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.