Stochastic Reservoir Theory Research Articles

STOCHASTIC RESERVOIR THEORY WITH CORRELATED DISCRETE INFLOWS ON A TWO-STEP TRANSITION MODEL

Stochastic reservoir theory has been developed with correlated discrete inflows on a two-step transition model by Klemes and on the basis of idea of joint probability of inflows and storage by Lloyd for Markovian inflows. Stationary distribution for any states of storage can be then calculated by the matrix algebra with the discrete representation for the amount of inflows and reservoir states.Numerical calculation is carried out by the correlated Binomial inputs. The results coincide with the exact solution on a randam-walk theory by Phatarfod and the approximate solution on one by Nagao and et al. This approach can be easily applied to the experimental distribution for sample data.

Design of Wastewater Storage Ponds at Land Treatment Sites. I: Parallels With Applied Reservoir Theory

The problem of designing a wastewater storage pond at a land treatment site is similar in many respects to sizing a water supply reservoir subject to variable inflows and outflows. The similarities and differences of the essential features involved in determining the capacity required for a wastewater storage pond and a water supply reservoir are compared and contrasted. In the companion paper, this analogy is exploited by showing how methods developed in applied stochastic reservoir theory can be extended to solve the wastewater storage problem at a land treatment operation.

Longitudinal Analysis of Employment and Unemployment Based on Matched Rotation Samples

ABSTRACT: The purpose of this paper is to provide methodology to fit longitudinal data on employment and unemployment generated by the rotation sampling schemes of national labour force surveys. The proposed methodology, referred to as infinite‐lag Markov models, is a generalisation of autoregressive Markov models developed for application in stochastic reservoir theory (Pegram 1980, Raftery 1985). Infinite‐lag Markov chains have infinite memory and, therefore, can usefully serve to model labour supply behaviour taking into account, in principle, the complete past work experience of individuals, and not just the most recent past or the most recent spell.After a brief review of the rotation sampling schemes of 20 national labour force surveys, the different types of longitudinal sequences that can be obtained from the rotation schemes are examined. A review of various models proposed in the literature for analysing longitudinal data on employment and unemployment, expressed under simplified assumptions and in discrete forms, set the stage for the formulation of the proposed infinite‐lag Markov model. The method is illustrated using matched longitudinal data derived from the US Current Population Survey.

Sums and weighted sums of a gamma Markov sequence

We derive the Laplace transforms of sums and weighted sums of random variables forming a Markov chain whose stationary distribution is gamma. Both seasonal and non-seasonal cases are considered. The results are applied to two problems in stochastic reservoir theory.

Sums and weighted sums of a gamma Markov sequence

We derive the Laplace transforms of sums and weighted sums of random variables forming a Markov chain whose stationary distribution is gamma. Both seasonal and non-seasonal cases are considered. The results are applied to two problems in stochastic reservoir theory.

An application of the Fokker-Planck equation in stochastic reservoir theory

The distribution of the storage and of the outflow of a reservoir with a piecewise linear constant operating rule and Gaussian white-noise input is derived by analytically solving the Fokker-Planck equation. The proposed operating rule may approximate the well-known standard policy or, by increasing the number of intervals with constant outflow, may approximate the operating rule of existing reservoirs. The form of the solution renders possible the probabilistic analysis of the behavior of a water reservoir without numerical calculations.

Discretization in stochastic reservoir theory with Markovian inflows

This paper considers the twin problems of the nature of discretization and the size of the unit of discretization used in stochastic reservoir theory. First, it is shown that it is possible to construct a discretization scheme which allows the release and the reservoir size to assume fractional values. The major part of the paper is concerned with the case where the inflows form a sequence of seasonal Markov dependent variables. A discretization scheme is suggested which gives better estimates of the probabilities of emptiness and fullness of the reservoir than those provided by the scheme due to Dearlove and Harris. A numerical comparison of these probabilities with those obtained by simulation is made for the case where the inflows follow a Thomas-Fiering model. Finally, the effect of the size of the unit of water on these probabilities is briefly discussed.

Stochastic hydrology: An introduction to wet statistics for dry statisticians

The paper is intended to give non-initiates some idea of the nature of stochastic hydrology. After a brief historical review it concentrates on three recent examples of stochastic modelling procedures that have aroused interest among hydrologists, namely the Hurst Effect, Short-Term Runoff Models, and Stochastic Reservoir Theory.

Some simple expressions for the probability of failure of a finite reservoir with Markovian input

In a previous paper the writer derived an explicit expression for the probability of failure of a discrete reservoir fed by a Markovian input. This is now simplified to expressions for particular cases which are characterized by the ratio of mean input to target draft. It is shown that the expressions yield some classical results in Stochastic Reservoir Theory.

Some aspects of stochastic reservoir theory — One more comment

Some aspects of stochastic reservoir theory — One more comment

Some aspects of stochastic reservoir theory — A further comment

Some aspects of stochastic reservoir theory — A further comment

Some aspects of stochastic reservoir theory — A comment

Some aspects of stochastic reservoir theory — A comment

Some aspects of stochastic reservoir theory — A reply

Some aspects of stochastic reservoir theory — A reply

Some aspects of stochastic reservoir theory

This paper examines the problem of the reservoir size-reliability-draft relationship. It compares the mathematicians' analytical efforts with the simulation techniques of the engineers and hydrologists, and suggests that the two methods should complement each other. It examines the various models for generating gamma Markov sequences and suggests a new one which is analytically more suitable to the problem in question. An alternative to the traditional formulation of the problem in terms of probability of failure is suggested, and a method based on random-walk techniques is employed to give close approximations. Finally, the effects of various parameters of the inflow distribution on the reservoir size to give the same reliability for a constant draft ratio are discussed.