The post-blackening (PB) approach introduced by the authors for modeling annual streamflows in an earlier work is extended to model periodic streamflows. This is basically a semi-parametric approach that blends a simple low-order, linear periodic parametric model with the moving block resampling scheme. The first part of the paper demonstrates the hybrid character of the PB model through Monte-Carlo simulations performed on hypothetical data sets drawn from a known population. Following this, the PB model is used for stochastic simulation of periodic streamflows of Beaver and Weber rivers in the US. The results show that the PB model is more consistent in reproducing a wide variety of statistics of periodic streamflows, compared to low-order linear periodic parametric models (Box-Jenkins type) and the periodic k-nearest-neighbor bootstrap (nonparametric) method. In addition, the PB model is able to preserve cross-year serial correlations as well as the month-to-year cross-correlations. This hybrid approach seems to offer considerable scope for improvement in hydrologic time series modeling.

Kasthrirengan Srinivasan

Hydrology

Model

Monte Carlo simulation

RIVER WATER

United States

water flow

Computational fluid dynamics

Computer simulation

Mathematical models

Monte Carlo methods

POST-BLACKENING (PB) APPROACH

Stream flow

ANNULAR FLOW

flow modeling

streamflow

annual variation

Monte Carlo analysis

CASTOR FIBER

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Post-blackening approach for modeling periodic streamflows

Journal of Hydrology

A novel simulation-optimization framework is proposed that enables the automation of the hybrid stochastic modeling process for synthetic generation of multi-season streamflows. This framework aims to minimize the drudgery, judgment and subjectivity involved in the selection of the most appropriate hybrid stochastic model. It consists of a multi-objective optimization model as the driver and the hybrid multi-season stochastic streamflow generation model, hybrid matched block boostrap (HMABB) as the simulation engine. For the estimation of the hybrid model parameters, the proposed framework employs objective functions that aim to minimize the overall errors in the preservation of storage capacities at various demand levels, unlike the traditional approaches that are simulation based. Moreover this framework yields a number of competent hybrid stochastic models in a single run of the simulation-optimization framework. The efficacy of the proposed simulation-optimization framework is brought out through application to two monthly streamflow data sets from USA of varying sample sizes that exhibit multi-modality and a complex dependence structure. The results show that the hybrid models obtained from the proposed framework are able to preserve the statistical characteristics as well as the storage characteristics better than the simulation based HMABB model, while minimizing the manual effort and the subjectivity involved in the modeling process. The proposed framework can be easily extended to model multi-site multi-season streamflow data. © 2011 Elsevier B.V.

Simulation-optimization framework for multi-season hybrid stochastic models

A hybrid model that blends two non-linear data-driven models, i.e. an artificial neural network (ANN) and a moving block bootstrap (MBB), is proposed for modelling annual streamflows of rivers that exhibit complex dependence. In the proposed model, the annual streamflows are modelled initially using a radial basis function ANN model. The residuals extracted from the neural network model are resampled using the non-parametric resampling technique MBB to obtain innovations, which are then added back to the ANN-modelled flows to generate synthetic replicates. The model has been applied to three annual streamflow records with variable record length, selected from different geographic regions, namely Africa, USA and former USSR. The performance of the proposed ANN-based non-linear hybrid model has been compared with that of the linear parametric hybrid model. The results from the case studies indicate that the proposed ANN-based hybrid model (ANNHM) is able to reproduce the skewness present in the streamflows better compared to the linear parametric-based hybrid model (LPHM), owing to the effective capturing of the non-linearities. Moreover, the ANNHM, being a completely data-driven model, reproduces the features of the marginal distribution more closely than the LPHM, but offers less smoothing and no extrapolation value. It is observed that even though the preservation of the linear dependence structure by the ANNHM is inferior to the LPHM, the effective blending of the two non-linear models helps the ANNHM to predict the drought and the storage characteristics efficiently. Copyright © 2007 John Wiley & Sons, Ltd.

Hydrological Processes

A nonlinear data-driven model for synthetic generation of annual streamflows

A new hybrid model is proposed for stochastic simulation of multiseason streamflows, as an improvement over the hybrid moving block bootstrap (HMBB) model introduced by the authors in an earlier work. In the proposed model, periodic streamflows are partially pre-whitened using a parsimonious linear periodic autoregressive/autoregressive moving average model and residuals are extracted. The nonoverlapping within-year blocks formed from the residuals are conditionally resampled using the matched-block bootstrap (MABB) to obtain innovations, which are then post-blackened to generate synthetic replicates. The use of MABB for resampling the residuals, in lieu of moving block bootstrap (that was used in the HMBB model), has resulted in improved simulation of streamflows. The effectiveness of the proposed model in reproducing a wide variety of statistical attributes (including strong dependence structure) is demonstrated through Monte-Carlo simulations on both hypothetical and real data sets. Through application to streamflows of the Weber river, USA, the proposed model is shown to be more efficient in predicting reservoir storage capacity and in preserving storage based performance statistics and critical run characteristics compared to low-order linear periodic parametric models (Box-Jenkins type) and the HMBB model. This model offers enough flexibility and is a viable alternative to the conventional models when hydrologic sequence exhibits strong dependence and if the presence of nonlinearity and/or multimodality is suspected in the underlying hydrologic process. However, the proposed hybrid model may not be appropriate, if long-term dependence is significant in the hydrologic data. © 2006 Elsevier B.V. All rights reserved.

Hybrid matched-block bootstrap for stochastic simulation of multiseason streamflows

The Hybrid approach introduced by the authors for at-site modeling of annual and periodic streamflows in earlier works is extended to simulate multi-site multi-season streamflows. It bears significance in integrated river basin planning studies. This hybrid model involves: (i) partial pre-whitening of standardized multi-season streamflows at each site using a parsimonious linear periodic model; (ii) contemporaneous resampling of the resulting residuals with an appropriate block size, using moving block bootstrap (non-parametric, NP) technique; and (iii) post-blackening the bootstrapped innovation series at each site, by adding the corresponding parametric model component for the site, to obtain generated streamflows at each of the sites. It gains significantly by effectively utilizing the merits of both parametric and NP models. It is able to reproduce various statistics, including the dependence relationships at both spatial and temporal levels without using any normalizing transformations and/or adjustment procedures. The potential of the hybrid model in reproducing a wide variety of statistics including the run characteristics, is demonstrated through an application for multi-site streamflow generation in the Upper Cauvery river basin, Southern India. © 2004 Elsevier B.V. All rights reserved.

Hybrid moving block bootstrap for stochastic simulation of multi-site multi-season streamflows

A nonparametric method for resampling multiseason hydrologic time series is presented. It is based on the idea of rank matching, for simulating univariate time series with strong and/or long-range dependence. The rank matching rule suggests concatenating with higher likelihood those blocks that match at their ends. In the proposed method, termed 'multiseason matched block bootstrap', nonoverlapping within-year blocks of hydrologic data (formed from the observed time series) are conditionally resampled using the rank matching rule. The effectiveness of the method in recovering various statistical attributes, including the dependence structure from finite samples generated from a known population, is demonstrated through a two-level hypothetical Monte Carlo simulation experiment. The method offers enough flexibility to the modeller and is shown to be appropriate for modelling hydrologic data that display strong dependence, nonlinearity and/or multimodality in the time series depicting the hydrologic process. The method is shown to be more efficient than the nonparametric 'k-nearest neighbor bootstrap' method in simulating the monthly streamflows that exhibit a complex dependence structure and bimodal marginal probability density. Even with short block sizes, this bootstrap method is able to predict the drought characteristics reasonably accurately. Copyright © 2005 John Wiley & Sons, Ltd.

Matched block bootstrap for resampling multiseason hydrologic time series

The post-blackening (PB) approach is introduced for modeling annual streamflows that exhibit significant dependence. This is a hybrid approach that blends a simple low-order, linear parametric model with the moving block resampling scheme. Empirical simulations performed using known hypothetical nonlinear parametric models, show that the hybrid model gains significantly by utilizing the merits of both the parametric model and the moving block resampling scheme (nonparametric). Following this, the performance of the PB model is tested with four annual streamflow records with complex dependence, drawn from different parts of the world. The results from these examples show that the PB approach exhibits a better performance in terms of preservation of summary statistics, dependence structure, marginal distribution, and drought characteristics of historical streamflows, compared to low-order linear parametric models and model based resampling schemes (nonparametric model). Furthermore, it offers flexibility to the modeler and is also simple to implement on a personal computer. This hybrid approach seems to offer considerable scope for improvement in hydrologic time series modeling and its applications to water resources planning. (C) 2000 Elsevier Science B.V.

Journal	Journal of Hydrology
ISSN	00221694
Open Access	No