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

### Climate formulas: Even extreme weather follows rules

02.01.2015

News from Climate Science: Once a month, climate researchers report on their latest findings in the newspaper "Hamburger Abendblatt." Prof. Valerio Lucarini is a theoretical meteorologist at Universität Hamburg’s Cluster of Excellence CliSAP. A native Italian, he previously worked in Bologna, Italy and in Reading, UK.

Extreme weather phenomena like disastrous monster waves, typhoons, and 100-year floods seem unpredictable. In order to make them foreseeable, climate researchers aim to translate them into strict mathematical formulas. This goal is part of my research focus in applied mathematics and theoretical meteorology at the Cluster of Excellence “Integrated Climate System Analysis and Prediction” CliSAP in Hamburg.

Extreme weather events share three common characteristics: They are rare, deviate significantly from mean values, and have tremendous ramifications for nature and societies. In a nutshell, extremes are atypical which makes them difficult to trace. Thus, statistics are crucial.

There are two approaches to determining extreme values such as regional flood risks. One method focuses on pinpointing the record water level per decade. This allows us to analyze one single value for each time unit. Hence, other aberrant high water levels occurring during the investigation period remain unconsidered. The second method, by contrast, takes into account all extreme values that exceed a certain limit. As a result, ten-year periods may indicate a random number of flood events or none at all. The outcomes of both approaches can be converted into curves depicting the frequency of certain extreme water levels.

Interestingly, all probabilities thus determined match one of four long-known standard curves—each named for the scientist who discovered it: Gumbel, Fréchet, Weibull und Pareto. So, even extremes are ruled by laws that enable us to establish the probability of future events. This is of great interest not only to climate researchers, but also to engineers, insurers, or finance experts. How high must dams be built to withstand floods within the next one hundred years? What financial losses due to major fires must be expected? How likely is a stock market crash?

A fundamental shortcoming of the above methods is their basic assumption that our climate system is invariable. Quite the contrary, our global climate depends on numerous external factors and is undergoing constant change. Therefore, I am collaborating with colleagues in France, Portugal, and Great Britain in order to find out how to incorporate climate change data into our extreme value distribution formulas. It is an incontrovertible fact that, as regards frequency, intensity, and spatial distribution, even the most chaotic weather follows universal laws. Researchers specializing in extremes examine these patterns as if through a magnifying glass. Events are more forceful and visible during unusual weather conditions. Thus, extremes are highly useful to climate research. They elucidate how a system—in our case the climate—behaves in principle.

Author: Prof. Dr. Valerio Lucarini