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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
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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).
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