Streamflow simulation: A nonparametric approach

Sharma, Ashish; Tarboton, David G.; Lall, Upmanu

doi:10.1029/96wr02839

Cited by 225 publications

(192 citation statements)

References 36 publications

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“…A non-parametric approach that uses empirical distribution functions (Lall 1995) has been emerging recently, with a potential to eliminate possible problems in fitting theoretical functions to historical data samples. One of the most popular is the kernel density function, which is defined as a weighted moving average of the empirical frequency distribution of the available data (Sharma et al 1997). The result is a distribution function guaranteed to fit the historical data in the probability range for which the data are available, and this virtually eliminates the need to run the goodness-of-fit tests required for fitting theoretical distributions.…”

Section: Methodsmentioning

confidence: 99%

An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series

Ilich¹

2013

Hydrological Sciences Journal

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A new method is presented to generate stationary multi-site hydrological time series. The proposed method can handle flexible time-step length, and it can be applied to both continuous and intermittent input series. The algorithm is a departure from standard decomposition models and the Box-Jenkins approach. It relies instead on the recent advances in statistical science that deal with generation of correlated random variables with arbitrary statistical distribution functions. The proposed method has been tested on 11 historic weekly input series, of which the first seven contain flow data and the last four have precipitation data. The article contains an extensive review of the results.Key words stochastic hydrology; correlated random variables; time series; empirical distribution Un algorithme efficace en trois étapes pour la génération stochastique multi-sites de séries chronologiques hydrologiques hebdomadaires Résumé Nous présentons une nouvelle méthode de génération de séries chronologiques hydrologiques multi-sites stationnaires. La méthode proposée peut gérer différentes durées du pas de temps et elle peut être appliquée à des séries d'entrée continues ou intermittentes. L'algorithme est différent des modéles de décomposition standard et de l'approche de Box-Jenkins. Il s'appuie au contraire sur les derniéres avancées statistiques traitant de la génération de variables aléatoires corrélées de fonctions de distribution statistique arbitraires. La méthode proposée a été testée sur 11 séries d'entrée historiques hebdomadaires, sept étant des données de débits, et quatre des données de précipitations. L'article présente une analyse approfondie des résultats.

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Section: Methodsmentioning

confidence: 99%

An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series

Ilich¹

2013

Hydrological Sciences Journal

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“…The derivation of equation (3) is presented by Sharma and O'Neill [2002] and Sharma et al [1997], except a bivariate kernel that is scaled by h 1 and h 2 is presented here. Sharma and O'Neill used the full covariance matrix to scale the kernel, in a process known as sphering [Fukunaga, 1972, p. 175].…”

Section: Univariate and Conditional Kernel Density Estimatorsmentioning

confidence: 99%

A nonparametric model for stochastic generation of daily rainfall amounts

Harrold

Sharma

Sheather

2003

Water Resources Research

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[1] This paper presents a model for stochastic generation of rainfall amounts on wet days that is nonparametric, accommodates seasonality, and reproduces important distributional and dependence properties of observed rainfall. The model uses kernel density estimation techniques, which minimize the assumptions that are made about the underlying probability density, and representation of seasonal variations is achieved through the use of a moving window approach. Four different classes of rainfall amount are considered and categorized according to the number of adjacent wet days, and the model is conditioned on the rainfall amount on the previous day. The proposed model can emulate the day-to-day features that exist in the historical rainfall record, including the lag 1 correlation structure of rainfall amounts. We link this model with long sequences of rainfall occurrence generated by the model of Harrold et al. [2003], which is designed to reproduce the longer-term variability of the observed record. The approach is applied to daily rainfall from Sydney, Australia, and the performance of the approach is demonstrated by presentation of model results at daily, seasonal, annual, and interannual timescales.

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“…Following in the spirit of our recent work [Lall and Sharma, 1996;Sharma et al, 1997], the purpose of this paper is to develop a nonparametric disaggregation methodology. The necessary joint probability density functions are estimated directly from the historic data using kernel density estimates.…”

Section: Since (2) Involves Linear Combinations Of Random Variablesmentioning

confidence: 99%

Disaggregation procedures for stochastic hydrology based on nonparametric density estimation

Tarboton¹,

Sharma²,

Lall³

1998

Water Resources Research

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138

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Abstract. Synthetic simulation of streamflow sequences is important for the analysis of water supply reliability. Disaggregation models are an important component of the stochastic streamflow generation methodology. They provide the ability to simulate multiseason and multisite streamflow sequences that preserve statistical properties at multiple timescales or space scales. In recent papers we have suggested the use of nonparametric methods for streamflow simulation. These methods provide the capability to model time series dependence without a priori assumptions as to the probability distribution of streamflow. They remain faithful to the data and can approximate linear or nonlinear dependence. In this paper we extend the use of nonparametric methods to disaggregation models. We show how a kernel density estimate of the joint distribution of disaggregate flow variables can form the basis for conditional simulation based on an input aggregate flow variable. This methodology preserves summability of the disaggregate flows to the input aggregate flow. We show through applications to synthetic data and streamflow from the San Juan River in New Mexico how this conditional simulation procedure preserves a variety of statistical attributes. IntroductionA goal of stochastic hydrology is to generate synthetic streamflow sequences that are statistically similar to observed streamflow records. Such synthetic streamflow sequences are useful for analyzing reservoir operation and stream management policies. Often, multiple reservoir sites and stream sections need to be considered as part of a system operation plan, and the operating horizon may extend from a few days to several years. For proper system operation it is important that the streamflow sequences generated for the different sites and/or time periods be "compatible." Practically, this suggests that (1) the flow recorded at a downstream gage be represented as the sum of the tributary flows and channel losses/ gains, (2) the annual flow represent a sum of the monthly flows, (3) the monthly fractions of flows in wet/dry years be representative of wet/dry years respectively, and (4)

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Streamflow simulation: A nonparametric approach

Cited by 225 publications

References 36 publications

An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series

An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series

A nonparametric model for stochastic generation of daily rainfall amounts

Disaggregation procedures for stochastic hydrology based on nonparametric density estimation

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