Conservation of absolute vorticity. MET 171A: Barotropic Midlatitude Waves. Draw a picture of planetary vorticity

Size: px

Start display at page:

Download "Conservation of absolute vorticity. MET 171A: Barotropic Midlatitude Waves. Draw a picture of planetary vorticity"

Mabel Bryant
6 years ago
Views:

Conservation of absolute vorticity : Barotropic Midlatitude Waves Recall the important terms in the vorticity equation in the middle troposphere, near the level of

or constrained, and that absolute vorticity chanes with the advective wind Draw a picture of planetary vorticity Move parcel south If absolute vorticity is conserved,

1 Conservation of absolute vorticity : Barotropic Midlatitude Waves Recall the important terms in the vorticity equation in the middle troposphere, near the level of non-diverence Lecture Outline 1. Conservation of Absolute Vorticity 2. Apparent Deepenin/Weakenin 3. Rossby Waves and the Beta Wind 4. Short Waves and Lon Waves 5. Pattern Characterization 6. Blockin ( ζ + f ) = V ( ζ + f ) And conservation of Absolute Vorticity d ( ζ + dt f ) = 0 These equations state that absolute vorticity followin a parcel is conserved or constrained, and that absolute vorticity chanes with the advective wind Draw a picture of planetary vorticity Move parcel south If absolute vorticity is conserved, what happens to relative vorticity Move parcel north If absolute vorticity is conserved, what happens to relative vorticity This is the idea, which fiures 6.1a -6.1d in Carlson are tryin to convey. Short wave over BC moves rapidly eastward throuh lonwave pattern Wave moves Southeastward and planetary vorticity decreases 1

December 2008, 500hPa heiht fields Assume the conservation of absolute vorticity is in play and look for occurrences of apparent deepenin and weakenin due to chanes in latitude of vorticity

2 December 2008, 500hPa heiht fields Assume the conservation of absolute vorticity is in play and look for occurrences of apparent deepenin and weakenin due to chanes in latitude of vorticity perturbation and influence of perturbed heiht field 12/08/08 over WA Note that absolute vorticity for disturbance is unchaned, perturbation is stroner ~ hence called apparent deepenin What have we been nelectin Waves: vortex superposed on backround flow Consider the typical trouh with NVA and equatorward flow upstream of vortmax and PVA, poleward flow downstream Trouh Ride Trouh Let s try this for an idealized trouh Wave reconstitutes itself downstream via advection of relative vorticity and advection of planetary vorticity Net influence is for evolution of flow field to be retarded Backround current V wind speed L Let s Call it the Beta Effect = V ( ζ + f ) = V βv Advection of vorticity Advection of relative vorticity Advection of planetary vorticity df β = dy Φ 0 - ΔΦ Φ 0 + ΔΦ Advection of vorticity = V Advection of ζ tries to propaate the wave this way ΔΦ > 0 L L Φ 0 H B Advection of f tries to propaate the wave this way ٠ y, north ٠ A C ٠ x, east 2

Rossby Waves Rossby waves result from the conservation of vorticity. The restorin force is β or, more enerally, the meridional radient of the absolute vorticity.

3 Rossby Waves Rossby waves result from the conservation of vorticity. The restorin force is β or, more enerally, the meridional radient of the absolute vorticity. The resultin circulation causes the wave to propaate westward relative to backround flow. Dispersion Relation df β = dy c β = u k 2 + l 2 c is the Rossby wave propaation speed, u zonal wind, k and l are zonal and meridional wavenumbers Scale Analysis = V Consider a disturbance with a fixed wavelenth Advection of relative vorticity by the wind field was stated to be proportional to inverse wavelenth cubed ~ favors short waves Beta effect is just proportional to meridional wind or wavelenth What does this mean for the relative roles of these terms for a shortwave versus a lonwave disturbance? Shortwaves = V Lonwaves = V The advection of relative vorticity dominates Wavelenths less than 1000km-3000km Generally small amplitude and fast movin ~ transient Baroclinic: meanin heiht and isotherms out of phase Important in development of surface features ~ e.., cycloenesis The advection of planetary vorticity is ALSO important. Wave propaation speed is weak eastward, stationary or westward Wavelenths less than 10,000km (wavenumber 4-5) Wind and temperature waves are parallel: Cold trouh, warm rides (barotropic) Controls weather reimes/patterns for 5-15 days or more Pattern Characterization Proressive: disturbance propaates in the same direction as backround flow (shortwaves in eneral) Stationary: disturbance whose propaation speed is 0. Retroressive: disturbance whose propaation opposes the backround flow Two eneral wave patterns: Zonal, hih index, lower wave number (2-4) Meridional, low index, hiher wave number (4-7) (this can be ambiuous) 3

Zonal hih index Meridional low index Examples of Pattern Characterization Blockin and Cutoffs http://www.met.sjsu.

meridional Blockin Characteristics of Blockin Persistent pronounced meridional flow Occurs durin low-index cycles - low index: zonal flow weak,

stanant warm air mass displaced poleward Amplification of Rossby Wave Ride/Trouh Pattern May reverse the typical meridional radient of

4 Zonal hih index Meridional low index Examples of Pattern Characterization Blockin and Cutoffs m - Look for proressive vs. reressive, and stationary - Look for zonal vs. meridional Blockin Characteristics of Blockin Persistent pronounced meridional flow Occurs durin low-index cycles - low index: zonal flow weak, meridional flow stron Results from an anomalous lon-wave ride that blocks the proression of short waves The anomolous ride is the result of a stanant warm air mass displaced poleward Amplification of Rossby Wave Ride/Trouh Pattern May reverse the typical meridional radient of eopotential heiht fields One or more closed anticyclones typically present in N.H. Climatoloy: Frequent in winter/sprin on west coast of continents Lifetime: 1-3 weeks Most frequent over W. N. America and W. Europe 4

5 Blockin Patterns Example from winter Lare amplitude Rossby Waves (tend to retrorade) Split flow redirects subtropical jet into SoCal; Pac NW blocked Neative PNA Downstream of major synoptic activity - synoptic scale waves pile up (baroclinic-> barotropic feedback) Blockin can persist for weeks Split flow upper-level ride Split Flow omea block Upper Level Ride Very common!! Omea Block 5

6 Cut off Lows The alter eo of Blockin Hihs Defined: cold cyclonic circulation displaced from the westerly current. Not advected with flow; hence may remain nearly stationary or retroress with beta-wind and severely impact reions for extended time period Steerin Concepts Forecastin was done larely usin the Barotropic model before the advent of better computin Many ood ideas came out that era Good forecasters could look at a weather map an know how the pattern would evolve without numerical uidance. On example of steerin flow. If the max cyclonic shear is on the If the max cyclonic shear is on upstream side of the trouh, the feature the downstream side of the will tend to move equatorward, trouh, the feature will tend to and deepen move poleward and weaken Liftin Diin 6

Development Theory. Chapter 10

Development Theory. Chapter 10 Chapter 1 Development Theory Development Theory In this section I will discuss: - further aspects of the structure and dynamics of synoptic-scale disturbances, and - derive Sutcliffe's development theory,