You forgot to account for surface friction....this is what causes the
imbalance between the PGF and coriolis near the surface.


"Julian Scarfe" wrote in message
...
I'm puzzled. Why is the rotation of wind direction between surface and
say
2000 ft as low as it is?

The classic explanation of the difference between surface wind and
geostrophic wind, e.g.

http://ww2010.atmos.uiuc.edu/(Gl)/gu...r/fw/fric.rxml

leads to a fairly easy quantitative conclusion. Looking at the diagram on
that page, you can do some trivial trigonometry and conclude that

(Coriolis force at surface) = (Pressure gradient force) *
cos(angle_of_veer)

[where angle_of_veer is the angle between the surface wind and the
geostrophic wind]

so

(Coriolis force at surface) = (Coriolis force of geostrophic wind) *
cos(angle_of_veer)

But since the coriolis force is proportional to the wind speed, then

(Wind speed at surface) = (Geostrophic wind speed) * cos(angle_of_veer)

So we should be able to relate the change in wind speed to the
angle_of_veer.

Angle Ratio of Surface wind to geostrophic wind

10 98.5%
20 94%
30 87%
60 50%

So far so good, but I don't think it tallies with reality. The pilot's
rule-of-thumb is that the wind at altitude veers 30 degrees and doubles in
strength. It varies but that's not unusual. It's not uncommon to see
doubling or tripling of wind speed as you cross the boundary layer, but
veer
angles don't often exceed 30 degrees. A 60 degree veer seems very
unusual.

But according to the formula above, a ratio of 50% should be associated
with
a 60 degree veer, or putting it the other way round a 30 degree veer
should
be associated with a much smaller increase in wind speed.

So where does the model above break down?

Julian Scarfe