Data from Climdex has been created by numerous authors over many years (see here for dataset citations) and are provided for use under several licenses, depending on the dataset you want to use and why.

The gridded datasets associated with HadEX2 and HadEX3 are available under the Creative Commons Attribution 4.0 license, while the station index files associated with these datasets are available under the Attribution-NonCommercial-ShareAlike 4.0 International license - where the station data has been shared by the provider. The gridded HadEX2 and HadEX3 data are available for commercial use while the station files that have been made public are not.

Both the gridded and station files associated with GHCNDEX are available under the Creative Commons Attribution 4.0 license and are available for commerical use.