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  • Articles  (103,568)
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  • 1
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    Stochastic environmental research and risk assessment 1 (1987), S. 1-2 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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  • 2
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    Stochastic environmental research and risk assessment 1 (1987), S. 3-16 
    ISSN: 1436-3259
    Keywords: Annual maximum ; partial duration series ; T-year estimate ; marshall-Olkin bivariate distribution ; Morgenstern bivariate distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract As a basis for development of the annual maximum distribution the so-called partial duration series with Poissonian occurrence times and exponentially distributed peak exceedance values has been selected. The model is generalized by allowing for a Markov dependence between succeeding peak values. Correlation values from p=0 to p=1 can be accounted for by introducing the Marshall-Olkin bivariate exponential distribution, which is presented in detail. The developed distribution function for the annual maximum is throughly analysed and a variety of distribution forms depending on the value of the correlation coefficient and the intensity in the Poisson process is hereby recognized. To a certain extent this might be considered as parallel to the scattering of hydrological regions with different generating mechanisms for the annual maxima.
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  • 3
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    Stochastic environmental research and risk assessment 1 (1987), S. 37-52 
    ISSN: 1436-3259
    Keywords: Cyclonic precipitation ; mathematical modeling ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A stochastic description is developed for extratropical cyclonic precipitation fields at synoptic and meso scales as they are typically observed by radars over the Earth. This description attempts to account I) for the synoptic scale behavior of a cyclonic storm (its birth, its synoptic scale motion trajectory, and its dissipation) II) for the synoptic-scale organizational structure of subsynoptic precipitation areas (rainbands, precipitation cores and raincells) within a cyclonic storm; and III) for the behavior of subsynoptic precipitation areas, in terms of their births, their spatial configuration evolutions, their motions, and their deaths (dissipation). The precipitation cores and the raincells are taken as the building blocks of the subsynoptic precipitation, areas within a cyclonic rainfield.
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  • 4
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    Stochastic environmental research and risk assessment 1 (1987), S. 81-100 
    ISSN: 1436-3259
    Keywords: Stochastic differential equations ; Itô calculus ; Stratovovich integrals ; Jump integrals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Fundamentals of the theory of stochastic calculus and stochastic differential equations (SDE's) which are finding increasing application in water resources engineering are reviewed. The basics of probability theory, mean square calculus and the Wiener, white Gaussian and compound Poisson processes are given in preparation for a discussion of the general Itô SDE with drift, diffusion and jump discontinuity terms driven by Gaussian white noise and compound Poissionian impulses. Also discussed are stochastic integration and the derivation of moment equations via the Itô differential rule. The lierature of SDE's is reviewed with an emphasis on the more accessible sources.
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  • 5
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    Stochastic environmental research and risk assessment 1 (1987), S. 53-66 
    ISSN: 1436-3259
    Keywords: Hurst range ; conditioned exchangeable, variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new theoretical interpretation is proposed for Hurst's empirical law which is applicable to discrete-valued inflows and is consistent with the existing interpretation for continuous-valued inflows. This is applied to independent net inflows {X r} having values +1 and −1 with unequal probabilities. With the aid of a new result on the exchangeability of symmetrically conditioned exchangeable variables, values of the resulting range are obtained and tabulated. It is found that the effect of skewness is very slight for skewness values between (about) 3 and −3, and that Hurst's own approximation, the “conditioned range”, is remarkably accurate.
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  • 6
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    Stochastic environmental research and risk assessment 1 (1987), S. 67-80 
    ISSN: 1436-3259
    Keywords: pattern analysis ; mixed-mode data ; event-covering ; discretization ; hydrometric data
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a pattern analysis technique that has been successfully applied to a set of hydrometric network data collected in British Columbia, Canada. This technique can extract information from a set of observed heterogeneous multivariate data. The data are represented as n-tuples of mixed discrete and continuous values. The technique is capable of screening out statistically irrelevant information. It is also able to detect inherent subgroups in the data through adopting an event-covering approach. The subgroup characteristics represent important empirical understanding even though there may be considerable probabilistic variation within each individual subgroup.
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  • 7
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    Stochastic environmental research and risk assessment 1 (1987), S. 17-36 
    ISSN: 1436-3259
    Keywords: Stochastic hydrology ; multivariate analysis ; information extraction ; information transfer ; structure of time series ; time series analysis ; spatial characteristics ; simulation of processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A stochastic approach to the analysis of hydrologic processes is defined along with a discussion of causes of tendency, periodicity and stochasticity in hydrologic series. Sources of temporal non-stationarity are described along with objectives and methods of analysis of processes and, in general, of information extraction from data. Transferred information as measured by correlation coefficients is compared with the transferable information as measured by entropy coefficients. Various multivariate approaches to hydrologic stochastic modeling are classified in light of complexities of spatial/temporal hydrologic processes. Alternatives of time series structural decomposition and modeling are compared. A special approach to modeling of space properties further contributes to approximate simulations of spatial/temporal processes over large areas. Several aspects of stochastic models in hydrology are concisely reviewed.
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  • 8
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    Stochastic environmental research and risk assessment 1 (1987), S. 101-116 
    ISSN: 1436-3259
    Keywords: Soil moisture ; stochastic processes ; stochastic differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The dynamics of water within the unsaturated root zone of the soil are represented by a pair of stochastic differential equations (SDE's), one representing the so-called “surplus” state of the moisture and the other the “deficit” condition. The inputs to the model are the climatically controlled random infiltration events and evapotranspiration which are modeled as a compound Poisson process and a Wiener (Brownian motion) process, respectively. The solutions to these SDE's are not in “close-form” but sample functions are obtained by numerical integration. The moment properties of the soil moisture evolution process have also been derived analytically including the mean, variance, covariance and autocorrelation functions. To illustrate the model, climatic parameters representing the “surplus” and “deficit” cases and properties of clay loam soil have been used to numerically derived the corresponding sample functions. With proper selection of all the parameters, physically realistic sample trajectories can be obtained for the model.
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  • 9
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    Stochastic environmental research and risk assessment 1 (1987), S. 127-134 
    ISSN: 1436-3259
    Keywords: Upland erosion ; annual erosion losses
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Point rainfall triggers the complex processes of overland flow and surface erosion. The probability density functions of rainfall duration and intensity are coupled with a physically based dynamic formulation of rainfall-runoff-sediment transport relationships for upland areas. When considering a single storm, rainfall depth alone is a poor predictor of sediment transport because of the dispersion introduced by the effect of rainfall intensity. On a long terms basis, however, the total amount of rainfall can be used to predict total erosion losses.
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  • 10
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    Stochastic environmental research and risk assessment 1 (1987), S. 117-126 
    ISSN: 1436-3259
    Keywords: equi-risk line ; detention pond ; urban runoff ; frequency analysis ; flood risk
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The expression of equi-risk line derived by the authors represents the relationship between discharge capacityy 0 u and storage capacityz 0 u to keep flood frequency under a certain risk level represented by the return periodT, i.e.,z 0/z 0 u ={(y 0 u −y 0 u )/y 0 u } S , wherey 0 u andz 0 u areT-year probability peak discharge and total volume of a hydrograph. The shape parametersS is evaluated in this paper for various release rules of the storage facilities and correlations of durations and peaks of hydrographs. The expression forS is: $$S = S_\infty + (S_0 - S_\infty )\exp ( - \sqrt p )$$ , whereS 0 andS ∞ are the values ofS forp=0 and ∞, andp is the exponent of a general storage-release relation,q=az' p, wherea is the storage constant, andz' andq are the volume of stored water and the corresponding release. The values ofS 0 andS ∞ are expressed in terms of the correlation coefficient ρ of durations and peaks of inflow hydrographs.
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  • 11
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    Stochastic environmental research and risk assessment 1 (1987), S. 135-140 
    ISSN: 1436-3259
    Keywords: Upland erosion ; annual soil losses
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Annual erosion losses from 135 experimental plots under a variety of soil types, vegetation cover densities and conservation practices in Iraq have been measured over a period of four years. The first three years of this data set demonstrate that annual erosion losses can be predicted from annual rainfall depths. The results obtained from regression analysis were then validated with the fourth year of soil erosion data. These results corroborate the theoretical findings of the companion paper in that long term erosion losses can be predicted from the total amount of rainfall.
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  • 12
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    Stochastic environmental research and risk assessment 1 (1987), S. 141-154 
    ISSN: 1436-3259
    Keywords: Contemporaneous ARMA models ; maximum likelihood estimation ; multivariate modelling ; stochastic hydrology ; time series analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In order to allow contemporaneous autoregressive moving average (CARMA) models to be properly applied to hydrological time series, important statistical properties of the CARMA family of models are developed. For calibrating the model parameters, efficient joint estimation procedures are investigated and compared to a set of uivariate estimation procedures. It is shown that joint estimation procedures improve the efficiency of the autoregressive and moving average parameter estimates, but no improvements are expected on the estimation of the mean vector and the variance covariance matrix of the model. The effects of the different estimation procedures on the asymptotic prediction error are also considered. Finally, hydrological applications demonstrate the usefulness of the CARMA models in the field of water resources.
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  • 13
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    Stochastic environmental research and risk assessment 1 (1987), S. 155-160 
    ISSN: 1436-3259
    Keywords: Gamma Markov ; estimation ; maximum likelihood estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The linearly regressive Gamma Markov sequence is being increasingly used as a model for geophysical phenomena, one of the reasons being that it is possible to determine the distribution of (weighted or otherwise) cumulative sums of such a sequence. In this paper we show briefly how to simulate such a sequence and its seasonal extension; we also show how to estimate its parameters. It is shown that the estimates obtained by the method of moments do not have a high efficiency, whereas those obtained by a modified maximum likelihood method have an efficiency close to unity.
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  • 14
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    Stochastic environmental research and risk assessment 1 (1987), S. 161-168 
    ISSN: 1436-3259
    Keywords: Inverse problem ; groundwater management ; groundwater response function ; stochastic control ; consistent parameter estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The response of groundwater basins to natural and anthropogenic inputs depends on many interrelated factors such as the values of groundwater flow and mass transport parameters. This work presents a theoretical analysis of the impact of parameter uncertainty on groundwater management decisions. It is shown that under classical, Bayesian, and deterministic assumptions about the parameter structure, the resulting management decisions could be very different. This underscores the importance of adopting the proper parameter structure and the need for using consistent methods to solve the inverse problem.
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  • 15
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    Stochastic environmental research and risk assessment 1 (1987), S. 185-198 
    ISSN: 1436-3259
    Keywords: Pattern matching ; tracking ; rainfall ; mesoscale ; radar
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a new feature-based matching algorithm for tracking mesoscale precipitation phenomena in radar image sequences. Distinct rainfall areas are identified in each image and characterized by a feature vector of shape descriptors, which provide a mathematical representation of the spatial characteristics of each identified area. Rainfall areas observed in consecutive images are matched by comparing the relative values of the features. Two match scoring algorithms are developed to generate the initial estimates of correct matches, which are then updated by likelihood measures based on relative location. The method is applied to mesoscale rainfall areas observed in sequences of radar-derived images of rainfall activity over Southwestern Ontario during the summers of 1980 and 1981.
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  • 16
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    Stochastic environmental research and risk assessment 1 (1987), S. 199-208 
    ISSN: 1436-3259
    Keywords: Extreme value distribution ; two-component distribution ; maximum entropy principle ; parameter estimation ; regional estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The two component extreme value (TCEV) distribution has recently been shown to account for most of the characteristics of the real flood experience. A new method of parameter estimation for this distribution is derived using the principle of maximum entropy (POME). This method of parameter estimation is suitable for application in both the site-specific and regional cases and appears simpler than the maximum likelihood estimation method. Statistical properties of the regionalized estimation were evaluated using a Monte Carlo approach and compared with those of the maximum likelihood regional estimators.
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  • 17
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    Stochastic environmental research and risk assessment 1 (1987), S. 169-184 
    ISSN: 1436-3259
    Keywords: Stochastic control and programming ; real-time hydrologic forecasting ; reservoir theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new approximate method of solution for stochastic optimal control problems with many state and control variables is introduced. The method is based on the expansion of the optimal control into the deterministic feedback control plus a caution term. The analytic, small-perturbation calculation of the caution term is at the heart of the new method. The developed approximation depends only on the first two statistical moments of the random inputs and up to the third derivatives of the cost functions. Its computational requirements do not exhibit the exponential growth exhibited by discrete stochastic DP and can be used as a suboptimal solution to problems for which application of stochastic DP is not feasible. The method is accurate when the cost-to-go functions are approximately cubic in a neighbourhood around the deterministic trajectory whose size depends on forecasting uncertainty. Furthermore, the method elucidates the stochastic optimization problem yielding insights which cannot be easily obtained from the numerical application of discrete DP.
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  • 18
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    Stochastic environmental research and risk assessment 1 (1987), S. 209-216 
    ISSN: 1436-3259
    Keywords: Transport ; sedimentation ; random walk ; Markov chain in continuous time ; distribution of maximum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A simple two-dimensional random walk model is developed for the motion of a particle in a fluid flow. Some earlier results for the persistent injection of particles into the flow are extended, and the distribution of the maximum number of particles in suspension over the period (0,t) is derived.
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  • 19
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    Stochastic environmental research and risk assessment 1 (1987), S. 217-240 
    ISSN: 1436-3259
    Keywords: Transport of fluid ; random network ; macro-permeability ; micro-geometry ; statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a detailed statistical analysis of Hagen-Poiseuille flow in plane random isotropic networks of interconnected channels. The emphasis is on statistico-geometrical features of networks that affect macroscopic permeability. It is shown that permeability of a network depends on its average co-ordination number, the first two moments of the channel length distribution and other explicitly identifiable geometrical features. Distributions of flow rates in channels and average flow rates are established by minimization of the rate of energy dissipation. Theoretical developments are interpreted in the context of classical statistical mechanics. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network.
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  • 20
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    Stochastic environmental research and risk assessment 1 (1987), S. 280-280 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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  • 21
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    Stochastic environmental research and risk assessment 1 (1987), S. 241-262 
    ISSN: 1436-3259
    Keywords: Martingale ; stochastic-convective ; stochastic-relativist ; spectral-integral ; perturbative ; statistical-mechanical
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The use of stochastic models in subsurface hydrology is growing at a logistic pace. To tie together a number of different stochastic methodologies for deriving subsurface transport equations, we have put together a brief review of some of the more common techniques. Our attention is confined to a few select methodologies so that we might delve in detail into assumptions required by the various approaches and their strengths and weaknesses. The methods reviewed include: Martingale, stochastic-convective, stochastic-relativist, spectral-integral, perturbative, statistical-mechanical, and generalized hydrodynamics. Within this list, we also have included a few stochastic methodologies which have been used solely to develop expressions for the dispersion tensor.
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  • 22
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    Stochastic environmental research and risk assessment 1 (1987), S. 297-302 
    ISSN: 1436-3259
    Keywords: Stochastic PDE ; Zakai equation ; nonlinear filtering ; distributed systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract We shall consider in this article a general class of stochastic PDE which in particular covers the Zakai equation of nonlinear filtering and natural formulations of distributed systems involving control variables. We use only fixed point arguments, hence we get uniqueness results. In the case of the Zakai equation, Galerkin approximations have been considered by Pardoux (1979) to derive the existence of the solution
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  • 23
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    Stochastic environmental research and risk assessment 1 (1987), S. 281-296 
    ISSN: 1436-3259
    Keywords: Stochastic groundwater flow ; semigroups ; random in time Gaussian process ; random physical parameters ; stochastic partial differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Two methods for the solution of partial differential equations (PDE) for the general case of random in time physical parameters are presented and their application to the solution of unsteady regional groundwater flow equations are illustrated. The first method is the semigroup approach which directly offers a solution without resorting to “closure approximations” (hierarchy techniques), perturbation techniques, or Montecarlo simulation techniques. The semigroup approach can also handle the general stochastic problem when randomness also appears as initial conditions, boundary conditions or forcing terms. The second method is an approximation scheme to obtain the semigroup solution in complex cases and permits the solution of equations with more than one random coefficient.
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  • 24
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    Stochastic environmental research and risk assessment 1 (1987), S. 303-318 
    ISSN: 1436-3259
    Keywords: Rainfall-runoff models ; forecasting ; unit hydrograph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Here we review the main thrusts of rainfall-runoff modelling with an eye toward the advantageous use of the massive date sets being accumulated and the modern computers capable of dealing effectively with such sets. More than a tutorial, this study is aimed at providing a unifying structure for analyzing available techniques. The closing section draws attention to the existence of an alternative methodology.
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  • 25
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    Stochastic environmental research and risk assessment 1 (1987), S. 263-279 
    ISSN: 1436-3259
    Keywords: Porous media ; heterogeneity ; groundwater ; dispersion ; stochastic theory ; plume evolution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The migration of contaminants in heterogeneous aquifers involves dispersive processes that act at different scales. The interaction of these processes as a plume evolves can be studied by micro-scale modelling whereby two scales, a local- or micro-scale and an aquifer- or macro-scale, are covered simultaneously. Local-scale dispersive processes are represented through the local dispersion coefficient in the transport equation, while large-scale dispersion due to heterogeneities is represented through the resolution of the flow field and the diffusive exchange between streamtubes. The micro-scale model provides both the high degree of resolution compatible with local-scale processes, and the extent required for the approach to asymptotic conditions, using grids of up to a million nodal points. The model is based on the dual potential-streamfunction formulation for flow, and the transport problem is formulated in a natural coordinate system provided by the flownet. Simulations can be used to verify stochastic theories of dispersion, without the restrictive assumptions inherent in the theory. For the two-dimensional case, results indicate convergence of the effective dispersivity to the theoretical macrodispersivity value. Convergence takes place within a travel distance of about 50 correlation lengths of the hydraulic conductivity field. However, the approach taken to asymptotic conditions, as well as the macrodispersivity value, may differ for different realizations of the same medium. The influence of early-time events such as plume splitting on the asymptotic convergence remains to be investigated.
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  • 26
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    Stochastic environmental research and risk assessment 10 (1996), S. 1-15 
    ISSN: 1436-3259
    Keywords: Spacings ; quantiles ; generalized Pareto distribution ; log-logistic distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The maximum product of spacings (MPS) method is discussed from the standpoint of information theory. MPS parameter and quantile estimates for the generalized Pareto distribution and the two parameter log-logistic distribution are compared with the maximum likelihood(ML) and probability weighted moment (PWM) estimates.
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  • 27
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    Stochastic environmental research and risk assessment 10 (1996), S. 17-37 
    ISSN: 1436-3259
    Keywords: Diffusion ; network ; reservoir ; power law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A diffusion approximation for a network of continuous time reservoirs with power law release rules is examined. Under a mild assumption on the inflow processes, we show that for physically reasonable values of the power law constants, the system of processes converges to a multi-dimensional Gaussian diffusion process. We also illustrate how the limiting Gaussian process may be used to compute approximations to the original system of reservoirs. In addition, we study the quality of our approximations by comparing them to results obtained by simulations of the original watershed model. The simulations offer support for the use of the approximation developed here.
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  • 28
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    Stochastic environmental research and risk assessment 10 (1996), S. 39-63 
    ISSN: 1436-3259
    Keywords: Saturated flow ; rainfall ; groundwater monitoring
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A numerical experiment of flow in variably saturated porous media was performed in order to evaluate the spatial and temporal distribution of the groundwater recharge at the phreatic surface for a shallow aquifer as a function of the input rainfall process and soil heterogeneity. The study focused on the groundwater recharge which resulted from the percolation of the excess rainfall for a 90-days period of an actual precipitation record. Groundwater recharge was defined as the water flux across the moving phreatic surface. The observed spatial non-uniformity of the groundwater recharge was caused by soil heterogeneity and is particularly pronounced during the stage of recharge peak (substantial percolation stage). During that stage the recharge is associated with preferential flow paths defined as soil zones of locally higher hydraulic conductivity. For the periods of low percolation intensity the groundwater recharge was exhibiting more uniform spatial characteristics. The temporal distribution of the recharge was found to be a function of the frequency and intensity of the rainfall events. Application of sampling design demonstrates the joint influence of the spatial and temporal recharge variability on the cost-effective monitoring of groundwater potentiometric surfaces.
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  • 29
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    Stochastic environmental research and risk assessment 10 (1996), S. 65-85 
    ISSN: 1436-3259
    Keywords: Streamflow ; drought ; tree-ring data ; renewal model ; geometric variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract It is shown that runs of low-flow annual streamflow in a coastal semiarid basin of Central California can be adequately modelled by renewal theory. For example, runs of below-median annual streamflows are shown to follow a geometric distribution. The elapsed time between runs of below-median streamflow are geometrically distributed also. The sum of these two independently distributed geometric time variables defines the renewal time elapsing between the initiation of a low-flow run and the next one. The probability distribution of the renewal time is then derived from first principles, ultimately leading to the distribution of the number of low-flow runs in a specified time period, the expected number of low-flow runs, the risk of drought, and other important probabilistic indicators of low-flow. The authors argue that if one identifies drought threat with the occurrence of multiyear low-flow runs, as it is done by water supply managers in the study area, then our renewal model provides a number of interesting results concerning drought threat in areas historically subject to inclement, dry, climate. A 430-year long annual streamflow time series reconstructed by tree-ring analysis serves as the basis for testing our renewal model of low-flow sequences.
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    Stochastic environmental research and risk assessment 10 (1996), S. 87-106 
    ISSN: 1436-3259
    Keywords: Climate change ; daily precipitation modelling ; generalized linear models ; iteratively reweighted least squares ; spline functions
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    Notes: Abstract The precipitation amounts on wet days at De Bilt (the Netherlands) are linked to temperature and surface air pressure through advanced regression techniques. Temperature is chosen as a covariate to use the model for generating synthetic time series of daily precipitation in a CO2 induced warmer climate. The precipitation-temperature dependence can partly be ascribed to the phenomenon that warmer air can contain more moisture. Spline functions are introduced to reproduce the non-monotonous change of the mean daily precipitation amount with temperature. Because the model is non-linear and the variance of the errors depends on the expected response, an iteratively reweighted least-squares technique is needed to estimate the regression coefficients. A representative rainfall sequence for the situation of a systematic temperature rise is obtained by multiplying the precipitation amounts in the observed record with a temperature dependent factor based on a fitted regression model. For a temperature change of 3°C (reasonable guess for a doubled CO2 climate according to the present-day general circulation models) this results in an increase in the annual average amount of 9% (20% in winter and 4% in summer). An extended model with both temperature and surface air pressure is presented which makes it possible to study the additional effects of a potential systematic change in surface air pressure on precipitation.
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    Stochastic environmental research and risk assessment 10 (1996), S. 107-126 
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    Keywords: Gaussian process ; spatial correlation ; anisotropy ; Fourier transform ; Gauss-Newton ; ECM ; measurement error ; signal extraction ; irregular data
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    Notes: Abstract This paper is concerned with developing computational methods and approximations for maximum likelihood estimation and minimum mean square error smoothing of irregularly observed two-dimensional stationary spatial processes. The approximations are based on various Fourier expansions of the covariance function of the spatial process, expressed in terms of the inverse discrete Fourier transform of the spectral density function of the underlying spatial process. We assume that the underlying spatial process is governed by elliptic stochastic partial differential equations (SPDE's) driven by a Gaussian white noise process. SPDE's have often been used to model the underlying physical phenomenon and the elliptic SPDE's are generally associated with steady-state problems. A central problem in estimation of underlying model parameters is to identify the covariance function of the process. The cumbersome exact analytical calculation of the covariance function by inverting the spectral density function of the process, has commonly been used in the literature. The present work develops various Fourier approximations for the covariance function of the underlying process which are in easily computable form and allow easy application of Newton-type algorithms for maximum likelihood estimation of the model parameters. This work also develops an iterative search algorithm which combines the Gauss-Newton algorithm and a type of generalized expectation-maximization (EM) algorithm, namely expectation-conditional maximization (ECM) algorithm, for maximum likelihood estimation of the parameters. We analyze the accuracy of the covariance function approximations for the spatial autoregressive-moving average (ARMA) models analyzed in Vecchia (1988) and illustrate the performance of our iterative search algorithm in obtaining the maximum likelihood estimation of the model parameters on simulated and actual data.
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    Stochastic environmental research and risk assessment 10 (1996), S. 127-150 
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    Keywords: Rainfall estimation ; indicator cokriging ; rain gage measurements
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Indicator cokriging (Journel 1983) is examined as a tool for real-time estimation of rainfall from rain gage measurements. The approach proposed in this work obviates real-time estimation of real-time statistics of rainfall by using ensemble or climatological statistics exclusively, and reduces computational requirements attendant to indicator cokriging by employing only a few auxiliary cutoffs in estimation of conditional probabilities. Due to unavailability of suitable rain gage measurements, hourly radar rain fall data were used for both indicator covariance estimation and a comparative evaluation. Preliminary results suggest that the indicator cokriging approach is clearly superior to its ordinary kriging counterpart, whereas the indicator kriging approach is not. The improvement is most significant in estimation of light rainfall, but drops off significantly for heavy rainfall. The lack of predictability in spatial estimation of heavy rainfall is borne out in the integral scale of indicator correlation: peaking to its maximum for cutoffs near the median, indicator correlation scale becomes increasingly smaller for larger cutoffs of rainfall depth. A derived-distribution analysis, based on the assumption that radar rainfall is a linear sum of ground-truth and a random error, suggests that, at low cutoffs, indicator correlation scale of ground-truth can significantly differ from that of radar rainfall, and points toward inclusion of rainfall intermittency, for example, within the framework proposed in this work.
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    Stochastic environmental research and risk assessment 10 (1996), S. 151-161 
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    Stochastic environmental research and risk assessment 10 (1996), S. 163-166 
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    Stochastic environmental research and risk assessment 10 (1996), S. 187-207 
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    Keywords: log-Gumbel distribution ; flood frequency analysis ; quantile estimation ; confidence intervals
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    Notes: Abstract The log-Gumbel distribution is one of the extreme value distributions which has been widely used in flood frequency analysis. This distribution has been examined in this paper regarding quantile estimation and confidence intervals of quantiles. Specific estimation algorithms based on the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood (ML) are presented. The applicability of the estimation procedures and comparison among the methods have been illustrated based on an application example considering the flood data of the St. Mary's River.
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    Stochastic environmental research and risk assessment 10 (1996), S. 167-186 
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    Keywords: Reservoir stochastic theory ; reliability ; mean ; variance ; indicator function ; storage bounds ; nonlinear programming ; simulation
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    Notes: Abstract A new formulation is presented for the analysis of reservoir systems synthesizing concepts from the traditional stochastic theory of reservoir storage, moments analysis and reliability programming. The analysis is based on the development of the first and second moments for the stochastic storage state variable. These expressions include terms for the failure probabilities (probabilities of spill or deficit) and consider the storage bounds explicitly. Using this analysis, expected values of the storage state, variances of storage, optimal release policies and failure probabilities — useful information in the context of reservoir operations and design, can be obtained from a nonlinear programming solution. The solutions developed from studies of single reservoir operations on both an annual and monthly basis, compare favorably with those obtained from simulation. The presentation herein is directed to both traditional reservoir storage theorists who are interested in the design of a reservoir and modern reservoir analysts who are interested in the long term operation of reservoirs.
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    Stochastic environmental research and risk assessment 10 (1996), S. 209-229 
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    Keywords: Infiltration-advance equation ; water spreading ; cellular automata ; irrigation ; surface hydrology ; hydrodynamics ; stochastic processes
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    Notes: Abstract A technique has been developed for predicting the irregular advance pattern often observed as water spreads on the surface of the ground. The technique is a combination of stochastic sketching, potential theory, probability theory, and a mass balance equation in the form of an advance equation. The technique can be used on flat as well as sloping terrain and addresses any form of obstructions or constraints to the flow of the water. The stochastic sketching portion of the technique uses cellular automata with transition probability movement rules to sketch the dynamics of small volume water elements in the defined environment. Randomly selected small volume flow path segments are computed and plotted. The envelope of these segments defines the wetted area and the advance front. Several examples are presented showing the patterns produced for various situations.
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    Stochastic environmental research and risk assessment 10 (1996), S. 231-251 
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    Keywords: Stochastic ; multiphase ; three phase ; heterogeneity
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    Notes: Abstract The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, α. These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter α. The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.
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    Stochastic environmental research and risk assessment 10 (1996), S. 295-317 
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    Keywords: Bayesion methods ; time series ; hydrology
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    Notes: Abstract A review of literature reveals the inadequacy of Intervention analysis and spectrum based methods to adequately quantify changes in hydrologic times series. A Bayesian method is used to investigate the statistical significance of observed changes in hydrologic times series and the results are reported herein. The Bayesian method is superior to the previous methods.
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    Stochastic environmental research and risk assessment 10 (1996), S. 253-278 
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    Keywords: Random fields ; stochastic processes ; fractals
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    Notes: Abstract This paper describes a new method for generating spatially-correlated random fields. Such fields are often encountered in hydrology and hydrogeology and in the earth sciences. The method is based on two observations: (i) spatially distributed attributes usually display a stationary correlation structure, and (ii) the screening effect of measurements leads to the sufficiency of a small search neighborhood when it comes to projecting measurements and data in space. The algorithm which was developed based on these principles is called HYDRO_GEN, and its features and properties are discussed in depth. HYDRO_GEN is found to be accurate and extremely fast. It is also versatile: it can simulate fields of different nature, starting from weakly stationary fields with a prescribed covariance and ending with fractal fields. The simulated fields can display statistical isotropy or anisotropy.
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    Stochastic environmental research and risk assessment 10 (1996), S. 279-294 
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    Keywords: Linear estimation ; interpolation ; kriging ; splines ; conditional
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    Notes: Abstract This work presents analytical expressions for the best estimate, conditional covariance function, and conditional realizations of a function from sparse observations. In contrast to the prevalent approach in kriging where the best estimates at every point are determined from the solution of a system of linear equations, the best-estimate function can be represented analytically in terms of basis functions, whose number depends on the observations. This approach is computationally superior when graphing a function estimate and is also valuable in understanding what the solution should look like. For example, one can immediately see that all “singularities” in the best-estimate function are at observation points.
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    Stochastic environmental research and risk assessment 10 (1996), S. 319-329 
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    Keywords: Particle tracking ; numerical methods ; random walks ; advection-dispersion equation ; stochastic processes
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    Notes: Abstract A formal statistical discussion of the origins of the random walk and its relation to the classic advection-dispersion equation is given. At issue is the common use of Gaussian distributed steps in producing the desired dispersive effects. Shown are alternative solutions to the basic Langevin equation describing mass displacements based on non-Gaussian, white increments. In particular, the results reveal that uniform or symmetric-triangular steps can be employed without loss of generality in accuracy of the solution (over all Peclet numbers) and may yield significant savings in the computational generation of the random deviates required in the Monte Carlo procedures of the random walk method.
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    Stochastic environmental research and risk assessment 10 (1996), S. 330-330 
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    Stochastic environmental research and risk assessment 11 (1997), S. 17-31 
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    Keywords: Bivariate density ; meta-Gaussian density ; normal quantile transform ; likelihood ratio dependence ; correlation coefficient
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    Notes: Abstract Convenient bivariate densities found in the literature are often unsuitable for modeling hydrologic variates. They either constrain the range of association between variates, or fix the form of the marginal distributions. The bivariate meta-Gaussian density is constructed by embedding the normal quantile transform of each variate into the Gaussian law. The density can represent a full range of association between variates and admits arbitrarily specified marginal distributions. Modeling and estimation can be decomposed into i) independent analyses of the marginal distributions, and ii) investigation of the dependence structure. Both statistical and judgmental estimation procedures are possible. Some comparisons to recent applications of bivariate densities in the hydrologic literature motivate and illustrate the model.
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    Stochastic environmental research and risk assessment 11 (1997), S. 33-50 
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    Keywords: Unit hydrograph ; uncertainty analysis ; linearly constrained Monte-Carlo simulation ; reliability analysis
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    Notes: Abstract Unit hydrographs (UHs), along with design rainfalls, are frequently used to determine the discharge hydrograph for design and evaluation of hydraulic structures. Due to the presence of various uncertainties in its derivation, the resulting UH is inevitably subject to uncertainty. Consequently, the performance of hydraulic structures under the design storm condition is uncertain. This paper integrates the linearly constrained Monte-Carlo simulation with the UH theory and routing techniques to evaluate the reliability of hydraulic structures. The linear constraint is considered because the water volume of each generated design direct runoff hydrograph should be equal to that of the design effective rainfall hyetograph or the water volume of each generated UH must be equal to one inch (or cm) over the watershed. For illustration, the proposed methodology is applied to evaluate the overtopping risk of a hypothetical flood detention reservoir downstream of Tong-Tou watershed in Taiwan.
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    Stochastic environmental research and risk assessment 11 (1997), S. 1-16 
    ISSN: 1436-3259
    Keywords: Nash cascade reservoir model ; rainfall-runoff ; EM algorithm ; filtering ; maximum likelihood estimation ; martingale estimating function
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    Notes: Abstract Abstract: Linear continuous time stochastic Nash cascade conceptual models for runoff are developed. The runoff is modeled as a simple system of linear stochastic differential equations driven by white Gaussian and marked point process noises. In the case of d reservoirs, the outputs of these reservoirs form a d dimensional vector Markov process, of which only the dth coordinate process is observed, usually at a discrete sample of time points. The dth coordinate process is not Markovian. Thus runoff is a partially observed Markov process if it is modeled using the stochastic Nash cascade model. We consider how to estimate the parameters in such models. In principle, maximum likelihood estimation for the complete process parameters can be carried out directly or through some form of the EM (estimation and maximization) algorithm or variation thereof, applied to the observed process data. In this research we consider a direct approximate likelihood approach and a filtering approach to an algorithm of EM type, as developed in Thompson and Kaseke (1994). These two methods are applied to some real life runoff data from a catchment in Wales, England. We also consider a special case of the martingale estimating function approach on the runoff model in the presence of rainfall. Finally, some simulations of the runoff process are given based on the estimated parameters.
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    Stochastic environmental research and risk assessment 2 (1988), S. 17-33 
    ISSN: 1436-3259
    Keywords: River flow forecasting ; discrete linear cascade model ; ARMAX ; coupled models ; Kalman filtering ; Danube
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    Notes: Abstract The objective of the paper is to compare three recursive linear state space models used to forecast river flow. The three models are as follows: (i) Purely deterministic discrete linear cascade model (DLCM); (ii) Purely stochastic autoregressive moving average (ARMAX) time series model; and (iii) Coupled deterministic (DLCM) — stochastic (ARMA) model. Description of DLCM is given shortly. The state space formulation of the ARMAX model enables the recursive estimation of random walk parameters and the forecast of flows by linear Kalman filtering. The correlated error sequence of DLCM is described by an ARMA model. The DLCM and ARMA models are put together in a coupled deterministic-stochastic model. The recursive conditional forecasting of the augmented state vector is performed by the linear Kalman-filter. The conditional output forecast is given by linear projection of thea priori state vector. Numerical investigations on River Danube data lead to the conclusion that the coupled deterministic-stochastic model is the most efficient forecasting model of all the three recursive techniques compared.
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    Stochastic environmental research and risk assessment 2 (1988), S. 61-72 
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    Keywords: Binary data ; censored observations ; autocorrelations ; acid rain
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    Notes: Abstract The properties of the well known estimator of the transition probabilities in a binary time series are investigated. A formula for the variance is obtained, which generally involves a double integral. However, in the case when the binary series is obtained by hard clipping of an AR(1) process, a good and fairly simple approximation is derived. In the MA(1) or MA(2) case exact formulae for the variance is given. In the appendix an excellent approximation to the fourth order cumulant of a clipped AR(1) process is derived, which may be of interest in other applications as well.
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    Stochastic environmental research and risk assessment 2 (1988), S. 175-188 
    ISSN: 1436-3259
    Keywords: Reservoir storage ; range ; adjusted range
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    Notes: Abstract It was remarked by Hurst in 1951 that the adjusted range gives the size of the smallest reservoir capable of providing a constant discharge equal to the mean inflow. Since that time this range and its rescaled modification, the Hurst range, have been widely discussed, not however primarily with a view to applying them to reservoir design problems, but rather on account of their possible relevance to the simulation of geophysical time series. Acknowledging the well-known conceptual weaknesses of adjusted ranges and the theoretical difficulties that inhibit their direct utilisation in the design and operation of real reservoirs, the authors argue that the interest displayed on ranges during the past few decades justifies the effort of eliminating one in particular of these weakness, namely their non-implementability as operating policies, a consequence of the fact that they can only be retrospectively evaluated. The paper proposes modifications in which the unknowable mean and standard deviation of future samples are replaced by the known mean and sample standard deviation of historical data, leading to the historically adjusted range and the historically rescaled and adjusted range. The latter is produced as an implementable approximation to Hurst's (1951) solution to the optimal reservoir problem. The expected values of the new ranges are evaluated and numerically tabulated.
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    Stochastic environmental research and risk assessment 2 (1988), S. 245-261 
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    Keywords: Geostatistics ; areal rainfall distribution ; areal reduction factor ; Gumbel distribution
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    Notes: Abstract Areal rainfall statistics are more relevant in flood hydrology and water resources management than point rainfall statistics when it comes to help designing dams or hydraulic structures. This paper presents a geostatistically based method to derive the areal statistics from point statistics. Assuming that the distribution models of point rainfall and areal belong to the same class of models and that the rainfall process is stationary, it is shown how the parameters of the areal distribution model can directly be computed from the parameters of the point distribution models in case of a non stationary process, an approximation is derived that yielded good results when applied to a mountainous region in Southern France. The method also allows the computation of the areal reduction factors in a very general form.
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    Stochastic environmental research and risk assessment 2 (1988), S. 303-315 
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    Keywords: Physically based stochastic models ; stochastic dynamic models ; statistical predictability ; internannual variability ; ARMA models ; water level variations
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    Notes: Abstract Several physically based stochastic dynamic models (SDM) are described including year-to-year variations of water volume in terminal and non-terminal lakes, streamflow of lake-fed rivers, and salinity of an inland sea (the Sea of Azov). All of these models are based upon the SDM of water volume of terminal lakes developed by Kritzky and Menkel in 1946 in co-operation with Kolomogorov. Explicit formulae are derived for second order statistical moments of the output processes, including variance, correlation function, spectra, etc., under the assumption that the forcing functions from stationary random sequences. The least-squares prediction problem is solved for both stationary and non-stationary cases. Some of the processes are shown to possess high statistical predictability. Actual predictions are compared with independent observations. Problems for further study are stated.
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    Stochastic environmental research and risk assessment 3 (1989), S. 1-16 
    ISSN: 1436-3259
    Keywords: Width function ; instantaneous unit hydrograph ; peak ; regression ; birth-death process
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    Notes: Abstract We investigate optimal predictors of the peak (S) and distance to peak (T) of the width function of drainage networks under the assumption that the networks are topologically random with independent and exponentially distributed link lengths. Analytical results are derived using the fact that, under these assumptions, the width function is a homogeneous Markov birth-death process. In particular, exact expressions are derived for the asymptotic conditional expectations ofS andT given network magnitudeN and given mainstream lengthH. In addition, a simulation study is performed to examine various predictors ofS andT, includingN, H, and basin morphometric properties; non-asymptotic conditional expectations and variances are estimated. The best single predictor ofS isN, ofT isH, and of the scaled peak (S divided by the area under the width function) isH. Finally, expressions tested on a set of drainage basins from the state of Wyoming perform reasonably well in predictingS andT despite probable violations of the original assumptions.
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    Stochastic environmental research and risk assessment 3 (1989), S. 68-69 
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    Stochastic environmental research and risk assessment 11 (1997), S. 173-192 
    ISSN: 1436-3259
    Keywords: Uncertainty analysis ; unit hydrograph ; regression analysis ; probabilistic point estimation methods
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    Notes: Abstract Hydrologic model parameters obtained from regional regression equations are subject to uncertainty. Consequently, hydrologic model outputs based on the stochastic parameters are random. This paper presents a systematic analysis of uncertainty associated with the two parameters, N and K, in Nash's IUH model from different regional regression equations. The uncertainty features associated with N and K are further incorporated to assess the uncertainty of the resulting IUH. Numerical results indicate that uncertainty of N and K from the regional regression equations are too significant to be ignored.
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    Stochastic environmental research and risk assessment 11 (1997), S. 145-171 
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    Keywords: Hydrologic regionalization ; unit hydrograph ; regression analysis ; multivariate regression ; seemingly unrelated regression ; validation
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    Notes: Abstract Hydrologic regionalization is a useful tool that allows for the transfer of hydrological information from gaged sites to ungaged sites. This study developed regional regression equations that relate the two parameters in Nash's IUH model to the basin characteristics for 42 major watersheds in Taiwan. In the process of developing the regional equations, different regression procedures including the conventional univariate regression, multivariate regression, and seemingly unrelated regression were used. Multivariate regression and seeming unrelated regression were applied because there exists a rather strong correlation between the Nash's IUH parameters. Furthermore, a validation study was conducted to examine the predictability of regional equations derived by different regression procedures. The study indicates that hydrologic regionalization involving several dependent variables should consider their correlations in the process of establishing the regional equations. The consideration of such correlation will enhance the predictability of resulting regional equations as compared with the ones from the conventional univariate regression procedure.
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    Stochastic environmental research and risk assessment 11 (1997), S. 193-210 
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    Keywords: Turbulence ; sediment ; fluvial ; river ; bursting process ; statistics
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    Notes: Abstract Entrainment of sediment particles from channel beds into the channel flow is influenced by the characteristics of the flow turbulence which produces stochastic shear stress fluctuations at the bed. Recent studies of the structure of turbulent flow has recognized the importance of bursting processes as important mechanisms for the transfer of momentum into the laminar boundary layer. Of these processes, the sweep event has been recognized as the most important bursting event for entrainment of sediment particles as it imposes forces in the direction of the flow resulting in movement of particles by rolling, sliding and occasionally saltating. Similarly, the ejection event has been recognized as important for sediment transport since these events maintain the sediment particles in suspension. In this study, the characteristics of bursting processes and, in particular, the sweep event were investigated in a flume with a rough bed. The instantaneous velocity fluctuations of the flow were measured in two-dimensions using a small electromagnetic velocity meter and the turbulent shear stresses were determined from these velocity fluctuations. It was found that the shear stress applied to the sediment particles on the bed resulting from sweep events depends on the magnitude of the turbulent shear stress and its probability distribution. A statistical analysis of the experimental data was undertaken and it was found necessary to apply a Box-Cox transformation to transform the data into a normally distributed sample. This enabled determination of the mean shear stress, angle of action and standard error of estimate for sweep and ejection events. These instantaneous shear stresses were found to be greater than the mean flow shear stress and for the sweep event to be approximately 40 percent greater near the channel bed. Results from this analysis suggest that the critical shear stress determined from Shield's diagram is not sufficient to predict the initiation of motion due to its use of the temporal mean shear stress. It is suggested that initiation of particle motion, but not continuous motion, can occur earlier than suggested by Shield's diagram due to the higher shear stresses imposed on the particles by the stochastic shear stresses resulting from turbulence within the flow.
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    Stochastic environmental research and risk assessment 11 (1997), S. 211-227 
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    Notes: Abstract The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 2-parameter generalized Pareto (GP2) distribution. Monte Carlo simulated data were used to evaluate this method and compare it with the methods of moments (MOM), probability weighted moments (PWM), and maximum likelihood estimation (MLE). The parameter estimates yielded by POME were comparable or better within certain ranges of sample size and coefficient of variation.
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    Stochastic environmental research and risk assessment 3 (1989), S. 281-292 
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    Keywords: Generalised Pareto distribution ; Peaks over threshold ; Probability weighted moments ; Regionalisation
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    Notes: Abstract A peaks over threshold (POT) method of analysing daily rainfall values is developed using a Poisson process of occurrences and a generalised Pareto distribution (GPD) for the exceedances. The parameters of the GPD are estimated by the method of probability weighted moments (PWM) and a method of combining the individual estimates to define a regional curve is proposed.
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    Stochastic environmental research and risk assessment 4 (1990), S. 27-41 
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    Keywords: Groundwater monitoring networks ; Information reliability ; Information scales ; Kalman filtering in groundwater
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The extensive use of groundwater resources has increased the need for developing cost-effective monitoring networks to provide an indication of the degree to which the subsurface environment has been affected by human activities. This study presents a cost-effective approach to the design of groundwater flow monitoring networks. The groundwater network design is formulated with two problem formats: maximizing the statistical monitoring power for specified budget constraint and minimizing monitoring cost for statistical power requirement. The statistical monitoring power constraint is introduced with an information reliability threshold value. A branch and bound technique is employed to select the optimal solution from a discrete set of possible network alternatives. The method is tested to the design of groundwater flow monitoring problem in the Pomona County, California.
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    Stochastic environmental research and risk assessment 4 (1990), S. 65-81 
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    Keywords: Lagoons ; Ponds ; Facultative ; First-order kinetics ; Complete mixing ; Probabilistic ; Uncertainty ; Environmental ; Stochastic differential equations
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    Notes: Abstract Two stochastic models are developed to describe the BOD output (i.e. effluent) variation of facultative aerated lagoons in series. One of the models uses the uncertainty analysis (UA) technique and the other is based on the moment equation solution methodology of stochastic differential equations (SDE's). The former considers a second-order approximation of the expectation (SOAE) and a first-order approximation of the variance (FOAV). The SDE model considers that output variability is accounted for by random variations in the rate coefficient. Comparisons are provided. Calibration and verification of the two models are aciieved by using field observations from two different lagoon systems in series. The predictive performances of the two models are compared with each other and with another SDE model, presented in a previous paper, that considers input randomness. The three methods show similar predictive performances and provide good predictions of the mean and standard deviation of the lagoon effluent BOD concentrations and thus are considered as appropriate methodologies.
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    Stochastic environmental research and risk assessment 4 (1990), S. 89-103 
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    Keywords: maximum precipitation depths ; extreme-value distributions ; seasonal variation ; partial duration series ; model misspecification
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    Notes: Abstract Quantile estimates of the annual maximum distribution can be obtained by fitting theoretical distributions to the maxima in separate seasons, e.g. to the monthly maxima. In this paper, asymptotic expressions for the bias and the variance of such estimates are derived for the case that the seasonal maxima follow a Gumbel distribution. Results from these expressions are presented for a situation with no seasonal variation and for maximum precipitation depths at Uccle/Ukkel (Belgium). It is shown that the bias is often negligible and that the variance reduction by using seasonal maxima instead of just the annual maxima strongly depends on the seasonal variation in the data. A comparison is made between the asymptotic standard error of quantile estimates from monthlymaxima with those from a partial duration series. Much attention is paid to the effect of model misspecification on the resulting quantile estimates of the annual maximum distribution. The use of seasonal maxima should be viewed with caution when the upper tail of this distribution is of interest.
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    Stochastic environmental research and risk assessment 4 (1990), S. 193-208 
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    Keywords: Stochastic tidal modeling ; parameter identification ; model calibration
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    Notes: Abstract In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as parameter fluctuations. Therefore the open boundary conditions are embedded into a stochastic environment and a constant gain extended Kalman filter is employed to identify the state of the system. Defining a error functional that measures the differences between the filtered state of the system and the measurements, a quasi Newton method is employed to determine the minimum of this functional. To reduce the computational burden, the gradient of the criterium that is required using the quasi Newton method is determined by solving the adjoint system.
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    Stochastic environmental research and risk assessment 4 (1990), S. 217-226 
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    Keywords: Exponential distribution ; bivariate exponential distribution ; distribution of flood volume ; partial duration series
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    Notes: Abstract A methodology based on the theory of stochastic processes is applied to the analysis of floods. The approach will be based on some results of the theory of extreme values over a threshold. In this paper, we focus on the estimation of the distribution of the flood volume in partial duration series analysis of flood phenomena, by using a bivariate exponential distribution of discharge exceedances and durations over a base level.
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    Stochastic environmental research and risk assessment 4 (1990), S. 254-254 
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    Stochastic environmental research and risk assessment 4 (1990), S. 277-294 
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    Keywords: Water distribution ; optimization ; nonlinear programming ; integer programming ; chance constraints ; rehabilation
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    Notes: Abstract This paper presents the mathematical development of an integer — nonlinear programming chance — constrained optimization model for the minimum cost rehabilitation/replacement of water distribution system components. Particular attention is given to the handling of uncertainties in the roughness factors and the loading conditions including both the random demand and preassure head requirements. The advantages of the proposed model include the ability to: 1) handle the optimal timing of rehabilitation/replacement for water distribution system components; 2) link a mixed-integer linear program solver, a nonlinear program solver, and a hydraulic simulator into an optimization framework; 3) handle the uncertainties of some of the variables; 4) incorporate various kinds of cost functions; and 5) handle multiple loading conditions.
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    Stochastic environmental research and risk assessment 4 (1990), S. 309-320 
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    Keywords: Entropy ; reliability ; redundancy ; water distribution networks ; nodal pair reliability
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    Notes: Abstract Entropy based expressions for measurement of reliability and redundancy have recently been reported. These measures approach assessment of the reliability of the distribution network from the intrinsic redundancy of the network layout. The paper extends earlier work on entropy functions by including a more explicit statement of the alternate paths available in the network and by recognizing that under certain circumstances, e.g., failure of some part of the network work, an outflow link from a node under normal working condition may become an inflow link to the same node. The measures are assessed by comparison with parameters measuring Nodal Pair Reliability and percentage of flow supplied at adequate pressure for a range of networks and link failure conditions in this networks. The entropy measures are shown to reflect changes in the network reliability, as measured by these two comparative parameters, very well.
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    Stochastic environmental research and risk assessment 5 (1991), S. 1-16 
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    Keywords: Partial duration series ; unbiased risk ; Bayesian risk
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    Notes: Abstract Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.
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    Stochastic environmental research and risk assessment 5 (1991), S. 55-68 
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    Keywords: Bivariate probability distribution ; random variables ; zero marginals ; Finch-Groblicki method
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    Notes: Abstract A vivariate probability density function (pdf),f(x 1,x 2), admissible for two random variables (X 1,X 2), is of the form $$f(x_1 x_2 ) = f_1 (x_1 )f_2 (x_2 )[1 + \rho \{ F_1 (x_1 ),F_2 (x_2 )\} ]$$ where ρ(u, v) (u=F 1(x 1),v=F 2(x 2)) is any function on the unit square that is 0-marginal and bounded below by−1 andF 1(x 1) andF 2(x 2) are cumulative distribution functions (cdf) of marginal probability density functionsf 1(x 1) andf 2(x 2). The purpose of this study is to determinef(x 1,x 2) for different forms of ρ(u,v). By considering the rainfall intensity and the corresponding depths as dependent random variables, observed and computed probability distributionsF 1(x 1),F(x 1/x 2),F 2(x 2), andF(x 2/x 1) are compared for various forms of ρ(u,v). Subsequently, the best form of ρ(u,v) is specified.
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    Stochastic environmental research and risk assessment 5 (1991), S. 77-87 
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    Keywords: Flood ; random ; distribution ; estimation ; probability ; entropy ; fractile constraints
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    Notes: Abstract The method of Relative Entropy with Fractile constraints (REF method) is explained and applied to model extreme compound hydrological phenomena, such as extreme sea levels under storm conditions. Also presented is a simple method of Tail Entropy Approximation (TEA), which amounts to a correction of traditional statistical estimates for extreme observations. Distribution assumptions are necessary but downplayed in the REF method, relegating the prior distribution to the role of an extrapolation function. The estimates are objective in an information-theoretical sense. They also satisfy a strict requirement of self-consistency that is generally not satisfied by standard statistical methods: invariance under monotonic transformations of the random variable. Historical records of storm surge levels in the Netherlands and annual maximum tidal heights for Sheerness, UK, are used as examples. Comparison is made with distributions obtained using other methods. It is concluded that the tail entropy approximation provides simple, objective estimates of extremes in the tail beyond the range of observations.
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    Stochastic environmental research and risk assessment 5 (1991), S. 125-134 
    ISSN: 1436-3259
    Keywords: Empirical Orthogonal Function analysis ; random fields ; simulation ; non-homogeneous fields
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    Notes: Abstract In several fields of Geophysics, such as Hydrology, Meteorology or Oceanography, it is often useful to generate random fields, displaying the same variabilitity as the observed variables. Usually, these synthetic data are used as forcing fields into numerical models, to test the sensitivity of their outputs to the variability of the inputs. Examples can be found in subsurface or surface Hydrology and in Meteorology with General Circulation Models (GCM). Different techniques have already been proposed, often based on the spectral representation of the random process, with, usually, assumptions of stationarity. This paper suggests that Empirical Orthogonal Function (EOF) analysis, which leads to the decomposition of the covariance kernel on the set of its eigen-functions, is a possible answer to this problem. The convergence and accuracy of the method are shown to depend mainly on the number of EOFs retained in the expansion of the covariance kemel. This result is confirmed by a comparison with the turning band method and a matrix technique. Furthermore, a synthetic example of non-homogencous fields shows the interest of EOF analysis in the direct simulation of such fields.
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    Stochastic environmental research and risk assessment 5 (1991), S. 173-188 
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    Keywords: Entropy ; spectral analysis ; streamflow forecasting ; univariate model
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    Notes: Abstract This paper, the first in a series of two, employs the principle of maximum entropy (POME) via maximum entropy spectral analysis (MESA) to develop a univariate model for long-term streamflow forecasting. Three cases of streamflow forecasting are investigated: forward forecasting, backward forecasting (or reconstruction) and intermittent forecasting (or filling in missing records). Application of the model is discussed in the second paper.
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    Stochastic environmental research and risk assessment 5 (1991), S. 155-171 
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    Keywords: Kinetic non-equilibrium ; residence time ; spatially variable chemical reactions
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    Notes: Abstract A method for simulating field scale transport of kinetically adsorbing solutes is described. The non-equilibrium adsorption is modeled as a birth and death process and is coupled with the particle tracking approach using the first two moments of the distribution of the particle residence time, i.e., the time that a solute particle stays in the liquid phase. A single residence time distribution, regardless of the initial and final phase, is demonstrated to yield an accurate description of chemical kinetics in the vast majority of field scale problems. The first two moments of the residence time distribution are derived as a function of chemical reaction rates and the transport time interval Δt. It is shown that the first moment of the residence time represents a measure of the speed of the chemical reaction relative to the transport time scale Δt which is chosen depending on the velocity field. The second moment of the residence time reflects the relative importance of the chemical kinetics versus local equilibrium conditions for the given transport time step Δt. The simulated spatial moments of the contaminant plume are compared in the one-dimensional case with available analytical solutions to demonstrate the accuracy of the proposed technique. A two-dimensional case for stratified formations is presented to study the transport behavior for heterogeneous velocity fields and variable distribution coefficient, hypothesized as being negatively correlated with hydraulic conductivity. The results show that the enhanced plume spreading and the statistics of the arrival time distribution appear to be more sensitive to the spatially variable distribution coefficient than to the kinetics alone. In fact, the second spatial moment was almost doubled in the case of spatially variable distribution coefficient.
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    Stochastic environmental research and risk assessment 5 (1991), S. 239-251 
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    Keywords: Parameter estimation ; maximum likelihood estimation ; stochastic partial differential equation
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    Notes: Abstract Part I of this series of two papers (Unny, 1989) dealt with the theoretical derivation of the moment equations for the stochastic partial differential equation in the water table depth forced by stochastic rainfall input. Part I also developed a maximum likelihood estimation procedure for parameter determination. The primary aim of the present manuscript is the application of the parameter estimation procedure to the Borden aquifer, an aquifer designated as an experimental site, where extensive field measurements have been carried out. Estimates of hydraulic conductivity and transmissivity for the Borden aquifer, derived from the maximum likelihood algorithm, have been compared with estimates obtained by “traditional” procedures. The paper also presents the simulated solution of the governing differential equation in the one dimensional problem applied to the Borden aquifer.
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    Stochastic environmental research and risk assessment 5 (1991), S. 280-294 
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    Stochastic environmental research and risk assessment 5 (1991), S. 261-266 
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    Keywords: Drought ; drought indices
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    Notes: Abstract Drought detection, monitoring and indices are closely related to its definition. The specific definition chosen for a particular drought analysis will affect the procedures one uses in drought detection and monitoring. The traditional Palmer Drought Severity Index (PDSI) has been proven to be ineffective in regions of predominantly irrigated agriculture. The recently developed ALERT (Automated Local Evaluation in Real Time) system is proposed for use in monitoring the spatial and temporal variations of drought in real time. The ALERT system uses standardized instruments, radio frequencies, software and hardware. It was originally developed as a flash flood waming system by local flood control districts and the National Weather Service. However, now it has expanded to over 100 other uses in the areas of natural and man-made disaster detection and warning. The successful ALERT system indicates the need for the continued development of a national drought monitoring index that is applicable to a wide range of climate, hydrologic and water resource environments.
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    Stochastic environmental research and risk assessment 6 (1992), S. 1-2 
    ISSN: 1436-3259
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    Stochastic environmental research and risk assessment 11 (1997), S. 523-547 
    ISSN: 1436-3259
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    Notes: Abstract Kernel density estimators are useful building blocks for empirical statistical modeling of precipitation and other hydroclimatic variables. Data driven estimates of the marginal probability density function of these variables (which may have discrete or continuous arguments) provide a useful basis for Monte Carlo resampling and are also useful for posing and testing hypotheses (e.g bimodality) as to the frequency distributions of the variable. In this paper, some issues related to the selection and design of univariate kernel density estimators are reviewed. Some strategies for bandwidth and kernel selection are discussed in an applied context and recommendations for parameter selection are offered. This paper complements the nonparametric wet/dry spell resampling methodology presented in Lall et al. (1996).
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    Stochastic environmental research and risk assessment 11 (1997), S. 459-482 
    ISSN: 1436-3259
    Keywords: Karhunen-Loéve expansion ; Empirical Orthogonal Functions ; stochastic simulation ; gaussian fields ; analytical covariance functions ; eigenfunctions ; kriging
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    Notes: Abstract Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.
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    Stochastic environmental research and risk assessment 12 (1998), S. 1-14 
    ISSN: 1436-3259
    Keywords: Key words: Exceedance probability ; trend ; stochastic variables ; non-stationarity
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    Notes: Abstract Studying the hypothetical case of a trend superimposed on a random stationary variable, we highlight the strong influence of possible non-stationarities on exceedance probability. After a general outline, the subject is analytically developed using the Gumbel distribution, emphasizing the quick increase of the exceedance probability over time in the presence of weak rising trends, and its sensitive underestimation where the non-stationarity goes unnoticed or is considered negligible. Finally the work is applied to hydrological series of rainfall and river flow.
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    Stochastic environmental research and risk assessment 12 (1998), S. 53-64 
    ISSN: 1436-3259
    Keywords: Key words: Risk ; clustering ; point process ; Poisson ; flood.
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    Notes: Abstract: Since the introduction into flood risk analysis, the partial duration series method has gained increasing acceptance as an appealing alternative to the annual maximum series method. However, when the base flow is low, there is clustering in the flood peak or flow volume point process. In this case, the general stochastic point process model is not suitable to risk analysis. Therefore, two types of models for flood risk analysis are derived on the basis of clustering stochastic point process theory in this paper. The most remarkable characteristic of these models is that the flood risk is considered directly within the time domain. The acceptability of different models are also discussed with the combination of the flood peak counted process in twenty years at Yichang station on the Yangtze river. The result shows that the two kinds of models are suitable ones for flood risk analysis, which are more flexible compared with the traditional flood risk models derived on the basis of annual maximum series method or the general stochastic point process theory.
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    Stochastic environmental research and risk assessment 12 (1998), S. 33-52 
    ISSN: 1436-3259
    Keywords: Keywords: Streamflow ; simulation ; nonparametric
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    Notes: Abstract A new approach for streamflow simulation using nonparametric methods was described in a recent publication (Sharma et al. 1997). Use of nonparametric methods has the advantage that they avoid the issue of selecting a probability distribution and can represent nonlinear features, such as asymmetry and bimodality that hitherto were difficult to represent, in the probability structure of hydrologic variables such as streamflow and precipitation. The nonparametric method used was kernel density estimation, which requires the selection of bandwidth (smoothing) parameters. This study documents some of the tests that were conduced to evaluate the performance of bandwidth estimation methods for kernel density estimation. Issues related to selection of optimal smoothing parameters for kernel density estimation with small samples (200 or fewer data points) are examined. Both reference to a Gaussian density and data based specifications are applied to estimate bandwidths for samples from bivariate normal mixture densities. The three data based methods studied are Maximum Likelihood Cross Validation (MLCV), Least Square Cross Validation (LSCV) and Biased Cross Validation (BCV2). Modifications for estimating optimal local bandwidths using MLCV and LSCV are also examined. We found that the use of local bandwidths does not necessarily improve the density estimate with small samples. Of the global bandwidth estimators compared, we found that MLCV and LSCV are better because they show lower variability and higher accuracy while Biased Cross Validation suffers from multiple optimal bandwidths for samples from strongly bimodal densities. These results, of particular interest in stochastic hydrology where small samples are common, may have importance in other applications of nonparametric density estimation methods with similar sample sizes and distribution shapes.
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    Stochastic environmental research and risk assessment 12 (1998), S. 15-32 
    ISSN: 1436-3259
    Keywords: Key words: Kalman filtering ; groundwater modelling ; inverse methods ; uncertainty analysis ; state prediction ; parameter estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The popularity of applying filtering theory in the environmental and hydrological sciences passed its first climax in the 1970s. Like so many other new mathematical methods it was simply the fashion at the time. The study of groundwater systems was not immune to this fashion, but neither was it by any means a prominent area of application. The spatial-temporal characteristics of groundwater flow are customarily described by analytical or, more frequently, numerical, physics-based models. Consequently, the state-space representations associated with filtering must be of a high order, with an immediately apparent computational over-burden. And therein lies part of the reason for the but modest interest there has been in applying Kalman filtering to groundwater systems, as reviewed critically in this paper. Filtering theory may be used to address a variety of problems, such as: state estimation and reconstruction, parameter estimation (including the study of uncertainty and its propagation), combined state-parameter estimation, input estimation, estimation of the variance-covariance properties of stochastic disturbances, the design of observation networks, and the analysis of parameter identifiability. A large proportion of previous studies has dealt with the problem of parameter estimation in one form or another. This may well not remain the focus of attention in the future. Instead, filtering theory may find wider application in the context of data assimilation, that is, in reconstructing fields of flow and the migration of sub-surface contaminant plumes from relatively sparse observations.
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    Stochastic environmental research and risk assessment 12 (1998), S. 65-82 
    ISSN: 1436-3259
    Keywords: Key words: Flood flow ; threshold ; generalized Pareto ; Poisson
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X T corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form.
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  • 84
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    Stochastic environmental research and risk assessment 12 (1998), S. 97-116 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract : The knowledge of the volume and duration of low-flow events in river channels is essential for water management and the design of hydraulics structures. In this study, both preceding characteristics, X 1 and X 2, are considered simultaneously via two types of bivariate distributions whose marginals are exponential. One of these bivariate distributions has been presented by Nagao and Kadoya (1971) and the other has been used by Singh and Singh (1991) to the study of rainfall intensity and rainfall depth. The results are applied to the low-flow series (“peaks-below-threshold”) of Lepreau River (station 01AQ001) in New Brunswick, Canada. These results show that the model that was successfully employed by Singh and Singh (1991) to study rainfall, presents certain difficulties when a very strong correlation, ρ, between the two random variables X 1 and X 2, exists. The model by Nagao and Kadoya (1971) seems to be more satisfactory for such situations, although this model seems also to be quite sensitive to variations in ρ.
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  • 85
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    Stochastic environmental research and risk assessment 12 (1998), S. 83-96 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.
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  • 86
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    Stochastic environmental research and risk assessment 12 (1998), S. 117-140 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, 〈S i i (t)〉, and the plume centroid covariance, R i i (t) (i=1,2), were simulated for the variance of Y=log T, σ Y 2=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ Y 2=0.1, all simulated 〈S i i (t)〉−S i i (0) and R i i (t) agree well with the first-order theoretical values, where S i i (0) are the initial values of S i i (t). For σ Y 2=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, 〈S 11(t)〉−S 11(0) and R 11(t), agree well with the first-order theoretical results but the simulated transverse moments 〈S 22(t)〉−S 22(0) and R 22(t) are significantly larger than the first-order values. For the same two larger values of σ Y 2 but the line sources parallel to μ, the simulated 〈S 11(t)〉−S 11(0) are larger than but the simulated R 11 are smaller than the first-order values, and both simulated 〈S 22(t)〉−S 22(0) and R 22(t) stay larger than the first-order values. For a fixed value of σ Y 2, the summations of 〈S i i (t)〉−S i i (0) and R i i , i.e., X i i (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X 11 are in good agreement with the first-order theory but the simulated X 22 are significantly larger than the first-order values. The simulated X 22, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of 〈S 22(t)〉−S 22(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ Y 2 is small.
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  • 87
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    Stochastic environmental research and risk assessment 12 (1998), S. 141-154 
    ISSN: 1436-3259
    Keywords: Key words: Ground truth ; geostatistical techniques ; areal reduction factor ; Rainfall process ; linear relationship.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Geostatistical techniques are used to quantify the reference mean areal rainfall (ground truth) from sparse raingaugenetworks. Based on the EPSAT-Niger event cumulative rainfall, a linear relationship between the ground truth considered as the mean area rainfall estimated from the densely available raingauge network and the area rainfall estimated from sparse network are derived. Also, a linear relationship between the ground truth and point rainfall is established. As it was reported experimentally by some authors, the slope of these relationships is less than one. Based on the geostatistical framework, the slope and the ordinate at the origin can be estimated as a function of the spatial structure of the rainfall process. It is shown that the slope is smaller than one. For the special case of one gauge inside a fixed area or a Field Of View (FOV), an areal reduction factor is derived. It has a limit value which depends only on the size of the area and the spatial structure of the rainfall process. The relative variance error of estimating the FOV cumulative rainfall from point rainfall is also given.
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    Stochastic environmental research and risk assessment 7 (1993), S. 195-204 
    ISSN: 1436-3259
    Keywords: Infinite dam ; resolvent operator ; Lévy process ; integrated Markov chain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract We consider an infinite-capacity storage system. The cumulative input to the system is assumed to be either (a) a non-decreasing Lévy process or (b) an integrated continuous-time Markov chain. Reward accumulates at a rate depending on the instantaneous release rate. The objective is to choose the release rule in such a way as to maximize the expected total discounted return. In this note we show how to determine the expected discounted return when the release rate is either constant or a linear function of the content.
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  • 89
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    Stochastic environmental research and risk assessment 7 (1993), S. 213-239 
    ISSN: 1436-3259
    Keywords: Stochastic hydrology ; perturbation ; random fields ; graph theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations.
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    Stochastic environmental research and risk assessment 8 (1994), S. 157-172 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Operator representations of stochastic subsurface flow equations allow writing their solutions implicitly or explicitly in terms of integro-differential expressions. Most of these representations involve Neumann series that must be truncated or otherwise approximated to become operational. It is often claimed that truncated Neumann series allow solving groundwater flow problems in the presence of arbitrarily large heterogeneities. Such claims have so far not been backed by convincing computational examples, and we present an analysis which suggests that they may not be justified on theoretical grounds. We describe an alternative operator representation due to Neuman and Orr (1993) which avoids the use of Neumann series yet accomplishes a similar purpose. It leads to a compact integro-differential form which provides considerable new insight into the nature of the solution. When written in terms of conditional moments, our new representation contains local and nonlocal effective parameters that depend on scale and information. As such, these parameters are not unique material properties but may change as more is learned about the flow system.
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  • 91
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    Stochastic environmental research and risk assessment 8 (1994), S. 185-205 
    ISSN: 1436-3259
    Keywords: Contaminant transport ; adsorption ; decay ; random walk ; killing ; Kolmogorov equations ; contamination of a well
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This study deals with the transport of a contaminant in groundwater. The contaminant is subject to first order decay or linear adsorption. Its displacement can be modeled by a random walk process in which particles are killed at exponentially distributed times. Dirichlet problems are derived for the rate and mean time at which contaminated particles reach a particular part of the boundary of a certain domain. These Dirichlet problems are solved asymptotically for two types of 2D-flow patterns: flow parallel to the boundary of a domain and arbitrary flow towards a well in an aquifer.
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  • 92
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    Stochastic environmental research and risk assessment 8 (1994), S. 109-116 
    ISSN: 1436-3259
    Keywords: Unsaturated ; nonlocal ; memory ; statistical physics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract As illustrated variously by wetting and drying scanning curves, flow in unsaturated porous media is inherently nonlocal. This nonlocality is also manifest in hysteresis in the classical Darcy conductivity. It is the authors' belief that most current theories of unsaturated/saturated flow are often inadequate, as they do not account for spatial nonlocality and memory. Here we provide a fundamental theory in which nonlocality of the flow constitutive theory is a natural consequence of force balances. The results are derived from general principles in statistical physics and under appropriate limiting conditions, the classical Darcy's Law is recovered for saturated flow. A notable departure in this theory from other nonlocal flow theories is that a classical Darcy type equation on a small scale need not exist.
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  • 93
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    Stochastic environmental research and risk assessment 12 (1998), S. 223-245 
    ISSN: 1436-3259
    Keywords: Key words: Stochastic differential equation ; spatial data ; irregularly sampled data ; parameter estimation.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract: A second order stochastic differential equation is used for modeling of water-table elevation. The data were sampled at the Borden Aquifer as a part of a tracer experiment. The purpose of the water-table data collection was to determine presence of a water flow. We argue that the water-table surface is a simple plane oscillating up and down in time according to an equation for a stochastic oscillator. We derive the model, estimate its parameters and provide arguments for goodness-of-fit of the model.
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    Stochastic environmental research and risk assessment 12 (1998), S. 267-283 
    ISSN: 1436-3259
    Keywords: Key words: Flood frequency analysis ; TCEV ; non-systematic information ; regional ; statistical gain.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract: Due to the social and economic implications, flood frequency analysis must be done with the highest precision. For this reason, the most suitable statistical model must be selected, and the maximum amount of information must be used. Floods in Mediterranean rivers can be produced by two different mechanisms, which forces the use of a non-traditional distribution like the TCEV. The information can be increased by using additional non-systematic data, or with a regional analysis, or both. Through the statistical gain concept, it has been shown that in most cases the use of additional non-systematic information can decrease the quantile estimation error in about 50%. In a regional analysis, the␣benefit of additional information in one station, is propagated to the rest of␣the␣stations with only a small decrease with respect to the at-site equivalent analysis.
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    Stochastic environmental research and risk assessment 12 (1998), S. 285-298 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions.
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  • 96
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    Stochastic environmental research and risk assessment 12 (1998), S. 247-266 
    ISSN: 1436-3259
    Keywords: Key words: Stochastic control ; dynamic programming ; reservoir systems ; hydrologic forecasting ; hydropower ; feedback control ; autoregressive models.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract : As with all dynamic programming formulations, differential dynamic programming (DDP) successfully exploits the sequential decision structure of multi-reservoir optimization problems, overcomes difficulties with the nonconvexity of energy production functions for hydropower systems, and provides optimal feedback release policies. DDP is particularly well suited to optimizing large-scale multi-reservoir systems due to its relative insensitivity to state-space dimensionality. This advantage of DDP encourages expansion of the state vector to include additional multi-lag hydrologic information and/or future inflow forecasts in developing optimal reservoir release policies. Unfortunately, attempts at extending DDP to the stochastic case have not been entirely successful. A modified stochastic DDP algorithm is presented which overcomes difficulties in previous formulations. Application of the algorithm to a four-reservoir hydropower system demonstrates its capabilities as an efficient approach to solving stochastic multi-reservoir optimization problems. The algorithm is also applied to a single reservoir problem with inclusion of multi-lag hydrologic information in the state vector. Results provide evidence of significant benefits in direct inclusion of expanded hydrologic state information in optimal feedback release policies.
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    Stochastic environmental research and risk assessment 12 (1998), S. 299-316 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a geostatistical approach to multi-directional aquifer stimulation in order to better identify the transmissivity field. Hydraulic head measurements, taken at a few locations but under a number of different steady-state flow conditions, are used to estimate the transmissivity. Well installation is generally the most costly aspect of obtaining hydraulic head measurements. Therefore, it is advantageous to obtain as many informative measurements from each sampling location as possible. This can be achieved by hydraulically stimulating the aquifer through pumping, in order to set-up a variety of flow conditions. We illustrate the method by applying it to a synthetic aquifer. The simulations provide evidence that a few sampling locations may provide enough information to estimate the transmissivity field. Furthermore, the innovation of, or new information provided by, each measurement can be examined by looking at the corresponding spline and sensitivity matrix. Estimates from multi-directional stimulation are found to be clearly superior to estimates using data taken under one flow condition. We describe the geostatistical methodology for using data from multi-directional simulations and address computational issues.
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    Stochastic environmental research and risk assessment 9 (1995), S. 33-47 
    ISSN: 1436-3259
    Keywords: Hidden markov models ; maximum likelihood estimation ; EM algorithm ; martingale estimating function ; forward-backward algorithm ; Monte Carlo ; filtering ; Nash cascade model ; rainfall runoff modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (Xn, n ≥ 0) or (Xt, t ≥ 0) for which the parameters are of interest and physically meaningful, and an observable process (Yn, n ≥ 0) or (Yt, t ≥ 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.
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    Stochastic environmental research and risk assessment 9 (1995), S. 117-132 
    ISSN: 1436-3259
    Keywords: River Quality ; network ; computer model ; Thermodynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In this paper, concepts of network thermodynamics are applied to a river water quality model, which is based on Streeter-Phelps equations, to identify the corresponding physical components and their topology. Then, the randomness in the parameters, input coefficients and initial conditions are modeled by Gaussian white noises. From the stochastic components of the physical system description of problem and concepts of physical system theory, a set of stochastic differential equations can be automatically generated in a computer and the recent developments on the automatic formulation of the moment equations based on Ito calculus can be used. This procedure is illustrated through the solution of an example of stochastic river water quality problem and it is also shown how other related problems with different configurations can be automatically solved in a computer using just one software.
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    Stochastic environmental research and risk assessment 9 (1995), S. 171-205 
    ISSN: 1436-3259
    Keywords: AR-AIC-Bayes filter ; autoregressive spectral density estimation ; diagnostic checks for ARMA models ; exploratory data analysis ; fast Fourier transform ; Hurst coefficient ; long-memory times series ; periodogram smoothing ; riverflow time series ; spectral density plots
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Current methods of estimation of the univariate spectral density are reviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements, rather than competes with, the popular ARMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Additionally, two new algorithms for fast computation of the autoregressive spectral density function are presented. For improving interpretation of results, a new style of plotting the spectral density function is suggested. Exploratory spectral analyses of a number of hydrological time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in natural time series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca.
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