1 This is the footer Midlatitude Weather systems Geraint Vaughan University of Manchester NCAS Director of Observations

Surface weather chart for 3 January 2007 (UK Met Office) 1110 km: 1° lat = 111 km

Salient features ● Surface pressure pattern dominated by highs and lows, on a scale ~ 10 3 km. We call this the synoptic scale

Salient features ● Surface pressure pattern dominated by highs and lows, on a scale ~ 10 3 km. We call this the synoptic scale ● Pressure excursions around ± 30 mb – much smaller than the total pressure of ~1000 mb.

Salient features ● Surface pressure pattern dominated by highs and lows, on a scale ~ 10 3 km. We call this the synoptic scale ● Pressure excursions around ± 30 mb – much smaller than the total pressure of ~1000 mb. ● Isobars give an indication of the wind speed by the geostrophic relation: wind tends to flow along isobars and its strength is proportional to pressure gradient

Time scale 00 h 3/1/07 00 h 4/1/07 Weather system takes ~ 1 day to pass over the UK – so synoptic timescale is around a day (10 5 s)

Fronts AVHRR IR image /1/07

Cold and warm fronts Cold front: narrow (~100 km), steep, can get line convection particularly on leading edge Warm front: broad (~300 km), layer cloud due to gentle upglide. Convection unusual. Motion of front Warm air Cold Air Warm air Cold Air

Occluded front Warm-type occlusions are much more common than cold type. This is determined by the static stability in the warm and cold frontal zones, not by the temperature difference between the two cold air masses Warm air Cold, unstable air Cold, stable air

Momentum equation The basic equation of dynamics is F=ma, Newton’s law. In the case of the atmosphere this equation becomes (a=F/m): On the left hand side is the acceleration of an air parcel The  p term is the pressure gradient acceleration The fkxU term is the Coriolis acceleration; f=2 Ω sin( λ ) where Ω is the Earth’s rotation rate and λ the latitude Geostrophy is defined by balance of the pressure gradient and Coriolis acceleration; the Geostrophic wind is then Geostrophic wind is proportional to pressure gradient and directed along isobars

Pressure coordinates Over the synoptic scale the atmosphere is very close to hydrostatic balance: We can use this fact to eliminate density from the momentum equation: This gives us a momentum equation which doesn’t include density: U is the horizontal wind velocity k is a unit vertical vector z is the height of a pressure surface.

Pressure surfaces: representing the flow above the surface Smoother patterns than at the surface; fronts not marked on these charts 700 and 300 mb charts show a similar pattern – synoptic scale features are generally coherent throughout the troposphere. That is, vertical scale of synoptic-scale features ~ 10 km Winds closer to geostrophic – no surface friction Very strong winds at 300 mb denote the jet stream. Jet stream is related to fronts, either at the surface or in the upper troposphere. Westerly winds increase with height: thermal wind equation vertical wind shear  horizontal T gradient 700 mb, ~ 3 km 300 mb, ~ 9 km

Fronts and jet streams in the general circulation Source: wikipedia Subtropical jet stream (actually the stronger of the two) is at the poleward edge of the Hadley circulation and is associated with an upper tropospheric front (no weather!) Polar jet stream is associated with the polar front. Note that the front must tilt with height otherwise a pressure discontinuity forms above the surface (∂p/∂z  1/T)

Formation of weather systems The commonest depiction of the formation of a weather system is the so-called Norwegian Model (e.g. Bjerknes and Solberg 1922) i.e. a small cyclonic perturbation grows on the polar front, pushing warm air poleward and cold air equatorward

Norwegian model of mature cyclone This was the first depiction in the literature of the schematic structure of a cyclone. All cyclones are different and most don’t look quite like this. But there are some salient features

Shapiro-Keyser model Frontal fracture Warm seclusion Isotherms A front is a region of strong temperature gradient. In the Norwegian model the cold front is the dominant feature; in the S-K model the warm front dominates From Schultz et al 1998

Why do cyclones form? Pressure is the weight of the air above you. So, if the pressure falls there must be less air above you – there must be divergence of air from the column above you We can formally express the wind as the sum of two components: U = U g + U a U g is the geostrophic wind and U a the ageostrophic wind. Now the divergence of U g is zero.

Ageostrophic wind Divergence is a property of the ageostrophic wind. We can write this as follows: i.e. the ageostrophic wind is proportional to acceleration, and is directed to the left (in the NH) when the flow accelerates U a, and hence divergence, is greatest at jet stream level. Indeed the pattern of the jet stream can initiate cyclone development

Convergence and divergence around a maximum in the jet stream Jet dU dt n Isotachs A B Jet Divergence Convergence dU dt > 0 < 0 acceleration UaUa Diagrams show a section of a 300 mb chart with a jet streak – a wind maximum. This induces C and D patterns in the air either side: C gives descent (p increase at surface) D gives ascent (p decrease at surface) “Vacuum cleaner effect”

Convergence and divergence forced by meanders in the jet stream U Convergence Divergence Air has to slow down to go round a trough, because the pressure gradient force must now provide a centripetal acceleration as well as balancing the Coriolis – therefore Coriolis force must weaken. The opposite is true in a ridge. Trough Ridge Trough-ridge patterns (short-wavelength Rossby waves) set up the conditions where low- level cyclones develop. But these patterns are themselves generated by the weather systems! So it’s chicken and egg…..

Growth of weather systems Jet stream Surface cyclone advects cold air south behind it and warm air north ahead of it. This changes the average temperature of the troposphere in those regions, intensifying the upper-air pattern Growth of cyclone -> distortion of jet stream -> more ageostrophic motion -> continued divergence -> growth of cyclone This process is called baroclinic instability. It requires conditions in the upper and lower troposphere to match up

Warm conveyor belt Low-level airstream flowing along and ahead of the cold front, and up and over the warm front. The most prominent airflow in a cyclone Very important for transporting pollutants out of the boundary layer Green: low altitude Yellow: high altitude This picture shows a kata-cold front, where the main ascent is over the warm front (ana- warm front). It is possible for most of the WCB flow to be up the cold frontal surface – this would be an ana-cold front.

Conveyor belt patterns: airflow w.r.t depression centre Mature cyclone, on the point of occluding Occluding cyclone. As the surface low intensifies, first the CCB then the WCB start to turn cyclonically. Bader et al 1995

Thermal wind equation Geostrophic relation in p coordinates takes the form: By differentiating this wrt pressure, we can derive an expression for wind shear, vertical gradient of horizontal wind: using ρ=p/rT from the ideal gas law So, vertical wind shear  horizontal T gradient: Jet streams and fronts are intimately linked