Can floods in large river basins be predicted from floods observed in small subbasins?

Recent results from the analysis of peak floods observed in nested watersheds have revealed the existence of a scale invariant relationship between peak floods and drainage area at the scale of a single rainfall‐runoff event. The relationship follows the power law E[Qe| A] = α(e)Aθ(e) where E[Qe| A] is the expected value of peak flood at a given drainage area A, α(e) is the intercept, and θ(e) is the exponent for a given rainfall‐runoff event ‘e’. These results also revealed that α(e) and θ(e) change from one rainfall‐runoff event to another. In this article, we show that a log‐linear relationship between α(e) and θ(e) can be used to simplify the problem of predicting α(e) and θ(e) from the physical characteristics of the catchment and rainfall. In particular, we show that α(e) can be predicted from peak floods observed in the smallest gauged subcatchment in the basin and its log‐linear relationship with θ(e) can be used to predict peak flood at any location in the basin. We demonstrate this using observed peak floods from the Iowa River basin in the Upper Midwest part of United States.