advanced synopticm. d. eastin frontogenesis – kinematics & dynamics
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Advanced Synoptic M. D. Eastin
Frontogenesis – Kinematics & Dynamics
Advanced Synoptic M. D. Eastin
Frontal Evolution: An Example
Kinematic Frontogenesis
• Three-Dimensional (3D) Frontogenesis• Two-Dimensional (2D) Frontogenesis• Deficiencies and Limitations
Dynamic Frontogenesis
• Review of QG Theory• Semi-geostrophic (SG) Theory• Conceptual Model• Impact of Ageostrophic Advection• Application of Q-vectors to Frontogenesis
Frontogenesis – Kinematics & Dynamics
Advanced Synoptic M. D. Eastin
Frontal EvolutionAn Example from Observations:
Boulder Tower Observations11-12 December 1975
Time-Height Cross-Section
Advanced Synoptic M. D. Eastin
An Example from Observations:
• Notice how the temperature gradient strengthens between 1200 and 0000 GMT• How does this strengthening occur (and so fast)?
Frontal Evolution
From Shapiro et al
(1985)
Advanced Synoptic M. D. Eastin
Definitions and Our Approach:
• Intensification → Frontogenesis• Weakening → Frontolysis
• The traditional measure of frontogenesis was introduced by Petterssen (1936) to explore the kinematic processes that influence the strength of the potential temperature (θ) gradient as a function of time – called the Frontogenetic Function (F)
F > 0 → Frontogenesis
F < 0 → Frontolysis
• We shall first examine the kinematic effects whereby advection, shear, and local heating act to increase the density gradient
• Then, we will examine the dynamic effects whereby forces induced as a result of the kinematic changes produce circulations that can enhance the kinematic effects
Dt
DF
Kinematic Frontogenesis
Advanced Synoptic M. D. Eastin
Three-dimensional (3D):
• If we expand total derivative applied to F using the thermodynamic equation – after much math – we arrive at:
• Which of these terms are “significant”? → Perform scale analysis
• Simply with a different coordinate system? → Transform to “front-normal”
Kinematic Frontogenesis
x
w
zx
v
yx
u
xdt
d
xp
p
cxF
p
011
y
w
zy
v
yy
u
xdt
d
yp
p
cy p
01
z
w
zz
v
yz
u
xdt
dp
zc
p
z p
0
Diabatic
Horizontal Deformation
Vertical Deformation
Tilting
Vertical Divergence
Weighting Factors = Magnitude of θ-gradient in one direction Magnitude of the total 3D θ-gradient
Advanced Synoptic M. D. Eastin
Two-dimensional (2D): In a “front-relative” coordinate system
• If we define our coordinate system so that our x’-axis is parallel to the front, and our y’-axis is perpendicular (or normal) to the front, then we can simply the 3D equation
[Equation 6.2 in Lackmann text]
Note: This equation describes frontogenesis in a Lagrangian sense (following the flow)
Thus, it will NOT indicate whether the overall front is intensifying → only along small sections of the front
Kinematic Frontogenesis
x’y’
yypy
v
yy
u
xF
Shearing TiltingConfluence Diabatic
Note: The “front-relative” wind components become
x’ → u’y’ → v’
Advanced Synoptic M. D. Eastin
Shearing Frontogenesis: In a “front-relative” coordinate system
• Describes the change in frontal strength due to differential potential temperature advection by the front-parallel (x’) wind component (u’)
• Stronger forcing near the surface
Kinematic Frontogenesis
yypy
v
yy
u
xF
Shearing TiltingConfluence Diabatic
Initial Time Later Time
Advanced Synoptic M. D. Eastin
Shearing Frontolysis: In a “front-relative” coordinate system
• Describes the change in frontal strength due to differential potential temperature advection by the front-parallel (x’) wind component (u’)
• Stronger forcing near the surface
Kinematic Frontogenesis
yypy
v
yy
u
xF
Shearing TiltingConfluence Diabatic
Initial Time Later Time
Advanced Synoptic M. D. Eastin
Confluence Frontogenesis: In a “front-relative” coordinate system
• Describes the change in frontal strength due to potential temperature advection by the front-normal (y’) wind component (v’)
• Strongest forcing near the surface
Kinematic Frontogenesis
yypy
v
yy
u
xF
Shearing TiltingConfluence Diabatic
Initial Time Later Time
Advanced Synoptic M. D. Eastin
Tilting Frontogenesis: In a “front-relative” coordinate system
• Describes the change in frontal strength due to differential potential temperature advection by vertical motion (ω) gradients in the front-normal (y’) direction
• Weak forcing at the surface (ω ~ 0)• Strongest forcing aloft (ω larger)
Kinematic Frontogenesis
yypy
v
yy
u
xF
Shearing TiltingConfluence Diabatic
Initial Time Later Time
Advanced Synoptic M. D. Eastin
Diabatic Frontogenesis: In a “front-relative” coordinate system
• Describes the change in frontal strength due to differential diabatic forcing on the potential temperature field
• Stronger forcing near the surface
• Processes: Radiation Surface Fluxes / Surface Properties Latent Heating / Evaporational Cooling
Kinematic Frontogenesis
yypy
v
yy
u
xF
Shearing TiltingConfluence Diabatic
Advanced Synoptic M. D. Eastin
Diabatic Forcing: Can be important!!!
• Notice how the equivalent potential temperature (θe) gradient behind the surface cold front changes significantly as the front passes over the Gulf Stream (upward heat and moisture fluxes)
Kinematic Frontogenesis
A
B C
Advanced Synoptic M. D. Eastin
Kinematic Frontogenesis
Equivalent Potential Temperature (θe)Surface Pressure
3D Frontogenetic Function (F)Surface Pressure
Regions we should expectfrontal intensification
and strong lift
Advanced Synoptic M. D. Eastin
Limitations and Deficiencies:
Potential temperature is treated as a passive scalar that is simply advected around by the geostrophic wind field (kinematics)
• Recall that QG theory assumes the flow is in hydrostatic and geostrophic balance (i.e., thermal wind balance) at all times
If we change the potential temperature field (or its gradient), should we not expect a similar change in the wind field (a dynamic response) that would be required maintain the thermal wind balance?
Fronts are observed to double their intensity within several hours, but kinematic frontogenesis suggests that it should take a day or more
Does the dynamic response to any initial kinematic changes to the potential temperature field further accelerate the frontogenesis?
Kinematic Frontogenesis
Advanced Synoptic M. D. Eastin
Review of QG Theory:
• We learned that geostrophic advection can disrupt thermal wind balance
• Ageostrophic flow (horizontal & vertical) come about in to restore the balance
Application to Frontogenesis:
Any air parcels entering a frontal zone should experience a rapid change in temperature gradient and thermal wind balance disruption
(QG Theory? → Not so fast!)
Recall: QG theory assume small Ro
“along-front” → L ~1000 km → Ro « 1 “cross-front” → L <100 km → Ro ~ 1
Dynamic Frontogenesis
L-En
R-En
R-EnL-En
LfURo /
Advanced Synoptic M. D. Eastin
Semi-Geostrophic (SG) Theory:
A modified version of QG theory specifically developed to address frontal circulations
Assumptions:
• Cartesian coordinates (x/y/z and u/v/w)• Boussinesq approximation (see text)• Front-relative coordinate system
along-front → x’ and u’ cross-front → y’ and v’
• Along-front flow → geostrophic (ug’)
Cross-front flow → total (vg’ + vag’)
Ageostrophic advection in the cross front directions can also modify the temperature and momentum fields
• Cross-front thermal gradient is in thermal wind balance with the where along-front geostrophic flow
Dynamic Frontogenesis
x’y’
y
b
z
uf g
g
b
Advanced Synoptic M. D. Eastin
Semi-Geostrophic (SG) Theory:
The full set of SG equations (see Section 6.3.1 in your text) can be combined to form a single diagnostic equation (called the Sawyer-Eliassen equation) that describes how geostrophic flow may disrupt thermal wind balance near a front, and the cross-front ageostrophic circulation works to restore balance.
where: and [Equation 6.16 in Lackmann text]
Dynamic Frontogenesis
g
b
222 Qz
v
yy
b
z
v
y
uff
y
w
z
b
z
g agagg
GeostrophicFlow
Cross-front AgeostrophicCirculation
y
v
yy
u
xp
RQ gg
2Cross-front
Q-vector
Advanced Synoptic M. D. Eastin
Conceptual Model: Frontogenesis
• Assume the low-level geostrophic flow (red vectors) is acting to concentrate the background thermal gradient (kinematic frontogenesis) → disturbs thermal wind balance
Note: The resulting low-level Q-vectors (black vectors / dots) point toward the “warm side” of the frontal zone
A. To restore balance, an ageostrophic cross-front circulation that (1) cools the warm air via expansion / ascent and (2) warms the cold air via compression / descent must develop
Note: As the thermal gradient intensifies, so does the Q-vector magnitude (enhancing Q-convergence and the cross-front circulation…)
Dynamic Frontogenesis
Initial Time Later Time “Cross-Front”Cross-section
A
B
BA
1 2Q2Q2 Q2Q2
Q2
Advanced Synoptic M. D. Eastin
Conceptual Model: Frontogenesis
• Assume the low-level geostrophic flow is acting to concentrate the background thermal gradient (via kinematic frontogenesis) → disturbs thermal wind balance
B. To restore balance, the Coriolis torque acting on the “down-gradient” cross-front ageostrophic flow will enhance the along-front geostrophic flow, which increases the along-front vertical shear, bringing the frontal zone back toward balance
Dynamic Frontogenesis
Intensification of the thermal gradientenhances the cross-front pressure gradientproducing down-gradient cross-front flow
[enhances the cross-front circulation]
Coriolis torque turns the opposing down-gradientcross-front flow into opposing along-front flow
[enhances the along-front vertical shear]
Advanced Synoptic M. D. Eastin
Conceptual Model: Example Case
Dynamic Frontogenesis
N
N
S
S
1000-mb Isentropes1000-mb Wind Barbs
1000-mb Frontogenesis850-mb Q-vectors
Cold
Cold
Cold
Warm
Warm
850-mb Omega (ω)850-mb Q-vectors
Isentropes and Omega (ω)
Advanced Synoptic M. D. Eastin
Impact of Ageostrophic Advection: Rapid Frontogenesis
Feedback Loop: As the thermal gradient intensifies, so does the Q-vector magnitude and the cross-front pressure gradient, enhancing both the Q-vector
convergence and the cross-front circulation…
Since the cross-front flow (which also intensifies the thermal gradient)is a combination of geostrophic advection and ageostrophic advection,the ageostrophic advection works to both restore thermal wind balanceand simultaneously enhance the thermal gradient
With no additional mechanism to offset the effects of ageostrophicadvection → rapid near-surface frontogenesis can occur!
Dynamic Frontogenesis
Q2Q2
Advanced Synoptic M. D. Eastin
Application of Q-Vectors:
The orientation of low-level Q-vectors to the low-level potential temperature gradient provides any easy method to infer frontogenesis or frontolysis from real-time data
• If the Q-vectors point toward warm air and cross the potential temperature gradient, then ageostrophic flow will produce frontogenesis
• If the Q-vectors point toward cold air and cross the potential temperature gradient, then ageostrophic flow will produce frontolysis
• If the Q-vectors point along the temperature gradient, then ageostrophic flow will have no impact on the temperature gradient and the frontal intensity will be steady-state
Q-vectors and Frontogenesis
Q-vectors
Example:
Note: The regions of expected and observed frontogenesis / frontolysis generally agree Part of the observed evolution is due to system motion and diabatic effects
Advanced Synoptic M. D. Eastin
Q-vectors and Frontogenesis
925-mb Q-vectors and Isentropes11 November 2012 at 12 UTC
925-mb Isentropes12 November 2012 at 00 UTC
Advanced Synoptic M. D. Eastin
ReferencesBluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume I: Principles of Kinematics and Dynamics.
Oxford University Press, New York, 431 pp.
Bluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume II: Observations and Theory of WeatherSystems. Oxford University Press, New York, 594 pp.
Keyser, D., M. J. Reeder, and R. J. Reed, 1988: A generalization of Pettersen’s frontogenesis function and its relation tothe forcing of vertical motion. Mon. Wea. Rev., 116, 762-780.
Lackmann, G., 2011: Mid-latitude Synoptic Meteorology – Dynamics, Analysis and Forecasting, AMS, 343 pp.
Schultz, D. M., D. Keyser, and L. F. Bosart, 1998: The effect of large-scale flow on low-level frontal structure and evolutionin midlatitude cyclones. Mon. Wea. Rev., 126, 1767-1791.
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