Weather is unpredictable. Small differences in initial conditions can develop into big differences in the pattern of circulation, in the timing and location of cyclones, rainfall etc. This is true no matter how good the initial observing system is.
The approach taken by organisations such as ECMWF or NCEP is to re-run numerical forecast models with a range of carefully chosen initial conditions. The collection of runs is called the ensemble. Ensemble prediction systems (EPS) give probabilistic forecasts for variables such as rainfall, temperature etc. Current operational EPS have 20 (GFS) or 51 (ECMWF) ensemble members from which the probability distributions are derived. ECMWF give an overview of their system here. The probability distributions capture part of the intrinsic uncertainty in weather or climate.
The graph below shows histograms of 20 ensemble member temperatures near some major cities. The data were extracted from NCEP GENS 16-day 2m temperature forecast produced at 00UTC 2 Feb 2010 (i.e GFS forecasts for 18 Feb).
The maps below show some corresponding ensemble statistics for the entire globe (1° resolution, equal area cylindrical projection).
The upper map indicates that forecast uncertainty (standard error) is high between 40° and 60° in both hemispheres (related to the chaotic behaviour of jet streams.) Currently, 16 day temperatures north of Lake Baikal in Siberia are very uncertain, for example. The contours indicate ensemble median temperatures.
Skewness in ensemble temperatures is shown in the lower map. For example, large negative skewness is found in north central US, eastern mediterranean, and Paraguay/Mato Grosso. This suggests tail risk of low temperatures relative to ensemble mean in these areas.
EPS is the future of weather and climate forecasting. These systems produce huge amounts of data. Building useful applications of EPS is both a challenge and an opportunity.
For anyone interested, the R code used to produce these graphs is given here.