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Statistical distributions of flood peak discharge often show heavy tail behavior, that is, extreme floods are more likely to occur than would be predicted by commonly used distributions that have exponential asymptotic behavior.
This heavy tail behavior may surprise flood managers and citizens, as human intuition tends to expect light tail behavior, and the heaviness of the tails is very difficult to predict, which may lead to unnecessarily high flood damage.
Despite its high importance, the literature on the heavy tail behavior of flood distributions is rather fragmented.
In this review, we provide a coherent overview of the processes causing heavy flood tails and the implications for science and practice.
Specifically, we propose nine hypotheses on the mechanisms causing heavy tails in flood peak distributions related to processes in the atmosphere, the catchment, and the river system.
We then discuss to which extent the current knowledge supports or contradicts these hypotheses.
We also discuss the statistical conditions for the emergence of heavy tail behavior based on derived distribution theory and relate them to the hypotheses and flood generation mechanisms.
We review the degree to which the heaviness of the tails can be predicted from process knowledge and data. Finally, we recommend further research toward testing the hypotheses and improving the prediction of heavy tails.
In some catchments, the distribution of annual maximum streamflow shows heavy tail behavior, meaning the occurrence probability of extreme events is higher than if the upper tail decayed exponentially. Neglecting heavy tail behavior can lead to an underestimation of the likelihood of extreme floods and the associated risk. Partly contradictory results regarding the controls of heavy tail behavior exist in the literature and the knowledge is still very dispersed and limited. To better understand the drivers, we analyze the upper tail behavior and its controls for 480 catchments in Germany and Austria over a period of more than 50 years. The catchments span from quickly reacting mountain catchments to large lowland catchments, allowing for general conclusions. We compile a wide range of event and catchment characteristics and investigate their association with an indicator of the tail heaviness of flood distributions, namely the shape parameter of the GEV distribution. Following univariate analyses of these characteristics, along with an evaluation of different aggregations of event characteristics, multiple linear regression models, as well as random forests, are constructed. A novel slope indicator, which represents the relation between the return period of flood peaks and event characteristics, captures the controls of heavy tails best. Variables describing the catchment response are found to dominate the heavy tail behavior, followed by event precipitation, flood seasonality, and catchment size. The pre-event moisture state in a catchment has no relevant impact on the tail heaviness even though it does influence flood magnitudes.
Stochastic modeling of precipitation for estimation of hydrological extremes is an important element of flood risk assessment and management. The spatially consistent estimation of rainfall fields and their temporal variability remains challenging and is addressed by various stochastic weather generators.
In this study, two types of weather generators are evaluated against observed data and benchmarked regarding their ability to simulate spatio-temporal precipitation fields in the Rhine catchment. A multi-site station-based weather generator uses an auto-regressive model and estimates the spatial correlation structure between stations. Another weather generator is raster-based and uses the nearest-neighbor resampling technique for reshuffling daily patterns while preserving the correlation structure between the observations.
Both weather generators perform well and are comparable at the point (station) scale with regards to daily mean and 99.9th percentile precipitation as well as concerning wet/dry frequencies and transition probabilities. The areal extreme precipitation at the sub-basin scale is however overestimated in the station-based weather generator due to an overestimation of the correlation structure between individual stations. The auto-regressive model tends to generate larger rainfall fields in space for extreme precipitation than observed, particularly in summer. The weather generator based on nearest-neighbor resampling reproduces the observed daily and multiday (5, 10 and 20) extreme events in a similar magnitude. Improvements in performance regarding wet frequencies and transition probabilities are recommended for both models.
Hydrodynamic interactions, i.e. the floodplain storage effects caused by inundations upstream on flood wave propagation, inundation areas, and flood damage downstream, are important but often ignored in large-scale flood risk assessments. Although new methods considering these effects sometimes emerge, they are often limited to a small or meso scale. In this study, we investigate the role of hydrodynamic interactions and floodplain storage on flood hazard and risk in the German part of the Rhine basin. To do so, we compare a new continuous 1D routing scheme within a flood risk model chain to the piece-wise routing scheme, which largely neglects floodplain storage. The results show that floodplain storage is significant, lowers water levels and discharges, and reduces risks by over 50%. Therefore, for accurate risk assessments, a system approach must be adopted, and floodplain storage and hydrodynamic interactions must carefully be considered.
Different upper tail indicators exist to characterize heavy tail phenomena, but no comparative study has been carried out so far. We evaluate the shape parameter (GEV), obesity index, Gini index and upper tail ratio (UTR) against a novel benchmark of tail heaviness - the surprise factor. Sensitivity analyses to sample size and changes in scale-to-location ratio are carried out in bootstrap experiments. The UTR replicates the surprise factor best but is most uncertain and only comparable between records of similar length. For samples with symmetric Lorenz curves, shape parameter, obesity and Gini indices provide consistent indications. For asymmetric Lorenz curves, however, the first two tend to overestimate, whereas Gini index tends to underestimate tail heaviness. We suggest the use of a combination of shape parameter, obesity and Gini index to characterize tail heaviness. These indicators should be supported with calculation of the Lorenz asymmetry coefficients and interpreted with caution.
Large-scale flood risk assessments are crucial for decision making, especially with respect to new flood defense schemes, adaptation planning and estimating insurance premiums. We apply the process-based Regional Flood Model (RFM) to simulate a 5000-year flood event catalog for all major catchments in Germany and derive risk curves based on the losses per economic sector. The RFM uses a continuous process simulation including a multisite, multivariate weather generator, a hydrological model considering heterogeneous catchment processes, a coupled 1D-2D hydrodynamic model considering dike overtopping and hinterland storage, spatially explicit sector-wise exposure data and empirical multi-variable loss models calibrated for Germany. For all components, uncertainties in the data and models are estimated. We estimate the median Expected Annual Damage (EAD) and Value at Risk at 99.5% confidence for Germany to be euro0.529 bn and euro8.865 bn, respectively. The commercial sector dominates by making about 60% of the total risk, followed by the residential sector. The agriculture sector gets affected by small return period floods and only contributes to less than 3% to the total risk. The overall EAD is comparable to other large-scale estimates. However, the estimation of losses for specific return periods is substantially improved. The spatial consistency of the risk estimates avoids the large overestimation of losses for rare events that is common in other large-scale assessments with homogeneous return periods. Thus, the process-based, spatially consistent flood risk assessment by RFM is an important step forward and will serve as a benchmark for future German-wide flood risk assessments.
Flood risk assessments are typically based on scenarios which assume homogeneous return periods of flood peaks throughout the catchment. This assumption is unrealistic for real flood events and may bias risk estimates for specific return periods. We investigate how three assumptions about the spatial dependence affect risk estimates: (i) spatially homogeneous scenarios (complete dependence), (ii) spatially heterogeneous scenarios (modelled dependence) and (iii) spatially heterogeneous but uncorrelated scenarios (complete independence). To this end, the model chain RFM (regional flood model) is applied to the Elbe catchment in Germany, accounting for the spatio-temporal dynamics of all flood generation processes, from the rainfall through catchment and river system processes to damage mechanisms. Different assumptions about the spatial dependence do not influence the expected annual damage (EAD); however, they bias the risk curve, i.e. the cumulative distribution function of damage. The widespread assumption of complete dependence strongly overestimates flood damage of the order of 100% for return periods larger than approximately 200 years. On the other hand, for small and medium floods with return periods smaller than approximately 50 years, damage is underestimated. The overestimation aggravates when risk is estimated for larger areas. This study demonstrates the importance of representing the spatial dependence of flood peaks and damage for risk assessments.
From precipitation to damage
(2018)
Flood risk assessments for large river basins often involve piecing together smaller-scale assessments leading to erroneous risk statements. We describe a coupled model chain for quantifying flood risk at the scale of 100,000 km(2). It consists of a catchment model, a 1D-2D river network model, and a loss model. We introduce the model chain and present two applications. The first application for the Elbe River basin with an area of 66,000 km(2) demonstrates that it is feasible to simulate the complete risk chain for large river basins in a continuous simulation mode with high temporal and spatial resolution. In the second application, RFM is coupled to a multisite weather generator and applied to the Mulde catchment with an area of 6,000 km(2). This approach is able to provide a very long time series of spatially heterogeneous patterns of precipitation, discharge, inundation, and damage. These patterns respect the spatial correlation of the different processes and are suitable to derive large-scale risk estimates. We discuss how the RFM approach can be transferred to the continental scale.
For attributing hydrological changes to anthropogenic climate change, catchment models are driven by climate model output. A widespread approach to bridge the spatial gap between global climate and hydrological catchment models is to use a weather generator conditioned on weather patterns (WPs). This approach assumes that changes in local climate are characterized by between-type changes of patterns. In this study we test this assumption by analyzing a previously developed WP classification for the Rhine basin, which is based on dynamic and thermodynamic variables. We quantify changes in pattern characteristics and associated climatic properties. The amount of between- and within-type changes is investigated by comparing observed trends to trends resulting solely from WP occurrence. To overcome uncertainties in trend detection resulting from the selected time period, all possible periods in 1901-2010 with a minimum length of 31 years are analyzed. Increasing frequency is found for some patterns associated with high precipitation, although the trend sign highly depends on the considered period. Trends and interannual variations of WP frequencies are related to the long-term variability of large-scale circulation modes. Long-term WP internal warming is evident for summer patterns and enhanced warming for spring/autumn patterns since the 1970s. Observed trends in temperature and partly in precipitation are mainly associated with frequency changes of specific WPs, but some amount of within-type changes remains. The classification can be used for downscaling of past changes considering this limitation, but the inclusion of thermodynamic variables into the classification impedes the downscaling of future climate projections.
This study refines the method for calibrating a glacio-hydrological model based on Hydrograph Partitioning Curves (HPCs), and evaluates its value in comparison to multidata set optimization approaches which use glacier mass balance, satellite snow cover images, and discharge. The HPCs are extracted from the observed flow hydrograph using catchment precipitation and temperature gradients. They indicate the periods when the various runoff processes, such as glacier melt or snow melt, dominate the basin hydrograph. The annual cumulative curve of the difference between average daily temperature and melt threshold temperature over the basin, as well as the annual cumulative curve of average daily snowfall on the glacierized areas are used to identify the starting and end dates of snow and glacier ablation periods. Model parameters characterizing different runoff processes are calibrated on different HPCs in a stepwise and iterative way. Results show that the HPC-based method (1) delivers model-internal consistency comparably to the tri-data set calibration method; (2) improves the stability of calibrated parameter values across various calibration periods; and (3) estimates the contributions of runoff components similarly to the tri-data set calibration method. Our findings indicate the potential of the HPC-based approach as an alternative for hydrological model calibration in glacierized basins where other calibration data sets than discharge are often not available or very costly to obtain.