13th Cyclone Workshop 25 October 2005 Pacific Grove, CA1 A Study of the Effect of Horizontal...

13th Cyclone Workshop 25 October 2005 Pacific Grove, CA13th Cyclone Workshop 25 October 2005 Pacific Grove, CA 11

A Study of the Effect of Horizontal Contrasts A Study of the Effect of Horizontal Contrasts in Static Stability on Frontal Behaviorin Static Stability on Frontal Behavior

Mark T. StoelingaMark T. Stoelinga

University of WashingtonUniversity of Washington


Vertical cross section through an Vertical cross section through an idealized lower-tropospheric cold frontidealized lower-tropospheric cold front

→ → consistent with many observed cold consistent with many observed cold fronts, textbooks, and well-established fronts, textbooks, and well-established theory (e.g., Hoskins and Bretherton theory (e.g., Hoskins and Bretherton 1972)1972)

Vertical cross section through an Vertical cross section through an idealized lower-tropospheric idealized lower-tropospheric forward-forward-tiltedtilted cold front cold front

→ → variants described by Sienkiewicz et variants described by Sienkiewicz et al. (1989); Hobbs et al. (1990,1996); al. (1989); Hobbs et al. (1990,1996); Martin et al. (1990); Steenburgh and Martin et al. (1990); Steenburgh and Mass (1994); Locatelli et al. (1995, 1998, Mass (1994); Locatelli et al. (1995, 1998, 2002a, 2002b); Neiman et al. (1998); 2002a, 2002b); Neiman et al. (1998); Schultz and Steenburgh (1999); Koch Schultz and Steenburgh (1999); Koch (2001); Stoelinga et al. (2002; 2003)(2001); Stoelinga et al. (2002; 2003)

SFC

700 hPa

SFC

700 hPa

200 km


Methodology:Methodology:

1.1. Using examples, establish a characteristic static Using examples, establish a characteristic static stability pattern associated with forward-tilted cold stability pattern associated with forward-tilted cold frontsfronts

2.2. Examine the effects of that distribution by applying Examine the effects of that distribution by applying the Sawyer-Eliassen equation to an idealized front the Sawyer-Eliassen equation to an idealized front with and without the characteristic static stability with and without the characteristic static stability pattern.pattern.


Question:Question:

Can the differences in circulation shed light on the Can the differences in circulation shed light on the plausibility ofplausibility of

1.1. Development of a forward-tilt in the lower Development of a forward-tilt in the lower troposphere?troposphere?

2.2. A stronger baroclinic zone above the surface than at A stronger baroclinic zone above the surface than at the surface?the surface?


The “Perfect CFA Storm”: 29-30 October 2004 The “Perfect CFA Storm”: 29-30 October 2004

Surface chart and radar summary 0600 UTC 30 Oct 2004Surface chart and radar summary 0600 UTC 30 Oct 2004

NOAA Surface Analysis and Radar Composite









22-km WRF model forecast valid 06 UTC 30 Oct 200422-km WRF model forecast valid 06 UTC 30 Oct 2004Colors: Colors: θθe; contours: e; contours: θθ; vectors: horizontal winds; vectors: horizontal winds

SurfaceFront

SquallLine















Other Examples… Other Examples…

Benjamin and Carlson (1986)Benjamin and Carlson (1986)

Low StabilityHigh Stability



Martin et al. (1990)Martin et al. (1990)

High StabilityLow Stability







Schultz and Steenburgh (1990)Schultz and Steenburgh (1990)


Idealized FrontIdealized Front

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9

300312

324

336

-40

-20

-20

0

20 20 40

0.4

0.4

0.8

Control front

Cross-front distance (km)

Hei

gh

t (km

)

1

0

1( , ) tan

rz z ysy z zz L

y

z


Idealized FrontIdealized Front

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9

300312

324

336

-40

-20

-20

0

20 20 40

0.4

0.4

0.8


Hei

gh

t (k

m)

Eliassen’s (1962) front


2 2 202 2 /yy yz zz gy x gy yN S F g u v Q

Sawyer-Eliassen CirculationSawyer-Eliassen Circulation

Static Stability

Shear/ Baroclinity

Absolute Vorticity

Shear Forcing

Deformation Forcing

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Forcing and circulation in control front


Hei

gh

t (km

) / 2g yv D

y

z


Modified FrontModified Front

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9

-6

-30

3

6

Theta perturbation


Hei

gh

t (km

)

Reduces thermal gradientReduces forcing at low levels

- PV+ PV

PV alteredCould alter reponse


-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Forcing and circulation in modified front


Hei

gh

t (km

)

Modified FrontModified Front

y

z


Control FrontControl Front

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Forcing and circulation in control front


Hei

gh

t (km

)

y

z


-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Circulation: modified minus control


Hei

gh

t (km

)

Modified minus Control FrontModified minus Control Front

y

z

Circulation due only to altered forcing, without altered response coefficients.


Frontogenesis in Control FrontFrontogenesis in Control Front

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Frontogenesis due to geostrophic deformation


Hei

gh

t (km

)

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Frontogenesis due to ageostrophic convergence


Hei

gh

t (km

)

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Frontolysis due to tilting


Hei

gh

t (km

)

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Total frontogenesis


Hei

gh

t (km

)


Frontogenesis in Modified FrontFrontogenesis in Modified Front

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Frontogenesis due to geostrophic deformation


Hei

gh

t (km

)

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Frontogenesis due to ageostrophic convergence


Hei

gh

t (km

)

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Frontolysis due to tilting


Hei

gh

t (km

)

-2000 -1500 -1000 -500 0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9Total frontogenesis


Hei

gh

t (km

)


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

1

2

3

4

5

6

7

8

9Maximum total frontogenesis at each height level

Frontogenesis (K/(100 km)/hour)

Hei

gh

t (k

m)

ControlFull perturbation

Half perturbation


ConclusionsConclusions

1.1. Forward-tilted cold fronts are characterized by a thermal gradient which Forward-tilted cold fronts are characterized by a thermal gradient which is both farther ahead of, and stronger than, that at the surface.is both farther ahead of, and stronger than, that at the surface.

2.2. They also appear to exhibit a characteristic lower-tropospheric potential They also appear to exhibit a characteristic lower-tropospheric potential temperature perturbation, with statically more stable air in the warm air temperature perturbation, with statically more stable air in the warm air and less stable air in the cold air.and less stable air in the cold air.

3.3. The Sawyer-Eliassen circulation implied by this perturbation (with The Sawyer-Eliassen circulation implied by this perturbation (with constant geost. deformation) inhibits frontal motion at the surface constant geost. deformation) inhibits frontal motion at the surface relative to that aloft. This is due mainly to the change in forcing relative to that aloft. This is due mainly to the change in forcing (Q),(Q), rather than the change in response modulation (PV).rather than the change in response modulation (PV).

4.4. The total frontogenesis (geost. + ageost.) resulting from this perturbation The total frontogenesis (geost. + ageost.) resulting from this perturbation moves the maximum frontogenesis away from the surface, to a height moves the maximum frontogenesis away from the surface, to a height near the top of the perturbation.near the top of the perturbation.

5.5. Frontogenesis is maximum above the surface as long as the potential Frontogenesis is maximum above the surface as long as the potential temperature gradient at the surface is no more than half that aloft. temperature gradient at the surface is no more than half that aloft.


Ongoing WorkOngoing Work

1.1. Examine effects of static stability contrasts in time-dependent Examine effects of static stability contrasts in time-dependent frontogenesis, using 2-D frontal models (e.g. Keyser and Pecnick 1988) frontogenesis, using 2-D frontal models (e.g. Keyser and Pecnick 1988) and 3-D baroclinic wave simulations.and 3-D baroclinic wave simulations.

2.2. Examine boundary-layer and precipitation processes that lead to, or feed Examine boundary-layer and precipitation processes that lead to, or feed back into, static stability contrasts.back into, static stability contrasts.



Why are fronts supposed to be tilted over the cold air and Why are fronts supposed to be tilted over the cold air and strongest at the surface?strongest at the surface?

Deformation Frontogenesis (QG)

y

z


Deformation Frontogenesis (SG)

Why are fronts supposed to be tilted over the cold air and Why are fronts supposed to be tilted over the cold air and strongest at the surface?strongest at the surface?

y

z

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