Extreme rainfalls increasingly common with higher temperatures

When modelling extreme events such as rainstorms, there are typically two types of data used: daily rain measurements, which naturally generate large amounts of data, and the largest daily amount during a year, so-called annual maxima. The latter is of better quality since it is more easily checked by experts. To be able to use the annual maxima data to detect changes in individual rainstorms, Helga has together with her supervisors David Bolin and Holger Rootzén developed a new statistical model that combines classical extreme value models for daily data and maxima data.

The model was applied to an area in the northeastern US, partly because it is an interesting area with many hurricanes, partly because a contact within NOAA (National Oceanic and Atmospheric Administration) could help extracting data, which stretched over a hundred years from the beginning of the 20th to the beginning of the 21st century. Scenarios for different temperature increases were considered, and as an example, it was found that the median frequency of extreme rainstorms in this area increased by approximately 80% with a temperature rise of one degree Celsius. However, the intensity of the individual rainstorms seems to remain unchanged.

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– When you intend to build, for example, a road or a bridge you do it according to certain standards, such as that it must be able to withstand a “50-year storm”. But it is probable that a rainstorm with a certain intensity will occur more and more often with rising temperatures, and one must then consider building drainage systems that can take care of large amounts of rain that will come more frequently.

Local weight-scale invariance introduced

The thesis also develops the theoretical framework for comparisons of extreme value models. When evaluating different statistical models to see which one is the most accurate, it is possible to compare them with each other using so-called scoring rules. If there are spatial variations in prediction uncertainty at different locations, many scoring rules will value these locations differently, which is a disadvantage when all locations are equally important. To be able to handle this for extreme value models a relaxation of local scale invariance, called local weight-scale invariance, was introduced, and simulations show that a scoring rule with this property compares models for spatial extreme value prediction more fairly than those without.

Scoring rules may also be useful for estimating spatial models. By maximising a ”leave-one-out score” (LOOS), Helga was able to show how different choices of scoring rule affect the robustness in the estimation of spatial models, that is, how sensitive the model is to outlier observations in the dataset that might otherwise affect the outcome very much. It is then possible to tailor the robustness of the model by choosing a scoring rule depending on for what it is to be used.

Mathematical and statistical models explain real-world problems

Helga has always been interested in math, which for her is something clear and distinct, and she has also always known that she wanted to work with math. She completed her bachelor’s degree in mathematics in Iceland. Since it was rather on the theoretical side, she also studied computer science, and then found the master’s programme Complex Adaptive Systems at Chalmers which combined both subjects. The degree project was done at FCC (Fraunhofer–Chalmers Centre for Industrial Mathematics), and Helga also started to work there. She found that research was fun and after some time came back to Mathematical Sciences, to an advertised doctoral position at the University of Gothenburg.

– It is a good environment to be in at the department and I have got to know so many helpful people. I will continue here, with a postdoctoral position at Chalmers in biostatistics. It will then be about analysis of dioxins in water but it is still mathematical and statistical models that are used to explain real problems. I will collaborate with chemists and biologists and bring my mathematical expertise. It is fun doing research where you produce something useful together!