Julian,
As other replies to your query have said, the rotation of wind direction in
the boundary layer is more complex than your simple calculation would
suggest.
The coupling of the flow in the free atmosphere, at, say, 700 to 1000 m
above the surface, with that near the ground critically depends on the
stability in the layer, the more unstable, the greater the coupling. Indeed,
in very stable conditions, coupling can virtually cease, and the surface
wind may give little indication in either direction or speed to the flow
above (e.g.. radiational cooling at night, and diurnal cycle of wind at the
surface), The surface roughness is also important, as it is the frictional
drag on the surface airflow that results in the vertical shear in the
boundary layer. I think it is this factor that your source fails to take
into account.
I can give you some figures from my forecasting days, obtained from
empirical studies 1) on the weather ships (i.e. over the open ocean) 2) over
land at Heathrow.

1) over the ocean (speed ratio, 10m/900m, knots. direction rotation
angle, degrees)
Stability Wind at 900m
up to 19 20-29 30-39 40-49
50
Very unstable 0.95 0 0.90 0 0.85 0 0.80 0 0.80 0
Very stable 0.75 15 0.70 20 0.65 20 0.60 20 0.55 25

2) over land
Very unstable(day) 0.65 5 0.55 5 0.50 10 0.50 10 0.35 15
Very stable (night) 0.30 45 0.25 40 0.25 35 0.30 30 no obs

See also Findlater,J., Harrower, T.N.S., Howkins, G.A., and Wright, H.L.,
1966: Surface and 900 mb wind relationships. Scientific Paper No 23. London.
HMSO.

Hope this is of help.

--
Bernard Burton
Wokingham, Berkshire, UK.


Satellite images at:
www.btinternet.com/~wokingham.weather/wwp.html
"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