Fuqing Zhang Shuguang Wang Penn State University Texas A&M University Spontaneous Balance Adjustment and Gravity Wave Emission from Jets/Fronts Fuqing Zhang Shuguang Wang Penn State University Texas A&M University

Jet/front Gravity Wave: Synoptic Environment (Uccelini and Koch 1987) Observations: 13 documented cases of mesoscale gravity waves; L~50-500km Preferred region: exit region of upper jet streak; cold side of surface front Leading hypothesis of wave generation: geostrophic adjustment

(Zhang 2004 JAS; Wang and Zhang 2007 MWR) Gravity Waves Generation from Baroclinic Life Cycles (Zhang 2004 JAS; Wang and Zhang 2007 MWR) 102h 108h 120h 114h Thick lines: 13-km pressure, D=2hPa; thin lines: divergence, negative, dashed; shaded: 8-km jet>55m/s

Wave Generation Hypothesis: Flow Imbalance and Spontaneous Balance Adjustment (Zhang 2004 JAS) Increasingly larger imbalance in developing baroclinic waves Imbalance maximized at exit region of upper jet streak, near strongest tropopause fold Mesoscale waves are continuously initiated downstream of the maximum imbalance Hypothesis: larger scale flow continuously produce imbalance as forcing gravity waves generated through spontaneous balance adjustment (Gray: pressure, D=5hPa; Bold: winds>55m/s; Thin: DNBE, positive, solid & shaded, negative, dashed)

Spontaneous Balance Adjustment vs Spontaneous Balance Adjustment vs. Forced Wave Responses (Plougonven and Zhang 2007 JAS) Separate the flow into large scale background flow AB and perturbations A’, A’ << AB A = AB+A’ A: winds, divergence, vorticity, potential temperatures, etc. Linearize the full model about the large scale flow AB with wave operator on the left hand side and forcing from the large scale (mostly balanced) flow on the right hand side. Solve linear model for disturbance fields forced by large scale flow. Reconcile different wave generation hypotheses (spontaneous emission, and geostrophic adjustment) in that the spontaneously generated waves are linearly forced responses to flow imbalance in vorticity, divergence or thermodynamic equations (Snyder et al. 1993, 2007; Ford 2000; Reeder and Griffiths 1996; Zhang 2004; etc.)

A Perturbation Model Linearized on NL Balanced State A linear disturbance model in a nonhydrostatic, compressible, Boussinesq flow on f plane, following Plougonven and Zhang (2007) Prognostic variables: divergence, vorticity, w, p and θ No horizontal staggering but equivalent to C grids; only w on full levels Time splitting (Skamarock and Klemp 1992), the RK 3rd order scheme for large time step and the KW78, SK92 scheme for small time step to treat sound waves Raleigh damping; 4th order advection; Biharmonic diffusion in the inner domain; Simple outflow lateral BCs, rigid top and bottom BCs (Wang 2008, Ph.D. Thesis)

Forcing to the Linearized Disturbance Model Fδ , Fθ and Fζ are forcing diagnosed from quasi-balanced dipole flow (MM5 output) in similar form as Plougonven and Zhang (2007) Forcing (the divergence forcing, vorticity forcing and thermodynamic forcing) The linear system can also be cast in a single equation of vertical velocity Gδ , Gθ and Gζ are equivalent forcing and can be compared directly .

Test: forcing within a QG diple jet B B A B Localized jet within the QG vortex dipole Place Gaussian shape divergence forcing

Response to prescribed forcing (Fδ) at different scales Divergence, Red (+) and blue (-); Green: wind speed (20, 25 30 m/s); black: forcing contoured at 1/e of the maximum w, Red (+) and blue (-); Green: wind speed (20, 25 30 m/s); Run linear model: Dx=30 km, Dz=200 m Two factors important for wave scales: scale of the forcing and environmental wind Wave pattern is sensitive to the scale of the wave forcing; environmental wind also exert strong control

Gravity Waves from Vortex Dipoles and Jets: Setup Surface Dipole Midlevel Dipole Tropopause Dipole 1800 km PV (every 0.5PVU) at 12.5km PV (every 0.5PVU) at 12.5km  (every 2K) at 0.5km Potential temperature (every 10 K) and wind speed (every 5m/s) ⊙ ⊙ ⊙ S N (Wang, Zhang&Snyder 2008 JAS)

Gravity Waves from a MM5 simulated Dipole Jet (Dx=30km, Dz=200m) Div. at 12.5km, wind speed (>15m/s) and PV (every 1PVU) at 11.5km D B A C Div,  and wind speed (>15 m/s) Div,  and wind speed (>15 m/s) A B C D 210th hour 540th hour Estimated characteristics of the gravity waves: Lh~300km, Lz~2km, and ωi ~1.4f These waves are similar to the simulations in Snyder et al. 2007 and Viduez 2008

Forcing diagnosed from balanced dipole flow using PV inversion the divergence forcing the vorticity forcing the thermodynamic forcing All forcing terms are calculated from balanced flow of the MM5 simulation at 210 h These forcing terms are smoothed by using a 600 km low-pass digital filter The divergence and thermodynamic forcing (Fδ and Fθ) are not localized Fζ has some localized structures (Wang 2008, Ph.D. Thesis)

Equivalent forcing diagnosed from balanced dipole flow Gδ +Gζ +Gθ Gδ Gζ The vorticity forcing term Gζ is the maximum among the three; Gζ has a localized quadruple structure; (Wang 2008, Ph.D. Thesis)

Response to forcing from balanced flow: horizontal divergence Linear model solution Contour interval: 0.05x10-6s-1 MM5 solution at 210h Contour interval: 0.1x10-6s-1 Horizontal divergence: red (+) and blue (-); wind speed (gray) Apply all forcing terms, wave pattern comparable to the MM5 solution Right phase, right pattern, amplitude only more than half of the MM5 solution

Response to forcing from balanced flow: vertical velocity Linear model solution Contour interval: 2.5x10-4ms-1 MM5 solution at 210h Contour interval: 5x10-4ms-1 Vertical velocity: red (+) and blue (-); wind speed (gray) Wave pattern from due to all forcing, also close to MM5-simulated wave pattern In addition to wave pattern, the linear model also has the ascent/descent couplet

Response to each individual forcing term To the thermodynamic Forcing, Fθ To the vorticity forcing, Fζ To the divergence forcing, Fδ Contour interval: 0.05x10-6s-1 The vorticity forcing is the leading contribution to gravity waves from the localized jets within the vortex dipoles.

Gravity waves from an idealized baroclinic jet (Zhang 2004 JAS) 114 h, Div. at 13 km; Jet Streak >55m/s Simulate gravity waves in idealized baroclinic waves at 30 km resolution (Zhang 2004 JAS; Wang and Zhang 2007 MWR; Lin and Zhang 2008 JAS) Gravity waves gradually appear and have several distinct phases at 114 h

Gravity waves from a baroclinic jet: Fourier decomposition W (cm/s) at 114h W after a BP filter W after a HP filter These waves are not monochromatic Two components can be found after applying digital filters: > Shorter scale wave component: λh=300km, 3.6f > Medium scale wave component: λh=450km, 2.5f

Linear wave response due to different forcing To all forcing terms To vorticity forcing To thermodynamic forcing To divergence forcing Both background flow and the forcing terms are time evolving Wave response in the jet exit region from linear model Both the vorticity and thermodynamic forcing generate waves with similar amplitude > Waves due to the vorticity forcing have shorter horizontal wavelengths > Waves due to the thermodynamic forcing have larger horizontal wavelengths The divergence forcing is less important

Linear wave responses: contributions from surface front and upper level jet/front system Forcing above 4km Forcing below 4km Thermodynamic forcing above 4km Vorticity forcing below 4km Forcing terms are split by setting their values above 4km or below 4 km zero. Forcing above 4 km generate medium scale waves with horizontal wavelengths ~ 450 km, > The thermodynamic forcing is the most important for these waves Forcing below 4 km generate shorter scale waves with horizontal wavelengths ~ 300 km, > The vorticity forcing is the most important for these waves

Summary of linear wave response from a linear model Gravity waves from vortex dipoles (Wang, Zhang&Snyder 2008 JAS): In the idealized forcing experiments, the wave pattern in the dipole wind environment from the linear wave operator is a robust feature, but the wave pattern depends on the forcing scales and forcing locations. The linear model wave solution in the dipole flow compares reasonably well with the MM5 solution, although the wave magnitude is only more than half of the latter. Gravity waves from a baroclinic jet (Zhang 2004 JAS) The thermodynamic forcing and the vorticity forcing are equally important to the gravity waves but the divergence forcing is again playing a lesser role. Two groups of wave packets are present in the linear responses. One is the shorter- scale waves having a horizontal wavelength ~ 300 km; the other is the medium- scale waves having a horizontal wavelength ~ 450 km. Forcing near the surface due to surface front is responsible for the shorter-scale waves, forcing from the middle/upper tropospheric jet/front system is responsible for the medium-scale waves.

Gravity waves from Jets: Observations Satellite image and numerical modeling (Wu and Zhang 2004) Possible sources: jet, convection, topography and front Difficulties with gravity wave modeling in real cases Jets are highly coupled with other baroclinic components: surface front, convection; Imbalance from initial conditions Propagation is important (Plougonven and Snyder 2005; Bühler and McIntyre 2005; Lin and Zhang 2008) 80 hPa 40 hPa 20 hPa 10 hPa 5 hPa 2 hPa δ at 80 hPa; GHT at 300 hPa; gray shaded: jet > 60m/s Model (MM5) simulation, 1800Z Jan 19, 2003 Radiance perturbation (AMSU-A) at 0630Z,Jan20

Monthly Mean Gravity Waves and Jet Streak of Jan 2003 MM5 30-km Simulation AMSU-A Observation and NCEP Analysis Monthly mean gravity-wave KE (wavelength between 200~600 km, m2 s-2 ) at 21 km (shaded) and jet streaks at 12 km (dash line) Monthly radiance variance (K2 ) map at channel 10 (shaded, 21 km equivalent) and NCEP analysis jet streaks at 200 hPa (dash line, around 12 km) *** AMSU-A data are provided by NOAA 15, 16, 17 with same specifications Favorite regions for gravity wave generations: Jet-Front GW: Northern and Western Atlantic Topographic GW: Rockies, Appalachian and Greenland

START08 RF02 flight track and altitude WRF prediction at 12km START08 RF02 flight track and altitude longest flat segment (from Canada back t=12200:19200s)

Concluding Remarks Physically-realistic long-lived vertically-propagating gravity waves with Lx=100-500 km are simulated to originate from upper-tropospheric jet streak exit region during the idealized baroclinic life cycles, consistent with past observational studies Residual of nonlinear balance equation is useful in diagnosing imbalance and predicting the location of wave generation A wave equation provides quantitative arguments that residual of nonlinear balance (large-scale imbalance) may force smaller-scale gravity waves Spontaneous balance adjustment (as a generalization of geostrophic adjustment) in which imbalance continuously produced by large-scale flows are spontaneously adjusted through radiating gravity waves, is a likely mechanism in generating these mesoscale gravity waves Real-data cases shows the significance of jet-front gravity waves for both tropos/stratosphere High-resolution mesoscale simulations for both idealized and real data studies are a promising test-bed for understanding mesoscale gravity waves Systematic observations and coordinated field campaigns are badly needed to verify mesoscale simulations