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  • Articles  (21,663)
  • Springer  (21,663)
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  • 1990-1994  (21,663)
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  • Articles  (21,663)
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  • 1
    Electronic Resource
    Electronic Resource
    Cost-effective network design for groundwater flow monitoring (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 27-41 
    Details
    ISSN: 1436-3259
    Keywords: Groundwater monitoring networks ; Information reliability ; Information scales ; Kalman filtering in groundwater
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01547730
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  • 2
    Electronic Resource
    Electronic Resource
    Probabilistic modeling of aerated lagoons: A comparison of methodologies (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 65-81 
    Details
    ISSN: 1436-3259
    Keywords: Lagoons ; Ponds ; Facultative ; First-order kinetics ; Complete mixing ; Probabilistic ; Uncertainty ; Environmental ; 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 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01547733
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  • 3
    Electronic Resource
    Electronic Resource
    Estimation of the annual maximum distribution from samples of maxima in separate seasons (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 89-103 
    Details
    ISSN: 1436-3259
    Keywords: maximum precipitation depths ; extreme-value distributions ; seasonal variation ; partial duration series ; model misspecification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543284
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  • 4
    Electronic Resource
    Electronic Resource
    Parameter identification in tidal models with uncertain boundary conditions (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 193-208 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic tidal modeling ; parameter identification ; model calibration
    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 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543083
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  • 5
    Electronic Resource
    Electronic Resource
    On the distribution of flood volume in partial duration series analysis of flood phenomena (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 217-226 
    Details
    ISSN: 1436-3259
    Keywords: Exponential distribution ; bivariate exponential distribution ; distribution of flood volume ; partial duration series
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543085
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  • 6
    Electronic Resource
    Electronic Resource
    Editorial note (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 254-254 
    Details
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544080
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  • 7
    Electronic Resource
    Electronic Resource
    Rehabilitation and replacement of water distribution system components considering uncertainties (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 277-294 
    Details
    ISSN: 1436-3259
    Keywords: Water distribution ; optimization ; nonlinear programming ; integer programming ; chance constraints ; rehabilation
    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 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544082
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  • 8
    Electronic Resource
    Electronic Resource
    Assessment of reliability in water distribution networks using entropy based measures (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 309-320 
    Details
    ISSN: 1436-3259
    Keywords: Entropy ; reliability ; redundancy ; water distribution networks ; nodal pair reliability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544084
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  • 9
    Electronic Resource
    Electronic Resource
    Evaluation of risk concepts in partial duration series (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 1-16 
    Details
    ISSN: 1436-3259
    Keywords: Partial duration series ; unbiased risk ; Bayesian risk
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544174
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  • 10
    Electronic Resource
    Electronic Resource
    Derivation of bivariate probability density functions with exponential marginals (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 55-68 
    Details
    ISSN: 1436-3259
    Keywords: Bivariate probability distribution ; random variables ; zero marginals ; Finch-Groblicki method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544178
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  • 11
    Electronic Resource
    Electronic Resource
    Entropy estimation of hydrological extremes (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 77-87 
    Details
    ISSN: 1436-3259
    Keywords: Flood ; random ; distribution ; estimation ; probability ; entropy ; fractile constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544180
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  • 12
    Electronic Resource
    Electronic Resource
    On the use of Empirical Orthogonal Function (EOF) analysis in the simulation of random fields (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 125-134 
    Details
    ISSN: 1436-3259
    Keywords: Empirical Orthogonal Function analysis ; random fields ; simulation ; non-homogeneous fields
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543054
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  • 13
    Electronic Resource
    Electronic Resource
    A univariate model for long-term streamflow forecasting (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 173-188 
    Details
    ISSN: 1436-3259
    Keywords: Entropy ; spectral analysis ; streamflow forecasting ; univariate model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544056
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  • 14
    Electronic Resource
    Electronic Resource
    Modeling kinetic non-equilibrium using the first two moments of the residence time distribution (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 155-171 
    Details
    ISSN: 1436-3259
    Keywords: Kinetic non-equilibrium ; residence time ; spatially variable chemical reactions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543057
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  • 15
    Electronic Resource
    Electronic Resource
    Stochastic partial differential equations in groundwater hydrology (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 239-251 
    Details
    ISSN: 1436-3259
    Keywords: Parameter estimation ; maximum likelihood estimation ; stochastic partial differential equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01544060
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  • 16
    Electronic Resource
    Electronic Resource
    Technical reports (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 280-294 
    Details
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543136
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  • 17
    Electronic Resource
    Electronic Resource
    Drought monitoring (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 261-266 
    Details
    ISSN: 1436-3259
    Keywords: Drought ; drought indices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543134
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  • 18
    Electronic Resource
    Electronic Resource
    In memory of Professor T. E. Unny (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 1-2 
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    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581670
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  • 19
    Electronic Resource
    Electronic Resource
    On the control of an infinite capacity storage system (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 195-204 
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    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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    URL: http://dx.doi.org/10.1007/BF01585598
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  • 20
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    Stochastic perturbation analysis of groundwater flow. Spatially variable soils, semi-infinite domains and large fluctuations (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 213-239 
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    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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    URL: http://dx.doi.org/10.1007/BF01585600
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  • 21
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    Operator and integro-differential representations of conditional and unconditional stochastic subsurface flow (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 157-172 
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    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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    URL: http://dx.doi.org/10.1007/BF01589896
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  • 22
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    Groundwater contaminant transport including adsorption and first order decay (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 185-205 
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    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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    URL: http://dx.doi.org/10.1007/BF01587234
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  • 23
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    Nonequilibrium statistical mechanical derivation of a nonlocal Darcy's Law for unsaturated/saturated flow (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 109-116 
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    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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    URL: http://dx.doi.org/10.1007/BF01589892
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    Inverse methods for subsurface flow: A critical review of stochastic techniques (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 1-26 
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    ISSN: 1436-3259
    Keywords: Inverse ; calibration ; estimation ; groundwater flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The development of stochastic methods for groundwater flow representation has undergone enormous expansion in recent years. The calibration of groundwater models, the inverse problem, has lately received comparable attention especially and almost exclusively from the stochastic perspective. In this review we trace the evolution of the methods to date with a specific view toward identifying the most important issues involved in the usefulness of the approaches. The methods are critiqued regarding practical usefulness, and future directions for requisite study are discussed.
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    URL: http://dx.doi.org/10.1007/BF01547729
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    Bayes estimate of the probability of exceedance of annual floods (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 55-64 
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    ISSN: 1436-3259
    Keywords: Predictive distribution ; Bayesian approximation ; parameter uncertainty ; non-informative prior ; method of moments ; Gumbel distribution ; 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 In this paper Lindley's Bayesian approximation procedure is used to obtain the Bayes estimate of the probability of exceedence of a flood discharge. The Bayes estimates of the probability of exceedence has been shown by S.K. Sinha to be equivalent to the estimate of the probability of exceedence from the predictive or Bayesian disribution, of a future flood discharge. The evaluation of complex ratios of multiple integrals common in a Bayesian analysis is not necessary using Lindley's procedure. The Bayes estimates are compared to those obtained by the method of maximum likelihood and the method of moments. The results show that Bayes estimates of the probability of exceedence are larger as expected, but have smaller posterior standard deviations.
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    URL: http://dx.doi.org/10.1007/BF01547732
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    Identification of wind stress on shallow water surfaces by optimal smoothing (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 105-119 
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    ISSN: 1436-3259
    Keywords: Kalman filtering ; Optimal smoothing ; Shallow water equations ; Wind stress ; On-line prediction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Using the state space approach, an on-line filter procedure for combined wind stress identification and tidal flow forecasting is developed. The stochastic dynamic approach is based on the linear twodimensional shallow water equations. Using a finite difference scheme, a system representation of the model is obtained. To account for uncertainties, the system is embedded into a stochastic environment. By employing a Kalman filter, the on-line measurements of the water-level available can be used to identify and predict the shallow water flow. Because it takes a certain time before a fluctuation in the wind stress can be noticed in the water-level measurements, an optimal fixed-lag smoother is used to identify the stress.
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    URL: http://dx.doi.org/10.1007/BF01543285
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    Advanced use into rainfall prediction of three-dimensionally scanning radar (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 135-150 
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    ISSN: 1436-3259
    Keywords: Radar ; rainfall prediction ; real-time prediction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A computational method for the determination of rainfall distribution for applications in short term rainfall prediction is presented here. The method is strongly influenced by the experience gained from the observation and analysis of data gathered on a heavy rainfall event in 1986 that occurred during the Baiu Season in Japan. The method is based on the concept that rainfall occurs as an interaction between an instability field, appropriately modeled, and a field of water vapor under the influence of topography. The results from this computational method showed good agreement with the temporal variation in the rainband that moved across the observation field in 1986. Towards determination of the parameters in the computational model, another method for the determination of the rainfield is also developed. This second method determines the rainfall distribution from estimation of the conversion rate of water vapor to liquid water through use of data from a three dimensional scanning radar. The results are consistent with those obtained from the first method.
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    Development of the instantaneous unit hydrograph using stochastic differential equations (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 151-160 
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    ISSN: 1436-3259
    Keywords: Instantaneous Unit Hydrograph ; Conceptual models ; 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 Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.
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    An exact solution of solute transport by one-dimensional random velocity fields (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 45-54 
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    ISSN: 1436-3259
    Keywords: Solute transport ; random velocity ; Lagrangian description ; travel time ; nonlinear effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.
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    Stochastic overland flows (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 89-104 
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    ISSN: 1436-3259
    Keywords: Overland flows ; nonlinear SPDE ; evolutionary probability distributions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths.
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    Analysis of macrodispersion through volume-averaging: Moment equations (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 5-25 
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    ISSN: 1436-3259
    Keywords: Solute transport ; Heterogeneity ; Dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Macrodispersion is spreading of a substance induced by spatial variations in local advective velocity at field scales. Consider the case that the steady-state seepage velocity and the local dispersion coefficients in a heterogeneous formation may be modeled as periodic in all directions in an unbounded domain. The equations satisfied by the first two spatial moments of the concentration are derived for the case of a conservative non-reacting solute. It is shown that the moments can be calculated from the solution of well-defined deterministic boundary value problems. Then, it is described how the rate of increase of the first two moments can be calculated at large times using a Taylor-Aris analysis as generalized by Brenner. It is demonstrated that the second-order tensor of macrodispersion (or effective dispersion) can be computed through the solution of steady-state boundary-value problems followed by the determination of volume averages. The analysis is based solely on volume averaging and is not limited by the assumption that the fluctuations are small. The large-time results are valid when the system is in a form of equilibrium in which a tagged particle samples all locations in an appropriately defined “phase space” with equal probability.
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    A theory of efficiency of storage-treatment systems (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 89-101 
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    ISSN: 1436-3259
    Keywords: Detention storage ; Pollution control ; Non-point pollutant runoff
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A simple expression is presented on the capability of storage-treatment systems to reduce non-point pollutant runoff load to natural waters. Their efficiency depends on the capacities of the facilities and probabilistic properties of runoff, such as interval, duration, volume, and concentration of runoff events. Assuming the compound Poisson process for runoff time series, the exact expressions of the ratio of treated load in terms of storage and treatment capacities are theoretically derived on the neighbourhoods of all boundaries of the domain on which the problem is defined. Then, an approximate expression over the whole domain is presented, of which the value and the first-order derivative coincide with those of the exact derived expressions near the boundaries. Accuracy is checked by Monte Carlo simulations.
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    On the generation of drought events using an alternating renewal-reward model (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 55-68 
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    ISSN: 1436-3259
    Keywords: Drought severity ; Drought duration ; Renewal-reward process
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This research study focused on the hypothesis that extreme drought and high streamflow events come from different independent populations with different probability distributions which need to be studied separately, rather than considering the streamflow population as a whole. The inability of traditional streamflow generator models to consistently reproduce the frequency of occurrence of severe droughts observed in the historical record has been questioned by many researchers. Our study focused on the development of astochastic event generator model which would be capable of doing so. This was accomplished in a two-step process by first generating the drought event, and then deriving the streamflows which comprised that event. The model considered for this analysis was an alternating renewal-reward procedure that cycles between eventon andoff times, and is representative of drought or high streamflow event duration. The reward gained while the event ison oroff represents drought severity or high streamflow surplus. Geometric and gamma distributions were considered for drought duration and deficit respectively. Model validation was performed using calculated required capacities from the sequent peak algorithm.
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    Probabilistic sensitivity and modeling of two-dimensional transport in porous media (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 103-121 
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    ISSN: 1436-3259
    Keywords: Probabilistic model ; Sensitivity ; Contaminant transport
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.
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    Contamination of a well in a uniform background flow (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 191-207 
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    ISSN: 1436-3259
    Keywords: Hydrodynamic dispersion ; Fokker-Planck equation ; backward equation ; boundary layer ; complex potential function ; fraction of contaminated particles that enter a well
    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 we describe the transport of pollution in groundwater in the neighbourhood of a well in a uniform background flow. We compute the rate at which contaminated particles reach the well as a function of the place of the source of pollution. The motion of a particle in a dispersive flow is seen as a random walk process. The Fokker-Planck equation for the random motion of a particle is transformed using the complex potential for the advective flow field. The resulting equation is solved asymptotically after a stretching transformation. Finally, the analytical solution is compared with results from Monte Carlo simulations with the random walk model. The method can be extended to arbitrary flow fields. Then by a numerical coordinate transformation the analytical results can still be employed.
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    Generation of runoff series at ungauged locations using empirical orthogonal functions in combination with kriging (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 255-269 
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    ISSN: 1436-3259
    Keywords: Emprical Orthogonal Functions ; interpolating runoff ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The method of Empirical Orthogonal Functions (EOF method) is combined with an objective interpolation technique, kriging, to generate runoff series at ungauged locations. In a case study the results are compared to series interpolated by a combination of EOF analysis and regression using catchment characteristics as independent variables. The results are also compared to linear weighting of an existing runoff series, a commonly used method for spatial interpolation. The influence of altitude on the runoff is studied comparing kriging based on 2 and 3 coordinates. The study showed that the capacity of EOF analysis combined with kriging is as good as the traditionally used linear weighting. The results, when altitude is included in the kriging, are improved.
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    Estimation of periodicities in hydrologic data (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 270-288 
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    ISSN: 1436-3259
    Keywords: Periodicities ; hydraulic cycle ; spectral methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Periodicites in hydrologic data are frequently estimated and studied. In some cases the periodic components are subtracted from the data to obtain the stochastic components. In other cases the physical reasons for the occurrence of these periodicities are investigated. Apart from the annual cycle in the hydrologic data, periods corresponding to the 11 year sunspot cycle, the Hale cycle and others have been detected. The conclusions from most of these studies depend on the reliability and robustness of the methods used to detect these periodicities. Several spectral analysis methods have been proposed to investigate periodicities in time series data. Several of these have been compared to each other. The methods by Siddiqui and Wang and by Damsleth and Spjotvoll, which are stepwise procedures of spectrum estimation, have not been evaluated. Two of the methods of spectral analysis proposed by Siddiqui and Wang and by Damsleth and Spjotvoll are investigated in this study by using generated and observed data. Siddiqui and Wang's method is found to be superior to the Damsleth and Spjotvoll's method.
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    On the shot-noise streamflow model and its applications (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 289-303 
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    ISSN: 1436-3259
    Keywords: Stream flow series ; shot-noise model ; sadolle-point approximation
    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 we consider the shot-noise model of streamflow series. We show how design discharge can be obtained by the stochastic intensity of thinned Poisson processes describing the peaks over a threshold. The main result concerns the stationary distribution of peaks. We derive an explicit expression for this limit distribution in terms of its Laplace transform. Approximation formulas are developed making use of the saddle point method for the asymptotic evaluation of contour integrals and the Post-Widder formula for inversion of Laplace transforms. We illustrate this methods on the case of Gamma-distributed shots. The stationary peak distribution is used to approximate the maximum value distribution for larger time intervals.
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    Flow through anisotropic networks (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 175-191 
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    ISSN: 1436-3259
    Keywords: Flow through porous media ; random network ; macro-permeability ; micro-geometry ; statistical mechanics ; anisotropy
    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 an analysis of Hagen-Poiseulle flow through plane random anisotropic networks of interconnected channels. Macroscopic permeability tensor of the network is expressed in terms of statistico-geometrical characteristics like the degree of anisotropy in channel orientations, average co-ordination number of the network and first two moments of channel length distribution. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network. The emphasis of the paper is on the effects of anisotropy on distributions of flow rates in channels. It is shown that, due to anisotropy the maximum flow rate generally occurs in channels that are not aligned along the direction of the macroscopic pressure gradient.
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    Editorial (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 253-254 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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    Predicting cumulative sediment depostition in large reservoirs (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 241-251 
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    ISSN: 1436-3259
    Keywords: Sedimentation ; Large Reservoirs ; Markov Chains
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Sediment deposition and its accumulation in a large resorvoir depends on the inflow and reservoir storage content, respectively. Because of this fact it is possible to model the cumulative deposition of sediment as an additive process defined on a bivariate Markov chain. Using the bivariate Markov chain model the mean and variance of the cumulative deposition of John Martin Reservoir, Colorado, U.S.A. are estimated and compared with observed sedimentation data.
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    On the optimal risk based design of highway drainage structures (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 295-308 
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    ISSN: 1436-3259
    Keywords: Risk-based design ; uncertainty analysis ; hydraulic design ; bridge ; culvert
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract For a proposed highway bridge or culvert, the total cost to the public during its expected service life includes capital investment on the structures, regular operation and maintenance costs, and various flood related costs. The flood related damage costs include items such as replacement and repair costs of the highway bridge or culvert, flood plain property damage costs, users costs from traffic interruptions and detours, and others. As the design discharge increases, the required capital investment increases but the corresponding flood related damage costs decrease. Hydraulic design of a bridge or culvert using a riskbased approach is to choose among the alternatives the one associated with the least total expected cost. In this paper, the risk-based design procedure is applied to pipe culvert design. The effect of the hydrologic uncertainties such as sample size and type of flood distribution model on the optimal culvert design parameters including design return period and total expected cost are examined in this paper.
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    Rainfall estimation using raingages and radar — A Bayesian approach: 2. An application (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 31-44 
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    ISSN: 1436-3259
    Keywords: Radar rainfall ; gage rainfall ; parameter uncertainty ; Bayesian estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In Seo and Smith (this issue), a set of estimators was built in a Bayesian framework to estimate rainfall depth at an ungaged location using raingage measurements and radar rainfall data. The estimators are equivalent to lognormal co-kriging (simple co-kriging in the Gaussian domain) with uncertain mean and variance of gage rainfall. In this paper, the estimators are evaluated via cross-validation using hourly radar rainfall data and simulated hourly raingage data. Generation of raingage data is based on sample statistics of actual raingage measurements and radar rainfall data. The estimators are compared with lognormal co-kriging and nonparametric estimators. The Bayesian estimators are shown to provide some improvement over lognormal co-kriging under the criteria of mean error, root mean square error, and standardized mean square error. It is shown that, if the prior could be assessed more accurately, the margin of improvement in predicting estimation variance could be larger. In updating the uncertain mean and variance of gage rainfall, inclusion of radar rainfall data is seen to provide little improvement over using raingage data only.
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    A Monte Carlo study of rainfall forecasting with a stochastic model (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 27-45 
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    ISSN: 1436-3259
    Keywords: Rainfall ; Precipitation ; Forecasting ; Real-time ; Modeling ; Simulation ; Stochastic ; Prediction ; Sampling ; Measurement ; Updating ; Filtering ; Estimation ; Short-term
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A procedure for short-term rainfall forecasting in real-time is developed and a study of the role of sampling on forecast ability is conducted. Ground level rainfall fields are forecasted using a stochastic space-time rainfall model in state-space form. Updating of the rainfall field in real-time is accomplished using a distributed parameter Kalman filter to optimally combine measurement information and forecast model estimates. The influence of sampling density on forecast accuracy is evaluated using a series of a simulated rainfall events generated with the same stochastic rainfall model. Sampling was conducted at five different network spatial densities. The results quantify the influence of sampling network density on real-time rainfall field forecasting. Statistical analyses of the rainfall field residuals illustrate improvement in one hour lead time forecasts at higher measurement densities.
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    Boundary element method for analyzing flow through a random semiconfined aquifer (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 81-88 
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    ISSN: 1436-3259
    Keywords: Helmholtz equation ; random parameter ; semiconfined aquifer ; groundwater flow ; boundary element method ; perturbation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract With the aid of perturbation technique a boundary element procedure is developed for solution of two-dimensional Helmholtz equation with a random parameter of small variability. The perturbation boundary element method does not require specification of probability density function of the parameter but only its mean and standard deviation. The method is used to analyze steady-state groundwater flows in a horizontal shallow semiconfined aquifer (homogeneous and isotropic) of probabilistic properties. To illustrate the applicability of the method, a simple numerical example is presented. As the nature of perturbation method suggests, the developed method is valid only when the perturbed value of the parameter is of a small order.
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    Drought description (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 255-260 
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    ISSN: 1436-3259
    Keywords: Drought ; probability ; stochastic process ; water management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract What constitutes a comprehensive description of drought, a description forming a basis for answering why a drought occurred is outlined. The description entails two aspects that are “naturally” coupled, named physical and economic, and treats the set of hydrologic measures of droughts in terms of their multivariate distribution, rather than in terms of a collection of the marginal distributions.
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    Farlie-Gumbel-Morgenstern bivariate densities: Are they applicable in hydrology? (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 47-54 
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    ISSN: 1436-3259
    Keywords: Bivariate density ; dependence structure ; correlation coefficient ; Farlie-Gumbel-Morgenstern density ; Farlie polynomial density
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Certain bivariate densities constructed from marginals have recently been suggested as models of hydrologic variates such as rainfall intensity and depth. It is pointed out that (i) these densities belong to the families of the Farlie-Gumbel-Morgenstern densities and the Farlie polynomial densities, which have been extensively studied in the statistical literature, and that (ii) these densities have a limited potential applicability in hydrology since they can model only weakly associated variates, whose product-moment correlationR is within the range |R|≤1/3, under the first family of densities, and |R|≤1/2 under the second family.
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    Statistical validation of GCM-simulated climates for the U.S. Great Lakes and the C.I.S. Emba and Ural River basins (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 69-80 
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    ISSN: 1436-3259
    Keywords: Hydrology ; global circulation models ; statistics ; climate change
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Many researchers use outputs from large-scale global circulation models of the atmosphere to assess hydrological and other impacts associated with climate change. However, these models cannot capture all climate variations since the physical processes are imperfectly understood and are poorly represented at smaller regional scales. This paper statistically compares model outputs from the global circulation model of the Geophysical Fluid Dynamics Laboratory to historical data for the United States' Laurentian Great Lakes and for the Emba and Ural River basins in the Commonwealth of Independent States (C.I.S.). We use maximum entropy spectral analysis to compare model and data time series, allowing us to both assess statistical predictabilities and to describe the time series in both time and frequency domains. This comparison initiates assessments of the model's representation of the real world and suggests areas of model improvement.
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    Comparison of non-Gaussian multicomponent and periodic autoregressive models for river flow (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 223-238 
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    ISSN: 1436-3259
    Keywords: River Flow Model ; Time Series ; Autoregressive
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The Non-Gaussian Multicomponent model for river flow (NGM) of Vandewiele and Dom is modified in order to facilitate maximum likelihood estimation. It is also generalized so that a wider variety of river flows at a diversity of time steps can be modeled. This model is applied to two basins in Belgium and France with very different areas, both at monthly and weekly time scale. Results on the quality of forecasting and simulation (especially simulation of low and high flow volumes) are compared with those of classical Periodic Autoregressive models (PAR). Results with NGM are always better, in most cases considerably better. This is due to the fact that NGM models explicitly take into consideration the presence of so called flow components, like baseflow and direct flow recession, which are phenomena well known to hydrologists.
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    On the lengths of crossing exursions: the case of a discrete normal process with underlying exponential autocovariance (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 167-182 
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    ISSN: 1436-3259
    Keywords: Crossing theory ; exponential autocovariance model ; discrete time series ; Weibull distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract An expression is derived for the probability distribution of excursion lengths above a fixed level, for the specific case of a discrete random process sampled from an underlying, continuous normal process with exponential autocovariance function. The expression can be integrated numerically for small excursion lengths, and used with time-series simulations to qualitatively reveal the form of the distribution. Such computations indicate that excursions lengths are well approximated by a Weibull distribution to at least the 0.95 probability value. The fit improves with increasing fixed level, and with decreasing time constant of the process. In addition, an expression is given for the expected number of crossings of a fixed level, analogous to well known formulae used in estimating expected values for the cases of a continuous process and a discrete stepped process.
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    A multivariate gamma distribution arising from a Markov model (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 183-190 
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    Keywords: Markov chains ; seasonality ; multivariate gamma distributions ; weighted sums of gammas
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A Markov chain{X t }, which has been useful for modelling in hydrology, can be specified by the Laplace transform (LT) of the conditional p.d.f. ofX t+1 givenX t =x t , which is assumed to be of the ‘exponential’ formH(θ)exp{-G(θ)x t }. For appropriate choice ofH andG the marginal distribution ofX t is the (univariate) gamma distribution. In this case, the joint p.d.f. ofX t +1,...,X t+n and its LT, are obtained, and this is extended to a seasonal version of the chain. A simple method of generating observations from these multivariate gamma distributions is noted, and the joint LT is applied to the problem of determining moments of weighted sums of such variables.
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    The use of geometric and gamma-related distributions for frequency analysis of water deficit (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 239-254 
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    ISSN: 1436-3259
    Keywords: Water deficit ; Geometric distribution ; Exponential distribution ; Deficit duration ; Deficit severity
    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 an approach to perform statistical frequency analysis of water deficit duration and severity using respectively the geometric and exponential distributions. Monthly mean water discharges are compared to a given threshold and classified in two mutually exclusive ways. This leads to a two state random variable such that: a success represents the absence of a water deficit event (mean monthly discharge exceeds threshold), and a failure, a water deficit event (mean monthly discharge is below threshold). If we suppose that this random variable gives rise to a Markov process of order 1, then the duration of a water deficit event X (consecutive months in deficit) will have a geometric distribution. In turn, the summation of discharges in deficit will give the severity of a water deficit event which can be represented by a one-parameter exponential distribution. The threshold or base level is taken as a percentile of the observed mean discharges of a given month. This base level, which varies from month to month, can be viewed as the limit of an acceptable deficit (or energetic failure) associated to a given empirical probability of being in deficit. The second step of the approach is to estimate the value of the parameter for each distribution using the maximum likelihood method. Expressions for the estimator of a given percentile, $$\hat x_q $$ , as well as its variance are deduced. Finally, the presented models are applied to observed data.
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    Development of unbiased plotting position formula for General Extreme Value distributions (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 1-13 
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    ISSN: 1436-3259
    Keywords: Unbiased plotting position ; General Extreme Value distribution ; order statistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Expressions for the expected values of GEV order statistics have been derived in simple summation form and in terms of probability weighted moments. Using exact plotting positions from GEV order statistics a new unbiased plotting position formula has been developed for the General Extreme Value distribution. The formula can, explicitly, take into account the coefficient of skewness, γ (or the shape parameter, k), of the underlying distribution. The developed formula better approximates the exact plotting positions as compared to other existing formulae and is quite easy to use.
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    The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 14-32 
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    Keywords: Stochastic hydrology ; random fields ; space transformation ; perturbation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.
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    Two kinds of moment ratio diagrams and their applications in hydrology (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 41-65 
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    ISSN: 1436-3259
    Keywords: Moment ratio diagrams ; Log-Pearson Type III ; Generalized Gamma ; geometric mean ; harmonic mean
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract We refocus attention on moment ratio diagrams and their uses in hydrology with four major objectives: (1) to summarize the information available in the literature about possible uses of the traditional moment ratio diagram introduced by Karl Pearson, which uses the coefficient of skewness and of kurtosis to compare the shapes of various distributions commonly used in hydrology; (2) to complete this traditional MRD by integrating into it the regions occupied by the log-Pearson Type III and generalized gamma distributions which are more and more used in hydrology; (3) to present another MRD which uses ratios of moments of orders −1 (harmonic mean), quasi zero (geometric mean) and 1 (arithmetic mean); (4) to stress the need to consider the different MRD's (along with the more recently introduced L-moment ratio diagrams) as complementary tools for choosing between distributions fitted to hydrologic data. Finally, using Monte Carlo simulation we compare the two types of diagrams as tools to identify and discriminate between different distributions.
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    Parameter identification in particle models (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 109-130 
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    ISSN: 1436-3259
    Keywords: Particle models ; transport equations ; parameter identification ; adjoint modelling ; cost function ; gradient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract For the simulation of the transport of dissolved matter particle models can be used. In this paper a technique is developed for the identification of uncertain parameters in these models. This model calibration is formulated as an optimization problem and is solved with a gradient based algorithm. Here adjoint particle tracks are used for the calculation of the gradient of the cost function. The performance of the calibration method is illustrated by simulations and an application to a river Rhine water quality calamity in November 1986.
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    Empirical Orthogonal Function (EOF) analysis of spatial random fields: Theory, accuracy of the numerical approximations and sampling effects (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 146-160 
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    Keywords: EOF analysis ; numerical approximations ; sampling effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Empirical Orthogonal Function (EOF) analysis of spatial random fields involves calculation of the eigenfunctions of the covariance kernel of the field. For real-world applications, a numerical approximation is necessary because the process is spatially discretized. An approximation for two-dimensional fields is proposed and then, analytical solutions of the integral problem are derived and used to study the accuracy of the numerical approximations. Sampling effects are also considered.
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    Solution of stochastic groundwater flow by infinite series, and convergence of the one-dimensional expansion (1994)
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    Stochastic environmental research and risk assessment 8 (1994), S. 139-155 
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    ISSN: 1436-3259
    Keywords: Porous media ; random media ; random fields ; groundwater flow ; stochastic hydrology ; stochastic partial differential equations ; perturbation methods ; Taylor expansions ; hierarchical systems ; Green's functions ; effective conductivity ; homogenization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper investigates analytical solutions of stochastic Darcy flow in randomly heterogeneous porous media. We focus on infinite series solutions of the steady-state equations in the case of continuous porous media whose saturated log-conductivity (lnK) is a gaussian random field. The standard deviation of lnK is denoted ‘σ’. The solution method is based on a Taylor series expansion in terms of parameter σ, around the value σ=0, of the hydraulic head (H) and gradient (J). The head solution H is expressed, for any spatial dimension, as an infinite hierarchy of Green's function integrals, and the hydraulic gradient J is given by a linear first-order recursion involving a stochastic integral operator. The convergence of the ‘σ-expansion’ solution is not guaranteed a priori. In one dimension, however, we prove convergence by solving explicitly the hierarchical sequence of equations to all orders. An ‘infinite-order stochastic solution is obtained in the form of a σ-power series that converges for any finite value of σ. It is pointed out that other expansion methods based on K rather than lnK yield divergent series. The infinite-order solution depends on the integration method and the boundary conditions imposed on individual order equations. The most flexible and general method is that based on Laplacian Green's functions and boundary integrals. Imposing zero head conditions for all orders greater than one yields meaningful far-field gradient conditions. The whole approach can serve as a basis for treatment of higher-dimensional problems.
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    A probability-weighted moment test to assess simple scaling (1994)
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    Stochastic environmental research and risk assessment 8 (1994), S. 173-183 
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    ISSN: 1436-3259
    Keywords: Probability weighted moment ; scaling in rainfall ; stable distribution
    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 statistically robust approach based on probability weighted moments to assess the presence of simple scaling in geophysical processes. The proposed approach is different from current approaches which rely on estimation of high order moments. High order moments of simple scaling processes (distributions) may not have theoretically defined values and consequently, their empirical estimates are highly variable and do not converge with increasing sample size. They are, therefore, not an appropriate tool for inference. On the other hand we show that the probability weighted moments of such processes (distributions) do exist and, hence, their empirical estimates are more robust. These moments, therefore, provide an appropriate tool for inferring the presence of scaling. We illustrate this using simulated Levystable processes and then draw inference on the nature of scaling in fluctuations of a spatial rainfall process.
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    A model for the generation of simultaneous daily discharges of two rivers at their point of confluence (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 255-276 
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    ISSN: 1436-3259
    Keywords: Stochastic hydrologic process ; daily discharges ; correlated generation ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A geomorphological study at the confluence of the Danube and the Isar in Bavaria required long series of daily discharges in both rivers. A model that generates simultaneous correlated streamflows in both rivers was developed and tested. The model is a modified shot noise model, first developed by Treiber (1975) for a single river, that was adapted to two rivers. It generates correlated pulses of events that produce flow for each river, and these pulses are then convoluted with a river specific systems function. The model, after being calibrated for the two rivers on the basis of 85 years of records, yields artificial series of discharges, in which the statistical properties of the historical records are reproduced. The performance of the model was tested with 20 generated series each 100 years long.
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    Errata toBuishand, T. A. andDemarée, G. R.: Estimation of the annual maximum distribution from samples of maxima in separate seasons. Stochastic Hydrol. Hydraul.4 (1900) 89–103 (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 321-321 
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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    Rainfall estimation using raingages and radar — A Bayesian approach: 1. Derivation of estimators (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 17-29 
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    ISSN: 1436-3259
    Keywords: Co-kriging ; parameter uncertainty ; Bayesian estimation ; radar rainfall ; gage rainfall
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Procedures for estimating rainfall from radar and raingage observations are constructed in a Bayesian framework. Given that the number of raingage measurements is typically very small, mean and variance of gage rainfall are treated as uncertain parameters. Under the assumption that log gage rainfall and log radar rainfall are jointly multivariate normal, the estimation problem is equivalent to lognormal co-kriging with uncertain mean and variance of the gage rainfall field. The posterior distribution is obtained under the assumption that the prior for the mean and inverse of the variance of log gage rainfall is normal-gamma 2. Estimate and estimation variance do not have closed-form expressions, but can be easily evaluated by numerically integrating two single integrals. To reduce computational burden associated with evaluating sufficient statistics for the likelihood function, an approximate form of parameter updating is given. Also, as a further approximation, the parameters are updated using raingage measurements only, yielding closed-form expressions for estimate and estimation variance in the Gaussian domain. With a reduction in the number of radar rainfall data in constructing covariance matrices, computational requirements for the estimation procedures are not significantly greater than those for simple co-kriging. Given their generality, the estimation procedures constructed in this work are considered to be applicable in various estimation problems involving an undersampled main variable and a densely sampled auxiliary variable.
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    Numerical methods for stochastic differential equations (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 172-172 
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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 numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to the peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, both theory and applications. The main emphasise is placed on the numerical methods needed to solve such equations. It assumes an undergraduate background in mathematical methods typical of engineers and physicists, through many chapters begin with a descriptive summary which may be accessible to others who only require numerical recipes. To help the reader develop an intuitive understanding of the underlying mathematicals and hand-on numerical skills exercises and over 100 PC Exercises (PC-personal computer) are included. The stochastic Taylor expansion provides the key tool for the systematic derivation and investigation of discrete time numerical methods for stochastic differential equations. The book presents many new results on higher order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation and variance-reduction methods. Besides serving as a basic text on such methods. the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable.
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    A Neumann expansion approach to flow through heterogeneous formations (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 207-226 
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    ISSN: 1436-3259
    Keywords: Stochastic groundwater flow ; Neumann expansion ; stochastic partial differential equation
    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 is used for the study of flow through highly heterogeneous aquifers. The mathematical model is represented by a random partial differential equation in which the permeability and the porosity are considered to be random functions of position, defined by the average value, constant standard deviation and autocorrelation function characterized by the integral scale. The Laplace transform of the solution of the random partial differential equation is first written as a solution of a stochastic integral equation. This integral equation is solved using a Neumann series expansion. Conditions of convergence of this series are investigated and compared with the convergence of the perturbation series. For mean square convergence, the Neumann expansion method may converge for a larger range of variability in permeability and porosity than the classic perturbation method. Formal expressions for the average and for the correlation moments of the pressure are obtained. The influence of the variability of the permeability and porosity on pressure is analyzed for radial flow. The solutions presented for the pressure at the well, as function of the permeability coefficient of variation, may be of practical interest for evaluating the efficiency of well stimulation operations, such as hydraulic fracturing or acidizing methods, aimed at increasing the permeability around the well.
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    Drought forecasting: Methodological topics from a systems perspective (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 267-279 
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    Keywords: Drought forecasts ; forecast lead time ; forecast skill ; forecast value ; limits of predictability ; propagation of uncertainty ; hydrometeorologic coupling ; drought management decisions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A systemic framework is presented for organizing knowledge about drought forecasting. It includes these topics: couplings among a descriptive drought model, monitoring system, and forecasting system; propagation of uncertainties; types of forecasts and attributes of performance such as the lead time and skill; sufficient measures of skill and economic value of forecasts; theoretical and operational limits of predictability; and the interface between forecasts and drought management decisions. Reviews of operational forecasts of the seasonal snowmelt runoff volumes and forecasts of the seasonal cyclone frequencies. temperature, and precipitation in the United States illustrate the methodological topics, outline the present limits of drought predictability, and suggest promising research paths. Among them are modeling of forecast uncertainties and their propagation from states of atmospheric circulation to states of a hydrologic regime, and exploring novel forms of the hydro-meteorologic coupling that would extend the lead time and/or increase the skill of long-range drought forecasts.
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    Bayesian analyses of seasonal runoff forecasts (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 295-322 
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    ISSN: 1436-3259
    Keywords: Runoff forecasts ; forecast uncertainty ; forecast skill ; forecast message ; Bayesian processor of forecasts ; sufficiency characteristic ; Bayesian correlation score ; stochastic disaggregation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Forecasts of seasonal snowmelt runoff volume provide indispensable information for rational decision making by water project operators, irrigation district managers, and farmers in the western United States. Bayesian statistical models and communication frames have been researched in order to enhance the forecast information disseminated to the users, and to characterize forecast skill from the decision maker's point of view. Four products are presented: (i) a Bayesian Processor of Forecasts, which provides a statistical filter for calibrating the forecasts, and a procedure for estimating the posterior probability distribution of the seasonal runoff; (ii) the Bayesian Correlation Score, a new measure of forecast skill, which is related monotonically to theex ante economic value of forecasts for decision making; (iii) a statistical predictor of monthly cumulative runoffs within the snowmelt season, conditional on the total seasonal runoff forecast; and (iv) a framing of the forecast message that conveys the uncertainty associated with the forecast estimates to the users. All analyses are illustrated with numerical examples of forecasts for six gauging stations from the period 1971–1988.
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    Announcements (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 3-4 
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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    URL: http://dx.doi.org/10.1007/BF01581671
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    Multiscale adaptive estimation of the conductivity field from head and tracer data (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 66-82 
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    ISSN: 1436-3259
    Keywords: Parameter identification ; multiscale ; transport ; adaptive
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Large scale fluctuations in the conductivity field are regionalized and estimated via a maximum likelihood, adjoint-state methodology. Small-scale fluctuations within each region are estimated adaptively via a Kalman-like stochastic filter. The variance and integral scale within each region are assumed to control the small-scale fluctuations. A Monte Carlo technique is used to examine the distribution of large-scale conductivity estimates.
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    Announcements (1994)
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    Stochastic environmental research and risk assessment 8 (1994), S. 156-156 
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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    URL: http://dx.doi.org/10.1007/BF01589895
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    Accuracy assessment of optimum interpolation in multichannel precipitation analysis (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 43-53 
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    ISSN: 1436-3259
    Keywords: Missing data ; Interpolation in hydrology ; Multichannel precipitation time series ; Spectral analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The accuracy of an optimum interpolation technique in filling missing values in multichannel (or multisite) hydrologic series containing time-coincident data gaps is examined. The applied methodology is based on the maximum entropy method (MEM) of spectral estimation or multivariate autoregressive modeling and heavily depends upon the properties of multichannel prediction error filter (PEF). Six precipitation time series spatially located within a hydrologic basin are used and time-coincident artificial gaps are created in all six series. The performance of the technique is assessed by comparing the filled-in series to the observed and by employing spectral analysis. The results reveal the usefulness of the method in multichannel hydrologic analysis.
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    Technical comments (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 83-88 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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    Gaussianity and linearity tests of hydrologic time series (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 121-134 
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    ISSN: 1436-3259
    Keywords: Hydrologic time series ; Linearity ; Gaussianity ; Hinich's test
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Although the non-Gaussian nature of many hydrologic time series is well recognized and their nonlinearity is suspected, neither property is well tested. This situation has existed partly because of a lack of appropriate tests. Recently Hinich (1982) has developed a test to test the linearity of time series which is based on the bispectral characteristics of the series. This test is used in this study to investigate the linearity and non-Gaussian characteristics of annual and daily rainfall and runoff series. The annual series may be modeled by linear models with Gaussian inputs. The daily data, on the other hand, often demonstrate nonlinear characteristics and are non-Gaussian as well.
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    Stochastic modelling of dispersion in shallow water (1990)
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    Stochastic environmental research and risk assessment 4 (1990), S. 161-174 
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    Keywords: advection-diffusion equation ; random walk model ; random flight model ; stochastic differential equation ; Fokker-Planck equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A random walk model to describe the dispersion of pollutants in shallow water is developed. By deriving the Fokker-Planck equation, the model is shown to be consistent with the two-dimensional advection-diffusion equation with space-varying dispersion coefficient and water depth. To improve the behaviour of the model shortly after the deployment of the pollutant, a random flight model is developed too. It is shown that over long simulation periods, this model is again consistent with the advection-diffusion equation. The various numerical aspects of the implementation of the stochastic models are discussed and finally a realistic application to predict the dispersion of a pollutant in the Eastern Scheldt estuary is described.
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    The first and the second e of the extreme value distribution, EV1 (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 69-76 
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    ISSN: 1436-3259
    Keywords: Peaks over threshold ; Binomial distribution ; Poisson distribution ; Generalised Pareto distribution ; Extreme-Value distribution, type I ; Generalised Extreme-Value distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In the peak over threshold model resulting in the Extreme-value distribution, type I, (EV1) the firste of the distribution function is based on the Poisson number of exceedances, and the seconde arises from the Exponentially distributed magnitudes. This paper, on the one hand, generalises the Poisson model to the (positive and negative) Binomial distribution, and, on the other hand, the Exponential distribution is generalised to the Generalised Pareto distribution. Lack of fit with respect to the Poisson and Exponential distribution is measured by statistics derived from those which would be locally most powerful if the estimates of the location and scale parameter were equal to the true parameter values. Ways of combining both statistics are discussed.
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    Stochastic overland flows (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 105-124 
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    ISSN: 1436-3259
    Keywords: Stochastic differential equations ; overland flows ; Monte-Carlo simulations
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The theory developed in Part I of this paper is now applied to study the probabilistic behavior of the depth at the outlet of an impermeable overland flow section under the diffusion and kinematic wave approximations. This process is excited by stochastic rainfields which are conceptualized from radar observations. The depth at the outflow section is of prime importance and the solution methodology concentrates on obtaining the evolutionary probability distribution function for this physical quantity. This theoretical distribution is then compared with the empirical distribution function obtained from a thousand Monte-Carlo simulations. The simplified theory leading to the Fokker-Planck equation is also investigated. It is observed that the ‘time window’ used for simulation purposes can affect the results. The theoretical methodology performs satisfactorily when compared to simulation results. Some of the notable features of the proposed methodology are presented and further suggestions for improvement and extension of this work are discussed.
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    Observed advantage for negative binomial over Poisson distribution in partial duration series (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 135-146 
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    ISSN: 1436-3259
    Keywords: Hydrology ; runoff ; partial duration series ; negative binomial distribution ; Poisson distribution
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The goodness of fit of the negative binomial and the Poisson distributions to partial duration series of runoff events is tested. The data have been recorded by eight hydrometric stations located on ephemeral rivers in Isreal. For each station, a number of threshold discharges are considered, by that series of nested subsamples are formed. Owing to size limitations, a Chi-square test is conducted on samples associated with low to moderate threshold discharges. Positive results, at a 5% significance level, are obtained in 30 out of the 53 tests of the Poisson distribution, and in 22 out of the 28 tests of the negative binomial distribution. The fit of the Poisson distribution to samples of conventionally recommended sizes (of 2 to 3 events per year) is found positive for five rivers and negative for the three other rivers The fit of the negative binomial distribution to these samples is found positive for six rivers, inconclusive for one river and short of data for the eighth river. Mixed results are obtained as the threshold level is raised. Therefore, no direct extrapolation is possible to samples associated with high thresholds. An indirect extrapolation is drawn through a comparison of the actual properties of the samples with those expected under a perfect fit of the distribution functions. Ranges of such properties are defined with respect to the properties of the tested samples and to the test results. The actual properties of nine of the eleven samples associated with high thresholds (i.e. mean number of events 〈-0.1year −1) are found within these ranges. This provides a hint for a probable good fit of either distribution, and particularly the negative binomial, to the occurrence frequency of high events.
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    A univariate model for long-term streamflow forecasting (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 189-205 
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    ISSN: 1436-3259
    Keywords: ARIMA model ; entropy ; Lagrange multipliers ; streamflow forecasting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper, the second in the series, verifies the entropy-based univariate model developed in the first paper for long-term streamflow forecasting on five rivers from different regions of the world. The results of the model are compared with the corresponding results of ARIMA and state-space model. The Lagrange multipliers of the univariate model are found similar to autocorrelation coefficients of the ARIMA model. Forecasts by ARIMA and univariate models were comparable for periodic streamflow, but for forecasting of highly variable streamflows the univariate model was superior.
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    Editorial (1991)
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    Stochastic environmental research and risk assessment 5 (1991), S. 253-254 
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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    URL: http://dx.doi.org/10.1007/BF01543132
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    The GF algorithm for reservoir storage, yield and spillage distributions for non-seasonal and seasonal independent inflow processes (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 135-149 
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    Keywords: Generating function ; finite stochastic reservoir ; seasonal inflow ; Markov chain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract a well-known generating function formula for the equilibrium storage distribution in a finite Moran reservoir having IID inflows and unit release is extended to apply to a class of nondecreasing staircase-like release policies withm unit increments,m〉1, and to seasonal inflows. The analysis is conducted in terms of an alternative to the Moran inflow-outflow sequencing scheme, with the release during a working interval controlled by the water level at the beginning of that interval. In addition to the storage, the equilibrium distributions of yield and spillage are obtained. Illustrative examples are provided.
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    An extreme value analysis of the flow of Burbage Brook (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 151-165 
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    ISSN: 1436-3259
    Keywords: Extreme values ; Generalized Pareto Distribution ; maximum likelihood ; peaks over threshold ; return levels ; river flows
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract An extreme value analysis of the flow of Burbage Brook is carried out by modelling peaks over a high threshold. The aims are to illustrate recently developed statistical techniques and to report on interesting features of the flow of the brook over a 58-year period. Peak flows are found to show marked seasonal variation and a downward trend. Then-year return level is estimated for various values ofn, and the reliability of the estimates is assessed.
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    Spatial variability and interpolation of daily precipitation amount (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 209-221 
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    ISSN: 1436-3259
    Keywords: geostatistics ; precipitation ; water balance models ; semivariogram ; kriging ; spatial variation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Daily precipitation amounts show spatial variation over sub-continential regions. Point measurements, representative for regions of land, have to be interpolated towards unobserved locations. In this study four days in 1984 were selected to investigate the spatial variability of daily precipitation amount in North-western Europe in relation to the meteorological conditions. Data were interpolated using Kriging. Crossvalidation was used to compare interpolated values with measured values. Large differences in the spatial structure of daily precipitation amount are obsered as a result of different meterological conditions. Stratification of the study area into a coastal, a mountainous and an interior stratum proved to be successful, reducing the Mean Squared Error of Prediction with up to 55%.
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    Optimal operation model of a single reservoir with drought duration explicitly concerned (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 123-134 
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    ISSN: 1436-3259
    Keywords: Reliability analysis ; Drought duration ; Reservoir operation ; Markov decision process
    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, a new model for a single reservoir operation optimization is proposed. The proposed model can design the optimal operation policy of a reservoir with explicit consideration of drought duration. The authors model this problem by formulating a single-stage loss function as a function of both the reservoir release and drought duration. Thereby the expected loss per period which is calculated based on the above extended single-stage loss function is minimized in infinite time horizon on the basis of Markov decision process (MDP) theory. The reliability indices are estimated as expected loss per period for specified extended loss functions. Finally, the features of the proposed model are illustrated through numerical analysis.
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    Spatial variability and interpolation of daily precipitation amount (1992)
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    Stochastic environmental research and risk assessment 6 (1992), S. 304-320 
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    ISSN: 1436-3259
    Keywords: geostatistics ; precipitation ; water balance models ; semivariogram ; kriging ; spatial variation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Daily precipitation amounts show spatial variation over sub-continential regions. Point measurements, represntative for regions of land, have to be interpolated towards unobserved locations. In this study four days in 1984 were selected to investigate the spatial variability of daily precipitation amount in north-western Europe in relation to the meteorological conditions. Data were interpolated using kriging. Crossvalidation was used to compare interpolated values with measured values. Large differences in the spatial structure of daily precipitation amount are observed as a result of different meteorological conditions. Stratification of the study area into a coast, a mountain and an interior stratum proved to be successful, reducing the Mean Squared Error of Prediction with up to 55%.
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    Announcements (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 83-83 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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    A scale-invariant approach to flood-frequency analysis (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 33-40 
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    Keywords: Fractal ; flood-frequency ; scale-invariant
    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 study historical flood-frequency records we plot the log of the number of floods on a river per unit time in which the peak discharge exceeds a specified value against the log of that value. For ten benchmark stations we find good correlations with scale-invariant (fractal) statistics. We suggest that the underlying physical processes associated with the generation of floods are sufficiently scale invariant over time scales from one to one hundred years that they provide a rational basis for the application of scale-invariant statistics. Our results fall within the range of flood-frequency estimates made by other statistical techniques. We propose that the ratio of the ten-year peak discharge to the one-year peak discharge β is a quantitative measure of flood potential. With scale invariance β is also the ratio of the one-hundred year flood to the ten-year flood. We find that the values of β for ten stations on rivers throughout the country range from 2.04 to 8.11 and find strong regional variations that can be correlated in terms of climate. Our results are consistent with the observed fractal statistics in sedimentary sections. We have also carried out R/S analyses for the ten stations and have obtained values of the Hurst exponent. We find that the Hurst exponent cannot be used for flood-frequency forecasting.
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    Evaluation of safety of hydraulic structures affected by migrating pits (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 131-145 
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    ISSN: 1436-3259
    Keywords: Safety ; reliability analysis ; uncertainty analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Because it can be carried by flowing water, a sand/gravel pit on the river bed could migrate downstream. Consequently, the presence of pits on river beds could pose a safety threat to in-stream hydraulic structures such as bridge piers. A pit migration model can be used to predict progressive changes of pit geometry as it migrates downstream. However, due to the existence of many uncertainties, the maximum pit depth cannot be predicted with certainty. This paper adopted a simple pit migration model and evaluated the uncertainty associated with the calculated maximum pit depth. Such information is essential for evaluating the probability that a migrating pit could pose a safety threat to a downstream hydraulic structure. Three reliability analysis techniques were applied and their performances were compared.
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    Evaluating the effect of land development on sediment transport using a probability density function (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 102-108 
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    ISSN: 1436-3259
    Keywords: Sedimentation ; probability density function ; synthetic study ; development
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract An important problem in sedimentation analysis is the development of a channel section that preserves, as best as possible, the current sedimentation regime even though the flood frequency tendencies have been altered due to land development within the catchment. In order to accomplish this task, a methodology is needed that estimates sediment transport capacity for various channel configurations. Such a procedure is described which allows the computation of the total sediment transport capacity for each of several T-year return frequency runoff hydrographs. This information is used to obtain an approximate probability distribution for the total sediment transport capacity, and the mean and standard deviation of this distribution are computed. Comparing the results for the catchment in its present state with a future developed state, using a selection of new channel parameters, indicates how to improve the channel to control changes in sedimentation due to development. The analysis procedure provides a basis for estimating a new channel configuration such that the new flow conditions retain, as best as possible, the existing condition sedimentation effects, and hence retain the natural sediment supply and transport trends even though runoff flow rates have changed due to land development within the catchment. The results of Wilson Creek are typical of the several sites examined, see Table 3 below. The T=2, T=5, T=25, and T=100 year values for total sediment transport capacity, in kilotons, are 6.9, 39.4, 61.3, and 96.7 with a mean of 17.1 and standard deviation of 19.3. After development with no change in the channel the respective values increase to: 17.9, 84.6, 128.1, and 258.0 with a mean of 39.1 and standard deviation of 44.3. A new channel can be constructed which will reduce these sediment transport capacity values, after development, to 5.2, 41.0, 62.0, and 124.8 with a mean of 17.4 and standard deviation of 22.0.
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    Parameter estimation for 3-parameter log-logistic distribution (LLD3) by Pome (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 163-177 
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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 principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 3-parameter log-logistic distribution (LLD3). 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). Simulation results showed that POME's performance was superior in predicting quantiles of large recurrence intervals when population skew was greater than or equal to 2.0. In all other cases, POME's performance was comparable to other methods.
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    On the validity of empirical power laws (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 179-194 
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    ISSN: 1436-3259
    Keywords: Hydrological processes ; power laws ; spurious self-correlation ; lake hydrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Empirical power laws are frequently used to relate parameters in complex hydrological and hydrometeorological processes. The validity of power laws relating two parameters with a common variable may be compromised by spurious influences of the common variable. Theoretical results are presented that allow both the spurious self-correlation coefficient and the slope of a spurious self-correlation to be determineda priori. Raising a common variable to a higher power in either parameter amplifies the spurious effects. Power law regression equations are not single-valued analytical functions and must not be treated as such. Because of the strong influence of a common variable on the correlation coefficient, the transfer of a common variable from one side of a power-law regression equation to another (by cross-multiplying) may severely distort the results. Examples from lake hydrology are presented.
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    A master equation for reactive solute transport in porous media (1993)
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    Stochastic environmental research and risk assessment 7 (1993), S. 255-268 
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    Keywords: Groundwater hydrology ; solute transport ; master equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The mean value of a density of a “cloud of points” described by a generalized Liouville equation associated with a convection dispersion equation governing adsorbing solute transport yields a joint concentration probability density. The general technique can be applied for either linear or nonlinear adsorption; here the application is restricted to linear adsorption in one-dimensional transport. The equation generated for the joint concentration probability density is in the general form of a Fokker-Planck equation, but with a suitable coordinate transformation, it is possible to represent it as a diffusion equation with variable coefficients.
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    URL: http://dx.doi.org/10.1007/BF01581614
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  • 91
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    Comparisons of Weibull- and exponential-based partial duration stochastic flood models (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 283-297 
    Details
    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 A stochastic flood model with a Weibull distribution for flood exceedances is examined and compared to the traditional exponential-based model in terms of predictive and descriptive properties. The model is based upon the traditional representation of the flood mechanism as a Poisson counting process. It is expected that the more flexible Weibull distribution will be capable of modeling flood series which exhibit a wider range of variability than the exponential model. The Weibull-based model is shown to possess predictive properties which are superior to the exponential model when samples exhibit coefficients of variation less than 1.5 and sample sizes are on the order of 2 events per year. These characteristics are shown to exist in many observed flood series in the Gulf Coast of the United States.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581616
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  • 92
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    Probabilistic assessment of travel times in groundwater modeling (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 19-55 
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    ISSN: 1436-3259
    Keywords: Indicator kriging ; stochastic simulation ; soft data ; Walker Lake ; sequential simulation ; scaling-up
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A Monte Carlo approach is described for the quantification of uncertainty on travel time estimates. A real (non synthetic) and exhaustive data set of natural genesis is used for reference. Using an approach based on binary indicators, constraint interval data are easily accommodated in the modeling process. It is shown how the incorporation of imprecise data can reduce drastically the uncertainty in the estimates. It is also shown that unrealistic results are obtained when a deterministic modeling is carried out using a kriging estimate of the transmissivity field. Problems related with using sequential indicator simulation for the generation of fields incorporating constraint interval data are discussed. The final results consists of 95% probability intervals of arrival times at selected control planes reflecting the original uncertainty on the transmissivity maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581389
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  • 93
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    Joint conditional simulations and the spectral approach for flow modeling (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 79-108 
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    ISSN: 1436-3259
    Keywords: Stochastic flow equations ; conditional simulation ; spectral representations ; joint conditioning
    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 data to condition single random fields has a well-established history. However, the joint use of data from several cross-correlated random fields is not as well developed. For example, the use of both transmissivity and head data in a steady state 2-d stochastic flow problem is essentially an inverse problem that is very important for both flow and transport predictions. This problem is addressed here by using a combination of numerical simulation and analytical methods and its application illustrated. The type of information conveyed by the different data categories is explored. The results presented are especially interesting in that head and transmissivity each give different information: Head values would appear to constrain the geometry of the paths while transmissivity data yields information about travel times. The linearized model is expanded to an iterative procedure and the “true” conditional distribution at several locations is compared with the iterative solution. The problem mentioned above is one with a special transfer function specified by the flow equation. In the second part of the paper a Fast Fourier Transform method for generation and conditioning of two or more random fields is introduced. This procedure is simple to implement, fast and very flexible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581391
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  • 94
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    Interpolation of runoff applying objective methods (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 269-281 
    Details
    ISSN: 1436-3259
    Keywords: Runoff ; stochastic interpolation ; objective analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The paper treats the problem of interpolating annual runoff from regular streamflow measurements in a regional scale applying objective methods. These methods are adapted to point processes like temperature and precipitation. Modifications are needed to account for the fact that streamflow is an integrated process following the hierarchical structure of river systems. The most straightforward method is therefore to relate the interpolation to the existing river network. For theoretical reasons it is preferable to interpolate the lateral inflow rather than the flow in the river itself. Procedures for the interpolation with the different approaches are developed and discussed. Special attention is put on the question how the equation of continuity can be satisfied. The Laagen drainage basin in southern Norway is used as a test area. The data consist of annual observations of streamflow and digital map information on river networks and drainage basin boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581615
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  • 95
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    Effective hydraulic conductivity of nonstationary aquifers (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 1-17 
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    ISSN: 1436-3259
    Keywords: Stochastic diffusion equations ; effective hydraulic conductivity ; correlation scale ; heterogeneous aquifers ; spectral representation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Assuming that the ln hydraulic conductivity in an aquifer is mathematically approximated by a spatial deterministic “surface”, or trend, plus a stationary random noise, we treat the problem of finding what the effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation of groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are presented for one- and three-dimensional finite and infinite domains. Stability criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, additional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581388
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  • 96
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    MMO: An improved estimator for log-Pearson type-3 distribution (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 219-231 
    Details
    ISSN: 1436-3259
    Keywords: Parameter estimation ; flood frequency analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A mixed method combining the method of moments and the method of optimization (MMO) was developed for estimating the parameters of the log-Pearson type 3 (LP3) distribution. The MMO estimates the parameters of mean and standard deviation by the method of indirect moments (MIM) and estimates the coefficient of skewness by minimizing both the relative root average square error (RRASE) and the relative average bias (RAB). Both the predictive capability and descriptive capability of six popular estimation methods were evaluated using 90 sets of observed flood data and six selected LP3 populations with 1000 samples for each selected sample size. The performance of the MMO was compared with those of five other selected estimation methods. A weighted ranking index (WRI) procedure was developed to help select the best combination of distribution and method for the Louisiana flood data. The WRI takes both the predictive capability and the descriptive capability into account in the evaluation. The combination of LP3/MMO was found to be the best combination for Louisiana flood data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01587236
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  • 97
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    Unsaturated flows in soils with self-similar hydraulic conductivity distribution (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 281-300 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic analysis ; unsaturated flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588758
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  • 98
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    Entropy principles in the prediction of water quality values at discontinued monitoring stations (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 301-317 
    Details
    ISSN: 1436-3259
    Keywords: Change ; discontinued stations ; entropy ; networks ; optimization ; prediction ; unbiased ; water quality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new methodology for predicting water quality values at discontinued water quality monitoring stations is proposed. The method is based upon the Principle of Maximum Entropy (POME) and provides unbiased predictions of water quality levels at upstream tributaries and on the mainstem of a river given observed changes in the distribution of the same water quality parameter at a downstream location. Changes in the values of water quality parameters which are known a priori to have occurred upstream, but which are not sufficiently large to account for all the observed change in the same water quality parameter at the downstream location are able to be incorporated in the method through the introduction of a new term in the basic entropy expression. Application of the procedure to water quality monitoring on the Mackenzie River in Queensland, Australia indicates the method has considerable potential for prediction of water quality at discontinued stations. The method also has potential for identifying the location of causes of observed changes in water quality at a downstream station.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588759
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  • 99
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    Sampling variance of a T-year flood estimated by curve-fitting (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 233-258 
    Details
    ISSN: 1436-3259
    Keywords: Flood ; China ; river ; sampling variance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The sampling variance of a T-year flood when estimated using a curve-fitting method results from the errors in hydrologic observations, plotting positions, and model-fitting. This paper develops a method to quantify the contribution of plotting positions to the sampling variance of the T-year flood magnitude. Application of the method to 150 flood-flow data sets of 41 rivers in the People's Republic of China show that the errors due to plotting positions contribute more to the sampling variance than others.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01587237
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  • 100
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    Determination of unit hydrographs by multiple storm analysis (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 269-280 
    Details
    ISSN: 1436-3259
    Keywords: Unit hydrograph ; least square methods ; regression analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper discusses the derivation of a unit hydrograph by multiple storm analysis using least squares methods. Variations of least squares method was generalized using the framework of weighted ridge analysis. The paper also shows two theorems to support using multi-storm analysis to derive UH. In addition, an issue was addressed on the scaling effect in the conventional multi-storm analysis which could create potential bias toward large storms in deriving a multi-storm UH. For that, a simple scaling procedure was proposed to reduce such potential bias problem. Numerical investigations were conducted to examine the performance of the scaling procedure by comparing with the conventional multi-storm analysis (without scaling) and the HEC-1 weighing procedures. Based on various performance criteria using a total of 39 storms from three watersheds, the proposed scaling procedure was found to produce a quite desirable UH.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588757
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