EM 1110-2-1100 (Part II)
(Change 1) 31 July 2003
(d) Synoptic-scale winds in nonequatorial regions are usually close to a geostrophic balance, given that
the isobars are nearly straight (i.e. the radius of curvature is large). For this balance to be valid, the flow must
be steady state or very nearly steady state. Furthermore, frictional effects, advective effects, and horizontal
and vertical mixing must all be negligible. In this case, the Navier-Stokes equation for atmospheric motions
reduces to the geostrophic balance equation given by
1 dp
Ug '
(II-2-10)
ρa f dn
where
Ug = geostrophic wind speed (located at the top of the atmospheric boundary layer)
dp/dn = gradient of atmospheric pressure orthogonal to the isobars
Wind direction at the geostrophic level is taken to be parallel to the local isobars. Hence, purely geostrophic
winds in a large storm would move around the center of circulation, without converging on or diverging from
the center.
(e) Figure II-2-12 may be used for simple estimates of geostrophic wind speed. The distance between
isobars on a chart is measured in degrees of latitude (an average spacing over a fetch is ordinarily used), and
the latitude position of the fetch is determined. Using the spacing as ordinate and location as abscissa, the
plotted, or interpolated, slant line at the intersection of these two values gives the geostrophic wind speed.
For example, in Figure II-2-9, a chart with 3-mb isobar spacing, the average isobar spacing (measured normal
to the isobars) over fetch F2 located at 37 deg N. latitude, is 0.70 deg latitude. Scales on the bottom and left
side of Figure II-2-12 are used to find a geostrophic wind of 34.5 m/s (67 kt).
(f) If isobars exhibit significant curvature, centrifugal effects can become comparable or larger than
Coriolis accelerations. In this situation, a simple geostrophic balance must be replaced by the more general
gradient balance. The equation for this motion is
2
Ug r
1 dp
Ugr '
(II-2-11)
%
ρa f dn
f rc
where
Ugr = gradient wind speed
rc = radius of curvature of the isobars
Winds near the centers of small extratropical storms and most tropical storms can be significantly affected
and even at times dominated by centrifugal effects, so the more general gradient wind approximation is
usually preferred to the geostrophic approximation. Gradient winds tend to form a small convergent angle
(about 5o to 10o) relative to the isobars.
(g) An additional complication results when the center of a storm is not stationary. In this case, the
steady-state approximation used in both the geostrophic and gradient approximations must be modified to
include non-steady-state effects. The additional wind component due to the changing pressure fields is
Meteorology and Wave Climate
II-2-19
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