Advances in shot noise modeling of daily streamflows

Abstract Univariate shot noise models for streamflow generation at short time scales are examined in detail, to reconsider the verification of the basic hypotheses behind the models, the problem of objectively evaluating their performances, and the importance of model parsimony. The classical approach to model estimation is shown to produce some inconsistencies in the inverse evaluation of the model input, in particular regarding the assumed independence and Poissonianity of the pulses; an alternative procedure for pulses identification is proposed, which enables the mentioned hypotheses to be respected. To evaluate model performances, two indices are proposed, respectively based on the comparison of real and generated flow duration curves (I1) and annual maxima statistics (I2). A method for explicitly accounting for the dependence of I1 and I2 on the number of model parameters is described. An application to seven daily streamflow time series in northern Italy demonstrates the validity of the proposed procedure for the identification of the input and the usefulness of the performance indices in discerning among competing models.

[1]  Zongxue Xu,et al.  Chain-dependent Markov correlation pulse model for daily streamflow generation , 2001 .

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

[3]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[4]  N. T. Kottegoda,et al.  Stochastic Modelling of Riverflow Time Series , 1977 .

[5]  A. Schumann,et al.  A conceptually based stochastic point process model for daily stream‐flow generation , 2002 .

[6]  Francesco Laio,et al.  Can continuous streamflow data support flood frequency analysis? An alternative to the partial duration series approach , 2003 .

[8]  Geoffrey G. S. Pegram,et al.  A continuous streamflow model , 1980 .

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

[10]  Jonathan R. M. Hosking,et al.  Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series , 1996 .

[11]  H. T. Mitosek.  On stochastic properties of daily river flow processes , 2000 .

[12]  P. Claps,et al.  Conceptually-based shot noise modeling of streamflows at short time interval , 1997 .

[13]  Jery R. Stedinger,et al.  The value of stochastic streamflow models in overyear reservoir design applications , 1988 .

[14]  Sheng Yue,et al.  The Gumbel logistic model for representing a multivariate storm event , 2000 .

[15]  H. Aksoy,et al.  A model for daily flows of intermittent streams , 2000 .

[16]  Gideon Weiss,et al.  Shot noise models for the generation of synthetic streamflow data , 1977 .

[17]  M. Kendall,et al.  The Advanced Theory of Statistics, Vol. 1: Distribution Theory , 1959 .

[18]  P. Cowpertwait,et al.  A Neyman-Scott shot noise model for the generation of daily streamflow time series , 1992 .

[19]  C. Cunnane,et al.  A note on the Poisson assumption in partial duration series models , 1979 .

[20]  S. Yue,et al.  A stochastic model for deriving the basic statistics of J‐day averaged streamflow , 1999 .

[21]  M. Parlange,et al.  Statistics of extremes in hydrology , 2002 .

[22]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[23]  Michael Bruen,et al.  An efficient and robust method for estimating unit hydrograph ordinates , 1984 .

[24]  M. Kendall,et al.  The Advanced Theory of Statistics: Volume 1, Distribution Theory , 1978 .

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

[26]  Vujica Yevjevich,et al.  Stochastic processes in hydrology , 1972 .

[27]  harald Cramer,et al.  Stationary And Related Stochastic Processes , 1967 .

[28]  H. Aksoy.  Pulse generation models for daily intermittent streamflows , 2004 .

[29]  Hafzullah Aksoy,et al.  Markov chain-based modeling techniques for stochastic generation of daily intermittent streamflows , 2003 .

[30]  Erich J. Plate,et al.  A STOCHASTIC MODEL FOR THE SIMULATION OF DAILY FLOWS / Modèle stochastique pour la simulation des débits journaliers , 1977 .

[31]  W. H. Van Der Molen,et al.  Advances in theoretical hydrology , 1993 .

[32]  Comparison of non-Gaussian multicomponent and periodic autoregressive models for river flow , 1992 .

[33]  R. Sneyers,et al.  Inventaire des modeles de processus stochastiques applicables a la description des debits journaliers des rivieres , 1970 .

[34]  H. Aksoy.  Pulse generation models for daily intermittent streamflows / Modèles de génération d’impulsions pour des débits journaliers intermittents , 2004 .

[35]  A non‐Gaussian multicomponent model for river flow , 1989 .