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Dynamic Height(a.k.a. Geopotential) Jessie Sagona Physical Oceanography November 20, 2007
What is Dynamic Height? • Definition: The amount of work required to move a unit mass of water vertically from sea level to a given point. Or, the gravitational potential energy per unit mass. • = ∫α dp = ∫g dz • Equivalent to geopotential in the atmosphere (but opposite sign). • Variable designation: Φ or D • Units: J/kg or m2/s2 (don’t let the word “height” in the name fool you!)
Geopotential Height • Z = (1/g0)∫g dz from sea level to a given height (or depth). Z is also equal to Φ/g0. • g0 is defined as 9.80665 m/s2, the value of g at 45º N. • Gravity is a function of both height and latitude. Geopotential height takes this into account and allows you to use a constant 9.80665 for “g”.
Why is this better than geometric height? • The PE of a parcel raised to a geometricheight (recall g varies) is equal to the PE of a parcel raised to geopotential height. • Lines of constant geopotential have constant PE geopotential height is numerically proportional to PE. • Note that Z is smaller than geometric height in the mid-latitudes.
Use, and misuse, of Φand Z • Geopotential height is the standard vertical coordinate in both the atmosphere and the ocean. • White et al. (2004) note that models often assume that surfaces of constant geopotential are spherically uniform across the planet not true. • The difference between geometric and geopotential height may be small near the surface for both atm. and ocean, but it should not be neglected when precise calculations are attempted!
References • NASA Goddard Earth Science Data website http://daac.gsfc.nasa.gov/PIP/shtml/geopotential_height.shtml Accessed 11-16-07. • AMS Glossary http://amsglossary.allenpress.com/glossary/search?id=dynamic-height1 Accessed 11-16-07. • White, A.A. et al. Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic. Quarterly Journal of the Royal Meteorological Society, 131, pp. 2081-2107. 2005.