Lecture 21: Midlatitude Cyclones (Ch 10)

• Bjerknes’ Polar Front Theory of the life cycle of midlatitude cyclone (illustrated by storm in Ab over the weekend)

• How the flow aloft factors into cyclone devlopment: vorticity and divergence, their connection with each other and with Rossby waves, and their relevance to storm initiation and development

12Z now corresponds to 05:00 MST12Z now corresponds to 05:00 MST

Fig. 10-1a

Life cycle of mid-latitude cyclone: pre-cursor stageLife cycle of mid-latitude cyclone: pre-cursor stage

• static front• wind “shear”• gravitational potential energy available• very “ordered” situation

Fig. 10-1a

• front clear at 850• surface trough• opposing wind direction

Example of the pre-Example of the pre-cursor stage (mountains cursor stage (mountains complicate the scenario)complicate the scenario)

Life cycle of mid-latitude cyclone: kink develops on frontLife cycle of mid-latitude cyclone: kink develops on front

• Why?• Order - - - > disorder• wind shear• available potential energy converts to kinetic• (later came to be known that arrival of an upper trough can be the trigger)

Fig. 10-1b

• distinct cold & warm fronts• generally system moves towards the east (but often with N or S motion too)• idea that storms travel not clearly formulated until modern communications• may live for more than a week

Life cycle of mid-latitude cyclone: mature phaseLife cycle of mid-latitude cyclone: mature phase

Fig. 10-1

• Low far from warm sector

Life cycle of mid-latitude cyclone: occluded (terminal) phaseLife cycle of mid-latitude cyclone: occluded (terminal) phase

Fig. 10-1

(off NAVCAN web site)(off NAVCAN web site)

(off CMC web site)(off CMC web site)

• storm formed (or deepened) overnight Saturday(12 mb fall since 12Z Sat)

• here still in “open wave” stage

• freezing contour has been swung far to the south by the storm

With increasing knowledge of winds aloft, came recognition of role With increasing knowledge of winds aloft, came recognition of role of mid- and upper troposphere in connection with storms… in of mid- and upper troposphere in connection with storms… in particular, role of “vorticity” associated with the upper waves:particular, role of “vorticity” associated with the upper waves:

• vorticity: rotation of an air parcel about a given axis (our interest: local vertical). Units [s-1]

• has two components, which add to give the “absolute vorticity”

• relative vorticity R (rotation relative to axes fixed on earth; R is

positive for counterclockwise (ie. cyclonic) rotation in N. hemisphere)• earth vorticity ( = f , Coriolis parameter) depends only on latitude

• “absolute vorticityabsolute vorticity”R

f

Relative vorticity breaks into two contributions,Relative vorticity breaks into two contributions,

shear termshear term

curvature termcurvature term

Sec. 10-1 Figs. 1 & 2

• on equator, no rotation about local vertical (f=0)

Earth vorticity and relative vorticityEarth vorticity and relative vorticity

Fig. 10-5

Positive relative vorticity due to Negative relative

vorticity due to

Easy to visualize that a parcel at pole that is stationary w.r.t. earth has rotation in space

Rossby wave & vorticityRossby wave & vorticity

No relative vorticity

North-south motion also changes the absolute vorticity as the earth component (f) changes…

Fig. 10-4

const.sin2 RR f

Simplest paradigm for Rossby waves:Simplest paradigm for Rossby waves:

=

Sec. 10-1 Fig. 2

• changes in vorticity matter in relation to storms because they “cause**” associated horizontal divergence/convergence that in turn associate with vertical motion and surface pressure changes

• divergence is the same thing as negative convergence (just as decceleration is negative acceleration)

• we can think of horizontal divergence (textbook symbol “ div ”) as “area-expansion in the horizontal plane”

“cause**” in quotes, because unless this is analysed mathematically, there are chicken/egg ambiguities

Horizontal convergence & divergenceHorizontal convergence & divergence

oror orororor

The plane of the paper is a constant height surface.

At time t=0 the east-west component “u” increases towards the east, the north-south component “v” increases towards the north…This results in horizontal divergence (area expansion)

The “shape” of the expanded areadoesn’t matter… it is controlledby the velocity gradients

i

j

0

y

v

x

u

(t=0)

(t=t)

0

x

u

0y

v

Hozizontal divergence is a “differential property of the velocity Hozizontal divergence is a “differential property of the velocity field”…field”…

Fig. 10-2b

• the cross-isobar wind in the friction layer causes low-level convergence (area shrinkage) and we have associated this with ascent (the air has “nowhere to go”)

• now unless this accumulating air is pumped off the column somewhere higher in the troposphere, mass in the columnis increasing, which will weakenthe storm

• but clearly divergence (area-expansion) aloft would be the ticket to keeping the storm alive (or deepening it)

• and it turns out that indeed the upper waves do cause a pattern of mid-tropospheric convergence and divergence

Fig. 10-6

Changing relative vorticity as parcel moves through transition zonesChanging relative vorticity as parcel moves through transition zones

(we’ll neglect changes in earth vorticity – valid if the wave amplitude is small)

Vorticity tendency & horiz. divergence aloft: “Vorticity Theorem”Vorticity tendency & horiz. divergence aloft: “Vorticity Theorem”

• rate of change of absolute vorticity following an air parcel is:

divt

• increasing vorticity (l.h.s. pos.) negative divergence convergence

• happens in ridge exit region

• decreasing vorticity (l.h.s. negative) positive divergence aloft

• happens in trough exit region

(p286)

• now ordinarily so 0

Fig. 10-7

Illustrates the ideal collaboration of upper wave & sfc stormIllustrates the ideal collaboration of upper wave & sfc storm• sfc convergence + upper divergence implies ascent… cloud + precip• sfc pressure trend result of a subtle imbalance• this pattern reliably valid for intense storms• topography complicates the pattern• Rossby waves not the only upper waves – short waves too

Fig. 10-8

Vorticity of the mid-tropospheric flow so important meteorologists Vorticity of the mid-tropospheric flow so important meteorologists like to display it on upper winds analysis…like to display it on upper winds analysis…

Analysed vorticity pattern at 500 mb is available on the web for 00Z, 12Z on Analysed vorticity pattern at 500 mb is available on the web for 00Z, 12Z on CMC 00h prog … gives analysed 500 mb height + vorticity shadingCMC 00h prog … gives analysed 500 mb height + vorticity shadingDarkest shading – largest (cyclonic) vorticity – trough axes Darkest shading – largest (cyclonic) vorticity – trough axes

Divergence aloft expected in south-central Ab… coincides roughly with area of storm that developed