Turning With The Wind
Throughout the whole of history. . . . meteorological
theory has been invariably
hampered by want of facts. Sir Napier Shaw
in Manual of Meteorology,
Cambridge University Press, 1926.
To understand how it can
be so variable it is worthwhile to examine (1) how the Coriolis force
combines with the friction force to balance the pressure force,
(2) how the combined effect is often decreased or increased by height-changes
in the pressure force and (3) how mixing by natural turbulence can reduce
or eradicate the resulting steering.
The pressure force is usually
called pressure-gradient force by meteorologists but it is often
termed simply pressure force, as it is here. It is caused by the
difference in pressure from one place to another as seen by the isobar
pattern on a surface weather map. It is directed toward low pressure but,
except near the equator, air seldom moves directly across the isobars to
lower pressure. Instead, near the ground wind speed is reduced by
friction, the effects of which decrease with height. This causes the wind
speed to increase with height. It is accompanied by increase in Coriolis
force acting to alter wind direction.
Pressure-force change with
height may completely alter steering created by the above effect. Mixing
by natural turbulence may also significantly reduce or eliminate steering.
Details of these processes are the subject of this tutorial. By understanding
them one should be able to anticipate the possible steering conditions
likely to be encountered in different situations. The first tutorial in
this series, Flying Times and Windy Times (FTAWT), can provide a good review
to help understand the processes involved.
The following sections comprise
this tutorial:
1. Introduction.
2. Coriolis "Force."
3. Friction Force.
4. Coriolis and Friction
Combined.
5. Pressure Force Changes.
6. Turbulent Mixing.
7. Summary.
There are nine figures,
each carefully chosen or constructed to aid comprehension. Identification
of the source of each is given in a listing following the Summary. All
figures should be examined carefully while reading the text.
1. The
Coriolis "Force."
The Coriolis force is defined
as an apparent force. It is included in nearly all analyses of atmospheric
motion in order to apply the basic laws of physics. Specifically, if one
wishes to reason with Newton's fundamental law that a body will stay at
rest, or move in a straight line at a constant speed, unless an unbalanced
external force acts on it, the motion must be measured relative to a fixed
object that, itself, is not changing speed or direction. Any place on the
earth's surface is continuously changing its direction relative to a distant
star, in effect a fixed object. Because we are interested in air motion
relative to the earth, an adjustment has to be made. Coriolis showed how
an analysis of motion relative to a turning frame of reference can be made
by simply adding a fictitious force in Newton's laws.
The problem may be visualized by thinking of the earth turning underneath the atmosphere while the air is moving in response only to a constant, horizontal change in atmospheric pressure from one place to another. If it moves, following Newton's law, in a straight line in a frame of reference separate from the earth, steady and fixed in space, the air will appear to move to the right, i.e., veer, in the Northern Hemisphere relative to the earths surface. In the Southern Hemisphere it will appear to move to the left, i.e., back.
If the wind happens to blow exactly along the equator the effect is absent. The difference between the two hemispheres arises because of the inherent difficulty in mapping the spherical earth on a flat surface. A geographical map of the southern hemisphere is shown from a different point of view than is done for one of the northern hemisphere. A typical map of Antarctica, for example, has the earth turning in a clockwise sense; one of the Arctic Ocean in a counterclockwise sense.
There is another complication. In the usual analysis scheme,
atmospheric motion parallel to the earth's surface is treated is if it
were always on flat planes tangent to the earth's surface at every point
the motion is examined. (A flat table-top on which a ball is resting may
be regarded as a plane tangent to the ball at the point where the ball
touches the table.) The fractional amounts of the earth's rotation that
such tangent planes experience vary with latitude. A tangent plane at the
equator does not turn about an axis perpendicular
to its own surface as the earth rotates.
A tangent plane at one of the poles, however, makes a complete revolution
about its own perpendicular axis every
time the earth does the same. Between the equator and poles, the amount
of the earth's rotation shared by a tangential plane increases with increase
in latitude.
The amount of turning relative
to the earth depends on the length of the path. For a specific time interval,
the faster the air moves, the longer the path and the greater the departure
from a straight line. In atmospheric analysis, the Coriolis force is treated
as a real force, always acting to displace the air perpendicular to its
direction of motion. At a specific latitude, it is proportional to the
product of the rate of turning of the earth and the wind speed.
3. The Friction Force.
Wind speed near the ground
is reduced by friction. The friction force may not be directed opposite
to the wind, for at the lowest speeds it may nearly balance the pressure
force as it would with no motion. But as height increases, the force of
friction decreases with height because of air's small viscosity. Above
two or three thousand feet the friction force, based at the ground, can
be ignored in upper atmospheric analyses. The wind speed increases with
height until the friction force becomes insignificant. That height defines
the atmospheric boundary layer in many contexts.
Tall vegetation, buildings,
and topographic irregularities all increase the friction force. They are
more effective in combining with the Coriolis force than are smooth surfaces
such as water, flat snow-covered fields or level and open meadows.
4. Coriolis and Friction Combined.
Figure 3 shows diagrams
of Coriolis and friction forces balancing the pressure force and the associated
wind velocities at two heights. They are plan views; that is, they show
forces and velocities in the horizontal plane at each of two different
heights. Blue dashed arrows represent wind velocities, the arrows pointing
into the direction the wind blows and the arrow lengths, the relative
speeds. All other arrows represent forces as labeled. Like wind arrows,
the force arrow lengths represent relative magnitudes and they point the
direction into which the force is directed.
(1) As friction decreases
with height, wind speed increases;
(2) As speed increases,
Coriolis force increases, always remaining
perpendicular to speed;
and
(3) The combination of friction
force decreasing with height while Coriolis force increases, the two always
balancing the pressure force, creates the change in wind direction.
By constructing diagrams
similar to those in Figure 3 one can easily show the following:
(1) It is the change
in wind speed with height, not the overall speed itself, that is related
to direction change;
(2) An increase in the Coriolis force for a specific speed (such as the increase with the increase in latitude) has the effect of decreasing the direction change;
(3) Increase in the friction force increases the direction change; and
(4) If the pressure force
changes direction with height it would add to or subtract from the direction
change.
If one imagines the boundary
layer to consist of a series of stacked force-balances such as those in
Figure 3, each above one with a lower speed, the pattern shown in Figure
4 emerges. It is shown in both plan and perspective views for the Northern
Hemisphere. The speed increases and direction veers with increase in height.
5. Height Changes
in the Pressure Force.
A height change of the overall horizontal pressure pattern can counteract or add to the Coriolis/friction turning. If the height change in the pressure pattern is such that a wind resulting from it would veer with height, the effect is to add to the Coriolis/friction veering (Northern Hemisphere). If it backs with height it could entirely eliminate the usual veering and replace it with backing.
Height changes in the boundary-layer pressure pattern are difficult to measure. However they are physically related to the horizontal temperature pattern in the entire layer of air in which the change is taking place. The latter relationship was used the by the author of Reference 3 to obtain the data used to construct Figure 8. Data from 1,857 upper- air soundings taken at Shreveport, LA, were analyzed (two each day, 5 AM and 5 PM) along with data from four surrounding stations to determine the horizontal temperature pattern. Each of the four stations is about 200 miles from Shreveport and all are spaced nearly uniformly in the cardinal directions. The height interval varied from the ground to about 2000 feet (winter) and 3000 feet (summer).
Summing the percentages gives
54.6% for backing and 45.4% for veering. Except for the lowest category,
0 to 10 degrees, backing has higher percentages in all categories. There
were, in fact, three times as many occurrences of backing as of veering
in the 0 to 40 degree category.
A pressure-pattern height change, physically related to a horizontal temperature pattern, is usually accompanied by influxes of either warmer or colder air. Influx of warmer air (warm-air advection) is associated with pressure pattern veering and of colder air (cold-air advection) with backing in the Northern Hemisphere. (A memory help: VW and BC.) It is the opposite in the Southern Hemisphere.
Advection is particularly
strong after frontal passages. For Shreveport, Figure 8 indicates that
except for the data in the 0 to 10 degree category, cold-air advection
yields stronger backing than warm-air advection yields for veering. This
result corresponds to the general experience that cold- front passages
are followed by greater changes in temperature than are warm- front passages
in the broad Mississippi River valley. Awareness of frontal situations
and wind patterns, as can be seen on an ordinary surface weather map, can
help make qualitative estimates of advection and its effect on steering
for planning or navigating a flight.
6. Turbulent Mixing.
As described in FTAWT, mixing
by natural boundary-layer turbulence, particularly prominent in the daytime,
tends to eliminate significant height changes of average wind speed. Measurements
of wind-direction height changes in the boundary layer show the same effect.
The data in Figures 5 and 6, for example, were obtained during periods
of minimal turbulent mixing, allowing a significant average wind-speed
increase with height and the consequent direction change. Such conditions
are most pronounced and most frequent in the early morning hours when turbulence
is inhibited by cooler (more dense) air at the ground overlain by warmer
(less dense) air. This makes steering in a morning flight, just after sunrise,
more reliable than it is just before sunset when daytime turbulent mixing
may still be very effective in reducing or eliminating steering.
As described in FAWT, Sections
3,4,and 5, the average temperature change with height is a good measure
of the average height-change of air density, and therefore of enhancement
or inhibition of turbulence mixing. However, it has to be compared with
the Dry Adiabatic Lapse Rate (DALR) which is the height decrease in
temperature for density constant with height. At 5.5 deg F. per thousand
feet, it is needed to account for the always-present average pressure decrease
with height.
The terms stable,
neutral and unstable (describing stability) are used for
layers of air, respectively, that have lapse rates less than, equal to,
and greater than the DALR. The corresponding lapse rates are often termed,
or described, as inversions, adiabatic, and superadiabatic.
As noted in FAWT, Section 4, sometimes a neutral layer is termed unstable,
presumably because turbulence is not inhibited by an inversion. In addition,
the term inversion is often applied only to a temperature increase with
height, instead of including a decrease less than the DALR. These terms
are illustrated in FAWT, Figure 7.
A close relationship between
lapse rate and veering is shown by the unique data plotted in Figure 9.
It was taken from Reference 3 and slightly modified for clarity and to
show approximate times of sunrise and sunset. Wind direction differences
between 1,459 and 146 feet and temperature differences between 1,459 and
40 feet were measured on a television tower near Oklahoma City. Measurements
taken every five minutes were averaged to obtain hourly values for 3-1/2
days in March. The period was selected for its minimum change in the direction
of the pressure force. Winds speeds were greater than 6 knots.
Different from FAWT, Figure 11, Figure 9 has lapse rate plotted (on the right side of the diagram) instead of the higher-level temperature minus that at the lower level. In other words, they both have stability increasing upward on their scales, but Figure 11 uses a negative quantity as defined above. The veering scale (on the left side of the diagram) goes from -20 to +80 following the custom of calling backing a negative veering.
In examining Figure 9, one
should keep in mind that lapse rates may change significantly with height.
The changes are especially pronounced at sunrise and sunset transition
times as shown in Figures 9 and 10 in FAWT. It follows that one should
expect veering to have corresponding changes.
There is clearly a close
correspondence between the two graphs in the overall daily changes. A statistical
analysis of the two sets of data by the author of Reference 3 produced
optimum correlation when veering followed the lapse rate by an hour. This
corresponds to the above-mentioned fact that changes in stability, in a
typical daily pattern, grow in depth beginning at the ground during transition
periods.
Other notable features of
these graphs are:
1.) Each of the three days has an afternoon period of a super-adiabatic lapse rate that lasts until very close to sunset. Periods of backing occur at these same time intervals for all three days. They are times when ballooning is hazardous because mid-day heating is producing large turbulent eddies and thermals;
2.) Both stability and veering decrease rapidly near, or shortly after sunrise, just the time balloonists may be hoping for reliable steering forecasts;
4.) Stability and veering both increase following sunset to within an hour or two of sunrise; and
5.) In keeping with descriptions
given above of forces involved, the absence of pressure force direction
changes with height leaves veering present most of the time. Backing occurs
only in afternoons, with strong, large-scale turbulence associated with
solar heating.
Figure 9 should be regarded
as an example of boundary-layer conditions that illustrate the principles
at work in controlling wind direction changes with height. One should expect
many different patterns to emerge as the temperature lapse rate responds
to normal transition-time changes and changes in cloudiness and overall
wind speed. An additional influence is pressure-force backing or veering.
Cold-air advection associated with pressure-force backing may increase
instability (and decrease veering) near the ground as it replaces ground
warmed earlier by the air it is replacing. The opposite occurs for warm-air
advection, i.e., stability and veering are increased.
In addition to being relatively
easy-to-measure the temperature lapse rate can be usefully estimated from
the degree of cloudiness for a specific location, time of day, time of
year and the overall wind speed. Figure 11 in FAWT shows how temperature
at 361 feet minus that at 36 feet, depended on cloudiness, wind speed and
time of day. They are two-year averages and can help one understand the
processes involved in controlling turbulence mixing in the boundary layer.
7. Summary.
The amount of steering hot-air
balloon pilots experience while ascending or descending in the first two
or three thousand feet of the atmosphere is variable. The variations are
particularly large during the popular flying times, a few hours after sunrise
and a few before sunset. The nature of the variations is described in terms
of the two basic causes of wind-direction change with height:
(1) The combination of friction
and Coriolis forces changing with height, and
(2) The pressure force changing
with height.
The friction force decreases
with height and causes wind speed to increase with height. The increase
in speed simultaneously causes the Coriolis force to increase. Because
the latter is always perpendicular to the wind, its increase results in
a wind direction change with height. In the Northern hemisphere an ascending
balloon would turn to the right, i.e., veer, and a descending one
would turn to the left, i.e., back. In the Southern Hemisphere the
effect is the opposite. The difference is due to the difference in mapping
that has the earth turning in opposite directions in the two hemispheres.
If the pressure force changes
direction with height it can add to, or subtract from, the friction-Coriolis
effect. It is physically related to a horizontal change in air temperature
throughout the layer. That, in turn, is usually associated with influx
of cold air (cold-air advection) or of warm-air (warm-air advection.) Cold-air
advection causes backing and warm-air advection veering. Without upper-air
measurements it is difficult to estimate quantitatively the amount of steering
to ascribe to this not uncommon situation. But its qualitative effect can
often be known by the wind direction throughout the boundary layer. In
the Northern Hemisphere north winds signal cold-air advection, hence backing,
and south winds warm-air advection, veering.
Steering from all the above
causes may be reduced or even eradicated by the mixing caused by natural
turbulence in the atmospheric boundary layer. Turbulence is greatest on
summer days and least on clear nights. Simultaneous measurements show a
close correspondence between steering and the temperature change with height.
It is greatest when the temperature increases with height and least when
the temperature decrease is equal to, or exceeds the dry adiabatic lapse
rate of 5.4 deg. F.
The change over of the boundary-layer
temperature structure, and hence a significant change in steering, during
transition periods makes forecasting steering difficult, especially without
appropriate upper-air measurements.
REFERFENCES.
Reference No. 1:
Donn, William L., 1975: Meteorology, Fourth Ed., McGraw-Hill.
Reference No. 2: Haltiner,
George J. and Frank L.Martin, 1957: Dynamical and Physical Meteorology,
McGraw-Hill.
Reference No.3: Mendenhall,
Bruce R., 1967: A Statistical Study of Frictional Veering in the Planetary
Boundary Layer, Atmospheric Science Paper No. 116, Department of Atmospheric
Science, Colorado State Univ., Fort Collins.
SOURCES OF FIGURES AND
DATA
Figure No. &_
Source
1. Reference No. 1.
2. The author.
3.
"
4.
"
5. Pibal data taken by the
author's students.
6. Data from Clarke, R.H.,
A.J. Dyer, R.R. Brook, D.J. Reid, and A.J. Troup, 1971: The Wangara
Experiment: Boundary-Layer Data. Division of Meteorological Physics
Technical Paper No.19, Commonwealth Scientific and Industrial Research
Organization, Australia.
7. Reference No.2.
8. Reference No. 3.
9.
"
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Email: donport@umich.edu