General circulation and meteorology B. Legras, IV Cloud systems associated with fronts

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1 General circulation and meteorology B. Legras, IV Cloud systems associated with fronts 1

2 Outline 1. Cloud systems associated with frontogenesis. Symmetric instability 3. Complements

3 Cold front from space observations 3 From the satellite meteorology course of ZAMG

4 Cold and warm fronts from satellite observations 4

5 Schematic of the cloud systems associated with warm and cold fronts 5

6 Radar images of the development of a cold front (radars waves are reflected by precipitating droplets) 6

7 7

8 8

9 Transverse section of the cloud structure associated with a cold front R.A. Houze 9

10 Band structure of the precipitations (radar) 10

11 Vertical motion over a narrow band Rapid drop of the temperature Initial stage of a cold front Two types of cold fronts The front moves forward faster than the flow. Less steep and vigourous than the kata front. Extended bands of precipitations. Mature stage of a cold front. 11

12 Outline 1. Cloud systems associated with frontogenesis. Symmetric instability 3. Complements 1

13 Inertial instability (prerequisite) Assumptions: (1) The basic flow is constant and geostrophic, such as u = w =0 and v =v g ( x), () The perturbed flow does not depend of y or z The absolute momentum is defined by M v + fx Equations of motion in x et y are therefore Du = f (M M g) Dt DM =0 Dt where M g =v g + f x is the moment of the basic low. By combining these two equations, we have Mg D u +u f =0 x Dt which appears as an harmonic oscillator equation for u. The stable or unstable nature of the oscillations depends of the sign of M g vg = +f x x In general, v g / x is dominated by f and the oscillations exhibit a frequency μ=± f ( v g / x + f ) close to f. 13 However, for v g / x + f <0 in the northen hemisphere, that is when the absolute vorticity is negative, an instability occurs. The rule is inverted in the southern hemisphere.

14 If the absolute vorticity remains negative, inertial oscillations ensue (southern hemisphere) 14

15 Symmetric instability (slantwise convection) A flow which is stable regarding both the inertial instability (in the horizoantl) and the convective instability (in the vertical) may be unstable with respect to slanted motion. The basic flow v g ( x, z) is quasi -geostrophic and independent of y. It satisfies the thermal wind balance f z v g = x b Thus, the generation of v ' depends on the angle of the trajectories of air parcels d'air moving sloping as with (u ',w ' ) with the surface M / z M F / S. x M with f v g = x ϕ The generation of b ' depends on the angle The non-hydrostatic Boussinesq equations with the surface b sloping as x b / z b S / N s. are linearized with respect to this We have used F, S N s defined earlier and we have basic flow by separating each field t b '= u ' S w ' N,s as a mean component ( b, ϕ ) t ( f v ' )= u ' F w ' S, plus a pertubation (u ', v ', w ', b ', ϕ ' ). hence We assume the perturbation is independent t ( z u ' x w ' )= f z t v ' x t b ' of y. The equations are = F z u ' + S ( x u ' z w ' )+ N s x w ' t u ' f v ' + x ϕ '=0 using S = F and N = S. x z x s z t v ' +u ' x v g +w ' z v g + f u ' =0 By introducing agian the vertical streamfunction t w ' b ' + z ϕ ' =0 t b ' +u ' x b +w ' z b =0 ψ, such that u '= z ψ et w ' = x ψ, x u ' + z w ' =0 we obtain = f x+ v g, the equation in v ' By denting M t ( x ψ+ z ψ)= F z ψ+ S x z ψ N s x ψ is + w ' z M =0 t v ' +u ' x M 15

16 Symmetric instability (continued) t ( x ψ+ z ψ)= F z ψ+ S x z ψ N s x ψ Within a finite domain, we look for a solution under i σ t i K ( x sin φ+ z cos φ) the form ψ=ψ0 e e, yielding the dispersion equation σ =N s sin φ S sin φ+ F cos φ Notice that there is no dependency in K! 1) Inertial oscillations : φ=0 et σ= F ) Brünt-Vaissala oscillations: φ= π et σ =N s 3) General case, we write σ =N s + F A cos (φ ϕ1 ) 16 The flow is unstable iff σ min <0 or q<0, ( M b) that is <0 ( x, z ) where A= ( N s F ) + 4 S 4 and the angle ϕ 1 is defined N s F S by sin ( ϕ 1)= and cos ( ϕ 1 )=. A A Introducing the Richardson number 1 Hence: σ min σ max = [(N s + F ) A ]= N s F S 4 z b f N 4 Ri= = 4, which characterizes Since the potential vorticity of the basis flow is ( z v g ) S 1 the ratio between thermal stratification q= z v g x b+( f + x v g ) z b= ( S 4 + N s F ) f and shear, the instability criterion is we have σ min σ max = f q. f R i <, that is Ri <1 si f x v g F Again, the criterion on q is reversed is the southern hemisphere

17 Generalisation of the symetric instability to the moist case and comparison with the convective and inertial instabilities Condition Convective al Inertial Symmetric Dry θ Inertial instability f+ζ < 0 Absolute symmetric instability PV < 0 () Absolute convective instability dθ/dz <0 (1,) Potential Potential convective instability dθe/dz < 0 θe N/A Condition Conditional convective N/A instability dθe*/dz < 0 -nal θe* 17 (1) : ζ= v g ug x y Potential symmetric instability Pve < 0 () Conditional symmetric instability Pve* < 0 () () : Revert the sign of the inequality in the southern hemisphere

18 R.A. Houze Symmetric instability for the generation of precipitation bands Region with negative PV We have here the moist moist potential vorticity where θ is replaced by θe. In the same way as the convective instability, the symmetric instability is potential, being realized only after saturaion is reached in the layer. 18

19 Indications that slantwise convection mixes cloudy air in the frontal region to make parallel the surfaces of moment M et of equivalent potential temperature. 19 K. Emanuel

20 It is easier to foresee the preence of a region of potential instability from the moist potential vorticity than from the diagramme of moment / potential temperature. 0

21 Attention: The conditional or potential symmetric instability is not enough to forecast the formation of precipitation bands. An ascending motion and air close to saturation are also requiredwhen these three conditions are met together in synoptic maps, the occurrence of precipitation bands can be forecasted. frontogenesis = d θ dt The 3 conditions are satisfied 1

22

23 Outline 1. Cloud systems associated with frontogenesis. Symmetric instability 3. Complements 3

24 Formation of convective zones above a stratiform cloud and crystal fallout R.A. Houze 4

25 Convective and stratiform precipitations 5 R.A. Houze

26 Stratiform precipitations formed by seeding precipitating crystals from the convective zone aloft. R.A. Houze 6

27 To go further book de R. Houze, Clouds dynamics, Academic Press book de Cotton, Bryan et van den Heever, Storm and cloud dynamics, Academic Press Course on the concept of symetric instability and its application Interactive course of satellite meteorology Ensemble of courses of meteorology intended for previsionists Review article by R. Houze on the mesp-scael convective systems 7

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