Models have been around for a very long time. Already 300 years before Christ, Aristotle considered the question of how to test whether theories are true or false. For this, he developed thought experiments about the meaning of life and for explaining the world. To this day, we all know thought experiments that are supported by hypotheses and that may be empirically confirmed or invalidated. For example, in ancient times people believed that the world was a flat disc. Over the centuries, this concept was challenged by many environmental observations. With Magellan's circumnavigation of the world in the 16th century, it was then finally proven: The earth is a sphere.

Since the start of the 20th century, not only technology and the natural sciences have developed rapidly – mathematical models have also taken on increasing importance. The film "Hidden Figures" provides a strong image of how, in 1964, Katherine Johnson and the Rocket Girls sit by the dozens for days working with slide rules in open-plan offices to calculate orbits for the first NASA satellites. Today, we could do this with a smartphone in less than a second, but the mathematics behind it would be the same. It is computing power that has increased by a factor of 1010 over the past 50 years. This enables us to describe increasingly complex phenomena in computational models and to solve systems of equations increasingly quickly.

However, computational models are ultimately only simplifications of reality and are never one hundred percent certain. On the one hand, this is because they are based on theoretical concepts which simplify the reality. On the other, they are based on model parameters that describe the properties of the system in which the phenomenon takes place. In modelling the terrestrial environment, there is the great difficulty that these model parameters can only be measured directly at a few points in nature, while they vary greatly from one point to the next. For example, the water level of a river is to be predicted after a heavy rainfall – here we are talking about modelling a hydrological precipitation event – our model, in addition to accounting for meteorological data, must also include not only the parameters of the river but also its watershed area, which may be several hundred thousand square kilometres in size. Despite comparatively good data availability, these parameters are also not available in Germany and must be derived from individual local measurements and transferred to the area, i.e. they must be "regionalised".

This step is associated with significant uncertainties, which is reflected in the result of the modelling – the prediction. Therefore, the more parameters the model includes, the more important it is to account for all combinations of parametric uncertainties in an overall uncertainty analysis. For example, in a weather forecast, we are already used to hearing not only a prediction of an amount of precipitation, but also the probability of its occurrence. This probabilistic approach, i.e. accounting for probability, is also widely used in infrastructure planning: For example, the risk of failure of the infrastructure can be accounted for when planning the overflow of dams. The 100-year probability of a flood height does not mean that it only occurs once every 100 years, but rather that there is a one percent probability that it will be exceeded in any year.
Environmental models deal with describing and predicting our environment, which is both a complex and sensitive system. Over the past 50 years, a well-founded set of modelling tools has been established and much experience has been gathered in their implementation in many areas of environmental research. In addition to mathematical equations that describe the system as well as possible, each model also requires initial values, boundary conditions and the model parameters already mentioned. It is still a big challenge to select these.

We at the UFZ have therefore been working specifically on model parametrisation over the past ten years. We have managed to achieve a new level of quality in hydrological modeling with the MPR approach (Multiscale Parameter Regionalisation). The concept here is to use relatively simple mathematical functions to link properties of areas such as topographic height, soil properties or vegetation, which satellites can measure at very high resolution, to the complex model parameter fields for which the details are unknown. The benefit is that instead of having to estimate several million unknown parameters as in conventional high-resolution models, only a few degrees of freedom of these functions need be estimated. This represents a true quantum leap in predictive ability. Furthermore, we use methods from theoretical physics to make our models scalable. In this way, the structure of the model parameter fields remains independent of the spatial resolution of the model, which is a further benefit.

For example, this "smart" modelling approach enabled us to simultaneously calculate rainfall runoff and soil moisture for hundreds of European streams within all watershed areas for a period of 50 to 100 years, while simultaneously quantifying the uncertainty of the projections. The results are the focus of the following feature article. This article explains how different degrees of global warming can affect drought, low water levels and floods in Europe.

And what comes next? Given the projections, we will attempt to estimate the total economic costs of the projected impacts. But above all, we will help to develop mitigation or adaptation strategies, as the impacts of these projections would be considerable, especially in Central Europe: The consequences would be low water levels in the rivers, significantly restricted navigability and insufficient cooling capacity for power plants. At the same time, electric power consumption would increase drastically in the affected summer months, as the use of air conditioning in private homes would become the standard with daytime temperatures of up to 40 degrees. Agriculture would have to be converted to artificial irrigation in large parts of the Federal Republic of Germany, where irrigation from aquifers will not be possible everywhere for several months.

Science has the task of estimating these consequences as accurately as possible. For us model developers, this means that we will constantly improve our models, as accurate conclusions regarding the consequences are important. Ultramodern Earth observation systems will also play a significant part. The new era of data science will help in processing and analysing the resulting big data in order to efficiently incorporate it into our models.