1. --- Introduction to Geophysical Fluid Dynamics
Ch. 7 Fundamentals of Atmospheric/Ocean Modeling
--- Introduction to Geophysical Fluid Dynamics

4. Variables and Units
Independent Variables
Values are independent of each other
x increases eastward
y increases northward
z increases upward
t time
Later we can use other coordinate systems
p decreases upward
latitude, longitude

5. Variables and Units
Dependent Variables
Values depend on other variables
wind speeds
u > 0 for eastward motion
v > 0 for northward motion
w > 0 for upward motion
Temperature T = T(x,y,z,t)
Pressure p = p(x,y,z,t)
Density  = (x,y,z,t)

6. Part II - The International Unit System (SI)
SI prefixes --
Factor Name  Symbol
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da  
Factor Name  Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro µ
10-9 nano n
10-12 pico p
 SI base units
Base quantity Name Symbol
length meter m
mass kilogram    kg
time second s
temperature       kelvin K
So, for Length…
1000 m = 1 km
1m = 1000 mm
And so forth. Much simpler!

7. As of 2005, only three countries hang on to the messy Imperial Units, Myanmar, Liberia, and the United States.

8. Part II - The International Unit System (SI)
SI prefixes --
Factor Name  Symbol
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da  
Factor Name  Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro µ
10-9 nano n
10-12 pico p
 SI base units
Base quantity Name Symbol
length meter m
mass kilogram    kg
time second s
temperature       kelvin K
SI derived units
Derived quantity Name Symbol
area square meter m2
volume cubic meter m3
speed, velocity meter per second m/s
acceleration meter per second squared   m/s2
mass density kilogram per cubic meter kg/m3
specific volume cubic meter per kilogram m3/kg

9. In meteorology/ocean, we almost always use SI units,
journals require it.
Force - Newtons (kg m/s)
Pressure - We still use millibars (mb)
1 mb = 100 Pa = 1 hPa (PASCALS N/m2) (hpa: hecto-pascal)
Pressure = force / unit area;
Must use correct (SI) units in calculations
Temperatures - Always use Kelvin in calculations
T(K) = T( C ) +273

10. Dimensions and Units
All physical quantities can be expressed in terms of basic dimensions
Mass M (Kg)
Length L (m)
Time T (s)
Temperature K (K)
Velocity = Distance / Time, so it has dimensions L/T, or m/s
Acceleration = Velocity / Time, so it has dimensions L/T2, or m/s2
Force = Mass x Acceleration, so it has dimensions M LT-2, or Kg m/s2
Pressure, density

25. Pressure Gradient Force (PGF)
pressure gradient: high pressure  low pressure
pressure differences exits due to unequal heating of Earth’s surface
spacing between isobars indicates intensity of gradient
flow is perpendicular to isobars
Figure 6.7

26. Pressure Gradient Force (PGF)
Figure 6.8a

41. Coriolis effect seen on a rotating platform, as 1 person throws a ball to another person.

42. Coriolis Effect Shell fired in N. Hem. deflects right.
In S. Hem., it deflects left.
Coriolis (1835): deflection due to Earth’s rotation
Consider object moving northward in N. Hem.:
As Earth rotates, speed of surface is greatest at Equator and 0 at Poles.
WWI, battle of Falkland Islands in S. Hem. British warships had guns which only correct for the N. Hem. Coriolis effect.
[KKC Fig.4-12]

43. Obj. A has greater eastward speed than B.
=> When A is moved northward, it ends up at X, ahead of B´.
=> Appears to be a ‘force’ deflecting the obj. to the right (Coriolis force)
Obj. moves southward (in N.Hem.) ends up further west => Coriolis deflection to right.
Consider obj. moving eastward:
It moves faster than Earth in circular orbit
=> incr. ‘centrifugal force’
=> obj. pushed away from Earth’s spin axis.

44. Obj. moving westward is deflected poleward => deflection to right (N.Hem.)
Mathematically E-W and N-S movements can be treated in same way => obj. moving in any horiz. direction deflects to the right in N. Hem., and to the left in S. Hem.
Coriolis effect 0 at Equator, & max. at Poles.
Strength of Coriolis force proportional to speed of obj.

45. The Coriolis Effect
objects in the atmosphere are influenced by the Earth’s rotation
Rotation of Earth is counter-clockwise
results in an ‘apparent’ deflection (relative to surface)
deflection to the right Northern Hemisphere (left, S. Hemisphere)
Greatest at the poles, 0 at the equator
Increases with speed of moving object
CE changes direction not speed

54. Geostrophic balance P diff. => pressure gradient force (PGF)
=> air parcel moves => Coriolis force
Geostrophy = balance between PGF & Coriolis force .
[Tarbuk & Lutgens 2003, Fig.17.5]

55. S. Hem. wind PGF Coriolis PGF Coriolis wind N. Hem.
Approx. geostrophic balance for large scale flow away from Eq.
Q: Why no geostrophic balance at Equator? A: No Coriolis force at Eq.
In N. Hem., geostrophic wind blow to the right of PGF (points from high to low P)
In S. Hem., geostrophic wind to left of PGF.
S. Hem.
wind
PGF
Coriolis
PGF
Coriolis
wind
N. Hem.

56. Converging contours of const
Converging contours of const. pressure (isobars) => faster flow => incr. CF & PGF
Get geostrophic
wind pattern
from isobars

57. Cyclone & Anticyclone
Large low pressure cells are cyclones, (high pressure cells anticyclones)
Air driven towards the centre of a cyclone by PGF gets deflected by Coriolis to spiral around the centre.
Spencer Fig.12.5

58. Difference between PGF & Coriolis (CF) is the centripetal force needed to keep parcel in orbit.
[Ahrens, 2003, Fig.9.26, 9.27]

59. Convergence & divergence
Cyclone has convergence near ground but divergence at upper level.
Anticyclone: divergence near ground, convergence at upper level.
[Ahrens 2003, Fig.9.33]

60. Pressure Gradient Force + Coriolis Force
Geostrophic
Wind

61. Upper Atmosphere Winds
upper air moving from areas of higher to areas of lower pressure undergo Coriolis deflection
air will eventually flow parallel to height contours as the pressure gradient force balances with the Coriolis force
this geostrophic flow (wind) may only occur in the free atmosphere (no friction)
stable flow with constant speed and direction

62. Supergeostrophic flow
Subgeostrophic flow

63. Geostrophic flow too simplistic  PGF is rarely uniform, height contours curve and vary in distance
wind still flows parallel to contours HOWEVER continuously changing direction (and experiencing acceleration)
for parallel flow to occur pressure imbalance must exist between the PGF and CE  Gradient Flow
Two specific types of gradient flow:
Supergeostrophic: High pressure systems, CE > PGF (to enable wind to turn), air accelerates
Subgeostrophic: Low pressure systems, PGF > CE, air decelerates
supergeostrophic and subgeostrophic conditions lead to airflow parallel to curved height contours

64. Friction factor at Earth’s surface  slows wind
varies with surface texture, wind speed, time of day/year and atmospheric conditions
Important for air within ~1.5 km of the surface, the planetary boundary layer
Because friction reduces wind speed it also reduces Coriolis deflection
Friction above 1.5 km is negligible
Above 1.5 km = the free atmosphere

65. Friction Ground friction slows wind => CF weakens.
CF+friction balances PGF.
Surface wind tilted toward low p region.
[Ahrens 2003, Fig.9.29]

66. Pressure Gradient + Coriolis + Friction Forces
Surface
Wind
Figure 6.8c

67. Cyclones, Anticyclones, Troughs and Ridges
4 broad pressure areas in Northern hemisphere
High pressure areas (anticyclones)  clockwise airflow in the Northern Hemisphere (opposite flow direction in S. Hemisphere)
Characterized by descending air which warms creating clear skies
Low pressure areas (cyclones)  counterclockwise airflow in N. Hemisphere (opposite flow in S. Hemisphere)
Air converges toward low pressure centers, cyclones are characterized by ascending air which cools to form clouds and possibly precipitation
In the upper atmosphere, ridges correspond to surface anticyclones while troughs correspond to surface cyclones

68. Surface and upper atmosphere air flow around high pressure systems (anticyclones)

69. Surface and upper atmosphere air flow around low pressure systems (cyclones)