Propagation of a Front, Encountering a Cold Air Layer

1
Propagation of a Front, Encountering a Cold Air
Layer

• Jeroen Derksen
• u.s.o. Aarnout van Delden

2
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

3
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

4
Introduction

• Typical setting over western Europe during
  winter.
• Cold air over Land.
• Relatively warm Sea.
• Decreasing propagation of a front
• Hard to forecast.
• Arrival of warm air forecasted to early
• Stalling front over cold air
• snow, sleet
• Hazardous weather.

5
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

6
Case Study

• 5 and 6 January 1995
• Satellite Infrared Photos
• ECMWF-data
• Height and Temperature of 1000hPa surface
• Equivalent Potential temperature
• Cross-section over the Netherlands

7
Case Study
Infrared Satellite Pictures
0903UTC 5 Jan
1942UTC 5 Jan
0936UTC 6 Jan
8
Case Study II
Isotherms and Height 1000hPa Sfc.
00UTC 5 Jan
9
Case Study III
Equivalent Potential Temperature 700hPa Sfc.
12UTC 5 Jan.
10
Case Study IV
Equivalent Potential Temperature 700hPa Sfc.
00UTC 6 Jan.
11
Case Study VI
Equivalent Potential Temperature 700hPa Sfc.
12UTC 5th
00UTC 5th
00UTC 6th
12UTC 6th
12
Case Study VII
Cross-section 52N, 5 Jan
00UTC
12UTC
13
Case Study VIII
Cross-section 52N, 6 Jan
00UTC
12UTC
14
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

15
Basic Equations

• Full set of Equations are not solvable
• Range of approximated sets developed.
• Geostrophic Balans
• Geostrophic momentum approximation

16
Geostrophic Balans

• Geostrophic Balans.
• Hydrostatic Balans
• Thermal Wind Balans

17
Thermal Wind Balance

• Difference in sign.
• Geostrophic disturbance leads away from thermal
  wind balance.
• Ageostrophic motion needed.

18
Geostrophic Momentum Approximation
19
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

20
Frontogenesis

• Geostrophic
• confluence of temperature field due to
  geostrophic wind field
• rotation of isentropes due to geostrophic shear
• Ageostrophic
• tilt of vertical temperature gradient onto
  horizontal due to horizontal gradient in vertical
  velocity
• differential diabatic heating

21
Frontogenesis II
22
Frontogenesis III
23
Frontogenesis IV
24
Frontogenesis V

• Radiation
• Latent Heat

25
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

26
Sawyer-Eliassen Eqn.

• Cross-frontal Circulation
• Based on Geostrophic Momentum Approximation.
• Assumptions
• Straight Front
• 2 Dimensional Front
• Coriolis Parameter Constant

27
System

• 2D
• Straight
• Cross-frontal circulation.

28
Sawyer-Eliassen Eqn. II

• ? Streamfunction
• a Measure of Static Stability
• b Cross-Frontal Temperature Gradient
• c Geostrophic Absolute Vorticity
• F Geostrophic Forcing

29
Examples
Reference Circulation
30
Examples II
Sign forcing changed
31
Examples III
a smaller
32
Examples IV
c larger
33
Examples V
Neg.
Pos.
b larger
34
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

35
Model

• No Differential Diabatic heating
• No North-South Temperature Gradient

36
Model II

• All the variables are obtained, using ECMWF-data,
  except for y.

37
Model III

• Solving S-E, using the Relaxation Scheme.
• Guessed Solution -gt Residu
• Residu -gt Next Solution
• etc.
• -gt Right Solution

38
Model IV

• Guessed solution on iteration step m
• Suppose next iteration step, m1, gives correct
  answer, using the old values of ? on step m on
  the surrounding gridpoints

39
Model V
40
Model VI
Boundary conditions

• Bottom ? 0.
• Both sides vertically integrated ua,, obtained
  from ECMWF-data.
• Top
• Difference both sides
• Continuity
• Difference spread over top

41
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

42
Result

• Sawyer-Eliassen Equation
• Forcing Geostrophic confluence
• Influence Boundaries?
• Larger Domain 19WL-29EL

43
Result 00UTC 5 Jan
red calculated circulation green observed
ageostrophic circulation
44
Result 06UTC 5 Jan
red calculated circulation green observed
ageostrophic circulation
45
Result 12UTC 5 Jan
red calculated circulation green observed
ageostrophic circulation
46
Result 18UTC 5 Jan
red calculated circulation green observed
ageostrophic circulation
47
Result 00UTC 6 Jan
red calculated circulation green observed
ageostrophic circulation
48
Contents

• Introdction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

49
Discussion

• 5 January Results are good.
• 6 january Results are not good.
• Which of the neglected terms is responsible?
• Confluence by total wind field
• Shear-term
• Tilting-term
• Differential Diabatic Heating

50
Discussion II

• Confluence by total wind field adds nothing new.
• Shear term stronger on the fifth than on the
  sixth.
• Tilting term to weak.
• Differential Diabatic heating?

51
Discussion III
Diabatic heating

• Time mean of 6 hours

Differential Diab. Heating
52
Discussion IV
Circulation, taking Diff. Diab. Heating into
account
06UTC 5 Jan.
red calculated circulation green observed
ageostrophic circulation
53
Discussion V
Circulation, taking Diff. Diab. Heating into
account
18UTC 5 Jan.
red calculated circulation green observed
ageostrophic circulation
54
Discussion VI
Circulation, taking Diff. Diab. Heating into
account
00UTC 6 Jan.
red calculated circulation green observed
ageostrophic circulation
55
Discussion VII
Circulation, taking Diff. Diab. Heating into
account
06UTC 6 Jan.
red calculated circulation green observed
ageostrophic circulation
56
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

57
Conclusion

• A circulation cell is present over the boundary
  of the cold air.
• It is present, partly due to
• confluence of the temperature field by the
  geostrophic wind field
• Differential Diabatic Heating
• This cell is responsible for an easterly wind at
  the surface.
• The advection of cold air by this wind physically
  blocks the oncoming warm air.

58
Contents

• Introduction
• Case Study
• Theory
• Basic Equations
• Frontogenesis
• Sawyer-Eliassen Equation
• Model
• Result
• Discussion
• Conclusions
• Recommendations

59
Recommendations

• Use higher resolution, in time and space.
• Make a more general model
• Dont assume the front to be North-South.
• Dont assume the front to be straight.
• Use a 3D model.
• Beware that processes are easily recognized.
• Study more events.

60
Any Questions?