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Ch. 6 Fundamentals of
Atmospheric/Ocean Modeling
--- Introduction to Geophysical Fluid
Dynamics
Variables and Units
1. 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
Variables and Units
1. 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)
Part II - The International Unit System (SI)
SI prefixes
SI base units
Base quantity
length
mass
time
temperature
Name
meter
kilogram
second
kelvin
Symbol
m
kg
s
K
So, for Length…
1000 m = 1 km
1m = 1000 mm
And so forth. Much simpler!
-Factor
1012
109
106
103
102
101
Name
tera
giga
mega
kilo
hecto
deka
Symbol
T
G
M
k
h
da
Factor
10-1
10-2
10-3
10-6
10-9
10-12
Name
deci
centi
milli
micro
nano
pico
Symbol
d
c
m
µ
n
p
As of 2005, only three countries hang on to the
messy Imperial Units, Myanmar, Liberia, and the
United States.
Part II - The International Unit System (SI)
SI prefixes
SI base units
Base quantity
length
mass
time
temperature
Name
meter
kilogram
second
kelvin
Symbol
m
kg
s
K
SI derived units
Derived quantity
area
volume
speed, velocity
acceleration
mass density
specific volume
Name
square meter
cubic meter
meter per second
meter per second squared
kilogram per cubic meter
cubic meter per kilogram
Symbol
m2
m3
m/s
m/s2
kg/m3
m3/kg
-Factor
1012
109
106
103
102
101
Name
tera
giga
mega
kilo
hecto
deka
Symbol
T
G
M
k
h
da
Factor
10-1
10-2
10-3
10-6
10-9
10-12
Name
deci
centi
milli
micro
nano
pico
Symbol
d
c
m
µ
n
p
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
Dimensions and Units
All physical quantities can be expressed in terms of basic dimensions
Mass
Length
Time
Temperature
M
L
T
K
(Kg)
(m)
(s)
(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
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
Pressure Gradient Force (PGF)
Figure 6.8a
• Coriolis effect seen on a rotating platform,
as 1 person throws a ball to another
person.
Coriolis Force
• Due to the rotation of
the Earth
• Objects appear to be
deflected to the right
(following the motion)
in the Northern
Hemisphere
• Speed is unaffected,
only direction
Fig. 6-9, p. 165
The Coriolis
Effect
• -The Coriolis force causes the wind to deflect to the right of its intended path in
the Northern Hemisphere and to the left of its intended path in the Southern
Hemisphere. It acts at a right angle to the wind.
• - The Coriolis force is largest at the pole and zero at the equator
• - The stronger the wind speed, the greater the deflection
• - The Coriolis force changes only wind direction, not wind speed.
• - We measure motion on the rotating Earth. Thus, we need to be concerned
with the Coriolis force
Geostrophic balance
• P diff. => pressure gradient force (PGF)
=> air parcel moves => Coriolis force
• Geostrophy = balance between PGF & Coriolis force .
• 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.
PGF
Coriolis
wind
N. Hem.
wind
S. Hem.
PGF
Coriolis
• Converging contours of const. pressure (isobars)
=> faster flow => incr. CF & PGF
Get geostrophic
wind pattern
from isobars
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.
Convergence & divergence
• Cyclone has convergence near ground but divergence at
upper level.
• Anticyclone: divergence near ground, convergence at
upper level.
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
Supergeostrophic flow
Subgeostrophic flow
• 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
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
Friction
• Ground
friction slows
wind => CF
weakens.
• CF+friction
balances
PGF.
• Surface wind
tilted toward
low p region.
Pressure Gradient + Coriolis + Friction Forces
Surface
Wind
Figure 6.8c
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
Surface and upper atmosphere air flow around high pressure systems (anticyclones)
Surface and upper atmosphere air flow around low pressure systems (cyclones)