Post-blackening approach for modeling dependent annual streamflows

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.

[1]  Hikmet Kerem Cigizoglu,et al.  Application of Gamma Autoregressive Model to Analysis of Dry Periods , 1998 .

[2]  D. Freedman,et al.  Bootstrapping a Regression Equation: Some Empirical Results , 1984 .

[3]  A. I. McLeod,et al.  Preservation of the rescaled adjusted range: 2. Simulation studies using Box‐Jenkins Models , 1978 .

[4]  Kil Seong Lee,et al.  An Approach for Frequency Analysis of Multiyear Drought Durations , 1986 .

[5]  Paul Dunne,et al.  Bootstrap Position Analysis for Forecasting Low Flow Frequency , 1997 .

[6]  Mario V. F. Pereira,et al.  Stochastic Streamflow Models for Hydroelectric Systems , 1984 .

[7]  Warren A. Hall,et al.  A Comparative Study of Critical Drought Simulation , 1971 .

[8]  N. Matalas.  Mathematical assessment of synthetic hydrology , 1967 .

[9]  Regina Y. Liu.  Moving blocks jackknife and bootstrap capture weak dependence , 1992 .

[10]  J. Stedinger,et al.  Water resource systems planning and analysis , 1981 .

[11]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

[12]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[13]  Upmanu Lall,et al.  Streamflow simulation: A nonparametric approach , 1997 .

[14]  P. Hall,et al.  On blocking rules for the bootstrap with dependent data , 1995 .

[15]  Jery R. Stedinger,et al.  A representation of spatial cross correlations in large stochastic seasonal streamflow models , 1988 .

[16]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[17]  D. Freedman.  On Bootstrapping Two-Stage Least-Squares Estimates in Stationary Linear Models , 1984 .

[18]  David R. Maidment,et al.  Handbook of Hydrology , 1993 .

[19]  Zekai Sen,et al.  Statistical Analysis of Hydrologic Critical Droughts , 1980 .

[20]  Z. Şen.  The theory of runs with applications to drought prediction — comment , 1989 .

[21]  On the application of the Bootstrap to assess the risk of deficient annual inflows to a reservoir , 1988 .

[22]  Soumendra N. Lahiri,et al.  On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models , 1996 .

[23]  Z. Şen.  Run-sums of annual flow series , 1977 .

[24]  D. W. Scott,et al.  Multivariate Density Estimation, Theory, Practice and Visualization , 1992 .

[25]  Hans R. Künsch,et al.  Second-order correctness of the blockwise bootstrap for stationary observations , 1996 .

[26]  Jose D. Salas,et al.  ARMA Model identification of hydrologic time series , 1982 .

[27]  Dennis P. Lettenmaier,et al.  Operational assessment of hydrologic models of long-term persistence , 1977 .

[28]  W. Härdle,et al.  Bootstrapping in Nonparametric Regression: Local Adaptive Smoothing and Confidence Bands , 1988 .

[29]  Z. Şen.  On the probability of the longest run length in an independent series , 1991 .

[30]  J. Stedinger,et al.  Multisite ARMA(1,1) and Disaggregation Models for Annual Streamflow Generation , 1985 .

[31]  Estimating correlations in multivariate streamflow models , 1981 .

[32]  H. Künsch.  The Jackknife and the Bootstrap for General Stationary Observations , 1989 .

[33]  A. I. McLeod,et al.  Advances in Box-Jenkins modeling: 1. Model construction , 1977 .

[34]  Thomas A. McMahon,et al.  River and Reservoir Yield , 1987 .

[35]  Upmanu Lall,et al.  A Nearest Neighbor Bootstrap For Resampling Hydrologic Time Series , 1996 .

[36]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[37]  David G. Tarboton,et al.  Kernel bandwidth selection for a first order nonparametric streamflow simulation model , 1998 .

[38]  I. Rodríguez‐Iturbe,et al.  Random Functions and Hydrology , 1984 .

[39]  Gary D. Tasker,et al.  A COMPARISON OF METHODS FOR ESTIMATING LOW FLOW CHARACTERISTICS OF STREAMS , 1987 .

[40]  A. Pewsey.  Exploring the Limits of Bootstrap , 1994 .

[41]  D. Helsel,et al.  Statistical methods in water resources , 2020, Techniques and Methods.

[42]  Analysis of surplus- and deficit-using runs , 1981 .

[43]  W. Zucchini,et al.  Bootstrap confidence intervals for design storms from exceedance series , 1989 .

[44]  Keith W. Hipel,et al.  Advances in Box‐Jenkins modeling: 2. Applications , 1977 .

[45]  Upmanu Lall,et al.  Recent advances in nonparametric function estimation: Hydrologic applications , 1995 .

[46]  R. Vogel,et al.  The moving blocks bootstrap versus parametric time series models , 1996 .

[47]  E. Carlstein.  The Use of Subseries Values for Estimating the Variance of a General Statistic from a Stationary Sequence , 1986 .

[48]  Joseph P. Romano,et al.  Bootstrap technology and applications , 1992 .

[49]  A. Bose.  Edgeworth correction by bootstrap in autoregressions , 1988 .

[50]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[51]  D. G. Watts,et al.  Application of Linear Random Models to Four Annual Streamflow Series , 1970 .

[52]  S. Lahiri.  On the moving block bootstrap under long range dependence , 1993 .

[53]  David G. Tarboton,et al.  Disaggregation procedures for stochastic hydrology based on nonparametric density estimation , 1998 .

[54]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[55]  Marshall E. Moss,et al.  An intercomparison of hydrological network-design technologies , 1991 .

[56]  Peter Hall.  Resampling a coverage pattern , 1985 .

[57]  Zekai Sen,et al.  Wet and Dry Periods of Annual Flow Series , 1976 .

[58]  Z. Sen,et al.  Critical drought analysis by second-order Markov chain. , 1990 .

[59]  S. N. Lahiri,et al.  On the Asymptotic Behaviour of the Moving Block Bootstrap for Normalized Sums of Heavy-Tail Random Variables , 1995 .

[60]  S. T. Buckland,et al.  Computer Intensive Statistical Methods: Validation, Model Selection, and Bootstrap , 1993 .

[61]  David G. Tarboton,et al.  A Nonparametric Wet/Dry Spell Model for Resampling Daily Precipitation , 1996 .

[62]  Jery R. Stedinger,et al.  Synthetic streamflow generation: 1. Model verification and validation , 1982 .

[63]  Kai Wu,et al.  Fitting Annual Floods with Zero-Flows , 1989 .

[64]  J. Bendat,et al.  Random Data: Analysis and Measurement Procedures , 1971 .

[65]  Z. Şen.  Autorun model for synthetic flow generation , 1985 .