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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.
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.