1) Atmospheric pressure is caused by the weight of air molecules pressing down on surfaces below. The random motion of air molecules propagates this pressure equally in all directions. 2) Atmospheric pressure is measured using a mercury barometer, with standard atmospheric pressure at sea level being approximately 1013 hPa. Global maps of current sea-level air pressure show values typically between 1005-1047 hPa. 3) Pressure gradients are weak near the Earth's surface because winds act to reduce differences in pressure over time, transporting air from high to low pressure areas.

1. 2. Atmospheric pressure

2. Molecular view of atmospheric pressure
EARTH SURFACE
gravity random
motion
• Weight of all air molecules is propagated to surface
by random motion of molecules
• Random motion of molecules causes pressure to be
applied in all directions

3. Measurement of atmospheric pressure with the mercury barometer
vacuum
A
h
Atmospheric pressure p = pA = rHg gh
Mean sea-level pressure:
p = 1.013x105 Pa = 1013 hPa
= 1013 mb
= 1 atm
= 760 mm Hg (torr)
atmospheric pressure
(weight of atmosphere per unit area of surface)
SI unit for pressure is the Pascal (Pa): 1 Pa = 1 kg m-1 s-2

4. Today’s sea-level pressure map
https://www.wpc.ncep.noaa.gov/basicwx/day0-7loop.html
Pressures are in a narrow range 1005-1047 hPa

5. Why are sea-level pressure gradients so weak?
Consider a pressure gradient at sea level operating on an elementary air parcel
dxdydz with mass dm = ρadxdydz where ρa is the air density:
p(x) p(x+dx)
Vertical area
dydz Pressure-gradient force
( ) ( )
=
dF p x dydz p x dx dydz
dpdydz
  

Acceleration
1
ρ
p
a
dF dp
a
dm dx
  
For Dp = 10 hPa over Dx = 100 km, a  10-2 m s-2 a 100 km/h wind in 3 h!
Wind transports air to from high to low pressure, decreasing Dp
On mountains, the surface pressure is lower, and the pressure-gradient force along the
Earth surface is balanced by gravity:
p(z)
p(z+Dz) p-gradient
gravity
Exerted force
p(x)dydz

6. Total mass ma of the atmosphere
Radius of Earth:
6380 km
Mean pressure at Earth's surface: 984 hPa
(less than 1013 hPa because of elevated land)
Total number of moles of air in atmosphere:
20
1.8 10 moles
a
a
a
m
N
M
  
Mol. wt. of air: 29 g mole-1 = 0.029 kg mole-1
2
18
4
5.13 10 kg
surface
a
R p
m
g

  
Molecular weight of air:
1
2 2 2 2 (0.78 28) (0.21 32) (0.01 40) 29.0 g mol
a i i N N O O Ar Ar
i
M C M C M C M C M 
          

9.81 m s-2 (atmosphere is thin enough
that this can be considered constant)

7. Mean vertical profiles of pressure and temperature
Tropopause
Stratopause
Troposphere has 85% of atmospheric mass, stratosphere has 15%, little above

8. Decrease of pressure with altitude: barometric law
Consider elementary slab of atmosphere at equilibrium between gravity and p-gradient
forces:
p(z)
p(z+dz) a
dp
g
dz
  r
hydrostatic
equation
for fluids
Ideal gas law:
a a
a
pM M g
dp
dz
RT p RT
r    
Assume uniform T and integrate:
/
( ) (0) 7.4 250
z H
a
RT
p z p e H T
M g

   
scale hei
with km (
ght K)
barometric law ( )
( ) 0.37 ( )
( )
( 5km)
2
p z
p z H p z
e
p z
p z
  
 
/
( ) (0) z H
a a
n z n e

unit area
g
1
a
dp
dz

r
1
a
dp
g
dz
 
r

9. Application of barometric law: the sea-breeze effect