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  • 1
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    Stochastic environmental research and risk assessment 1 (1987), S. 1-2 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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  • 2
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    Stochastic environmental research and risk assessment 1 (1987), S. 3-16 
    ISSN: 1436-3259
    Keywords: Annual maximum ; partial duration series ; T-year estimate ; marshall-Olkin bivariate distribution ; Morgenstern bivariate distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract As a basis for development of the annual maximum distribution the so-called partial duration series with Poissonian occurrence times and exponentially distributed peak exceedance values has been selected. The model is generalized by allowing for a Markov dependence between succeeding peak values. Correlation values from p=0 to p=1 can be accounted for by introducing the Marshall-Olkin bivariate exponential distribution, which is presented in detail. The developed distribution function for the annual maximum is throughly analysed and a variety of distribution forms depending on the value of the correlation coefficient and the intensity in the Poisson process is hereby recognized. To a certain extent this might be considered as parallel to the scattering of hydrological regions with different generating mechanisms for the annual maxima.
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  • 3
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    Stochastic environmental research and risk assessment 1 (1987), S. 37-52 
    ISSN: 1436-3259
    Keywords: Cyclonic precipitation ; mathematical modeling ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A stochastic description is developed for extratropical cyclonic precipitation fields at synoptic and meso scales as they are typically observed by radars over the Earth. This description attempts to account I) for the synoptic scale behavior of a cyclonic storm (its birth, its synoptic scale motion trajectory, and its dissipation) II) for the synoptic-scale organizational structure of subsynoptic precipitation areas (rainbands, precipitation cores and raincells) within a cyclonic storm; and III) for the behavior of subsynoptic precipitation areas, in terms of their births, their spatial configuration evolutions, their motions, and their deaths (dissipation). The precipitation cores and the raincells are taken as the building blocks of the subsynoptic precipitation, areas within a cyclonic rainfield.
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  • 4
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    Stochastic environmental research and risk assessment 1 (1987), S. 81-100 
    ISSN: 1436-3259
    Keywords: Stochastic differential equations ; Itô calculus ; Stratovovich integrals ; Jump integrals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Fundamentals of the theory of stochastic calculus and stochastic differential equations (SDE's) which are finding increasing application in water resources engineering are reviewed. The basics of probability theory, mean square calculus and the Wiener, white Gaussian and compound Poisson processes are given in preparation for a discussion of the general Itô SDE with drift, diffusion and jump discontinuity terms driven by Gaussian white noise and compound Poissionian impulses. Also discussed are stochastic integration and the derivation of moment equations via the Itô differential rule. The lierature of SDE's is reviewed with an emphasis on the more accessible sources.
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  • 5
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    Stochastic environmental research and risk assessment 1 (1987), S. 53-66 
    ISSN: 1436-3259
    Keywords: Hurst range ; conditioned exchangeable, variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new theoretical interpretation is proposed for Hurst's empirical law which is applicable to discrete-valued inflows and is consistent with the existing interpretation for continuous-valued inflows. This is applied to independent net inflows {X r} having values +1 and −1 with unequal probabilities. With the aid of a new result on the exchangeability of symmetrically conditioned exchangeable variables, values of the resulting range are obtained and tabulated. It is found that the effect of skewness is very slight for skewness values between (about) 3 and −3, and that Hurst's own approximation, the “conditioned range”, is remarkably accurate.
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  • 6
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    Stochastic environmental research and risk assessment 1 (1987), S. 67-80 
    ISSN: 1436-3259
    Keywords: pattern analysis ; mixed-mode data ; event-covering ; discretization ; hydrometric data
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a pattern analysis technique that has been successfully applied to a set of hydrometric network data collected in British Columbia, Canada. This technique can extract information from a set of observed heterogeneous multivariate data. The data are represented as n-tuples of mixed discrete and continuous values. The technique is capable of screening out statistically irrelevant information. It is also able to detect inherent subgroups in the data through adopting an event-covering approach. The subgroup characteristics represent important empirical understanding even though there may be considerable probabilistic variation within each individual subgroup.
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  • 7
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    Stochastic environmental research and risk assessment 1 (1987), S. 17-36 
    ISSN: 1436-3259
    Keywords: Stochastic hydrology ; multivariate analysis ; information extraction ; information transfer ; structure of time series ; time series analysis ; spatial characteristics ; simulation of processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A stochastic approach to the analysis of hydrologic processes is defined along with a discussion of causes of tendency, periodicity and stochasticity in hydrologic series. Sources of temporal non-stationarity are described along with objectives and methods of analysis of processes and, in general, of information extraction from data. Transferred information as measured by correlation coefficients is compared with the transferable information as measured by entropy coefficients. Various multivariate approaches to hydrologic stochastic modeling are classified in light of complexities of spatial/temporal hydrologic processes. Alternatives of time series structural decomposition and modeling are compared. A special approach to modeling of space properties further contributes to approximate simulations of spatial/temporal processes over large areas. Several aspects of stochastic models in hydrology are concisely reviewed.
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  • 8
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    Stochastic environmental research and risk assessment 1 (1987), S. 101-116 
    ISSN: 1436-3259
    Keywords: Soil moisture ; stochastic processes ; stochastic differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The dynamics of water within the unsaturated root zone of the soil are represented by a pair of stochastic differential equations (SDE's), one representing the so-called “surplus” state of the moisture and the other the “deficit” condition. The inputs to the model are the climatically controlled random infiltration events and evapotranspiration which are modeled as a compound Poisson process and a Wiener (Brownian motion) process, respectively. The solutions to these SDE's are not in “close-form” but sample functions are obtained by numerical integration. The moment properties of the soil moisture evolution process have also been derived analytically including the mean, variance, covariance and autocorrelation functions. To illustrate the model, climatic parameters representing the “surplus” and “deficit” cases and properties of clay loam soil have been used to numerically derived the corresponding sample functions. With proper selection of all the parameters, physically realistic sample trajectories can be obtained for the model.
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  • 9
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    Stochastic environmental research and risk assessment 1 (1987), S. 127-134 
    ISSN: 1436-3259
    Keywords: Upland erosion ; annual erosion losses
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Point rainfall triggers the complex processes of overland flow and surface erosion. The probability density functions of rainfall duration and intensity are coupled with a physically based dynamic formulation of rainfall-runoff-sediment transport relationships for upland areas. When considering a single storm, rainfall depth alone is a poor predictor of sediment transport because of the dispersion introduced by the effect of rainfall intensity. On a long terms basis, however, the total amount of rainfall can be used to predict total erosion losses.
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  • 10
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    Stochastic environmental research and risk assessment 1 (1987), S. 117-126 
    ISSN: 1436-3259
    Keywords: equi-risk line ; detention pond ; urban runoff ; frequency analysis ; flood risk
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The expression of equi-risk line derived by the authors represents the relationship between discharge capacityy 0 u and storage capacityz 0 u to keep flood frequency under a certain risk level represented by the return periodT, i.e.,z 0/z 0 u ={(y 0 u −y 0 u )/y 0 u } S , wherey 0 u andz 0 u areT-year probability peak discharge and total volume of a hydrograph. The shape parametersS is evaluated in this paper for various release rules of the storage facilities and correlations of durations and peaks of hydrographs. The expression forS is: $$S = S_\infty + (S_0 - S_\infty )\exp ( - \sqrt p )$$ , whereS 0 andS ∞ are the values ofS forp=0 and ∞, andp is the exponent of a general storage-release relation,q=az' p, wherea is the storage constant, andz' andq are the volume of stored water and the corresponding release. The values ofS 0 andS ∞ are expressed in terms of the correlation coefficient ρ of durations and peaks of inflow hydrographs.
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  • 11
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    Stochastic environmental research and risk assessment 1 (1987), S. 135-140 
    ISSN: 1436-3259
    Keywords: Upland erosion ; annual soil losses
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Annual erosion losses from 135 experimental plots under a variety of soil types, vegetation cover densities and conservation practices in Iraq have been measured over a period of four years. The first three years of this data set demonstrate that annual erosion losses can be predicted from annual rainfall depths. The results obtained from regression analysis were then validated with the fourth year of soil erosion data. These results corroborate the theoretical findings of the companion paper in that long term erosion losses can be predicted from the total amount of rainfall.
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  • 12
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    Stochastic environmental research and risk assessment 1 (1987), S. 141-154 
    ISSN: 1436-3259
    Keywords: Contemporaneous ARMA models ; maximum likelihood estimation ; multivariate modelling ; stochastic hydrology ; time series analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In order to allow contemporaneous autoregressive moving average (CARMA) models to be properly applied to hydrological time series, important statistical properties of the CARMA family of models are developed. For calibrating the model parameters, efficient joint estimation procedures are investigated and compared to a set of uivariate estimation procedures. It is shown that joint estimation procedures improve the efficiency of the autoregressive and moving average parameter estimates, but no improvements are expected on the estimation of the mean vector and the variance covariance matrix of the model. The effects of the different estimation procedures on the asymptotic prediction error are also considered. Finally, hydrological applications demonstrate the usefulness of the CARMA models in the field of water resources.
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  • 13
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    Stochastic environmental research and risk assessment 1 (1987), S. 155-160 
    ISSN: 1436-3259
    Keywords: Gamma Markov ; estimation ; maximum likelihood estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The linearly regressive Gamma Markov sequence is being increasingly used as a model for geophysical phenomena, one of the reasons being that it is possible to determine the distribution of (weighted or otherwise) cumulative sums of such a sequence. In this paper we show briefly how to simulate such a sequence and its seasonal extension; we also show how to estimate its parameters. It is shown that the estimates obtained by the method of moments do not have a high efficiency, whereas those obtained by a modified maximum likelihood method have an efficiency close to unity.
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  • 14
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    Stochastic environmental research and risk assessment 1 (1987), S. 161-168 
    ISSN: 1436-3259
    Keywords: Inverse problem ; groundwater management ; groundwater response function ; stochastic control ; consistent parameter estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The response of groundwater basins to natural and anthropogenic inputs depends on many interrelated factors such as the values of groundwater flow and mass transport parameters. This work presents a theoretical analysis of the impact of parameter uncertainty on groundwater management decisions. It is shown that under classical, Bayesian, and deterministic assumptions about the parameter structure, the resulting management decisions could be very different. This underscores the importance of adopting the proper parameter structure and the need for using consistent methods to solve the inverse problem.
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  • 15
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    Stochastic environmental research and risk assessment 1 (1987), S. 185-198 
    ISSN: 1436-3259
    Keywords: Pattern matching ; tracking ; rainfall ; mesoscale ; radar
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a new feature-based matching algorithm for tracking mesoscale precipitation phenomena in radar image sequences. Distinct rainfall areas are identified in each image and characterized by a feature vector of shape descriptors, which provide a mathematical representation of the spatial characteristics of each identified area. Rainfall areas observed in consecutive images are matched by comparing the relative values of the features. Two match scoring algorithms are developed to generate the initial estimates of correct matches, which are then updated by likelihood measures based on relative location. The method is applied to mesoscale rainfall areas observed in sequences of radar-derived images of rainfall activity over Southwestern Ontario during the summers of 1980 and 1981.
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  • 16
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    Stochastic environmental research and risk assessment 1 (1987), S. 199-208 
    ISSN: 1436-3259
    Keywords: Extreme value distribution ; two-component distribution ; maximum entropy principle ; parameter estimation ; regional estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The two component extreme value (TCEV) distribution has recently been shown to account for most of the characteristics of the real flood experience. A new method of parameter estimation for this distribution is derived using the principle of maximum entropy (POME). This method of parameter estimation is suitable for application in both the site-specific and regional cases and appears simpler than the maximum likelihood estimation method. Statistical properties of the regionalized estimation were evaluated using a Monte Carlo approach and compared with those of the maximum likelihood regional estimators.
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  • 17
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    Stochastic environmental research and risk assessment 1 (1987), S. 169-184 
    ISSN: 1436-3259
    Keywords: Stochastic control and programming ; real-time hydrologic forecasting ; reservoir theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new approximate method of solution for stochastic optimal control problems with many state and control variables is introduced. The method is based on the expansion of the optimal control into the deterministic feedback control plus a caution term. The analytic, small-perturbation calculation of the caution term is at the heart of the new method. The developed approximation depends only on the first two statistical moments of the random inputs and up to the third derivatives of the cost functions. Its computational requirements do not exhibit the exponential growth exhibited by discrete stochastic DP and can be used as a suboptimal solution to problems for which application of stochastic DP is not feasible. The method is accurate when the cost-to-go functions are approximately cubic in a neighbourhood around the deterministic trajectory whose size depends on forecasting uncertainty. Furthermore, the method elucidates the stochastic optimization problem yielding insights which cannot be easily obtained from the numerical application of discrete DP.
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  • 18
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    Stochastic environmental research and risk assessment 1 (1987), S. 209-216 
    ISSN: 1436-3259
    Keywords: Transport ; sedimentation ; random walk ; Markov chain in continuous time ; distribution of maximum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A simple two-dimensional random walk model is developed for the motion of a particle in a fluid flow. Some earlier results for the persistent injection of particles into the flow are extended, and the distribution of the maximum number of particles in suspension over the period (0,t) is derived.
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  • 19
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    Stochastic environmental research and risk assessment 1 (1987), S. 217-240 
    ISSN: 1436-3259
    Keywords: Transport of fluid ; random network ; macro-permeability ; micro-geometry ; statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents a detailed statistical analysis of Hagen-Poiseuille flow in plane random isotropic networks of interconnected channels. The emphasis is on statistico-geometrical features of networks that affect macroscopic permeability. It is shown that permeability of a network depends on its average co-ordination number, the first two moments of the channel length distribution and other explicitly identifiable geometrical features. Distributions of flow rates in channels and average flow rates are established by minimization of the rate of energy dissipation. Theoretical developments are interpreted in the context of classical statistical mechanics. Analytical results are illustrated and verified using numerical analysis of flow in a simulated random network.
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  • 20
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    Stochastic environmental research and risk assessment 1 (1987), S. 280-280 
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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  • 21
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    Stochastic environmental research and risk assessment 1 (1987), S. 241-262 
    ISSN: 1436-3259
    Keywords: Martingale ; stochastic-convective ; stochastic-relativist ; spectral-integral ; perturbative ; statistical-mechanical
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The use of stochastic models in subsurface hydrology is growing at a logistic pace. To tie together a number of different stochastic methodologies for deriving subsurface transport equations, we have put together a brief review of some of the more common techniques. Our attention is confined to a few select methodologies so that we might delve in detail into assumptions required by the various approaches and their strengths and weaknesses. The methods reviewed include: Martingale, stochastic-convective, stochastic-relativist, spectral-integral, perturbative, statistical-mechanical, and generalized hydrodynamics. Within this list, we also have included a few stochastic methodologies which have been used solely to develop expressions for the dispersion tensor.
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  • 22
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    Stochastic environmental research and risk assessment 1 (1987), S. 297-302 
    ISSN: 1436-3259
    Keywords: Stochastic PDE ; Zakai equation ; nonlinear filtering ; distributed systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract We shall consider in this article a general class of stochastic PDE which in particular covers the Zakai equation of nonlinear filtering and natural formulations of distributed systems involving control variables. We use only fixed point arguments, hence we get uniqueness results. In the case of the Zakai equation, Galerkin approximations have been considered by Pardoux (1979) to derive the existence of the solution
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  • 23
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    Stochastic environmental research and risk assessment 1 (1987), S. 281-296 
    ISSN: 1436-3259
    Keywords: Stochastic groundwater flow ; semigroups ; random in time Gaussian process ; random physical parameters ; stochastic partial differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Two methods for the solution of partial differential equations (PDE) for the general case of random in time physical parameters are presented and their application to the solution of unsteady regional groundwater flow equations are illustrated. The first method is the semigroup approach which directly offers a solution without resorting to “closure approximations” (hierarchy techniques), perturbation techniques, or Montecarlo simulation techniques. The semigroup approach can also handle the general stochastic problem when randomness also appears as initial conditions, boundary conditions or forcing terms. The second method is an approximation scheme to obtain the semigroup solution in complex cases and permits the solution of equations with more than one random coefficient.
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  • 24
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    Stochastic environmental research and risk assessment 1 (1987), S. 303-318 
    ISSN: 1436-3259
    Keywords: Rainfall-runoff models ; forecasting ; unit hydrograph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Here we review the main thrusts of rainfall-runoff modelling with an eye toward the advantageous use of the massive date sets being accumulated and the modern computers capable of dealing effectively with such sets. More than a tutorial, this study is aimed at providing a unifying structure for analyzing available techniques. The closing section draws attention to the existence of an alternative methodology.
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  • 25
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    Stochastic environmental research and risk assessment 1 (1987), S. 263-279 
    ISSN: 1436-3259
    Keywords: Porous media ; heterogeneity ; groundwater ; dispersion ; stochastic theory ; plume evolution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The migration of contaminants in heterogeneous aquifers involves dispersive processes that act at different scales. The interaction of these processes as a plume evolves can be studied by micro-scale modelling whereby two scales, a local- or micro-scale and an aquifer- or macro-scale, are covered simultaneously. Local-scale dispersive processes are represented through the local dispersion coefficient in the transport equation, while large-scale dispersion due to heterogeneities is represented through the resolution of the flow field and the diffusive exchange between streamtubes. The micro-scale model provides both the high degree of resolution compatible with local-scale processes, and the extent required for the approach to asymptotic conditions, using grids of up to a million nodal points. The model is based on the dual potential-streamfunction formulation for flow, and the transport problem is formulated in a natural coordinate system provided by the flownet. Simulations can be used to verify stochastic theories of dispersion, without the restrictive assumptions inherent in the theory. For the two-dimensional case, results indicate convergence of the effective dispersivity to the theoretical macrodispersivity value. Convergence takes place within a travel distance of about 50 correlation lengths of the hydraulic conductivity field. However, the approach taken to asymptotic conditions, as well as the macrodispersivity value, may differ for different realizations of the same medium. The influence of early-time events such as plume splitting on the asymptotic convergence remains to be investigated.
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  • 26
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    Stochastic environmental research and risk assessment 2 (1988), S. 17-33 
    ISSN: 1436-3259
    Keywords: River flow forecasting ; discrete linear cascade model ; ARMAX ; coupled models ; Kalman filtering ; Danube
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The objective of the paper is to compare three recursive linear state space models used to forecast river flow. The three models are as follows: (i) Purely deterministic discrete linear cascade model (DLCM); (ii) Purely stochastic autoregressive moving average (ARMAX) time series model; and (iii) Coupled deterministic (DLCM) — stochastic (ARMA) model. Description of DLCM is given shortly. The state space formulation of the ARMAX model enables the recursive estimation of random walk parameters and the forecast of flows by linear Kalman filtering. The correlated error sequence of DLCM is described by an ARMA model. The DLCM and ARMA models are put together in a coupled deterministic-stochastic model. The recursive conditional forecasting of the augmented state vector is performed by the linear Kalman-filter. The conditional output forecast is given by linear projection of thea priori state vector. Numerical investigations on River Danube data lead to the conclusion that the coupled deterministic-stochastic model is the most efficient forecasting model of all the three recursive techniques compared.
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  • 27
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    Stochastic environmental research and risk assessment 2 (1988), S. 61-72 
    ISSN: 1436-3259
    Keywords: Binary data ; censored observations ; autocorrelations ; acid rain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The properties of the well known estimator of the transition probabilities in a binary time series are investigated. A formula for the variance is obtained, which generally involves a double integral. However, in the case when the binary series is obtained by hard clipping of an AR(1) process, a good and fairly simple approximation is derived. In the MA(1) or MA(2) case exact formulae for the variance is given. In the appendix an excellent approximation to the fourth order cumulant of a clipped AR(1) process is derived, which may be of interest in other applications as well.
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  • 28
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    Stochastic environmental research and risk assessment 2 (1988), S. 175-188 
    ISSN: 1436-3259
    Keywords: Reservoir storage ; range ; adjusted range
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract It was remarked by Hurst in 1951 that the adjusted range gives the size of the smallest reservoir capable of providing a constant discharge equal to the mean inflow. Since that time this range and its rescaled modification, the Hurst range, have been widely discussed, not however primarily with a view to applying them to reservoir design problems, but rather on account of their possible relevance to the simulation of geophysical time series. Acknowledging the well-known conceptual weaknesses of adjusted ranges and the theoretical difficulties that inhibit their direct utilisation in the design and operation of real reservoirs, the authors argue that the interest displayed on ranges during the past few decades justifies the effort of eliminating one in particular of these weakness, namely their non-implementability as operating policies, a consequence of the fact that they can only be retrospectively evaluated. The paper proposes modifications in which the unknowable mean and standard deviation of future samples are replaced by the known mean and sample standard deviation of historical data, leading to the historically adjusted range and the historically rescaled and adjusted range. The latter is produced as an implementable approximation to Hurst's (1951) solution to the optimal reservoir problem. The expected values of the new ranges are evaluated and numerically tabulated.
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  • 29
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    Stochastic environmental research and risk assessment 2 (1988), S. 245-261 
    ISSN: 1436-3259
    Keywords: Geostatistics ; areal rainfall distribution ; areal reduction factor ; Gumbel distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Areal rainfall statistics are more relevant in flood hydrology and water resources management than point rainfall statistics when it comes to help designing dams or hydraulic structures. This paper presents a geostatistically based method to derive the areal statistics from point statistics. Assuming that the distribution models of point rainfall and areal belong to the same class of models and that the rainfall process is stationary, it is shown how the parameters of the areal distribution model can directly be computed from the parameters of the point distribution models in case of a non stationary process, an approximation is derived that yielded good results when applied to a mountainous region in Southern France. The method also allows the computation of the areal reduction factors in a very general form.
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    Stochastic environmental research and risk assessment 2 (1988), S. 303-315 
    ISSN: 1436-3259
    Keywords: Physically based stochastic models ; stochastic dynamic models ; statistical predictability ; internannual variability ; ARMA models ; water level variations
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    Notes: Abstract Several physically based stochastic dynamic models (SDM) are described including year-to-year variations of water volume in terminal and non-terminal lakes, streamflow of lake-fed rivers, and salinity of an inland sea (the Sea of Azov). All of these models are based upon the SDM of water volume of terminal lakes developed by Kritzky and Menkel in 1946 in co-operation with Kolomogorov. Explicit formulae are derived for second order statistical moments of the output processes, including variance, correlation function, spectra, etc., under the assumption that the forcing functions from stationary random sequences. The least-squares prediction problem is solved for both stationary and non-stationary cases. Some of the processes are shown to possess high statistical predictability. Actual predictions are compared with independent observations. Problems for further study are stated.
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    Stochastic environmental research and risk assessment 3 (1989), S. 1-16 
    ISSN: 1436-3259
    Keywords: Width function ; instantaneous unit hydrograph ; peak ; regression ; birth-death process
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract We investigate optimal predictors of the peak (S) and distance to peak (T) of the width function of drainage networks under the assumption that the networks are topologically random with independent and exponentially distributed link lengths. Analytical results are derived using the fact that, under these assumptions, the width function is a homogeneous Markov birth-death process. In particular, exact expressions are derived for the asymptotic conditional expectations ofS andT given network magnitudeN and given mainstream lengthH. In addition, a simulation study is performed to examine various predictors ofS andT, includingN, H, and basin morphometric properties; non-asymptotic conditional expectations and variances are estimated. The best single predictor ofS isN, ofT isH, and of the scaled peak (S divided by the area under the width function) isH. Finally, expressions tested on a set of drainage basins from the state of Wyoming perform reasonably well in predictingS andT despite probable violations of the original assumptions.
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    Stochastic environmental research and risk assessment 3 (1989), S. 68-69 
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    Stochastic environmental research and risk assessment 3 (1989), S. 281-292 
    ISSN: 1436-3259
    Keywords: Generalised Pareto distribution ; Peaks over threshold ; Probability weighted moments ; Regionalisation
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    Notes: Abstract A peaks over threshold (POT) method of analysing daily rainfall values is developed using a Poisson process of occurrences and a generalised Pareto distribution (GPD) for the exceedances. The parameters of the GPD are estimated by the method of probability weighted moments (PWM) and a method of combining the individual estimates to define a regional curve is proposed.
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    Stochastic environmental research and risk assessment 2 (1988), S. 155-160 
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    Stochastic environmental research and risk assessment 2 (1988), S. 161-174 
    ISSN: 1436-3259
    Keywords: Floods ; estimation ; quantiles ; generalized gamma ; generalized moments ; standard error
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    Notes: Abstract The generalized gamma (GG) distribution has a density function that can take on many possible forms commonly encountered in hydrologic applications. This fact has led many authors to study the properties of the distribution and to propose various estimation techniques (method of moments, mixed moments, maximum likelihood etc.). We discuss some of the most important properties of this flexible distribution and present a flexible method of parameter estimation, called the “generalized method of moments” (GMM) which combines any three moments of the GG distribution. The main advantage of this general method is that it has many of the previously proposed methods of estimation as special cases. We also give a general formula for the variance of theT-year eventX T obtained by the GMM along with a general formula for the parameter estimates and also for the covariances and correlation coefficients between any pair of such estimates. By applying the GMM and carefully choosing the order of the moments that are used in the estimation one can significantly reduce the variance ofT-year events for the range of return periods that are of interest.
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    Stochastic environmental research and risk assessment 2 (1988), S. 239-244 
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    Stochastic environmental research and risk assessment 2 (1988), S. 201-212 
    ISSN: 1436-3259
    Keywords: Flood risk ; flood frequency analysis ; generalised extreme value distributions
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    Notes: Abstract Conventional flood frequency analysis is concerned with providing an unbiased estimate of the magnitude of the design flow exceeded with the probabilityp, but sampling uncertainties imply that such estimates will, on average, be exceeded more frequently. An alternative approach is therefore, to derive an estimator which gives an unbiased estimate of flow risk: the difference between the two magnitudes reflects uncertainties in parameter estimation. An empirical procedure has been developed to estimate the mean true exceedance probabilities of conventional estimates made using a GEV distribution fitted by probability weighted moments, and adjustment factors have been determined to enable the estimation of flood magnitudes exceeded with, on average, the desired probability.
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    Stochastic environmental research and risk assessment 2 (1988), S. 263-279 
    ISSN: 1436-3259
    Keywords: Cyclonic rain fields ; cyclone center behavior ; stochastic model
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    Notes: Abstract Earlier the authors have developed a stochastic geometric model for extratropical cyclonic precipitation fields at synoptic and meso scales as they are typically observed by weather radars over the mainland U S A (see Kavvas and Puri 1983; Kavvas et al. 1987). Here the earlier mathematical development of the model is further extended by incorporating the stochastic description of cyclone center births and their evolutions over U S A into the model.
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    Stochastic environmental research and risk assessment 2 (1988), S. 315-316 
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    Stochastic environmental research and risk assessment 3 (1989), S. 31-49 
    ISSN: 1436-3259
    Keywords: Reservoir operation ; prediction ; Kalman filtering ; flood prevention ; fuzzy control
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    Notes: Abstract Japan has traditionally performed flood prevention through the construction and use of dikes, storage reservoirs, and basins which are costly and time consuming options. Another non-structural option is to operate the flood control system appropriately with a view to reducing flood damage. In this paper, a flood control system combining the runoff prediction model in the whole river basin with the reservoir operation is discussed. Different models of the runoff process are introduced in order to compare their accuracies and the computational time for the flood forecasting system. The reservoir operational rule is formulated in terms of fuzzy inference theory. Historical data are applied in a case study for verification of the proposed theories.
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    Stochastic environmental research and risk assessment 3 (1989), S. 69-69 
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    Stochastic environmental research and risk assessment 3 (1989), S. 154-154 
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    Stochastic environmental research and risk assessment 3 (1989), S. 155-178 
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    Keywords: Stochastic differential equations ; Stochastic Taylor formula ; Numerical methods ; Simulations ; Strong convergence ; Weak convergence
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    Notes: Abstract The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest.
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    Stochastic environmental research and risk assessment 3 (1989), S. 217-226 
    ISSN: 1436-3259
    Keywords: Stochastic integral equation method ; rainfall-runoff models ; confidence interval
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    Notes: Abstract The stochastic integral equation method (S.I.E.M.) is used to evaluate the relative performance of a set of both calibrated and uncalibrated rainfall-runoff models with respect to prediction errors. The S.I.E.M. is also used to estimate confidence (prediction) interval values of a runoff criterion variable, given a prescribed rainfall-runoff model, and a similarity measure used to condition the storms that are utilized for model calibration purposes. Because of the increasing attention given to the issue of uncertainty in rainfall-runoff modeling estimates, the S.I.E.M. provides a promising tool for the hydrologist to consider in both research and design.
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    Stochastic environmental research and risk assessment 3 (1989), S. 241-260 
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    Keywords: Hat matrix ; Mahalanobis distance ; Additive outliers ; Innovation outliers ; Influential data ; Autoregressive models ; Threshold autoregression ; Lake Huron
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    Notes: Abstract A practical method is developed for outlier detection in autoregressive modelling. It has the interpretation of a Mahalanobis distance function and requires minimal additional computation once a model is fitted. It can be of use to detect both innovation outliers and additive outliers. Both simulated data and real data re used for illustration, including one data set from water resources.
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    Stochastic environmental research and risk assessment 3 (1989), S. 293-316 
    ISSN: 1436-3259
    Keywords: Confined aquifer ; Transmissivity identification ; Geostatistics ; Inverse problem ; Ill-posedness ; Ill-conditioning ; Stability analysis ; Regularization
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract In recent years, geostatistical concepts have been applied to the inverse problem of transmissivity estimation from piezometric head data. It has been claimed that such methods overcome various difficulties encountered in other approaches. However, the reconstruction of transmissivity from head measurements is ill-posed as it depends on derivatives of the head field. Consequently, any accurate method for its solution is likely to encounter numerically ill-conditioned systems. This paper reviews the geostatistical approach, and uses the stability analyses of linear algebra to show that, as the amount of available data increases and the discretization of the system is refined, both a numerically ill-conditioned parameter estimation problem and ill-conditioned cokriging equations may appear. Therefore, while the geostatistical approach does have conceptual appeal, it does not avoid the fundamental difficulties arising out of the ill-posed nature of transmissivity identification. Instead, the method is likely to be quite sensitive to these difficulties, so care must be taken in its formulation to minimize their effects. A means to stabilize the geostatistical method is suggested and numerical experiments that highlight key points of our analysis are given.
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    Meteorology and atmospheric physics 39 (1988), S. 169-183 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Notes: Summary The observed daily pressure fields over the Arctic are compared with those obtained from a control run of the Goddard Institute for Space Studies (GISS) General Circulation Model using a classification typing procedure developed by Kirchhofer (1973) and a rotated principal components analysis for both data sets. The simulated patterns appear quite realistic in both frequency and geographical characteristics, although the model data show greater extremes and more closed cells. The procedure described provides a potentially useful method for evaluating the synoptic representativeness of GCM simulations.
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    Meteorology and atmospheric physics 39 (1988), S. 132-168 
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    Notes: Summary An analysis of mesoscale gravity wave events during the severe weather outbreak in the Red River Valley on 10–11 April 1979 is presented utilizing surface pressure data and the 3 h rawinsonde data from the AVE-SESAMEI special network. The unique data set provided by the SESAME field experiment makes it possible to relate the wavelike characteristics observed at the surface to the variability of the temperature, humidity, and wind fields over a deep tropospheric layer that act to initiate and sustain the waves over long distances and time periods. Three different wave events (A, B, and C) were identified via spectral analysis and cross-correlation techniques. They all have similar periods, approximately 3 h, but different phase velocities. All three wave events are generated and propagate in the exit region or anticyclonic side of upperlevel jet streaks. Convection and wind shear are shown to be unlikely contributors to the generation of event A, which is probably related to the development of a strong divergent field in association with an upper-tropospheric jet streak and to the ensuing mass adjustment process. Events B and C also appear in a region of strong ageostrophic motion associated with an upper-level jet streak. However, the low values of the Richardson number (Ri) at the critical levels of these two waves suggest vertical wind shear as a likely contributor to their generation and/or maintenance. A linear stability analysis confirms, with unprecedent spatial and temporal resolution, that a modal structure is present in the atmosphere whose characteristics are consistent with those of waves B and C. Three-hourly rawinsonde data show strong temporal and spatial variability throughout the troposphere in the wind, temperature, and humidity fields when the waves are present. Convective systems, as detected by radar, are closely linked to the waves, although not in a consistent manner: cells intensify or develop at the passage of a wave trough in event A, at the passage of a wave ridge in event C, and at the passage of a wave trough or ridge in event B, depending on the geographic location of the cells. For all three events, maximum rainfall recorded at the surface is associated with a wave ridge with a time lag of approximately 1 h.
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    Meteorology and atmospheric physics 39 (1988), S. 184-196 
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    Notes: Summary In this paper, analytic solutions of the nonhydrostatic and hydrostatic forms of Long's model were obtained under two different sets of vertical boundary conditions: The first uses a sumusoidal obstacle at the lower boundary and a rigid-lid top for the upper boundary. The second set applies an isolated obstacle of the “Witch of Agnesi” type at the lower boundary, while still using a rigid lid at the top. Following the solution evaluations, comparisons between the nonhydrostatic and hydrostatic solutions were processed in order to describe several influences introduced by using the hydrostatic assumption in this model. Through comparisons we have found that, in the case of a sinusoidal lower boundary condition, the hydrostatic solution is obtained as the zero mode of the nonhydrostatic solution. The influence of the hydrostatic assumption on the model solution is trivial in this case. When an isolated lower boundary condition is applied, however, the solutions illustrate dramatic differences, showing the significance of the effect of hydrostatic assumption on this model's solutions. These effects vary considerably with the model parameters as well. The comparison results also reveal that the realization of the hydrostatic assumption in this model's solutions is accomplished through the vertical boundary conditions used in the model evaluations.
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    Notes: Summary To investigate the effect of atmospheric turbulence on microwave communication links, temperature and water vapor pressure have been measured and radio refractivity has been computed, during different meteorological conditions, in the atmospheric boundary layer of an urban site. The cospectra between temperature (T) and water vapor pressure (e) have been found to be either negative over the whole range of frequencies, or the low-frequency end of the cospectrum is of opposite sign relative to higher frequency end. In both cases cospectra follow a−5/3 law in the inertial subrange, in agreement with the theoretical predictions. The coherence spectra clearly show that the temperature and humidity fluctuations are highly coherent within the inertial subrange under both convective and stable conditions. The relative contribution ofC T 2 ,C eT andC e 2 to the real refractive index structure parameterC n 2 is examined and discussed.
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    Meteorology and atmospheric physics 22 (1973), S. 119-134 
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Es wurden Folgen von hemisphärischen Fünftagemitteln des Helligkeitsminimums zur Zeichnung der Änderungen der arktischen Packeisgrenze in drei Sommern und zur Lokalisierung der Extreme zu bestimmten Zeiten benützt. Mittel und Extreme der vom Meereis auf der Hemisphäre bedeckten Flächen wurden in ihrer Abhängigkeit von der Zeit gemessen. Es wird die geographische Verteilung von größeren Flächen von offenem Wasser innerhalb der Eisdecke (Polynyas) gezeigt und die Form des Zerfalls des Meereises in den hauptsächlichen kontinentalen Einbuchtungen beschrieben; dabei zeigt sich eine beträchtliche Ähnlichkeit in jedem Sommer. Es wird auch der Nachweis erbracht, daß offenkundig wesentliche Unterschiede in der Ausdehnung der Eisdecke zwischen 1. Oktober 1969 und dem entsprechenden Datum von 1970 bestehen, die mit dem beobachteten Stärkeunterschied der südwestlichen Winde im Oktober beider Jahre qualitativ in Übereinstimmung sind.
    Notes: Summary Sequences of hemispheric five day mean minimum brightness mosaics are used to plot the variation in the Antarctic pack ice edge for three summer seasons and to locate extremes at particular dates. Average and extreme areas of sea ice over the hemisphere are measured as a function of time. The geographical distribution of major polynyas is shown and the decay pattern of sea ice in the main continental embayments is described and found to show considerable similarity in each season. Some evidence is shown that apparent substantial differences in ice extent between October 1st, 1969 and the corresponding date in 1970 are qualitatively consistent with observed variations in the strength of the southern westerlies in October of both years.
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    Meteorology and atmospheric physics 22 (1973), S. 227-256 
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    Description / Table of Contents: Zusammenfassung Quantitative Strahlungsmessungen des geo-synchronen NASA-ATS-3-Satelliten wurden für die Entwicklung und Erprobung statistischer Methoden von Flugplatzprognosen über kurze Zeiträume (0–6 Stunden) benützt. Resultate von über 800 stündlichen Wettersituationen, die an einer Anzahl verschiedener Stationen beobachtet wurden, zeigen, daß Wolkenhöhe und Himmelsbedeckung durch dichte Wolken mit Erfolg gemessen und vorhergesagt werden können. Die Vorhersage dieser Parameter besitzt größeren Erfolg als die Annahme von Persistenz über Zeiträume von mehr als zwei Stunden. Statistische Vorhersagen, die allein auf der Verwendung von Satellitendaten beruhen, zeigen bessere Qualität als Vorhersagen, die auf Parametern der 500mb-Fläche begründet waren. Die globable Anwendbarkeit dieser auf Satellitendaten beruhenden Vorhersagen kann durch die Berücksichtigung gewisser Kriterien, wie z. B. lokale Verhältnisse, in der Ableitung und der Anwendung der multiplen Regressionsgleichungen verbessert werden. Wenn man die gegenwärtige Qualität der kurzfristigen Wettervorhersage betrachtet, so bieten die hier berichteten ersten Resultate der Verwendung geo-synchroner Satellitendaten eine vielversprechende Möglichkeit zur Verbesserung der Vorhersagen im kurzfristigen Zeitbereich.
    Notes: Summary Quantitative radiance measurements from NASA's ATS-3 geosynchronous satellite have been used to develop and test a statistical forecst method to predict air terminal weather over the very short range (0–6 hours) time period. Results from more than 800 hourly weather situations at a wide range of U. S. weather stations show that the parameters of ceiling and total opaque cloud cover can be specified or predicted with skill, exceeding peristence forecasts for time periods greater than two hours. Statistical predictions based on satellite data alone are much better than those based on some 500mb upper air parameters tested. The potential global applications of the satellite data-based forecasts can apparently be improved by the use of certain criteria, such as region of interest, in developing and applying the multiple regression equation. Considering the present status of objective short range weather forecasting, these first results using geosynchronous satellite data demonstrate a new potential for improved forecasts at this scale.
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    Meteorology and atmospheric physics 22 (1973), S. 297-310 
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Ergebnisse von in der Zeit von 1967–1969 in Poona mit örtlichen Blitzzählern durchgeführten Gewitterbeobachtungen werden vorgelegt. Wenn je Stunde mehr als zwanzig Impulse auf einem 5 V/m-Zähler registriert werden, kann eine positive Korrelation zwischen der durchschnittlichen Gesamtippuloszahl und der Anzahl der Tage, an denen Donner gehört wurde, festgestellt werden. Es wird gezeigt, daß, obwohl ein einzelnes isoliertes Gewitter das normale Bild der Gewittertätigkeit in einem Monat oder in einer Jahreszeit verfälschen kann, ein langfristiger statistischer Durchschnitt mit größerer Zuverlässigkeit als besserer Index für elektrische Aktivität genommen werden kann als die gegenwärtige „akustische” Methode der Gewitterbeobachtung.
    Notes: Summary The results of thunderstorm observations made with local lightning flash counters at Poona during 1967–1969 are presented. A positive correlation between the average total count when the count exceeds 20 per hour on a 5V/m counter, and the number of days per month when thunder is heard has been established. The diurnal and seasonal variations in thunderstorm activity are described. It is seen that although a single isolated storm can vitiate the normal pattern of thunderstorm activity in a month or season, a long term statistical average can be taken with a greater degree of confidence as a better index of electrical activity than the current aural method of observation of thunderstorms.
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    Meteorology and atmospheric physics 34 (1985), S. 3-26 
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    Description / Table of Contents: Zusammenfassung Die zweidimensionale, numerische Simulierung der Seebrisenentwicklung über einer großen Sandbank an der Nordseeküste Deutschlands wird beschrieben. Das hier angewandte Modell enthält eine detaillierte Behandlung der Bodenfeuchte, welche eine Auswertung des Effektes differenzierter Oberflächencharakteristika auf die Luftströmung erlaubt. Rechnungsresultate zeigen, daß der Kontrast zwischen Sandbank und benachbartem, trockenem Land, die gezeitenbewirkte Überflutung der Sandbank und die nach Osten vorrückende Seebrise der Ostsee eine wichtige Rolle in der Entwicklung von mesoskalaren Strömungsverteilungen im Gebiet der Sandbank spielen.
    Notes: Summary Two-dimensional numerical simulations of sea breeze development over a large sandbar on the North Sea coast of Germany are reported. The numerical model used in these experiments contains a detailed treatment of soil moisture, which allows evaluation of the effects of differential surface characteristics on the airflow pattern. Results of the simulations indicate that the contrast between the moist sandbar and adjacent dry land, the tidal inundation of the sandbar, and the westward penetration of the Baltic sea breeze play important roles in the development of mesoscale airflow patterns in the sandbar region.
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    Meteorology and atmospheric physics 21 (1972), S. 247-272 
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Die Arbeit befaßt sich mit einer Untersuchung der atmosphärisch-elektrischen Zustände und Vorgänge in 700 bis 3000 m Höhe während Niederschlages verschiedenster Arten. Die Beziehung zwischen Potentialgradient (Feldstärke)E oder Spitzenentladungsstromi po und NiederschlagsstromdichteI pr läßt sich durch Regressionsgerade darstellen, deren Charakter bei gleichmäßigem Niederschlag unabhängig ist von der Art des Niederschlages und von der Höhe. Die Niederschlagsrate spielt nur eine nebensächliche Rolle und bestimmt nicht den Charakter der oben genannten Beziehungen. Bei gleichmäßigem Niederschlag sind Polarität vonE,I pr undi po durch den Aggregatzustand des Niederschlages bestimmt. Bei Schneefall sindE,i po positiv,I pr negativ. In Regen gelten umgekehrte Vorzeichen. Der Vorzeichenwechsel erfolgt, wenn Schneepartikel im freien Fall schmelzen, was im Mittel bei +1,1°C erfolgt. Der bekannte Spiegelbildeffekt gilt als Regel, nicht jedoch als exaktes Gesetz. Eine Reihe von Beobachtungen über Abweichungen von der strengen Spiegelung der Werte weist darauf hin, daß die Theorie nicht gelten kann, welche darauf beruht, daß primär hohe Werte vonE Spitzenentladungen auslösen, die ihrerseits Ionen erzeugen, welche durch Niederschlag eingefangen werden, so daßE undI pr spiegelbildlich verlaufen. Vielmehr werden durch niederschlags-elektrische Prozesse primärE und sekundäri po beeinflußt. Die Ladung an Wolkenunterseiten ist — außer beim Gewitter — für niederschlags-elektrische Vorgänge ohne Belang. Im Niederschlag wird das Verhalten der luftelektrischen Größen durch die niederschlags-physikalischen Vorgänge in der allernächsten Umgebung vom Beobachtungspunkt bestimmt. Die oben genannten Polaritäten der luftelektrischen Größen während Niederschlages gelten nur für gleichmäßigen Niederschlag. Nimmt die atmosphärische Stabilität unter einen gewissen Schwellenwert ab, so treten Polaritätswechsel der atmosphärisch-elektrischen Größen auf, die nichts mit dem Aggregatzustand und auch nichts mit der elektrischen Ladung an der Wolkenunterseite (außer im Gewitter) zu tun haben. Die Häufigkeit der Polaritätswechsel läßt sich als Funktion der Austausch-Intensität über der Station darstellen. Diese Beziehung kann für praktische Zwecke der Bestimmung des Turbulenzgrades verwendet werden.
    Notes: Summary This paper is concerned with a study of the atmospheric electrical conditions and processes at 700 up to 3000 m a. s. l. during precipitations of the most varied kind. The relation between potential gradientE or, respectively, point discharge currenti po , and precipitation current densityI pr may be represented by regression lines whose character during steady precipitations is independent of the kind of precipitation or altitude a. s. l. The precipitation rate plays only a subordinate part and does not control the character of the above mentioned relations. During steady precipitations the polarities ofE,I pr andi po are determined by the physical state of the precipitations. During snowfall,E andi po are positive,I pr is negative; during rainfall, the opposite signs apply. The sign reversal takes place when snow particles melt in free fall, which, as an average, takes place at +1.1° C. The well-known mirror image effect applies as a rule rather than an exact law. A number of observations regarding deviations from the strict mirroring of the values indicate that the theory cannot be valid which claims that high primary values ofE would trigger point discharges which, in turn, generate ions that are captured by precipitation, with the result thatE andI pr proceed in a mirror-inverted manner. The truth is that by processes of precipitation electricity,E is primarily influenced, andi po secondarily. The charge on cloud bases, except in thunderstorms, is irrelevant to precipitation electrical processes. In precipitation, the behavior of the atmospheric electrical quantities is governed by the precipitation physical processes in the most immediate vicinity of the observation site. The above mentioned polarities of the atmospheric electric quantities during precipitation are applicable only to steady precipitations. If the atmospheric stability is decreased below a certain threshold value, polarity changes of the atmospheric electrical quantities will occur which have nothing to do with the physical state nor with the electric charge on the cloud base (except in thunderstorms). The frequency of the polarity changes may be presented as a function of the exchange intensity above the station. This relation may be used for practical purposes of determining the degree of turbulence.
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    Meteorology and atmospheric physics 21 (1972), S. 299-306 
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Die Ladungsübertragung infolge von Zusammenstoß und nachfolgender Trennung von Wassertropfen, die in einem elektrischen Felde fallen, ist untersucht worden. Die übertragene Ladungq wurde, gemessen bei Werten der FeldstärkeE, des Tropfenradiusr, des RadienverhältnissesR/r, der Zusammenstoß-GeschwindigkeitV und dem Winkel Θ in den Bereichen von 0,5 bis 80 kV/m fürE, 200 bis 600 μm fürr, 1,0 bis 3,0 fürR/r, 0,5 bis 3 m/sec fürV und 0 bis 90° für Θ. Θ bedeutet den Winkel zwischen der Feldrichtung und der Verbindungslinie der Tropfenmittelpunkte im Augenblick der Trennung. Zwei gleich große Ströme von Tropfen wurden aus hypodermischen Kanülen ausgestoßen (durch Beeinflussung des Wasserstromes durch diese). Diese Ströme wurden dann zum Zusammenstoßen gebracht in einem Raum, in der durch zwei Elektroden ein elektriches Feld aufrechterhalten wurde. Die einzelnen Tropfen stießen vorübergehend zusammen, bewegten sich dann umeinander und trennten sich wieder, wonach jeder der beiden Ströme in einem isolierten Gefäß aufgefangen wurde, welches zur Ladungsmessung mit einem Elektrometer verbunden war. Die gemessenen Ladungen waren im allgemeinen in guter Übereinstimmung mit den aus der Gleichungq = 1,1 · 10-10 γ1 E r 2 Cos Θ berechneten, worin γ1 eine Funktion vonR/r darstellt. Aufgrund dieser Gleichung, der Marshall-Palmerschen Tropfengrößen-Verteilungsfunktion und annehmbarer Werte für die Trennungswahrscheinlichkeit zusammenstoßender Tropfen durchgeführte Berechnungen zeigten, daß Zusammenstöße zwischen Regentropfen in elektrifizierten Wolken zu einer Zerstörung des bestehenden Feldes kräftig beitragen.
    Notes: Summary Studies have been made of the charge transfer resulting from the collision and separation of water drops falling in an electric field. The charge transferq was measured for values of field strengthE, impact velocityV, drop radiiR, r, radius ratioR/r, and angle Θ ranging from 0.5 to 80 kV/m, 0.5 to 3 m·sec−1, 200 to 600 μ, 1.0 to 3.0 and 0 to 90 degrees respectively, where Θ is the angle between the field and the line of centres of the drops at the moment of separation. Two uniformly sized drop-streams were ejected from hypodermic needles by modulating the flow of water through them and then collided between a pair of electrodes across which a potential difference existed. The drops coalesced temporarily, swung around each other and separated, each resulting stream being collected in a vessel connected to an electrometer in order to measure the charge. The measured values ofq were generally in good agreement with theoretical values derived from the equationq = 1.1 · 10-10 γ1 E r 2 Cos Θ, where γ1 is a function ofR/r. Calculations based on this equation, the Marshall-Palmer drop-size distribution and established values of separation probabilities of colliding drops showed that collisions between raindrops within electrified clouds will act powerfully to dissipate the existing fields.
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    Meteorology and atmospheric physics 21 (1972), S. 329-338 
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Bekanntlich wird die Messung luftelektrischer Elemente durch Wind beeinflußt, und Tage mit starkem Wind werden gewöhnlich als luftelektrisch gestört bezeichnet, wobei eine Grenze bei 6 m/sec gesetzt wird. Der Einfluß horizontaler Winde auf das luftelektrische Feld ist zwar durch die Änderungen der Raumladungsdichte erklärbar; es wird hier aber gezeigt, daß der beobachtete Einfluß auf den luftelektrischen Vertikalstrom nicht vollständig durch Änderungen der örtlichen Leitfähigkeit und des Feldes erklärt werden kann. Das Vorhandensein eines vertikalen Advektionsstromes von der Größe ɛ0χ e υ x (∂E z /∂ x ) wird dargelegt, und es wird durch Berechnung gezeigt, daß er dann bedeutsam ist, wenn große Raumladungsdichten durch den Wind horizontal bewegt werden (zum Beispiel bei Staubstürmen und beim Auftreten von Spitzenentladungen). Da dieser vertikale Advektionsstrom zu υ x (∂E z /∂ x ) proportional ist, wird empfohlen, anstelle des üblichenv x diesen Parameter als Kriterium zur Bestimmung der Windstörung bei luftelektrischen Schönwettermessungen zu verwenden.
    Notes: Summary The measured values of electrical parameters of the atmosphere are known to be affected by wind, and days with strong winds (v x 〉6 m s−1) are normally classified as electrically disturbed. While the effect of horizontal wind on the electric field is readily explained in terms of changes in the spacecharge density, it is shown from electrodynamical considerations that the observed effect on the air-earth current cannot always be attributed solely to changes in the local conductivity and electric field. The existence of a vertical current of advection of magnitude ɛ0χ e υ x (∂E z /∂x) is revealed, and shown by calculations to be important (for instance during dust-storms and pointdischarge) when large space-charge concentrations are advected by wind. Since the current of advection is proportional tov x (∂E z /∂x), it is suggested that this parameter rather thanv x be used as a criterion for deciding wind-disturbed measurements of routine fair-weather atmospheric electric parameters.
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    Meteorology and atmospheric physics 21 (1972), S. 399-412 
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    Description / Table of Contents: Zusammenfassung Zur Bestimmung der spezifischen Ozonzerstörungsrate der Meeresoberfläche wurden Profilmessungen zwischen 1 m und 20 m Höhe über der offenen See durchgeführt. Der Gradient der Ozonkonzentration erwies sich in den Grenzen der Meßgenauigkeit als unabhängig von der Horizontal-Windgeschwindigkeit. Im Geschwindigkeitsintervall 1 m/sec bis 10 m/sec ergab sich für stabile Schichtung ein mittlerer Gradient von (0,23±0,12) γ/m, für instabile Schichtung (0,09±0,018) γ/m bei einer angenommenen Ozonkonzentration von 100 γ in 25 m Höhe. Im betrachteten Windgeschwindigkeitsintervall sind somit der vertikale Ozonfluß und die spezifische Ozonzerstörungsrate der Meeresoberfläche proportional zur Windgeschwindigkeit. Für die Ozonzerstörungsrateq gilt als Zusammenhang mit der mittleren Windgeschwindigkeit $$\bar u_{10} $$ in 10 m Höhe $$q = (1,7 \pm 0,6)10^{ - 5} \cdot \bar u_{10} [cm/\sec ]$$ Oberhalb 30 m Höhe ergaben Ballonsondierungen ein konstantes Mischungsverhältnis von Ozon und Luft.
    Notes: Summary The specific ozone destruction rate at the ocean surface was estimated from profile measurements between 1 m and 20 m height above the open sea. The ozone concentration gradient turned out to be independent of the horizontal wind velocity within the instrumental error range. Within the velocity interval of 1 m/sec to 10 m/sec a mean gradient of (0.23±0.12) γ/m for stable stratification and of (0.09±0.018) γ/m for unstable stratification were obtained. Both values base upon an assumed ozone concentration of 100 γ at 25 m altitude. Thus, the vertical flux of ozone and the specific ozone destruction rate of the ocean surface are proportional with the wind velocity. Between the specific ozone destruction rateq and the average wind velocity $$\bar u_{10} $$ at 10 m height the relation $$q = (1.7 \pm 0.6)10^{ - 5} \cdot \bar u_{10} [cm/\sec ]$$ holds. Above 30 m height the results of balloon soundings indicate the mixing ratio ozone/air to be constant with altitude.
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    Meteorology and atmospheric physics 21 (1972), S. 353-372 
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    Topics: Geography , Physics
    Description / Table of Contents: Summary Daily global cloud observations effectuated by means of the meteorological sattelites ESSA 3 and 5 in the year 1967 which made possible the global observation of terrestrial weather phenomena are the base of this paper. The author primarily treats vortex structures which led to the formation of cloud spirals. In 1967, over the entire globe 405 vortices with spiral structure appeared, 180 of them over the northern hemisphere and 225 over the southern hemisphere. The source regions were the North-Atlantic and North-Pacific on the northern hemisphere, on the southern hemisphere the source regions formed a broad belt encircling the entire globe. The paths of the vortices are directed mainly to north-east over the northern hemisphere, but to east-south-east over the southern hemisphere. The source regions of the vortex structures in one series are often cloud bands with a length of 5000 to 10000 km. They begin near the equator and cross the oceans. These bands are quasi-stationary, often have a life-time of 3 to 5 days, and show a strong bundling over certain areas of the earth. Above all, four bundles emerge building up the shape of a “fish-bone”. Over the Atlantic one bundle extends from the tropical Central-America in north-eastward direction to the middle North-Atlantic, the counter-bundle from the tropical regions of the Amazon to the south-east, crossing Brazil, to the South-Atlantic. Over the Pacific Ocean one finds similar long cloud-bundles extending from the equator in north-eastern and south-eastern direction. These four bundles direct one's attention to certain regions of the earth, which might be of great importance for the air exchange between the hemispheres. These are especially two regions: one of them is situated at the transition region from the North-American to the South-American, the second one in the equatorial region between Southeast-Asia and Australia.
    Notes: Zusammenfassung Dieser Arbeit liegen tägliche globale Wolkenbeobachtungen der meteorologischen Satelliten ESSA 3 und 5 des Jahres 1967 zugrunde [1], die eine Totalbetrachtung irdischer Wettervorgänge ermöglichen. In der vorliegenden Untersuchung wurden vor allem Wirbelstrukturen behandelt, die zur Bildung von Wolkenspiralen geführt haben. Im Jahre 1967 traten auf der ganzen Erde 405 Wirbel mit Spiralstruktur auf, davon 180 auf der Nordhemisphäre und 225 auf der Südhemisphäre. Als Quellenherde traten auf der Nordhemisphäre Nordatlantik und Nordpazifik hervor, auf der Südhemisphäre ergab sich eine Anordnung der Quellgebiete in Form eines breiten Gürtels, der um den Globus herumläuft. Die Wirbelbahnen verlaufen auf der Nordhemisphäre überwiegend in nordöstlicher, auf der Südhemisphäre in ostsüdöstlicher Richtung. Die Ursprungsgebiete der Wirbelstrukturen in einer Serie sind häufig Wolkenbänder mit einer Länge von 5000 bis 10000 Kilometern. Sie entspringen in der Nähe des Äquators und verlaufen quer über die Meere. Diese Bänder, die quasistationär sind und häufig eine Lebensdauer von drei bis fünf Tagen haben, zeigen über bestimmten Gebieten des Globus eine starke Bündelung. Vor allem treten vier Bündel hervor, die ein „Fischgrätenmuster” bilden. Über dem Atlantik verläuft ein Bündel vom tropischen Mittelamerika nach Nordosten bis zum mittleren Nordatlantik, das „Gegenbündel” von den tropischen Gebieten des Amazonenstromes nach Südosten über Brasilien zum Südatlantik. Über dem Pazifischen Ozean lassen sich ganz ähnliche, vom Äquator nordost- bzw. südostwärts verlaufende Bündel von Langen Wolkenbändern finden. Die vier Bündel weisen auf ganz bestimmte Regionen der Erde hin, die beim Luftaustausch zwischen den Hemisphären von großer Bedeutung sein dürften. Es sind dies besonders zwei Regionen: die erste liegt an der Übergangsstelle vom nordamerikanischen zum südamerikanischen Kontinent, die zweite in der äquatorialen Region zwischen Südostasien und Australien.
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    Meteorology and atmospheric physics 22 (1973), S. 33-46 
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    Description / Table of Contents: Summary The importance of each term of the vorticity equation in (x, y, p, t)-coordinates (advection-, divergence and curlterm) for the production and reduction of vorticity is examined. In two synoptic situations the values of these terms are calculated for large areas. Except in the divergence term, calculations are made geostrophically. It is shown that in a stationary Ω-situation mainly the advection-and divergence term are responsible for vorticity changes. By contrast, strong cyclonic development can be appreciably influenced by the curl term, whose contribution to vorticity creation rises considerably in such a case.
    Notes: Zusammenfassung Die Bedeutung der verschiedenen Terme der Vorticitygleichung (Advektions-, Divergenz- und Rotationsterm) für die Produktion und Reduktion von Vorticity wird anhand von zwei Wetterlagen untersucht. Mittels der geostrophischen Approximation und einem Verfahren zur Berechnung der Vertikalbewegung wind die räumliche und zeitliche Verteilung jedes Terms berechnet. Es zeigt sich, daß bei einer entwicklungsarmen Wetterlage vor allem der Advektions- und Divergenzterm maßgebend für Vorticityänderungen sind, daß hingegen in den Verlauf einer starken Entwicklung auch der Rotationsterm wesentlich eingreifen kann.
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    Meteorology and atmospheric physics 23 (1974), S. 1-8 
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    Description / Table of Contents: Zusammenfassung Daten der thermischen Struktur der Atmosphäre, die mit dem mehrere Strahlungsbänder umfassenden SIRS-Instrument (Satellite Infrared Radiometer Spectrometer) des Nimbus III gemessen wurden, wurden zur Berechnung von Parametern der allgemeinen Zirkulation in der Nordhemisphäre herangezogen. Die thermische Struktur unterhalb der 10mb-Fläche wird mittels einer Regressionsmethode bestimmt, welche die Schichtdicke zwischen Isobarenflächen als abhängige Veränderliche benützt. Die täglich berechneten Parameter der allgemeinen Zirkulation umfassen die zonale mittlere und die wirbelpotentielle Energie sowie die zonale und wirbelkinetische Energie. Unabhängig davon wurden dieselben Parameter von Netzdaten des National Meteorological Center (NMC) bestimmt. Ein Vergleich zwischen den beiden Kollektiven von Daten zeigt, daß Maxima, Minima und allgemeine Tendenzen in beiden Berechnungen gut übereinstimmen. Die mittels SIRS berechneten Energiewerte stellen allerdings eine Unterschätzung dar. Die Energieveränderungen in der mittleren Stratosphäre während des Zusammenbruches des Polarwirbels werden als Beispiel angeführt.
    Notes: Summary General circulation parameters in the northern hemisphere are calculated using atmospheric thermal structure obtained from Nimbus III SIRS multi-channel radiance information. The thermal structure up to 10 mb is obtained by using a regression technique with thickness between pressure levels as the dependent variable. General circulation parameters calculated on a daily basis include zonal and eddy available potential energy, and zonal and eddy kinetic energy. A second set of calculations is performed using National Meteorological Center (NMC) grid data. A comparison of the two sets of calculations indicates that, although the energies calculated from the SIRS-derived structure underestimate the actual energies, maxima, minima and trends are well identified. An example of mid-stratospheric energy changes during a breakdown of the polar-night vortex is also given.
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    Meteorology and atmospheric physics 23 (1974), S. 13-27 
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    Description / Table of Contents: Zusammenfassung Der Gesamtozongehalt kann auf globaler Basis täglich von Satelliten aus gemessen werden, die die Erde umkreisen. Solche Messungen wurden durch den Nimbus-III-Satelliten durchgeführt. Ein Vergleich der zeitlichen und longitudinalen Veränderlichkeit der von der Stratosphäre emittierten langwelligen Strahlung in 60° südlicher Breite mit dem Gesamtozongehalt zeigte, daß niedrige (hohe) Strahlungswerte gut mit niedrigen (hohen) Gesamtozonwerten übereinstimmen. Die Phasengeschwindigkeit der nach Osten wandernden “Ozonwellen” ist in der Winterhemisphäre am größten. Die Ostwärtsbewegung nimmt gegen niedere Breiten der Winterhalbkugel ab. In äquatorialen Breiten scheinen sich die Wellen langsam gegen Westen zu bewegen. Im Sommer der Nordhemisphäre wandern die Wellen langsam gegen Osten. Die Intensität der “Ozonwellen” ändert sich ebenfalls mit der geographische Breite. Die zeitlichen und räumlichen Änderungen im Gesamtozongehalt sind hauptsächlich an die Bewegungen troposphärischer Drucksysteme geknüpft. Die starken, horizontalen Ozongradienten, welche häufig in der Winterhemisphäre beobachtet wperden, hängen mit intensiven baroklinen Zonen in der unteren Stratosphäre und der oberen Troposphäre zusammen, die sich ebenfalls nach Osten hin bewegen. Unter Annahme einer gleichförmigen zonalen Grundströmung konnten in der Ozonverteilung Rossby-Wellen festgestellt werden, deren Wellenlänge zwischen 2500 und 3700 km variierte.
    Notes: Summary With total ozone sensors on earth-orbitung satellites the ozone distribution over the entire earth may be measured daily. The conclusions from some of the Nimbus III measurements are discussed in this paper. A comparison of time-longitude variations of stratospheric radiance values at 60°S with values of the total ozone indicated that low (high) radiance values correspond very closely with the low (high) total ozone amounts. The speed at which these ozone ‘waves’ progress eastward is greatest in the winter hemisphere. The speed of eastward progression decreases as one approaches the lower latitudes in the winter hemisphere. In the equatorial region the progression of the ozone ‘waves’ appears to be slowly westward. In the Northern Hemisphere the waves progress slowly eastward during summer. The intensity of the ozone ‘waves’ was also observed to change with latitude. These temporal and spatial fluctuations are related mainly to the motion of dynamic tropospheric systems. The extremely tight ozone gradients, which may be seen in the winter hemisphere data, have been shown to be associated with strong baroclinic zones in the lower stratosphere and upper troposphere, which are moving eastward. Assuming uniform zonal velocity we found Rossby wavelengths that varied from 2500 to 3700 km.
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    Papers in regional science 24 (1970), S. 6-21 
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    Papers in regional science 24 (1970), S. 24-37 
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    Papers in regional science 24 (1970), S. 39-45 
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    Papers in regional science 24 (1970), S. 84-101 
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    Papers in regional science 24 (1970), S. 103-125 
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    Papers in regional science 24 (1970), S. 47-81 
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    Papers in regional science 24 (1970), S. 140-155 
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    Papers in regional science 24 (1970), S. 127-138 
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    Papers in regional science 24 (1970), S. 157-162 
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    Papers in regional science 24 (1970), S. 163-170 
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    Papers in regional science 24 (1970), S. 171-181 
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    Papers in regional science 25 (1970), S. 6-31 
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    Papers in regional science 31 (1973), S. 50-71 
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    Papers in regional science 31 (1973), S. 94-124 
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    Papers in regional science 31 (1973), S. 83-92 
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    Papers in regional science 32 (1974), S. 203-212 
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    Topics: Geography , Economics
    Notes: Conclusion I have argued that the current thrust toward land use planning on an extensive scale is a significant movement. It appears to respond to real societal forces and has mustered a consensus, albeit one that appears to have serious internal conflicts. For planners and regional scientists, the creation of regional planning agencies offers more than the opportunity for jobs. We have argued for many years that we are developing theories and techniques that allow us to understand regional phenomena in ways that are pragmatic and useful. Some of us may have the opportunity to find out how real those claims are. Our future as organized professional groups may depend on the answer.
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    Papers in regional science 33 (1974), S. 13-31 
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    Papers in regional science 30 (1973), S. 7-13 
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    Papers in regional science 30 (1973), S. 113-139 
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    Papers in regional science 30 (1973), S. 159-182 
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    Topics: Geography , Economics
    Notes: Conclusions The results show that the utility framework is consistent with the observed shopping and work-trip patterns in the Detroit Metropolitan Area. Specifically, they show that an entropy utility function (exponential resistance function) explains the data better than a gravity utility function (power resistance function). Tripmaking is influenced by the income and location of the individual. The low-income households made fewer trips than the higher income households which is most likely related to the lack of automobile availability particularly in a region like Detroit where public transportation is underdeveloped. Various suggestions have emerged for further research in spatial interaction.
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    Stochastic environmental research and risk assessment 2 (1988), S. 34-34 
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
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  • 84
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    Stochastic environmental research and risk assessment 3 (1989), S. 85-96 
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    Keywords: Stochastic equations ; irregularly spaced observations ; prediction, interpolation ; random fields
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The steady state two dimensional groundwater flow equation with constant transmissivities was studied by Whittle in 1954 as a stochastic Laplace equation. He showed that the correlation function consisted of a modified Bessel function of the second kind, order 1, multiplied by its argument. This paper uses this pioneering work of Whittle to fit an aquifer head field to unequally spaced observations by maximum likelihood. Observational error is also included in the model. Both the isotropic and anisotropic cases are considered. The fitted field is then calculated on a two dimensional grid together with its standard deviation. The method is closely related to the use of two-dimensional splines for fitting surfaces to irregularly spaced observations.
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    Stochastic environmental research and risk assessment 3 (1989), S. 71-84 
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    Keywords: Hydraulics ; quasilinearization ; simulation ; stochastic ; estuarine system ; Monte Carlo methods ; random differential equations ; parameter uncertainty
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A new methodology is presented for the solution of the stochastic hydraulic equations characterizing steady, one-dimensional estuarine flow. The methodology is predicated on quasi-linearization, perturbation methods, and the finite difference approximation of the stochastic differential operators. Assuming Manning's roughness coefficient is the principal source of uncertainty in the model, stochastic equations are presented for the water depths and flow rates in the estuarine system. Moment equations are developed for the mean and variance of the water depths. The moment equations are compared with the results of Monte Carlo simulation experiments. The results confirm that for any spatial location in the estuary that (1) as the uncertainty in the channel roughness increases, the uncertainty in mean depth increases, and (2) the predicted mean depth will decrease with increasing uncertainty in Manning'sn. The quasi-analytical approach requires significantly less computer time than Monte Carlo simulations and provides explicit
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    Stochastic environmental research and risk assessment 3 (1989), S. 135-153 
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    Keywords: Stochastic partial differential equations ; maximum likelihood estimation ; parameter estimation ; moment equations ; stodhastic contaminant transport
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    Notes: Abstract Many problems in hydraulics and hydrology are described by linear, time dependent partial differential equations, linearity being, of course, an assumption based on necessity. Solutions to such equations have been obtained in the past based purely on deterministic consideration. The derivation of such a solution requires that the initial conditions, the boundary conditions, and the parameters contained within the equations be stipulated in exact terms. It is obvious that the solution so derived is a function of these specified, values. There are at least four ways in which randomness enters the problem. i) the random initial value problem; ii) the random boundary value problem; iii) the random forcing problem when the non-homogeneous part becomes random and iv) the random parameter problem. Such randomness is inherent in the environment surrounding the system, the environment being endowed with a large number of degrees of freedom. This paper considers the problem of groundwater flow in a phreatic aquifer fed by rainfall. The goveming equations are linear second order partial differential equations. Explicit form solutions to this randomly forced equation have been derived in well defined regular boundaries. The paper also provides a derivation of low order moment equations. It contains a discussion on the parameter estimation problem for stochastic partial differential equations.
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    Stochastic environmental research and risk assessment 3 (1989), S. 179-190 
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    Keywords: Groundwater ; Stochastic ; Monte Carlo simulation ; First order Taylor series approximation
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The expected head and standard deviation of the head from the first order Taylor series approximation is compared to Monte Carlo simulation, for steady flow in a confined aquifer with transmissivity as a random variable. Emphasis is on the effect of changes in the covariance structure of the transmissivity, and pumping rates, on the errors in the first order Taylor series approximation. The accuracy of the first order Taylor series approximation is found to be particularly sensitive to pumping rates. With significant pumping the approximation is found to under estimate both the expected drawdown and head variance, and the error increases as the pumping rate increases. This can lead to large errors in probability constraints based on moments from the first order Taylor series approximation.
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    Stochastic environmental research and risk assessment 3 (1989), S. 227-240 
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    Keywords: Kalman filter ; Maximum likelihood estimation ; Periodic models ; Stochastic hydrology ; Time series analysis
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    Notes: Abstract An exact maximum likelihood procedure is presented for estimating the parameters of a periodic autogressive-moving average (PARMA) model. To develop an estimator which is both statistically and computationally efficient, the PARMA class of models is written using a state-space representation and a Kalman filtering algorithm is used to estimate the parameters. In order to demonstrate how to fit PARMA models in practice, the most appropriate types of PARMA models are identified for fitting to two average monthly riverflow time series and the new estimator is employed for estimating the model parameters.
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    Stochastic environmental research and risk assessment 2 (1988), S. 51-59 
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    Keywords: Soil moisture ; stochastic modelling ; shot noise models ; infiltrated rainfall ; evapotranspiration ; water balance ; root zone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract An attempt is made to estimate the expected contribution of rainfall to soil moisture during the irrigation season. Effective rainfall and evapotranspiration are the parameters considered in the water balance carried out in the root zone. Rainfall occurrence is simulated by a Poisson process whereas evapotranspiration is described by a simple deterministic function of potential evapotranspiration and soil moisture in the root zone. Using the theory of shot noise models a closed form solution is derived from the expected soil moisture in the root zone at the end of the time interval (0,t]. For illustration purposes the proposed model is applied to a series of data from Mikra meteorological station in Greece.
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    Stochastic environmental research and risk assessment 2 (1988), S. 35-50 
    ISSN: 1436-3259
    Keywords: Stochastic models ; spectral analysis
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Autoregressive (AR) and Autoregressive-moving average (ARMA) methods of spectral analysis have been developed and are being increasingly used as alternatives to traditional methods of spectral analysis. Two of these methods developed by Marple and Friedlander are tested in this study by using generated data from models with known spectra. The Blackman-Tukey spectral estimates are also compared to the Marple and Friedlander estimates. The variability of the Marple and Friedlander estimates with sample sizes is investigated. Although both Marple's and Friedlander's methods are satisfactory, Friedlander's method is preferred because of its ability to handle a wider class of models.
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    Stochastic environmental research and risk assessment 2 (1988), S. 73-78 
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    Keywords: Instantaneous unit hydrograph ; channel networks ; linear channel routing ; topological randomness
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    Notes: Abstract The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude,N, tends asymptotically, asN grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, $$\xi \sqrt n$$ , where ξ is a mean link wave travel time.
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    Stochastic environmental research and risk assessment 2 (1988), S. 113-136 
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    Keywords: spatial statistics ; hydrogeologic mapping ; trend analysis ; groundwater hydrology
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The properties of linear spatial interpolators of single realizations and trend components of regionalized variables are examined in this work. In the case of the single realization estimator explicit and exact expressions for the weighting vector and the variances of estimator and estimation error were obtained from a closed-form expression for the inverse of the Lagrangian matrix. The properties of the trend estimator followed directly from the Gauss-Markoff theorem. It was shown that the single realization estimator can be decomposed into two mutually orthogonal random functions of the data, one of which is the trend estimator. The implementation of liear spatial estimation was illustrated with three different methods, i.e., full information maximum likelihood (FIML), restricted maximum likelihood (RML), and Rao's minimum norm invariant quadratic unbiased estimation (MINQUE) for the single realization case and via generalized least squares (GLS) for the trend. The case study involved large correlation length-scale in the covariance of specific yield producing a nested covariance structure that was nearly positive semidefinite. The sensitivity of model parameters, i.e., drift and variance components (local and structured) to the correlation length-scale, choice of covariance model (i.e., exponential and spherical), and estimation method was examined. the same type of sensitivity analysis was conducted for the spatial interpolators. It is interesting that for this case study, characterized by a large correlation length-scale of about 50 mi (80 km), both parameter estimates and linear spatial interpolators were rather insensitive to the choice of covariance model and estimation method within the range of credible values obtained for the correlation length-scale, i.e., 40–60 mi (64–96 km), with alternative estimates falling within ±5% of each other.
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    Stochastic environmental research and risk assessment 2 (1988), S. 189-200 
    ISSN: 1436-3259
    Keywords: Point process ; rainfall model ; renewal Cox process
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A probabilistic model for the temporal description of daily rainfall at a fixed point is presented. The model is a member of the family of point process models. Model development is based on statistics estimated from rainfall data in Lebanon. Scale considerations for Markovian models and a theory of projection are used to determine the continuous process of alternation between dry and wet periods. The wet spells are defined by a number of storms each of which is associated with a storm depthY i and an interstorm time intervalT i. Computational results are presented for data from Lebanon. The model is successful in preserving the structure of the occurrence process, as well as the distributional properties of the rainfall amount.
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    Stochastic environmental research and risk assessment 2 (1988), S. 213-239 
    ISSN: 1436-3259
    Keywords: Unit hydrograph ; effective rainfall ; linear routing ; link-node model ; probabilistic model
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The design storm approach, where the subject criterion variable is evaluated by using a synthetic storm pattern composed of identical return frequencies of storm pattern input, is shown to be an effective approximation to a considerably more complex probabilistic model. The single area unit hydrograph technique is shown to be an accurate mathematical model of a highly discretized catchment with linear routing for channel flow approximation, and effective rainfalls in subareas which are linear with respect to effective rainfall output for a selected “loss” function. The use of a simple “loss” function which directly equates to the distribution of rainfall depth-duration statistics (such as a constant fraction of rainfall, or a ϕ-index model) is shown to allow the pooling of data and thereby provide a higher level of statistical significance (in estimating T-year outputs for a hydrologic criterion variable) than use of an arbitrary “loss” function. The above design storm unit hydrograph approach is shown to provide the T-year estimate of a criterion variable when using rainfall data to estimate runoff.
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    Stochastic environmental research and risk assessment 2 (1988), S. 295-302 
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    Keywords: Nonlinear structures ; skewed distribution ; Markov chain ; annual data
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    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Nonlinear serial dependence and skewness of annual hydrologic time series {X t } have been challenging the classical theory of Gaussian stochastic processes, particularly if the study of extremes (dry or wet years) is required as it is often the case. In this paper, a new and general model is proposed assuming that the geophysical system which is responsible forX t can take different states and that this state process is modeled by a Markov chain. At each time,X t is generated from a statistical distribution which depends on the state that has occurred. This model can preserve non-linear structures of serial dependence and it can produce a skewed marginal distribution ofX t without any transformation. A successful application of this model to the study of annual rainfall at Fortaleza (Northeast of Brazil) is also presented.
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    Stochastic environmental research and risk assessment 2 (1988), S. 281-294 
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    Keywords: precipitation field ; stochastic time-space evolution ; simulation
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    Notes: Abstract The time-space evolution of an extratropical cyclonic precipitation field over U S A is simulated in a stochastic setting as outlined in Kavvas et al. (1988). The birth of a cyclonic storm is characterized by the simultaneous birth of a cyclone center and births of subsynoptic precipitation areas (SPA) at preferred locations around the cyclone center. The precipitation cores and cells which are used as the fundamental building blocks of the SPAs are approximated by circular precipitation areas (CPA) of different sizes. The time space evolution of the precipitation field after the birth is governed by (1) the movement of the synoptic cyclone described by the cyclone center trajectory, (2) independent nonidentically distributed random velocities of the individual CPAs relative to the cyclone center, (3) the births of new CPAs in time and space relative to the cyclone center, (4) the independent evolution in time of the individual spatially uniform intensities of the existing CPAs, (5) the expansion and shrinkage of the existing CPAs in the course of movement and (6) the dissipation (death) of a random number of existing CPAs within the cyclonic system. The computer simulation, the results of which are presented in this paper, successfully reproduced the general mesoscale and synoptic scale features of the radar detected cyclonic rain fields as observed by Austin and Houze (1972), Houze et al. (1976), Hobbs (1978), Hobbs and Locatelli (1978), Houze (1981), Houze and Hobbs (1982) and others.
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    Stochastic environmental research and risk assessment 3 (1989), S. 17-29 
    ISSN: 1436-3259
    Keywords: Stochastic optimization ; linear programming ; simplex method ; Karmarkar's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated.
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    Stochastic environmental research and risk assessment 3 (1989), S. 51-67 
    ISSN: 1436-3259
    Keywords: Spatial rainfall estimation ; kriging ; ordinary co-kriging ; disjunctive co-kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4×4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.
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    Stochastic environmental research and risk assessment 3 (1989), S. 97-110 
    ISSN: 1436-3259
    Keywords: ARMA processes ; fractionally differencedARMA processes ; long memory ; spectral density ; maximum likelihood estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A class of regression type estimators of the parameterd in a fractionally differencedARMA (p, q) process is introduced. This class is an extension of the estimator considered by Geweke and Porter-Hudak. In a simulation study, we compared three estimators from this class together with two approximate maximum likelihood estimators which are based on two separate approximations to the likelihood. One approximation ignores the determinant term in the likelihood and the other includes a compensating factor for the determinant. When the determinant term is included, the estimate tends to be much less biased and is in general superior to the other estimate. The approximate maximum likelihood estimator out performed, by a large margin, the regression type estimators for pureARIMA (0,d,0) processes. However, forARIMA (1,d,1) processes, a regression type estimator turned out to be the best for realizations of length 400 in 3 out of the 5 cases we tried.
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    Stochastic environmental research and risk assessment 3 (1989), S. 111-133 
    ISSN: 1436-3259
    Keywords: Rainfall-runoff models ; random channel network ; regionalization ; flood frequency ; instanteous unit hydrograph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A rainfall-runoff model is used in conjunction with a probabilistic description of the input to this model to obtain simple regression-like relations for basin runoff in terms of basin and storm characteristics. These relations, similar to those sought in regionalization studies, are computed by evaluating the conditional distribution of model output given basin and storm characteristics. This method of conditioning provides a general way of examining model sensitivity to various components of model input. The resulting relations may be expected to resemble corresponding relations obtained by regionalization using actual runoff to the extent that the rainfall-runoff model and the model input specification are physically realistic. The probabilistic description of model input is an extension of so-called “random-model” of channel networks and involves postulating an ensemble of basins and associated probability distributions that mimic the variability of basin characteristics seen in nature. Application is made to small basins in the State of Wyoming. Parameters of the input variable distribution are estimated using data from Wyoming, and basin-scale relations are estimated both, parametrically and nonparametrically using model-generated runoff from simulated basins. Resulting basin-scale relations involving annual flood quantiles are in reasonable agreement with those presented in a previous regionalization study, but error estimates are smaller than those in the previous study, an artifact of the simplicity of the rainfall-runoff model used in this paper. We also obtain relations for peak of the instantaneous unit hydrograph which agree fairly well with theoretical relations given in the literature. Finally, we explore the issues of sensitivity of basin-scale, relations and error estimates to parameterization of the model input probability distribution and of how this sensitivity is related to making inferences about a particular ungaged basin.
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