If we gradually clean out data files more than one month old, first delete the old files, then delete directories left empty after the first step.

find $HOME/$DIR -mtime +31 -type f -delete; find $HOME/$DIR -type d -empty -delete

One could put it in crontab, for example,

@weekly find $HOME/$DIR -mtime +31 -type f -delete; find $HOME/$DIR -type d -empty -delete