Frontogenesis – Kinematics & Dynamics Advanced Synoptic M. D. Eastin

Frontogenesis – Kinematics & Dynamics 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 Advanced Synoptic M. D. Eastin

Boulder Tower Observations Time-Height Cross-Section Frontal Evolution An Example from Observations: Boulder Tower Observations 11-12 December 1975 Time-Height Cross-Section Advanced Synoptic M. D. Eastin

Frontal Evolution An Example from Observations: Notice how the temperature gradient strengthens between 1200 and 0000 GMT How does this strengthening occur (and so fast)? From Shapiro et al (1985) Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis 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 Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis 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” 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

Kinematic Frontogenesis 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 x’ y’ Shearing Tilting Confluence Diabatic Note: The “front-relative” wind components become x’ → u’ y’ → v’ Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis 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 Shearing Tilting Confluence Diabatic Initial Time Later Time Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis 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 Shearing Tilting Confluence Diabatic Initial Time Later Time Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis 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 Shearing Tilting Confluence Diabatic Initial Time Later Time Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis 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) Shearing Tilting Confluence Diabatic Initial Time Later Time Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis 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 Shearing Tilting Confluence Diabatic Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis 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) A B C Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis Two-Dimensional (2D): Analysis Example Many software packages can compute / plot the 3D or 2D frontogenetic function Can be useful for weather forecasting → Identify and track frontal locations → Anticipate differential frontal motions → Identify regions of strongest forcing (correspond to regions of strong lift) Equivalent Potential Temperature (θe) Surface Pressure 3D Frontogenetic Function (F) Regions we should expect frontal intensification and strong lift Advanced Synoptic M. D. Eastin

Kinematic Frontogenesis 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? Advanced Synoptic M. D. Eastin

Dynamic Frontogenesis 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 L-En R-En Advanced Synoptic M. D. Eastin

Dynamic Frontogenesis 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 x’ y’ Advanced Synoptic M. D. Eastin

Cross-front Ageostrophic Dynamic Frontogenesis 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] Geostrophic Flow Cross-front Ageostrophic Circulation Cross-front Q-vector Advanced Synoptic M. D. Eastin

Dynamic Frontogenesis 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…) Initial Time Later Time “Cross-Front” Cross-section A B 1 2 Q2 Advanced Synoptic M. D. Eastin

Dynamic Frontogenesis 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 Intensification of the thermal gradient enhances the cross-front pressure gradient producing down-gradient cross-front flow [enhances the cross-front circulation] Coriolis torque turns the opposing down-gradient cross-front flow into opposing along-front flow [enhances the along-front vertical shear] Advanced Synoptic M. D. Eastin

Dynamic Frontogenesis Conceptual Model: Example Case N S 1000-mb Isentropes 1000-mb Wind Barbs 1000-mb Frontogenesis 850-mb Q-vectors Cold Warm 850-mb Omega (ω) Isentropes and Omega (ω) Advanced Synoptic M. D. Eastin

Dynamic Frontogenesis 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 balance and simultaneously enhance the thermal gradient With no additional mechanism to offset the effects of ageostrophic advection → rapid near-surface frontogenesis can occur! Q2 Advanced Synoptic M. D. Eastin

Q-vectors and Frontogenesis 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 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 Advanced Synoptic M. D. Eastin

925-mb Q-vectors and Isentropes Q-vectors and Frontogenesis 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 925-mb Q-vectors and Isentropes 11 November 2012 at 12 UTC 925-mb Isentropes 12 November 2012 at 00 UTC Advanced Synoptic M. D. Eastin

References Advanced Synoptic M. D. Eastin Bluestein, 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 Weather Systems. 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 to the 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 evolution in midlatitude cyclones. Mon. Wea. Rev., 126, 1767-1791. Advanced Synoptic M. D. Eastin