The National Research Council (NRC) about once per decade does a major assessment of U.S. graduate programs.

While this assessment displays a wealth of incommensurate data (collected in 2005-2006), the data is inevitably organized into linear rankings by choosing weights for the various categories and averaging.

The methodology is different in this 2010 NRC assessment than before, but possibly the closest to the classical approach, which was comparisons of institutions by experts, is the NRC regression-based quality score (archived link).

This ranks UCSD mathematics research quality as 13th in the U.S.

Ranking has always been subjective, since the basic issue is impact of the research, and this is hard to quantify.

The ( archived link) website containing NRC data allows one to look at many metrics and to play with weighted averages of these metrics. It is fun to fiddle the weights and make up an ordering of your own.