Air mass models of fronts

Chapter 13

Air mass models of fronts

Margules’ model for a stationary front

Extension of Margules’ model to a moving front

 The question is: can Margules' model be extended to a uniformly translating front?

 Suppose we add a uniform geostrophic wind component normal to the surface front in both air masses.

 Would this give a more realistic, yet dynamically consistent solution?

 We can anticipate difficulties.

 Recall that in strict geostrophic flow over level ground with f = constant, the local surface pressure cannot change!

 Observations show that the approach of a warm front is

heralded by a fall in surface pressure, while the passage of a cold front is frequently accompanied by a sharp rise in

pressure.

 Such pressure changes may be expected simply on

hydrostatic grounds; for example, all things being equal, the replacement of warm air of density ₁ with a layer of colder air with density ₂ and depth d would constitute a surface pressure rise of g(₂  ₁)d.

 Hovever, according to Sutcliffe, there can be no surface

pressure change because a geostrophic wind blows parallel to the isobars. Recall that:

s h

0

p g dz g w

t ^

 

    





s h

0

p g dz g w

t ^

 

    





 Brunt (1939) showed that this is true even when there is an air-mass discontinuity.

 Significantly, Brunt's analysis assumes that there is no vertical motion on either side of the discontinuity, but it applies, neverthless, to the basic Margules' model.

The translating Margules' model

 The inconsistency in the naive extension of Margules' solution to a translating front is clearly exposed by considering the surface pressure distribution.

 First we rederive Margules' formula in a different way to that in Chapter 5.

2h 2 2

1 p

 f  

u  k _{1h 1}

1

1 p

 f   u  k

cold warm

w2

z 0

 



w1

z 0

 

 p₁ p₂

p₂ = p₁ + g(₂ – ₁)(h – z) h

z

2 1

2 2

1 p 1 p h

x x g x

     

    

2h  (0, v )2

u

1h  (0, v )1

u

cold warm

2 2

2

fv 1 p

x

 

 

1 1

1

fv 1 p

x

 

  

.

2 1

2 2

1 p 1 p h

x x g x

     

    

2h  (u , v )2 2

u

1h  (u , v )1 1

u

1 1

v 1 p

f x

 



2 2

v 1 p

f x

 



2 1

2

( )

g  g   

 Margules formula

2 1

f (v v ) g h

x

 

  



Before we assumed that  = 1

cold warm

2 2

2

fv 1 p

x

 

 

1 1

1

fv 1 p

x

 

 

Surface isobars in the moving Margules' cold front model in the case where there is no subsiding motion in the warm air overlying the frontal discontinuity.

Vertical cross-section of the moving Margules' cold front model when there is subsiding motion in the warm air overlying the frontal discontinuity

Mass flux contributions to the net surface pressure rise in a vertical column of air in the post-frontal region of the moving Margules' cold front

The uniformly translating cold front model of Davies (1984)

surface isobars

vertical cross-section

Cross-front variation of surface pressure at time t = 0

Time-series of surface pressure at x = 0

End of

Chapter 13