Linking space–time variability of river runoff and rainfall fields: a dynamic approach

Statistical self-similarity in the spatial and temporal variability of rainfall, river networks, and runoff processes has been observed in many empirical studies. To theoretically investigate the relationships between the various time and space scales of variability in rainfall and runoff process we propose a simplified, yet physically based model of a catchment–rainfall interaction. The channel network is presented as a random binary tree, having topological and hydraulic geometry properties typically observed in real river networks. The continuous rainfall model consists of individual storms separated by dry periods. Each given storm is disaggregated in space and time using the random cascade model. The flow routing is modelled by the network of topologically connected nonlinear reservoirs, each representing a link in the channel network. Running the model for many years of synthetic rainfall time series and a continuous water balance model we generate an output, in the form of continuous time series of water discharge in all links in the channel network. The main subject of study is the annual peak flow as a function of catchment area and various characteristics of rainfall. The model enables us to identify different physical processes responsible for the empirically observed scaling properties of peak flows.

[1]  M. Sivapalan,et al.  A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy and entropy, and the second law of thermodynamics , 1998 .

[2]  Murugesu Sivapalan,et al.  Application of the meta‐channel concept: Construction of the meta‐channel hydraulic geometry for a natural catchment , 1995 .

[3]  Garrison Sposito,et al.  Scale Dependence and Scale Invariance in Hydrology , 1998 .

[4]  Tests of peak flow scaling in simulated self-similar river networks , 2001 .

[5]  B. Bobée,et al.  Two kinds of moment ratio diagrams and their applications in hydrology , 1993 .

[6]  Merab Menabde.  Bounded lognormal cascades as quasi-multiaffine random processes , 1998 .

[7]  Oscar J. Mesa,et al.  Multiscaling theory of flood peaks: Regional quantile analysis , 1994 .

[8]  J. Hosking.  L‐Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics , 1990 .

[9]  B. Mandelbrot,et al.  Directed recursion models for fractal growth , 1989 .

[10]  Merab Menabde,et al.  Multiscaling properties of rainfall and bounded random cascades , 1997 .

[11]  A. Rinaldo,et al.  Fractal River Basins , 2001 .

[12]  Merab Menabde,et al.  A simple scaling model for extreme rainfall , 1999 .

[13]  J. Smith,et al.  Representation of basin scale in flood peak distributions , 1992 .

[14]  L. B. Leopold,et al.  The hydraulic geometry of stream channels and some physiographic implications , 1953 .

[15]  W. H. Kirby,et al.  Summary of flood-frequency analysis in the United States , 1987 .

[16]  R. Srikanthan,et al.  A space and time model for design storm rainfall , 1999 .

[17]  Murugesu Sivapalan,et al.  Temporal scales and hydrological regimes: Implications for flood frequency scaling , 1997 .

[18]  Renzo Rosso,et al.  Scaling and muitiscaling models of depth-duration-frequency curves for storm precipitation , 1996 .

[19]  M. Gordon Wolman,et al.  Fluvial Processes in Geomorphology , 1965 .

[20]  Murugesu Sivapalan,et al.  An investigation into the physical causes of scaling and heterogeneity of regional flood frequency , 1997 .

[21]  Merab Menabde,et al.  Multiaffine random field model of rainfall , 1999 .

[22]  Murugesu Sivapalan,et al.  Modeling of rainfall time series and extremes using bounded random cascades and levy‐stable distributions , 2000 .

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

[24]  Bernard Bobée,et al.  Towards a systematic approach to comparing distributions used in flood frequency analysis , 1993 .

[25]  V. Gupta,et al.  Scale Dependence and Scale Invariance in Hydrology: Spatial Variability and Scale Invariance in Hydrologic Regionalization , 1998 .

[26]  P. S. Eagleson.  Dynamics of flood frequency , 1972 .

[27]  Thomas M. Over,et al.  On scaling exponents of spatial peak flows from rainfall and river network geometry , 1996 .