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Stability
• Thermodynamic diagrams provide a
graphical method of showing changes in the
character of air parcels as they move
vertically in the atmosphere.
1884
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Emagram
By H. Hertz
Pressure - straight,
horizontal lines
Temperature - straight,
vertical lines
Dry adiabats - slightly
curved lines
Moist adiabats - curved lines
Does not have area
proportional to energy
1922
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Tephigram
By Sir William
Napier Shaw
Isobars logarithmic
curved-slope up
to right
Temp. straight linesslope up to right
Dry adiabats
(potential temp.) straight lines
Sat. adiabats appreciably curved.
1927
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Also called a
Pseudoadiabatic
Diagram
Isobars- straight
horizontal lines
Temp. straight vertical
lines
Dry adiabats
(potential temp.) straight lines
Sat. adiabats - curved.
Sat. Mixing Ratio lines
- essentially straight.
Does not have area
proportional to energy.
1947
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Skew-T/Log-P Diagram
Modification of Emagram
by N. Herlofson.
Isobars- straight
horizontal lines
Large angle between
Isotherms and dry adiabats
Dry adiabats
(potential temp.) curved lines
Sat. adiabats - curved.
Sat. Mixing Ratio lines
- essentially straight.
Typical sets of lines - Review
• Pressure: (P) (isobar) Horizontal solid
lines or slanted dashed, depending of
diagram.
• Height: (z) Horizontal solid or diagonal
dashed, depending on diagram.
• Temperature: (T) (isotherm) Vertical solid
lines - or slanted (usually lower left to upper
right), depending on the diagram.
• Mixing ratio (isohume) (r) (rs): slanted
dotted lines (or colored) - May be lower
right to upper left, or lower left to upper
right - depends on diagram.
• Dry Adiabat (constant entropy) (constant
potential temperature) (Gd) (Q): Solid, thick
lines (or colored) - lower right to upper left,
or vertical depending on graph.
• Moist Adiabat (constant liquid water
potential temperature) (QL, Gs): Dashed
lines, lower right to upper left, or lower left
to upper right, or colored.
• A plotted point on a thermodynamic
diagram expresses a different character of
the air depending on the position of that
point with respect to different sets of lines.
• Environmental temperature and dew point
profiles.
– Show state of the atmosphere at a particular
location and a particular interval of time.
• State: Two points (unsaturated) or one point
(saturated) to show the state of the air at a
particular height (pressure).
• Dry (unsaturated) processes: Moving
unsaturated parcels of air vertically in the
environmental air.
• Moist (saturated) processes: Moving
saturated parcels of air vertically in the
environmental air.
• Lifting Condensation Level: zLCL  0.125 T  Td 
• Condensed water: rL = rT - rs
– Rising air
• Cloud base forms at LCL
– Descending air
• Temperature represents rs
• Liquid water evaporates back into air.
• Precipitation: rT decreases by amount of
precipitation.
– rT cannot decrease below rs.
• Example: pg. 127
– Note Error:
– Work problem graphically.
Buoyancy
• The force acting down on the
top face of the object is equal
to the weight of the fluid above
the object.
• The force acting up on the
weight  m g
bottom face of the object is
   Vol  g
equal to the weight of the fluid
above the bottom of the object.
Force acts in all directions
equally at any point in a fluid.
• FB = F1 - F2 = buoyant force on
object due to fluid pressure.
• FB = fgA(h2) - fgA(h1)
• FB = fgA(Dh) = fgV
• Net force = weight object - FB = ogV- fgV
• Net force per unit mass of the object = oVg   f gV
because mo = oV
o V
o   f
eq. 6.1
Net Force

g
mo
o


• Since P = RT, then for an air parcel in the
environmental air, we can write:
 P
P 



Net Force  RTv par RTv env 
 
g

P
m par




RT

v par

Tv env  Tv par

Net Force  T v par Tv env
 
1
m par

 Tv par



Tv env  Tv par 


 g  
 T
 g



v env


• The equation can also be written for Virtual
Potential Temperature giving equation 6.2b.
• Note: pg. 129, using equations 3:10 and
3:11, not 2:21 and 2:22, 6.2b should be:
F v e   v p

g
m
v e
• Note: a force/mass is an acceleration.
Static Stability
• Static: Not moving.
• A parcel is statically stable if the buoyancy
force acting on it is opposite to the direction
of displacement.
• A parcel is statically unstable if the
buoyance force acts in the same direction as
the displacement.
• A parcel is statically neutral if no buoyance
force acts on the parcel.
Mixed Layer Depth Determination
• Mixed Layer: Typically the lowest 200 meters to
4 km of the atmosphere where air warmed by the
earth’s surface (becoming unstable) causing air
parcels to rise. Depth is variable with location
and time. Often develops during daytime with
strong heating.
– Turbulence develops in the Mixed Layer.
• Stable layers develop during nighttime cooling.
• Neutral layers develop during overcast, little
heating, conditions.
• From surface temperature, lift parcel
vertically in atmosphere. Follow dry
adiabat, or isentrope (Q). Where parcel
temperature becomes same as environment,
this is the height of the Mixed Layer Depth.
Convection Condensation Level
• Suppose you have a morning sounding. The Mixed layer is
very low, the air is stable.
• You want to know to what temperature the air near the
ground must reach to cause clouds to form in the afternoon
and at what height would be the bases.
• From the surface dew point extend line upward parallel to
the mixing ratio lines until it intersects the sounding. This is
the CCL.
• From this point, extend a line downward parallel to the dry
adiabats to the surface.
• The temperature at this point is the temperature the air near
the ground must reach.
Brunt-Vaisala Frequency
• It is frequency of oscillation of an air parcel
produced by the restoring force (net force of
buoyancy and gravity) acting on the air parcel
which has been displaced from its equilibrium
level in an unsaturated, stably stratified
atmosphere. (units of radians/s)
NB V
g DTv 

 
 G d
Tv  Dz 
NB V
g DQv


Tv Dz
Dynamic Stability in stably stratified air
• Shear is the change in wind with distance.
Since wind is a vector, changing wind speed
or changing direction, or both, produces
shear.
• Shear may occur in the horizontal or
vertical, or both.
• Turbulence: A state of fluid flow in which
the instantaneous velocities exhibit irregular
and apparently random fluctuations.
• Consider only vertical shear and the
resulting turbulence that might occur. The
flow shows the air to be stably stratified.
• This process of frictional dissipation of energy is
described by Richardson’s rhyme:
– Big whirls have little whirls which feed on their
velocity.
– Little whirls have lesser whirls, and so on to
viscosity.
• Viscosity (or internal friction) is the molecular
property of a fluid which enables it to support
tangential stresses for a finite time and thus
resist deformation.
• When that ability breaks down, the spontaneous
growth of small scale waves, turbulence, in a stably
stratified atmosphere results.
• The bulk Richardson number provides an
indication of the stability. When the Richardson
number is less than a critical value (Critical
Richardson Number, 0.25) the flow becomes
dynamically unstable. More negative it is the
greater the dynamic instability
Ri 
g  DTv  G d  Dz Dz

Tv  DU   DV 
2
2

• Both the static stability (potential for
turbulence from vertical motions of air in
the atmosphere) and the dynamic stability
(potential for turbulence from shear
considerations) should be considered for
turbulence determinations.
• Problems: N1, N2, N3, N4, N5 (80 - 70
kPa), N6, N7, N8, U9, U10.
• SHOW ALL EQUATIONS USED AND
CALCULATIONS