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*Aviation Meteorology *
Atmospheric thermodynamics 2 and dynamics
Rev. 16b ? page content was last changed July 1, 2009
consequent to editing by RA-Aus member Dave Gardiner
www.redlettuce.com.au <http://www.redlettuce.com.au>
Module content
* 1.7 Insolation and temperature <#atmospheric_temperature>
* 1.8 The electromagnetic wave spectrum <#electromagnetic_spectrum>
* 1.9 Tropospheric global heat transfer <#global_heat_transfer>
* 1.10 Temperature lapse rate <#temperature_lapse_rate>
* 1.11 Adiabatic processes and lapse rates <#adiabatic_processes>
* 1.12 Atmospheric stability <#atmospheric_stability>
* 1.13 Convergence and divergence <#atmospheric_convergence>
* 1.14 Momentum, Coriolis effect and vorticity <#atmospheric_momentum>
* 1.15 Thermal gradients and the thermal wind <#thermal_wind>
1.7 Insolation and atmospheric temperature
1.7.1 Insolation
The Earth's surface and the atmosphere are warmed mainly by *insolation*
? incoming solar electromagnetic radiation. The amount of insolation
energy reaching the outer atmosphere is about 1.36 kilowatts per m².
About 10% of the radiation is in the near end of the *ultraviolet* range
(0.1 to 0.4 microns), 40% in the *visible light* range ( 0.4 to
0.7microns), 49% in the short-wave *infrared* range (0.7 to 3.0 microns
) and 1% is higher energy and X-ray radiation; refer to section 1.8
<#electromagnetic_spectrum>. The X-rays are blocked at the outer
atmosphere, and most of the atmospheric absorption of insolation takes
place in the upper stratosphere and the thermosphere. There is little
direct insolation warming in the troposphere, which is mostly warmed by
contact with the surface and subsequent convective and mechanical
mixing; refer to section 1.7.4 <#heat_transport>.
On a sunny day 75% of insolation may reach the Earth's surface; on an
overcast day only 15%. On average, 51% of insolation is absorbed by the
surface as thermal energy ? 29% as direct radiation and 22% as diffused
radiation; i.e. scattered by atmospheric dust, water vapour and air
molecules; refer to section 12.1
<../meteorology/section12.html#light_scatter>. About 4% of the radiation
reaching the surface is directly reflected, at the same wavelength, from
the surface back into space. Typical surface reflectance values
(*albedo*) are shown below:
Soils 5?10% Snow, dependent on age 40?90%
Desert 20?40% Water, sun high in sky 2?10%
Forest 5?20% Water, sun low in sky 10?80%
Grass 15?25%
In the insolation input diagram shown below it can be seen that about
26% of insolation is directly reflected back into space by the
atmosphere but 19% is absorbed within it as thermal energy, with much of
the UV radiation being absorbed within the stratospheric ozone layer.
Clouds reflect 20% and absorb 3%, and atmospheric gases and particles
reflect 6% and absorb 16%.
atmospheric insolation
Altogether some 70% of insolation is absorbed at the Earth's surface and
in the upper atmosphere, but eventually all this absorbed radiation is
re-radiated back into space as long-wave (3 to 30 microns) infrared. The
result of radiation absorption and re-radiation is that the mean
atmospheric surface temperature is maintained at 15 °C.
1.7.2 Terrestrial radiation
The surface?atmosphere radiation emission diagram below shows that some
6% of input is lost directly to space as long-wave infrared from the
surface. Atmospheric O_2 , N_2 , and argon cannot absorb the long-wave
radiation. Also there is a window in the radiation spectrum between 8.5
and 11 microns where infrared radiation is not absorbed to any great
extent by the other gases. About 15% of the received energy is emitted
from the surface as long-wave radiation, and absorbed by water vapour
and cloud droplets within the troposphere, and by carbon dioxide in the
mesosphere. This is actually a net 15%; the total is much greater but
the remainder is counter-balanced by downward long-wave emission from
the atmosphere.
atmospheric radiation
Radiation emitted upwards into space, principally nocturnal cooling, is
re-radiated from clouds (26%) plus water vapour, O_3 and CO_2 (38%). The
atmosphere then has a net long-wave energy deficit, after total upwards
emission (64%) and absorption (15%). This is equivalent to 49% of solar
input and a short-wave insolation excess of 19% (16% + 3% absorbed)
resulting in a total atmospheric energy deficit equivalent to 30% of
insolation.
1.7.3 Energy balance
The surface has a radiation surplus of 30% of solar input: 51% short
wave absorbed less 21% long wave emitted. This surplus thermal energy is
convected to the atmosphere by sensible heat flux (7%) and by latent
heat flux (23%). The latent heat flux is greater because the ratio of
global water to land surface is about 3:1. Over oceans, possibly 90% of
the heat flux from the surface is in the form of latent heat. Conversely
over arid land, practically all heat transfer to the atmosphere is in
the form of sensible heat.
Overall the earth?atmosphere radiation/re-radiation system is in
balance. But between latitudes 35°N and 35°S more energy is stored than
re-radiated, resulting in an energy surplus. But between the 35°
latitudes and the poles there is a matching energy deficit. There is
also a diurnal and a seasonal variation in the radiation balance. The
average daily solar radiation measured at the surface in Australia is
7.5 kW hours/m² in summer and 3.5 kW hours/m² in winter.
/All substances emit electromagnetic radiation in amounts and
wavelengths dependent on their temperature. The hotter the substance,
the shorter will be the wavelengths at which maximum emission takes
place. The sun, at 6000 K, gives maximum emission at about 0.5 microns
in the visible light band. The Earth, at 288 K, gives maximum emission
at about 9 microns in the long-wave infrared band./
1.7.4 Tropospheric transport of surface heating and cooling
The means by which surface heating or cooling is transported to the
lower troposphere are:
* by *conduction* ? air molecules coming into contact with the
heated (or cooled) surface are themselves heated (or cooled) and
have the same effect on adjacent molecules; thus an air layer only
a few centimetres thick becomes less (or more) dense than the air
above
* by *convective mixing* ? occurs when the heated air layer tries to
rise and the denser layer above tries to sink. Thus small
turbulent eddies build and the heated layer expands from a few
centimetres to a layer hundreds, or thousands, of feet deep
depending on the intensity of solar heating; refer to section
3.3.1 <../meteorology/section3.html#lifting_sources>. Convective
mixing is more important than mechanical mixing for heating air,
and is usually dominant during daylight hours. In hot, dry areas
of Australia the convective mixing layer can extend beyond 10 000 feet
* by *mechanical mixing* ? where wind flow creates frictional
turbulence; refer to section 3.3.2
<../meteorology/section3.html#frictional_turbulence>. Mechanical
mixing dominates nocturnally when surface cooling and conduction
create a cooler, denser layer above the surface ? thus stopping
convective mixing. If there is no wind mechanical mixing cannot
occur, refer to section 3.4 <../meteorology/section3.html#fog>.
The term *(planetary) boundary layer* is used to describe the lowest
layer of the atmosphere, roughly 1000 to 6000 feet thick, in which the
influence of surface friction on air motion is important. It is also
referred to as the friction layer or the *mixed layer*. The boundary
layer will equate with the mechanical mixing layer if the air is stable
and with the convective mixing layer if the air is unstable. The term
*surface boundary layer* or *surface layer* is applied to the thin layer
immediately adjacent to the surface, and part of the planetary boundary
layer. Within this layer the friction effects are more or less constant
throughout, rather than decreasing with height, and the effects of
daytime heating and night-time cooling are at a maximum. The layer is
roughly 50 feet deep, and varies with conditions.
1.7.5 Heat advection
Advection is transport of heat, moisture and other air mass properties
by horizontal winds.
* *Warm advection* brings warm air into a region.
* *Cold advection* brings cold air into a region.
* *Moisture advection* brings moister air and is usually combined
with warm advection.
* Advection is *positive* if higher values are being advected
towards lower values, and *negative* if lower values are being
advected towards higher; e.g. cold air moving into a warmer region.
Advection into a region may vary with height; e.g. warm, moist advection
from surface winds while upper winds are advecting cold, dry air.
Back to top <#top>
1.8 Electromagnetic wave spectrum
The electromagnetic spectrum stretches over 60 octaves, the frequency
doubling within each octave. For example, the frequencies in octave #18
range from 68.58 MHz to 137.16 MHz ? which includes the aviation VHF
NAV/COMMS <../comms/licence.html#frequencies> band. In a vacuum,
electromagnetic waves propagate at a speed close to 300 000 km/sec. The
frequency can be calculated from the wavelength thus:
* Frequency in kHz = 300 000/wavelength in metres
* Frequency in MHz = 300/wavelength in metres or 30 000/ wavelength
in centimetres
* Frequency in GHz = 30/wavelength in centimetres
The very high frequency [VHF] band used in civil aviation radio
communications lies in the 30 to 300 MHz frequency range ? thus the 10
metre to 1 metre wavelength range. The other civil aviation voice
communications band is in the high frequency [HF] range; 3 to 30 MHz or
100 to 10 metres.
The amplitude of the wave is proportional to the energy of vibration.
The table below shows the wave length ranges ? beginning in nanometres
[nm] and progressing through micrometres [microns], millimetres, metres
and kilometres ? and the associated radiation bands.
energy spectrum
1.9 Tropospheric global heat transfer
Precipitation is less than evaporation between 10° and 40° latitudes ?
the difference being greatest at about 20°. Polewards and equatorwards
of these bands precipitation is greater than evaporation. The transfer
of atmospheric water vapour, containing latent heat, is polewards at
latitudes greater than 20° and equatorwards at lower latitudes. Most of
the vertical heat transfer is in the form of latent heat, but possibly
65% of the atmospheric horizontal transfer is in the form of sensible
heat following condensation of water vapour. Horizontal latent heat
transfer occurs primarily in the lower troposphere.
The general wind circulation
<../meteorology/section4.html#general_circulation> within the
troposphere and the water circulation within the oceans transfers heat
from the energy surplus zones (refer to section 1.7
<#atmospheric_temperature>) to the energy deficit zones, thereby
maintaining the global heat balance. About 70% is transferred by the
atmosphere and 30% by the oceans. The large mid-latitude eddies, and the
cyclones and anticyclones in the broad westerly wind belt that flows
around the southern hemisphere, play a particularly important part in
the transfer of the excess heat energy from low to high latitudes and in
the mixing of cold Antarctic air into the mid-latitudes.
Back to top <#top>
1.10 Temperature lapse rates in the troposphere
The temperature lapse rates in the troposphere vary by latitude,
climatic zone and season, and vary between less than 0 °C/km (i.e.
increasing with height) at the winter poles to more than 8 °C/km over a
summer sub-tropical ocean. In the mid-latitudes the temperature reduces
with increasing height at varying rates, but averages 6.5 °C/km or about
2 °C per 1000 feet. However, within any tropospheric layer, temperature
may actually increase with increasing height. This reversal of the norm
is a *temperature inversion* condition. If the temperature in a layer
remains constant with height then an *isothermal layer* condition
exists. At night, particularly under clear skies, the air in the mixed
layer cools considerably, but the long-wave radiation from the higher
levels is weak and the air there cools just 1 °C or so. Consequently a
*nocturnal inversion* forms over the mixed layer, the depth of which
depends on the temperature drop and the amount of mechanical mixing
(refer to section 3.4 <../meteorology/section3.html#fog>).
*Tropospheric average temperature lapse rate profile*
temperature lapse rate profile
The altitude of the tropopause, and thus the thickness of the
troposphere, varies considerably. Typical altitudes are 55 000 feet in
the tropics with a temperature of ?70 °C and 29 000 feet in polar
regions with a temperature of ?50 °C. Because of the very low surface
temperatures in polar regions and the associated low-level inversion,
the temperature lapse profile is markedly different from the
mid-latitude norms. In mid-latitudes the height of the troposphere
varies seasonally and daily with the passage of high and low pressure
systems.
In the chart above, an exaggerated environmental temperature lapse rate
profile has been superimposed to illustrate the temperature layer
possibilities ? starting with a superadiabatic lapse layer at the
surface, a normal lapse rate layer above it then a temperature inversion
layer and an isothermal layer.
Back to top <#top>
1.11 Adiabatic processes and lapse rates
An *adiabatic process* is a thermodynamic process where a change occurs
without loss or addition of heat, as opposed to a *diabatic process* in
which heat enters or leaves the system. Examples of the latter are
evaporation from the ocean surface, radiation absorption and turbulent
mixing.
An adiabatic temperature change occurs in a vertically displaced parcel
of air due to the change in pressure and volume (refer to the gas
equation in section 1.2 <../meteorology/section1a.html#gas_laws>)
occurring during a short time period, with little or no heat exchange
with the environment. Upward displacement and consequent expansion
causes cooling; downward displacement and subsequent compression causes
warming. In the troposphere, the change in temperature associated with
the vertical displacement of a parcel of dry (i.e. not saturated) air is
very close to 3 °C per 1000 feet, or 9.8 °C / km, of vertical motion;
this is known as the *dry adiabatic lapse rate* [DALR]. As ascending
moist air expands and cools in the adiabatic process, the excess water
vapour condenses after reaching dewpoint and the latent heat of
condensation <../meteorology/section1a.html#latent_heat> is released
into the parcel of air as sensible heat, thus slowing the
pressure-induced cooling process. This condensation process continues
while the parcel of air continues to ascend and expand. The process is
reversed as an evaporation process in descent and compression. The
adiabatic lapse rate for saturated air, the * saturated adiabatic lapse
rate* [SALR], is dependent on the amount of moisture content, which is
dependent on temperature and pressure. The chart below shows the SALR at
pressures of 500 and 1000 mb (or hPa), and temperatures between ?40 °C
and +40 °C.
salr
The chart shows that on a warm day the SALR near sea level is about 1.2
°C / 1000 feet. At about 18 000 feet ? the 500 mb level ? the rate
doubles to about 2.4 °C / 1000 feet.
The * environment lapse rate* [ELR] is ascertained by measuring the
actual vertical distribution of temperature at that time and place. The
ELR may be equal to or differ from the DALR or SALR of a parcel of air
moving within that environment. In the atmosphere, parcels of air are
stirred up and down by turbulence and eddies that may extend several
thousand feet vertically in most wind conditions. These parcels mix and
exchange heat with the surrounding air thus distorting the adiabatic
processes.
If the rate of ground heating by solar radiation is rapid, the mixing of
heated bubbles of air may be too slow to induce a well-mixed layer with
a normal DALR. The ELR, up to 2000?3000 feet agl, may be much greater
than the DALR. Such a layer is termed a *superadiabatic layer*, and will
contain strong thermals and downdraughts.
Back to top <#top>
1.12 Atmospheric stability
Atmospheric stability is the air's resistance to any disturbing effect.
It can be defined as the ability to resist the narrowing of the spread
between air temperature and dewpoint. *Stable air* cools slowly with
height and vertical movement is limited. If a parcel of air, after being
lifted, is cooler than the environment, the parcel ? being more dense
than the surrounding air ? will tend to sink back and conditions are stable.
The temperature of unstable air drops more rapidly with an increase in
altitude, i.e. the ELR is steep. If a lifted parcel is warmer, and thus
less dense than the surrounding air, the parcel will continue to rise
and conditions are unstable. *Unstable air*, once it has been lifted to
the lifting condensation level
<../meteorology/section3.html#lifting_sources>, keeps rising through
free convection. Instability can cause upward or downward motion. When
saturated air containing little or no condensation, is made to descend
then adiabatic warming causes the air to become unsaturated almost
immediately and further descent warms it at the DALR.
If the ELR lies between the DALR and the SALR, a state of *conditional
instability* exists. Thus, if an unsaturated parcel of air rises from
the surface, it will cool at the DALR and so remain cooler than the
environment, and conditions are stable. However, if the parcel passes
dewpoint during the ascent it will then cool at a slower rate and, on
further uplift, become warmer than the environment and so become
unstable. High dewpoints are an indication of conditional instability.
The figure below demonstrates some ELR states with the consequent
stability condition:
lapse rate stability
* ELR #1 is much greater than the DALR (and the SALR), thus
providing absolute instability. This condition is normally found
only near the ground in a superadiabatic layer ? although a deep
superadiabatic layer exists in the hot, dry tropical continental
air of northern Australia in summer.
* ELR # 2 between the DALR and the SALR demonstrates conditional
instability. It is stable when the air parcel is unsaturated, i.e.
the ELR is less than the DALR; and unstable when it is saturated,
i.e. the ELR is greater than the SALR.
* ELR #3 indicates absolute stability, where the ELR is less than
the SALR (and the DALR).
* *Neutral equilibrium* would exist if the ELR equals the SALR and
the air was saturated, or if the ELR equals the DALR and the air
was unsaturated.
The following diagram is an example of atmospheric instability and cloud
development, and compares environment temperature and that of a rising
air parcel with a dewpoint of 11 °C.
salr convection
The amount of energy that could be released once surface-based
convection is initiated in humid air is measured as *convective
available potential energy* [CAPE]. CAPE is measured in joules per
kilogram of dry air. It may be assessed by plotting the vertical profile
of balloon radiosonde readings for pressure, temperature and humidity on
a tephigram (a special meteorological graph format); and also plotting
the temperatures that a rising parcel of air would have in that
environment. On the completed tephigram, the area between the plot for
environment temperature profile and the plot for the rising parcel
temperature profile is directly related to the CAPE, which in turn is
directly related to the maximum vertical speed in a cumulonimbus [Cb]
updraught <../groundschool/umodule21.html#thunderstorm>.
One form of *aerological diagram* is used to determine the stability of
the atmosphere ? and thus potential thermal activity ? by plotting the
ELR from radiosonde data and comparing that with the DALR and SALR lines
on the diagram. For more information go to the aviation section
<http://www.bom.gov.au/reguser/by_prod/aviation/> of the Australian
Bureau of Meteorology website and look in the 'Sports Aviation' box for
'How to use the Aerological Diagram'. While there also look in the
'Learning' box for the 'Aviation eHelp' section.
Back to top <#top>
1.13 Convergence, divergence and subsidence
Synoptic scale <../meteorology/section5.html> atmospheric vertical
motion is found in cyclones and anticyclones, and is caused mainly by
air mass convergence or divergence from horizontal motion.
Meteorological *convergence* indicates retardation in air flow with an
increase in air mass in a given volume due to net three-dimensional
inflow. Meteorological *divergence*, or negative convergence, indicates
acceleration with a decrease in air mass. Convergence is the contraction
and divergence is the spreading of a field of flow.
If, for example, the front end of moving air mass layer slows down, the
air in the rear will catch up ? converge ? and the air must move
vertically to avoid local compression. If the lower boundary of the
moving air mass is at surface level, all the vertical movement must be
upward. If the moving air mass is just below the tropopause, all the
vertical movement will be downward because the tropopause inhibits
vertical motion. Conversely, if the front end of a moving air mass layer
speeds up, then the flow diverges. If the air mass is at the surface,
then downward motion will occur above it to satisfy mass conservation
principles. If the divergence is aloft, then upward motion takes place.
Rising air must diverge before it reaches the tropopause, and sinking
air must diverge before it reaches the surface. As the surface pressure
is the weight per unit area of the overlaying column of air, and even
though divergences in one part of the column are largely balanced by
convergences in another, the slight change in mass content (thickness)
of the overriding air changes the pressure at the surface.
The following diagrams illustrate some examples of convergence and
divergence:
fields-of-flow
Note: referring to the field of flow diagrams above, the spreading apart
(*diffluence*) and the closing together (*confluence*) of streamlines
alone do not imply existence of divergence or convergence, as there is
no change in air mass if there is no cross-isobar flow or vertical flow.
/ (An *isobar* is a curve along which pressure is constant, and is
usually drawn on a constant height surface such as mean sea level.)/
Divergence or convergence may be induced by a change in surface drag;
for instance, when an airstream crosses a coastline. An airstream being
forced up by a front will also induce convergence. For convergence /
divergence in upper-level waves, refer to Rossby waves
<../meteorology/section4.html#rossby_waves>. Some divergence /
convergence effects may cancel each other out; e.g. deceleration
associated with diverging streamlines.
Developing anti-cyclones
<../meteorology/section4.html#sub_tropical_highs> ? 'highs' and high
pressure ridges are associated with converging air aloft, and consequent
wide-area subsidence with diverging air below. This subsidence usually
occurs from 20 000 down to 5000 feet, typically at the rate of 100 ? 200
feet per hour. The subsiding air is compressed and warmed adiabatically
at the DALR, or an SALR, and there is a net gain of mass within the
developing high. Some of the converging air aloft rises and, if
sufficiently moist, forms the cirrus cloud often associated with
anti-cyclones.
As the pressure lapse rate is exponential and the DALR
<../meteorology/section1b.html#adiabatic_processes> is linear the upper
section of a block of subsiding air usually sinks for a greater distance
(refer to section 2.1 ISA table <../groundschool/umodule2.html#isa>) and
hence warms more than the lower section. If the bottom section also
contains layer cloud, the sinking air will only warm at a SALR until the
cloud evaporates. Also, when the lower section is nearing the surface,
it must diverge rather than descend and thus adiabatic warming stops.
With these circumstances it is very common for a *subsidence inversion*
to consolidate at an altitude between 3000 and 6000 feet. The weather
associated with large-scale subsidence is almost always dry. However, in
winter, persistent low cloud and fog can readily form in the stagnant
air due to low thermal activity below the inversion, producing
'anti-cyclonic gloom'. In summer there may be a haze or smoke layer at
the inversion level, which reduces horizontal visibility at that level ?
although the atmosphere above will be bright and clear. Aircraft
climbing through the inversion layer will usually experience a wind
velocity change.
vertical convergence/divergence
Developing cyclones
<../meteorology/section5.html#extratropical_cyclones>, 'lows' or
'depressions' and low-pressure troughs are associated with diverging air
aloft and uplift of air, leading to convergence below. There is a net
loss of mass within an intensifying low as the rate of vertical outflow
is greater than the horizontal inflow, but if the winds continue to blow
into a low for a number of days, exceeding the vertical outflow, the low
will fill and disappear. The same does not happen with anti-cyclones,
which are much more persistent.
vertical motion about a low
A trough may move with pressure falling ahead of it and rising behind
it, giving a system of pressure tendencies due to the motion but with no
overall change in pressure, i.e. no development, no deepening and no
increase in convergence.
Back to top <#top>
1.14 Momentum, Coriolis effect and vorticity
1.14.1 Momentum definitions
*Angular velocity*
The rate of change of angular position of the rotating Earth = *W* =
7.29 x 10^?5 radians per second. (One radian = 57.2958°, 2p radians
= 360°) or, the rate of angular rotation around a cyclone or
anticyclone = *w*. (A rotor that spins at 1000 rpm has twice the
angular velocity of one spinning at 500 rpm).
*Tangential angular velocity*
The tangential angular velocity of a point on the Earth's surface is
the product of its radial distance (*r*) from the Earth's rotational
axis and *W = Wr*. The radial distance from the rotational axis is
zero at the poles increasing to maximum at the equator.
*Angular momentum*
The angular momentum of a point on the Earth's surface is the
product of the tangential angular velocity and mass (*m*), and the
radial distance from the rotational axis =*mWr²*. If mass is
presumed at unity then angular momentum = *Wr²*.
Or, angular momentum for a rotating air mass is the product of *w*
and the radius of curvature = *wr*.
*Conservation of angular momentum*
The principle of conservation of angular momentum states that the
total quantity of energy (mass x velocity) of a system of bodies;
e.g. Earth?atmosphere, not subject to external action, remains
constant. Friction reduces the angular momentum of an air mass
rotating faster than the Earth, e.g. a westerly wind, but the 'lost'
omentum is imparted to the Earth, thus the angular momentum of the
Earth?atmosphere system is conserved.
1.14.2 Coriolis effect
*Coriolis effect * /(named after Gaspard de Coriolis, 1792 ? 1843)/ is a
consequence of the principle of conservation of angular momentum. The
Coriolis or *geostrophic force* is an apparent or hypothetical force
that only acts when air is moving. A particle of air or water at 30° S
is rotating west to east with the Earth's surface at a tangential
velocity of about 1450 km/hour. If that particle of air starts to move
towards the equator, the conservation principle requires that the
particle continue to rotate eastward at 1450 km/hour even though the
rotational speed of the Earth' surface below it is accelerating as the
particle closes with the equator, which is rotating at 1670 km/hour.
Tangential eastward velocity at the Earth's surface Equator 1670
km/hour 464 metres/sec
15° South 1613 km/hour 448 metres/sec
30° South 1446 km/hour 402 metres/sec
45° South 1181 km/hour 328 metres/sec
60° South 835 km/hour 232 metres/sec
75° South 432 km/hour 120 metres/sec
90° South 0 km/hour 0 metres/sec
Thus air or water moving towards the equator is deflected westward
relative to the Earth's surface, but not deflected relative to space.
Conversely, air moving from low latitudes, with high rotational speed
and momentum, is deflected eastward, i.e. as a westerly wind, when
moving to higher latitudes with lower rotational speeds.
The Coriolis force is directed perpendicular to the Earth's axis, i.e.
in a plane parallel to the equatorial plane, so it has maximum effect on
horizontal air movement at the poles and no effect on horizontal air
movement at the equator. The direction of its action is perpendicular to
the particle velocity and to the left in the southern hemisphere. The
rate of turning, or curvature, of a moving particle of air or water is
proportional to *2VW* sine *f*, where * V* is the north/south component
of the particle's velocity and *f* is the latitude. Because sine 90° = 1
and sine 0° = 0, then the Coriolis must be at maximum at the poles and
zero at the equator, as expressed above. The Coriolis effect stops
turning the moving air only when it has succeeded in turning it at right
angles to the force that initiated the movement ? a pressure or thermal
gradient.
The *Coriolis parameter*, *f = 2W* sine *f*, is the local component of
the Earth's rotation about its axis that contributes to air circulation
in the local horizontal plane. It is assumed negative in the southern
hemisphere and positive in the northern hemisphere.
1.14.3 Vorticity
*Vorticity* or *spin* is the measure of rotation of a fluid about
three-dimensional axes. Vorticity in the horizontal plane, i.e. about
the vertical axis, is the prime concern in planetary scale and synoptic
scale systems.
*Relative vorticity* is taken as horizontal motion, relative to the
Earth's surface, about the local vertical axis and is measured as
circulation per unit area. It is assumed to be negative if cyclonic and
positive if anticyclonic. Relative vorticity * z = 2w*.
*Absolute vorticity* is the relative vorticity plus the Coriolis
parameter ? which is maximum at the poles and zero at the equator.
Relative vorticity is related to horizontal divergence and convergence
through the principle of conservation of angular momentum. In the
cyclonic movement of air around a low pressure system the fractional
decrease in horizontal area due to convergence is matched by a
fractional increase in spin, thus conserving the angular momentum. With
both increasing vorticity and convergence at lower levels, the vertical
extent of the air column is stretched adiabatically and the upper-level
divergence lifts to higher levels.
Conversely, in anticyclonic rotation, the fractional increase in the
surface area of the system, due to lower level divergence, is matched by
a fractional decrease in spin. With decreasing vorticity and divergence
at a lower level, the vertical extent of the air column shrinks
adiabatically and the upper level convergence sinks to lower levels.
The relationship is expressed in the principle of *conservation of
potential absolute vorticity* equation:
Coriolis parameter + relative vorticity / vertical depth of the air
column ( *D* ) = constant or, *f + z / D* = constant
Thus as the Coriolis at a given southern latitude is constant and
negative, a reduction in the depth of a column at that latitude requires
*z* to become more positive with consequent anticyclonic rotation.
Conversely, an increase in depth requires * z* to become more negative
with consequent cyclonic rotation. The principle accounts for the
development of wave patterns <../meteorology/section4.html#rossby_waves>
in upper air flow. The cyclonic curvature of the isobars can be seen on
surface synoptic charts resulting from the easterly / south-easterly
trade wind encountering the mountain ranges along the north Queensland
coast. The initial reduction in vertical depth as the airstream
encounters the barrier, followed by the increase in depth on the western
side, induces anticyclonic and cyclonic curvature.
Back to top <#top>
1.15 Thermal gradients and the thermal wind concept
The rate of fall in pressure with height is less in warm air than in
cold, and columns of warm air have a greater vertical extent than
columns of cold air. Consider two adjacent air columns having the same
msl pressure; the *isobaric surfaces* (surfaces of constant pressure)
are at higher levels in the warm air column, which result in a
*horizontal pressure gradient* from the warm to the cold air ? this
increases with height, i.e. the temperature gradient causes increasing
wind to higher levels. The horizontal pressure gradient increases as the
*horizontal thermal gradient* increases ? this is known as the *thermal
wind mechanism*.
thermal wind mechanism
The isobaric surface contours vary with height so the geostrophic wind
<../meteorology/section6.html#geostrophic> velocity above a given point
also varies with height. The wind vector difference between the two
levels above the point ? the vertical wind shear ? is called the
*thermal wind*, i.e. the wind vector component caused by temperature
difference rather than pressure difference. On an upper air thickness
chart <../meteorology/section4.html#thickness_chart> which indicates the
heat content of the troposphere, the thermal wind is aligned with the
geopotential height lines or with the isotherms on an upper-air
*constant pressure level chart* (*isobaric surface chart*), and the
thicker (warmer) air is to the left looking downwind.
/ A *geopotential height line* is a curve of constant height, i.e. the
height/thickness contours relating to an isobaric surface, usually shown
in decametres or metres above the 1000 mb surface or msl on an upper air
chart. An *isotherm* is a curve connecting points of equal temperature
and is usually drawn on a constant pressure surface or a constant height
surface. An *isopleth* is the generic name for all isolines or contour
lines. /
thermal wind vector
The speed of the thermal wind is proportional to the thermal gradient;
the closer the contour spacing, the stronger the thermal wind. If the
horizontal thermal gradient maintains much the same direction through a
deep atmospheric layer ? for instance there are no upper level highs or
lows, and the gradient is strong with the colder air to the south ? then
the thermal wind will increase with height, eventually becoming a
constant westerly vector. The resultant high-level wind will be high
speed and nearly westerly.
Generally, colder air is to the south so that the thermal wind vector
tends westerly. But if the horizontal thermal gradient reverses
direction with height, then an easterly thermal wind will occur above
that level and the upper-level westerly geostrophic wind speed will
decrease with height. Because the direction of the thermal gradient is
reversed above the tropopause, the thermal wind reverses to easterly.
The horizontal thermal gradient is at maximum just below the tropopause,
where the jet stream <../meteorology/section4.html#jet_streams> occurs.
At latitude 45° S a temperature difference of 1 °C in 100 km will cause
an increase in thermal wind of 10 m/sec (or about 20 knots) for every 10
000 feet of altitude ? giving jet stream speeds at 30 000 feet, ignoring
geostrophic wind. Temperature contrasts between air masses at the polar
front will be greatest during winter, giving the strongest jet stream.
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