SAMA_L1_4Feb2023.pptx

Atmospheric Physics
Atmospheric thermodynamics: Lecture 1
Structure of the atmosphere and vertical distribution of temperature
South Asian Meteorological Association
Online lectures on
Fundamentals of Atmospheric, Weather & Climate Sciences
Prof. D. V. Bhaskar Rao
Honorary Professor
Department of Meteorology and Oceanography
Andhra University

Structure of the atmosphere and vertical distribution of temperature
• Composition of the atmosphere,
• Vertical structure of the atmosphere,
• Lapse rate: dry adiabatic, moist adiabatic,
• potential temperature,
• virtual temperature
Lecture 1

Atmosphere could be understood as a layer of a gas or a mixture of
gases that envelop (surround) a planet. A planet holds the
atmosphere due to the force of gravity.
Earth has an atmosphere, as of all the planets in our solar system,
which provide air to breath that sustains life; that keeps our planet
warm, and protecting from harmful ultraviolet (UV) radiation.
The earth’s atmosphere extends up to about 500 km, of which 99%
lies within the lowest 32 km from the earth surface.
Composition of the atmosphere

The earth’s atmosphere is composed of several gases, of which nitrogen
(78%) and oxygen (21%) constitute ~99%.
Several other gases constitute the remaining ~1% that include,
importantly for weather and climate, carbon dioxide (387 ppm), ozone
(0.04 ppm), Chlorofluorocarbons (CFCs, 0.0002 ppm), and a variable
amount of water vapour (0-4%; ~1% at sea level that decreases with
altitude).
Composition of the atmosphere

Composition of the Atmosphere near the Earth's Surface
Permanent Gases Variable Gases
Gas Name
Chemical
Formula
Percent
(by Volume)
Dry Air
Gas
(and Particles)
Symbol
Percent
(by Volume)
Parts per
Million (ppm)*
Nitrogen N2 78.08 Water Vapor H2O 0 to 4
Oxygen O2 20.95 Carbon Dioxide CO2 0.0387 387
Argon Ar 0.93 Methane CH4 0.00017 1.7
Neon Ne 0.0018 Nitrous Oxide N2O 0.00003 0.3
Helium He 0.0005 Ozone O3 0.000004 0.04
Hydrogen H2 0.00005
Particles (dust,
soot, etc.)
0.00001 0.01-0.15
Xenon Xe 0.000009
Chlorofluorocarb
ons (CFCs)
0.00000002 0.0002
*For CO2, 387 parts per million means that out of every million air molecules, 387 are CO2 molecules.

Nitrogen:
• Colourless, odourless, non-toxic gas
• Nitrogen (cycle) undergoes transformations as it moves between
the atmosphere, the land, the water and living things
• Nitrogen is needed to make chlorophyll in plants, which is used in
photosynthesis.
• Nitrogen is an important fertiliser, but it contributes to increasing
emissions of a greenhouse gas 300 times more potent than carbon
dioxide
Constituents of the atmosphere

Oxygen:
• Constitutes 21%.
• Essential for all living things (for respiration).
• Obligatory for burning.
• In the stratosphere, UV-light splits oxygen molecules into oxygen
atoms, which react with other oxygen molecules to produce ozone.
These contribute to the formation of ozone in the stratosphere.

Carbon Dioxide (CO2)
• CO2 constitutes only 0.03% of the atmosphere.
• Second most important greenhouse gas on Earth
• Its presence is significant because it is opaque to the outgoing terrestrial
radiation and transparent to the incoming solar radiation.
• CO2 concentration has been increasing, in recent decades, due to human
activities such as burning fossil fuels and deforestation. The amount of
carbon dioxide has increased by 35% since 1750. This is of concern as it is
contributing to increase of the greenhouse effect leading to global
warming.

Water vapour
• Water vapour is the gaseous phase of water.
• Water can exist in the atmosphere in all its three states (i.e.) vapour, liquid and
ice.
• Under typical atmospheric conditions, water vapor is produced by evaporation
and depleted by condensation.
• Water vapor is lighter or less dense than dry air. The density of dry air is
1.27 g/L and water vapor has much lower density of 0.0048 g/L at the standard
temperature (273.15 K ) and pressure (1013.25 hPa)

Water vapour (contd.)
• Water vapor is the most important greenhouse gas on Earth. It significantly
contributes to warming of the earth’s atmosphere.
• It contributes to redistribution of heat energy because of its possible phase changes:
In the process of evaporation (liquid to gas) energy is absorbed from environment
In the process of condensation (gas to liquid) energy is released to the environment
• It plays an important role to the stability and instability of the atmosphere. Its lesser
density triggers convection currents that lead to the formation of clouds.

Methane
• Methane is also an important greenhouse gas.
• Since 1750, methane concentrations have increased by more than
150%, (mainly due to human activity), contributing to global
warming.
• Main sources of methane are agriculture (about 25% of the total),
followed by the energy sector, which includes emissions from coal,
oil, natural gas and biofuels.

Nitrous oxide
• Another important greenhouse gas.
• Since 1750, nitrous oxide concentrations have increased by more
than 20%, mainly due to human activity, raising concern about
possible global warming.
• Nitrous oxide is sourced chiefly from agriculture, burning of fossil
fuels

Ozone
• Mostly found in the stratosphere where it forms the ozone
layer (~20 - 30 km above the ground surface).
• The ozone layer absorbs Sun’s ultraviolet radiation, that is harmful
to humans.
• Very little of ozone is found near the ground where it is a toxic
pollutant.
• Ozone in the upper troposphere acts as a greenhouse gas. It
absorbs terrestrial radiation and consequently contributes to global
warming

Aerosols
• Human activities release aerosols into the atmosphere
• Affect passage of solar radiation through the atmosphere.
• Influence cloud formation.
• Aerosols are also known as "Particulate" air pollution

Chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs)
CFCs and HCFCs are fully or partly halogenated hydrocarbons that
contain carbon (C), hydrogen (H), chlorine (Cl), and fluorine (F), produced
as volatile derivatives of methane, ethane, and propane.
Many CFCs are used as refrigerants, propellants (in aerosol applications),
and solvents.
CFCs are inert gases, stay in the atmosphere for long time without getting
destroyed. From the surface they drift upwards towards the stratosphere,
where the CFC molecules are broken up by ultraviolet radiation, releasing
chlorine atoms, which will destroy ozone molecules.
Ozone depletion in the stratosphere enhances vulnerability to UV radiation.

Vertical structure of the atmosphere
Gas constant
The gas constant is the constant of proportionality that relates the energy scale in
physics to the temperature scale and the scale used for amount of substance.
The gas constant R is defined as the Avogadro constant NA multiplied by the
Boltzmann constant k (or kB):
R = NA k
The SI value of the molar gas constant is = 8.31446261815324 J K−1 mol−1
The dimensions are M1 L2 T-2 K-1

Gas constant
The gas constant for a particular gas is R = R*⁄m
The gas constant for dry air is Rd = 287 J K-1 kg-1
[molar mass of dry air = 0.028964 kg mol-1]
The gas constant for water vapor is Rv = 461 J K-1 kg-1
[molar mass of water vapour = 0.0180153 kg mol-1]

Density
Air density can be defined as the number of air molecules per unit volume.
Near sea level, its value is about 2.7x1019 molecules per cm3.
The density of dry air at 15° C at sea level, in metric units, is 1.225 kg m-3
Air (gas molecules) is easily compressed, i.e., its number density increases
when squeezed into a smaller volume. Solids and liquids on the other hand are
not easily compressed.
Since air density is the number of air molecules in a given volume, air density
is maximum at the surface or sea level and decreases upward in the
atmosphere.

Pressure
Pressure is defined as the force exerted per unit area. Pressure is dependent on the
magnitude of the applied force and the area to which the force is being applied.
The greater the force exerted, and smaller the surface area, the higher is the pressure
Atmospheric air pressure results from the Earth's gravitational pull on the overlying
air. Without gravity, air molecules would spread out, and the pressure would be close
to zero.
The weight of the atmosphere acts as a force on the surface of the Earth. The amount
of force exerted over a surface area is called atmospheric pressure.

Pressure
At sea level, the average air pressure is 1013 hPa (mb), meaning that the total weight
of all the air above the sea level weighs enough to cause 1013 hPa of air pressure.
Since the air (a gas) is a fluid, the pressure force acts in all directions, not just
downward. The pressure force thus decreases with height.
The International System of Units, denoted as the SI system, is derived from the
metric system.

Pressure
The SI unit of pressure is pascal (represented as Pa) which is equal to one newton per
square metre (Nm-2 or kg m-1s-2). The unit Pa came into use since 1971. Prior to that
pressure in SI was expressed in newtons per square metre.
Dimension: M L−1 T−2
1 pascal = 10 dyne/cm2 = 0.01 mbar. 1 atm = 101,325 Pascals = 760 mm Hg
An atmosphere (atm) is a unit of measurement equal to the average air pressure
at sea level at a temperature of 15 degrees Celsius (59 degrees Fahrenheit). One
atmosphere is 1,013 hPa (or millibars), or 760 millimeters (29.92 inches) of mercury.
In meteorology, pressure is expressed as hPa (or mb)

Vertical variation of pressure and density

Temperature
• The degree of hotness or coldness of an object.
• Temperature, is an intensive property similar to pressure or density. It is
independent of the quantity of the matter—as distinctly different from extensive
properties, such as mass or volume.
• There are three temperature scales in use today, the Fahrenheit (°F) temperature
scale, the Celsius (°C) temperature scale (widely used) and the Kelvin (K) scale.

Temperature
Celsius (or centigrade) scale considers the freezing point (0°C ) and the boiling points
(100°C) of water, with the interval being divided into 100 equal parts.
The Kelvin scale starts from absolute zero, the lowest possible temperature at which
no energy is present. The Kelvin scale (absolute temperature scale) is obtained by
shifting the Celsius scale by 273.15° such that 0oK is equal to -273.15oC, 0oC is
equal to 273.15 kelvins.
Fahrenheit devised temperature scale, considering 0o as the temperature of an equal
ice-salt mixture, selected the values of 320 and 212° that correspond to the freezing
and boiling points of water, with the interval being divided into 180 equal parts.

The temperature conversion formula
C = K − 273.15
C = (F − 32) × 5⁄9
F = C (9⁄5) + 32
K = (F − 32) × 5⁄9 + 273.15
F = (K – 273.15) × 9⁄5 + 32

Vertical variation of temperature
Atmospheric measurements, through radiosonde, aircraft and rockets, have
revealed that the atmospheric temperature is not uniform.
For long, people felt that temperature decreased with altitude, by feeling the
temperatures atop a mountain and at the base.
Radiosonde measurements, started in early 1900s, disclosed that temperature
abruptly increased in a layer above 10-18 km in contrast to decrease of
temperature with altitude near the surface.
This discovery of the reversing temperature trends led to the division of the
atmosphere into layers based on their temperature variations.

Troposphere
 It is the lowermost layer of the atmosphere, containing ~75% of the total
mass.
 All the weather changes (including cloud activity) occur in this layer.
 The height of the troposphere varies with latitude, from equator to pole,
about 18 km at the equator decreasing towards poles where its height is
about 8 km. Higher thickness at the equator is because of the transport
of heat upwards to higher altitudes by strong convection currents.

Troposphere
• In the troposphere, the temperature decreases with height at a rate of
~6℃ per kilometre of height.
 The higher temperatures at the ground are due to the reason that the
atmosphere is transparent to the incoming solar radiation, allowing most
of the radiation (if not cloudy) to be absorbed by the ground. Thus, the
air gets heated up from the warm ground below and the air temperature
reduces at altitudes upward from the ground.

Troposphere
 In the troposphere, under typical conditions, a shallow inversion layer
may be noticed where the air temperature increases with increasing
altitude.
 These inversion layers can be important in weather forecasting e.g., the
formation of a temperature inversion just above the cold ground surface
during long winter nights. This type of inversion may lead to fog
formation, which will persist into the morning hours till the ground
surface is enough heated from Sun radiation.

Tropopause
 Tropopause is a zone that separates the troposphere from the
stratosphere.
 The temperature in this zone is isothermal with temperatures to be
about -80℃ over the equator and about -45℃ over the poles.
 Hence, it is called the tropopause.
 This zone acts as a "lid" on the rising air, and so the clouds are typically
confined to below the tropopause region.

Stratosphere
 This is the second layer of the atmosphere, immediately above
the troposphere and extends up to a height of ~50 km.
 In this layer, temperature increases with altitude due to the
presence of ozone that absorbs ultraviolet radiation from the Sun.
This denotes stable stratification, and so negligible mixing and
convection.

Stratosphere
 Weather phenomena are absent in this layer, that is why aeroplanes
fly in the stratosphere for a smooth ride (less turbulence).
 The stratosphere contains little water vapour and so clouds do not
form here. Polar stratospheric clouds sometimes appear in the lower
stratosphere near the poles during winter when the temperatures dip
below -78°C.
 Atmospheric wind circulations, sometimes lead to holes in the ozone
layer due to certain chemical reactions that destroy ozone.

Mesosphere
 Mesosphere extends up to a height of about 80 km.
 In this layer, temperature decreases with increasing altitude and drops
down to minus 100℃ at the height of 80 km. The temperature
decrease with altitude is due to radiative cooling by CO2 , by emission of
thermal radiation upward into space, and lesser radiative heating due to
lower density.
 Meteorites burn in this layer on entering the atmosphere from outer
space.
 Its upper limit is mesopause which separates the mesosphere and
thermosphere.

Thermosphere
The lower part of the thermosphere, extending from ~80 to 400 km is
also known as the Ionosphere.
 Thermosphere has the highest temperatures, because a lot of UV
radiation is absorbed by the molecules present and also because of
very low pressure that prohibits transfer of energy between particles.
 Radio waves transmitted from the earth are reflected back to the
earth by this layer.
 This layer is referred to as ionosphere because it contains electrically
charged particles called ions.

Exosphere
 The uppermost layer of the atmosphere, above the thermosphere,
is called the exosphere.
 This layer gradually merges with outer space.

• Lapse rate is the rate at which temperature decreases with altitude.
• Lapse rate is dependent on the temperature, pressure, and the
degree of saturation, which are all influenced by altitude.
• In the troposphere, atmospheric pressure decrease as altitude
increases. Therefore, rising air parcels tend to expand with
decreasing pressure and so cool. Apart from heating from the
ground surface below, a parcel of air tend to cool. In general,
temperature decreases with height.
Lapse Rate

The concept of air parcel is important here. It is a small volume
element of air, with independent characteristics of temperature and
humidity to the surrounding air (atmosphere). This is true in the
atmosphere as evident by the observed weather phenomena of
different spatial and time scales amidst the existing atmosphere.
Lapse Rate

The concept of “adiabatic” process is widely implicated in atmospheric
thermodynamics. An adiabatic process is the thermodynamic process
in which there is no exchange of heat between the parcel and its
surrounding atmosphere. This means that heat is not exchanged
neither during expansion (ascending) nor compression (descending)
and also that the process can either be reversible or irreversible.
Lapse Rate

• The lapse rates in different states of the atmosphere is to be
understood. For this purpose, the characterisation of lapse rate in
idealised dry and saturated atmospheric conditions is important along
with the environmental and standard lapse rates.
• The environmental lapse rate is derived using measurements
temperatures at different altitudes, which denotes the in situ (i.e.)
actual rate of change in temperature in the atmosphere. The
environmental lapse rate depends on the location and in situ
atmospheric conditions.
• The standard lapse rate imply the average of all the records of
environmental lapse rates at a location.
Lapse Rate

• The dry adiabatic lapse rate ( Γd ) is the rate at which temperature of a
parcel of dry air decreases with height as the parcel is lifted by a
reversible adiabatic process.
• The dry adiabatic rate is -9.8 0C per kilometer. The dry lapse rate is a
constant.
• This dry adiabatic lapse rate Γd is g/Cpd, where g is the
gravitational acceleration and cpd is the specific heat of dry air at
constant pressure.
Dry adiabatic lapse rate

where q is the specific humidity; cpv and cpd are the specific heats of
water vapor and dry air.
Moist-unsaturated adiabatic lapse rate
The adiabatic lapse rate of unsaturated air containing water vapor.
This differs from that of dry air Γd ( g/cpd ) by a small factor
Γd =
𝑔
1 −𝑞 𝐶𝑝𝑑+𝑞 𝐶𝑝𝑣
Since Cpd = 1004 J kg−1 K−1 and Cpv = 1865 J kg−1 K−1, the specific heat
capacity of moist air is slightly higher than that of dry air (by less than 1%).
The dry adiabatic lapse rate of moist unsaturated air is slightly lower than
that of dry air. However, the difference is very small and is often ignored in
practical applications.

Moist (wet) adiabatic lapse rate, is the rate at which temperature changes
with height in a completed saturated atmosphere.
The moist adiabatic rate is lesser than the dry adiabatic rate as it is
dependent on the amount of water vapor present. Saturated air parcels
cool more slowly than unsaturated parcels due to the heat generated
through the process of condensation (change of phase from water vapour
to liquid)
Moist adiabatic lapse rate

Moist adiabatic lapse rate
The mathematical expression for the moist adiabatic lapse rate. Γm is given as
where g is the gravitational acceleration, Cpd is the specific heat at
constant pressure of dry air, rv is the mixing ratio of water vapor, Lv is the latent
heat of vaporization, R is the gas constant for dry air, ϵ is the ratio of the gas
constants for dry air and water vapor, and T is temperature.

Potential temperature
The potential temperature () of an air parcel is defined as the
temperature that the parcel of air would attain if it were lifted
(expanded) or lowered (compressed) adiabatically from its existing
pressure and temperature to a standard pressure p0 (generally taken as
1000 hPa).
An expression for the potential temperature of an air parcel can be
derived in terms of its pressure p, temperature T, and the standard
pressure p0 as follows.
For an adiabatic transformation (dq = 0). Thus, the first law of
thermodynamics can be expressed as

using p  = R T
Integrating the equation from p0 upward (where T =  ), we get
or

Taking antilog on both sides, we get
or
In this equation, R  Rd = 287 J K-1 kg-1
Cp = Cpd = 1004 J K-1 kg-1
and R/ Cp = 0.286

Potential temperature of a parcel is conserved as it moves in
the atmosphere under adiabatic conditions.
Potential temperature is an important parameter in
atmospheric thermodynamics, as atmospheric processes
are often close to adiabatic.

Virtual temperature
In an atmosphere, which contains both dry and moist air, the gas
constants for dry and moist air have to be used since Rv is higher
than Rd
Since Rv is a variable that depends on the amount of water
vapour present, it may be desirable to use Rd as representative of
the entire volume by making an appropriate correction for the
air temperature.
This temperature is referred to as “virtual temperature” and a
mathematical expression can be derived.

Virtual temperature
The density  of the moist air is
where V is the volume of the moist air, md and mv are mass of dry and
water vapour, ’d and ’v are the partial densities of dry air and water
vapour.
The ideal gas equations for water vapour and dry air could be written as
where e and pd are the partial pressures exerted by water vapour
and dry air respectively.
and

Virtual temperature
The total pressure is
Combining the above four equations, we get
or
where  =
𝑅𝑑
𝑅𝑣
= 0.622

Virtual temperature
The above equation can be written as
where
Tv is called the virtual temperature. It is the temperature that the dry air
would attain in order to have the same density as the moist air at the
same pressure.

Virtual temperature
In the gas equation, Rd is for gas constant for dry air, and gas constant for
moist air (Rv ) is to be used separately if temperature T is to be replaced
or corrected appropriate to the moisture content ( q – specific humidity)
present such that Rd can be used for the mixed air.
Tv = Rv q T + (1 - q) Rd T = (1 – q) T +
𝑅𝑣
𝑅𝑑
q T
Since Rd = 287.3 J Kg-1 K-1 and Rv = 461.5 J Kg-1 K-1
Tv = T – q T + A q T (where A =
𝑅𝑣
𝑅𝑑
= 1.606 )
Tv = T (1 + A q – q) = T (1 + q (A – 1))
Tv = (1 + 0.606 q) T

Virtual temperature
This virtual temperature Tv (in the place of actual temperature)
is used for moist air in the ideal gas equation.
The virtual temperature is always greater than the actual
temperature because moist air is less dense than dry air at the
same temperature and pressure. However, the virtual
temperature may exceed the actual temperature by only a few
degrees even for very warm and moist air.

Thanks for your kind attention

SAMA_L1_4Feb2023.pptx

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