a direct proportionality existing for each latitude. 
A strong gradient means contours
are close together. For example, if winds were geostrophic, height contours would be 3 × further
apart for 20 kt winds than for 60 kt winds at 30 °N. Geostrophic wind speed is inversely
proportional with the sine of latitude though, so height contours would be twice as close at
the North Pole than at 30 °N for 60 kt winds at each. If a little confusing, then the diagram to
left may help. I thought avoiding further complication using geopotential height would be best
here, which requires small adjustments because of latitudinal and vertical variations with
respect to height.
Perhaps you can see that for curved flow (gradient winds), this exact proportionality is not
true because of term 3. If you recall our coordinate system, s is positive for counterclockwise
flow (normal Northern Hemisphere cyclonic flow); so pressure gradient is balanced with an extra
term. Thus for the same height gradient (contour spacing), winds are weaker for
positive flow and stronger for negative flow. For normal atmospheric situations where
applicable, the curvature term 3 is typically smaller than the coriolis term 2. So for the above
example of 60 kt winds at 30 °N, wind would be perhaps 45 kt for cyclonic flow or 80 kt for
anticylonic flow as illustrated.
Analysis Techniques
Below are a surface, 850 mb, and 500 mb charts for 00 UTC 3 January 1999 (6 PM CDT 2 January
1999). A strong snowstorm was occurring over the southwest Great Lakes and surrounding regions
@ that time - click on images (which open in a new window) for additional commentary, but
commentary is best read after the entire text of this article is :
Surface chart
850 mb chart
500 mb chart
Let's first consider height contours on the upper air charts (850 &
500 mb). Height contours above the atmospheric boundary layer should generally be parallel with
winds. This is not exactly so for several reasons - the most important of which are (geostrophic)
flow adjustment processes, relatively small amounts of friction, and influence of convective
disturbances and mesoscale (generally a few to a few hundred km spatial scale) storm circulations.
The latter is not so important for a winter storm such as this. Regarding spacing, linear
interpolation is almost never bad - often a good first approximation; but then should be adjusted
for wind speed. As illustrated above, contour spacing should be roughly inversely proportional
with wind speed (twice as close together for twice as fast winds, etc.), with adjustments for
curvature and latitude. This is not a strict rule, but gradient wind is not a bad approximation
above the ABL. Before objective analysis was so common, graphical guides such as that shown below
were used :
This is a transparent plastic object which can be placed over a map of the specified projection
and scale. The bottom diagram shows how height/pressure contours correspond with geostrophic wind
speeds. Characteristics mentioned above of how contour spacing corresponds with geostrophic wind
speed are evident - spacing of straight contours on a map should theoretically be the distance
slanted lines are from the bottom horizontal line. The series of curves to its upper right are
curvature parameters for gradient winds. Please notice that the numbers shown are not curvature
radius r as defined above. They are actually opposite - 0 corresponding with a straight contour
line and increasing numbers corresponding with sharper curvature. The 2 tables above list how
gradient wind speeds should be adjusted from geostrophic values for specific curvature radii.
This is not presented for use, but simply as a good illustration of some of the concepts
discussed, how they affect chart analysis, and a practical solution for dealing with this. An
analyst would not examine every curve & line, making sure that they correspond with the guide;
but do spot checks for making sure the analysis is generally accurate and consistent, and use
it for questionable regions and realism of supposed small-scale features such as shortwave trofs
(small wavelength trofs). I don't think I have any maps of the type this is valid for, so the
main thing I use it for now is a hard, flat writing surface 
If you want this diagram further explained though, please ask.
Contours of surface altimeter settings are similar with geopotential height contours; though
with friction being much more important, winds tend to flow toward low pressure and away from
high pressure as well as around. The same basic characteristic of strong winds corresponding
with close contours exists, though factors such as flow over variable surfaces and sometimes
inconsistent wind measurement heights make a strict equation impossible.
A general tendency you likely notice is how contours can sharply vary at the surface but
become progressively smoother further aloft. This is mainly because of surface friction, that
fronts are generally best defined near the surface, that most atmospheric turbulence occurs in
the lower atmosphere, and because surface data is much more abundant than aloft. If more data
were available aloft, perhaps those maps wouldn't appear quite as smooth. I suppose I analyzed
the 500 mb chart a little like a klutz, but the worse problem would be portraying features
which aren't present. Some shortwave trofs and microridges may be present at 500 mb which aren't
analyzed, but my advice is not assuming so unless you have good evidence that such features
exist - such as a locally sharp height gradient which corresponds well with shifting or turning
winds, a clearly associated feature on satellite or radar imagery, etc. I had neither of the
available for this analysis, but I think the charts are sufficient for illustrative purposes.
Regarding isotherms, linear interpolation is often very good. Exceptions may be locations
where you know a gradient is likely sharper because of a surface front, cloudy or clear areas,
etc. These should also be smooth unless a good reason is known why they shouldn't.
For any type of contours, be aware of an undesirable tendency of steering around stations.
Remember that the data is not perfect, and drawing a curve which does not interpolate can be
correct. Some data points may be grossly unrepresentative, and probably should be ignored.
I mention a few examples above along with the charts.
Text and embedded images are copyright of Joseph Bartlo, though may be used with proper crediting.
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These are illustrated to
left with their force balances. Because centrifugal force exists only in curved flow,
gradient wind is valid for it - if it can be
considered valid - see
item 17 in scetion B (main site);
but geostrophic wind only for straight flow. Both neglect friction, which
is not a bad approximation above the atmospheric boundary layer (ABL), especially in the middle
atmosphere. Both flow parallel with isobars and (geopotential) height contours, which
are nearer where winds are strongest. "How near?" is actually a rather important question
for chart analysis, as shown below.