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(3) How do I obtain the uncertainty estimate data based on the ERA5 EDA system?

Uncertainty estimates are available from the Copernicus Climate Change Service (C3S) Climate Data Store (CDS), as part of the  ERA5 dataset, and there as 'Product type' = 'Ensemble mean' and 'Ensemble spread'.

For 'authorized' users of ECMWF (e.g. National Meteorological Services, but not for users self-registered at ECMWF), the The uncertainty data is archived, as along with 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).

Public catalogue:  uncertainty estimate data is not publicly available (stream=enda, with type=em and type=es; http://apps.ecmwf.int/data-catalogues/era5/?class=ea&stream=enda&expver=1)

(type=em), Ensemble standard deviation (type=es) and Scaled ensemble standard deviation (type=ses). MARS catalogue entry point (restricted): http://apps.ecmwf.int/mars-catalogue/?class=ea&stream=enda&expver=1. See also: How to download ERA5 data via the ECMWF Web API.

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On MARS, there are two ensemble spread values: ensemble standard deviation (es) and scaled ensemble standard deviation (ses). What is the difference between them and which one should be used?

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.

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