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Urban agglomerations exhibit complex emergent features of which Zipf’s law, i.e., a power-law size distribution, and fractality may be regarded as the most prominent ones. We propose a simplistic model for the generation of citylike structures which is solely based on the assumption that growth is more likely to take place close to inhabited space. The model involves one parameter which is an exponent determining how strongly the attraction decays with the distance. In addition, the model is run iteratively so that existing clusters can grow (together) and new ones can emerge. The model is capable of reproducing the size distribution and the fractality of the boundary of the largest cluster. Although the power-law distribution depends on both, the imposed exponent and the iteration, the fractality seems to be independent of the former and only depends on the latter. Analyzing land-cover data, we estimate the parameter-value gamma approximate to 2.5 for Paris and its surroundings. DOI: 10.1103/PhysRevE.87.042114

While sea level rise is one of the most likely consequences of climate change, the provoked costs remain highly uncertain. Based on a block-maxima approach, we provide a stochastic framework to estimate the increase of expected damages with sea level rise as well as with meteorological changes and demonstrate the application to two case studies. In addition, the uncertainty of the damage estimations due to the stochastic nature of extreme events is studied. Starting with the probability distribution of extreme flood levels, we calculate the distribution of implied damages in a specific region employing stage-damage functions. Universal relations of the expected damages and their standard deviation, which demonstrate the importance of the shape of the damage function, are provided. We also calculate how flood protection reduces the damages leading to a more complex picture, where the extreme value behavior plays a fundamental role. Citation: Boettle, M., D. Rybski, and J. P. Kropp (2013), How changing sea level extremes and protection measures alter coastal flood damages, Water Resour. Res., 49, 1199-1210, doi: 10.1002/wrcr.20108.

Analyzing insurance-loss data we derive stochastic storm-damage functions for residential buildings. On district level we fit power-law relations between daily loss and maximum wind speed, typically spanning more than 4 orders of magnitude. The estimated exponents for 439 German districts roughly range from 8 to 12. In addition, we find correlations among the parameters and socio-demographic data, which we employ in a simplified parametrization of the damage function with just 3 independent parameters for each district. A Monte Carlo method is used to generate loss estimates and confidence bounds of daily and annual storm damages in Germany. Our approach reproduces the annual progression of winter storm losses and enables to estimate daily losses over a wide range of magnitudes. Citation: Prahl, B. F., D. Rybski, J. P. Kropp, O. Burghoff, and H. Held (2012), Applying stochastic small-scale damage functions to German winter storms, Geophys. Res. Lett., 39, L06806, doi: 10.1029/2012GL050961.

Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms, and urban growth is one of the most eminent transformative processes. We analyze global land cover data and extract cities as defined by maximally connected urban clusters. The analysis of the city size distribution for all cities on the globe confirms Zipf’s law. Moreover, by investigating the percolation properties of the clustering of urban areas we assess the closeness to criticality for various countries. At the critical thresholds, the urban land cover of the countries undergoes a transition from separated clusters to a gigantic component on the country scale. We study the Zipf-exponents as a function of the closeness to percolation and find a systematic dependence, which could be the reason for deviating exponents reported in the literature. Moreover, we investigate the average size of the clusters as a function of the proximity to percolation and find country specific behavior. By relating the standard deviation and the average of cluster sizes—analogous to Taylor’s law—we suggest an alternative way to identify the percolation transition. We calculate spatial correlations of the urban land cover and find long-range correlations. Finally, by relating the areas of cities with population figures we address the global aspect of the allometry of cities, finding an exponent δ ≈ 0.85, i.e., large cities have lower densities.

Winter storms are the most costly natural hazard for European residential property. We compare four distinct storm damage functions with respect to their forecast accuracy and variability, with particular regard to the most severe winter storms. The analysis focuses on daily loss estimates under differing spatial aggregation, ranging from district to country level. We discuss the broad and heavily skewed distribution of insured losses posing difficulties for both the calibration and the evaluation of damage functions. From theoretical considerations, we provide a synthesis between the frequently discussed cubic wind-damage relationship and recent studies that report much steeper damage functions for European winter storms. The performance of the storm loss models is evaluated for two sources of wind gust data, direct observations by the German Weather Service and ERA-Interim reanalysis data. While the choice of gust data has little impact on the evaluation of German storm loss, spatially resolved coefficients of variation reveal dependence between model and data choice. The comparison shows that the probabilistic models by Heneka et al. (2006) and Prahl et al. (2012) both provide accurate loss predictions for moderate to extreme losses, with generally small coefficients of variation. We favour the latter model in terms of model applicability. Application of the versatile deterministic model by Klawa and Ulbrich (2003) should be restricted to extreme loss, for which it shows the least bias and errors comparable to the probabilistic model by Prahl et al. (2012).

Winter storms are the most costly natural hazard for European residential property. We compare four distinct storm damage functions with respect to their forecast accuracy and variability, with particular regard to the most severe winter storms. The analysis focuses on daily loss estimates under differing spatial aggregation, ranging from district to country level. We discuss the broad and heavily skewed distribution of insured losses posing difficulties for both the calibration and the evaluation of damage functions. From theoretical considerations, we provide a synthesis between the frequently discussed cubic wind–damage relationship and recent studies that report much steeper damage functions for European winter storms. The performance of the storm loss models is evaluated for two sources of wind gust data, direct observations by the German Weather Service and ERA-Interim reanalysis data. While the choice of gust data has little impact on the evaluation of German storm loss, spatially resolved coefficients of variation reveal dependence between model and data choice. The comparison shows that the probabilistic models by Heneka et al. (2006) and Prahl et al. (2012) both provide accurate loss predictions for moderate to extreme losses, with generally small coefficients of variation. We favour the latter model in terms of model applicability. Application of the versatile deterministic model by Klawa and Ulbrich (2003) should be restricted to extreme loss, for which it shows the least bias and errors comparable to the probabilistic model by Prahl et al. (2012).

We perform a systematic study of all cities in Europe to assess the Urban Heat Island (UHI) intensity by means of remotely sensed land surface temperature data. Defining cities as spatial clusters of urban land cover, we investigate the relationships of the UHI intensity, with the cluster size and the temperature of the surroundings. Our results show that in Europe, the UHI intensity in summer has a strong correlation with the cluster size, which can be well fitted by an empirical sigmoid model. Furthermore, we find a novel seasonality of the UHI intensity for individual clusters in the form of hysteresis-like curves. We characterize the shape and identify apparent regional patterns.

Most climate change impacts manifest in the form of natural hazards. Damage assessment typically relies on damage functions that translate the magnitude of extreme events to a quantifiable damage. In practice, the availability of damage functions is limited due to a lack of data sources and a lack of understanding of damage processes. The study of the characteristics of damage functions for different hazards could strengthen the theoretical foundation of damage functions and support their development and validation. Accordingly, we investigate analogies of damage functions for coastal flooding and for wind storms and identify a unified approach. This approach has general applicability for granular portfolios and may also be applied, for example, to heat-related mortality. Moreover, the unification enables the transfer of methodology between hazards and a consistent treatment of uncertainty. This is demonstrated by a sensitivity analysis on the basis of two simple case studies (for coastal flood and storm damage). The analysis reveals the relevance of the various uncertainty sources at varying hazard magnitude and on both the microscale and the macroscale level. Main findings are the dominance of uncertainty from the hazard magnitude and the persistent behaviour of intrinsic uncertainties on both scale levels. Our results shed light on the general role of uncertainties and provide useful insight for the application of the unified approach.

In contrast to recent advances in projecting sea levels, estimations about the economic impact of sea level rise are vague. Nonetheless, they are of great importance for policy making with regard to adaptation and greenhouse-gas mitigation. Since the damage is mainly caused by extreme events, we propose a stochastic framework to estimate the monetary losses from coastal floods in a confined region. For this purpose, we follow a Peak-over-Threshold approach employing a Poisson point process and the Generalised Pareto Distribution. By considering the effect of sea level rise as well as potential adaptation scenarios on the involved parameters, we are able to study the development of the annual damage. An application to the city of Copenhagen shows that a doubling of losses can be expected from a mean sea level increase of only 11 cm. In general, we find that for varying parameters the expected losses can be well approximated by one of three analytical expressions depending on the extreme value parameters. These findings reveal the complex interplay of the involved parameters and allow conclusions of fundamental relevance. For instance, we show that the damage typically increases faster than the sea level rise itself. This in turn can be of great importance for the assessment of sea level rise impacts on the global scale. Our results are accompanied by an assessment of uncertainty, which reflects the stochastic nature of extreme events. While the absolute value of uncertainty about the flood damage increases with rising mean sea levels, we find that it decreases in relation to the expected damage.

Costs of sea dikes
(2017)

Failure to consider the costs of adaptation strategies can be seen by decision makers as a barrier to implementing coastal protection measures. In order to validate adaptation strategies to sea-level rise in the form of coastal protection, a consistent and repeatable assessment of the costs is necessary. This paper significantly extends current knowledge on cost estimates by developing - and implementing using real coastal dike data - probabilistic functions of dike costs. Data from Canada and the Netherlands are analysed and related to published studies from the US, UK, and Vietnam in order to provide a reproducible estimate of typical sea dike costs and their uncertainty. We plot the costs divided by dike length as a function of height and test four different regression models. Our analysis shows that a linear function without intercept is sufficient to model the costs, i.e. fixed costs and higher-order contributions such as that due to the volume of core fill material are less significant. We also characterise the spread around the regression models which represents an uncertainty stemming from factors beyond dike length and height. Drawing an analogy with project cost overruns, we employ log-normal distributions and calculate that the range between 3x and x/3 contains 95% of the data, where x represents the corresponding regression value. We compare our estimates with previously published unit costs for other countries. We note that the unit costs depend not only on the country and land use (urban/non-urban) of the sites where the dikes are being constructed but also on characteristics included in the costs, e.g. property acquisition, utility relocation, and project management. This paper gives decision makers an order of magnitude on the protection costs, which can help to remove potential barriers to develop-ing adaptation strategies. Although the focus of this research is sea dikes, our approach is applicable and transferable to other adaptation measures.