Abstract :
The physical processes governing floods in river basins are highly variable in space and time. Spatial variability produces a very large number of values of the parameters governing production of runoff from hills and its transport through channels. Most of these parameters cannot be measured, and the number of different values that they can take increases with spatial scale. By contrast the aggregated behavior of peak flows exhibits statistical scale invariance at successively larger spatial scales. Statistical scaling is an emergent property of a complex physical system, which is not built into the physical equations. The slopes and the intercepts of log–log linear relationships describing scale invariance are called ‘scaling parameters’, which can be estimated empirically. Scaling theory provides a new mathematical framework for interpreting empirical scaling parameters in terms of numerical and analytical solutions of physical equations and thereby testing different hypotheses. We illustrate this central idea using three flood-scaling parameters that have been estimated from two experimental basins in the United States, Walnut Gulch, AZ, and Goodwin Creek, MS. Scaling theory unifies spatial scaling flood statistics with physical processes, which has been a long-standing, fundamental open hydrology problem. The scaling framework provides the scientific foundations for solving the global problem of prediction of floods from ungauged and poorly gauged basins.
