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Lackmann, Chapter 1: Basics of atmospheric motion time scales of atmospheric variability Lovejoy 2013, EOS time scales of atmospheric variability Lovejoy 2013, EOS (1) Scales of atmospheric motion Note two spectral extremes: [shifted x10 to right] (a) A maximum at about 2000 km (b) A minimum at about 500 km SD k 5 3 inertial subrange 1000 Gage and Nastrom (1985) 100 10 wavelength [km] 1 Energy cascade synoptic scale Big whirls have little whirls that feed on their velocity; and little whirls have lesser whirls, and so on to viscosity. -Lewis Fry Richardson FA=free atmos. BL=bound. layer L = long waves WC = wave cyclones TC=tropical cyclones cb=cumulonimbus cu=cumulus CAT=clear air turbulence From Ludlam (1973) Scales of atmospheric motion Markowski & Richardson 2010, Fig. 1.1 Scales of atmospheric motion • Air motions at all scales from planetary-scale to microscale explain weather: – planetary scale: low-frequency (10 days – intraseasonal) e.g. blocking highs (~10,000 km) – explains low-frequency anomalies size such that planetary vort adv > relative vort adv • hydrostatic balance applies • – v g b v g synoptic scale: cyclonic storms and planetary-wave features: baroclinic instability (~3000 km) – deep stratiform clouds smaller features, whose relative vort adv > planetary vort adv • size controlled by b=df/dy • hydrostatic balance applies • – mesoscale: waves, fronts, thermal circulations, terrain interactions, mesoscale instabilities, upright convection & its mesoscale organization: various instabilities – synergies (100-500 km) – stratiform & convective clouds time scale between 2p/N and 2p/f • hydrostatic balance usually applies • – 2p/N ~ 2p/10-2 ~ 10 minutes 2p/f = 12 hours/sin(latitude) = 12 hrs at 90°, 24 hrs at 30° microscale: cumuli, thermals, K-H billows, turbulence: static instability (1-5 km) – convective clouds Size controlled by entrainment and perturbation pressures • no hydrostatic balance • g Z f y Z RT ( 2) p gp (1) u g 1.4 thermal wind balance geostrophic wind hypsometric eqn ug plug (2) into (1) RT u g g gp p f y R T fp y finite difference expression: R p T u g f p y ug greater thickness ug=0 lower thickness y this is the thermal wind: an increase in wind with height due to a temperature gradient The thermal wind blows ccw around cold pools in the same way as the geostrophic wind blows ccw around lows. The thermal wind is proportional to the T gradient, while the geostrophic wind is proportional to the pressure (or height) gradient. Let’s verify qualitatively that climatological temperature and wind fields are roughly in thermal wind balance. For instance, look at the meridional variation of temperature with height (in Jan) Around 30-45 ºN, temperature drops northward, therefore westerly winds increase in strength with height. thermal wind The meridional temperature gradient is large between 30-50ºN and 1000-300 hPa Therefore the zonal wind increases rapidly from 1000 hPa up to 300 hPa. Question: Why, if it is colder at higher latitude, doesn’t the wind continue to get stronger with altitude ? There is definitively a jet ... Answer: above 300 hPa, it is no longer colder at higher latitudes... pT tropopause pT pT pT Z500 v g 500 g ˆ k Z 500 f Z500-Z1000 vg u g v g R T T R R ˆ , , k T p p p fp y x fp fp g g vT 500,1000 v g 500 v g1000 kˆ Z 500 Z1000 kˆ Z f f baroclinicity • • The atmosphere is baroclinic if a horizontal temperature gradient is present The atmosphere is barotropic if NO horizontal temperature gradient exists – the mid-latitude belt typically is baroclinic, the tropical belt barotropic • The atmosphere is equivalent barotropic if the temperature gradient is aligned with the pressure (height Z) gradient – in this case, the wind increases in strength with height, but it does not change direction equivalent barotropic baroclinic geostrophic wind at various levels cold Z warm T height temperature gradient gradient warm vT vg 2 vg1 vg1 vg1 cold 1.4.2 Geostrophic T advection: cold air advection (CAA) & warm air advection (WAA) highlight areas of cold air advection (CAA) & warm air advection (WAA) WAA CAA WAA & CAA geostrophic temperature advection: the solenoid method geostrophic wind: g g Z Z vg kˆ Z , f f y x g vg Z f geo. temperature advection is: vg T the magnitude is: g vg T Z T f the smaller the box, the stronger the temp advection fatter arrow: larger T gradient T Thermal wind and geostrophic temperature advection Let us use the natural coordinate and choose the s direction along the thermal wind (along the isotherms) and n towards the cold air. Rotating the x-axis to the s direction, the advection equation is: local T change T advection ∂T ∂T Vn , ∂ t ∂ n (not et hat ∂T 0) ∂ s where Vn is the average wind speed perpendicular to the thermal wind. The sign of Vn cold warm vT vg 2 vg1 VT Vn warm + VT Vn cold - Thermal wind and temperature advection ∂T ∂T Vn , ∂ t ∂ n ∂T (not et hat 0) ∂ s VT VT Vn ∂T >0 ∂ t WAA + Vn - ∂T <0 ∂ t CAA If the wind veers with height, Vn is positive and there is warm advection. If the wind is back with height, Vn is negative and there is cold advection. thermal wind and temperature advection Procedure to estimate the temperature advection in a layer: 1. On the hodograph showing the upper- and low-level wind, draw the thermal wind vector. 2. Apply the rule that the thermal wind blows ccw around cold pools, to determine the temperature gradient, and the unit vector n (points to cold air) 3. Plot the mean wind Vn , perpendicular to the thermal wind. Note that Vn is positive if it points in the same direction as n. Then the wind veers with height, and you have warm air advection. If there is warm advection in the lower layer, or cold advection in the upper layer, or both, the environment will become less stable. example y vT vg 850 vg1000 vg1000 Vn Vn 0 n s vg 850 x ∂T >0 ∂ t veering wind warm air advection between 1000-850 hPa friction-induced near-surface convergence into lows/trofs 1.5 vorticity shear and curvature vorticity a f a or ? a v a Hovmoller diagrams (Fig. 1.20)