Temperature
• Lapse rate- decrease of temperature with height: G
= - dT/dz
• Environmental lapse rate (G) order 6C/km in free
atmosphere
• Gd- dry adiabatic lapse rate- rate at which an
unsaturated parcel cools when lifted= 9.8 C/km
• Gs- saturated adiabatic lapse rate- rate at which a
saturated parcel cools when lifted= 4-9.8 C/km
Stability
• Vertical momentum equation
– vertical accelerations due to imbalance between
downward directed gravitational force and upward
directed pressure gradient force
• Stable- adiabatic parcel displaced from original
altitude accelerated back towards original altitude
• Neutral- adiabatic parcel displaced from original
altitude. continues to move at a constant speed
• Unstable- adiabatic parcel displaced from original
altitude continues to accelerate away from original
altitude
Stability
• Absolutely Stable: G< Gd
• Absolutely Unstable: G> Gd
• Conditionally Unstable: Gs < G< Gd
Lapse Rate
Whiteman (2000)
Parcel Theory
Whiteman (2000)
Skew-T log P diagrams
• Plot vertical profile of temperature,
moisture, wind as a function of elevation
• Skewed to draw attention to vertical
variations in temperature that deviate from
typical 6C/km decrease with height
• Dew point temperature- absolute measure of
water vapor = f(e)
Stability
• Adiabatic parcel conserves
potential temperature q as it
rises or sinks
• Stable atmosphere: d q /dz >
0
• Neutral atmosphere: d q /dz
=0
• Unstable atmosphere d q /dz
<0
Stable
atm
z
q
Planetary Boundary Layer
• PBL-Layer in atmosphere affected by
interaction with the surface
• Free atmosphere- atmospheric layer above
the PBL in which state variables largely
unaffected by the surface
PBL
• Daytime convective boundary layer
–
–
–
–
Neutral lapse rate above surface
Parcels move freely vertically
Strong mixing
Can be several thousand meters deep over western U.S.
• Nocturnal stable layer
– Temperature usually increases with height away from
the surface – inversion
– Parcels flow horizontally
– Little mixing
– Usually few hundred meters deep
Diurnal PBL Evolution
Whiteman (2000)
Diurnal Change in Temperature
Whiteman (2000)
Surface based temperature
inversion
Whiteman (2000)
Elevated Inversion
Whiteman (2000)
Diurnal changes in stability
Whiteman (2000)
Whiteman(2000)
Mountain/Valley PBL
Mountain PBL
Barry (1992)
Free Air vs. Mountain
Barry (1992)
Valley vs. Summit
Barry (1992)
Influence of Wind Speed
Barry (1992)
Influence of cloud cover
Barry (1992)
Diurnal Temperature Range
Barry (1992)
Diurnal Temperature Range: Western U.S.
A. Reinecke
Wind Speed
• Terrain controls wind speed and direction
• However, some general characteristics of wind
speed vs. altitude
• Mid-latitudes:
– Wind speed increases with height
– Mt. Washington 1915 m: 23m/s in winter;12m/s in
summer averages
• Tropics
– Wind speed decreases with height
– New Guinea 4250 m: 2 m/s DJF average
– El Misti Peru 4760 m 5 m/s average
Wind Speed over Summit
• Vertical compression of airflow over
mountain accelerates air
• Friction retards flow
– Small scale roughness effects (<10 m
dimension)
– Form drag (10m<topography<1km)
• Dynamical pressure perturbations created
• Proportional to slope2
• Influences atmosphere through considerable depth
Vertical compression
• Consider case first of steady state,
incompressible fluid flowing through
constriction: Bernoulli effect
Conservation of
energy:
Kinetic Energy +
work down by
pressure force +
potential energy =
0
Vertical compression
• (U22 – U12)/2 + (p2 – p1)/r + g(z2 – z1) = 0
1
U2 > U1
z2 = z1 so
p2 < p1
2
Lower pressure in
constriction
Vertical compression
• (U22 – U12)/2 + (p2 – p1)/r + g(z2 – z1) = 0
2
1
U2 > U1
z2 = z1 so
p2 < p1
Lower pressure
over summit
Wind over Hill
Barry 1992
Free Air vs. Summit
Wind speed less at the
summit than in the
nearby free air
Barry (1992)
Roughness Effects
• For well-mixed conditions (near neutral
lapse rate)
• U2 = u1 ln (z2/zo)/ln(z1/z0)
• Roughness length zo=.5 h A/S where h
height of obstacle, A- silhouette area, S
surface area A/S< .1
• Zo- height where wind approaches 0
Terrain Roughness
Zo (m)
Classification
Description
.0002
Very smooth
Water,pavement
.03
open
Prairie or farm
.25
Rough
High crops
.5
Very rough
>2
Chaotic
Scattered
bldgs/orchards
Towns/forests