Flood risk models provide important information for disaster planning through estimating flood damage to exposed assets, such as houses. At large scales, computational constraints or data coarseness leads to the common practice of aggregating asset data using a single statistic (e.g., the mean) prior to applying non-linear damage functions. While this simplification has been shown to bias model results in other fields, the influence of aggregation on flood risk models has received little attention. This study provides a first order approximation of such errors in 344 damage functions using synthetically generated depths. We show that errors can be as high as 40 % of the total asset value under the most extreme example considered, but this is highly sensitive to the level of aggregation and the variance of the depth values. These findings identify a potentially significant source of error in large-scale flood risk assessments introduced, not by data quality or model transfers, but by modelling approach.

With the increase in flood related disaster damages, the expansion of computation power, and the availability of global data, the development and application of meso- and macro-scale flood risk models has increased dramatically in the past decade

Such scaling issues are not unique to flood risk models. Many fields find it convenient (or necessary) to simplify the system under study by averaging or aggregating some variable or computational unit

Within a flood vulnerability model, flood damage functions (

Aggregation and scaling issues are rarely considered in the flood risk model literature.

In a recent large-scale study,

In this paper we summarize work to improve our understanding of the effect of aggregation on a particular component of flood risk models: the flood damage function. We accomplish this by producing a first order approximation of the potential aggregation error for a general flood risk models, the first attempt of its kind we are aware of. To provide as broad an evaluation as possible, a library of 344 damage functions are evaluated against a single indicator variable: synthetically generated flood depth. These results are then analyzed to elucidate the potential significance and behaviour of aggregation on flood risk models.

To evaluate the sensitivity of flood damage functions to the aggregation of input variables, a library of 344 damage functions are evaluated against synthetically generated water depths at various levels of aggregation. Statistics describing the difference between raw function outputs and the aggregated analogues are then computed on each function and each level of aggregation to describe the response of the function to aggregation.

For this study, we focus on direct tangible economic functions for estimating the relative loss to buildings from flood depth. From

Summary of flood damage models from

Relative loss vs. anchor depth (

Each of the 344 selected discrete functions have a distinct shape, depth domain (from

To generate the synthetic depth values, the independent variable domain (depths) is discretized from 0.0 to 2.0 to produce 30 anchor depth values (

Relative loss error for three levels of aggregation (

Using each of the 360 synthetic depth arrays on each of the 344 functions, a set of relative loss arrays (RL

Aggregation error potentials calculated with Eq. (

Three example damage functions (

A clock-wise rotation can also be seen in Fig.

Figure

Examining the relation of error to

To provide a simple metric for the 344 functions covered in Table

To better understand the potential and magnitude of errors introduced through averaging of flood risk models, a novel first order evaluation of 344 flood damage functions was performed using synthetically generated depth data. While the character and magnitude of aggregation errors will depend on the specifics of a given flood risk model, the general approach applied here demonstrates that low-depth floods tend to have negative errors while high-depth floods have positive errors. Further, we demonstrate that overall, error tends to be negative for the 344 damage functions considered.

The findings reported here provide useful information for flood risk modellers evaluating the appropriateness and extent of aggregation to include in their models. For example, in areas with high depth variance where models with large aggregation error potential (

Future work should evaluate the performance of the normal distribution applied here to synthetically generate depths. Also, a more generalizeable measure of curvature (e.g., local derivative) could be explored to more clearly classify and communicate the aggregation error potential of different functions. By extending the first order approximations developed here, the flood risk model domain could be segregated into areas with more or less sensitivity to aggregation errors. In this way, the accuracy of large-scale flood risk models could be improved without drastically increasing the computational requirements.

Python scripts are provided here under the MIT license:

Function library is provided in

SB prepared the manuscript, developed the concept, performed the analysis and computation. BM and HK reviewed the manuscript and supervised the work.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

This article is part of the special issue “ICFM9 – River Basin Disaster Resilience and Sustainability by All”. It is a result of The 9th International Conference on Flood Management, Tsukuba, Japan, 18–22 February 2023.

The authors thank Kai Schröter for participating in early discussions and helping with the damage function database. We would also like to thank the ICFM9 organizers for both the conference and funding this publication.

The research presented in this article was conducted within the research training group “Natural Hazards and Risks in a Changing World” (NatRiskChange) funded by the Deutsche Forschungsgemeinschaft (DFG; grant no. GRK 2043/2).

This paper was edited by Mohamed Rasmy and reviewed by two anonymous referees.