共查询到20条相似文献，搜索用时 172 毫秒
1.
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
2.
《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
3.
《水文科学杂志》2013,58(3)
Abstract The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation and lag-one autocorrelation. In the first part of the study, the marginal distributional properties of hydrological processes and the state scaling behaviour were investigated. This second part of the study is devoted to joint distributional properties of hydrological processes. Specifically, it investigates the time dependence structure that may result from the ME principle and shows that the time scaling behaviour (or the Hurst phenomenon) may be obtained by this principle under the additional general condition that all time scales are of equal importance for the application of the ME principle. The omnipresence of the time scaling behaviour in numerous long hydrological time series examined in the literature (one of which is used here as an example), validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. 相似文献
4.
John Sutcliffe Stephen Hurst Ayman G. Awadallah Emma Brown Khaled Hamed 《水文科学杂志》2016,61(9):1557-1570
ABSTRACTH.E. Hurst spent some 60 years studying the Nile for the Egyptian government, and laid the foundation for a monumental set of hydrological records and investigations. His studies of the size of over-year reservoirs needed to maintain a given yield from Nile flows showed that this was greater than that based on random series. This finding, known as the Hurst phenomenon, was confirmed by other natural series and led to important advances in practical and theoretical statistics. His work led to the design of the Aswan High Dam and to continued research in Egypt.
Editor D. Koutsoyiannis; Guest editor E. Eris 相似文献
5.
Temporal variations of the main hydrological variables over 16 years were systematically investigated based on the results from an integrated hydrological modeling at the Sagehen Creek watershed in northern Sierra Nevada. Temporal scaling of these variables and damping effects of the hydrological system as well as its subsystems, i.e., the land surface, unsaturated zone, and saturated zone, were analyzed with spectral analyses. It was found that the hydrological system may act as a cascade of hierarchical fractal filters which sequentially transfer a non-fractal or less correlated fractal hydrological signal to a more correlated fractal signal. The temporal scaling of simulated infiltration (SI), simulated actual evapotranspiration (SET), simulated recharge (SR), measured baseflow (MBF), measured streamflow (MSF) exist and the temporal autocorrelation of these variables increase as water moves through the system. The degree of the damping effect of the subsystems is different and is strongest in the unsaturated zone compared with that of the land surface and saturated zone. The temporal scaling of the simulated groundwater levels (Sh) also exists and is strongly affected by the river: the temporal autocorrelation of Sh near the river is similar to that of the river stage fluctuations and increases away from the river. There is a break in the temporal scaling of Sh near the river at low frequencies due to the effect of the river. Temporal variations of the simulated soil moisture (Sθ) is more complicated: the value of the scaling exponent (β) for Sθ increases with depth as water moves downwards and its high-frequency fluctuations are damped by the unsaturated zone. The temporal fluctuations of measured precipitation and SI are fractional Gaussian noise, those of SET, SR, MBF, and MSF are fractional Brownian motion (fBm), and those of Sh away from the river are 2nd-order fBm based on the values of β obtained in this study. 相似文献
6.
AbstractRiver basins are by definition temporally-varying systems: changes are apparent at every temporal scale, in terms of changing meteorological inputs and catchment characteristics due to inherently uncertain natural processes and anthropogenic interventions. In an operational context, the ultimate goal of hydrological modelling is predicting responses of the basin under conditions that are similar or different to those observed in the past. Since water management studies require that anthropogenic effects are considered known and a long hypothetical period is simulated, the combined use of stochastic models, for generating the inputs, and deterministic models that also represent the human interventions in modified basins, is found to be a powerful approach for providing realistic and statistically consistent simulations (in terms of product moments and correlations, at multiple time scales, and long-term persistence). The proposed framework is investigated on the Ferson Creek basin (USA) that exhibits significantly growing urbanization during the last 30 years. Alternative deterministic modelling options include a lumped water balance model with one time-varying parameter and a semi-distributed scheme based on the concept of hydrological response units. Model inputs and errors are respectively represented through linear and nonlinear stochastic models. The resulting nonlinear stochastic framework maximizes the exploitation of the existing information by taking advantage of the calibration protocol used in this issue. 相似文献
7.
A problem frequently met in engineering hydrology is the forecasting of hydrological variables conditional on their historical observations and the hindcasts and forecasts of a deterministic model. On the contrary, it is a common practice for climatologists to use the output of general circulation models (GCMs) for the prediction of climatic variables despite their inability to quantify the uncertainty of the predictions. Here we apply the well-established Bayesian processor of forecasts (BPF) for forecasting hydroclimatic variables using stochastic models through coupling them with GCMs. We extend the BPF to cases where long-term persistence appears, using the Hurst-Kolmogorov process (HKp, also known as fractional Gaussian noise) and we investigate its properties analytically. We apply the framework to calculate the distributions of the mean annual temperature and precipitation stochastic processes for the time period 2016–2100 in the United States of America conditional on historical observations and the respective output of GCMs. 相似文献
8.
《水文科学杂志》2013,58(3)
Abstract Abstract Identification of the presence of scaling in the river flow process has been a challenging problem in hydrology. Studies conducted thus far have viewed this problem essentially from a stochastic perspective, because the river flow process has traditionally been assumed to be a result of a very large number of variables. However, recent studies employing nonlinear deterministic and chaotic dynamic concepts have reported that the river flow process could also be the outcome of a deterministic system with only a few dominant variables. In the wake of such reports, a preliminary attempt is made in this study to investigate the type of scaling behaviour in the river flow process (i.e. chaotic or stochastic). The investigation is limited only to temporal scaling. Flow data of three different scales (daily, 5-day and 7-day) observed in each of three rivers in the USA: the Kentucky River in Kentucky, the Merced River in California and the Stillaguamish River in Washington, are analysed. It is assumed that the dynamic behaviour of the river flow process at these individual scales provides clues about the scaling behaviour between these scales. The correlation dimension is used as an indicator to distinguish between chaotic and stochastic behaviours. The results are mixed with regard to the type of flow behaviour at individual scales and, hence, to the type of scaling behaviour, as some data sets show chaotic behaviour while others show stochastic behaviour. They suggest that characterization (chaotic or stochastic) of river flow should be a necessary first step in any scaling study, as it could provide important information on the appropriate approach for data transformation purposes. 相似文献
9.
《水文科学杂志》2013,58(3)
Abstract The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation (CV) and lag one autocorrelation. In this first part of the study, the marginal distributional properties of hydrological variables and the state scaling behaviour are investigated. Application of the ME principle under these very simple conditions results in the truncated normal distribution for small values of CV and in a nonexponential type (Pareto) distribution for high values of CV. In addition, the normal and the exponential distributions appear as limiting cases of these two distributions. Testing of these theoretical results with numerous hydrological data sets on several scales validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. Both theoretical and empirical results show that the state scaling is only an approximation for the high return periods, which is merely valid when processes have high variation on small time scales. In other cases the normal distributional behaviour, which does not have state scaling properties, is a more appropriate approximation. Interestingly however, as discussed in the second part of the study, the normal distribution combined with positive autocorrelation of a process, results in time scaling behaviour due to the ME principle. 相似文献
10.
A long time series (170 years) of daily flows of the river Warta (Poland) are subject to fractal analysis. A binary variable (renewal stream) illustrating excursions of the process of flow is examined. The raw series is subject to de-seasonalization and normalization. Fractal dimensions of crossings of Warta flows are determined using a novel variant of the box-counting method. Temporal variability of the flow process is studied by determination of fractal dimensions for shifted horizons of 10 or 30 years length. Spectral properties are compared between the time series of flows, and the fractional Brownian motion which describes both the fractal structure of the process and the Hurst phenomenon. The approach may be useful in further studies of non-stationary of the process of flow, analysis of extreme hydrological events and synthetic flow generation. 相似文献
11.
ABSTRACTTurbulence is considered to generate and drive most geophysical processes. The simplest case is isotropic turbulence. In this paper, the most common three-dimensional power-spectrum-based models of isotropic turbulence are studied in terms of their stochastic properties. Such models often have a high order of complexity, lack stochastic interpretation and violate basic stochastic asymptotic properties, such as the theoretical limits of the Hurst coefficient, when Hurst-Kolmogorov behaviour is observed. A simpler and robust model (which incorporates self-similarity structures, e.g. fractal dimension and Hurst coefficient) is proposed using a climacogram-based stochastic framework and tested over high-resolution observational data of laboratory scale as well as hydro-meteorological observations of wind speed and precipitation intensities. Expressions of other stochastic tools such as the autocovariance and power spectrum are also produced from the model and show agreement with data. Finally, uncertainty, discretization and bias related errors are estimated for each stochastic tool, showing lower errors for the climacogram-based ones and larger for power spectrum ones. 相似文献
12.
Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields 总被引：1，自引：1，他引：0
The fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) random field models have many applications in the environmental sciences. An issue of practical interest is the permissible range and the relations between different fractal exponents used to characterize these processes. Here we derive the bounds of the covariance exponent for fGn and the Hurst exponent for fBm based on the permissibility theorem by Bochner. We exploit the theoretical constraints on the spectral density to construct explicit two-point (covariance and structure) functions that are band-limited fractals with smooth cutoffs. Such functions are useful for modeling a gradual cutoff of power-law correlations. We also point out certain peculiarities of the relations between fractal exponents imposed by the mathematical bounds. Reliable estimation of the correlation and Hurst exponents typically requires measurements over a large range of scales (more than 3 orders of magnitude). For isotropic fractals and partially isotropic self-affine processes the dimensionality curse is partially lifted by estimating the exponent from measurements along fixed directions. We derive relations between the fractal exponents and the one-dimensional spectral density exponents, and we illustrate the relations using measurements of paper roughness.The author would like to acknowledge helpful comments from two anonymous referees. 相似文献
13.
This paper gives the exact solution in terms of the Karhunen–Loève expansion to a fractional stochastic partial differential equation on the unit sphere \({\mathbb {S}}^{2} \subset {\mathbb {R}}^{3}\) with fractional Brownian motion as driving noise and with random initial condition given by a fractional stochastic Cauchy problem. A numerical approximation to the solution is given by truncating the Karhunen–Loève expansion. We show the convergence rates of the truncation errors in degree and the mean square approximation errors in time. Numerical examples using an isotropic Gaussian random field as initial condition and simulations of evolution of cosmic microwave background are given to illustrate the theoretical results. 相似文献
14.
ABSTRACTThe trends in hydrological and climatic time series data of Urmia Lake basin in Iran were examined using the four different versions of the Mann-Kendall (MK) approach: (i) the original MK test; (ii) the MK test considering the effect of lag-1 autocorrelation; (iii) the MK test considering the effect of all autocorrelation or sample size; and (iv) the MK test considering the Hurst coefficient. Identification of hydrological and climatic data trends was carried out at monthly and annual time scales for 25 temperature, 35 precipitation and 35 streamflow gauging stations selected from the Urmia Lake basin. Mann-Kendall and Pearson tests were also applied to explore the relationships between temperature, precipitation and streamflow trends. The results show statistically significant upward and downward trends in the annual and monthly hydrological and climatic variables. The upward trends in temperature, unlike streamflow, are much more pronounced than the downward trends, but for precipitation the behaviour of trend is different on monthly and annual time scales. Furthermore, the trend results were affected by the different approaches. Specifically, the number of stations showing trends in hydrological and climatic variables decreased significantly (up to 50%) when the fourth test was considered instead of the first and the absolute value of the Z statistic for most of the time series was reduced. The results of correlations between streamflow and climatic variables showed that the streamflow in Urmia Lake basin is more sensitive to changes in temperature than those of precipitation. The observed decreases in streamflow and increases in temperature in the Urmia Lake basin in recent decades may thus have serious implications for water resources management under the warming climate with the expected population growth and increased freshwater consumption in this region.
Editor Z. W. Kundzewicz; Associate editor Q. Zhang 相似文献
15.
《水文科学杂志》2013,58(4)
Abstract The issue of data size (length) requirement for correlation dimension estimation continues to be the nucleus of criticisms on the (low) correlation dimensions reported for hydrological series. The present study addresses this issue from the viewpoints of both the existing theoretical guidelines and the practical reality. For this purpose, correlation dimension analysis is carried out for various data sizes from each of three types of series: (a) stochastic series (artificially generated using a random number generation technique); (b) chaotic series (artificially generated using the Henon map equation); and (c) hydrological series (real flow data observed on the Göta River in Sweden). The outcomes of the analysis of the (artificial) stochastic and chaotic series are used as a basis for interpreting the outcomes of the hydrological series. It is found that reliable dimension results for the stochastic and chaotic series are obtained even when the data size is only a few hundred points (i.e. no underestimation of dimension for small data sizes is visible), with no significant change in the scaling regimes (of the dimension plots) with respect to data size. This implies that the dimension results obtained for the hydrological series even with a few hundred points are also close to the actual ones. The insignificant difference in the scaling regimes for the various data sizes further supports this point. These results lead to the conclusions that: (1) the issue of data size requirement for correlation dimension estimation is more of a myth than reality; (2) the dimension estimates reported thus far for hydrological series could indeed be close to the actual ones (unless influenced by factors other than data size, e.g. delay time, noise, zeros, intermittency). 相似文献
16.
Abstract During recent decades, intensive research has focused on techniques capable of generating rainfall time series at a fine time scale that are (fully or partially) consistent with a given series at a coarser time scale. Here we theoretically investigate the consequences on the ensemble statistical behaviour caused by the structure of a simple and widely-used approach of stochastic downscaling for rainfall time series, the discrete Multiplicative Random Cascade. We show that synthetic rainfall time series generated by these cascade models correspond to a stochastic process which is non-stationary, because its temporal autocorrelation structure depends on the position in time in an undesirable manner. Then, we propose and theoretically analyse an alternative downscaling approach based on the Hurst-Kolmogorov process, which is equally simple but is stationary. Finally, we provide Monte Carlo experiments which validate our theoretical results. Editor Z.W. Kundzewicz Citation Lombardo, F., Volpi, E., and Koutsoyiannis, D., 2012. Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades. Hydrological Sciences Journal, 57 (6), 1052–1066. 相似文献
17.
William Barham 《地球物理与天体物理流体动力学》2019,113(5-6):505-526
ABSTRACTA system of stochastic differential equations is formulated describing the heat and salt content of a two-box ocean. Variability in the heat and salt content and in the thermohaline circulation between the boxes is driven by fast Gaussian atmospheric forcing and by ocean-intrinsic, eddy-driven variability. The eddy forcing of the slow dynamics takes the form of a colored, non-Gaussian noise. The qualitative effects of this non-Gaussianity are investigated by comparing to two approximate models: one that includes only the mean eddy effects (the “averaged model”), and one that includes an additional Gaussian white-noise approximation of the eddy effects (the “Gaussian model”). Both of these approximate models are derived using the methods of fast averaging and homogenisation. In the parameter regime where the dynamics has a single stable equilibrium the averaged model has too little variability. The Gaussian model has accurate second-order statistics, but incorrect skew and rare-event probabilities. In the parameter regime where the dynamics has two stable equilibria the eddy noise is much smaller than the atmospheric noise. The averaged, Gaussian, and non-Gaussian models all have similar stationary distributions, but the jump rates between equilibria are too small for the averaged and Gaussian models. 相似文献
18.
A. SZOLLOSI-NAGY 《水文科学杂志》2013,58(1):163-176
19.
Jens R?der Raimon Tolosana-Delgado Fred A. Hamprecht 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(7):865-879
The aim of this paper is to compare four different methods for binary classification with an underlying Gaussian process with
respect to theoretical consistency and practical performance. Two of the inference schemes, namely classical indicator kriging
and simplicial indicator kriging, are analytically tractable and fast. However, these methods rely on simplifying assumptions
which are inappropriate for categorical class labels. A consistent and previously described model extension involves a doubly
stochastic process. There, the unknown posterior class probability f(·) is considered a realization of a spatially correlated Gaussian process that has been squashed to the unit interval, and
a label at position x is considered an independent Bernoulli realization with success parameter f(x). Unfortunately, inference for this model is not known to be analytically tractable. In this paper, we propose two new computational
schemes for the inference in this doubly stochastic model, namely the “Aitchison Maximum Posterior” and the “Doubly Stochastic
Gaussian Quadrature”. Both methods are analytical up to a final step where optimization or integration must be carried out
numerically. For the comparison of practical performance, the methods are applied to storm forecasts for the Spanish coast
based on wave heights in the Mediterranean Sea. While the error rate of the doubly stochastic models is slightly lower, their
computational cost is much higher. 相似文献
20.
Abstract The aim of this paper is to quantify meteorological droughts and assign return periods to these droughts. Moreover, the relation between meteorological and hydrological droughts is explored. This has been done for the River Meuse basin in Western Europe at different spatial and temporal scales to enable comparison between different data sources (e.g. stations and climate models). Meteorological drought is assessed in two ways: using annual minimum precipitation amounts as a function of return period, and using troughs under threshold as a function of return period. The Weibull extreme value type 3 distribution has been fitted to both sources of information. Results show that the trough-under-threshold precipitation is larger than the annual minimum precipitation for a specific return period. Annual minimum precipitation values increase with spatial scale, being most pronounced for small temporal scales. The uncertainty in annual minimum point precipitation varies between 68% for the 30-day precipitation with a return period of 100 years, and 8% for the 120-day precipitation with a return period of 10 years. For spatially-averaged values, these numbers are slightly lower. The annual discharge deficit is significantly related to the annual minimum precipitation. Citation Booij, M. J. & de Wit, M. J. M. (2010) Extreme value statistics for annual minimum and trough-under-threshold precipitation at different spatio-temporal scales. Hydrol. Sci. J. 55(8), 1289–1301. 相似文献