##### Abstract

Intense floods of short duration are called flash floods. They often occur during intense rainfall in small to moderate sized catchments. The time from the causative event (usually rainfall) to the peak of the runoff can be very short, in the order of a few hours. Such sudden floods can cause significant damage, partly because they are difficult to forecastforecast.

It is usual in hydrology to distinguish between forecasting and predictionprediction of floods. Forecasting aims at estimating the magnitude of the runoff as a response to a certain event in the near future whereas prediction aims at estimating the runoff magnitude as a response to a design event (for instance the 100-year flood), or an event which is associated with a particular exceedence probability. This thesis deals with prediction which means that the goal is to find the design runoff of a flash flood rather than tomorrow's runoff.

which typically have short or no measurement record, and the small data sets makes it difficult to estimate the return period of a flash flood. Instead of using a sparse data set of runoff, a more comprehensive data set of precipitation data may be used to find the return period. The rational formula relates the regional variable

Floods can be predicted on the basis of a flood-frequency analysisflood-frequency analysis. Flood-frequency analysis seeks to estimate the magnitude of peak flow or areal rainfall of a certain return period. It uses independent extreme values to estimate the empirical or theoretical return period. The empiricalreturn period!empirical return period cannot give estimates higher than the length of the measurement record. That is, 32 years of measurements cannot give estimates of the 50-year or 100-year flood. This can be obtained by finding the theoreticalreturn period. This is a curve which is fitted to the inverse of the cumulative distrbution function of peak flow. The quality of the flood frequency analysis depends on the length of the measurement record and a long record is always preferable.

A way to bypass the problem of short data series is to use measurement records from stations nearby by regional flood-frequency analysis. Large catchments usually have a dense observation network and floods in catchments without measurements (ungaged catchments) can be estimated from measurements elsewhere.

This method is not transferrable to smaller catchments, which, for one, often lack measurements and secondly This is not the case in smaller cathments,

where most flash floods occur, because measurements from larger catchments are not representative for smaller ones. A different framework is necessary to predict flash floods.

The lack of runoff data has always been a problem for hydrologists. However, rainfall measurements have been extensively used to lengthen the runoff record. This will also be used in this thesis.

This thesis is a first attempt to develop a model of estimating flash floods by using the derived distribution method, where rainfall data is used instead of the sparse data set of runoff. SKRIV OM?

\paragraphThe rational model

Today, several operational flash flood forecasting models exist (Borga et al. 2007, Blöschl et al. 2008 among others). These spatially distributed hydrological models takes rainfall as input variables and estimate the runoff of a specific rainfall event. As far as we know, no standard prediction models exist which estimates the design runoff of flash floods. This thesis discusses how such a model can be developed by a derived distribution approachderived distribution approach of rainfall and runoff coefficients, which are the two factors in the rational model.

The rational model

Q_m^3/s = CAR,

represents an easy way of modelling rainfall-runoff processes. It states that the hydrograph peak (also called the peak flow)

Q increases with the catchment area A and the maximum catchment areal rainfall intensity \barR,

R. In the equation above, Q is given in m^3/s. It can easily be recalculated to the same dimensions as the rainfall (mm/day) by dividing by the catchment area (in square metres) and including a conversion factor of 86400 seconds/day.

Q = 86400 \cdot Q_m^3/s/A = CR

Streamflow which is given in m^3/s will be called discharge and if it is recalculated to mm/day it will be called runoffrunoff.

Naturally, runoff depends on rainfall , which has spatially stable and uniform statistical parameters,

but it also depends on local catchment characteristics such as the catchment's response to rainfall and antecendent soil moisture conditionsantecedent soil moisture conditions. The runoff coefficient C takes these local effects into account. nevn at den er konstant.

When the rational model was developed in 1851, C was assumed to be constant. Even in more recent works, C is still regarded as a constant. However, this view seems too simple because it assumes that the distribution and thereby the return periodreturn period, is the same for rainfall and runoff: a 50-year flood would only result from a 50-year rainfall. Or viewed differently, all extreme rainfall events would give extreme runoff. In this study, it will rather be assumed that extreme runoff is controlled not only by rainfall, but also by the runoff coefficient. Instead of assuming C constant, it

it is assumed that extreme runoff is dependent on antecedent soil moisture conditions, that is, extreme rainfall will only cause extreme runoff if the catchment is wet as the rainfall event starts. The fact that flood generation depends on antecedent soil moisture conditions has previously been formulated by among others by Beldring 2002, Merz 2009 and Norbiato et al. 2008.

Runoff coefficients should be regarded as a random variable which depends on moisture conditions. C will be regarded as a random variable which depends on moisture conditions.

Here, the groundwater levelgroundwater level will be used as an indicator of antecedent soil moisture conditions.

Before a prediction model can be developed further studies of the runoff coefficient is needed. First of all: is the runoff coefficient constant or a random variable? Secondly: does it depend on gruoundwater levels and is it an indicator which describes the soil moisture conditions sufficiently?

The objective of the study is thus to describe the developmen a model for estimating the peak runoff Q, for flash floods on the basis of areal precipitation R by taking moisture conditions into consideration. Before doing so some assumptions about the runoff coefficient needs to be investigated. The model assumes that the runoff coefficient is a random variable. In order to investigate this the relationship between estreme areal rainfall and runoff needs to be checked. For larger rivers which have longer and denser measurements records, regional flood-frequency analysis is the preferred way of modelling floods. However, in small catchments which lack measurements, regional flood-frequency analysis cannot be performed. Prediction of flash floods can instead be done by the model developed in this thesis.