Gravity Waves from Midlatitude Weather Systems

Shuguang Wang Columbia Univ.

Fuqing ZhangPenn State Univ.

Event-based gravity wave studies

– Observational studies of low troposphere gravity waves: e.g., Johnson (1929), Brunk (1949), Tepper (1951), Williams (1953), Gossard and Munk (1954), Matusmoto et al. (1967), Ferguson (1967), Bosart and Cussen (1973), Uccellini (1975), Eom (1975), Miller and Sanders (1980), Vincent and Homan (1983), Stobie et al. (1983), Pennick and Young (1984), Bosart and Sanders (1986), Bosart and Seimon (1988), Koch and Golus (1988), Koch and Dorian (1988), DeMaria et al. (1989), Schneider (1990), Ramamurthy et al. (1990, 1993), Monsert and Thorpe (1993), Bosart et al. (1998), Richter (1969), Hardy and Katz (1969), Browning (1972), Koch et al. (1988, 1993), Ralph et al. (1993), Trexler and Koch (2000), Kusunoki et al. (2000), Wakimoto and Bosart (2000), Rauber et al. (2001), Yang et al. (2001), Jewett et al. (2003)

– Event-based, over North American continent– Based on surface, sounding, radar, wind profiler etc. – Common wave characteristics: horizontal wavelength 50-500

km, period of several hours, phase speed of several tens m/s

Gravity Wave Climatology(Koppel, Bosart and Keyser 2000, MWR; Wang and Geller 2003, Wang et al. 2005)

Large-amplitude waves derived from hourly MSLP change > 4.25 hPa

Events based study of low troposphere gravity waves 1038 such events identified, of which 46% were associated with convection

Gravity wave environment in the typical midlatitude weather systems(Uccelini and Koch 1987)

jet

• Exit region of the upper-level jet streak where flow is strongly diffluent and unbalanced• Cold side of a surface frontal boundary• Sources: jets and flow imbalance, surface fronts, and moist convection

Generation mechanism: geostrophic adjustment due to initial imbalance

(Rossby 1938, Cahn 1945, Matsumoto 1961, Blumen 1972, Van Tuyl and Young 1982, Fritts and Luo 1992,O’Sullivan and Dunkerton 1995, Weglarz and Lin 1998, Chagnon and Bannon 2004)

Time scale ~ 1 day

Generation mechanism: shear instability(e.g., Jones 1968; Mastrantonio et al. 1976; Shen and Lin 1999)

Propagating gravity waves with wavelengths on the order of ten to a few hundreds of kilometers can be generated from the unstable tropospheric jet with 0<Ri<0.15 (shear instability, mode I)

upper-level jet low-level jet

Generation mechanism: fronts and frontogenesis(Ley and Peltier 1978, Gall et al. 1989, Snyder et al. 1993, Reeder and Griffins 1997)

Source of gravity waves: Convection (e.g., Alexander et al. 1995, Pandya and Durran 1996, Chu and Lin 2000, Lane et al. 2001, Fovell 2002)

Proposed mechanisms for gravity wave from convective cells:– Thermal forcing (Alexander et al. 1995)– Obstacle effects (Clark et al. 1986, Pfister 1993a,b)– Mechanic oscillator (Fovell et al. 1992)

Source of gravity waves: deep convection Hoffmann and Alexander, 2010

Using AIRS to identify gravity waves tied to convective eventsSeveral hot spots for convective GWs during summer time over North America continent

Night Day

C

D

Observations of Bosart et al. (1998, MWR):

GW generated at 06~07 Z, wavelength ~ 100km,phase speed ~ 27m/s, amplitude ~ 7-8 mb

From conceptual models to real events: a large-amplitude GW event of 4 January 1994: Bosart et al. (1998), Zhang et al. (2001) and Zhang et al. (2003)

Simulations of Zhang et al. (2001, QJ):

GW generated at 06~07 Z, wavelength ~ 100km,phase speed ~ 25m/s, amplitude ~ 3-4 mb

Schematic Wave Generation Model (Zhang et al. 2001, QJ)

Initiation Stage (left)Generation of the incipient gravity wave immediatelydownstream of the maximumimbalance and developmentof a split front due to warmocclusion

Development Stage (right)The incipient wave merges with thesplit front, resulting in its rapidamplification and scale contraction.Therefore, “localized” convectionis triggered and the dominant gravitywave developed at the surface.

Gravity Wave Synoptic Environment(Uccelini and Koch 1987)

jet

•Exit region of the upper-level jet streak where flow is strongly diffluent and unbalanced•Cold side of a surface frontal boundary•Likely generation and maintenance mechanisms: geostrophic adjustment and wave ducting

Gravity Waves: Baroclinic Wave & Geostrophic Adjustment(O’Sullivan and Dunkerton 1995)

Day 10

Day 11

horizontal/vertical wavelengths of ~150/2.5 km, phase speed ~8m/s, frequency ~4f

Zoom in: w & θ with 10km grid spacingdivergence (green) and pressure (blue) at 13km; isotach (brown) and wind at 8 km

Jet Streak >40m/s

114h after balanced initialization of baroclinic waves

GWs Generated in Idealized Baroclinic Jet-front Systems(Zhang 2004)

GWs in other types of baroclinic jet-front systems(Plougonven et al 2007)

In “anticyclone” life cycles: gravity waves in exit region of jet streaks

Gravity waves in moist life cycles?

Relating gravity waves to synoptic waves

114h 144h 48h 111h

128 km, 2.0 km 161, 2.2 85, 4.0 145, 2.2

3.63f 3.22f 11.0f 3.54f

• Wang and Zhang 2007: Frequency of GWs positively correlates to growth rates of BWs, and stronger flow imbalance

Jet Streak ~ 30 m/s

Translate slowly

Jet-dipole: a further idealized wave generation scenario from local jet streak

(Snyder et al. 2007, Wang et. al. 2009 JAS)

1800 km

PV (every 0.5PVU) at 12.5km

jet

+

-

Positive/negative potential vorticity anomalies

Vortex dipole: two counter rotating vortices

Potential vorticity inversion to create balanced jet

Integrate a mesoscale model up to 25 days. Dz=200m, Dx=90, 30km

BA

A

B

Gravity waves from a vortex dipole jet

Div, Θ and wind speedDiv. at 12.5km, wind speed (>15m/s) and PV (every 1PVU) at 11.5km

Dipole solution at 8.75 day

• GWs are continuously emitted as jet-dipole translate • Stationary within the moving frame of the dipole• Estimated wave characteristics: Lh ~ 300 km, Lz ~ 2 km, and ωi ~1.4 f

C

D

C D

Gravity waves from a vortex dipole jet

Div, Θ and wind speed (>15 m/s)Div. at 12.5km, wind speed (>15m/s) and PV (every 1PVU) at 11.5km

• GWs are continuously emitted as jet-dipole translate • Stationary within the moving frame of the dipole• Estimated wave characteristics: Lh ~ 300 km, Lz ~ 2 km, and ωi ~1.4 f

Dipole solution at 22.5 day

Wave source mechanism: forced, linear responses

• Separate the flow into large scale background flow AB and perturbations

A’, A’ << AB

A = AB+A’• Linearization about the large scale flow AB (Zhang and Plougonven 2007)

L: linear operatorG terms: Forcing from the large scale (balanced) flow

• Standard linearization for perturbation problems in simple terms

• But linear operator is not symmetric, not self-adjoint, and can be singular

Gδ = Dγ∂Fδ

∂z Gς = f∂Fς

∂zGθ = −

gΘΔFθ

L(w') =Gδ + Gς + Gθ

Linear response in jet-dipoleWang and Zhang 2010, Snyder et al. 2009

• Impose all forcing terms, wave pattern comparable to the MM5 solution

• Right phase, right pattern, amplitude close to (more than half of) the MM5 solution

Linear model solution

MM5 solution at 8.75 d

Contour interval: 0.05x10-6s-1

Contour interval: 0.1x10-6s-1

Horizontal divergence: red (+) and blue (-); wind speed (gray)

Concluding Remarks• Physically based gravity wave parameterization needs better

understanding of source mechanisms• Numerous observational and numerical studies have demonstrated

that weather systems are significant sources of gravity waves above: jet-imbalance, surface fronts and moist convections

• Increasing evidence of generation of gravity waves from jet. Understanding of the source mechanism is incomplete

• Gravity waves from midlatitude convection are much less known• Gravity waves from the oceanic storm track regions are even less

characterized • Generation versus Propagation. Who wins?

Real-data Modeling of gravity waves studies– Detailed 4D structures are available from real-data modeling– Zhang and Fritsch (1987), Schneider (1990), Powers and Reed

(1993), Pokrandt et al. (1996) and Powers (1997), Trexler and Koch (2000, MWR), Rauber et al. (2001, MWR), (Kaplan et al. 1997), (Zhang and Koch 2000), Koch and Zhang 2001; Koch et al. 2001, Zhang et al. (2001) and Zhang et al. (2003), Zhang et al. 2001, Jewett et al. (2003). QJ, Wu and Zhang 2004, Zulicke and Peters (2006)

Event-based Gravity wave studies

– Observational studies of low troposphere gravity waves: e.g., Johnson (1929), Brunk (1949), Tepper (1951), Williams (1953), Gossard and Munk (1954), Matusmoto et al. (1967), Ferguson (1967), Bosart and Cussen (1973), Uccellini (1975), Eom (1975), Miller and Sanders (1980), Vincent and Homan (1983), Stobie et al. (1983), Pennick and Young (1984), Bosart and Sanders (1986), Bosart and Seimon (1988), Koch and Golus (1988), Koch and Dorian (1988), DeMaria et al. (1989), Schneider (1990), Ramamurthy et al. (1990, 1993), Monsert and Thorpe (1993), Bosart et al. (1998), Richter (1969), Hardy and Katz (1969), Browning (1972), Koch et al. (1988, 1993), Ralph et al. (1993), Trexler and Koch (2000), Kusunoki et al. (2000), Wakimoto and Bosart (2000), Rauber et al. (2001), Yang et al. (2001), Jewett et al. (2003), Plougonven et al. 2003

– Detailed 4D structures are available from real-data modeling: Zhang and Fritsch (1987), Schneider (1990), Powers and Reed (1993), Pokrandt et al. (1996) and Powers (1997), Trexler and Koch (2000, MWR), Rauber et al. (2001, MWR), (Kaplan et al. 1997), (Zhang and Koch 2000), Koch and Zhang 2001; Koch et al. 2001, Zhang et al. (2001) and Zhang et al. (2003), Zhang et al. 2001, Jewett et al. (2003). QJ, Wu and Zhang 2004, Zulicke and Peters (2006)

– Events based, over North American continent, few over ocean– Based on surface, sounding obs, significant profiler and radar obs – Common wave characteristics: horizontal wavelength 50-500 km,

period of several hours, phase speed of 15-40 m/s

Gravity Wave Environment in the typicial Midlatitude Weather System(Uccelini and Koch 1987)

jet

• Along the warm conveyer belt (WCB), moisture is transported to promote convection

Maintenance Mechanism: Wave-CISK(Lindzen 1974; Raymond 1975, 1982)

Latent heat in convection forced waves which in turn organize convection orgravity waves initiate convection which in turn strength the gravity waves

Eom (1975)

Schematic of Raymond (1975)

Schematic of Koch et al. (1993)

GW OBS from Space(Wu and Zhang 2004)

radiance perturbationson 20 Jan 2003 from different satellite (AMSU) channels at

80, 50, 25, 10, 5 and 2 mb

Jet (shaded) and height at 300mb and horizontal divergence (red and blue) at 80mb

Gravity Waves and Jet Streak from MM5 Simulation(Zhang, Wu and Wang)

39h

84h69h

54h

Maintenance Mechanism: Wave Ducting

CD,n=C−U ≈ NHπ(0.5+n)

T~O(2πτi)

Ducting Criteria 1. Statically stable low layer as a duct, thick enough

to hold 1/4 vertical wavelength (Region 1)2. No critical layer in the duct 3. Critical level with low Ri in upper layer with

conditional instability (Regional 2)

Schematic representation of typical environment for mesoscale waves and precipitation bands over New England with typical wavelength of 100km, period of 1h and phase speed of 25m/s

Theory (Lindzen and Tung 1976)Observational Composite (Marks 1975)

How these waves are generated?

• Geostrophic adjustment (Rossby 1938; Uccelini and Koch 1987; O’Sullivan and Dunkerton 1995)

• Balance adjustment due to flow imbalance (the residual of nonlinear balance equation) (Zhang 2004; Wang and Zhang 2007)

• Spontaneous response (Snyder et al. 1993, 2007)

• Spontaneous adjustment emission in rotating shallow water (Ford et al. 2000, Vanneste and Yavneh 2004, Plougonven and Zeitlin 2002,)

• Point to the same direction: forcing/linear response