A distribution function approach to modelling basin sediment yield

Abstract A new approach to basin sediment yield modelling is proposed based on distribution function theory which provides both a plausible description of sediment removal and translation as supply- and transport-limited processes, and a model structure suitable for automatic parameter optimisation by gradient-based procedures. The mathematical description of accumulation of sediment, and its removal by direct runoff, is capable of representing the exhaustion of sediment supplies during a storm event, and the increasing availability of sediment as the inter-storm period lengthens. Translation of water and sediment to the basin outlet is accomplished using a linear convolution integral operation, and an inverse Gaussian probability density function is proposed as a suitable two-parameter form for the instantaneous unit hydrograph. The relation of this distribution to the convection-diffusion equation, and its extension to represent settling out of sediment from suspension, are discussed. An extension of the distribution function model to incorporate a drainage (or baseflow) component is introduced as one means of representing hydrographs with protracted recessions.

[1]  Shōitirō Hayami.  On the Propagation of Flood Waves , 1951 .

[2]  L. Lapidus,et al.  Mathematics of Adsorption in Beds. VI. The Effect of Longitudinal Diffusion in Ion Exchange and Chromatographic Columns , 1952 .

[3]  R. A. Greenkorn,et al.  Dispersion during flow in porous media with bilinear adsorption , 1973 .

[4]  J. Soni.  Unsteady sediment transport law and prediction of aggradation parameters , 1981 .

[5]  J. J. Fried,et al.  Dispersion in Porous Media , 1971 .

[6]  Desmond E. Walling,et al.  The reliability of suspended sediment load data , 1981 .

[7]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[8]  M. Wolman.  Changing needs and opportunities in the sediment field , 1977 .

[9]  A. J. Raudkivi,et al.  Loose Boundary Hydraulics , 2020 .

[10]  Wr White,et al.  MATHEMATICAL SIMULATION OF SEDIMENT MOVEMENT IN STREAMS. , 1981 .

[11]  N. Crawford,et al.  DIGITAL SIMULATION IN HYDROLOGY' STANFORD WATERSHED MODEL 4 , 1966 .

[12]  H. D. Miller,et al.  The Theory Of Stochastic Processes , 1977, The Mathematical Gazette.

[13]  W. Graf.  Hydraulics of Sediment Transport , 1984 .

[14]  R. Moore,et al.  A distribution function approach to rainfall runoff modeling , 1981 .

[15]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1974 .

[16]  P. R. Johnston,et al.  Parameter optimization for watershed models , 1976 .

[17]  J. L. Folks,et al.  The Inverse Gaussian Distribution and its Statistical Application—A Review , 1978 .

[18]  M. Tweedie.  Statistical Properties of Inverse Gaussian Distributions. II , 1957 .