Dynamic computational grids improve storm surge models


News from Climate Science: Once a month, climate researchers report on their latest findings in the newspaper "Hamburger Abendblatt". Nicole Beisiegel describes extreme weather conditions.

The mathematician Nicole Beisiegel has now developed a new method for more realistic computer simulations of flooding.

Typhoon Haiyan and Hurricane Katrina demonstrated how important it is to warn people of extreme events well in advance, allowing them to get to safety. Today, computer simulations often serve as the basis for risk analyses. My work involves the creation of these scenarios for storm surges at the interface between geosciences and mathematics. Together with colleagues, I develop processes and computer programs that mathematically describe complex natural phenomena. For example, my model can be used to calculate how high the water level will be where, and how quickly it will move in a particular direction.

To accomplish this, first of all we transform natural laws into mathematical equations so that modern computers can process them. This starts with overlaying the region in question with a computational grid made up of triangles. I can then enter the current values for direction and speed (momentum) and the amount of moving water (mass) at predetermined points on these triangles. These values are subsequently fed into mathematical equations for the conservation of mass and momentum, which are used to simulate the peaks and valleys in momentum and water levels. The smaller the triangles are, the higher the resolution and the more accurate the model.
This last point is a key factor – one of the greatest challenges for flood modeling is to accurately represent processes involving different scales, and even with all of the computing resources at our disposal, we can’t calculate all these processes simultaneously.

For realistic simulations we have to take into account various parameters that affect the movement of the water – for example, the profile of the coast and the type of land covered by the body of water, along with the driving effect of the wind. Using our grids we can accurately represent this complex geometry. Our main aim is to also calculate the small-scale phenomena such as the transition from wet to dry as precisely as possible. To better illustrate all of these effects, I have based my model on an adaptive computational grid.

Adaptive computational grids save computer resources by only creating a fine mesh and thus high definition where it is needed. At transitions and margins – such as between wet and dry – the grid provides a high level of resolution. In less relevant areas a, coarser mesh is sufficient. This automatic adaptation offers an intelligent method for accurately and efficiently simulating flooding, reducing the cost and time needed for the calculations without sacrificing precision. At the same time, it was very important for us that our model be practical and easily understood. With this in mind we developed it so that other professionals could quickly learn how to use it.

My method has shown itself to be highly reliable in theory, and the first practical tests have confirmed this. To be absolutely sure that the simulated values are realistic, in the next step (known as validation) I will test them using data from past extreme events. I will start with the example of Hurricane Ike, which swept over Texas in 2008 with winds of over 150 km/h and flooded the densely populated coast along the Gulf of Mexico. After it has been validated, my method will contribute to better storm-surge modeling and therefore to improved early warning systems.

Author: Nicole Beisiegel


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