FLEMO_flash is built based on self-reported flash flood losses along with associated information of the affected companies and households. The data was collected through different surveys using computer-aided telephone interviews with representatives of affected companies and households following three highly damaging flash flood occurrences in Germany (Kellermann et al., 2020; Kreibich et al., 2017). These include the 2002 event in the Elbe catchment in Eastern Germany, the 2016 heavy precipitation event, and the most recent July 2021 event in Western Germany. The variables potentially influencing losses are extracted and homogenized from the datasets of the 2002, 2016, and 2021 flood surveys. The variables are grouped into five categories, as presented in Table 1 for companies and Table 2 for households, respectively. An overview of all variables, along with the corresponding survey questions, response categories, and details on variable construction, is presented in Tables S1 and S2 in the Supplement. The loss variable represented as relative loss (rloss), is defined as the ratio between the reported loss and replacement cost on the [0, 1] interval. A value of 0 indicates no loss, while 1 indicates complete loss (Kreibich and Dimitrova, 2010; Schoppa et al., 2020; Sieg et al., 2017). For companies, losses are estimated for three categories of assets – buildings, equipment, and goods and stock. For households, losses are estimated for buildings and contents. Survey responses with no data on loss were excluded from the dataset.

Since the surveys covered regions affected by both flash floods and riverine floods, we applied a terrain-based filtering to exclude riverine cases. We calculated the median slope within a 10 km radius around the location of each observation using the Digital Elevation Model with a 90 m resolution from the Shuttle Radar Topographic Mission. This process was repeated for 14 reference municipalities known to have experienced flash flood events in the past or described as prone to flash floods (see Table A1). The minimum value among the median slope from these 14 municipalities was then used as the slope threshold (see Table S4). Observations with slope values equal to or above this threshold were classified as flash flood cases. Other metrics, such as river basin concentration time, may indeed provide a more process-based characterization of flash flood potential. Nevertheless, we used slope alone as a pragmatic solution that balances two competing needs: maintaining physical relevance in identifying flash flood prone companies and households and retaining a sufficient number of data points for robust model development. The cases with longer warning lead times in the sample are likely to be due to warnings of high precipitation than to flood-specific warnings.

The final database available for developing loss models consists of 241, 379, 355, 1131, 1448 observations for company building, equipment, goods and stock, household building, and contents, respectively. The percentage of missing data for different variables in each of the asset is summarized in Fig. S1 in the Supplement (companies) and Fig. S2 (households) in the supplement. To maximise the amount of training data for model building, we employed the k nearest neighbour technique to impute the missing data. We tested a range of k-neighbours for our datasets (k=1, 3, 5, 7, 9) and selected the value with best performance.

Flood damage processes vary by region, flood type, and asset type (Mohor et al., 2020; Sairam et al., 2021; Wagenaar et al., 2018). To derive the most significant drivers of flash flood losses from our list of variables, this study adopts a data-driven feature selection approach to the empirical data. Feature selection involves identifying variables that have the highest influence on the target variable (i.e. relative loss). We train multiple models – nonlinear models: Random Forest (RF), Extreme Gradient Boosting (XGBoost), and linear model: Elastic Net (EN).

RF is an ensemble machine learning method primarily used for classification and regression tasks, developed by Breiman (2001). RF generates an ensemble of decision trees, each trained on a random subset of the data using bootstrap sampling. At each node within these trees, a random subset of features is considered for splitting. The final prediction for a given input is obtained by averaging the predictions from all individual trees. This approach helps RF reduce overfitting and enhances the model's generalization ability. XGBoost, similarly to RF, is an ensemble learning algorithm that benefits from a decision tree-based structure. However, the key difference compared to RF is that in XGBoost, each tree corrects the errors from the previous ones. The process starts with a simple model and iteratively adds trees that focus on the residuals or errors made by the existing ensemble. With its efficient implementation, XGBoost demonstrates superior performance and handles large-scale data more effectively than RF (Chen and Guestrin, 2016). While RF and XGBoost are non-linear models, EN is a regularization technique used in linear regression, combining both Lasso (L1) and Ridge (L2) regularization penalties. It effectively addresses multicollinearity in datasets by shrinking the less influential predictors toward zero (Lasso) while additionally providing some degree of regularization to prevent overfitting (Ridge). EN's ability to handle correlated features and select relevant predictors makes it a valuable tool in regression tasks (Zou and Hastie, 2005).

During training, we employed a nested cross-validation framework with 10 splits and 10 repeats, resulting in a total of 100 evaluations. We selected the best set of hyperparameters, which obtained the least mean absolute error, which was then applied to the final feature selection. From each resulting final model, we derived the feature importance. Next, we calculated each variable's weighted feature importance and overall rank. The final selection of the variables (Fig. 1) is elaborated upon in the results section.

Based on the identified features, a multivariate probabilistic Flood Loss Estimation MOdel (Bayesian Network – BN) is calibrated for predicting flash flood losses (Jensen and Nielsen, 2007; Kitson et al., 2023; Scutari and Denis, 2021). BNs are probabilistic graphical models where the predictor and target variables are connected through a directed acyclic graph (DAG). Each variable is depicted as a node, and related nodes are connected through arcs. These connections allow for the estimation of conditional probability distributions, facilitating an understanding of the underlying processes and probabilistic estimation of rloss (Vogel et al., 2018). The continuous variables are discretized using an equal frequency discretization approach (Scutari and Denis, 2021), and a discrete BN is formulated. The number of bins is determined based on the model performance against different numbers of bins – the number of bins resulting in the best model performance is chosen. The specification of a discrete BN involves defining a set of variables (X1, …, Xn), constructing a DAG representing the probabilistic dependencies among variables, and obtaining the conditional probability distribution PXiparents(Xi) for each variable (Xi) in the DAG, where parents(Xi) denotes the parents of node Xi in the DAG. The final joint probability distribution for the set of variables connected in a discrete BN is formulated as (Pearl, 1988): 1PX1,,…,Xn=∏i=1nPXiparentsXi. Within the predicted bins of the discrete BN (rloss bins), we fit a continuous distribution by applying weighted sampling to the empirical loss data, resulting in a smoothed representation of the loss distribution (Schoppa et al., 2020). For further details on the BN structure learning we refer to Sect. S1 in the supplement and Fig. A1.

An ensemble of linear and non-linear machine learning models ensures that both linear and non-linear relationships between the predictors and flood loss are captured. Water depth emerges as the most important predictor of damage across all asset types (Fig. 1), which is consistent with previous loss models (Kreibich et al., 2010; Merz et al., 2013; Schoppa et al., 2020; Sieg et al., 2017; Thieken et al., 2008). For companies, emergency measures success and number of employees are also significant factors influencing the flood loss estimation. Among other flood characteristics, duration is ranked fourth for building (Fig. 1a), velocity is ranked third for equipment (Fig. 1b), and contamination is the fifth most significant driver for goods and stock (Fig. 1c), respectively. In case of households, human stability and contamination are most important hazard variables after water depth.

The significance of water depth and emergency measures has also been emphasized by Hasanzadeh Nafari et al. (2016) in case of fluvial flood losses. Exposure variables such as number of employees significantly influence company losses. Additionally in case of households, losses are more influenced by variables representing flood vulnerability such as knowledge about emergency action (Fig. 1d and e). These findings are in line with the previous studies (Kreibich et al., 2005; Sairam et al., 2019; Zander et al., 2023) that highlight the potential for adaptation measures to reduce flood losses. By quantitatively comparing the varied drivers of flash flood losses, these results also emphasize the importance of multivariable loss estimation models that capture the interplay across these drivers and their influence on losses.

Although flow velocity has been identified as a significant contributor to flash flood losses (Kreibich and Dimitrova, 2010), it does not appear among the most significant factors in the current study. In our analysis, we represent hydrodynamic forces using velocity (v) and human stability (hs). While velocity provides a subjective yet direct measure of local strength of flow current, human stability reflects on the perceived difficulty of standing in flood waters. As shown in Fig. 1d and e, human stability emerges as the second most influential factor affecting loss in households, indicating that the combined effect of water depth and velocity play a crucial role for the flash flood model.

The loss processes described by FLEMO_flash is illustrated using the predictive density of predicted losses under scenarios of hazard, exposure and vulnerability. For brevity, this section primarily focusses on the FLEMO_flash model for household buildings (Fig. 5), with a similar interpretation, results of other asset types are shown in Figs. S3–S6. The nodes of the model comprise of water depth, human stability, inundation duration, contamination, knowledge about emergency action, and relative losses, each with 7, 4, 7, 5, 6, and 8 classes, respectively. The CPT was populated with joint probabilities to find the predictive density of loss given the condition of other nodes. The conditional probability of rloss based only on water depth indicates a monotonic relationship. Shallow inundations are associated with very low losses, while deeper water substantially increases the probability of severe losses (Fig. 5e). The highest probabilities are concentrated along the diagonal, confirming this trend. For instance, depths < 0.28 m are most likely associated with very low losses (<0.017), whereas depths ≥ 2.3 m are strongly associated with high losses (>0.42). Similar patterns of increasing loss probability with greater water depth are observed across all asset types (Figs. S3–S6). Water depth also influences human stability: while shallow flooding results in low instability, extreme depths markedly increase the probability of instability (0.54) (Fig. 5b).

Contamination emerges as another important driver of losses. In uncontaminated conditions (class 0), the probability of very low losses (<0.01) is high (0.82). Conversely, under severe contamination (class 4), the probability of very high losses (>0.427) increases to 0.30 (Fig. 5c), reflecting the destructive impact of oils, chemicals, and sewage entering buildings (Kreibich et al., 2005; Laudan et al., 2020). Households exposed to inundation lasting [13–50) h showed a high probability of experiencing moderate contamination levels (classes 1–2). Knowledge about emergency action shows a strong mitigating effect. The CPT (Fig. 5d) demonstrates that households with low awareness (Ke≤2) face a high probability of severe losses, whereas households with very good knowledge (Ke≥5) display a substantially higher probability of reduced losses. Comparable findings are observed for household contents (Fig. S6c). This agrees with Kreibich et al. (2021), who also reported that clear awareness of emergency actions substantially reduces damages. Importantly, socioeconomic status indirectly shapes vulnerability, as higher-income groups are more likely to report very clear knowledge of emergency actions after receiving warnings (Fig. S6b).

For companies (Figs. S3–S5), the CPT results reveal consistent patterns across buildings, equipment, and goods and stock. Smaller companies (with fewer employees or smaller premises) show higher probabilities of severe losses, whereas larger firms and premises are more strongly associated with lower loss outcomes (Figs. S3b, S4d and S5c). Across all asset types, the success of emergency measures emerges as a dominant factor, as unsuccessful measures are strongly associated with a high probability of severe losses (Figs. S3d, S4b and S5a). Contamination further amplifies losses, with severe categories linked to markedly higher probabilities of loss. Together, these results emphasize that hazard intensity (water depth, velocity, contamination), exposure (number of employees, size premises) and vulnerability factors (effectiveness of emergency measures) interactively determine relative losses for companies.

Further, we analyse to what extent these adaptation strategies are helpful in reducing rloss. Through feature selection and Bayesian Networks we identified emergency measures success (ms) and knowledge about emergency action (ke) for companies and private households respectively, as the significant variables within the Markov Blanket of rloss. We applied the FLEMO_flash model to derive predictive densities of rloss. Results were summarized using the median and associated uncertainty (25th and 75th percentiles) for selected combinations of hazard, exposure, and vulnerability conditions, rather than displaying the full predictive densities (Fig. 6). For clarity of interpretation, Fig. A1 illustrates step by step how predictive densities are derived from the posterior distributions using kernel density estimation based on 1000 resampled values. Figure A2 provides an overview of the posterior and predictive densities across varying levels of measure success under same conditions of water depth and number of employees.

For company building, the rloss Markov blanket consists of water depth (wd), number of employees (emp), and emergency measures success (ms). The incurred loss increases with increasing water depth but combining the water depth and number of employees, the relative loss experienced by companies with 9 to 12 employees is higher compared to those with 38 or more employees. We further investigate the role of successful implementation of emergency measures in reducing loss. For example, when considering only water depth and number of employees, companies with 38 or more employees, inundated by water depths ranging from 1.85 to 2.40 m above the ground, experience a rloss of 0.38. However, with successful implementation of emergency measures (ms=3), this rloss decreases to 0.20, representing a substantial 47 % reduction. On the other hand, when emergency measures were perceived to be ineffective (ms=1), the rloss increases to 0.50, marking a 32 % increase in estimated losses.

For household buildings, considering hazard and exposure with a water depth of ≥2.3 m above ground and no contamination, the predicted rloss is 0.22. However, when residents had clarity on emergency actions (Ke≥5) this loss decreases to 0.05, reflecting a 77 % reduction. Conversely, when residents did not have clear knowledge on emergency action (Ke≤2), the rloss rises to 0.27, a 23 % increase. Similarly, for household contents, we observed that when considering only water depths (hazard) of height 2.3 m above ground, the rloss is 0.38. With (Ke≥5), this loss drops to 0.17, a 55 % reduction. In contrast, with (Ke≤2), the rloss increases to 0.44, representing a 16 % rise. These findings highlight the potential of successful implementation of emergency measures and knowledge about emergency action in reducing flash flood losses (Barendrecht et al., 2020; Berghäuser et al., 2023; Bubeck et al., 2013; Sairam et al., 2019; Surminski and Thieken, 2017). While residents with high knowledge about emergency actions are more likely to take effective emergency measures, thereby reducing the severity of flood loss (Kreibich et al., 2005; Sairam et al., 2019), the knowledge about emergency action (ke) variable as considered in this study, does not capture which exact actions respondents undertook. Though the specific actions likely varied across respondents, empirical evidence indicates that having clear knowledge of emergency action generally contributes to reduced flood losses, consistent with previous findings (Kreibich et al., 2021).