Presentation on theme: "1.4 thermal wind balance ug plug (2) into (1) ug ug=0 y"— Presentation transcript:
1 1.4 thermal wind balance ug plug (2) into (1) ug ug=0 y geostrophic windhypsometric eqnugplug (2) into (1)uggreater thicknessug=0lower thicknessyfinite difference expression:this is the thermal wind: an increase in wind with height due to a temperature gradientThe 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.
2 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)
3 Around ºN, temperature drops northward, therefore westerly winds increase in strength with height.
4 thermal windThe meridional temperature gradient is large between 30-50ºN and hPaTherefore the zonal wind increases rapidly from 1000 hPa up to 300 hPa.
5 Question:Why, if it is colder at higher latitude, doesn’t the wind continue to get stronger with altitude ?
12 baroclinicityThe atmosphere is baroclinic if a horizontal temperature gradient is presentThe atmosphere is barotropic if NO horizontal temperature gradient existsthe mid-latitude belt typically is baroclinic, the tropical belt barotropicThe atmosphere is equivalent barotropic if the temperature gradient is aligned with the pressure (height Z) gradientin this case, the wind increases in strength with height, but it does not change directionequivalent barotropicbaroclinicgeostrophic wind at various levelscoldcoldwarmwarmheight gradienttemperature gradient
13 1.4.2 Geostrophic T advection: cold air advection (CAA) & warm air advection (WAA)
14 highlight areas of cold air advection (CAA) & warm air advection (WAA)
16 geostrophic temperature advection: the solenoid method geostrophic wind:fatter arrow: larger T gradientcoldlower height Zgreater Zwarmgeo. temperature advection is:greater Zthe magnitude is:lower Zcoldwarmthe smaller the box, the stronger the temp advection
17 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 changeT advectionwhere is the average wind speed perpendicular to the thermal wind.The sign of +-VTwarmcold
18 Thermal wind and temperature advection WARMVTVTCOLD-+COLDWARMWAACAAIf 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.
19 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.
20 example COLD WARM y 5°C n s 10°C x veering wind warm air advection between hPa
21 friction-inducednear-surfaceconvergence into lows/trofs
31 time scales of atmospheric variability Lovejoy 2013, EOS “what is climate”: Dynamics and types of scaling variability: representative temperature series fromweather (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 (bottomto top: 2.86 K, 27.8 K, K, and 7.27 K; dashed lines indicate means). The resolutions are280 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); andVostok (Antarctica).Lovejoy 2013, EOS
32 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 surfaceseries (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 inAntarctica (EPICA) Antarctic series at a 50-year resolution. Also shown is the interglacialwindow (rectangle) and reference slopes H = −0.4, +0.4, −0.1, and −0.5 (Gaussian white noise).Lovejoy 2013, EOS
33 (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 subrange1000100101wavelength [km]Gage and Nastrom (1985)
34 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 RichardsonFA=free atmos.BL=bound. layerL = long wavesWC = wave cyclonesTC=tropical cyclonescb=cumulonimbuscu=cumulusCAT=clear air turbulenceFrom Ludlam (1973)