A huge amount of the work in analyzing measurements of earth's atmosphere in order to assess climate variability consists of clever applications of the SVD.
See for example [this paper](https://doi.org/10.1142/9789812703347_0007) by Coughlin and Tung or [these notes](https://atmos.uw.edu/~dennis/552_Notes_ftp.html) from a course taught by Dennis Hartmann (which was my intro to the subject).