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TO 6.2.1 A) Describe the evolution of a typical baroclinic wave from an incipient wave on a baroclinic zone, during intensification, through to final occlusion. Relate the development of the wave to changes in its associated fields and processes. Stage 1: incipient 1. 2. 3. Begins along a pre-existing low-level baroclinic (frontal) zone Perturbation is first started in upper levels prior to the low level with a short wave move in to disturb the flow aloft, which produces a region of upper-level divergence over the frontal zone of low level The upper-level divergence results in a wavelike kink near surface Stage 2: Development 1. 2. 3. The frontal zone fractures in the vicinity of the low center with cold front pushing south-ward and warm front moving northward. The low center starts to deepen. The winds cyclonically blow into the low center A cooperative interaction starts between the upper level and surface flows: The initiated surface cyclonic circulation begins to produce and enhance T advection in the low-level, which amplifies the upper level waves and increases wind aloft. The upper trough intensifies and produces stronger PVA, which further cause stronger upper-level divergence, and surface convergence. Thus, the cyclonic circulation strengthens, and surface low becomes deepen. The stronger low-level circulation induces stronger PTA to amplify upper waves, and so on. A positive feed back starts. This process is called “self-development” of a cyclone Meanwhile, warm air rises from the surface low and along warm front, and cold air descends behind the cold front, a damping (“self-limiting”) influence of the vertical motions occurs as adiabatic cooling in the regions of ascent (warm air mass) and local warming in the regions of descent (cold air mass), which decrease the thermal contrast of two air masses. The damping influence latter is largely offset by the effects of condensation heating as cloud and precipitation set in as a result of vertical motion, the latent heating is crucial for the further development of the cyclone Stage 3: Mature 1. 2. 3. A fully developed open wave with several tight isobars encircle the wave’s apex, the central pressure is now much lower. The winds blow more vigorously and converge toward the low’s center. The cold front moves close to the warm front, squeezing the warm sector into a smaller area Cloud and Precipitation form in a wide band ahead of the warm front and along a narrow band of the cold front, at the same time, latent heating The troughs at 500 and 1000mb are nearly in phase. As a consequence, the thermal advection and energy conversion become weak, amplitude of upper wave reaches its max., and surface pressure reaches its lowest value Stage 4: Occluded 1. 2. 3. Advanced cold front overtakes the warm front, the low system becomes occluded. Warm sector air gets lifted off surface. Surface low and upper level low center becomes vertically stacked, storm becomes weaken and dissipation as this vertical structure is cutting off its energy resource. (thick lines: 500mb; dashed line: thickness; thin contour: 1000mb) 1 B) Sketch diagrams of a typical baroclinic wave at any stage of its development. Including: 1000-500 hPa thickness, vorticity patterns, surface fronts, surface isobars, relate to upper level features. Incipient Occluded Development C) Sketch diagrams of a typical comma at any stage of its development, and relate it to various surface and upper level features and cloud patterns A: Multi-layered cirrostratus shield B: middle-level comma cloud C B A C B A C: deformation zone cirrus 2 D) Define “Self-development’ and ‘self-limitation’ 1. During the advance of an upper-level trough relative to a surface baroclinic zone, the upperlevel divergence initiates the surface circulation. The initiated surface cyclonic circulation begins to produce and enhance T advection in the low-level, which amplifies the upper level waves and increases wind aloft. The upper trough intensifies and produces stronger PVA, which further cause stronger upper-level divergence, and surface convergence. Thus, the cyclonic circulation strengthens, and surface low becomes deepen. The stronger low-level circulation induces stronger PTA to amplify upper waves, and so on. A positive feed back starts. This process is called ‘self-development’ of a cyclone. 2. Meanwhile, warm air rises from the surface low and along warm front, and cold air descends behind the cold front, a damping (self-limiting) influence of the vertical motions occurs as adiabatic cooling in the regions of ascent (warm air mass) and local warming in the regions of descent (cold air mass), which decrease the thermal contrast of two air masses. The damping influence latter is largely offset by the effects of condensation latent heating as cloud and precipitation set in as a result of vertical motion. E) Describe how a secondary circulation is set up over a surface low and high and 500 ridge and trough 1. During the stage of cyclone development, surface low is usually located downstream (east) of 500mb trough where PVA and upper level divergence are the strongest; while NVA and convergence are strongest downstream (east) of 500mb ridge where the surface High is located. Thus, rising motion occurs above the surface low and subsidence above the surface high. 2. Cold advection dig the trough with downward motion at the rear of the cold front, and warm advection build the ridge with upward motion ahead of warm front. 3. The secondary circulation (vertical motions) in a developing baroclinic system always acts to oppose the horizontal advection fields. Thus, the divergent motions tend partly to cancel the vorticity advection and the adiabatic T changes owing to vertical motion tend to cancel partly the thermal advection. F) Recognize cyclogenesis patterns on satellite imagery, and be able to identify the stage of development of the cyclone from the imagery. 3 Type 1: Meridional Trough or Baroclinic Zone Cyclogenesis 1. The short wave disturbance which initiates development moves around the trough within the baroclinic zone 2. This type is most prevalent along the U.S. east coast and adjacent coastal waters 3. Sequence of development of the major cloud systems: Baroclinic Zone Cirrus deck begins to wave into an ‘S’ pattern Vorticity comma (forms under the cirrus deck, then emerges) Deformation cirrus 4. During the early phases, the surface low centre and front are on the warm or anticyclonic side of the jet axis. The low transforms to the cold side of the jet during the developmental cycle 5. The strongest development begins in the middle and lower troposphere and evolves upward with time. The storm evolves to a type ‘A’ mature storm pattern and may change to a type ‘B’ pattern if development continues 6. This type of cyclogenesis is most similar to the “classical frontal wave model” Type 2: Split Flow or Diffluent Flow Cyclogenesis 1. 2. 3. 4. The short wave disturbance which initiates development moves on the warm side of the established jetfrontal zone, within the diffluent upper air flow pattern. This type is most prevalent over the great plains east of the Rockies. Sequence of development of the major cloud systems: Deformation cirrus. Vorticity comma. (forms rapidly southeast of the cirrus pattern) Baroclinic zone cirrus deck (forms over the comma). During the early phases, the surface low centre and front are not well defined or organized. Surface low becomes consolidated on the cold or cyclonic side of the jet axis and the surface front tends to lag behind the upper level baroclinic zone. 4 5. The closed circulation centre develops sooner and more rapidly in the middle and upper troposphere. The storm usually evolves directly to a type "B" mature storm pattern; with development east of the divide the system may evolve with a dry surge structure. The first two stages of development of split (or diffluent) flow cyclogenesis. The third and fourth stages of development of split (or diffluent) flow cyclogenesis Types 3: Cold Air Vortex (3A) and Induced Wave Cyclogenesis (3B) 1. 2. 3. 4. 5. 6. The short wave disturbance which initiates development moves on the cold side of established jet-front zone, within a confluent upper air flow pattern. This type is most prevalent over the open ocean. Sequence of development of the major cloud systems: 3A: Vorticity Comma. Baroclinic zone cirrus. Deformation zone cirrus. 3B: Vorticity Comma. Wave on baroclinic zone. Deformation zone cirrus. Early development of weather on the cold side of the jet. The strongest development begins in the middle troposphere during the early phases, but the nature of subsequent vertical development is more variable than Type I or II. The surface low forms or moves within the cold side of the jet. 5 6 TO 6.2.2 A) State and explain the implications of the assumptions of the quasi-geostrophic approximation 1. 2. We assume a synoptic scale, nearly geostrophic, and mid-latitude flow. Quasi-geostrophic assumption: real wind replaced by geo-strophic wind in advection terms, but not in divergence term (since the small ageostrophic components of the flow describe the development of the system) 3. Relative vorticity is approximated by the geostrophic vorticity in the vorticity equation 4. Beta-plane approximation (f = fo + βy) is used in the advection term in the vorticiy equation, and fplane approximation (f = fo) elsewhere 5. The relative vorticity (ζ) is typically about an order of magnitude smaller than the planetary vorticity in mid-latitudes (except for very strongly sheared flows at jet-stream level). The relative vorticity in the divergence term for the vorticity equation is neglected. 6. The tilting-twisting term is generally ignored since synoptic-scale motions are assumed to be almost horizontal. 7. Inviscid fluid (frictionless) 8. Incompressible assumption: horizontal inflow must be compensated by vertical outflow. 9. Hydrostatic assumption: states that the rate of decrease of pressure with height is proportional to the density of the air. Pressure falls more slowly with height in a warm airmass than in a cold airmass. This is an excellent assumption for synoptic-scale flows (downward gravity force = upward pressure gradient force). Vertical acceleration << g (no exceeding 0.01 ms-1) 10. Adiabatic assumption: no heat fluxes into or out of the particular volume of air, this is a good shortrange (less than one day) approximation 11. Ideal gas law is used for air. 12. Assumed a static stability parameter B) Identify and qualitatively explain the terms in the quasi-geostrophic vorticiy, thermodynamic energy, omega and geopotential tendency equations Thermodynamic energy equation Explanation: Left side: change of thickness Right-side Term1: thickness advection by geostrophic wind (PTA enhances the thickness) Right-side Term2: adiabatic T change caused by vertical motion (vertical motion decreases the rate of thickness change) Assumptions: Adiabatic (no latent release, sensible heating) Hydrostatic ( ) Geostrophic (Vg V) To be used for: Diagnosis temperature changes 7 Vorticity equation: (unsimplified) (a) (b) (c) (d) Assumptions: Ignore “tilting-twisting” term (d), because synoptic-scale motions are assumed to be almost horizontal The relative vorticity (ζ) is typically about an order of magnitude smaller than the planetary vorticity in mid-latitudes (except for very strongly sheared flows at jet-stream level). The relative vorticity in the divergence term (c) is neglected The velocity in advection term (a) is approximated by Vg (note we cannot do this in divergence term) Relative vorticity is approximated by geostrophic vorticity (g ) Beta-plan approximation (f = fo + βy) used in the advection term, while f-plane (f = fo) used elsewhere So we got Q-G vorticity equation: Explanation: Left side: the local rate of change of relative vorticity Right-side term 1: the advection of absolute vorticity by the geostrophic wind (PVA increase vorticity; NVA decrease vorticity) Right-side term 2: local planetary vorticity times divergence of real wind (conservation of absolute angular momentum: convergence implies “spin-up” or an increase of vorticity, just as the figure skaters spin faster when they bring in their arms. Conversely, divergence implies a decrease of vorticity) Use Q-G vorticity equation explain “why short-wave progress eastward”: In Q-G vorticity Eq. (ignore divergence term): For short waves, Adv. of g >> Adv. of f net PVA (NVA) downstream of the trough (ridge) the wave moves downwards; For long waves, Adv. of g ~ Adv. of f cancel each other out long waves move slowly (compared to SW) 8 Geopotential tendency equation: (eliminate in energy Eq. and Q-G. Vorticity) Where Used to: estimate the rate of change of geopotential heights – in time and in space assess the relative importance of different physical forcings on the geopotential Assumptions: assume synoptic scale, mid-latitude flow nearly geostrophic hydrostatic atmosphere (very small vertical accelerations) no friction (inviscid) adiabatic flow (constant entropy) Explanation: Left side: 3-D Laplacian of , proportional to - (if sinusoidal distribution) f Right-side term1: geostrophic advection of absolute vorticity; = f0 Vg g vg , these two terms will y tend to work against one another. For very short waves, relative vorticity advection will dominate, and the wave will propagate to the east rapidly. For very long waves the advection of planetary vorticity will dominate, and the wave will move very slowly westward, i.e., it will retrogress. Right-side term 2: geostrophic differential advection of thickness; f 02 R Vg T = p p ; warm advection (decreasing with height) increases geopotential, and cold advection (decreasing with height) reduces geopotential fall cold Geopotenti al vorticity advection advection decrea sing with height rise warm Other important points: The vertical impact of PVA or NVA is shallower for short waves than for long waves. For very long waves the geopotential tendency is impacted all the way to the surface (not so for short waves) PVA (NVA) can propagate but NOT deepen/strengthen troughs/ridges (as at trough or ridge, VA=0) Differential cold/warm advection can deepen/strengthen troughs/ridges 9 QG Omega Equation state: (eliminate in energy Eq. and Q-G. Vorticity) Assumptions: assume synoptic scale, mid-latitude flow scale analysis, dropping very small terms for synoptic scale motions Q-G approximation (real wind replaced by geostrophic wind in adv. terms, but not in divergence term. Thus called Quasi-Geostrophic, not Geostrophic) hydrostatic atmosphere (very small vertical accelerations) no friction (inviscid) diabatic heating effects are ignored (adiabatic flow) Explanation: Left side: 3-D Laplacian of , proportional to - Right-side term1: differential geostrophic advection of absolute vorticity; PVA increase (decrease) with height ascent (descent); V500 ( 500 f ) ; PTA p Right-side term2: 2-D Laplacian (divergence of gradient) of thickness advection; Vg ascent; NTA descent ri sin g cold vorticity advectionincrease with height advection warm sin king Other important points: At any level, PVA = divergence; NVA = convergence Any convergence at SFC forces air up (air uncompressible); any divergence aloft also help air going up (sucking air from lower levels) VA and TA can be in opposite sign, so not obvious to see the results (see Figure below) 500-mb VA may not be good indicator of differential VA in 1000-500mb layer. QG vertical motion is not caused by these terms QG vertical motion is a response to Vg advection which destroys the geostrophic balance QG Omega is not a physical reality, similar to thermal winds, i.e., not measurable Ageostrophic flow (which is to restore the destroyed geostrophic balance) 10 C) Describe the effect of wavelength on the motion of upper level waves in terms of planetary and relative vorticity (Using QG vorticity equation Eq.). 1. 2. 3. 4. 5. The advection of absolute vorticity is composed of two terms, the relative vorticity advection and the planetary vorticity advection. These two terms tend to compete with each other, and the direction of motion of the wave is dependant upon which component is stronger. For short waves, the advection of relative vorticity is greater than the advection of planetary vorticity. Thus, the net vorticity advection is positive/negative downstream of the trough/ridge and the wave moves downstream. For long wave, the relative vorticity advections are weaker so the planetary and relative vorticity advections are comparable and largely cancel each other out. Thus, the long waves move very slowly in comparison with the short waves. For very long waves the advection of planetary vorticity dominates, and the wave will move very slowly westward, i.e., it will retrogress. D) Explain the effect of vorticity and thickness advection on the movement and amplification of upper wave, referring to the influence of wavelength (Using potential tendency Eq.) 1. Vorticity advections cannot amplify wave, but can propagate the trough and ridge since such advections are close to zero in the vicinity of troughs and ridges. 2. Cold air advection decreasing with height results in falling heights. Conversely, warm air advection decreasing with height results in a rising of heights. It is differential thickness advection that is responsible for the amplification of upper waves. Cold air flooding into the low levels of a trough will dig the trough and warm air pushing into a ridge will build the ridge, thereby amplifying the wave. 3. Vertical impact of PVA and NVA is shallower for short wave than for long waves. E) Explain the effect of vorticity and thickness advection on the vertical velocity fields, including the influence of airmass stability (Using QG Omega Eq.). 1. PVA contributes to ascent; NVA causes subsidence (more accurately: PVA increases (decreases) with height ascent (descent); NVA decreases (increases) with height ascent (descent)) 2. PTA contributes to ascent, NTA tends to induce subsidence. 3. Stable air mass tends to prevent vertical motion, instable air mass favors vertical motion. F) State and explain in physical terms the wavelength restrictions on baroclinic development derived from the two-level quasi-geostrophic mode (short wave cut-off and long wave damping) 1. Short wave cut-off: as relative vorticity is larger for shorter wavelength systems than for longer wavelength systems. Thus, vertical motions are more intense since the magnitudes of the regions of PVA and NVA are larger. The intense vertical motion results in adiabatic cooling and warming, which reduce the rate of thickness change, and thus decrease thermal advection, and limit the amplification of shortwave, and eventually cut-off [in the notes, it says the parcel with considerable vertical velocity will exceed the slope of the potential temperature slope EAPE can no longer be produced and the flow becomes barocilinically stable producing shortwave cut off] 2. The growth of long waves is damped due to the requirement for conservation of absolute vorticity (f + = constant). If a long wave amplifies, the flow between the troughs and ridges becomes more meridional. Northward (or southward) moving air will feel a greater increase (or decrease) in f. However, if the wavelength is too long then there will not be enough variation in the relative vorticity along the trajectory to balance the variations in f. To compensate, the flow will adjust itself so that air moving northward veers (turns anticyclonically) while southbound air backs (curves cyclonically). Thus, the growth is damped until the wavelength decreases. 11 G) Define isentropic potential vorticity and explain why it is a useful quantity in the study of atmospheric flow patterns 1. Isentropic Potential vorticity (IPV) is a conserved quantity in adiabatic, frictionless flow, and is defined as the product of the absolute vorticity and static stability on an isentropic surface. 1 PVU = 10-6 KKg-1m2s-1 2. Why it is useful? its “elegant” – contains all dynamics in a compact formulation PV is a conserved quantity following the motion of a parcel, therefore can be used as a tracer of air movement – used to describe the evolution of flow patterns during significant synoptic events such as rapid cyclogenesis, blocking and retrogression of longwaves 3) PV fields can be inverted to regain velocity and thermodynamic fields. It is derived directly from the equations of motion and thermodynamic balances, so it is possible to deduce the T, P and wind fields from the PV distribution if a number of assumptions are made (like QG) 4) Some atmospheric processes may be described in terms of the interaction of PV anomalies with the background structure of the atmosphere. For example, when a strong upper-level PV anomaly moves over a low-level baroclinic zone, cyclogenesis usually results. There is no need to invoke secondary circulations (vertical motions) as drivers of the development. In addition, a superposition principle may be used to describe the interaction of PV anomalies at different levels in the atmosphere, interactions which lead to changes in the circulations at these levels. 1) 2) * Some other points to know: PV increase rapidly with height in the stratosphere because of high static stability. So it becomes easy to identify stratosphere air in contrast to troposphere air The PV value at the tropopause in mid-latitudes is about 2 PVU In tropics, the tropopause is hard to define using PV (need to just potential temperature) In mid-latitudes, some surfaces consist of both tropospheric and stratospheric air H) Explain the invertibility principle of potential vorticity. 1. 2. The invertibility principle of potential vorticity states that a knowledge of the spatial distribution of PV is sufficient to determine the overall structure of the flow As it is derived directly from the equations of motion and thermodynamic balances, thus it is possible to deduce the T, p and wind fields from the PV distribution if a number of assumptions are made OUT W IN C isotach 12 I) Explain the role of an isentropic potential vorticity anomaly in cyclogenesis. Using QG theory: an upper level vorticity maxium induces upward motion in the PVA area. Stretching of the column due to vertical motion can help to spin-up the low-level circulation which is aided by low-level warm advection and more vertical motion. Using PV theory: 1. The positive IPV anomaly at upper levels has a strong cyclonic circulation associated with it. A weaker extension of this circulation extends down to the surface 2. As the anomaly moves over the baroclinic zone, this low level circulation induces a wave in the thermal field, the wave crest forming a positive temperature anomaly. This positive temperature anomaly is equivalent to a positive IPV anomaly. 3. This new centre establishes its own cyclonic circulation, the upwards extension of which can eventually reinforce the flow about the upper centre, and slow down the eastward progression of upper level PV anomaly. Thus, a process of mutual reinforcement (positive feedback) is established. 4. The circulations induced by both centers can be superimposed to yield the net circulation. Note that the warm center on surface is slightly to the east of the upper IPV anomaly This schematic picture shows cyclogenesis associated with the arrival of an upper air IPV anomaly over a low level baroclinic region. On the left, the upper air cyclonic IPV anomaly, indicated by a solid plus sign and associated with the low tropopause shown, has just arrived over a region of significant low level baroclinicity. The circulation induced by the anomaly is indicated by solid arrows, and potential temperature contours are shown on the ground. The low level circulation is shown above the ground for clarity. The advection by this circulation leads to a warm temperature anomaly somewhat ahead of the upper IPV anomaly as indicated on the right, and marked with an open plus sign. This warm anomaly induces the cyclonic circulation indicated by the open arrows. If the equatorward motion at upper levels advects high-PV polar lower-stratospheric air, and the poleward motion advects low-PV subtropical uppertropospheric air, then the action of the upper-level circulation induced by the surface potential temperature anomaly will, in effect, reinforce the upper air IPV anomaly and slow down its eastward progression. 13 T.O. 6.2.3 A) Describe methods of estimating vertical velocity, including their limitations 1. Kinematic method: Based on continuity equation Thus, increasing div. with height ascent, decreasing div. with height descent Problems: Small error in u and v can result in large error in vertical velocity Cumulative errors of all lower levels 2. Dynamic methods: 1) QG omega equation: QG vertical motion is a response to Vg advection which destroys the thermal wind balance. upward vertical motion PVA + PTA ; downward vertical motion NVA + NTA Limitation: VA and TA can be in opposite signs; 500-mb VA may not be a good indicator of the differential VA in the 1000-500-mb layer 2) Q-vector: Problem: time-consuming to identify the area of convergence of Q vector. B) Describe situations in which the quasi-geostrophic omega equation is liable to be inaccurate 1. 2. 3. 4. When the scale is less than synoptic motions such as frontal zone, convection, hurricane etc. When diabatic heating processes occur (latent heat release; sensible heat) When strong boundary layer forcing such as friction stress and local terrain effect Out of mid-latitude C) List and describe the terms in the full omega equation which are important to consider when estimating vertical velocity in both the boundary layer and free atmosphere In boundary layer: Besides differential vorticity advection and thickness advection, frictional stress at the surface, latent heat release, sensible heat transfer, surface terrain effect are important to consider when estimating vertical velocity. In free atmosphere: Besides the differential vorticity advection and the Laplacian of thickness advection, differential deformation, divergence, and twisting effects, Beta effect, differential vertical advection of vorticity, latent heat release and sensible heat transfer are important to consider when estimating vertical velocity. 14 D) Explain the relationship between divergence and vertical velocity Low level convergence and upper level divergence results in upward motion Low level divergence and upper-level convergence lead to subsidence. E) Given upper level and surface charts for idealized synoptic situations, describe the vertical velocity profile. Important contributors to vertical motion: 1. Vorticity advection 2. Thermal advection 3. Latent heat release 4. Sensible heat transfer 5. Boundary layer forcing: friction stress and orographic lifting 250mb chart: vorticity advection strong along jet streak, right entrance and left exit divergence, upward motion. Left entrance and right exit of jet, convergence downward motion 500mb chart: vorticity advection and thickness advection. PVA area in downstream of the trough, div. ascent; NVA upstream of the trough, descent. PTA ascent and NTA descent. 700 or 850mb chart: latent heat release (cloud and precipitation area) and thermal advection. Surface chart: 1. sensible heating by underlying surface. 2. Low center convergence, high center divergence. 3. Surface roughness. 4. Pressure tendency effect as pressure fall is the results of divergence aloft. F) Use the Q-vector approach to estimate vertical motion 1. A serious limitation of the traditional QG omega equation is that it involves two terms which tend to oppose one another, and is difficult to qualitatively determine even whether up or down, and need a simpler and unambiguous depiction of vertical motion. 2. It points in a direction perpendicular and to the right of the geostrophic change vector along the x-axis (with cold air to the left) with a magnitude that is proportional to the amplitude of the vector change of the geostrophic wind multiplied by the strength of the T gradient. Advantages of Q-Vector: Forcing terms can be solved on a single constant-pressure surface (as opposed to the multiple vertical levels required by the quasi-geostrophic omega equation) 2) No partial cancellation among the forcing terms as often in the traditional formulation 3) No terms are neglected as with the Trenberth approximation 4) The forcing terms are independent of the coordinate system on which they are evaluated 5) Q-vector field (or divergence of Q) may be plotted to indicate the synoptic-scale vertical motion field and the ageostrophic wind etc 1) 3. Usefulness of Q-vectors: Qualitatively and unambiguously identify regions of ascent/descent by the divergence of Q. 15 Indicates the enhancement and dissipation of fronts: when Q-vectors point towards warmer (colder) air one may immediately recognize frontogenesis (frontolysis) Q-vector points in the same direction as the lower-level ageostrophic motion (always point to the ascending region) and in the opposite direction to the upper-troposphere ageostrophic motion Q-vector provides an elegant explanation of the interdependent relationships between geostrophic wind, vertical motion, and thermal wind balance: Geostrophic advections destroy geostrophic balance, or likewise, thermal wind balance Environment responds to this by generating an ageostrophic flow This flow adjusts the magnitude of the thermal wind to match the modified strength of the thermal gradient Q-vectors for barocilnic wave Q-vector in Jet, and ageostrophic flow (which is to restore the destroyed geostrophic balance) 16 Q-vector in frontogenesis, and ageostrophic flow (which is to restore the destroyed thermal wind balance) Q-vector in frontolysis G) Describe Zwack’s diagnostic divergence method for calculating the vertical velocity profile Instead of calculating vertical velocity at a given level, the divergence is estimated at all levels. Vertical motion is then calculated through a vertical integration of the equation of continuity, i.e., considering the additive effects of divergence from the ground up. 17 H) Construct qualitative vertical velocity profiles given standard upper and surface charts (see answer to E) I) Identify physical processes that can contribute to vertical motion but which are not accounted for by the quasi-geostrophic omega equation 1. 2. 3. 4. Latent Heat Release: Convection on satellite imagery, precip. on radar) Sensible Heat Transfer: SFC temp Boundary layer forcing (frictional stress, orographic lifting, divergence/convergence, wind barbs etc) Pressure tendency 18 TO 6.2.4 A) Illustrate and explain the relationship between the temperature and wind fields based upon the geostrophic thermal wind equation Vg g ˆ k T Z fT Thermal wind law relates the vertical structure of the wind fields to the horizontal temperature distribution. It states in the presence of a horizontal temperature gradient, the wind speed must increase with increasing height. Thermal wind is the vector difference between the geostrophic wind at two different levels in the vertical, it blows ‘parallel’ to the thickness contours with cold air to the left, the magnitude of thermal wind is proportional to the thickness gradient. The reason is: the differences in thickness between two pressure levels are a result of differences in the mean temperature for a layer. Hence, greater thicknesses in a warm region of the atmosphere contrasted with lower thicknesses in a cold region of the atmosphere lead to increasingly sloped pressure surfaces aloft, i.e., increasing horizontal pressure gradients which leads to stronger winds aloft: So, if there is a zone of strong T gradient such as a frontal surface, there must be a corresponding zone of strong winds somewhere above that surface. Then if at some other point above these strong winds the T gradient reverses itself, the winds above will begin to diminish. This is how Jet stream and upper front created. Backing - Cold air advection and Veering, Warm air advection. B) Define a front dynamically in terms of temperature, wind, stability and vorticity Front is an elongated zone (~ 1000km long; ~100 km wide) of strong horizontal T gradient (hyperbaroclinic zone) cyclonic wind shear and vorticity relatively large static stability vertical depth to at leas 850mb (for surface fronts) C) Discuss the applicability of an idealized frontal model to actual fronts, indicating where and when the model is most successful and how observed fronts depart from the ideal 1. Frontal zone in the Bergon model continuously extends from surface up to upper troposphere, in the real case, surface fronts and upper fronts can exist independently of one another and they form in different processes. 19 2. The classical model of fronts included a model of the precipitation patterns with a broad area of stratiform precipitation associated with the warm front, and the narrow line of convective precipitation along the cold front. In reality, the weather relative to the cold front varied from case to case. This prompted Bergeron to introduce “anafront” and “katafront”. Anafronts resemble the original polar front model. Cloud forms along and behind the surface front, and heavier convective precipitation is confined to a narrow band along the front. The katafront has warm air flowing down the frontal surface, and usually develops in conjunction with a mature system or a rapidly developing synoptic disturbance. In this case, mid-level cloud and its associated precipitation occur ahead of the surface frontal position. 3. Idealized model of front is continuous, but in reality, it could be incontinuous. 4. Idealized model thought jet stream was near the tropopause, but in reality, it could be much lower than that. D) Discuss the formation and evolution of a surface front including the processes of frontogenesis and frontlysis. 1. 2. 3. 4. At the first stage, the surface stationary front usually forms along the axis of dilatation in a horizontal deformation zone where horizontal T gradient and wind shear tend to be increased by the stretching of the flow. If convergence is presented along with deformation, see figure bellow, frontogenesis is greatly enhanced. Near the surface, convergence is created by friction with air flow inward to the low With the support from upper level and the surface cyclone development, the frontal zone fractures in the vicinity of the low center with cold front pushing south-ward and warm front moving northward The cold front is more active and moves faster than the warm front, squeezing the warm air off the ground, and forming a trowal with cloud and precipitation associated. With combined effects from adiabatic cooling of warm air and heating of cold air, diabatic processes, and turbulence mixing, the warm air and cold air eventually mix together and diffuse, the temperature contrast no longer exit, Trowal disappear. E) Discuss the contribution of the following processes to surface frontogenesis and frontlysis 1. 2. 3. 4. Geostrophic deformation is the dominant processes leading to frontogenesis, which increases horiz. T gradient and wind shear. A front will form along the axis of dilatation. It would be frontolytic if the isotherms were oriented to lie within 45 degrees of the axis of contraction. Divergence: frontogenesis is enhanced if convergence is present along with deformation, which causes packing of isotherms, frontogenesis; divergence frontolysis Surface friction increases the possibility of frontogenesis. When high values of vorticity are maintained in frontal zone, the convergence is greatly enhanced by the effects of surface friction on the surface wind field. The added convergence hastens frontogenesis. If without the convergence of frontal zone, friction would dissipate vorticity and cause frontlysis Diabatic processes: sensible heating (radiative heating/cooling, conduction from the surface) and latent heat release are very important to low level thermal structure. If diabatic processes causes greater thermal contrast between two airmasses, then contribute to frontogenesis, otherwise, causes frontolysis. It may mask presence of surface or low-level front 20 F) Explain the formation and structure of upper tropospheric fronts 1. 2. 3. 4. The formation of upper fronts was coupled to tropopause folding where intrusions of air from stratosphere can be found, in some cases, in the lower troposphere Vertical motions play an important role in the formation of upper level frontogenesis, the transverse circulation (associated with tropopause folding) with subsidence on both sides of the upper front, but ascent ahead of the upper front In order for the thermal contrast to develop, the orientation of the axis of deformation must be such that adiabatic warming (due to subsidence) is maximized on the warm side of the frontal zone Because of point 2 (mentioned above), it is appropriate to analyze the upper front at the back edge of the cloud and precipitation area. G) Define and describe the jet-stream and define the jet axis and core 1. 2. 3. The jet stream refers to a narrow current of strong winds concentrated along a quasi-horizontal axis (jet axis) in the upper troposphere Typically, a jet stream is thousands of kilometers long, a few hundred kilometers wide and a few kilometers in depth It has one or more velocity maxima, the strongest vertical and horizontal wind shears are in the frontal mixing zone The core is the strongest winds in the stream, is located at the level where the horizontal temperature gradient vanishes, and in the warm air below the tropopause. Upper tropospheric fronts and jet streams are so closely linked that they are often considered two ways of talking about the same thing. The latter emphasizes the winds while the former refers to the T or density field. H) Based on the thermal wind relationship, explain the position and intensity of the jet with relation to the front and the tropopause. Throughout the troposphere, air is warmer near the equator, colder at the poles, and there is a frontal zone at mid-latitudes where T rapidly decreases toward the north. This sharp horizontal T gradient along the frontal zone causes geostrophic wind increasing with height and the greatest wind aloft in the middle latitudes based on the thermal wind relationship; The Jet core must be located in the warm side of the front zone, otherwise the thermal wind law doesn’t help explain the high speed of upper level wind (the strong T gradient zone must be under the Jet in vertical) However, the tropopause is lower near the poles than near the equator, thus, temperature begins increasing with height at a lower altitude near the poles than near the equator. This causes a T reversal in the 21 stratosphere, where the air is cold near the equator and warmer over the poles, thus, above the tropopause, the wind becomes weaken because of the reversed horizontal T gradient. Thus jet core is located below the tropopause. J) Describe and explain the secondary circulations about jet maxima. Secondary circulation: Divergence (ascent) in the right entrance and left exit, convergence (descent) in the left-entrance and right exit, therefore, there is a thermally (warm air rising, and cold air descending) direct vertical circulation in the entrance region, and a thermally indirect circulation in the exit region. Explanation: 1. Ageostrophic wind: As an air parcel enters a jet streak, its geostrophic wind speed increase. But the Coriolis force needs time to adjust, and can not balance the increased pressure gradient, therefore, ageostrophic wind blows to the left towards lower height As the air parcel exits the jet streak, its geostrophic wind speed decreases, coriolis force is bigger than pressure gradient force, and an ageostrophic wind blows toward greater height 2. From energy point of view, air gains kinetic energy and therefore must lose potential energy. The loss of potential energy means the air parcel must move to lower geopotential heights 3. Vorticity advection: PVA in the left exit and right entrance at jet-streak, causing divergence; NVA in the left entrance and right exit, causing convergence. 4. Q-vector 22 K) Explain the propagation of jet maxima in relation to the secondary circulation. As ahead of the jet maximum, there will be subsidence to the right of the jet stream, and ascent to the left. According to the thermal wind law, this means that there will be subsidence in the warm air and ascent in the cold air ahead of the jet. So, in this area, the warm air will warm adiabatically and the cold air will cool, increasing the thermal contrast, meaning that this circulation is frontogenetic. To the rear of the jet maximum, the opposite circulation is taking place, meaning that this area is frontolytic. Hence by the thermal wind law the maximum winds aloft will move downstream where the maximum temperature gradient is being formed. This is why you will see jet maxima always moving downstream in the 250mb flow. L) Explain the life cycle of a mid-latitude cyclone and its relationship to the polar front as described by the Bergen school. According to Bergen model, an extratropical cyclone begins as a small perturbation superimposed on a pre-existing front – the polar front. This creates a cyclonic circulation with a warm front developing east of the cyclone and a cold front to the west. These fronts progress with the cyclonic circulation and the cold front eventually catches up to the warm front, forcing all of the warm air aloft near the centre of the cyclone and leaving a vortex to weaken in the cold air. M) Describe some of the modifications that have been proposed to the Bergen model, including split fronts, trowals and cold fronts aloft. 1. A “trowal” is the trough of warm air aloft, and is analyzed at the back edge of middle cloud and precipitation south of the low center Occlusion: The process of the cold front catching up to the warm front is called an occlusion. The occlusion is a surface feature. Warm occlusion develops when the cold air wrapping around the low center is modified so that it is warmer when it arrives to meet the cold air that is unmodified Cold occlusion develops if the cold air is cooled as it wraps around the low Warm occlusion Cold occlusion 2. Upper cold front (UCF) or Cold front aloft (CFA): A warm front at the surface a cold front aloft (CFA), which produces the main precipitation at the surface 23 a surface trough, some 200-300 km behind the leading edge of the CFA, which may or may not take the form of a cold front The cold front aloft (CFA) model (from Hobbs, et al 1990) 3. Split front model: a cold front aloft, a surface cold front in the trough The split front model 4. 5. 6. 7. Three airmass cyclone model Conveyor belt model marine cyclone model (mentioned in next page) rapidly deepening cyclones over land (many similarities the horizontal and vertical structures to the marine cyclone model; One of the main differences was the absence of the secluded pool of warm air at the surface near the centre of the cyclone in its later stages) 24 N) Explain the life cycle and potential applications of the marine cyclone model 1. The incipient cyclone forms along a broad, continuous baroclinic zone. 2. The previously continuous front “fractures” near the centre of the intensifying cyclone, leaving a relatively barotropic area near the low centre. At the same time the frontal gradients intensify along the warm and cold fronts. 3. The cold front propagates eastward perpendicular to the warm front. This stage of cyclogenesis is termed the “T-bone”, which is what the frontal structure resembles. At this point the warm front is “bent-back” north of the low centre. 4. The bent-back warm front encircles the low centre, forming a relatively warm core “seclusion” about the low centre. It should be noted that the warm air near the low centre did not originate in the warm sector of the low. The seclusion near the centre of the cold low develops from the manner in which the baroclinic zone wraps around the low. * Main drawback: it may apply to only one specific area of the world, so that it cannot be universally applied to cyclones. It is yet to be shown conclusively that this life cycle occurs in rapidly deepening cyclones over land 25