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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Stochastic environmental research and risk assessment 10 (1996), S. 1-15 
    ISSN: 1436-3259
    Keywords: Spacings ; quantiles ; generalized Pareto distribution ; log-logistic distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The maximum product of spacings (MPS) method is discussed from the standpoint of information theory. MPS parameter and quantile estimates for the generalized Pareto distribution and the two parameter log-logistic distribution are compared with the maximum likelihood(ML) and probability weighted moment (PWM) estimates.
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  • 2
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    Stochastic environmental research and risk assessment 10 (1996), S. 17-37 
    ISSN: 1436-3259
    Keywords: Diffusion ; network ; reservoir ; power law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A diffusion approximation for a network of continuous time reservoirs with power law release rules is examined. Under a mild assumption on the inflow processes, we show that for physically reasonable values of the power law constants, the system of processes converges to a multi-dimensional Gaussian diffusion process. We also illustrate how the limiting Gaussian process may be used to compute approximations to the original system of reservoirs. In addition, we study the quality of our approximations by comparing them to results obtained by simulations of the original watershed model. The simulations offer support for the use of the approximation developed here.
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  • 3
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    Stochastic environmental research and risk assessment 10 (1996), S. 39-63 
    ISSN: 1436-3259
    Keywords: Saturated flow ; rainfall ; groundwater monitoring
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A numerical experiment of flow in variably saturated porous media was performed in order to evaluate the spatial and temporal distribution of the groundwater recharge at the phreatic surface for a shallow aquifer as a function of the input rainfall process and soil heterogeneity. The study focused on the groundwater recharge which resulted from the percolation of the excess rainfall for a 90-days period of an actual precipitation record. Groundwater recharge was defined as the water flux across the moving phreatic surface. The observed spatial non-uniformity of the groundwater recharge was caused by soil heterogeneity and is particularly pronounced during the stage of recharge peak (substantial percolation stage). During that stage the recharge is associated with preferential flow paths defined as soil zones of locally higher hydraulic conductivity. For the periods of low percolation intensity the groundwater recharge was exhibiting more uniform spatial characteristics. The temporal distribution of the recharge was found to be a function of the frequency and intensity of the rainfall events. Application of sampling design demonstrates the joint influence of the spatial and temporal recharge variability on the cost-effective monitoring of groundwater potentiometric surfaces.
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  • 4
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    Stochastic environmental research and risk assessment 10 (1996), S. 65-85 
    ISSN: 1436-3259
    Keywords: Streamflow ; drought ; tree-ring data ; renewal model ; geometric variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract It is shown that runs of low-flow annual streamflow in a coastal semiarid basin of Central California can be adequately modelled by renewal theory. For example, runs of below-median annual streamflows are shown to follow a geometric distribution. The elapsed time between runs of below-median streamflow are geometrically distributed also. The sum of these two independently distributed geometric time variables defines the renewal time elapsing between the initiation of a low-flow run and the next one. The probability distribution of the renewal time is then derived from first principles, ultimately leading to the distribution of the number of low-flow runs in a specified time period, the expected number of low-flow runs, the risk of drought, and other important probabilistic indicators of low-flow. The authors argue that if one identifies drought threat with the occurrence of multiyear low-flow runs, as it is done by water supply managers in the study area, then our renewal model provides a number of interesting results concerning drought threat in areas historically subject to inclement, dry, climate. A 430-year long annual streamflow time series reconstructed by tree-ring analysis serves as the basis for testing our renewal model of low-flow sequences.
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  • 5
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    Stochastic environmental research and risk assessment 10 (1996), S. 87-106 
    ISSN: 1436-3259
    Keywords: Climate change ; daily precipitation modelling ; generalized linear models ; iteratively reweighted least squares ; spline functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The precipitation amounts on wet days at De Bilt (the Netherlands) are linked to temperature and surface air pressure through advanced regression techniques. Temperature is chosen as a covariate to use the model for generating synthetic time series of daily precipitation in a CO2 induced warmer climate. The precipitation-temperature dependence can partly be ascribed to the phenomenon that warmer air can contain more moisture. Spline functions are introduced to reproduce the non-monotonous change of the mean daily precipitation amount with temperature. Because the model is non-linear and the variance of the errors depends on the expected response, an iteratively reweighted least-squares technique is needed to estimate the regression coefficients. A representative rainfall sequence for the situation of a systematic temperature rise is obtained by multiplying the precipitation amounts in the observed record with a temperature dependent factor based on a fitted regression model. For a temperature change of 3°C (reasonable guess for a doubled CO2 climate according to the present-day general circulation models) this results in an increase in the annual average amount of 9% (20% in winter and 4% in summer). An extended model with both temperature and surface air pressure is presented which makes it possible to study the additional effects of a potential systematic change in surface air pressure on precipitation.
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  • 6
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    Stochastic environmental research and risk assessment 10 (1996), S. 107-126 
    ISSN: 1436-3259
    Keywords: Gaussian process ; spatial correlation ; anisotropy ; Fourier transform ; Gauss-Newton ; ECM ; measurement error ; signal extraction ; irregular data
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper is concerned with developing computational methods and approximations for maximum likelihood estimation and minimum mean square error smoothing of irregularly observed two-dimensional stationary spatial processes. The approximations are based on various Fourier expansions of the covariance function of the spatial process, expressed in terms of the inverse discrete Fourier transform of the spectral density function of the underlying spatial process. We assume that the underlying spatial process is governed by elliptic stochastic partial differential equations (SPDE's) driven by a Gaussian white noise process. SPDE's have often been used to model the underlying physical phenomenon and the elliptic SPDE's are generally associated with steady-state problems. A central problem in estimation of underlying model parameters is to identify the covariance function of the process. The cumbersome exact analytical calculation of the covariance function by inverting the spectral density function of the process, has commonly been used in the literature. The present work develops various Fourier approximations for the covariance function of the underlying process which are in easily computable form and allow easy application of Newton-type algorithms for maximum likelihood estimation of the model parameters. This work also develops an iterative search algorithm which combines the Gauss-Newton algorithm and a type of generalized expectation-maximization (EM) algorithm, namely expectation-conditional maximization (ECM) algorithm, for maximum likelihood estimation of the parameters. We analyze the accuracy of the covariance function approximations for the spatial autoregressive-moving average (ARMA) models analyzed in Vecchia (1988) and illustrate the performance of our iterative search algorithm in obtaining the maximum likelihood estimation of the model parameters on simulated and actual data.
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  • 7
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    Stochastic environmental research and risk assessment 10 (1996), S. 127-150 
    ISSN: 1436-3259
    Keywords: Rainfall estimation ; indicator cokriging ; rain gage measurements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Indicator cokriging (Journel 1983) is examined as a tool for real-time estimation of rainfall from rain gage measurements. The approach proposed in this work obviates real-time estimation of real-time statistics of rainfall by using ensemble or climatological statistics exclusively, and reduces computational requirements attendant to indicator cokriging by employing only a few auxiliary cutoffs in estimation of conditional probabilities. Due to unavailability of suitable rain gage measurements, hourly radar rain fall data were used for both indicator covariance estimation and a comparative evaluation. Preliminary results suggest that the indicator cokriging approach is clearly superior to its ordinary kriging counterpart, whereas the indicator kriging approach is not. The improvement is most significant in estimation of light rainfall, but drops off significantly for heavy rainfall. The lack of predictability in spatial estimation of heavy rainfall is borne out in the integral scale of indicator correlation: peaking to its maximum for cutoffs near the median, indicator correlation scale becomes increasingly smaller for larger cutoffs of rainfall depth. A derived-distribution analysis, based on the assumption that radar rainfall is a linear sum of ground-truth and a random error, suggests that, at low cutoffs, indicator correlation scale of ground-truth can significantly differ from that of radar rainfall, and points toward inclusion of rainfall intermittency, for example, within the framework proposed in this work.
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  • 8
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    Stochastic environmental research and risk assessment 10 (1996), S. 151-161 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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  • 9
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    Stochastic environmental research and risk assessment 10 (1996), S. 163-166 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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  • 10
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    Stochastic environmental research and risk assessment 10 (1996), S. 187-207 
    ISSN: 1436-3259
    Keywords: log-Gumbel distribution ; flood frequency analysis ; quantile estimation ; confidence intervals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The log-Gumbel distribution is one of the extreme value distributions which has been widely used in flood frequency analysis. This distribution has been examined in this paper regarding quantile estimation and confidence intervals of quantiles. Specific estimation algorithms based on the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood (ML) are presented. The applicability of the estimation procedures and comparison among the methods have been illustrated based on an application example considering the flood data of the St. Mary's River.
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  • 11
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    Stochastic environmental research and risk assessment 10 (1996), S. 167-186 
    ISSN: 1436-3259
    Keywords: Reservoir stochastic theory ; reliability ; mean ; variance ; indicator function ; storage bounds ; nonlinear programming ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new formulation is presented for the analysis of reservoir systems synthesizing concepts from the traditional stochastic theory of reservoir storage, moments analysis and reliability programming. The analysis is based on the development of the first and second moments for the stochastic storage state variable. These expressions include terms for the failure probabilities (probabilities of spill or deficit) and consider the storage bounds explicitly. Using this analysis, expected values of the storage state, variances of storage, optimal release policies and failure probabilities — useful information in the context of reservoir operations and design, can be obtained from a nonlinear programming solution. The solutions developed from studies of single reservoir operations on both an annual and monthly basis, compare favorably with those obtained from simulation. The presentation herein is directed to both traditional reservoir storage theorists who are interested in the design of a reservoir and modern reservoir analysts who are interested in the long term operation of reservoirs.
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  • 12
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    Stochastic environmental research and risk assessment 10 (1996), S. 209-229 
    ISSN: 1436-3259
    Keywords: Infiltration-advance equation ; water spreading ; cellular automata ; irrigation ; surface hydrology ; hydrodynamics ; stochastic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A technique has been developed for predicting the irregular advance pattern often observed as water spreads on the surface of the ground. The technique is a combination of stochastic sketching, potential theory, probability theory, and a mass balance equation in the form of an advance equation. The technique can be used on flat as well as sloping terrain and addresses any form of obstructions or constraints to the flow of the water. The stochastic sketching portion of the technique uses cellular automata with transition probability movement rules to sketch the dynamics of small volume water elements in the defined environment. Randomly selected small volume flow path segments are computed and plotted. The envelope of these segments defines the wetted area and the advance front. Several examples are presented showing the patterns produced for various situations.
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  • 13
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    Stochastic environmental research and risk assessment 10 (1996), S. 231-251 
    ISSN: 1436-3259
    Keywords: Stochastic ; multiphase ; three phase ; heterogeneity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, α. These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter α. The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.
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  • 14
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    Stochastic environmental research and risk assessment 10 (1996), S. 295-317 
    ISSN: 1436-3259
    Keywords: Bayesion methods ; time series ; hydrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A review of literature reveals the inadequacy of Intervention analysis and spectrum based methods to adequately quantify changes in hydrologic times series. A Bayesian method is used to investigate the statistical significance of observed changes in hydrologic times series and the results are reported herein. The Bayesian method is superior to the previous methods.
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  • 15
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    Stochastic environmental research and risk assessment 10 (1996), S. 253-278 
    ISSN: 1436-3259
    Keywords: Random fields ; stochastic processes ; fractals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper describes a new method for generating spatially-correlated random fields. Such fields are often encountered in hydrology and hydrogeology and in the earth sciences. The method is based on two observations: (i) spatially distributed attributes usually display a stationary correlation structure, and (ii) the screening effect of measurements leads to the sufficiency of a small search neighborhood when it comes to projecting measurements and data in space. The algorithm which was developed based on these principles is called HYDRO_GEN, and its features and properties are discussed in depth. HYDRO_GEN is found to be accurate and extremely fast. It is also versatile: it can simulate fields of different nature, starting from weakly stationary fields with a prescribed covariance and ending with fractal fields. The simulated fields can display statistical isotropy or anisotropy.
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  • 16
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    Stochastic environmental research and risk assessment 10 (1996), S. 279-294 
    ISSN: 1436-3259
    Keywords: Linear estimation ; interpolation ; kriging ; splines ; conditional
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This work presents analytical expressions for the best estimate, conditional covariance function, and conditional realizations of a function from sparse observations. In contrast to the prevalent approach in kriging where the best estimates at every point are determined from the solution of a system of linear equations, the best-estimate function can be represented analytically in terms of basis functions, whose number depends on the observations. This approach is computationally superior when graphing a function estimate and is also valuable in understanding what the solution should look like. For example, one can immediately see that all “singularities” in the best-estimate function are at observation points.
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  • 17
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    Stochastic environmental research and risk assessment 10 (1996), S. 319-329 
    ISSN: 1436-3259
    Keywords: Particle tracking ; numerical methods ; random walks ; advection-dispersion equation ; stochastic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A formal statistical discussion of the origins of the random walk and its relation to the classic advection-dispersion equation is given. At issue is the common use of Gaussian distributed steps in producing the desired dispersive effects. Shown are alternative solutions to the basic Langevin equation describing mass displacements based on non-Gaussian, white increments. In particular, the results reveal that uniform or symmetric-triangular steps can be employed without loss of generality in accuracy of the solution (over all Peclet numbers) and may yield significant savings in the computational generation of the random deviates required in the Monte Carlo procedures of the random walk method.
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  • 18
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    Stochastic environmental research and risk assessment 10 (1996), S. 330-330 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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  • 19
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    Stochastic environmental research and risk assessment 11 (1997), S. 17-31 
    ISSN: 1436-3259
    Keywords: Bivariate density ; meta-Gaussian density ; normal quantile transform ; likelihood ratio dependence ; correlation coefficient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Convenient bivariate densities found in the literature are often unsuitable for modeling hydrologic variates. They either constrain the range of association between variates, or fix the form of the marginal distributions. The bivariate meta-Gaussian density is constructed by embedding the normal quantile transform of each variate into the Gaussian law. The density can represent a full range of association between variates and admits arbitrarily specified marginal distributions. Modeling and estimation can be decomposed into i) independent analyses of the marginal distributions, and ii) investigation of the dependence structure. Both statistical and judgmental estimation procedures are possible. Some comparisons to recent applications of bivariate densities in the hydrologic literature motivate and illustrate the model.
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  • 20
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    Stochastic environmental research and risk assessment 11 (1997), S. 33-50 
    ISSN: 1436-3259
    Keywords: Unit hydrograph ; uncertainty analysis ; linearly constrained Monte-Carlo simulation ; reliability analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Unit hydrographs (UHs), along with design rainfalls, are frequently used to determine the discharge hydrograph for design and evaluation of hydraulic structures. Due to the presence of various uncertainties in its derivation, the resulting UH is inevitably subject to uncertainty. Consequently, the performance of hydraulic structures under the design storm condition is uncertain. This paper integrates the linearly constrained Monte-Carlo simulation with the UH theory and routing techniques to evaluate the reliability of hydraulic structures. The linear constraint is considered because the water volume of each generated design direct runoff hydrograph should be equal to that of the design effective rainfall hyetograph or the water volume of each generated UH must be equal to one inch (or cm) over the watershed. For illustration, the proposed methodology is applied to evaluate the overtopping risk of a hypothetical flood detention reservoir downstream of Tong-Tou watershed in Taiwan.
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  • 21
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    Stochastic environmental research and risk assessment 11 (1997), S. 1-16 
    ISSN: 1436-3259
    Keywords: Nash cascade reservoir model ; rainfall-runoff ; EM algorithm ; filtering ; maximum likelihood estimation ; martingale estimating function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Abstract: Linear continuous time stochastic Nash cascade conceptual models for runoff are developed. The runoff is modeled as a simple system of linear stochastic differential equations driven by white Gaussian and marked point process noises. In the case of d reservoirs, the outputs of these reservoirs form a d dimensional vector Markov process, of which only the dth coordinate process is observed, usually at a discrete sample of time points. The dth coordinate process is not Markovian. Thus runoff is a partially observed Markov process if it is modeled using the stochastic Nash cascade model. We consider how to estimate the parameters in such models. In principle, maximum likelihood estimation for the complete process parameters can be carried out directly or through some form of the EM (estimation and maximization) algorithm or variation thereof, applied to the observed process data. In this research we consider a direct approximate likelihood approach and a filtering approach to an algorithm of EM type, as developed in Thompson and Kaseke (1994). These two methods are applied to some real life runoff data from a catchment in Wales, England. We also consider a special case of the martingale estimating function approach on the runoff model in the presence of rainfall. Finally, some simulations of the runoff process are given based on the estimated parameters.
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  • 22
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    Stochastic environmental research and risk assessment 11 (1997), S. 173-192 
    ISSN: 1436-3259
    Keywords: Uncertainty analysis ; unit hydrograph ; regression analysis ; probabilistic point estimation methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Hydrologic model parameters obtained from regional regression equations are subject to uncertainty. Consequently, hydrologic model outputs based on the stochastic parameters are random. This paper presents a systematic analysis of uncertainty associated with the two parameters, N and K, in Nash's IUH model from different regional regression equations. The uncertainty features associated with N and K are further incorporated to assess the uncertainty of the resulting IUH. Numerical results indicate that uncertainty of N and K from the regional regression equations are too significant to be ignored.
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  • 23
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    Stochastic environmental research and risk assessment 11 (1997), S. 145-171 
    ISSN: 1436-3259
    Keywords: Hydrologic regionalization ; unit hydrograph ; regression analysis ; multivariate regression ; seemingly unrelated regression ; validation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Hydrologic regionalization is a useful tool that allows for the transfer of hydrological information from gaged sites to ungaged sites. This study developed regional regression equations that relate the two parameters in Nash's IUH model to the basin characteristics for 42 major watersheds in Taiwan. In the process of developing the regional equations, different regression procedures including the conventional univariate regression, multivariate regression, and seemingly unrelated regression were used. Multivariate regression and seeming unrelated regression were applied because there exists a rather strong correlation between the Nash's IUH parameters. Furthermore, a validation study was conducted to examine the predictability of regional equations derived by different regression procedures. The study indicates that hydrologic regionalization involving several dependent variables should consider their correlations in the process of establishing the regional equations. The consideration of such correlation will enhance the predictability of resulting regional equations as compared with the ones from the conventional univariate regression procedure.
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  • 24
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    Stochastic environmental research and risk assessment 11 (1997), S. 193-210 
    ISSN: 1436-3259
    Keywords: Turbulence ; sediment ; fluvial ; river ; bursting process ; statistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Entrainment of sediment particles from channel beds into the channel flow is influenced by the characteristics of the flow turbulence which produces stochastic shear stress fluctuations at the bed. Recent studies of the structure of turbulent flow has recognized the importance of bursting processes as important mechanisms for the transfer of momentum into the laminar boundary layer. Of these processes, the sweep event has been recognized as the most important bursting event for entrainment of sediment particles as it imposes forces in the direction of the flow resulting in movement of particles by rolling, sliding and occasionally saltating. Similarly, the ejection event has been recognized as important for sediment transport since these events maintain the sediment particles in suspension. In this study, the characteristics of bursting processes and, in particular, the sweep event were investigated in a flume with a rough bed. The instantaneous velocity fluctuations of the flow were measured in two-dimensions using a small electromagnetic velocity meter and the turbulent shear stresses were determined from these velocity fluctuations. It was found that the shear stress applied to the sediment particles on the bed resulting from sweep events depends on the magnitude of the turbulent shear stress and its probability distribution. A statistical analysis of the experimental data was undertaken and it was found necessary to apply a Box-Cox transformation to transform the data into a normally distributed sample. This enabled determination of the mean shear stress, angle of action and standard error of estimate for sweep and ejection events. These instantaneous shear stresses were found to be greater than the mean flow shear stress and for the sweep event to be approximately 40 percent greater near the channel bed. Results from this analysis suggest that the critical shear stress determined from Shield's diagram is not sufficient to predict the initiation of motion due to its use of the temporal mean shear stress. It is suggested that initiation of particle motion, but not continuous motion, can occur earlier than suggested by Shield's diagram due to the higher shear stresses imposed on the particles by the stochastic shear stresses resulting from turbulence within the flow.
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  • 25
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    Stochastic environmental research and risk assessment 11 (1997), S. 211-227 
    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 The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 2-parameter generalized Pareto (GP2) distribution. Monte Carlo simulated data were used to evaluate this method and compare it with the methods of moments (MOM), probability weighted moments (PWM), and maximum likelihood estimation (MLE). The parameter estimates yielded by POME were comparable or better within certain ranges of sample size and coefficient of variation.
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  • 26
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    Stochastic environmental research and risk assessment 4 (1990), S. 27-41 
    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.
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  • 27
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    Stochastic environmental research and risk assessment 4 (1990), S. 65-81 
    ISSN: 1436-3259
    Keywords: Lagoons ; Ponds ; Facultative ; First-order kinetics ; Complete mixing ; Probabilistic ; Uncertainty ; Environmental ; Stochastic differential equations
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    Notes: Abstract Two stochastic models are developed to describe the BOD output (i.e. effluent) variation of facultative aerated lagoons in series. One of the models uses the uncertainty analysis (UA) technique and the other is based on the moment equation solution methodology of stochastic differential equations (SDE's). The former considers a second-order approximation of the expectation (SOAE) and a first-order approximation of the variance (FOAV). The SDE model considers that output variability is accounted for by random variations in the rate coefficient. Comparisons are provided. Calibration and verification of the two models are aciieved by using field observations from two different lagoon systems in series. The predictive performances of the two models are compared with each other and with another SDE model, presented in a previous paper, that considers input randomness. The three methods show similar predictive performances and provide good predictions of the mean and standard deviation of the lagoon effluent BOD concentrations and thus are considered as appropriate methodologies.
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    Stochastic environmental research and risk assessment 4 (1990), S. 89-103 
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    Keywords: maximum precipitation depths ; extreme-value distributions ; seasonal variation ; partial duration series ; model misspecification
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    Notes: Abstract Quantile estimates of the annual maximum distribution can be obtained by fitting theoretical distributions to the maxima in separate seasons, e.g. to the monthly maxima. In this paper, asymptotic expressions for the bias and the variance of such estimates are derived for the case that the seasonal maxima follow a Gumbel distribution. Results from these expressions are presented for a situation with no seasonal variation and for maximum precipitation depths at Uccle/Ukkel (Belgium). It is shown that the bias is often negligible and that the variance reduction by using seasonal maxima instead of just the annual maxima strongly depends on the seasonal variation in the data. A comparison is made between the asymptotic standard error of quantile estimates from monthlymaxima with those from a partial duration series. Much attention is paid to the effect of model misspecification on the resulting quantile estimates of the annual maximum distribution. The use of seasonal maxima should be viewed with caution when the upper tail of this distribution is of interest.
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    Stochastic environmental research and risk assessment 4 (1990), S. 193-208 
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    Keywords: Stochastic tidal modeling ; parameter identification ; model calibration
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    Notes: Abstract In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as parameter fluctuations. Therefore the open boundary conditions are embedded into a stochastic environment and a constant gain extended Kalman filter is employed to identify the state of the system. Defining a error functional that measures the differences between the filtered state of the system and the measurements, a quasi Newton method is employed to determine the minimum of this functional. To reduce the computational burden, the gradient of the criterium that is required using the quasi Newton method is determined by solving the adjoint system.
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    Stochastic environmental research and risk assessment 4 (1990), S. 217-226 
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    Keywords: Exponential distribution ; bivariate exponential distribution ; distribution of flood volume ; partial duration series
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    Notes: Abstract A methodology based on the theory of stochastic processes is applied to the analysis of floods. The approach will be based on some results of the theory of extreme values over a threshold. In this paper, we focus on the estimation of the distribution of the flood volume in partial duration series analysis of flood phenomena, by using a bivariate exponential distribution of discharge exceedances and durations over a base level.
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    Stochastic environmental research and risk assessment 4 (1990), S. 254-254 
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    Stochastic environmental research and risk assessment 4 (1990), S. 277-294 
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    Keywords: Water distribution ; optimization ; nonlinear programming ; integer programming ; chance constraints ; rehabilation
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    Notes: Abstract This paper presents the mathematical development of an integer — nonlinear programming chance — constrained optimization model for the minimum cost rehabilitation/replacement of water distribution system components. Particular attention is given to the handling of uncertainties in the roughness factors and the loading conditions including both the random demand and preassure head requirements. The advantages of the proposed model include the ability to: 1) handle the optimal timing of rehabilitation/replacement for water distribution system components; 2) link a mixed-integer linear program solver, a nonlinear program solver, and a hydraulic simulator into an optimization framework; 3) handle the uncertainties of some of the variables; 4) incorporate various kinds of cost functions; and 5) handle multiple loading conditions.
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    Stochastic environmental research and risk assessment 4 (1990), S. 309-320 
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    Keywords: Entropy ; reliability ; redundancy ; water distribution networks ; nodal pair reliability
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    Notes: Abstract Entropy based expressions for measurement of reliability and redundancy have recently been reported. These measures approach assessment of the reliability of the distribution network from the intrinsic redundancy of the network layout. The paper extends earlier work on entropy functions by including a more explicit statement of the alternate paths available in the network and by recognizing that under certain circumstances, e.g., failure of some part of the network work, an outflow link from a node under normal working condition may become an inflow link to the same node. The measures are assessed by comparison with parameters measuring Nodal Pair Reliability and percentage of flow supplied at adequate pressure for a range of networks and link failure conditions in this networks. The entropy measures are shown to reflect changes in the network reliability, as measured by these two comparative parameters, very well.
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    Stochastic environmental research and risk assessment 5 (1991), S. 1-16 
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    Keywords: Partial duration series ; unbiased risk ; Bayesian risk
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    Notes: Abstract Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.
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    Stochastic environmental research and risk assessment 5 (1991), S. 55-68 
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    Keywords: Bivariate probability distribution ; random variables ; zero marginals ; Finch-Groblicki method
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    Notes: Abstract A vivariate probability density function (pdf),f(x 1,x 2), admissible for two random variables (X 1,X 2), is of the form $$f(x_1 x_2 ) = f_1 (x_1 )f_2 (x_2 )[1 + \rho \{ F_1 (x_1 ),F_2 (x_2 )\} ]$$ where ρ(u, v) (u=F 1(x 1),v=F 2(x 2)) is any function on the unit square that is 0-marginal and bounded below by−1 andF 1(x 1) andF 2(x 2) are cumulative distribution functions (cdf) of marginal probability density functionsf 1(x 1) andf 2(x 2). The purpose of this study is to determinef(x 1,x 2) for different forms of ρ(u,v). By considering the rainfall intensity and the corresponding depths as dependent random variables, observed and computed probability distributionsF 1(x 1),F(x 1/x 2),F 2(x 2), andF(x 2/x 1) are compared for various forms of ρ(u,v). Subsequently, the best form of ρ(u,v) is specified.
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    Stochastic environmental research and risk assessment 5 (1991), S. 77-87 
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    Keywords: Flood ; random ; distribution ; estimation ; probability ; entropy ; fractile constraints
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    Notes: Abstract The method of Relative Entropy with Fractile constraints (REF method) is explained and applied to model extreme compound hydrological phenomena, such as extreme sea levels under storm conditions. Also presented is a simple method of Tail Entropy Approximation (TEA), which amounts to a correction of traditional statistical estimates for extreme observations. Distribution assumptions are necessary but downplayed in the REF method, relegating the prior distribution to the role of an extrapolation function. The estimates are objective in an information-theoretical sense. They also satisfy a strict requirement of self-consistency that is generally not satisfied by standard statistical methods: invariance under monotonic transformations of the random variable. Historical records of storm surge levels in the Netherlands and annual maximum tidal heights for Sheerness, UK, are used as examples. Comparison is made with distributions obtained using other methods. It is concluded that the tail entropy approximation provides simple, objective estimates of extremes in the tail beyond the range of observations.
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    Stochastic environmental research and risk assessment 5 (1991), S. 125-134 
    ISSN: 1436-3259
    Keywords: Empirical Orthogonal Function analysis ; random fields ; simulation ; non-homogeneous fields
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    Notes: Abstract In several fields of Geophysics, such as Hydrology, Meteorology or Oceanography, it is often useful to generate random fields, displaying the same variabilitity as the observed variables. Usually, these synthetic data are used as forcing fields into numerical models, to test the sensitivity of their outputs to the variability of the inputs. Examples can be found in subsurface or surface Hydrology and in Meteorology with General Circulation Models (GCM). Different techniques have already been proposed, often based on the spectral representation of the random process, with, usually, assumptions of stationarity. This paper suggests that Empirical Orthogonal Function (EOF) analysis, which leads to the decomposition of the covariance kernel on the set of its eigen-functions, is a possible answer to this problem. The convergence and accuracy of the method are shown to depend mainly on the number of EOFs retained in the expansion of the covariance kemel. This result is confirmed by a comparison with the turning band method and a matrix technique. Furthermore, a synthetic example of non-homogencous fields shows the interest of EOF analysis in the direct simulation of such fields.
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    Stochastic environmental research and risk assessment 5 (1991), S. 173-188 
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    Keywords: Entropy ; spectral analysis ; streamflow forecasting ; univariate model
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    Notes: Abstract This paper, the first in a series of two, employs the principle of maximum entropy (POME) via maximum entropy spectral analysis (MESA) to develop a univariate model for long-term streamflow forecasting. Three cases of streamflow forecasting are investigated: forward forecasting, backward forecasting (or reconstruction) and intermittent forecasting (or filling in missing records). Application of the model is discussed in the second paper.
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    Stochastic environmental research and risk assessment 5 (1991), S. 155-171 
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    Keywords: Kinetic non-equilibrium ; residence time ; spatially variable chemical reactions
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    Notes: Abstract A method for simulating field scale transport of kinetically adsorbing solutes is described. The non-equilibrium adsorption is modeled as a birth and death process and is coupled with the particle tracking approach using the first two moments of the distribution of the particle residence time, i.e., the time that a solute particle stays in the liquid phase. A single residence time distribution, regardless of the initial and final phase, is demonstrated to yield an accurate description of chemical kinetics in the vast majority of field scale problems. The first two moments of the residence time distribution are derived as a function of chemical reaction rates and the transport time interval Δt. It is shown that the first moment of the residence time represents a measure of the speed of the chemical reaction relative to the transport time scale Δt which is chosen depending on the velocity field. The second moment of the residence time reflects the relative importance of the chemical kinetics versus local equilibrium conditions for the given transport time step Δt. The simulated spatial moments of the contaminant plume are compared in the one-dimensional case with available analytical solutions to demonstrate the accuracy of the proposed technique. A two-dimensional case for stratified formations is presented to study the transport behavior for heterogeneous velocity fields and variable distribution coefficient, hypothesized as being negatively correlated with hydraulic conductivity. The results show that the enhanced plume spreading and the statistics of the arrival time distribution appear to be more sensitive to the spatially variable distribution coefficient than to the kinetics alone. In fact, the second spatial moment was almost doubled in the case of spatially variable distribution coefficient.
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    Stochastic environmental research and risk assessment 5 (1991), S. 239-251 
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    Keywords: Parameter estimation ; maximum likelihood estimation ; stochastic partial differential equation
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    Notes: Abstract Part I of this series of two papers (Unny, 1989) dealt with the theoretical derivation of the moment equations for the stochastic partial differential equation in the water table depth forced by stochastic rainfall input. Part I also developed a maximum likelihood estimation procedure for parameter determination. The primary aim of the present manuscript is the application of the parameter estimation procedure to the Borden aquifer, an aquifer designated as an experimental site, where extensive field measurements have been carried out. Estimates of hydraulic conductivity and transmissivity for the Borden aquifer, derived from the maximum likelihood algorithm, have been compared with estimates obtained by “traditional” procedures. The paper also presents the simulated solution of the governing differential equation in the one dimensional problem applied to the Borden aquifer.
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    Stochastic environmental research and risk assessment 5 (1991), S. 280-294 
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    Stochastic environmental research and risk assessment 5 (1991), S. 261-266 
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    Keywords: Drought ; drought indices
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    Notes: Abstract Drought detection, monitoring and indices are closely related to its definition. The specific definition chosen for a particular drought analysis will affect the procedures one uses in drought detection and monitoring. The traditional Palmer Drought Severity Index (PDSI) has been proven to be ineffective in regions of predominantly irrigated agriculture. The recently developed ALERT (Automated Local Evaluation in Real Time) system is proposed for use in monitoring the spatial and temporal variations of drought in real time. The ALERT system uses standardized instruments, radio frequencies, software and hardware. It was originally developed as a flash flood waming system by local flood control districts and the National Weather Service. However, now it has expanded to over 100 other uses in the areas of natural and man-made disaster detection and warning. The successful ALERT system indicates the need for the continued development of a national drought monitoring index that is applicable to a wide range of climate, hydrologic and water resource environments.
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    Stochastic environmental research and risk assessment 6 (1992), S. 1-2 
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    Stochastic environmental research and risk assessment 11 (1997), S. 523-547 
    ISSN: 1436-3259
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    Notes: Abstract Kernel density estimators are useful building blocks for empirical statistical modeling of precipitation and other hydroclimatic variables. Data driven estimates of the marginal probability density function of these variables (which may have discrete or continuous arguments) provide a useful basis for Monte Carlo resampling and are also useful for posing and testing hypotheses (e.g bimodality) as to the frequency distributions of the variable. In this paper, some issues related to the selection and design of univariate kernel density estimators are reviewed. Some strategies for bandwidth and kernel selection are discussed in an applied context and recommendations for parameter selection are offered. This paper complements the nonparametric wet/dry spell resampling methodology presented in Lall et al. (1996).
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    Stochastic environmental research and risk assessment 11 (1997), S. 459-482 
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    Keywords: Karhunen-Loéve expansion ; Empirical Orthogonal Functions ; stochastic simulation ; gaussian fields ; analytical covariance functions ; eigenfunctions ; kriging
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    Notes: Abstract Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.
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    Stochastic environmental research and risk assessment 12 (1998), S. 1-14 
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    Keywords: Key words: Exceedance probability ; trend ; stochastic variables ; non-stationarity
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    Notes: Abstract Studying the hypothetical case of a trend superimposed on a random stationary variable, we highlight the strong influence of possible non-stationarities on exceedance probability. After a general outline, the subject is analytically developed using the Gumbel distribution, emphasizing the quick increase of the exceedance probability over time in the presence of weak rising trends, and its sensitive underestimation where the non-stationarity goes unnoticed or is considered negligible. Finally the work is applied to hydrological series of rainfall and river flow.
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    Stochastic environmental research and risk assessment 12 (1998), S. 53-64 
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    Keywords: Key words: Risk ; clustering ; point process ; Poisson ; flood.
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    Notes: Abstract: Since the introduction into flood risk analysis, the partial duration series method has gained increasing acceptance as an appealing alternative to the annual maximum series method. However, when the base flow is low, there is clustering in the flood peak or flow volume point process. In this case, the general stochastic point process model is not suitable to risk analysis. Therefore, two types of models for flood risk analysis are derived on the basis of clustering stochastic point process theory in this paper. The most remarkable characteristic of these models is that the flood risk is considered directly within the time domain. The acceptability of different models are also discussed with the combination of the flood peak counted process in twenty years at Yichang station on the Yangtze river. The result shows that the two kinds of models are suitable ones for flood risk analysis, which are more flexible compared with the traditional flood risk models derived on the basis of annual maximum series method or the general stochastic point process theory.
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    Stochastic environmental research and risk assessment 12 (1998), S. 33-52 
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    Keywords: Keywords: Streamflow ; simulation ; nonparametric
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    Notes: Abstract A new approach for streamflow simulation using nonparametric methods was described in a recent publication (Sharma et al. 1997). Use of nonparametric methods has the advantage that they avoid the issue of selecting a probability distribution and can represent nonlinear features, such as asymmetry and bimodality that hitherto were difficult to represent, in the probability structure of hydrologic variables such as streamflow and precipitation. The nonparametric method used was kernel density estimation, which requires the selection of bandwidth (smoothing) parameters. This study documents some of the tests that were conduced to evaluate the performance of bandwidth estimation methods for kernel density estimation. Issues related to selection of optimal smoothing parameters for kernel density estimation with small samples (200 or fewer data points) are examined. Both reference to a Gaussian density and data based specifications are applied to estimate bandwidths for samples from bivariate normal mixture densities. The three data based methods studied are Maximum Likelihood Cross Validation (MLCV), Least Square Cross Validation (LSCV) and Biased Cross Validation (BCV2). Modifications for estimating optimal local bandwidths using MLCV and LSCV are also examined. We found that the use of local bandwidths does not necessarily improve the density estimate with small samples. Of the global bandwidth estimators compared, we found that MLCV and LSCV are better because they show lower variability and higher accuracy while Biased Cross Validation suffers from multiple optimal bandwidths for samples from strongly bimodal densities. These results, of particular interest in stochastic hydrology where small samples are common, may have importance in other applications of nonparametric density estimation methods with similar sample sizes and distribution shapes.
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    Stochastic environmental research and risk assessment 12 (1998), S. 15-32 
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    Keywords: Key words: Kalman filtering ; groundwater modelling ; inverse methods ; uncertainty analysis ; state prediction ; parameter estimation
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    Notes: Abstract The popularity of applying filtering theory in the environmental and hydrological sciences passed its first climax in the 1970s. Like so many other new mathematical methods it was simply the fashion at the time. The study of groundwater systems was not immune to this fashion, but neither was it by any means a prominent area of application. The spatial-temporal characteristics of groundwater flow are customarily described by analytical or, more frequently, numerical, physics-based models. Consequently, the state-space representations associated with filtering must be of a high order, with an immediately apparent computational over-burden. And therein lies part of the reason for the but modest interest there has been in applying Kalman filtering to groundwater systems, as reviewed critically in this paper. Filtering theory may be used to address a variety of problems, such as: state estimation and reconstruction, parameter estimation (including the study of uncertainty and its propagation), combined state-parameter estimation, input estimation, estimation of the variance-covariance properties of stochastic disturbances, the design of observation networks, and the analysis of parameter identifiability. A large proportion of previous studies has dealt with the problem of parameter estimation in one form or another. This may well not remain the focus of attention in the future. Instead, filtering theory may find wider application in the context of data assimilation, that is, in reconstructing fields of flow and the migration of sub-surface contaminant plumes from relatively sparse observations.
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    Stochastic environmental research and risk assessment 12 (1998), S. 65-82 
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    Keywords: Key words: Flood flow ; threshold ; generalized Pareto ; Poisson
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    Notes: Abstract This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X T corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form.
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    Stochastic environmental research and risk assessment 12 (1998), S. 97-116 
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    Notes: Abstract : The knowledge of the volume and duration of low-flow events in river channels is essential for water management and the design of hydraulics structures. In this study, both preceding characteristics, X 1 and X 2, are considered simultaneously via two types of bivariate distributions whose marginals are exponential. One of these bivariate distributions has been presented by Nagao and Kadoya (1971) and the other has been used by Singh and Singh (1991) to the study of rainfall intensity and rainfall depth. The results are applied to the low-flow series (“peaks-below-threshold”) of Lepreau River (station 01AQ001) in New Brunswick, Canada. These results show that the model that was successfully employed by Singh and Singh (1991) to study rainfall, presents certain difficulties when a very strong correlation, ρ, between the two random variables X 1 and X 2, exists. The model by Nagao and Kadoya (1971) seems to be more satisfactory for such situations, although this model seems also to be quite sensitive to variations in ρ.
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    Stochastic environmental research and risk assessment 12 (1998), S. 83-96 
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    Notes: Abstract Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.
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    Stochastic environmental research and risk assessment 12 (1998), S. 117-140 
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, 〈S i i (t)〉, and the plume centroid covariance, R i i (t) (i=1,2), were simulated for the variance of Y=log T, σ Y 2=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ Y 2=0.1, all simulated 〈S i i (t)〉−S i i (0) and R i i (t) agree well with the first-order theoretical values, where S i i (0) are the initial values of S i i (t). For σ Y 2=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, 〈S 11(t)〉−S 11(0) and R 11(t), agree well with the first-order theoretical results but the simulated transverse moments 〈S 22(t)〉−S 22(0) and R 22(t) are significantly larger than the first-order values. For the same two larger values of σ Y 2 but the line sources parallel to μ, the simulated 〈S 11(t)〉−S 11(0) are larger than but the simulated R 11 are smaller than the first-order values, and both simulated 〈S 22(t)〉−S 22(0) and R 22(t) stay larger than the first-order values. For a fixed value of σ Y 2, the summations of 〈S i i (t)〉−S i i (0) and R i i , i.e., X i i (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X 11 are in good agreement with the first-order theory but the simulated X 22 are significantly larger than the first-order values. The simulated X 22, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of 〈S 22(t)〉−S 22(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ Y 2 is small.
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    Stochastic environmental research and risk assessment 12 (1998), S. 141-154 
    ISSN: 1436-3259
    Keywords: Key words: Ground truth ; geostatistical techniques ; areal reduction factor ; Rainfall process ; linear relationship.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Geostatistical techniques are used to quantify the reference mean areal rainfall (ground truth) from sparse raingaugenetworks. Based on the EPSAT-Niger event cumulative rainfall, a linear relationship between the ground truth considered as the mean area rainfall estimated from the densely available raingauge network and the area rainfall estimated from sparse network are derived. Also, a linear relationship between the ground truth and point rainfall is established. As it was reported experimentally by some authors, the slope of these relationships is less than one. Based on the geostatistical framework, the slope and the ordinate at the origin can be estimated as a function of the spatial structure of the rainfall process. It is shown that the slope is smaller than one. For the special case of one gauge inside a fixed area or a Field Of View (FOV), an areal reduction factor is derived. It has a limit value which depends only on the size of the area and the spatial structure of the rainfall process. The relative variance error of estimating the FOV cumulative rainfall from point rainfall is also given.
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    Stochastic environmental research and risk assessment 7 (1993), S. 195-204 
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    Keywords: Infinite dam ; resolvent operator ; Lévy process ; integrated Markov chain
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    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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  • 56
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    Stochastic environmental research and risk assessment 7 (1993), S. 213-239 
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    Keywords: Stochastic hydrology ; perturbation ; random fields ; graph theory
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    Notes: Abstract As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations.
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    Stochastic environmental research and risk assessment 8 (1994), S. 157-172 
    ISSN: 1436-3259
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    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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    Stochastic environmental research and risk assessment 8 (1994), S. 185-205 
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    Keywords: Contaminant transport ; adsorption ; decay ; random walk ; killing ; Kolmogorov equations ; contamination of a well
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    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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    Stochastic environmental research and risk assessment 8 (1994), S. 109-116 
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    Keywords: Unsaturated ; nonlocal ; memory ; statistical physics
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    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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    Stochastic environmental research and risk assessment 12 (1998), S. 223-245 
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    Keywords: Key words: Stochastic differential equation ; spatial data ; irregularly sampled data ; parameter estimation.
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    Notes: Abstract: A second order stochastic differential equation is used for modeling of water-table elevation. The data were sampled at the Borden Aquifer as a part of a tracer experiment. The purpose of the water-table data collection was to determine presence of a water flow. We argue that the water-table surface is a simple plane oscillating up and down in time according to an equation for a stochastic oscillator. We derive the model, estimate its parameters and provide arguments for goodness-of-fit of the model.
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    Stochastic environmental research and risk assessment 12 (1998), S. 267-283 
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    Keywords: Key words: Flood frequency analysis ; TCEV ; non-systematic information ; regional ; statistical gain.
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    Notes: Abstract: Due to the social and economic implications, flood frequency analysis must be done with the highest precision. For this reason, the most suitable statistical model must be selected, and the maximum amount of information must be used. Floods in Mediterranean rivers can be produced by two different mechanisms, which forces the use of a non-traditional distribution like the TCEV. The information can be increased by using additional non-systematic data, or with a regional analysis, or both. Through the statistical gain concept, it has been shown that in most cases the use of additional non-systematic information can decrease the quantile estimation error in about 50%. In a regional analysis, the␣benefit of additional information in one station, is propagated to the rest of␣the␣stations with only a small decrease with respect to the at-site equivalent analysis.
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    Stochastic environmental research and risk assessment 12 (1998), S. 285-298 
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    Notes: Abstract We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions.
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    Stochastic environmental research and risk assessment 12 (1998), S. 247-266 
    ISSN: 1436-3259
    Keywords: Key words: Stochastic control ; dynamic programming ; reservoir systems ; hydrologic forecasting ; hydropower ; feedback control ; autoregressive models.
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    Notes: Abstract : As with all dynamic programming formulations, differential dynamic programming (DDP) successfully exploits the sequential decision structure of multi-reservoir optimization problems, overcomes difficulties with the nonconvexity of energy production functions for hydropower systems, and provides optimal feedback release policies. DDP is particularly well suited to optimizing large-scale multi-reservoir systems due to its relative insensitivity to state-space dimensionality. This advantage of DDP encourages expansion of the state vector to include additional multi-lag hydrologic information and/or future inflow forecasts in developing optimal reservoir release policies. Unfortunately, attempts at extending DDP to the stochastic case have not been entirely successful. A modified stochastic DDP algorithm is presented which overcomes difficulties in previous formulations. Application of the algorithm to a four-reservoir hydropower system demonstrates its capabilities as an efficient approach to solving stochastic multi-reservoir optimization problems. The algorithm is also applied to a single reservoir problem with inclusion of multi-lag hydrologic information in the state vector. Results provide evidence of significant benefits in direct inclusion of expanded hydrologic state information in optimal feedback release policies.
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    Stochastic environmental research and risk assessment 12 (1998), S. 299-316 
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a geostatistical approach to multi-directional aquifer stimulation in order to better identify the transmissivity field. Hydraulic head measurements, taken at a few locations but under a number of different steady-state flow conditions, are used to estimate the transmissivity. Well installation is generally the most costly aspect of obtaining hydraulic head measurements. Therefore, it is advantageous to obtain as many informative measurements from each sampling location as possible. This can be achieved by hydraulically stimulating the aquifer through pumping, in order to set-up a variety of flow conditions. We illustrate the method by applying it to a synthetic aquifer. The simulations provide evidence that a few sampling locations may provide enough information to estimate the transmissivity field. Furthermore, the innovation of, or new information provided by, each measurement can be examined by looking at the corresponding spline and sensitivity matrix. Estimates from multi-directional stimulation are found to be clearly superior to estimates using data taken under one flow condition. We describe the geostatistical methodology for using data from multi-directional simulations and address computational issues.
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    Stochastic environmental research and risk assessment 9 (1995), S. 33-47 
    ISSN: 1436-3259
    Keywords: Hidden markov models ; maximum likelihood estimation ; EM algorithm ; martingale estimating function ; forward-backward algorithm ; Monte Carlo ; filtering ; Nash cascade model ; rainfall runoff modeling
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (Xn, n ≥ 0) or (Xt, t ≥ 0) for which the parameters are of interest and physically meaningful, and an observable process (Yn, n ≥ 0) or (Yt, t ≥ 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.
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    Stochastic environmental research and risk assessment 9 (1995), S. 117-132 
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    Keywords: River Quality ; network ; computer model ; Thermodynamics
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In this paper, concepts of network thermodynamics are applied to a river water quality model, which is based on Streeter-Phelps equations, to identify the corresponding physical components and their topology. Then, the randomness in the parameters, input coefficients and initial conditions are modeled by Gaussian white noises. From the stochastic components of the physical system description of problem and concepts of physical system theory, a set of stochastic differential equations can be automatically generated in a computer and the recent developments on the automatic formulation of the moment equations based on Ito calculus can be used. This procedure is illustrated through the solution of an example of stochastic river water quality problem and it is also shown how other related problems with different configurations can be automatically solved in a computer using just one software.
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    Stochastic environmental research and risk assessment 9 (1995), S. 171-205 
    ISSN: 1436-3259
    Keywords: AR-AIC-Bayes filter ; autoregressive spectral density estimation ; diagnostic checks for ARMA models ; exploratory data analysis ; fast Fourier transform ; Hurst coefficient ; long-memory times series ; periodogram smoothing ; riverflow time series ; spectral density plots
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Current methods of estimation of the univariate spectral density are reviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements, rather than competes with, the popular ARMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Additionally, two new algorithms for fast computation of the autoregressive spectral density function are presented. For improving interpretation of results, a new style of plotting the spectral density function is suggested. Exploratory spectral analyses of a number of hydrological time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in natural time series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca.
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    Stochastic environmental research and risk assessment 9 (1995), S. 215-237 
    ISSN: 1436-3259
    Keywords: Computation ; discretization ; entropy ; networks ; time averaging ; water quality
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The computational aspects of using a new, entropy-based, theory to predict water quality values at discontinued water quality monitoring stations are discussed. The main computational issues addressed are the level of discretization used in converting the continuous probability distribution of water quality values to the discrete levels required for the entropy function, and the choice of the interval of time for which to assign the value of the water quality (period of time averaging) through the entropy function. Unlike most cases of entropy applications involving discretization of continuous functions the results of using entropy theory to predict water quality values at discontinued monitoring stations in this application appear to be insensitive to the choice of the level of discretization even down to the very coarse level discretization associated with only eight intervals. However, depending on the length of record available the choice of the time interval for which the water quality values are assigned (period for time averaging) appear to have a significant impact on the accuracy of the results.
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    Stochastic environmental research and risk assessment 4 (1990), S. 1-26 
    ISSN: 1436-3259
    Keywords: Inverse ; calibration ; estimation ; groundwater flow
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    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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    Stochastic environmental research and risk assessment 4 (1990), S. 55-64 
    ISSN: 1436-3259
    Keywords: Predictive distribution ; Bayesian approximation ; parameter uncertainty ; non-informative prior ; method of moments ; Gumbel distribution ; maximum likelihood estimates
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    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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    Stochastic environmental research and risk assessment 4 (1990), S. 105-119 
    ISSN: 1436-3259
    Keywords: Kalman filtering ; Optimal smoothing ; Shallow water equations ; Wind stress ; On-line prediction
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    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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    Stochastic environmental research and risk assessment 4 (1990), S. 135-150 
    ISSN: 1436-3259
    Keywords: Radar ; rainfall prediction ; real-time prediction
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    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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    Stochastic environmental research and risk assessment 4 (1990), S. 151-160 
    ISSN: 1436-3259
    Keywords: Instantaneous Unit Hydrograph ; Conceptual models ; Stochastic differential equations
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    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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    Stochastic environmental research and risk assessment 5 (1991), S. 45-54 
    ISSN: 1436-3259
    Keywords: Solute transport ; random velocity ; Lagrangian description ; travel time ; nonlinear effects
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    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 environmental research and risk assessment 5 (1991), S. 89-104 
    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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    Stochastic environmental research and risk assessment 6 (1992), S. 5-25 
    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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    Stochastic environmental research and risk assessment 6 (1992), S. 89-101 
    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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    Stochastic environmental research and risk assessment 6 (1992), S. 55-68 
    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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    Stochastic environmental research and risk assessment 6 (1992), S. 103-121 
    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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    Stochastic environmental research and risk assessment 6 (1992), S. 191-207 
    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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    Stochastic environmental research and risk assessment 6 (1992), S. 255-269 
    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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    Stochastic environmental research and risk assessment 6 (1992), S. 270-288 
    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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    Stochastic environmental research and risk assessment 6 (1992), S. 289-303 
    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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    Stochastic environmental research and risk assessment 9 (1995), S. 13-32 
    ISSN: 1436-3259
    Keywords: Distributed parameter filter ; shallow water equations ; distributed dynamical systems ; data assimilation ; white Gaussian noise
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Distributed parameter filtering theory is employed for estimating the state variables and associated error covariances of a dynamical distributed system under highly random tidal and meteorological influences. The stochastic-deterministic mathematical model of the physical system under study consists of the shallow water equations described by the momentum and continuity equations in which the external forces such as Coriolis force, wind friction, and atmospheric pressure are considered. White Gaussian noises in the system and measurement equations are used to account for the inherent stochasticity of the system. By using an optimal distributed parameter filter, the information provided by the stochastic dynamical model and the noisy measurements taken from the actual system are combined to obtain an optimal estimate of the state of the system, which in turn is used as the initial condition for the prediction procedure. The approach followed here has numerical approximation carried out at the end, which means that the numerical discretization is performed in the filtering equations, and not in the equations modelling the system. Therefore, the continuous distributed nature of the original system is maintained as long as possible and the propagation of modelling errors in the problem is minimized. The appropriateness of the distributed parameter filter is demonstrated in an application involving the prediction of storm surges in the North Sea. The results confirm excellent filter performance with considerable improvement with respect to the deterministic prediction.
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    Stochastic environmental research and risk assessment 9 (1995), S. 77-88 
    ISSN: 1436-3259
    Keywords: Extreme rainfalls ; partial duration series ; regional estimation ; Bayes' theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Based on the Partial Duration Series model a regional Bayesian approach is introduced in the modelling of extreme rainfalls from a country-wide system of recording raingauges in Denmark. The application of the Bayesian principles is derived in case of both exponential and generalized Pareto-distributed exceedances. The method is applied to, respectively, the total precipitation depth and the maximum 10 minutes rain intensity of individual storms from 41 stations. By means of the regional analysis prior distributions of the parameters in the Partial Duration Series model are estimated. It is shown that the regional approach significantly reduces the uncertainty of the T-year event estimator compared to estimation based solely on at-site data. In addition, the regional approach provides quantile estimates at non-monitored sites.
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    Meteorology and atmospheric physics 15 (1965), S. 32-45 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary Two cases of invasions of cold air into the Alpine region which have occurred in April 1962 are investigated. The polar air intruded from the north with a vertical extension up to 2500 m on the frontside of an upper trough. The Tiros observations combined with the synoptic and aerological data permitted to generalize a formerly derived formula valid for upper troughs for cold fronts [4]. It could be shown that the cold front caused bad weather as well north of the Alps as south of them when it passed below the frontside of the upper trough. Closed systems of clouds at cold fronts orginate more probably at the front of troughs than at their backside, where downstreams perforate the cloud cover.
    Abstract: Résumé On examine ici le comportement de deux invasions d'air froid d'origine polaire qui se sont manifestées dans les Alpes en avril 1962. L'air polaire a pénétré dans la région des Alpes en venant du nord. Il avait une épaisseur de 2500 m et se déplaçait à l'avant d'un couloir dépressionnaire en altitude. Les observations du satellite météorologique “Tiros” combinées aux valeurs synoptiques et aérologiques permettent de généraliser une règle établie précédemment, règle qui concerne les fronts froids liés à des couloirs dépressionnaires en altitude [4]. Il en résulte que le front froid, en franchissant la partie antérieure d'un couloir, provoque un temps maussade aussi bien au nord qu'au sud des Alpes. Des systèmes nuageux compactes se forment en général de préférence à l'avant des couloirs dépressionnaires en altitude, car, à l'arrière de ceux-ci, les mouvements de subsideance qui y règnent provoquent des trouées dans la nappe nuageuse.
    Notes: Zusammenfassung Es werden zwei im April 1962 in den Alpen sich auswirkende polare Kaltlufteinbrüche untersucht. Die Polarluft drang von Norden her in den Alpenraum mit einer vertikalen Erstreckung bis zu 2500 m ein, und zwar an der Vorderseite eines Höhentroges. Die Tiros-Beobachtungen, kombiniert mit den synoptischen und aerologischen Meßdaten, erlaubten eine Verallgemeinerung einer früher abgeleiteten Höhentrogregel für Kaltfronten [4]. Es ergab sich, daß beim Unterlaufen der Höhentrog-Vorderseite die Kaltfront sowohl an der Alpennordseite als auch an der Alpensüdseite Schlechtwetter verursacht. Geschlossene Wolkensysteme an Kaltfronten entstehen ganz allgemein eher an der Trogvorderseite als an der Trogrückseite, wo absteigende Luftbewegungen die Wolkendecke durchlöchern.
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    Meteorology and atmospheric physics 15 (1965), S. 50-61 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Der Zusammenhang zwischen der mittleren vektoriellen Windscherung und dem Scherungsintervall wird analysiert. Dabei kann gezeigt werden, daß diese Beziehung von der Erhaltungsneigung (Persistenz) der Scherungsvektoren mit dem Intervall abhängt. Dasselbe gilt für die Beziehung der Streuungen mit dem Scherungsintervall. Die Persistenz nimmt bei zunehmendem Scherungsintervall nach einem exponentiellen Gesetz ab. Daraus läßt sich ein Exponent für den oben erwähnten und vom Autor an anderer Stelle [7] abgeleiteten Zusammenhang zwischen mittlerer vektorieller Windscherung und Scherungsintervall von ungefährt 1/2 berechnen. Für Extremwerte scheint dagegen der Exponent um 1/3 zu liegen. Dies mag damit erklärt werden, daß Abweichungen von der zweidimensionalen normalen zirkulären Verteilung auftreten, die exponentiell mit wachsendem Scherungsintervall abnehmen und somit den Exponenten verkleinern.
    Abstract: Résumé On analyse ici la relation existant entre le cisaillement vectoriel moyen du vent et l'intervalle en altitude de ce cisaillement. On peut ainsi démontrer que cette relation dépend de la persistance du vecteur de cisaillement avec l'intervalle. Il en va de même de la relation entre la dispersion et l'intervalle de cisaillement. La persistance diminue exponentiellement avec l'augmentation de l'intervalle. On peut calculer un exposant d'environ 1/2 pour la relation mentionnée plus haut et déduite d'autre par par le même auteur [7]. Dans des cas extrèmes, cet exposant est d'à peu près 1/3. Cela peut être expliqué par le fait que l'on rencontre des écarts de la répartition normale circulaire à deux dimensions. Ceux-ci diminuent exponentiellement avec l'accroissement de l'intervalle de cisaillement et font, par conséquent, diminuer la valeur de l'exposant.
    Notes: Summary The relationship between the mean of the vector shears and the shear interval is analyzed and linked to the persistence of vector shears with the shear interval. A similar relationship exists between the standard deviation of the vector shears and the shear interval. As the persistence follows an exponential law, decreasing reciprocally with the shear interval, the relationship between mean vector shears and the shear interval Δh assumes a power law with exponent around 1/2. The exponent of 1/3 found in relationships between extreme values and shear interval may be attributed to deviations of the frequency distribution of vector shear values from the bivariate circular distribution.
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    Meteorology and atmospheric physics 15 (1965), S. 109-117 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary Observations with a RHI radar show that the so-called bright band, which is a layer of especially strong radar reflectivity, is only to be seen during the dissipating stage of convective precipitation cells (showers, thunderstorms). During the developing and mature stage of the cells one cannot observe the bright band.
    Abstract: Résumé Des relevés radar faits au moyen d'un appareil RHI montrent que l'apparition qu'il est convenu d'appeler «bright band» ne s'observe qu'au moment de la désagrégation de cellules convectives de précipitations (averses ou orages). La «bright band» est une couche dans laquelle la réflexion radar est spécialement intense. Si les dites cellules sont en formation ou bien développées, on n'observe par contre pas de «bright band».
    Notes: Zusammenfassung Radarbeobachtungen mit einem RHI-Radargerät zeigen, daß das sogenannte Bright Band, eine Schicht besonders starker Radar-Reflektivität, nur im Auflösungsstadium konvektiver Niederschlagszellen (Schauer, Gewitter) zu beobachten ist. Im Bildungs- und Reifestadium der Zellen wird das Bright Band nicht beobachtet.
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    Meteorology and atmospheric physics 16 (1967), S. 169-180 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary On the basis of a spring blocking-situation, which lasted for 16 days (March 2 to 18, 1955), the author studied the dynamic processes in building up and maintaining of a blocking-situation. Whereas during the preceding period of the blocking a northward transport of angular momentum of the air had occurred, during the blocking itself the angular momentum is transported southward. Besides, the author has analyzed thoroughly the development phases of 25 blockings, which had occurred in a period of eight years, and gives a table with the most important results.
    Abstract: Résumé On étudie ici les phénomènes dynamiques qui se produisent lors de l'établissement et du maintien d'une situation de blocage. Pour ce faire, on se sert d'une situation de printemps qui a duré 16 jours (du 2 au 18 mars 1955). Pendant la période précédent le blocage, on constate un déplacement vers le nord du moment de rotation absolu de la vitesse de l'air. Pendant la période de blocage elle-même, le moment de rotation absolu se décale au contraire vers le sud. On analyse en outre très exactement l'évolution de 25 cas de blocage répartis sur 8 ans. Les résultats les plus importants de cette analyse sont rapportés sous forme de tables.
    Notes: Zusammenfassung An Hand einer 16tägigen Frühjahrblockingsituation (2. 3. bis 18. 3. 1955) wurden die dynamischen Vorgänge bei der Bildung und Aufrechterhaltung der Blockinglage studiert. Während in der Vorperiode des Blockings ein Nordwärtstransport von absolutem Rotationsmoment der Geschwindigkeit der Luft stattfindet, wird während der Blockingsituation selbst das absolute Rotationsmoment nach Süden verfrachtet. Weiters wurden die Entwicklungsvorgänge von 25 Blockingfällen während eines Zeitraumes von acht Jahren genau analysiert und die wichtigsten Ergebnisse tabellarisch zusammengestellt.
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    Meteorology and atmospheric physics 16 (1967), S. 181-211 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary Based on 21 571 daily upper wind measurements the authors derive the dependences on altitude of the scalar and vector means of the wind speed, of the zonal and meridional components, of the mean resultant wind and of the constancy of the wind up to 30 km above Vienna for each month and also the annual variation of the wind speed and of the frequency distributions of the wind directions for the various levels. The peculiarities are thoroughly discussed and explanations could be given for most of them. One finds out that, during the transitional seasons, the upper winds show a remarkable behaviour in some months, which cannot be explained easily. The annual variations of the scalar as well as of the vectorial mean wind speeds present double-waves even in the troposphere, apart of the lowest levels. Partly, the extremes of these double-waves in the upper troposphere, are inverse to those in the lower stratosphere. At altitudes above 18 km the transition from the winter westerlies to the summer easterlies in spring advances only gradually from the larger heights to the lower ones, however, the reverse transition occurs very sharply with the change from August to September. Therefore, in investigations of the upper winds, it is very necessary to use the data of the single months separately as in seasonal combinations some essential characteristics are obscured.
    Abstract: Résumé Partant de 21 571 mesures journalières du vent en altitude, mesures effectuées à Vienne (Autriche), les auteurs discutent et cherchent à expliquer les particularités de cet élément météorologique. Pour ce faire, ils ont établi pour chaque mois la variation de la valeur scalaire et vectorielle de la vitesse du vent, ses composantes zonale et méridienne, la translation de l'air qui en résulte, la persistance du vent avec l'altitude jusqu'à 30 km ainsi que la variation annuelle de la vitesse du vent et la répartition des fréquences de sa direction aux différents niveaux. Il en découle que, durant les périodes de transition entre les saisons, les conditions de vent en altitude présentent un comportement particulier au quelques mois, ce qui n'est pas facile à expliquer. La variation annuelle des valeurs scalaires et vectorielles de la vitesse du vent présentent, abstraction faite des couches voisines du sol, mais dans la troposphère déjà, des ondulations doubles dont les extrêmes sont opposés, dans la troposphère supérieure, à ceux de la basse stratosphère. Aux altitudes supérieures à 18 km, le changement des courants d'ouest, dominent durant l'hiver, à ceux d'est qui se rencontrent en été se fait progressivement au printemps des couches les plus élevées vers les plus basses. Le phénomène inverse se produit par contre brusquement d'août à septembre. Il est par conséquent indispensable, dans les recherches des conditions de vent en altitude, de considérer les mois individuellement, car un groupement par saison en estomperait les caractéristiques principales.
    Notes: Zusammenfassung Aus 21 571 täglichen Höhenwindmessungen werden für jeden Monat die Änderungen der skalaren und der vektoriellen Mittelwerte der Windgeschwindigkeit, der zonalen und der meridionalen Komponenten der Windgeschwindigkeit, der resultierenden Luftversetzung und der Beständigkeit des Windes mit der Höhe bis 30 km über Wien sowie der Jahresgang der Windgeschwindigkeit und der Häufigkeitsverteilung der Windrichtungen für die verschiedenen Höhenstufen abgeleitet und in ihren Besonderheiten eingehend diskutiert und zu erklären versucht. Dabei ergibt sich, daß in den Übergangsjahreszeiten die Höhenwindverhältnisse in einzelnen Monaten ein auffallendes Verhalten zeigen, das nicht einfach zu erklären ist. Die Jahresgänge der skalaren wie auch der vektoriellen Geschwindigkeitswerte weisen auch, abgesehen von den bodennahen Schichten, bereits in der Troposphäre Doppelwellen auf, deren Extreme in der oberen Troposphäre zum Teil den Extremen in der unteren Stratosphäre entgegengesetzt sind. In Höhen über 18 km erfolgt der Übergang von der im Winter vorherrschenden westlichen Strömung zum sommerlichen Ostwind im Frühling allmählich von den höchsten Schichten nach unten fortschreitend, der umgekehrte Übergang vom August zum September dagegen sehr scharf. Es ist daher notwendig, bei Untersuchungen der Höhenwindverhältnisse die einzelnen Monate besonders in Betracht zu ziehen, da bei einer Zusammenfassung nach Jahreszeiten wesentliche Merkmale verwischt werden.
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    Meteorology and atmospheric physics 16 (1967), S. 242-259 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Die Wärmebilanzgleichung für die Unterseite von schwimmendem Meereis wird an Hand von Beobachtungen der Eistemperatur, der Wassertemperatur, der Strömungsgeschwindigkeit und der Eisdickenänderung ausgewertet. Unter der Annahme gleicher Austauschkoeffizienten für Bewegungsgröße, Wärme und Salzgehalt (im Mittel 24 cm2 sec−1) ergibt sich für die ozeanische Grenzschicht ein außerordentlich kleiner Gradient der Wassertemperatur (durchschnittlich zwischen 2.10−5 und 4.10−4°C/Meter), der durch direkte Beobachtungen schwer nachzuweisen ist. Es ist zu vermuten, daß ein beträchtlicher Teil der Wärmeabgabe von der relativ warmen atlantischen Wassermasse an die arktische Atmosphäre durch Öffnungen in der Meereisdecke erfolgt.
    Abstract: Résumé On établit l'équation du bilan thermique valable pour la surface inférieure de la glace marine dérivante. Pour ce faire, on se sert d'observations de la température de la glace, de celle de l'eau, de la vitesse du courant et des variations de l'épaisseur de la glace. En admettant que les coefficients d'échange sont les mêmes pour la quantité de mouvement, la chaleur et le taux de salinité (en moyenne 24 cm2 sec−1), il résulte pour la couche limite un gradient extrêmement faible de la température de l'eau (situé en moyenne entre 2·10−5 et 4·10−4°C/m); un tel gradient est difficile à prouver au moyen d'observations directes. On peut supposer qu'une partie importante de la chaleur transmise par l'eau relativement chaude de l'Atlantique à l'atmosphère arctique passe au travers des lacunes de la couche de glace recouvrant l'océan.
    Notes: Summary The heat balance equation for the bottom surface of floating sea ice is evaluated on the basis of observations of ice temperature, water temperature, current velocity, and ablation or accretion of ice. Assuming equality of the eddy diffusivities for momentum, heat, and salt (average 24 cm2 sec−1) it is shown that the temperature gradient in the oceanic boundary layer is extremely small (averages between 2.10−5 and 4.10−4°C/meter) and difficult to measure directly. It is suggested that a large part of the heat transfer from the relatively warm Atlantic water to the arctic atmosphere may occur through open leads in the ice cover.
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    Meteorology and atmospheric physics 16 (1967), S. 260-266 
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    Description / Table of Contents: Summary In this investigation the anomaly-effect on the ionosphericE-layer critical frequency (ordinary component,f 0 E), which is observed frequently during the forenoon hours, has been calculated for 80 selected diurnal variations on simplified conditions. The received results are compared with Appleton's theory.
    Abstract: Résumé L'effet du retardement de la fréquence critique de la couche-E ionospherique (composante ordinaire,f 0 E) qu'on peut observer souvent durant les heures avant midi, est examiné pour 80 enregistrements diurnes á conditions simplifiées. Les résultats reçus sont comparés avec la théorie d'Appleton.
    Notes: Zusammenfassung Der zeitliche Verlauf der Vormittags-Anomalie in den Tagesgängen der kritischen Frequenzen der normalenE-Schicht (Verlangsamung des Anstieges der Elektronendichte kurz vor dem Ortsmittag im Vergleich zur Chapman-Schicht) wurde unter vereinfachten Voraussetzungen für 80 ausgewählte Tagesgänge des Jahres 1958 berechnet. Die erhaltenen Ergebnisse werden mit der Appletonschen Theorie verglichen.
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    Meteorology and atmospheric physics 16 (1967), S. 301-313 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary The position, direction and speed of the high-tropospheric jet-streams in the years 1955 to 1963 were determined from the 300 mb chart of the Daily Weather Map of the German Weather Service. The seasonal variations of the positions, intensities and directions of the polarfront jet (PFJ) and subtropic jet (STJ) in the region between 20° W and 20° E and between 35° N and 70° N have been evaluated and are discussed here.
    Abstract: Résumé En partant des cartes journalières de la surface de 300 mb éditées par le service météorologique de la République fédérale d'Allemagne, on a déterminé la position, la direction et la vitesse des courants “jets” de la troposphère supérieure et cela pour la période 1955 à 1963. On indique et on discute les variations saisonnières de la position, de l'intensité et de la direction du “jet” accompagnant le front polaire (PFJ) et du “Jet” subtropical (STJ). La zone étudiée s'étend entre le 20ème méridien E et le 20ème méridien W, respectivement entre les 35ème et 70ème paralèlles N.
    Notes: Zusammenfassung Aus der 300mb-Fläche der täglichen Wetterkarte des deutschen Wetterdienstes wurden für den Zeitraum von 1955 bis 1963 Lage, Richtung und Geschwindigkeit der hochtroposphärischen Strahlströme bestimmt. Die jahreszeitlichen Änderungen der Positionen, Intensitäten und Richtungen des Polarfront-Jet (PFJ) und des Subtropen-Jet (STJ) werden für den Bereich von 20° W bis 20° E und von 35° N bis 70° N angegeben und diskutiert.
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    Meteorology and atmospheric physics 16 (1967), S. 314-320 
    ISSN: 1436-5065
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    Description / Table of Contents: Summary The variations of the total ozone amount at ten european stations were correlated in couples. The correlation coefficients decrease exponentially with increasing distance of the stations. From this exponential law the mean extension of low stratospheric air-parcels was determined to be 670 km. On computing the correlation coefficients a time shift was observed which demonstrates the predominantly zonal west east ozone transport.
    Abstract: Résumé On a établi les corrélations des variations de l'ozone total relevé à 10 stations enropéennes prises deux par deux. Les coefficients de corrélation qui en résultent sont, en moyenne, en relation exponentielle avec la distance séparant les stations. De cette diminution, on a estimé à 670 km l'étendue moyenne des gouttes d'air stratosphériques. Un décalage dans le temps, lors du calcul des coefficients de corrélation, montre clairement le transport généralement zonal de l'ozone de l'ouest vers l'est.
    Notes: Zusammenfassung Die Variationen des Gesamtozonbetrages an zehn europäischen Stationen wurden paarweise korreliert. Die Korrelationskoeffizienten fallen im Mittel exponentiell mit der Entfernung der Stationen ab. Aus diesem Abfall wurde die mittlere Ausdehnung stratosphärischer Luftpakete mit 670 km abgeschätzt. Eine zeitliche Verschiebung bei der Berechnung der Korrelationskoeffizienten veranschaulicht den vorwiegend zonalen West-Ost-Ozontransport.
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    Meteorology and atmospheric physics 16 (1967), S. 382-388 
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    Meteorology and atmospheric physics 17 (1968), S. 8-16 
    ISSN: 1436-5065
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    Description / Table of Contents: Zusammenfassung An Hand eines konkreten Falles wird gezeigt, daß die Aufspaltung des Jet Streams in mehrere Äste, wie dies häufig über den Vereinigten Staaten an der Vorderseite intensiver Jet Maxima beobachtet wird, mit der Erhaltung der potentiellen Vorticity innerhalb einer Luftschicht, die sich über ein Hindernis bewegt, erklärt werden kann. Ein derartiges Hindernis kann einerseits durch ein Gebirge gegeben sein, wie etwa die Rocky Mountains, andererseits aber auch durch eine sich nur langsam fortbewegende Kaltluftmasse in der unteren Troposphäre. Eine solche ist für Kaltluftausbrüche im Zusammenhang mit intensiven Strahlströmen charakteristisch.
    Abstract: Résumé En se basant sur un cas particulier, on montre que la subdivision d'un courant “jet” en plusieurs bras distincts — fait souvent observé au dessus des Etats Unis d'Amérique à l'avant de la zone d'intensité maximum — peut s'expliquer par la conservation de l'énergie tourbillonnaire potentielle d'une couche d'air se déplaçant sur un obstacle. Un tel obstacle peut être soit une importante chaîne de montagnes telles que les Rocheuses, soit une masse d'air froid se déplaçant lentement dans la basse troposphère, comme c'est typiquement le cas lorsqu'une invasion d'air froid est liée à un fort courant “jet”.
    Notes: Summary It is shown from a case study that the splitting of jet streams into several branches, which is frequently observed over the United States on the leading edges of intense maxima, may be explained by conservation of potential vorticity within an atmospheric layer moving over an obstacle. Such an obstacle may be a large mountain barrier, such as the Rocky Mountains, or a slowmoving dome of cold air in the lower troposphere, as is typical for cold outbreaks associated with strong jet streams.
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    Meteorology and atmospheric physics 17 (1968), S. 17-29 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Es wird eine systematische Phänomenologie der luftelektrischen Erscheinungen innerhalb und in der Umgebung von Wolken und Niederschlägen, soweit sie nicht mit Gewittern verbunden sind, entwickelt. Sie erstreckt sich auf niedrige Schichtwolken, Cumulus humilis, Cumuli im Wachstumsstadium sowie Cu congestus und schließt typische stabile Aufgleitprozesse mit Übergang von Altocumulus über Altostratus in Nimbostratus bei absinkender Basis ein. Die schlüsselhafte Bedeutung des Aggregatzustandes der Niederschläge und des Turbulenzgrades innerhalb der Wolken für das Verständnis der atmosphärisch-elektrischen Prozesse und ihrer Systematisierung im Rahmen einer Phänomenologie wird dargestellt.
    Abstract: Résumé On développe ici un système des phénomènes électriques atmosphériques au voisinage et à l'intérieur des nuages et des précipitations, pour autant que ces deux catégories d'hydrométéores ne soient pas liées à des orages. Cette classification s'étend aux nuages stratiformes bas, aux cumulus humilis, aux cumulus en plein développement ainsi qu'aux cumulus congestus, Elle englobe en outre des processus de glissement ascendant stables et typiques tels que le passage de l'altocumulus au nimbus en passant par l'altostratus et cela par abaissement de la base du nuage. On souligne la signification de l'état des précipitations et du degré de turbulence à l'intérieur du nuage pour la compréhension des processus électriques atmosphériques et leur systématisation.
    Notes: Summary An attempt is made to develop a systematic, phenomenological classification of non-thunderstorm clouds based on the electrical characteristics of such clouds, and to derive a similar classification of precipitation from the electrical properties of hydrometeors. The system, as proposed, will cover low stratus, cumulus humilis, convective cumulus and cumulus congestus, and also the cloud configuration associated with stable upslide situations characterized by a continuous transition, in time and space, from altocumulus to altostratus and nimbostratus, with the bases of the latter steadily losing altitude. The significance of the physical state of hydrometeors and of the intensity of turbulence in clouds as a key to atmospheric-electrical phenomena, and the interpretation and phenomenological classification thereof, is stressed.
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    Meteorology and atmospheric physics 17 (1968), S. 88-89 
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    Meteorology and atmospheric physics 17 (1968), S. 61-77 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Summary In the present paper the authors investigate the stream field over the Alpine region. For the comparison of the wind frequencies observed at two stations the representation of the frequencies of wind direction in matrix notation proved to be very useful. From such a matrix one can immediately read off the frequencies of the simultaneous wind directions at the stationB, when the direction at the stationA is held fast. The frequency distributions of the wind directions at the single stationsA andB result as the sums of the columns and of the rows of the wind matrix. The matrix allows to specify index numbers (e. g. the trace of the matrix) which characterize the simultaneous wind conditions at a pair of stations,AB, the change of direction from one station to the other and so on.
    Abstract: Résumé Dans le présent travail, on étudie le champ des courants dans la région des Alpes. Pour comparer la fréquence du vent à 2 stations, il est apparu que la représentation de la fréquence des directions du vent sous forme de matrice était parfaitement utilisable. Il est possible de tirer immédiatement d'une telle matrice la direction du vent dans une stationB en partant de la direction du vent observée au même moment en une stationA. La répartition des fréquences de la direction du vent aux stationsA etB résulte de la somme des colonnes, respectivement des lignes de la matrice. Une telle matrice permet également de tirer des grandeurs caractéristiques de la paire des stationsA etB. Ces grandeurs expliquent mieux l'apparition simultanée des mêmes directions (trace de la matrice), les rotations du vent d'une station par rapport à l'autre, etc.
    Notes: Zusammenfassung In der vorliegenden Arbeit wird das Strömungsfeld im Bereich der Alpen untersucht. Für einen Vergleich der Windhäufigkeiten zwischen zwei Stationen stellte sich eine Darstellung der Häufigkeiten der Windrichtungen in Matrixform als sehr brauchbar heraus. Man kann aus einer solchen Windmatrix bei einer festgehaltenen Windrichtung in der StationA sofort die Häufigkeiten der gleichzeitigen Windrichtungen in der StationB ablesen. Die Häufigkeitsverteilungen der Windrichtungen an den einzelnen StationenA undB ergeben sich aus der Summe der Spalten bzw. der Zeilen der Windmatrix. Mittels einer solchen Windmatrix ist man auch in der Lage, für das betreffende StationspaarAB charakteristische Kenngrößen anzugeben, die das gleichzeitige Auftreten von Windrichtungen (Spur der Matrix), die Drehung des Windes und dergleichen mehr beschreiben.
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    Meteorology and atmospheric physics 17 (1968), S. 78-87 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Auf einer Fläche von etwa 0,3 km2 wurde am Hintereis- und Langtaufererjochferner (Ötztaler Alpen) die Verteilung der Deformationen und der Spannungen an der Oberfläche bestimmt. Dazu wurde in den Jahren von 1957 bis 1963 ein Pegelnetz, bestehend aus 30 Pegeln in etwa 2750 m Seehöhe, vermessen. Die Gletscheroberfläche zeigt beim Zusammenfluß beider Gletscher ein Gebiet ohne Spalten, bedingt durch hohe Kompressionen, und ein Gebiet mit Querspalten, die durch seitliche Quetschung in Verbindung mit kleinen Zugspannungen entstehen. Die Spaltenbildung stimmt mit der Spannungsverteilung in bezug auf Größe und Richtung des Spannungszustandes überein.
    Abstract: Résumé On a déterminé la répartition des déformations et des tensions à la surface des glaciers du Hintereis et du Langtaufererjoch (Alpes de l'Ötztal, Autriche) et cela sur, une surface de 0.3 km2. Ces mesures furent effectuées de 1957 à 1963 et on s'est servi pour cela d'un, réseau de 30 échelles nivométriques situées à environ 2750 m d'altitude. La surface présente, au confluent des deux glaciers une zone sans crevasses due à de hautes compressions et une zone zébrée de crevasses transversales dues à des forces de compression, latérale liées à de petites tensions. La formation des crevasses correspond à la répartition des tensions et cela aussi bien en ce qui concerne leur direction que leur importance.
    Notes: Summary The distribution of strain-rates and stresses was determined in an area of approximately 0.3 km2. For this purpose a network of 30 stakes was established on the Hintereisferner and Langtaufererjochferner (Oetztal Alps, Austria) in an altitude of approximately 2750 m in the years between 1957 and 1963. The region of the confluence of the Hintereisferner and the Langtaufererjochferner shows both, an area without crevasses, where high compressing strainrates and stresses occur, and an area with transverse crevasses formed by high lateral compressive stresses in combination with small tensile stresses. The formation of crevasses is a good agreement with the distribution of stresses concerning direction and magnitude.
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