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Richard RotunnoRichard Rotunno
National Center for Atmospheric Research , USA
Dynamic Mesoscale Mountain Meteorology
Lecture 5: Orographic Precipitation
Topics
Lecture 1 : Introduction, Concepts, Equations
Lecture 2: Thermally Driven Circulations
Lecture 3: Mountain Waves
Lecture 4: Mountain Lee Vortices
Lecture 5: Orographic Precipitation
Orographic Precipitation
• Large – Scale (Wind, Humidity, Stability)
• Mesoscale dynamics of orographic air flow
• Fine-scale air motions and microphysics
= saturation vapor density
⇒U
)3,,,,,( EffectsDCoriolisStabilityULHww=
H
L0z
Large-ScaleFlow
Microphysics
Dynamics
dzz
zxwDt
DxC
z
vsvs ∫∞
∂∂
−≈−≡0
),()(ρρ
)(xC
vsρ
= Column-Integrated Condensation
UTypes of OrographicEffects
MoistU
airflowcsmicrophysi ττ <<
U
Ls <<1000
smU /10=L UL /km100km10
s10000s1000
MoistMicrophysics
par
parenvgBρ
ρρ
δenvρ
parρg
Displacement
= density“env” = environment“par” = parcel
ρ
Effects of Water in the Air on Buoyancy
lvd ρρρρ ++=moist air is a mixture
TRRp vvdd )( ρρ +=gas law
d
lvw
d
vv
v
d qqR
R
ρρρ
ρρε +
≡≡≡ ;;
TRTq
qRp d
w
vd
(ρερ ≡⎟⎟
⎠
⎞⎜⎜⎝
⎛
++
=−
11 1
/ definitions
gas law
= densitysubscript d = dry airsubscript v = water vaporsubscript l = liquid water
ρ
env
envpar
T
TTgB (
((−
=
( )TqqTq
qT lv
w
v −+≅⎟⎟⎠
⎞⎜⎜⎝
⎛
+
+=
−
61.011
1 1ε(
δ
g
water vapor less dense than air
liquid water moredense than air
substitute for T( ρ
δ
g
Main Effect on Buoyancy through Phase Change
1st Law of Thermodynamics
Dt
DqL
Dt
DQ
Dt
Dp
Dt
DTc vsp −==−
ρ1
condensation latent heat release
CTKggqCgcalc
gcalL
vs
po
o
5.2001.124.600
1
11
1
≅Δ⇒−=−=Δ=≅
−
−−
−
Air Parcel Behavior with Phase Change
)(zTenv
)(δparT
δ
Temperature
z
Latent Heat Release Reduces Stability
dry moist
22dm NN <
x
hUdz
zzxw
x
hUzxw
z
vs
∂∂
∂∂
−→∂∂
≅ ∫∞
~),(),(0
0ρ
)(xhx
Strong Stability,Blocking
?~),(),(0
0 dzz
zxwx
hUzxw
z
vs∫∞
∂∂
−→∂∂
≠ρ
Weak Stability,No Blocking
Dynamics:Stable Flow
⇒U
⇒U
• With Weak Static Stability No Blocking Linear Theory (see Lecture 3) Expected to be OK
Topography(Oregon)
Obs Linear Theory
Smith, Bonneau and Barstaad (J. Atmos. Sci., 2004)
Air Parcel Behavior with Phase Change
)(zTenv)(δparT0>δ
Temperature
z
Latent Heat Release can Produce Asymmetric Effects
dry
moist
0<δ
Fundamental Nonlinearity
0 <−=0 >−=
δδδδ
ifNBifNB
d
m2
2
Upward Displacement:Parcel Remains Saturated
Downward Displacement:Parcel May Desaturate
Barcilon, Jusem and Drazin (1979)
δ
g
Saturated Conditions Upstream, UnsaturatedConditions Downstream/ (Foehn)Wind
Miglietta and Rotunno (J. Atmos. Sci., 2005)
Piedmont Flood November 1994 (Obs Rain 06z 5 Nov –06z 6 Nov)
Rotunno and Ferretti (2001)
Warm, Moist
12 Z 5 Nov 1994 Milan 00 Z 6 Nov 1994 Milan
Nearly Moist Neutral
Air Parcel Behavior with Phase Change
)(zTenv
)(δparT
δ
Temperature
z
Latent Heat Release can Produce Instability
dry moist
Measure of Linear Stability
∫=1
0
z
z
BdzCAPEGlobal Measure:
Convective Available
Potential Energy
2N
( ) pdTTRBdzzp
zp
envpard
z
z
ln)(
)(
0
1
1
0
∫∫ −=((
Emanuel (1994)
parTenvT
envpar TT >
0z
1z
smCAPEw /502~2max −×=
dzz
zxwzCz
vs∫∞
∂∂
−=0
),()( 0ρ
maxw
!!!/72/01./2)()( 30max0 hmmmKgsmzwzC vs =××=≈ ρ
Good News:Upslope Flow Can Provide Lift to Overcome Threshold ( E.g. Stable Layers)
Orographic Effect on Moist Convection
⇒U
⇒U
Bad News:Upslope Wind Moves Cells Downwind Rain Accumulation Small
Typical Rain Cell Life Cycle
Cold Air OutflowByers and Braham (1948)
Good News: Cool Air Outflows May Initiate New Cells Upstream
⇒U
Chu and Lin (2000)
Bad News: Cool Air Outflows May Propagate Too Far Upstream
⇒U
Chu and Lin (2000)
)(zU
Good News:Rain Accumulation Large if Wind Varies with Height such that Cells are Stationary wrt Mountain
Big Thompson FloodColorado, 1976
Caracena et al. (1979)
Caracena et al. (1979)
Summary
- Dynamics of orographic air flow strongly influenced by latent heating
- Stable Case: Latent heating renders flow less stable making possible flow over tall mountains condensing large amounts of water vapor
- Unstable Case: Convective cells may produce large amounts of condensed water, but motion of cells wrt to mountain makes detailed prediction difficult.