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  • Articles  (10)
  • random fields  (5)
  • runoff  (5)
  • 1990-1994  (10)
  • 1975-1979
  • Architecture, Civil Engineering, Surveying  (10)
  • 1
    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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  • 2
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585600
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  • 3
    Electronic Resource
    Electronic Resource
    The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 14-32 
    Details
    ISSN: 1436-3259
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581564
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  • 4
    Electronic Resource
    Electronic Resource
    Solution of stochastic groundwater flow by infinite series, and convergence of the one-dimensional expansion (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 139-155 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589894
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  • 5
    Electronic Resource
    Electronic Resource
    Observed advantage for negative binomial over Poisson distribution in partial duration series (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 135-146 
    Details
    ISSN: 1436-3259
    Keywords: Hydrology ; runoff ; partial duration series ; negative binomial distribution ; Poisson distribution
    Source: Springer Online Journal Archives 1860-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543055
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  • 6
    Electronic Resource
    Electronic Resource
    Stochastic space transforms in subsurface hydrology — Part 2: Generalized spectral decompositions and plancherel representations (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 117-138 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic hydrology ; random fields ; space transformations ; generalized functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In earlier publications, certain applications of space transformation operators in subsurface hydrology were considered. These operators reduce the original multi-dimensional problem to the one-dimensional space, and can be used to study stochastic partial differential equations governing groundwater flow and solute transport processes. In the present work we discuss developments in the theoretical formulation of flow models with space-dependent coefficients in terms of space transformations. The formulation is based on stochastic Radon operator representations of generalized functions. A generalized spectral decomposition of the flow parameters is introduced, which leads to analytically tractable expressions of the space transformed flow equation. A Plancherel representation of the space transformation product of the head potential and the log-conductivity is also obtained. A test problem is first considered in detail and the solutions obtained by means of the proposed approach are compared with the exact solutions obtained by standard partial differential equation methods. Then, solutions of three-dimensional groundwater flow are derived starting from solutions of a one-dimensional model along various directions in space. A step-by-step numerical formulation of the approach to the flow problem is also discussed, which is useful for practical applications. Finally, the space transformation solutions are compared with local solutions obtained by means of series expansions of the log-conductivity gradient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589893
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  • 7
    Electronic Resource
    Electronic Resource
    A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 259-268 
    Details
    ISSN: 1436-3259
    Keywords: Rainfall ; runoff ; modeling ; uncertainty ; stochastics ; stochastic integral equations
    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 very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588756
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  • 8
    Electronic Resource
    Electronic Resource
    Hydrology research priorities for Dryland Agriculture in India (1993)
    Springer
    Water resources management 7 (1993), S. 93-107 
    Details
    ISSN: 1573-1650
    Keywords: Hydrology research ; India ; dryland agriculture ; runoff
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geography
    Notes: Abstract A conceptual approach was described and used to identify priorities for the cooperating centres of the All India Coordinated Research Project for Dryland Agriculture (AICRPDA). The approach was based on AICRPDA centre information, soil available water, runoff estimates, and rainfall at each centre. Lines of equal runoff were derived from the runoff-rainfall curves of the major dryland soils. Two scenarios were described, one where vertisols are cropped during the rainy season and the second where they are left under fallowed conditions during the rainy season. Three water management zones were identified for each scenario: less than 100 mm of runoff, 100 to 260 mm of runoff and greater than 260 mm of runoff. Depending on the scenario, each AICRPDA centre was incorporated into one of the three water management zones. Research orientation and priorites were set for each zone. Research efforts in the low rainfall zone can be based on small areas and in-situ water conservation. In the medium runoff zone, research can be based on areas ranging in size from 10 to 100 ha and water harvesting techniques. For the high runoff zone, greater efforts have to be put on runoff and erosion control and also on drainage response alleviating the problems created by waterlogging over large areas of 100 to 10 000 ha. Secondary priorities were also identified for each zone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00872476
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  • 9
    Electronic Resource
    Electronic Resource
    Darcian flood generation modelling (1994)
    Springer
    Water resources management 8 (1994), S. 313-326 
    Details
    ISSN: 1573-1650
    Keywords: Darcian flow ; modelling ; porous media ; runoff ; flood generation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geography
    Notes: Abstract This paper discusses experience of the use of Darcy's law for porous media flow in the context of practical modelling of flood generation. Specific drawbacks to the straightforward use of single porosity Darcian formulations for flood generation are discussed with reference to modelled examples. A quick flow component is frequently found to be needed to supplement modelled porous medium flow to match flashy stream hydrographs and observed rates of change of flow. This can in cases be justified in the field with reference to underdrainage, surface flow, natural piping and the occurrence of macropores. Rough limits are given for pure Darcian hydrograph rises under specified conditions: a range of simple methods is suggested for modelling the addition of a fast flow component where it is appropriate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00872404
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  • 10
    Electronic Resource
    Electronic Resource
    Empirical orthogonal function analysis of rainfall and runoff series (1991)
    Springer
    Water resources management 4 (1991), S. 235-250 
    Details
    ISSN: 1573-1650
    Keywords: Spatial data analysis ; stochastic hydrology ; empirical orthogonal functions ; rainfall ; runoff
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geography
    Notes: Abstract Empirical orthogonal functions (EOF) have been used to characterize spatial variability of daily and monthly rainfall and runoff in Indiana. Data from a few of the surrounding states have also been used in the analysis. After a brief discussion of the theory underlying EOF analysis, results of data analysis are presented. These results indicate that the data can be efficiently compressed and that hydrologically and meteorologically homogeneous areas can be objectively delineated by using EOF analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00430339
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