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Today, more than half of the world’s population lives in urban areas. With a high density of population and assets, urban areas are not only the economic, cultural and social hubs of every society, they are also highly susceptible to natural disasters. As a consequence of rising sea levels and an expected increase in extreme weather events caused by a changing climate in combination with growing cities, flooding is an increasing threat to many urban agglomerations around the globe.
To mitigate the destructive consequences of flooding, appropriate risk management and adaptation strategies are required. So far, flood risk management in urban areas is almost exclusively focused on managing river and coastal flooding. Often overlooked is the risk from small-scale rainfall-triggered flooding, where the rainfall intensity of rainstorms exceeds the capacity of urban drainage systems, leading to immediate flooding. Referred to as pluvial flooding, this flood type exclusive to urban areas has caused severe losses in cities around the world. Without further intervention, losses from pluvial flooding are expected to increase in many urban areas due to an increase of impervious surfaces compounded with an aging drainage infrastructure and a projected increase in heavy precipitation events. While this requires the integration of pluvial flood risk into risk management plans, so far little is known about the adverse consequences of pluvial flooding due to a lack of both detailed data sets and studies on pluvial flood impacts. As a consequence, methods for reliably estimating pluvial flood losses, needed for pluvial flood risk assessment, are still missing.
Therefore, this thesis investigates how pluvial flood losses to private households can be reliably estimated, based on an improved understanding of the drivers of pluvial flood loss. For this purpose, detailed data from pluvial flood-affected households was collected through structured telephone- and web-surveys following pluvial flood events in Germany and the Netherlands.
Pluvial flood losses to households are the result of complex interactions between impact characteristics such as the water depth and a household’s resistance as determined by its risk awareness, preparedness, emergency response, building properties and other influencing factors. Both exploratory analysis and machine-learning approaches were used to analyze differences in resistance and impacts between households and their effects on the resulting losses. The comparison of case studies showed that the awareness around pluvial flooding among private households is quite low. Low awareness not only challenges the effective dissemination of early warnings, but was also found to influence the implementation of private precautionary measures. The latter were predominately implemented by households with previous experience of pluvial flooding. Even cases where previous flood events affected a different part of the same city did not lead to an increase in preparedness of the surveyed households, highlighting the need to account for small-scale variability in both impact and resistance parameters when assessing pluvial flood risk.
While it was concluded that the combination of low awareness, ineffective early warning and the fact that only a minority of buildings were adapted to pluvial flooding impaired the coping capacities of private households, the often low water levels still enabled households to mitigate or even prevent losses through a timely and effective emergency response.
These findings were confirmed by the detection of loss-influencing variables, showing that cases in which households were able to prevent any loss to the building structure are predominately explained by resistance variables such as the household’s risk awareness, while the degree of loss is mainly explained by impact variables.
Based on the important loss-influencing variables detected, different flood loss models were developed. Similar to flood loss models for river floods, the empirical data from the preceding data collection was used to train flood loss models describing the relationship between impact and resistance parameters and the resulting loss to building structures. Different approaches were adapted from river flood loss models using both models with the water depth as only predictor for building structure loss and models incorporating additional variables from the preceding variable detection routine.
The high predictive errors of all compared models showed that point predictions are not suitable for estimating losses on the building level, as they severely impair the reliability of the estimates. For that reason, a new probabilistic framework based on Bayesian inference was introduced that is able to provide predictive distributions instead of single loss estimates. These distributions not only give a range of probable losses, they also provide information on how likely a specific loss value is, representing the uncertainty in the loss estimate.
Using probabilistic loss models, it was found that the certainty and reliability of a loss estimate on the building level is not only determined by the use of additional predictors as shown in previous studies, but also by the choice of response distribution defining the shape of the predictive distribution. Here, a mix between a beta and a Bernoulli distribution to account for households that are able to prevent losses to their building’s structure was found to provide significantly more certain and reliable estimates than previous approaches using Gaussian or non-parametric response distributions.
The successful model transfer and post-event application to estimate building structure loss in Houston, TX, caused by pluvial flooding during Hurricane Harvey confirmed previous findings, and demonstrated the potential of the newly developed multi-variable beta model for future risk assessments. The highly detailed input data set constructed from openly available data sources containing over 304,000 affected buildings in Harris County further showed the potential of data-driven, building-level loss models for pluvial flood risk assessment.
In conclusion, pluvial flood losses to private households are the result of complex interactions between impact and resistance variables, which should be represented in loss models. The local occurrence of pluvial floods requires loss estimates on high spatial resolutions, i.e. on the building level, where losses are variable and uncertainties are high.
Therefore, probabilistic loss estimates describing the uncertainty of the estimate should be used instead of point predictions. While the performance of probabilistic models on the building level are mainly driven by the choice of response distribution, multi-variable models are recommended for two reasons:
First, additional resistance variables improve the detection of cases in which households were able to prevent structural losses.
Second, the added variability of additional predictors provides a better representation of the uncertainties when loss estimates from multiple buildings are aggregated.
This leads to the conclusion that data-driven probabilistic loss models on the building level allow for a reliable loss estimation at an unprecedented level of detail, with a consistent quantification of uncertainties on all aggregation levels. This makes the presented approach suitable for a wide range of applications, from decision support in spatial planning to impact- based early warning systems.

Natural extreme events are an integral part of nature on planet earth. Usually these events are only considered hazardous to humans, in case they are exposed. In this case, however, natural hazards can have devastating impacts on human societies. Especially hydro-meteorological hazards have a high damage potential in form of e.g. riverine and pluvial floods, winter storms, hurricanes and tornadoes, which can occur all over the globe. Along with an increasingly warm climate also an increase in extreme weather which potentially triggers natural hazards can be expected. Yet, not only changing natural systems, but also changing societal systems contribute to an increasing risk associated with these hazards. These can comprise increasing exposure and possibly also increasing vulnerability to the impacts of natural events. Thus, appropriate risk management is required to adapt all parts of society to existing and upcoming risks at various spatial scales. One essential part of risk management is the risk assessment including the estimation of the economic impacts. However, reliable methods for the estimation of economic impacts due to hydro-meteorological hazards are still missing. Therefore, this thesis deals with the question of how the reliability of hazard damage estimates can be improved, represented and propagated across all spatial scales. This question is investigated using the specific example of economic impacts to companies as a result of riverine floods in Germany.
Flood damage models aim to describe the damage processes during a given flood event. In other words they describe the vulnerability of a specific object to a flood. The models can be based on empirical data sets collected after flood events. In this thesis tree-based models trained with survey data are used for the estimation of direct economic flood impacts on the objects. It is found that these machine learning models, in conjunction with increasing sizes of data sets used to derive the models, outperform state-of-the-art damage models. However, despite the performance improvements induced by using multiple variables and more data points, large prediction errors remain at the object level. The occurrence of the high errors was explained by a further investigation using distributions derived from tree-based models. The investigation showed that direct economic impacts to individual objects cannot be modeled by a normal distribution. Yet, most state-of-the-art approaches assume a normal distribution and take mean values as point estimators. Subsequently, the predictions are unlikely values within the distributions resulting in high errors. At larger spatial scales more objects are considered for the damage estimation. This leads to a better fit of the damage estimates to a normal distribution. Consequently, also the performance of the point estimators get better, although large errors can still occur due to the variance of the normal distribution. It is recommended to use distributions instead of point estimates in order to represent the reliability of damage estimates.
In addition current approaches also mostly ignore the uncertainty associated with the characteristics of the hazard and the exposed objects. For a given flood event e.g. the estimation of the water level at a certain building is prone to uncertainties. Current approaches define exposed objects mostly by the use of land use data sets. These data sets often show inconsistencies, which introduce additional uncertainties. Furthermore, state-of-the-art approaches also imply problems of missing consistency when predicting the damage at different spatial scales. This is due to the use of different types of exposure data sets for model derivation and application. In order to face these issues a novel object-based method was developed in this thesis. The method enables a seamless estimation of hydro-meteorological hazard damage across spatial scales including uncertainty quantification. The application and validation of the method resulted in plausible estimations at all spatial scales without overestimating the uncertainty.
Mainly newly available data sets containing individual buildings make the application of the method possible as they allow for the identification of flood affected objects by overlaying the data sets with water masks. However, the identification of affected objects with two different water masks revealed huge differences in the number of identified objects. Thus, more effort is needed for their identification, since the number of objects affected determines the order of magnitude of the economic flood impacts to a large extent.
In general the method represents the uncertainties associated with the three components of risk namely hazard, exposure and vulnerability, in form of probability distributions. The object-based approach enables a consistent propagation of these uncertainties in space. Aside from the propagation of damage estimates and their uncertainties across spatial scales, a propagation between models estimating direct and indirect economic impacts was demonstrated. This enables the inclusion of uncertainties associated with the direct economic impacts within the estimation of the indirect economic impacts. Consequently, the modeling procedure facilitates the representation of the reliability of estimated total economic impacts. The representation of the estimates' reliability prevents reasoning based on a false certainty, which might be attributed to point estimates. Therefore, the developed approach facilitates a meaningful flood risk management and adaptation planning.
The successful post-event application and the representation of the uncertainties qualifies the method also for the use for future risk assessments. Thus, the developed method enables the representation of the assumptions made for the future risk assessments, which is crucial information for future risk management. This is an important step forward, since the representation of reliability associated with all components of risk is currently lacking in all state-of-the-art methods assessing future risk.
In conclusion, the use of object-based methods giving results in the form of distributions instead of point estimations is recommended. The improvement of the model performance by the means of multi-variable models and additional data points is possible, but small. Uncertainties associated with all components of damage estimation should be included and represented within the results. Furthermore, the findings of the thesis suggest that, at larger scales, the influence of the uncertainty associated with the vulnerability is smaller than those associated with the hazard and exposure. This leads to the conclusion that for an increased reliability of flood damage estimations and risk assessments, the improvement and active inclusion of hazard and exposure, including their uncertainties, is needed in addition to the improvements of the models describing the vulnerability of the objects.

Even though quite different in occurrence and consequences, from a modeling perspective many natural hazards share similar properties and challenges. Their complex nature as well as lacking knowledge about their driving forces and potential effects make their analysis demanding: uncertainty about the modeling framework, inaccurate or incomplete event observations and the intrinsic randomness of the natural phenomenon add up to different interacting layers of uncertainty, which require a careful handling. Nevertheless deterministic approaches are still widely used in natural hazard assessments, holding the risk of underestimating the hazard with disastrous effects. The all-round probabilistic framework of Bayesian networks constitutes an attractive alternative. In contrast to deterministic proceedings, it treats response variables as well as explanatory variables as random variables making no difference between input and output variables. Using a graphical representation Bayesian networks encode the dependency relations between the variables in a directed acyclic graph: variables are represented as nodes and (in-)dependencies between variables as (missing) edges between the nodes. The joint distribution of all variables can thus be described by decomposing it, according to the depicted independences, into a product of local conditional probability distributions, which are defined by the parameters of the Bayesian network. In the framework of this thesis the Bayesian network approach is applied to different natural hazard domains (i.e. seismic hazard, flood damage and landslide assessments). Learning the network structure and parameters from data, Bayesian networks reveal relevant dependency relations between the included variables and help to gain knowledge about the underlying processes. The problem of Bayesian network learning is cast in a Bayesian framework, considering the network structure and parameters as random variables itself and searching for the most likely combination of both, which corresponds to the maximum a posteriori (MAP score) of their joint distribution given the observed data. Although well studied in theory the learning of Bayesian networks based on real-world data is usually not straight forward and requires an adoption of existing algorithms. Typically arising problems are the handling of continuous variables, incomplete observations and the interaction of both. Working with continuous distributions requires assumptions about the allowed families of distributions. To "let the data speak" and avoid wrong assumptions, continuous variables are instead discretized here, thus allowing for a completely data-driven and distribution-free learning. An extension of the MAP score, considering the discretization as random variable as well, is developed for an automatic multivariate discretization, that takes interactions between the variables into account. The discretization process is nested into the network learning and requires several iterations. Having to face incomplete observations on top, this may pose a computational burden. Iterative proceedings for missing value estimation become quickly infeasible. A more efficient albeit approximate method is used instead, estimating the missing values based only on the observations of variables directly interacting with the missing variable. Moreover natural hazard assessments often have a primary interest in a certain target variable. The discretization learned for this variable does not always have the required resolution for a good prediction performance. Finer resolutions for (conditional) continuous distributions are achieved with continuous approximations subsequent to the Bayesian network learning, using kernel density estimations or mixtures of truncated exponential functions. All our proceedings are completely data-driven. We thus avoid assumptions that require expert knowledge and instead provide domain independent solutions, that are applicable not only in other natural hazard assessments, but in a variety of domains struggling with uncertainties.

The terrestrial biosphere impacts considerably on the global carbon cycle. In particular, ecosystems contribute to set off anthropogenic induced fossil fuel emissions and hence decelerate the rise of the atmospheric CO₂ concentration. However, the future net sink strength of an ecosystem will heavily depend on the response of the individual processes to a changing climate. Understanding the makeup of these processes and their interaction with the environment is, therefore, of major importance to develop long-term climate mitigation strategies. Mathematical models are used to predict the fate of carbon in the soil-plant-atmosphere system under changing environmental conditions. However, the underlying processes giving rise to the net carbon balance of an ecosystem are complex and not entirely understood at the canopy level. Therefore, carbon exchange models are characterised by considerable uncertainty rendering the model-based prediction into the future prone to error. Observations of the carbon exchange at the canopy scale can help learning about the dominant processes and hence contribute to reduce the uncertainty associated with model-based predictions. For this reason, a global network of measurement sites has been established that provides long-term observations of the CO₂ exchange between a canopy and the atmosphere along with micrometeorological conditions. These time series, however, suffer from observation uncertainty that, if not characterised, limits their use in ecosystem studies. The general objective of this work is to develop a modelling methodology that synthesises physical process understanding with the information content in canopy scale data as an attempt to overcome the limitations in both carbon exchange models and observations. Similar hybrid modelling approaches have been successfully applied for signal extraction out of noisy time series in environmental engineering. Here, simple process descriptions are used to identify relationships between the carbon exchange and environmental drivers from noisy data. The functional form of these relationships are not prescribed a priori but rather determined directly from the data, ensuring the model complexity to be commensurate with the observations. Therefore, this data-led analysis results in the identification of the processes dominating carbon exchange at the ecosystem scale as reflected in the data. The description of these processes may then lead to robust carbon exchange models that contribute to a faithful prediction of the ecosystem carbon balance. This work presents a number of studies that make use of the developed data-led modelling approach for the analysis and interpretation of net canopy CO₂ flux observations. Given the limited knowledge about the underlying real system, the evaluation of the derived models with synthetic canopy exchange data is introduced as a standard procedure prior to any real data employment. The derived data-led models prove successful in several different applications. First, the data-based nature of the presented methods makes them particularly useful for replacing missing data in the observed time series. The resulting interpolated CO₂ flux observation series can then be analysed with dynamic modelling techniques, or integrated to coarser temporal resolution series for further use e.g., in model evaluation exercises. However, the noise component in these observations interferes with deterministic flux integration in particular when long time periods are considered. Therefore, a method to characterise the uncertainties in the flux observations that uses a semi-parametric stochastic model is introduced in a second study. As a result, an (uncertain) estimate of the annual net carbon exchange of the observed ecosystem can be inferred directly from a statistically consistent integration of the noisy data. For the forest measurement sites analysed, the relative uncertainty for the annual sum did not exceed 11 percent highlighting the value of the data. Based on the same models, a disaggregation of the net CO₂ flux into carbon assimilation and respiration is presented in a third study that allows for the estimation of annual ecosystem carbon uptake and release. These two components can then be further analysed for their separate response to environmental conditions. Finally, a fourth study demonstrates how the results from data-led analyses can be turned into a simple parametric model that is able to predict the carbon exchange of forest ecosystems. Given the global network of measurements available the derived model can now be tested for generality and transferability to other biomes. In summary, this work particularly highlights the potential of the presented data-led methodologies to identify and describe dominant carbon exchange processes at the canopy level contributing to a better understanding of ecosystem functioning.

Semi-arid areas are, due to their climatic setting, characterized by small water resources. An increasing water demand as a consequence of population growth and economic development as well as a decreasing water availability in the course of possible climate change may aggravate water scarcity in future, which often exists already for present-day conditions in these areas. Understanding the mechanisms and feedbacks of complex natural and human systems, together with the quantitative assessment of future changes in volume, timing and quality of water resources are a prerequisite for the development of sustainable measures of water management to enhance the adaptive capacity of these regions. For this task, dynamic integrated models, containing a hydrological model as one component, are indispensable tools. The main objective of this study is to develop a hydrological model for the quantification of water availability in view of environmental change over a large geographic domain of semi-arid environments. The study area is the Federal State of Ceará (150 000 km2) in the semi-arid north-east of Brazil. Mean annual precipitation in this area is 850 mm, falling in a rainy season with duration of about five months. Being mainly characterized by crystalline bedrock and shallow soils, surface water provides the largest part of the water supply. The area has recurrently been affected by droughts which caused serious economic losses and social impacts like migration from the rural regions. The hydrological model Wasa (Model of Water Availability in Semi-Arid Environments) developed in this study is a deterministic, spatially distributed model being composed of conceptual, process-based approaches. Water availability (river discharge, storage volumes in reservoirs, soil moisture) is determined with daily resolution. Sub-basins, grid cells or administrative units (municipalities) can be chosen as spatial target units. The administrative units enable the coupling of Wasa in the framework of an integrated model which contains modules that do not work on the basis of natural spatial units. The target units mentioned above are disaggregated in Wasa into smaller modelling units within a new multi-scale, hierarchical approach. The landscape units defined in this scheme capture in particular the effect of structured variability of terrain, soil and vegetation characteristics along toposequences on soil moisture and runoff generation. Lateral hydrological processes at the hillslope scale, as reinfiltration of surface runoff, being of particular importance in semi-arid environments, can thus be represented also within the large-scale model in a simplified form. Depending on the resolution of available data, small-scale variability is not represented explicitly with geographic reference in Wasa, but by the distribution of sub-scale units and by statistical transition frequencies for lateral fluxes between these units. Further model components of Wasa which respect specific features of semi-arid hydrology are: (1) A two-layer model for evapotranspiration comprises energy transfer at the soil surface (including soil evaporation), which is of importance in view of the mainly sparse vegetation cover. Additionally, vegetation parameters are differentiated in space and time in dependence on the occurrence of the rainy season. (2) The infiltration module represents in particular infiltration-excess surface runoff as the dominant runoff component. (3) For the aggregate description of the water balance of reservoirs that cannot be represented explicitly in the model, a storage approach respecting different reservoirs size classes and their interaction via the river network is applied. (4) A model for the quantification of water withdrawal by water use in different sectors is coupled to Wasa. (5) A cascade model for the temporal disaggregation of precipitation time series, adapted to the specific characteristics of tropical convective rainfall, is applied for the generating rainfall time series of higher temporal resolution. All model parameters of Wasa can be derived from physiographic information of the study area. Thus, model calibration is primarily not required. Model applications of Wasa for historical time series generally results in a good model performance when comparing the simulation results of river discharge and reservoir storage volumes with observed data for river basins of various sizes. The mean water balance as well as the high interannual and intra-annual variability is reasonably represented by the model. Limitations of the modelling concept are most markedly seen for sub-basins with a runoff component from deep groundwater bodies of which the dynamics cannot be satisfactorily represented without calibration. Further results of model applications are: (1) Lateral processes of redistribution of runoff and soil moisture at the hillslope scale, in particular reinfiltration of surface runoff, lead to markedly smaller discharge volumes at the basin scale than the simple sum of runoff of the individual sub-areas. Thus, these processes are to be captured also in large-scale models. The different relevance of these processes for different conditions is demonstrated by a larger percentage decrease of discharge volumes in dry as compared to wet years. (2) Precipitation characteristics have a major impact on the hydrological response of semi-arid environments. In particular, underestimated rainfall intensities in the rainfall input due to the rough temporal resolution of the model and due to interpolation effects and, consequently, underestimated runoff volumes have to be compensated in the model. A scaling factor in the infiltration module or the use of disaggregated hourly rainfall data show good results in this respect. The simulation results of Wasa are characterized by large uncertainties. These are, on the one hand, due to uncertainties of the model structure to adequately represent the relevant hydrological processes. On the other hand, they are due to uncertainties of input data and parameters particularly in view of the low data availability. Of major importance is: (1) The uncertainty of rainfall data with regard to their spatial and temporal pattern has, due to the strong non-linear hydrological response, a large impact on the simulation results. (2) The uncertainty of soil parameters is in general of larger importance on model uncertainty than uncertainty of vegetation or topographic parameters. (3) The effect of uncertainty of individual model components or parameters is usually different for years with rainfall volumes being above or below the average, because individual hydrological processes are of different relevance in both cases. Thus, the uncertainty of individual model components or parameters is of different importance for the uncertainty of scenario simulations with increasing or decreasing precipitation trends. (4) The most important factor of uncertainty for scenarios of water availability in the study area is the uncertainty in the results of global climate models on which the regional climate scenarios are based. Both a marked increase or a decrease in precipitation can be assumed for the given data. Results of model simulations for climate scenarios until the year 2050 show that a possible future change in precipitation volumes causes a larger percentage change in runoff volumes by a factor of two to three. In the case of a decreasing precipitation trend, the efficiency of new reservoirs for securing water availability tends to decrease in the study area because of the interaction of the large number of reservoirs in retaining the overall decreasing runoff volumes.