean circulation explorer mission. Numerical results show that the integral estimators have smaller global root mean square errors than the point‐wise ones but they are not efficient practically. The integral estimator of the biased type is the most suited due to its smallest global root mean square error comparing to the rest of the estimators. Due largely to the omission errors of Earth gravity models the point‐wise estimators are not sensitive to the Earth gravity model commission error; therefore, the use of high‐degree Earth gravity models is very influential for reduction of their root mean square errors. Also it is shown that the use of the ocean circulation explorer Earth gravity model does not significantly reduce the root mean square errors of the presented estimators in the presence of Earth gravity model08. All estimators are applied in the region of Fennoscandia and a cap size of 2° for numerical integration and a maximum degree of 2500 for generation of band‐limited kernels are found suitable for the integral estimators. 相似文献
20.
N. A. Silant'ev 《地球物理与天体物理流体动力学》2013,107(2-4):183-197
Abstract The exact numerical and approximate analytical solutions of the simplest nonlinear integral equation with second order nonlinearity for the averaged Green function are presented. It is assumed that the turbulence is stationary, homogeneous, isotropic and incompressible. Numerous examples of turbulent spectra are considered (peak-like spectrum, spectra of Kolmogorov's type with different forms of “pumping” regions, stepwise spectra etc.). Special emphasis is given to investigating the case of so called “frozen” turbulence when the parameter ξ =u 0τ/R→∞ where uτ0,R 0 are characteristic velocity, lifetime and space scale of turbulent pulsations, respectively. It is shown that these solutions allow us to calculate the turbulent diffusivities accurately for arbitrary spectra with any values of the parameter ξ. The results take into account the possible helicity of turbulence concerned only with scalar passive fields (number density and temperature). 相似文献