CliSAP successfully finished in 2018. Climate research continues in the Cluster of Excellence "CLICCS".

### Flooding and Evacuation: Using Mathematical Models to Predict Affected Areas

29.06.2015

News from Climate Science: Once a month, climate researchers report on their latest findings in the newspaper "Hamburger Abendblatt". Anja Jeschke is investigating equations for shallow water waves at the Cluster of Excellence.

Flood warning! In the event of a storm surge warning, people living in at-risk coastal areas may have to be evacuated. But who can stay, and who needs to go? Misjudging the impacts could have serious consequences. My new computational model could soon help to more accurately predict which areas will actually be flooded. This could be especially important in the future, since rising sea levels could make major storm surges a more frequent occurrence.

Ordering an evacuation is a radical step. Nevertheless, since safeguarding human lives has to remain the top priority, no area is too small to be evacuated. At the same time, an evacuation is a costly affair, and the larger the area, the higher the costs. Further, if a predicted surge ultimately turns out to be comparatively harmless, “needless” wide-scale evacuations can breed frustration among those affected. If this happens more than once, they may lose their faith in flood warnings in general. As such, predicting the affected area as precisely as possible is extremely important.

At the Cluster of Excellence for climate research CliSAP, my colleagues and I are working to develop mathematical models that will allow us to accurately simulate these extreme scenarios. The shallow water equations, mathematical formulas that describe the physical movements of water under simplified conditions, form part of the basis of our models. But for the constantly changing processes on coastlines, they aren’t sufficiently precise, which means I also need to take the length of the inbound wave into account. Shorter waves disperse more slowly; longer ones do so more rapidly. In order to more realistically simulate when the waves will hit the coast and how large they’ll be when they get there, I want to add this aspect to the calculations.

There are two different formulas that can help me describe the influence of the wave’s length: the Boussinesq approximation and a more recent correction. Since each has its own strengths and weaknesses, which one is better suited to my model? The Boussinesq approximation is definitely the safer bet: first proposed in 1872, it’s been frequently used ever since and does a good job of describing the relevant physical processes. On the other hand, its depiction of the influence of the wave’s length is so complex that there’s no way it could be flexibly integrated into my model.

In contrast, the correction takes a different approach to the wave’s length, so I could add it to my computational model fairly easily. That being said, it’s also relatively new and therefore not as established as its predecessor – and its depiction of physical phenomena is less precise.
To compensate for this problem, I have adapted the correction so that it can better describe physical processes. The results of an initial comparison for a simple scenario were amazing: my “new and improved” correction yielded exactly the same results as the Boussinesq approximation. That means in the future, we’ll have a more flexible mathematical tool that promises more accurate predictions of coastal flooding.

Author: Anja Jeschke

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