Meteorology

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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
ENV 111: Introduction to Meteorology
Lecture 2
Change of meteorological parameters with height
Air temperature
Air Density
Air Pressure
ndettoel@2016 ENV 111: Introduction to Meteorology
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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Change of atmospheric parameters
The vertical structure of the atmosphere changes continuously but
mainly due to physical parameters like:
⇒ Air temperature
⇒ Air pressure
⇒ Air density
The atmospheric air can be become warmer or cooler from purely
mechanical causes (potential temperature changes)
Inside the atmosphere, air temperature changes continuously
adiabatically
The temperature lapse rate is expressed as:
γ = −δT/δz
ndettoel@2016 ENV 111: Introduction to Meteorology

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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Temperature lapse rate and inversion
The moisture in the atmosphere affects the lapse rate hence its value
for dry and moist air is different:
⇒ Theoretical dry vertical lapse rate equals to 1 ◦
C/100 m
⇒ The moist vertical adiabatic lapse rate occurs in an air mass with water
vapour and during its ascent it is cooled adiabatically
⇒ Due to condensation of water vapour, latent heat is released hence the rate of
temperature decrease with height is smaller:
γ = −0.5 ◦
C/100 m
ndettoel@2016 ENV 111: Introduction to Meteorology
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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Temperature lapse rate and inversion
At high altitudes, air temperature can be estimated by using the ideal
gas law in conjunction with lapse rate:
p = ρ(R/M) ∗ T or p = ρRa ∗ T
⇒ R is the universal gas constant (8.314Jmol−1
K−1
;
⇒ Ra is the specific constant of gasses, i.e. 287.05Jkg−1
K−1
for dry
air
Sometimes a temperature inversion occurs hence an inversion layer is
created
ndettoel@2016 ENV 111: Introduction to Meteorology

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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Temperature inversion
Figure 13 : Schematic representation of
temperature inversion
The layer is characterized by
the height of the inversion
base and its own height
The temperature inversion is
classified according to the
height at which it occurs
ndettoel@2016 ENV 111: Introduction to Meteorology
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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Temperature inversion
Figure 14 : Schematic representation of a
surface - subsidence inversion
⇒ Surface inversion
Occurs due to cooling of the
Earth’s surface during the night
⇒ Subsidence inversion
When the cold air mass descend
from the upper atmosphere to
the Earth’s surface
Subsidence inversion lasts longer
(few days) than a surface (hours)
ndettoel@2016 ENV 111: Introduction to Meteorology

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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Temperature inversion
Figure 15 : Schematic representation of a
frontal inversion
⇒ Frontal inversion
Occurs when, at a specific height in
the lower troposphere, warm air
mass override a cold air layer which
extends to the Earth’s surface
In general an inversion occurs for a
few meters or a few 100 m from the
Earth’s surface
An inversion is directly related to
other weather phenomena (e.g. fog),
visibility reduction and air pollution
ndettoel@2016 ENV 111: Introduction to Meteorology
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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Variation of air pressure and density
Figure 16 : Both air pressure and air density decrease
Gravity holds air
molecules close to
Earth’s surface
This squeeze (compress)
air molecules close
together
So gravity also influences
the weight of the air
ndettoel@2016 ENV 111: Introduction to Meteorology

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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Air pressure and density variation
The density of air (or any substance) is determined by the masses of
atoms and molecules and the amount of space between them
So the molecular density of air is the number of molecules in a given
volume
More molecules are near Earth’s surface than at higher levels; air
density is greatest at the surface and decreases upwards
Air molecules are in constant motion. The resulting collision of air
molecules exert a push (force) on the colliding surface
Air molecules occupy space and have weight
ndettoel@2016 ENV 111: Introduction to Meteorology
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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Air pressure and density variation
The weight of the air
molecules acts as a force
upon the Earth
Atmospheric pressure
(air pressure) is the
amount of force exerted
over an area of surface
The mass of air above
the surface affects the
surface air pressure
ndettoel@2016 ENV 111: Introduction to Meteorology

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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Air pressure and density variation
Atmospheric pressure always decreases with increasing height
Like air density, air pressure decreases rapidly at first, then more
slowly at higher levels
The pressure at any level in the atmosphere may be measured in
terms of the total mass of air above any point
Millibar (mb) is the most common unit used on surface weather maps.
Its metric equivalent is hectopascal (hPa)
ndettoel@2016 ENV 111: Introduction to Meteorology
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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Air pressure and density variation
The variation of density with height can also be estimated using the
ideal gas equation
Integrate the ideal gas equation to get:
dp = ρRadT + RaTdp
Suppose the atmosphere is balanced hydrostatically
dp = −ρgdz
Then, we get:
−ρgdz = ρRadT + RaTdρ
ndettoel@2016 ENV 111: Introduction to Meteorology

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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Air pressure and density variation
Divide the equation with density (ρ) and rearrange it to get:
d(lnρ) = −g/(RaT) dz − d(lnT)
Suppose the layer examined is isothermal, (i.e. temperature is
constant), then
d(lnρ) = −g/(Ra
¯T) dz
Integrate the equation from z1 = 0 to z2 = z with corresponding
values of density ρ0 and ρz, we finally get:
ρz = ρ0 ∗ e (gz/Ra
¯T)
So in an isothermal atmosphere, the air density decreases
exponentially with height
ndettoel@2016 ENV 111: Introduction to Meteorology
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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Air pressure and density variation
If the average temperature in the troposphere is about 250 K, one can
show that:
ρz = ρ0 ∗ 10 −(z/17)
Meaning that in the troposphere the air density decreases with a
factor of 10 every 17 km of height (i.e. in the same way as the
pressure)
The change of the atmospheric pressure with height can be easily
estimated by using the hydrostatic equation
dp(z)/dz = −ρ(z)g
And also by using the ideal gas equation:
ρ(z) = Map(z)/RT(z)
We obtain:
dp(z)/dz = Magp(z)/RT(z)
ndettoel@2016 ENV 111: Introduction to Meteorology

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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Air pressure and density variation
Let H(z) = RT(z)/Mag be the characteristic length for the pressure
decrease with height
Then we obtain:
dlnp(z)/dz = −1/H(z)
If the variation of temperature against height is very negligible, the
characteristic length is independent of height
(i.e. H(z) = H = constant)
dp(z)/dz = −ρ(z)g
So upon integrating the equation, we get:
p(z)/p0 = e (z/H)
In the troposphere, the average temperature is about 250 K, one can
also show that:
p(z) = p0 ∗ 10 −(z/17)
ndettoel@2016 ENV 111: Introduction to Meteorology
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Introduction Earth’s atmosphere Evolution Composition Vertical structure Vertical variation
Review questions
1 Briefly explain the production and natural destruction of carbon
dioxide near Earths surface. Give two reasons for the increase of
carbon dioxide over the past 100-plus years.
2 How does the atmosphere protect inhabitants at Earth’s surface
3 On the basis of temperature, list the layers of the atmosphere from
the lowest layer to the highest.
4 Even though the actual concentration of oxygen is close to 21 percent
(by volume) in the upper stratosphere, explain why, without proper
breathing apparatus, you would not be able to survive there
5 Show that between the surface and the height of 11 km, the
temperature (◦
C) at height z is T(z) = 15 − 0.0065z
ndettoel@2016 ENV 111: Introduction to Meteorology