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1.4 thermal wind balance geostrophic wind hypsometric eqn plug (2) into (1) finite difference expression: this is the thermal wind: an increase in wind with height due to a temperature gradient greater thickness lower thickness y ugug ugug 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. u g =0

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Lets 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)

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Around 30-45 N, temperature drops northward, therefore westerly winds increase in strength with height.

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The meridional temperature gradient is large between 30-50N and 1000-300 hPa thermal wind Therefore the zonal wind increases rapidly from 1000 hPa up to 300 hPa.

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Question: Why, if it is colder at higher latitude, doesnt the wind continue to get stronger with altitude ?

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There is definitively a jet...

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Answer: above 300 hPa, it is no longer colder at higher latitudes... tropopause

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Z 500

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Z 500 -Z 1000

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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 height gradient temperature gradient warm cold baroclinic warm cold geostrophic wind at various levels

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1.4.2 Geostrophic T advection: cold air advection (CAA) & warm air advection (WAA)

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highlight areas of cold air advection (CAA) & warm air advection (WAA) CAA WAA

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WAA & CAA

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geostrophic temperature advection: the solenoid method lower height Z greater Z geostrophic wind: warm cold warm cold lower Z greater Z fatter arrow: larger T gradient geo. temperature advection is: the magnitude is: the smaller the box, the stronger the temp advection

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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: Thermal wind and geostrophic temperature advection where is the average wind speed perpendicular to the thermal wind. local T change T advection The sign of + - VTVT VTVT warm coldwarm cold

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If the wind veers with height, is positive and there is warm advection. If the wind is back with height, is negative and there is cold advection. + - VTVT VTVT WARM COLD WAACAA Thermal wind and temperature advection

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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, perpendicular to the thermal wind. Note that 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. thermal wind and temperature advection

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example x y WARM COLD n veering wind warm air advection between 1000-850 hPa 10C 5C s

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friction-induced near-surface convergence into lows/trofs

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1.5 vorticity shear and curvature vorticity

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Hovmoller diagrams (Fig. 1.20)

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time scales of atmospheric variability Lovejoy 2013, EOS

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time scales of atmospheric variability

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Gage and Nastrom (1985) [shifted x10 to right] Note two spectral extremes: (a) A maximum at about 2000 km (b) A minimum at about 500 km 1 10010 1000 wavelength [km] (1) Scales of atmospheric motion inertial subrange

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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) 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

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Markowski & Richardson 2010, Fig. 1.1 Scales of atmospheric motion

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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 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 =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 2 /N and 2 /f hydrostatic balance usually applies microscale: cumuli, thermals, K-H billows, turbulence: static instability (1-5 km) convective clouds Size controlled by entrainment and perturbation pressures no hydrostatic balance 2 /N ~ 2 /10 -2 ~ 10 minutes 2 /f = 12 hours/sin(latitude) = 12 hrs at 90, 24 hrs at 30