# 1.4 thermal wind balance ug plug (2) into (1) ug ug=0 y

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1.4 thermal wind balance ug plug (2) into (1) ug ug=0 y
geostrophic wind hypsometric eqn ug plug (2) into (1) ug greater thickness ug=0 lower thickness y finite difference expression: 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 ºN, temperature drops northward, therefore westerly winds increase in strength with height.

thermal wind The meridional temperature gradient is large between 30-50ºN and 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...
tropopause

Z500

Z500-Z1000

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 cold warm warm height gradient temperature gradient

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

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

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 where is the average wind speed perpendicular to the thermal wind. The sign of      + - VT warm cold

Thermal wind and temperature advection
WARM VT VT COLD - + COLD WARM WAA CAA 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.

thermal wind and temperature advection
Procedure to estimate the temperature advection in a layer: On the hodograph showing the upper- and low-level wind, draw the thermal wind vector. 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.

example COLD WARM y 5°C n s 10°C x veering wind  warm air advection
between hPa

friction-induced near-surface convergence into lows/trofs

1.5 vorticity shear and curvature vorticity

Hovmoller diagrams (Fig. 1.20)

time scales of atmospheric variability
Lovejoy 2013, EOS “what is climate”: Dynamics and types of scaling variability: representative temperature series from weather (space scales and timescales), macroweather, and climate scales (bottom to top, respectively). Each sample is 720 points long and was normalized by its overall range (bottom to top: 2.86 K, 27.8 K, K, and 7.27 K; dashed lines indicate means). The resolutions are 280 meters, 1 hour, 20 days, and 1 century, and the data are from an aircraft at 200 mbar (north Pacific); Lander, Wyoming; the twentieth century reanalysis (20CR, 75°N, 100°W); and Vostok (Antarctica). Lovejoy 2013, EOS

time scales of atmospheric variability
Temperature standard deviations S(Δt). (top left) Grid point scale (2° × 2°) daily fluctuations globally averaged from the 20CR. (bottom left) The same fluctuations, but for the global average (brown line), and the average of the three in situ global surface series (red line) as well as S(Δt) from three multiproxy Northern Hemisphere reconstructions (green line) [see Lovejoy and Schertzer, 2012a]. (right) The European Project for Ice Coring in Antarctica (EPICA) Antarctic series at a 50-year resolution. Also shown is the interglacial window (rectangle) and reference slopes H = −0.4, +0.4, −0.1, and −0.5 (Gaussian white noise). Lovejoy 2013, EOS

(1) Scales of atmospheric motion
Note two spectral extremes: (a) A maximum at about 2000 km (b) A minimum at about 500 km [shifted x10 to right] inertial subrange 1000 100 10 1 wavelength [km] Gage and Nastrom (1985)

Energy cascade synoptic scale FA=free atmos. BL=bound. layer
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 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 mesoscale: waves, fronts, thermal circulations, terrain interactions, mesoscale instabilities, upright convection & its mesoscale organization: various instabilities – synergies ( km) – stratiform & convective clouds time scale between 2p/N and 2p/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 2p/N ~ 2p/10-2 ~ 10 minutes 2p/f = 12 hours/sin(latitude) = 12 hrs at 90°, 24 hrs at 30°

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