Document Type


Date of Degree

Spring 2015

Degree Name

PhD (Doctor of Philosophy)

Degree In

Civil and Environmental Engineering

First Advisor

Witold F. Krajewski

Second Advisor

Ricardo Mantilla


Key theoretical and empirical results from the past two decades have established that peak discharges exhibit power-law, or scaling, relation with drainage area across multiple scales of time and space. This relationship takes the form Q(A)= $#945;AΘ where Q is peak discharge, A is the drainage area, Θ is the flood scaling exponent, and α is the intercept. Motivated by seminal empirical studies that show that the flood scaling parameters α and Θ change from one rainfall-runoff event to another, this dissertation explores how certain rainfall and catchment physical properties control the flood scaling exponent and intercept at the rainfall-runoff event scale using a combination of extensive numerical simulation experiments and analysis of observational data from the Iowa River basin, Iowa. Results show that Θ generally decreases with increasing values of rainfall intensity, runoff coefficient, and hillslope overland flow velocity, whereas its value generally increases with increasing rainfall duration. Moreover, while the flood scaling intercept is primarily controlled by the excess rainfall intensity, it increases with increasing runoff coefficient and hillslope overland flow velocity. Results also show that the temporal intermittency structure of rainfall has a significant effect on the scaling structure of peak discharges. These results highlight the fact that the flood scaling parameters are able to be estimated from the aforementioned catchment rainfall and physical variables, which can be measured either directly or indirectly using in situ or remote sensing techniques. The dissertation also proposes and demonstrates a new flood forecasting framework that is based on the scaling theory of floods. The results of the study mark a step forward to provide a physically meaningful framework for regionalization of flood frequencies and hence to solve the long standing hydrologic problem of flood prediction in ungauged basins.

Public Abstract

For decades, engineers have been challenged with estimating design floods of a given probability of occurrence, which is required while designing hydraulic structures. The problem is often solved using historical annual maximum peak discharge data obtained from a location upstream of the site of interest. However, as most of the basins in the world are ungauged, there are limited streamflow gauging sites from which the necessary information can be obtained. In the 1960’s, the U.S. Geological Survey came up with a regional flood frequency estimation technique that can be used for flood prediction in ungauged basins. This purely statistical method often uses drainage area alone to predict design floods. Review of the regional equations show that the parameters of the power-law relation between peak discharge and drainage area change from one geographic region to another. Moreover, the regional flood frequency equations established for different regions of the U.S. kept changing every time they are updated to include the latest peak discharge observations. This shows the sensitivity of the method to the length of historical data, which has huge implications to the overall cost of hydraulic structures. The overarching goal of this dissertation is to contribute towards providing a physical foundation for the regional equations by investigating the physical mechanisms that control the scaling invariance of peak discharges with drainage area at the rainfall-runoff event scale. The dissertation also proposes and demonstrates a new flood forecasting framework that is based on the scaling theory of floods.


publicabstract, flood forecasting, flood frequency, Peak discharge, regulated flood frequency, river network, scaling invariance


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Copyright 2015 Tibebu Bekele Ayalew