Orographic Precipitation II: Effects of Phase Change on Orographic Flow Richard Rotunno National Center for Atmospheric Research, USA
Condensation D Dt vs w( x, ) vs U Large-Scale Flow 0 H L Dynamics w = w( H, L, U, Stability, Coriolis,3D Effects) vs = saturation vapor density
Effects of Water in the Air on Buoyancy g par B = g env par Displacement δ env par = density env = environment par = parcel
l v d + + = moist air is a mixture T R R p v v d d ) ( + = gas law d l v w d v v v d q q R R ε + ; ; R T T q q R p d w v d ( ε + + = 1 1 1 / definitions gas law = density subscript d = dry air subscript v = water vapor subscript l = liquid water
substitute T ( for ( ( T T B = g par ( T env env ( T = 1+ q 1+ v ε q w 1 T ( 1+ 0.61q q )T v l g water vapor less dense than air liquid water more dense than air δ
Main Effect on Buoyancy through Phase Change 1 st Law of Thermodynamics g δ c p DT Dt 1 Dp Dt = DQ Dt = L Dq Dt vs L 600cal g cp =.24cal g Δq = 1g Kg vs 1 1 o 1 1 C =.001 ΔT 2.5 o C condensation latent heat release
Air Parcel Behavior with Phase Change dry moist T env () δ T par (δ ) Temperature Latent Heat Release Reduces Stability
x h U d x w x h U x w vs ~ ), ( ), ( 0 0 h(x) x Strong Stability, Blocking ~? ), ( ), ( 0 0 d x w x h U x w vs Weak Stability, No Blocking Dynamics:Stable Flow U U
Weak Stability, No Blocking U Large-Scale Flow 0 H L Simplest Model Rainout = Condensation R( x) = 0 w( x, ) vs d
Simple Model Overestimates R d liq d( c + r ) = dt dt = d dt vs + R Introduce Time Lags d dt c = d dt vs τ c c Conversion from Cloud droplets to Raindrops d r dt = + c τ c r τ r Precipitation Smith and Barstaad (2004)
U Moist Moist τ << microphysics 1000s << U =10m / L 100km 10km s L / U τ L U 10000s 1000s airflow τ ~ τ + τ microphysics c r
Transfer Function Transform of precipitation field Terrain transform Rˆ( k, l) = C iσhˆ( k, l) w [1 imλ ][1 + iστ ][1 + c iστ ] r σ = Uk +Vl Airflow dynamics: Uplift penetration Cloud physics: conversion Cloud physics: fallout Each bracket shifts and reduces precipitation
Triangle Ridge: Three models Raw upslope Airflow dynamics only Full linear model
With Weak Static Stability No Blocking Linear Theory Applied to Oregon Climate Topography (Oregon) Obs Linear Theory Smith, Bonneau and Barstaad (J. Atmos. Sci., 2004)
Air Parcel Behavior with Phase Change moist δ > 0 T () env T (δ ) par δ < 0 dry Temperature Latent Heat Release can Produce Asymmetric Effects
Fundamental Nonlinearity g δ Upward Displacement: Parcel Remains Saturated Downward Displacement: Parcel May Desaturate B B = N = N m 2 2 d δ δ if if δ δ > < 0 0 Barcilon, Jusem and Drain (1979)
Saturated Conditions Upstream, Unsaturated Conditions Downstream/ (Foehn)Wind Miglietta and Rotunno (J. Atmos. Sci., 2005)
Piedmont Flood November 1994 (Obs Rain 06 5 Nov 06 6 Nov) Warm, Moist Rotunno and Ferretti (2001)
12 Z 5 Nov 1994 Milan 00 Z 6 Nov 1994 Milan Nearly Moist Neutral
Air Parcel Behavior with Phase Change dry moist T env () δ T par (δ ) Temperature Latent Heat Release can Produce Instability
Global Measure: Convective Available Potential Energy CAPE = 1 0 Bd 1 p( 0 ) ( ( 0 Bd = R d p( ( ) T T d ln p 1 ) par env Emanuel (1994)
1 T env T par 0 T par > T env
w max = 2 CAPE ~ 2 50m / s w max C( 0 ) = w( x, ) 0 vs d 3 C( 0) wmaxvs ( 0) = 2m / s.01kg / m = 72 mm / h!!!
U Orographic Effect on Moist Convection Good News: Upslope Flow Can Provide Lift to Overcome Threshold ( E.g. Stable Layers)
U Bad News: Upslope Wind Moves Cells Downwind Rain Accumulation Small
Typical Rain Cell Life Cycle Byers and Braham (1948) Cold Air Outflow
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)
U () Good News:Rain Accumulation Large if Wind Varies with Height such that Cells are Stationary wrt Mountain
Big Thompson Flood Colorado, 1976 Caracena et al. (1979)
Caracena et al. (1979)
Summary - Dynamics of orographic air flow strongly coupled to latent heating - Stable Case: Latent heating renders flow less stable making possible flow over tall mountains condensing large amounts of water vapor. Microphysics present major uncertainties, however. - Unstable Case: Convective cells may produce large amounts of condensed water, but motion of cells wrt to mountain makes detailed prediction difficult.