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

On Thu, 5 Feb 2004 09:14:31 -0000, Julian Scarfe wrote in


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?

As John Whitby suggests, stability may well be a factor, but is not built
into that simple model. Another factor, related I think, is the model,
being so simple, is probably based on laminar flow theory - to make
understanding easier. Introduce turbulent flow, which we have to in the
real atmosphere to varying degrees, and the simplicity of that model is
seen to introduce errors when it comes to making any calculations.

--
Mike 55.13°N 6.69°W Coleraine posted to uk.sci.weather 05/02/2004 13:21:41 UTC

On Thu, 5 Feb 2004 09:14:31 -0000, Julian Scarfe wrote in


So where does the model above break down?

"Mike Tullett" wrote in message
...

As John Whitby suggests, stability may well be a factor, but is not built
into that simple model. Another factor, related I think, is the model,
being so simple, is probably based on laminar flow theory - to make
understanding easier. Introduce turbulent flow, which we have to in the
real atmosphere to varying degrees, and the simplicity of that model is
seen to introduce errors when it comes to making any calculations.

John, Mike, thanks for the replies.

To clarify, I'm sure the variation in wind speed within the boundary layer
is complex and depends on a multitude of factors. The main issue for me is
the dependence of direction on speed. As far as I can see, provided the
only force acting, other than the coriolis and pressure gradient forces, is
frictional (along the velocity vector) then the balance of forces guarantees
the relationship

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

I can imagine that tubulence introduces random errors, but empirically it
looks to me as if

(Wind speed at surface) is much less than (Geostrophic wind speed) *
cos(veer)

or putting it another way

veer is much less than arccos ((Wind speed at surface)/(Geostrophic wind
speed))

Julian Scarfe

"Julian Scarfe" wrote in message news:rtvUb.17887
So where does the model above break down?

John, Mike, thanks for the replies.

To clarify, I'm sure the variation in wind speed within the boundary layer
is complex and depends on a multitude of factors. The main issue for me
is
the dependence of direction on speed. As far as I can see, provided the
only force acting, other than the coriolis and pressure gradient forces,
is
frictional (along the velocity vector) then the balance of forces
guarantees
the relationship

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

I can imagine that tubulence introduces random errors, but empirically it
looks to me as if
(Wind speed at surface) is much less than (Geostrophic wind speed) *
cos(veer)
or putting it another way
veer is much less than arccos ((Wind speed at surface)/(Geostrophic wind
speed))

Julian Scarfe


I agree the simple model you suggest does give *wrong* answers for amount of
backing. Your equation suggests, for example, that given a Geostrophic wind
of 35 knots and a mean surface wind of about 23 knots ( a not unreasonable
value) the backing should be of the order of 48deg - which is certainly far
too large (20 to 30 deg is more likely).
So, as has been suggested, other forces are involved in the *real*
atmosphere.
John
--
York,
North Yorkshire.
(Norman Virus Protected)

On Thu, 5 Feb 2004 17:56:40 -0000, Julian Scarfe wrote in

snip
To clarify, I'm sure the variation in wind speed within the boundary layer
is complex and depends on a multitude of factors. The main issue for me is
the dependence of direction on speed. As far as I can see, provided the
only force acting, other than the coriolis and pressure gradient forces, is
frictional (along the velocity vector) then the balance of forces guarantees
the relationship
snip

Ah now I can spot the problem with that simple model when you wrote
"...frictional (along the velocity vector).." The form of friction is not
as simple as that affecting an object moving in contact with the ground.
Instead, it is a form of internal friction called "eddy viscosity"
(hundreds of times more important than molecular viscosity) and, whilst
opposing motion, isn't necessarily "along the velocity vector". In fact it
can be at quite a large angle to it.

If you go to the next page on that website you will see an interactive
diagram, where you can change the amount of surface roughness and height
above the ground. Let the slider fall to 10 metres and you will see the
friction arrow is about 40 degrees to the wind arrow, as opposed to the 0
degrees as shown on the simple model on previous page.

My guess is the first diagram is better suited as an "average" for the
Ekman Layer (The Friction or Boundary Layer) - not to any one height within
it. Mind you I have to admit it formed the core of one or two of my
lectures:-)

Here is the link to that interactive graph.

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

or http://makeashorterlink.com/?N2E233057

--
Mike 55.13°N 6.69°W Coleraine posted to uk.sci.weather 05/02/2004 20:20:19 UTC

"Mike Tullett" wrote in message
...

Ah now I can spot the problem with that simple model when you wrote
"...frictional (along the velocity vector).." The form of friction is not
as simple as that affecting an object moving in contact with the ground.
Instead, it is a form of internal friction called "eddy viscosity"
(hundreds of times more important than molecular viscosity) and, whilst
opposing motion, isn't necessarily "along the velocity vector". In fact it
can be at quite a large angle to it.

Ah, got it!

Thanks for that, and the links, Mike.

And thank you to everyone who replied. Lots of useful stuff -- particularly
Bernard's empirical ratios and angles.

Julian Scarfe

On Fri, 6 Feb 2004 08:45:29 -0000, Julian Scarfe wrote in


Ah now I can spot the problem with that simple model when you wrote
"...frictional (along the velocity vector).." The form of friction is not
as simple as that affecting an object moving in contact with the ground.
Instead, it is a form of internal friction called "eddy viscosity"
(hundreds of times more important than molecular viscosity) and, whilst
opposing motion, isn't necessarily "along the velocity vector". In fact it
can be at quite a large angle to it.

Ah, got it!

Thanks for that, and the links, Mike.

And thank you to everyone who replied. Lots of useful stuff -- particularly
Bernard's empirical ratios and angles.

I'm pleased we seem to have got to the bottom of this problem. In fact, it
caused me to go back to material I last dealt with many years ago and it
refreshed my ageing brain:-) As someone else pointed out, dealing
mathematically with this type friction - eddy viscosity - is pretty
horrendous and probably beyond me now.

One peculiarity of the speed profile in the boundary layer, is that both
theory suggests (whether based on Ekman's original simplified work, or
later modified work) and actual observation of winds shows - for a small
height range near the top, the wind goes super-geostrophic.

This change of direction and speed is also observed in wind induced surface
movement of the seas (Ekman Transport). The surface movement is about 45
degrees to the right wind direction, but it veers increasingly with depth.
This veering leads to another peculiarity. At a certain depth in the
water, the direction of movement is exactly opposite to that of the surface
flow, but the speed is tiny in comparison. The effect of the wind ceases
at about 100m - the Depth of Friction Influence.

--
Mike 55.13°N 6.69°W Coleraine posted to uk.sci.weather 06/02/2004 15:47:06 UTC

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

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