...
The uncertainty as defined for ERA5 by the Ensemble of Data Assimilations (EDA) system is not a classical measure of error with respect to the ERA5 reanalysis product. The EDA takes into account mostly random uncertainties in the observations, sea surface temperature (SST) and the physical parametrizations of the model. In principle, as long as these uncertainties are properly described and there are no additional sources of uncertainty, then the EDA will properly describe the reanalysis uncertainties. However, systematic model errors are not taken into account by the EDA and the errors (uncertainties) as defined by the EDA are uncorrelated Furthermore, for affordability reasons the EDA has a lower resolution than ERA5 itself, so the EDA system is unable to directly describe all the uncertainties of ERA5. Therefore, in summary, there are limitations on the use of the EDA system for uncertainty estimation in ERA5 because not all the uncertainties are accounted for and also because the EDA system was not actually designed for uncertainty estimation. Nevertheless, comparison of uncertainties provides excellent information on when and where the reanalysis products are more or less accurate (such as for recent dates compared to 30 years ago when fewer observations were available), and where for a given day or season there are larger uncertainties (such as close to tropical cyclones or in the storm tracks).
(3) How do I obtain the uncertainty estimate data based on the ERA5 EDA system?
The uncertainty data is archived, as all ERA5 data, in ECMWF's data archive MARS. Uncertainty data is archived in stream 'Ensemble data assimilation' (enda), as Ensemble mean (type=em), Ensemble standard deviation (type=es) and Scaled ensemble standard deviation (type=ses).
...
In general we recommend using the raw ensemble standard deviation (spread) values ("es" fields in MARS) instead of the scaled ensemble standard deviation ("ses" fields in MARS). In fact, the Climate Data Store (CDS) only contains the raw ensemble standard deviation fields. The scaled ensemble standard deviation is used to compute background error statistics for the higher resolution ERA5 model and contains much fewer variables and levels. The scaled ensemble standard deviation is only available at step=3h from the forecasts starting at 06 and 18 UTC on model levels (and at the "surface" for brightness temperature), while the ensemble standard deviation is available every 3h to step=18h, on model, pressure, potential temperature and potential vorticity levels and also at the surface. Users are encouraged to compute additional (beside ensemble mean and standard deviation) uncertainty parameters based on the raw ensemble members.
...
The main problem with the extra-tropical and tropical cyclones in terms of uncertainty is the fact that due to the lower resolution of the EDA system, the EDA members systematically overestimate the central pressure of the cyclone (i.e. the pressure is not sufficiently low). This means that the spread among the members remains small and consequently the EDA shows lower uncertainties than in reality. On the other hand the spatial pattern of the uncertainties correspond rather well with the actual cyclones. This is demonstrated for some extra-tropical cyclones like cyclone Desmond: 2015120500, cyclone Xaver: 2013120500 or the Great Storm of 1987 in the UK. In all of these cases the maximum spread values don't exceed 1 hPa, which is quite small. The pattern of large spread values is scattered throughout the domain, though the primary cyclones are reasonably well-marked in the uncertainty field (particularly for the 1987 storm). For tropical cyclones the spread values can be larger, as it is for a cyclone near to Japan in 1987 or for the Haiyan typhoon near to the Philippines. It is very interesting to see the case of Hurricane Sandy, where the region with the largest uncertainties is not fully in agreement with the location of the hurricane's eye, but with some peaks to the east and west of it (the values are larger to the east). This indicates the uncertainties related to the position of the hurricane. So overall the EDA spread can give a qualitative idea of the uncertainties relating to active systems such as cyclones, but it is unable to provide the right uncertainty amplitude due to the lower resolution of the EDA system.
...