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Any data in the CDS catalogue can be accessed in these two ways. And since such data is kept online, access is usually fast. Some parts of the ERA5 dataset are not listed in the CDS catalogue. These are only accessible through the CDS API service. An example is ERA5 model level data that resides in the the ECMWF's MARS tape archive. The extraction of such data from tape can lead to significantly longer retrieval times than data that is available online.
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