Bayesian modeling of hydrographs

[1] This article presents a new approach to model yearly hydrographs with daily or weekly streamflow measurements. The method considers yearly hydrographs as a sample of functions to be modeled nonparametrically in a Bayesian setting. The functional data analysis framework provides great flexibility to reproduce the features of yearly hydrographs, while the Bayesian probabilistic model ensures statistical coherence between the flood variables and the shapes of flood events. The proposed methodology is applied to two samples of hydrographs from two watersheds in the province of Quebec.

[1]  W. L. Lane,et al.  Applied Modeling of Hydrologic Time Series , 1997 .

[2]  Franklin F. Snyder,et al.  Synthetic unit‐graphs , 1938 .

[3]  T. Gasser,et al.  Convergence and consistency results for self-modeling nonlinear regression , 1988 .

[4]  J. Friedman,et al.  FLEXIBLE PARSIMONIOUS SMOOTHING AND ADDITIVE MODELING , 1989 .

[5]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[6]  Adrian F. M. Smith,et al.  Automatic Bayesian curve fitting , 1998 .

[7]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[8]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[9]  L. Joseph,et al.  Bayesian Statistics: An Introduction , 1989 .

[10]  T. Gasser,et al.  Statistical Tools to Analyze Data Representing a Sample of Curves , 1992 .

[11]  C. Robert The Bayesian choice : a decision-theoretic motivation , 1996 .

[12]  Michel Lang,et al.  Development of regional flood-duration–frequency curves based on the index-flood method , 2002 .

[13]  A. V. Vecchia,et al.  Aggregation and Estimation for Low-Order Periodic ARMA Models , 1983 .

[14]  Jose D. Salas,et al.  Shifting level modelling of hydrologic series , 1980 .

[15]  J. Ramsay Monotone Regression Splines in Action , 1988 .

[16]  Jose D. Salas,et al.  Estimation and validation of contemporaneous PARMA Models for streamflow simulation , 1996 .

[17]  Taha B. M. J. Ouarda,et al.  The Gumbel mixed model for flood frequency analysis , 1999 .

[18]  J. O. Ramsay,et al.  Functional Data Analysis (Springer Series in Statistics) , 1997 .

[19]  Xuming He,et al.  Monotone B-Spline Smoothing , 1998 .

[20]  L. K. Sherman Streamflow from rainfall by the unit-graph method , 1932 .

[21]  J. Dooge A general theory of the unit hydrograph , 1959 .

[22]  Jose D. Salas,et al.  Estimation of ARMA Models with seasonal parameters , 1982 .

[23]  Unit hydrographs to model quick and slow runoff components of streamflow , 2000 .

[24]  Taha B. M. J. Ouarda,et al.  Approach for Describing Statistical Properties of Flood Hydrograph , 2002 .

[25]  Young K. Truong,et al.  Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture , 1997 .

[26]  Charles E. Heckler,et al.  Applied Multivariate Statistical Analysis , 2005, Technometrics.

[27]  Young K. Truong,et al.  Polynomial splines and their tensor products in extended linearmodeling , 1997 .

[28]  R. Ogden,et al.  Essential Wavelets for Statistical Applications and Data Analysis , 1996 .