How to estimate the uncertainty distribution X’ of Eq. (2) in ensemble forecasting? The principle is to describe all possible uncertainty sources in a modeling system as accurately and completely as possible and then to incorporate all those uncertainties (perturbation terms) into the numerical model to be integrated in time to produce a finite size ensemble of forecasts. As an approximation to a theoretically infinite ensemble, the finite size ensemble is then used as the basis to estimate probabilistic distribution and uncertainty or confidence of a forecast. Below is a brief summary of currently existing approaches. Based on the approaches used, EPS could be classified into three general categories: 1-Dimensional, 2-Dimensional and 3-Dimensional systems.

1-Dimensional EPS

2-Dimensional EPS