A hybrid stochastic model for multiseason streamflow simulation
TL;DR: In this article, a hybrid model is presented for stochastic simulation of multiseason streamflows, which involves partial prewhitening of the streamflows using a parsimonious linear periodic parametric model, followed by resampling the resulting residuals using moving block bootstrap to obtain innovations and subsequently postblackening these innovations to generate synthetic replicates.
Abstract: A hybrid model is presented for stochastic simulation of multiseason streamflows. This involves partial prewhitening of the streamflows using a parsimonious linear periodic parametric model, followed by resampling the resulting residuals using moving block bootstrap to obtain innovations and subsequently postblackening these innovations to generate synthetic replicates. This model is simple and is efficient in reproducing both linear and nonlinear dependence inherent in the observed streamflows. The first part of this paper demonstrates the hybrid character of the model through stochastic simulations performed using monthly streamflows of Weber River (Utah) that exhibit a complex dependence structure. In the latter part of the paper the hybrid model is shown to be efficient in simulating multiseason streamflows, through an example of the San Juan River (New Mexico). This model ensures annual-to-monthly consistency without the need for any adjustment procedures. Furthermore, the hybrid model is able to preserve both within-year and cross-year monthly serial correlations for multiple lags. Also, it is seen to be consistent in predicting the reservoir storage (validation) statistic at low as well as high demand levels.
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TL;DR: The modified K-NN approach is found to exhibit better performance in terms of capturing the features present in the data and is compared to both a parametric periodic autoregressive and a nonparametric index sequential method for streamflow generation, each widely used in practice.
Abstract: This paper presents a lag-1 modified K-nearest neighbor K-NN approach for stochastic streamflow simulation. The simula- tion at any time t given the value at the time t1 involves two steps: 1 obtaining the conditional mean from a local polynomial fitted to the historical values of time t and t1, and 2 then resampling i.e., bootstrapping a residual at one of the historical observations and adding it to the conditional mean. The residuals are resampled using a probability metric that gives more weight to the nearest neighbor and less to the farthest. The "residual resampling" step is the modification to the traditional K-NN time-series bootstrap approach, which enables the generation of values not seen in the historical record. This model is applied to monthly streamflow at the Lees Ferry stream gauge on the Colorado River and is compared to both a parametric periodic autoregressive and a nonparametric index sequential method for streamflow generation, each widely used in practice. The modified K-NN approach is found to exhibit better performance in terms of capturing the features present in the data. The need to identify alternatives that will improve upon the ISM motivated the research presented in this paper. The ISM is a "nonparametric" method in that it makes no assumption of the functional form of the underlying model; instead, the method is data-driven. Keeping with the "nonparametric" spirit of ISM, we developed the proposed modified K-nearest neighbor K-NN method. The proposed approach retains all the aspects of the traditional K-NN time series bootstrap technique developed by Lall and Sharma 1996, but the "modification" enables simu- lating values not seen in the historical record. We evaluate the performance of our proposed approach by applying it to the monthly streamflow data from U.S. Geological Survey USGS stream gauge 09380000 located on the Colorado River at Lees Ferry, Arizona. We also compare the modified K-NN method with the ISM and a first-order periodic autoregressive model PAR1, each widely used in practice. The paper is organized as follows: a brief background on stochastic streamflow modeling including a description of the ISM and the PAR models is first presented, for the benefit of readers. Our proposed approach is then presented. A description of the results and summary conclude the presentation.
120 citations
TL;DR: In this article, the authors extended the hybrid approach introduced by the authors for at-site modeling of annual and periodic streamflows in earlier works to simulate multi-site multi-season streamflows.
75 citations
TL;DR: A simple model that employs the k-nearest neighbor resampling algorithm with gamma kernel perturbation (denoted as KGK model), which enables generation of data that are not the same as the historical data.
Abstract: Various parametric and nonparametric models have been suggested in literature for stochastic generation of seasonal streamflows. State-of-the-art nonparametric models are reviewed herein and their drawbacks identified. We developed a simple model that employs the k-nearest neighbor resampling algorithm with gamma kernel perturbation (denoted as KGK model), which enables generation of data that are not the same as the historical data. For preserving the annual variability two approaches are developed. The first one employs the aggregate variable concept (KGKA model), and the second one uses a pilot variable that leads the generation of the seasonal data (KGKP model). The pilot variable refers to the annual data that has been previously generated, but its role is not for disaggregation but rather for conditioning the state that guides the generation of seasonal flows. The proposed models have been compared with a currently available nonparametric model that considers the reproduction of the interannual vari...
62 citations
TL;DR: It was found that critical water-energy synergies and tradeoffs exist, and there is a possibility for integrated water and energy management to achieve better outcomes.
51 citations
TL;DR: Nonlinear deterministic methods are a viable complement to linear stochastic ones for studying river flow dynamics, if sufficient caution is exercised in their applications and in interpreting the outcomes.
Abstract: Whether or not river flow exhibits nonlinear determinism remains an unresolved question. While studies on the use of nonlinear deterministic methods for modeling and prediction of river flow series are on the rise and the outcomes are encouraging, suspicions and criticisms of such studies continue to exist as well. An important reason for this situation is that the correlation dimension method, used as a nonlinear determinism identification tool in most of those studies, may possess certain limitations when applied to real river flow series, which are always finite and often short and also contaminated with noise (e.g. measurement error). In view of this, the present study addresses the issue of nonlinear determinism in river now series using prediction as a possible indicator. This is done by (1) reviewing studies that have employed nonlinear deterministic methods (coupling phase-space reconstruction and local approximation techniques) for river flow predictions and (2) identifying nonlinear determinism (or linear stochasticity) based on the level of prediction accuracy in general, and on the prediction accuracy against the phase-space reconstruction parameters in particular (termed as the 'inverse approach'). The results not only provide possible indications to the presence of nonlinear determinism in the river flow series studied, but also support, both qualitatively and quantitatively, the low correlation dimensions reported for such. Therefore, nonlinear deterministic methods are a viable complement to linear stochastic ones for studying river flow dynamics, if sufficient caution is exercised in their applications and in interpreting the outcomes.
37 citations
References
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Book•
01 Jan 1970
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
Abstract: From the Publisher:
This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.
19,748 citations
01 Jan 1986
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
Abstract: Introduction. Survey of Existing Methods. The Kernel Method for Univariate Data. The Kernel Method for Multivariate Data. Three Important Methods. Density Estimation in Action.
15,499 citations
TL;DR: In this article, the authors discuss the problem of estimating the sampling distribution of a pre-specified random variable R(X, F) on the basis of the observed data x.
Abstract: We discuss the following problem given a random sample X = (X 1, X 2,…, X n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X, F), on the basis of the observed data x. (Standard jackknife theory gives an approximate mean and variance in the case R(X, F) = \(\theta \left( {\hat F} \right) - \theta \left( F \right)\), θ some parameter of interest.) A general method, called the “bootstrap”, is introduced, and shown to work satisfactorily on a variety of estimation problems. The jackknife is shown to be a linear approximation method for the bootstrap. The exposition proceeds by a series of examples: variance of the sample median, error rates in a linear discriminant analysis, ratio estimation, estimating regression parameters, etc.
14,483 citations
TL;DR: This revision of a classic, seminal, and authoritative book explores the building of stochastic models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control.
Abstract: From the Publisher:
This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.
12,650 citations
Book•
28 Oct 1997TL;DR: In this paper, a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis, is given, along with a disk of purpose-written S-Plus programs for implementing the methods described in the text.
Abstract: This book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. Included with the book is a disk of purpose-written S-Plus programs for implementing the methods described in the text. Computer algorithms are clearly described, and computer code is included on a 3-inch, 1.4M disk for use with IBM computers and compatible machines. Users must have the S-Plus computer application. Author resource page: http://statwww.epfl.ch/davison/BMA/
6,420 citations