A Study of Scale Effects in Flood Frequency Response

The effects of relative climatic and catchment scales on flood frequency response are studied with the aid of a dimensionless derived flood frequency equation. The dimensionless frequency is developed by applying the method of derived distributions from probability theory to an Instantaneous Unit Hydrograph (IUH) runoff model and a probabilistic areal rainfall model. The derived distribution approach provides a theoretical framework for treating the scale interactions in a systematic way, while the dimensionless formulation makes for a straightforward generalization of the results. The component models in the frequency are characterized by various scales, so that the frequency itself is an implicit function of those scale effects. Catchment/climate interaction works in two notable ways: 1) through the ratio λ* of characteristic storm duration to catchment response time and 2) through the shape of the input areal rainfall intensity distribution as it is affected by the relative correlation and catchment scales, lumped in the dimensionless correlation parameter b *. With regards to catchment scale, these two parameters have opposite effects on frequency skewness. However, in most cases the areal averaging effect is dominant and the net effect shows that flood frequency behavior in small catchments should be flashier and more highly skewed than in large catchments. These same properties are often observed in real data.

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