When planning flood protection, agencies are confronted with uncertainty in the design flood magnitude. In particular, the required capacity may increase in the future and render the protection insufficient. This problem can be adressed by applying a safety factor to the design capacity. We propose a Bayesian quantitative sequential decision model that identifies a cost-optimal safety factor in the face of uncertainty. It takes into account the flexibility of the protection system, that is, how costly it is to adjust. We focus on the description of the decision model and on the concept of flexibility, investigating only the effect of uncertainty from the historic flood record. Extension to other types of uncertainty is possible. The model is implemented for a catchment in Germany. Various degrees of uncertainty are investigated by using different lengths of historic records. The optimal safety factor decreases with decreasing uncertainty and with increasing system flexibility. K E Y W O R D SBayesian decision analysis, decision support under uncertainty, flexible protection strategies, flood protection, natural hazards, safety factor, uncertainty quantification

Abstract. Technical flood protection is a necessary part of integrated strategies to protect riverine settlements from extreme floods. Many technical flood protection measures, such as dikes and protection walls, are costly to adapt after their initial construction. This poses a challenge to decision makers as there is large uncertainty in how the required protection level will change during the measure lifetime, which is typically many decades long. Flood protection requirements should account for multiple future uncertain factors: socioeconomic, e.g., whether the population and with it the damage potential grows or falls; technological, e.g., possible advancements in flood protection; and climatic, e.g., whether extreme discharge will become more frequent or not. This paper focuses on climatic uncertainty. Specifically, we devise methodology to account for uncertainty associated with the use of discharge projections, ultimately leading to planning implications. For planning purposes, we categorize uncertainties as either “visible”, if they can be quantified from available catchment data, or “hidden”, if they cannot be quantified from catchment data and must be estimated, e.g., from the literature. It is vital to consider the “hidden uncertainty”, since in practical applications only a limited amount of information (e.g., a finite projection ensemble) is available. We use a Bayesian approach to quantify the “visible uncertainties” and combine them with an estimate of the hidden uncertainties to learn a joint probability distribution of the parameters of extreme discharge. The methodology is integrated into an optimization framework and applied to a pre-alpine case study to give a quantitative, cost-optimal recommendation on the required amount of flood protection. The results show that hidden uncertainty ought to be considered in planning, but the larger the uncertainty already present, the smaller the impact of adding more. The recommended planning is robust to moderate changes in uncertainty as well as in trend. In contrast, planning without consideration of bias and dependencies in and between uncertainty components leads to strongly suboptimal planning recommendations.

The dissipation of potential energy of multiply charged Ar ions incident on Cu has been studied by complementary electron spectroscopy and calorimetry at charge states between 2 and 10 and kinetic energies between 100 eV and 1 keV. The emitted and deposited fractions of potential energy increase at increasing charge state, showing a significant jump for charge states q > 8 due to the presence of L-shell vacancies in the ion. Both fractions balance the total potential energy, thus rendering former hypotheses of a significant deficit of potential energy obsolete. The experimental data are reproduced by computer simulations based on the extended dynamic classical-over-the-barrier model.

Technical flood protection is a necessary part of integrated strategies to protect riverine settlements from extreme floods. Many technical flood protection measures, such as dikes and protection walls, are costly to adapt after their initial construction. This poses a challenge to decision makers as there is large uncertainty in how the required protection level will change during the measure life time, which is typically many decades long. Flood protection requirements should account for multiple future 10 uncertain factors: socio-economic, e.g. whether the population and with it the damage potential grows or falls; technological, e.g. possible advancements in flood protection; and climatic, e.g. whether extreme discharge will become more frequent or not. We focus here on the planning implications of the uncertainty in extreme discharge. We account for the sequential nature of the decision process, in which the adequacy of the protection is regularly revised in the future based on the discharges that have been observed by that point and that reduce uncertainty. For planning purposes, we categorize uncertainties as either 15 'visible', if they can be quantified from available catchment data, or 'hidden', if they cannot be quantified from catchment data and must be estimated, e.g. from literature. It is vital to consider the hidden uncertainty, since in practical applications only a limited amount of information (e.g. through projections, historic record) is available. We use a Bayesian approach to quantify the visible uncertainties and combine them with an estimate of the hidden uncertainties to learn a joint probability distribution of the parameters of extreme discharge. The methodology is integrated into an optimization framework and applied to a pre-20 alpine case study to give a quantitative, cost-optimal recommendation on the required amount of flood protection.

Abstract. Planning authorities are faced with a range of questions when planning flood protection measures: is the existing protection adequate for current and future demands or should it be extended? How will flood patterns change in the future? How should the uncertainty pertaining to this influence the planning decision, e.g., for delaying planning or including a safety margin? Is it sufficient to follow a protection criterion (e.g., to protect from the 100-year flood) or should the planning be conducted in a risk-based way? How important is it for flood protection planning to accurately estimate flood frequency (changes), costs and damage? These are questions that we address for a medium-sized pre-alpine catchment in southern Germany, using a sequential Bayesian decision making framework that quantitatively addresses the full spectrum of uncertainty. We evaluate different flood protection systems considered by local agencies in a test study catchment. Despite large uncertainties in damage, cost and climate, the recommendation is robust for the most conservative approach. This demonstrates the feasibility of making robust decisions under large uncertainty. Furthermore, by comparison to a previous study, it highlights the benefits of risk-based planning over the planning of flood protection to a prescribed return period.

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