Weather models map the events in the atmosphere with the help of mathematical formulas. These numerical forecast models are now the standard method of producing weather forecasts. Considerable progress has been made in recent decades in understanding the chemical and physical processes in the atmosphere. Furthermore, the spatial resolution (mesh size) of the numerical models has greatly improved.

### How uncertainty arises

Despite the progress that has been made, some processes can still not adequately be represented by numerical models. Some are still represented by means of parameterisation, whereby a process is not represented physically on the basis of one or more physical laws, but in a simplified way using a surrogate method.

Further uncertainty arises when the values of the individual parameters describing the state of the atmosphere at the beginning of the numerical simulation are not definitively known. This is the case in spite of the fact that frequent observations and measurements (e.g. those taken at ground-level weather stations and various observation networks for gathering atmospheric data enable continual improvements to be made.

These values (also called initial conditions) are important for initiating the model simulations. Due to the chaotic nature of the atmosphere, small differences or uncertainties in the initial conditions can lead to large differences between simulations produced by the same numerical forecasting model.

### How uncertainty is quantified

Consequently, every weather forecast is subject to a certain degree of uncertainty. To quantify this uncertainty, a so-called ensemble approach is used for the numerical models. This means that several scenarios are calculated for the same time period using the same numerical model, but with slight adjustments, e.g. to the initial conditions that are entered as the starting parameters for the simulations. In contrast, when a single scenario is calculated and represented, this is referred to as a deterministic approach.