Content

• 1.7 Insolation and temperature
• 1.8 The electromagnetic wave spectrum
• 1.9 Tropospheric global heat transfer
• 1.10 Temperature lapse rate
• 1.11 Adiabatic processes and lapse rates
• 1.12 Atmospheric stability
• 1.13 Convergence and divergence
• 1.14 Momentum, Coriolis effect and vorticity
• 1.15 Thermal gradients and the 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. 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.

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. 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:

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%.

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 O₂, N₂, 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.

Radiation emitted upwards into space, principally nocturnal cooling, is re-radiated from clouds (26%) plus water vapour, O₃ and CO₂ (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. 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. 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.

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.

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 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.

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 within the troposphere and the water circulation within the oceans transfers heat from the energy surplus zones (refer to section 1.7) 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.

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).

Tropospheric average 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.

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) 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 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.

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.

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, 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:

• 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.

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.

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 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.

1.13 Convergence, divergence and subsidence

Synoptic scale 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:

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. Some divergence / convergence effects may cancel each other out; e.g. deceleration associated with diverging streamlines.

Developing anti-cyclones — '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 is linear the upper section of a block of subsiding air usually sinks for a greater distance (refer to section 2.1 ISA table) 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.

Developing 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.

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.

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.

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 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.

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.

The isobaric surface contours vary with height so the geostrophic wind 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 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.

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 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.