ࡱ> O@ bjbjFF ,,krFFFFZ Z Z n 8΅†n N:$R1]Z (w<((FFaGK(<Fb(Z (: Z  pyFAd$a00n n FFFFZ >,$An n IRUD0(n n RUUniversity of the West Indies/ Caribbean Institute of Meteorology and Hydrology INTRODUCTION TO METEOROLOGY - XIII METE1011 Ahrens- Chapter 13 4. Mid-latitude cyclones The conceptual model of the mid-latitude cyclone was developed by J. Bjerknes towards the end of the First World War (1928). His analysis and results illustrate the essential structure as well as the dynamics process associated with the mid-latitude cyclone. Introduction into the Life Cycle of the mid-latitude cyclone. Polar Front Theory The polar front cold, which circumvents the earth in the global circulation pattern separates polar air from subtropical air. RELATION OF FRONTS TO CYCLONES There is a systemic relationship between cyclones and fronts, in that the cyclones are usually associated with waves along fronts primarily cold fronts. Cyclones come into being or intensify because pressure falls more rapidly at one point than it does in the surrounding area. Cyclogenesis can occur anywhere, but in middle and high latitudes, it is most likely to occur on  INCLUDEPICTURE "http://www.tpub.com/weather2/jpg/4_27_1.jpg" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.tpub.com/weather2/jpg/4_27_2.jpg" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.tpub.com/weather2/jpg/4_27_3.jpg" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.tpub.com/weather2/jpg/4_27_4.jpg" \* MERGEFORMATINET  Figure 4-1.Vertical view of a frontal system (clouds not shown). a frontal trough. When a cyclone (or simply low) develops on a front, the cyclogenesis begins at the surface and develops gradually upward as the cyclone deepens. The reverse also occurs; closed circulations aloft sometime work their way downward until they appear on the surface chart. These cyclones rarely contain fronts and are quasi-stationary or drift slowly westward and/or equatorward. Every front, however, is associated with a cyclone. Fronts move with the counterclockwise flow associated with Northern Hemisphere cyclones and clockwise with the flow of Southern Hemisphere cyclones. The middle latitudes are regions where cold and warm air masses continually interact with each other. This interaction coincides with the location of the polar front. When the polar front moves southward, it is usually associated with the development and movement of cyclones and with outbreaks of cold polar air. The cyclonic circulation associated with the polar front tends to bring polar air southward and warm moist tropical air northward. During the winter months, the warm airflow usually occurs over water and the cold air moves southward over continental areas. In summer the situation is reversed. Large cyclones that form on the polar front are usually followed by smaller cyclones and are referred to as families. These smaller cyclones tend to carry the front farther southward. In an ideal situation these cyclones come in succession, causing the front (in the Northern Hemisphere) to lie in a southwest to northeast direction. Every moving cyclone usually has two significant lines of convergence distinguished by thermal properties. The discontinuity line on the forward side of the cyclone where warm air overrides cold air which receding is the warm front; the discontinuity line in the rear portion of the cyclone where cold air displaces warm air is the cold front. The polar front is subject to cyclonic development along it. When wind, temperature, pressure, and upper level influences are right, waves form along the polar front. Wave cyclones normally progress along the polar front with an eastward component at an average rate of 25 to 30 knots, although 50 knots is not impossible, especially in the case of stable waves. These waves may ultimately develop into full-blown low-pressure systems with gale force winds. The development of a significant cyclone along the polar front depends on whether the initial wave is stable or unstable. Wave formation is more likely to occur on slowly moving or stationary fronts like the polar front than on rapidly moving fronts. Certain areas are preferred localities for wave cyclogenesis. The Rockies, the Ozarks, and the Appalachians are examples in North America. .  INCLUDEPICTURE "http://www.tpub.com/weather2/jpg/4_29_1.jpg" \* MERGEFORMATINET  Figure 4-2.Life cycle of a stable wave cyclone.  INCLUDEPICTURE "http://www.tpub.com/weather2/jpg/4_29_2.jpg" \* MERGEFORMATINET  Figure 4-3.Life cycle of an unstable frontal wave. Initial stages (A) - Initially, a stationary front represents the polar front. Circulation around a high to the north and to the south sets up cyclonic shear along the front. Frontal Wave (B - C) - Development starts as a wave kink along the front. Cold air pushes equatorward forcing warm air aloft. Warm air is forced to override cold air as it recedes to the north. Open wave (D) fronts become defined and a circulation develops around a central low encircled by several isobars. Along the cold front is a thin area of precipitation, while the area of precipitation exists ahead on the warm front and is known as over-running. The area between the two front is known as the warm sector. The now developed cyclone is steered east to northeast by upper level winds. Occlusion stage- most intense (E) The cold front moves faster than the warm front squeezing the warm air off the surface. At this point, an occluded front forms and the storm is at its most intense. The point of the occlusion where the warm, cold and occluded fronts meet is called the triple point. A secondary low now form at this point. Dissipating stage (F and G); The secondary low may move off as a new storm, while the intense storm gradually dissipates. The cold air cuts off the warm air from the surface, this the supply of energy is also cut off. The life cycle of a cyclone can last a few days to a week. Cyclone Energetics- The cyclone converts Available Potential Energy (APE) that is centre of mass to Kinetic Energy (KE) manifested in wind motion. APE is large APE is 0   adiabatic redistribution Fig 4.4. The transformation of energy, which takes place within a mid-latitude cyclone. Sequence of Events Developing cyclone Warm air rising Air masses tries to attain equilibrium Cold air sinking Open Wave  APE > KE Condensation supplies energy Increase in wind circulation - Intensification Occlusion  Mature Cyclone KE is greatest Cold air catches up and undercuts warm air Dissipation Stage APE = 0 Warm air is cut off at surface Friction is greatest. Convergence and divergence-  a.    b.       Fig 4.5. a- speed divergence and speed convergence; b- directional divergence and convergence. CONVERGENCE AND DIVERGENCE (SIMPLE MOTIONS) Simply stated, convergence is defined as the increase of mass within a given layer of the atmosphere, while divergence is the decrease of mass within a given layer of the atmosphere. Convergence For convergence to take place, the winds must result in a net inflow of, air into that layer. We generally associate this type of convergence with low-pressure areas, where convergence of winds toward the center of the low results in an increase of mass into the low and an upward motion. In meteorology, we distinguish between two types of convergence as either horizontal or vertical convergence, depending upon the axis of the flow. Divergence Winds in this situation produce a net flow of air outward from the layer. We associate this type of divergence with high-pressure cells, where the flow of air is directed outward from the center, causing a downward motion. Divergence, too, is classified as either horizontal or vertical. DIRECTIONAL WIND SHEAR The simplest forms of convergence and divergence are the types that result from wind direction alone. Two flows of air need not be moving in opposite directions to induce divergence, nor moving toward the same point to induce convergence, but maybe at any angle to each other to create a net inflow of air for convergence or a net outflow for divergence. (Fig 4.5-b) WIND SPEED (VELOCITY) SHEAR Convergence is occurring when wind speeds are decreasing downstream; that is, mass is accumulating upstream. Conversely, divergence is occurring when wind speeds are increasing downstream; that is, mass is being depleted upstream. (Fig 4.5-a) DIRECTIONAL AND SPEED WIND SHEAR Wind speed in relation to the wind direction is also a valuable indicator. For example, on a streamline analysis chart we can analyze both wind direction and wind speed, variations in wind speed along the streamlines, or the convergence or divergence of the streamlines.         Fig. 4.6- illustrates the above effects. The following are some of the combinations or variations of wind speed and direction: . In a field of parallel streamlines (wind flow), if the wind speed is decreasing downstream (producing a net inflow of air for the layer), convergence is taking place. If the flow is increasing downstream (a net outflow of air from the layer), divergence is occurring. . In an area of uniform wind speed along the streamlines, if the streamlines diverge (fan out), divergence is occurring; if the streamlines converge (come together), convergence is taking place. . Normally, the convergence and divergence components are combined. The fact that streamlines converge or diverge does not necessarily indicate convergence or divergence. We must also consider the wind speedswhether they are increasing or decreasing downstream in relation to whether the streamlines are spreading out or coming together. . If, when looking downstream on the streamlines, the wind speed increases and the streamlines diverge, divergence is taking place. On the other hand, if the wind speed decreases downstream and the streamlines come together, convergence is taking place. There are other situations where it is more difficult to determine whether divergence or convergence is occurring, such as when the wind speed decreases downstream and the wind flow diverges, as well as when wind speed increases downstream and the wind flow converges. A special evaluation then must be made to determine the net inflow or outflow. DIVERGENCE AND CONVERGENCE (COMPLEX MOTIONS) In this section we will be discussing high-level convergence and divergence in relation to downstream contour patterns and the associated advection patterns. Low tropospheric advection certainly plays a large role in pressure change mechanisms. Since the term divergence is meant to denote depletion of mass, while convergence is meant to denote accumulation of mass. Mass divergence in the entire column of air produces pressure or height falls, while mass convergence in the entire column of air produces pressure or height rises at the base of the column. Divergence/Convergence and Surface Pressure Systems The usual distribution of divergence and convergence relative to moving pressure systems is as follows: . In advance of the low, convergence occurs at low levels and divergence occurs aloft, with the level of nondivergence at about 600 hPa. . In the rear of the low, there is usually convergence aloft and divergence near the surface. The low-level convergence ahead of the low occurs usually in the stratum of strongest warm advection, and the low-level divergence in the rear of the low occurs in the stratum of strongest cold advection. The low-level divergence occurs primarily in the friction layer (approximately 3,000 ft) and is thought to be of minor importance in the modification of thickness advection compared with heating and cooling from the underlying surfaces. Divergence/Convergence Features Aloft In advance of the low, the air rises in response to the low-level convergence, with the maximum ascending motion at the level of nondivergence eventually becoming zero at the level of maximum horizontal divergence (approximately 300 hPa). In the rear of the low, the reverse is true; that is, descending motion in the surface stratum. In deepening systems, the convergence aloft to the rear of the low is small or may even be negative (divergence). In filling systems, the divergence aloft in advance of the low is small or even negative (convergence). Divergence and upper-height falls are associated with high-speed winds approaching weak contour gradients which are cyclonically curved. Figure 4.7 illustrates contour patterns associated with height falls, -Convergence and upper-height rises are associated with the following: . Low-speed winds approaching straight or cyclonically curved strong contour gradients. See figure 4.9, view (A). . High-speed winds approaching anticyclonically curved weak contour gradients. (B). See figure 4.7, view  INCLUDEPICTURE "http://www.tpub.com/weather1/1.htm9.gif" \* MERGEFORMATINET  Figure 4.7.-Divergence Illustrated.  INCLUDEPICTURE "http://www.tpub.com/weather1/1.htm8.gif" \* MERGEFORMATINET  Figure 4.8.-Convergence Illustrated. Note that the associated height rises or falls occur downstream and to the left of the flow, as illustrated in figure 4.9. IMPORTANCE OF CONVERGENCE AND DIVERGENCE Convergence and divergence have a pronounced effect upon the weather occurring in the atmosphere. Vertical motion, either upward or downward, is recognized as an important parameter in the atmosphere. For instance, extensive regions of precipitation associated with extra-tropical cyclones are regions of large-scale upward motion. Similarly, the nearly cloud-free regions in large anticyclones are regions in which air is subsiding. Vertical motions also affect temperature, humidity, and other meteorological elements. Changes in Stability When convergence or divergence occurs, whether on a large or small scale, it may have a very pronounced effect on the stability of the air. For example, when convection is induced by convergence, air is forced to rise without the addition of heat. If this air is unsaturated, it cools first at the dry adiabatic rate; or if saturated at the moist rate. The end result is that the air is cooled, which will increase the instability of that air column due to a net release of heat. Clouds and weather often result from this process. Conversely, if air subsides, and this process is produced by convergence or divergence, the sinking air will heat at the dry adiabatic lapse rate due to compression. The warming at the top of an air column will increase the stability of that air column by reducing the lapse rate. Such warming often dissipates existing clouds or prevents the formation of new clouds. If sufficient warming due to the downward motion takes place, a subsidence inversion is produced. Mid- Level Support When the isotherms are almost parallel to the height lines the atmosphere is said to be barotropic. When the isotherms cross the height lines, the winds blow across the contours causing temperature advection, the atmosphere is baroclinic. In the region of baroclinicity: Cold advection Cold air is transported from an area of colder sit to an area of warmer temperatures. Temperature decreases Takes place on the west side of troughs. Warm advection Warm air is transported from an area of warmer sit to an area of colder temperatures. Temperature increases Takes place on the east side of troughs The thickness contours are the best indicators of cold air advection and warm air advection, since they indicate the temperature of the mean layer, has hence are good indicators of baroclinicity. Tight contour spacing (i.e. higher winds) occurring on the west side of a 500mb trough usually indicates that the trough is digging or intensifying [stronger cold air advection]. If the tighter contours are to the east side of the trough, this indicates that the trough is lifting or weakening [stronger warm air advection]. Above the area of baroclinicity lies the polar jet, and at the surface, lies the polar front. Short waves will induce development or intensification of surface storm systems. Upper level Air patterns  60 - 120  | | Fig. 4.9 Long wave A. Long Waves ( Rossby) There are 3 6 waves that surround the earth (120 60 longitude). They move relatively slow; at < 4 longitude /day They are quasi-barotropic density only a function of pressure; temperature fairly constant (very temperature gradient associated with long waves) Ridges warm, troughs are cold. Longer the wavelength, the faster the regression. Longest waves tend to move west at the upper levels. Vertical motion and divergence ~ 1cm/sec Sinking to the east of the ridges due to maximum in upper convergence. Rising to the east of troughs due to maximum in upper divergence (very small on the large scale). Vertical structure amplitude increases with height up to tropopause B. Short Waves Generally 15 60 longitude; several may be imbedded in long wave. Speed ~ 30 longitude a day. Baroclinic density dependent on T; feeds on temperature gradient. Warm advection on the east side and cold advection on the west side of trough good for extratropical cyclogenesis. Vertical motion and divergence same as in long wave but considerably stronger (~ 5 to10 cm/sec) Ridges are warm, troughs are cold , therefore much more well defined temperature gradients. Sharp amplitude due to tight thermal gradient; tends to dampen with height. C. Cut off Lows lows aloft with one (1) or more closed contours Cold systems with coldest temperature at center. Quasi barotropic with small temperature gradient. They move slowly, Amplify or stay the same with height little temperature advection, Set up in split flow. Fig 4.10: Cut of low. Often stationary; then suddenly takes off, making them difficult to forecast. D. Blocking High often associated with cutoff low block the westerlies; warm systems move very slowly or are stationary quasi barotropic increasing amplitude in vertical Fig 4.10: Blocking High. Omega (() block- very stationary; 1 2 weeks (late winter/early spring). Tropopause Tropopause discovered near the 1900 is the region where stratosphere warmed by solar radiation (O3 absorbs UV radiation). Definition: 1st order discontinuity in lapse rate of temperature Location changes with latitude, seasons and diurnally Tropics: 18km; p = 80 to 100 mb ( = 375 to 400 K; sharply defined; T = -80 C Mid- latitudes: equator ward of the polar jet stream 12km; p = 200 mb ( = 325 to 340 K; sharply defined; T = -60 C Higher in summer than in winter (thickness is higher). Polar: North of polar jet 9km; p = 300 to 400 mb ( = 300 to 310 K; sharply defined; T = -45 to -55 C It can be difficult to locate in some cases; near fronts and jet streams sometimes have multiple tropopause levels or folding. e.g Fig 4.12: Polar Jet and the tropopause; Side view  Cold Warm  ML Tropopause PTropopause COLD Air WARM Air Front SFC Dynamic importance. Marks start of region of strong static stability damping of vertical motion, convection, etc. (In other word form a cap on top of the troposphere. reversal of north-south temperature gradient, therefore jet stream is located near the tropopause. Jet Stream A jet stream is a narrow, shallow, meandering stream of relatively strong winds in the atmosphere. In the upper atmosphere winds must be 50 knots or greater to be classified as a jet stream. general westerly wind belt around globe isotach maximum on the daily chart Jet streams are usually 1000 to 5000 km in length, 1 to 2 km in depth and 100 to 200 km in width. Vertical shears (difference between top and bottom of jet core) associated with the jet streams are generally 10 to 20 knots per km, while horizontal shears are of the order of 10 knots per km. Wind speed maximum usually near the tropopause where temperature gradient reverses in stratosphere- recall thermal wind /thickness usually located above frontal zones- strong (T.  EMBED PictPub.Image.8  Fig. 4.13. Schematic isotherms (dashed lines, C) and isotachs (thin solid lines, meters per second) in the vicinity of the polar front. Heavy lines indicate boundaries of the frontal zone and tropopause. (After Palmen and Newton, 1969) Figure 4.13, a schematic vertical section normal to the polar front and the upper westerlies, shows, in idealized form, the most commonly observed features of the front and the associated jet stream. The figure illustrates the sharp increase of wind with height, which is found in frontal layers where the horizontal temperature gradient is strong, the pronounced decrease of wind speed with height above the tropopause, where the horizontal temperature gradient is reversed from that in the troposphere, is also demonstrated. The occurrence of an intense jet core above the frontal zone is, of course, not a mere coincidence, but rather a consequence of the thermal wind balance. The figure also shows that the axis of the core of strongest winds is nearly vertical from 500 mb to about 250 mb, where the winds are strongest. (Above this level the axis slopes equatorward with elevation). The polar front jet is strongest and moves farther south in winter, at the same time the level of the strongest winds rises as the jet axis shifts from high to low latitudes. For example, when the jet is centred at 470N the strongest winds may be at 250 mb; while when the jet is located at 390N the strongest winds may occur at 200 mb. Velocity maxima (jet streaks) and minima along the jet axis are connected with the short waves in the westerlies and usually move downstream with the speed of the waves. The polar front jet is marked by both horizontal and vertical shear. Large values of the vertical wind shear are restricted to a narrow zone along the vertical axis of the jet. North and south of the core there is little variation of wind speed with height. In the horizontal, cyclonic shear is found to the north of the jet while on the southern side the shear is anticyclonic. The strongest cyclonic and anticyclonic horizontal shears normal to the jet axis are found at the level of strongest winds and about 200 km north and south of the axis. The cyclonic shear to the left of the axis is greater than the anticyclonic shear to the right of the axis and often amounts to several times the Coriolis parameter. At the level of the jet in mid latitudes the earths vorticity (positive) is greater than the anticyclonic vorticity (negative) resulting from the shear. As a result positive absolute vorticity is found both north and south of the jet, with a maximum to the north and a minimum to the south as shown in Fig. 4.15a. Fig 4.14: Top view jet streaks strongest wind region; the jet move slower than the air through it. Side View       Located ~250 50mb; 100 to 200 kts in mid latitudes.  EMBED PictPub.Image.8  Fig 4.15 b: Strongest upper level divergence At point C, left exit and weaker upper level divergence at point B, right entrance. LORI => Left Out Right In Other Jets Subtropical Jet ~25N associated with upper level temperature gradient along the poleward side of the Hadley circulation. Small variability smaller wind maxima Wind speeds ~ 80 to 100 kts Polar jet ~between 30 50 N; associated with mid-latitude surface systems along the polar front. Maxima may not always be on the same level The polar jet may sometimes merge with the subtropical jet. Occasionally, the polar jet splits into two jets streams. The northern branch and the southern branch. (Pay attention to both the 300 mb and 200 mb charts.) Velocity max. 100 kts at ~300 mb Velocity max. 150 kt at ~200 mb Fig 16: Flow through a jet maxima or jet streak. VORTICITY Consider vorticity as the spin of a parcel of air. Absolute vorticity (a) is composed of two (2) parts such that: a =  + f where f = 2 ( sin ( , which is the vertical component of fluid rotation of calm air due to the earth s rotation (the coriolis parameter). Positive spin is counterclockwise in the Northern Hemisphere. And  = measure of the rotation of the wind relative to the ground; hence the term relative vorticity: Positive  indicates  counterclockwise spin. In natural coordinates vorticity is given by  EMBED Equation.3  (2) n > 0 to the left of the flow R > 0 for cyclonic flow.  = curvature term + shear term Equation 6.2 affords a simple physical interpretation of the relative vorticity. The first term, V/R, is the curvature term and represents the angular velocity of solid rotation of a particle about a vertical axis through the instantaneous centre of curvature. If the wind backs or turns counterclockwise in the Northern Hemisphere, there is cyclonic vorticity. Conversely, veering or clockwise rotation then anticyclonic vorticity. Fig 17a. Curvature term:      Take V >0. For cyclonic flow , R > 0 For anticyclonic flow, R < 0 then then V/R > 0; curvature term is positive and V/R < 0; curvature term negative There is cyclonic spin. There is anticyclonic spin.  Fig 17b: Vorticity advection:    NVA to east of ridge; west of trof PVA to west of ridge; east of trof SINKING RISING The second term, - EMBED Equation.3 , is called the shear term and represents the effective angular velocity of the air particle produced by distortion due to horizontal velocity differences. If the wind speed decreases to the left of the motion (- EMBED Equation.3 > 0) the shear term is positive and contributes to cyclonic vorticity. On the other hand, if the wind speed increases to the left of the motion (- EMBED Equation.3 < 0) the shear term is negative and contributes to anti-cyclonic vorticity. Fig 18: The Shear term.        Shear term is positive => cyclonic spin Shear term is negative => anticyclonic spin The contribution of each term to the vorticity is illustrated in Fig. 19 The shear term is most easily assessed by considering a wind maximum.   A C     B D Fig: 19: Shear contribution positive to the left of wind maximum and negative to the right of the wind maximum. Therefore: Quadrants C and B - Positive vorticity advection (PVA) Quadrants A and D - Negative vorticity advection (NVA). So, the vicinity of the wind maxima, there is PVA and upward vertical motion to the left front and right rear quadrants. (LORI) Why is positive vorticity advection related to upward motion First, in most cases a is positive since |f| > | r|. Therefore all air parcels have some cyclonic spin. Consider the analogy to an ice skater who is spinning cyclonically. If the skater s arms are outstretched, the skater spins more slowly. 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