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

A rather complex subject Julian. Stability is also a factor. In very stable
conditions it is not *that* unusual for the the surface wind to be 40 or 50
deg backed from Geostrophic. Your 'rule of thumb' of a 50% increase in speed
between the surface and 2000FT is rather large and probably applies mainly
to daytime and unstable airmasses. At low wind speeds local topography
becomes very important.
Cheers
John
York,
North Yorkshire.
(Norman Virus Protected)

"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

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

"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

"Isohume" wrote in message
...
You forgot to account for surface friction....this is what causes the
imbalance between the PGF and coriolis near the surface.

No, take a look at the diagram. I just resolved the forces perpendicular to
the surface friction.

Julian Scarfe

Julian Scarfe wrote:
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



In addition to the other reasons already posted:

The difference of 2000 feet near sea level, corresponds to a
pressure-level difference of approximately 60 mb. Because of horizontal
temperature differences, or other dynamic effects, the pattern of
pressure distribution at 2000 ft is different than that at the surface,
and thus the pressure forces producing the airflow at 2000 feet, are
different than the pressure forces producing the airflow at the surface.

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

"Julian Scarfe" , while facing east, summoned the
courage to declaim:

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?

hmmm, I'm fairly certain that it has to do with the fact that eddy
viscosity is not uniform with height in the PBL. But I've had a
couple of glasses of wine tonight, and am not up to doing the math...


--
Dogs flew spaceships! The Aztecs invented the vacation! Men and
women are the same sex! Our forefathers took drugs! Your brain
is not the boss! Yes, that's right - Everything you know is WRONG!

On Thu, 5 Feb 2004 23:39:17 -0000, Julian Scarfe wrote in


"Isohume" wrote in message
...
You forgot to account for surface friction....this is what causes the
imbalance between the PGF and coriolis near the surface.

No, take a look at the diagram. I just resolved the forces perpendicular to
the surface friction.

I agree with that, based on the simple model. Julian - did you see my
other post pointing out the friction force at any one height wasn't
necessarily opposite to motion. That makes your calculation miss out a
contribution *from* friction - this has to be incorporated therefore.

--
Mike 55.13°N 6.69°W Coleraine posted to uk.sci.weather 06/02/2004 07:43:06 UTC