**All our forecasts and reanalyses use a numerical model to make a prediction. We have developed our own atmospheric model and data assimilation system which is called the Integrated Forecasting System (IFS). We also use and develop community models to represent other components of the Earth system.**

To produce a weather forecast we need to model the dynamics of the atmosphere and the physical processes that occur, such as the formation of clouds, and the other processes in the Earth system that influence the weather such as atmospheric composition, the marine environment and land processes.

Any forecast we produce is limited by the fact that the atmosphere is chaotic (we can never fully know the exact initial state of the atmosphere) and that our numerical models cannot perfectly represent the laws of physics governing the dynamic equations. We also have to simplify our models of many processes which occur at very small scales, such as cloud formation. This means that all forecasts will have some uncertainty associated with them. We pioneer methods to quantify the forecast uncertainty and provide a probabilistic forecast.

## The Integrated Forecasting System (IFS)

The comprehensive Earth-system model developed at ECMWF in co-operation with Météo-France forms the basis for all our data assimilation and forecasting activities. All the main applications required are available through one computer software system called the Integrated Forecasting System (IFS).

Since summer 2023, ECMWF has also been developing a machine learning model, the Artificial Intelligence/Integrated Forecasting System (AIFS). This model is currently in its beta phase, and experimental runs are available on our charts pages.

## Why probability forecasting?

Traditionally numerical weather prediction has advanced progressively by improving single, ‘deterministic’ forecasts with an increasing model accuracy and decreasing initial condition errors. However, the meteorological atmosphere is a chaotic system on time scales of a few days and weeks, depending on the spatial scales of interest. (The climatic system is also chaotic, but on much longer timescales.) Also the behaviour of our numerical simulations of the atmosphere would continue to be affected by the problems typical of model simulations of chaotic dynamical systems even if we could have perfect initial conditions, write perfectly accurate evolution equations and solve them with perfect numerical schemes, just because of the limited number of significant digits used by any computer (Lorenz, 1963).

Looking at the problem from a slightly more fundamental point of view, a forecast explicitly cast in probability terms is better not only because it provides the user with an estimate of the error ‘of the day’, but because it is more ‘truthful’. So a probability forecast conveys a message which explicitly reminds the user that there is always a forecast uncertainty which should be considered, computed and taken into account when making any practical use of the forecast. In fact even ‘deterministic’ forecasts are in reality probability forecasts in disguise, since an error bar (even if only an average error bar) can and should always be associated with it. That error bar implies a probability distribution of predicted future states around a central value.