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Abstract. The derivation of the flood risk maps requires an estimation of maximum inundation extent for a flood with a given return period, e.g. 100 or 500 yr. The results of numerical simulations of flood wave propagation are used to overcome the lack of relevant observations. In practice, deterministic 1-D models are used for that purpose. The solution of a 1-D model depends on the initial and boundary conditions and estimates of model parameters based on the available noisy observations. Therefore, there is a large uncertainty involved in the derivation of flood risk maps using a single realisation of a flow model. Bayesian conditioning based on multiple model simulations can be used to quantify this uncertainty; however, it is too computer-time demanding to be applied in flood risk assessment in practice, without further flow routing model simplifications. We propose robust and feasible methodology for estimating flood risk. In order to decrease the computation times the assumption of a gradually varied flow and the application of a steady state flow routing model is introduced. The aim of this work is an analysis of the influence of those simplifying assumptions and uncertainty of observations and modelling errors on flood inundation mapping and a quantitative comparison with deterministic flood extent maps. Apart from the uncertainty related to the model structure and its parameters, the uncertainty of the estimated flood wave with a specified probability of return period (so-called 1-in-10 yr, or 1-in-100 yr flood) is also taken into account. In order to derive the uncertainty of inundation extent conditioned on the design flood, the probabilities related to the design wave and flow model uncertainties are integrated. In the present paper that integration is done whilst taking into account the dependence of roughness coefficients on discharge. The roughness is parameterised based on maximum annual discharges. This approach allows for the relationship between flood extent and flow values to be derived, thus giving a cumulative assessment of flood risk. The methods are illustrated using the Warsaw reach of the River Vistula as a case study. The results indicate that deterministic and stochastic flood inundation maps cannot be quantitatively compared. We show that the proposed simplified approach to flood risk assessment can be applied even when breaching of the embankment occurs, with the condition that the flooded area is small enough to be filled rapidly.

Flood risk assessment is customarily performed using a design flood. Observed past flows are used to derive a flood frequency curve which forms the basis for a construction of a design flood. The simulation of a distributed model with the 1-in-T year design flood as an input gives information on the possible inundation areas, which are used to derive flood risk maps. The procedure is usually performed in a deterministic fashion, and its extension to take into account the design flood-and flow routing model uncertainties is computer time consuming. In this study we propose a different approach to flood risk assessment which consists of the direct simulation of a distributed flow routing model for an observed series of annual maximum flows and the derivation of maps of probability of inundation of the desired return period directly from the obtained simulations of water levels at the model cross sections through an application of the Flood Level Frequency Analysis. The hydraulic model and water level quantile uncertainties are jointly taken into account in the flood risk uncertainty evaluation using the Generalized Likelihood Uncertainty Estimation (GLUE) approach. An additional advantage of the proposed approach lies in smaller uncertainty of inundation predictions for long return periods compared to the standard approach. The approach is illustrated using a design flood level and a steady-state solution of a hydraulic model to derive maps of inundation probabilities.

The paper addresses the problem of determination of the energy and momentum coefficients for flows through a partly vegetated channel. These coefficients are applied to express the fluid kinetic energy and momentum equations as functions of a mean velocity. The study is based on laboratory measurements of water velocity distributions in a straight rectangular flume with stiff and flexible stems and plastic imitations of the Canadian waterweed. The coefficients were established for the vegetation layer, surface layer and the whole flow area. The results indicate that the energy and momentum coefficients increase significantly with water depth and the number of stems per unit channel area. New regression relationships for both coefficients are given.

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