Rossby parameter

The Rossby parameter (or simply beta $\backslash beta$) is a number used in geophysics and meteorology which arises due to the meridional variation of the Coriolis force caused by the spherical shape of the Earth. It is important in the generation of Rossby waves. The Rossby parameter $\backslash beta$ is given by[http://amsglossary.allenpress.com/glossary/search?id=rossby-parameter1 Glossary of Meteorology] {{webarchive|url=https://web.archive.org/web/20070816025249/http://amsglossary.allenpress.com/glossary/search?id=rossby-parameter1 |date=2007-08-16 }}, American Meteorological Society.[http://mesolab.meas.ncsu.edu/~linyl/mea713/Ch1_Note.doc Lecture Notes] {{webarchive|url=https://web.archive.org/web/20060908102254/http://mesolab.meas.ncsu.edu/~linyl/mea713/Ch1_Note.doc |date=2006-09-08 }} for Atmospheric Science Mesoscale Dynamics (MEA 713). North Carolina State University. Accessed 14 July 2007.

:$\backslash beta\; =\; \backslash frac\{\backslash partial\; f\}\{\backslash partial\; y\}\; =\; \backslash frac\{1\}\{a\}\; \backslash frac\{d\}\{d\backslash phi\}\; (2\; \backslash omega\; \backslash sin\backslash phi)\; =\; \backslash frac\{2\backslash omega\; \backslash cos\backslash phi\}\{a\}$

where $f$ is the Coriolis parameter, $\backslash phi$ is the latitude, $\backslash omega$ is the angular speed of the Earth's rotation, and $a$ is the mean radius of the Earth. Although both involve Coriolis effects, the Rossby parameter describes the variation of the effects with latitude (hence the latitudinal derivative), and should not be confused with the Rossby number.