image © AzriSuratmin/iStock/Thinkstock
image © AzriSuratmin/iStock/Thinkstock
No NWP model can produce consistently or precisely correct forecasts and there must be some uncertainty in the results of each forecast. The value of NWP forecasts would be greatly enhanced if the quality of those forecasts could be assessed beforehand. Methods have been, and continue to be, developed to provide advance knowledge on the certainty (or uncertainty) of a particular forecast, and what possible alternative developments might occur. This is in parallel with improving the observational network, the data assimilation system, and the NWP models themselves.
The ECMWF forecast ensemble is based upon the idea that incorrect forecasts result from a combination of initial analysis errors and model deficiencies. Errors in the initial analysis dominate during the first five days or so.
Forecast models can produce incorrect results because of:
But even very good analysis systems and forecast models are prone to errors.
Analysis errors amplify most easily where the the atmosphere is most sensitive to small differences, in particular where strong baroclinic systems develop. These errors then move downstream and further amplify or change, and thereby affect the large-scale flow.
To investigate the impact of the effects listed above an ensemble of forecasts is run from many (currently 50) different “perturbed” initial states and one "unperturbed" analysis. The different perturbations are derived at analysis time during the generation of the ensemble.
The ENS forecast suite is run using each of the perturbed analyses as a starting point. For the perturbed ensemble members, further perturbations are continually inserted during execution in order to deal with:
The perturbations are supplied by:
The ensemble control member is run using the unperturbed analysis and without additional perturbations during execution.
The 51 forecasts give a range of results which may diverge radically or remain broadly similar.
Processing the ensemble of forecasts is computationally expensive. In order to save computation time the ensemble members are run with a lower resolution than the HRES (currently 18km compared to 9km for HRES).
The way in which the perturbed forecasts differ from each other gives valuable information on weather patterns that are likely to develop or, often equally importantly, not develop.
When the forecasts of perturbed ensemble members more or less agree with the control forecast then the atmosphere can be considered to be in a predictable state. Any of the expected analysis errors would not have a significant impact. In this a case it would be possible to issue a categorical forecast with reasonably high certainty.
When forecasts of perturbed ensemble members deviate significantly from the control forecast and from each other, the atmosphere can be considered to be in a rather unpredictable state. In this case it would not be possible to issue a categorical forecast with any certainty.
Guidance is given elsewhere within the this User Guide regarding:
Fig5.1: An ensemble of forecasts produces a range of possible scenarios rather than a single predicted value.
The initial condition or analysis is the control member. Small perturbations added to or subtracted from the initial distribution of a parameter give several (50 at ECMWF) additional analyses for use by ensemble members. Each analysis is slightly different from the initial condition and the distribution of initial temperatures is shown by the small peak on the diagram. However, each ensemble analysis has the same probability.
The ensemble members evolve through the forecast period in slightly different ways. The diagram shows schematically changes through the forecast period of temperature of each ensemble member.
The distribution of the ensemble member forecasts gives an indication of the likelihood of occurrence of the different scenarios. A few ensemble members are grouped to give a similar forecast that is cooler (3 members) or much warmer (2 members) than the initial conditions. These are shown by small peaks in ensemble member numbers on the right of the diagram. But the majority show a modest warming over initial conditions shown by the larger peak. Each individual solution has equal probability with the others. But while the solutions associated with the smaller peaks are possible, the solution associated with the larger peak is more probable.
The ensemble mean forecast, or if required the ensemble median forecast (not necessarily the same as the ensemble mean) can be calculated from the ensemble. This tends to average out the less predictable atmospheric scales. The accuracy of the ensemble mean can be estimated theoretically by the spread of the ensemble. So, on average, the expected ensemble mean error is proportional to ensemble spread. Importantly, the probability of alternative developments may be calculated from the ensemble. This is particularly important where assessing the risk of extreme or high-impact weather.
The ensemble spread is a measure of the difference between the members and is represented by the standard deviation (Std) with respect to the EM. On average, small spread indicates high forecast accuracy of the ensemble mean, and indeed of the ensemble members in general; larger spread corresponds to lower forecast accuracy of the ensemble mean, and of most of the ensemble members. The ensemble spread is flow-dependent and in relative terms will vary for different parameters (e.g. in winter anticyclonic conditions over land spread might be relatively high for 2m temperature, but relatively low for mean sea level pressure). Spread usually increases with the forecast range, but there can be cases when the spread is larger at shorter forecast ranges than at longer ranges. This might happen when the first days are characterized by strong synoptic systems with complex structures but are followed by large-scale ““fair weather”” high pressure systems.
The spread around the ensemble mean as a measure of accuracy applies only to the ensemble mean forecast error. It does not apply to the median, nor the control, nor HRES, even if they happen to lie mid-range within the ensemble. The spread of the ensemble, relative to a particular ensemble member (including the control member) is, for example, about 41% larger than the spread around the ensemble mean (see Fig5.2).
Fig5.2: The diagram shows schematically the relation between the spread of the ensemble for the whole forecast range (orange shaded area). The EM (red line) lies in the middle of the ensemble spread whereas any individual ensemble member (blue line), can lie anywhere within the spread. The Control (green line), which does not constitute a part of the plume, can even on rare occasions (theoretically on average 4% of the time) be outside the plume.
Forecasts from a good ensemble should:
Systematic errors can be detected:
(Note: In older material there may be references to issues that have subsequently been addressed)