Transcript Slide 1
Lecture 21: Midlatitude Cyclones (Ch 10) 12Z now corresponds to 05:00 MST • 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 Life cycle of mid-latitude cyclone: pre-cursor stage Fig. 10-1a • static front • wind “shear” • gravitational potential energy available • very “ordered” situation Example of the precursor stage (mountains complicate the scenario) • front clear at 850 • surface trough • opposing wind direction Fig. 10-1a Life cycle of mid-latitude cyclone: kink develops on front Fig. 10-1b • 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) Life cycle of mid-latitude cyclone: mature phase Fig. 10-1 • 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: occluded (terminal) phase Fig. 10-1 • Low far from warm sector • storm formed (or deepened) overnight Saturday (12 mb fall since 12Z Sat) • here still in “open wave” stage (off CMC web site) (off NAVCAN web site) • freezing contour has been swung far to the south by the storm With increasing knowledge of winds aloft, came recognition of role of mid- and upper troposphere in connection with storms… in 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 wR (rotation relative to axes fixed on earth; wR is positive for counterclockwise (ie. cyclonic) rotation in N. hemisphere) • earth vorticity ( = f , Coriolis parameter) depends only on latitude • “absolute vorticity” f w R Relative vorticity breaks into two contributions, shear term Sec. 10-1 Figs. 1 & 2 curvature term Earth vorticity and relative vorticity Easy to visualize that a parcel at pole Positive relative vorticity due to that is stationary w.r.t. earth has rotation in space Fig. 10-5 • on equator, no rotation about local vertical (f=0) Negative relative vorticity due to Rossby wave & vorticity Fig. 10-4 No relative vorticity North-south motion also changes the absolute vorticity as the earth component (f) changes… Simplest paradigm for Rossby waves: wR f wR 2 sin const. = Sec. 10-1 Fig. 2 Horizontal convergence & divergence • 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 “areaexpansion in the horizontal plane” or “cause**” in quotes, because unless this is analysed mathematically, there are chicken/egg ambiguities or or Hozizontal divergence is a “differential property of the velocity field”… 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 area doesn’t matter… it is controlled by the velocity gradients (t=t) ˆj iˆ u v 0 x y (t=0) v 0 y u 0 x • 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 column is increasing, which will weaken Fig. 10-2b the storm • but clearly divergence (areaexpansion) 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 Changing relative vorticity as parcel moves through transition zones Fig. 10-6 (we’ll neglect changes in earth vorticity – valid if the wave amplitude is small) Vorticity tendency & horiz. divergence aloft: “Vorticity Theorem” • rate of change of absolute vorticity following an air parcel is: div t • now ordinarily 0 (p286) so • decreasing vorticity (l.h.s. negative) positive divergence aloft • happens in trough exit region • increasing vorticity (l.h.s. pos.) negative divergence convergence • happens in ridge exit region Illustrates 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. 10-7 Vorticity of the mid-tropospheric flow so important meteorologists like to display it on upper winds analysis… Fig. 10-8 Analysed vorticity pattern at 500 mb is available on the web for 00Z, 12Z on CMC 00h prog … gives analysed 500 mb height + vorticity shading Darkest shading – largest (cyclonic) vorticity – trough axes Divergence aloft expected in south-central Ab… coincides roughly with area of storm that developed