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Global Circulation

Stull Chapter 11

Radiative Differential Heating Net radiative heating in tropics and net radiative cooling at poles creates and imbalance in the atmosphere/ocean system.
Thermal Wind Relationship The relationship between horizontal and vertical temperature gradient of geostrophic wind. dUg/dz=(-g/Tvfc)(dTv/dy) dVg/dz=(g/Tvfc)(dTv/dx) The north-south temperature gradient alters the east-weest geostrophic winds with height, and vice versa.
Thermal Wind Components UTH=Ug2-Ug1=-(g/fc)(dTH/dy) VTH=Vg2-Vg1=(g/fc)(dTH/dx) *Implies that the thermal wind is parallel to the thickness contours (cold temps to left in N hemisphere).
What is the Thermal Wind? The vector difference between geostrophic winds at two different heights or pressures.
Troposphere Trends The tropopause is lower near poles than near equator. Causing the air over the equator to be colder and warmer over the poles in the stratosphere.
Thickness vs. Isobars Greater TH btwn P sfcs in warmer equatorial air than colder polar air causes isobars to become more tilted at mid-latitudes as tropopause is approached. Regions with greatest tilt have greatest S-N P gradient -- drives fastest geostrophic wind.
Jet Stream Fast geostrophic wind occurs in region greatest S-N P gradient; @ tropopause in mid-lat; move N in summer, S in winter. Velocity +, E-W, in N/S hemis. Mark boundary btwn cold air & warm air b/c T dif generates jet stream winds (thermal wind relationship).
Jet Stream Speeds Actual average speeds of 40 m/s are observed over a three-month average in the winter hemisphere. Velocities up to 100 m/s can be observed on individual days.
Angular Momentum- Theoretical Eastward angular momentum conserved as it moves northward from a source latitude [phi]s to a destination [phi]d.
Angular Momentum and the Earth Radius - Earth's axis to [phi]: R[phi]=ReCos([phi]) Tangential velocity - Earth at [phi]: U[phi]=[omega]R[phi]=[omega]ReCos([phi]) Air parcel - source to dest., velocity relative to Earth: U'=[omega]Re((Cos([phi]s)^2/Cos([phi]d))-cos([phi]d)).
Angular Momentum - Actual Angular momentum is not conserved b/c P gradient, Coriolis, and turbulent drag forces act on the air. The actual vertical circulation pattern extends only to about 30 deg N and S (Hadley Cell).
Relative Vorticity A measure of the rotation of fluids about a vertical axis relative to Earth's sfc. Positive in counterclockwise direction. [Zeta]r=dV/dx-dU/dy [Zeta]r=-dM/dn+M/R If the fluid is rotating as a solid body, [Zeta]r=2M/R
Absolute Vorticity Measure with respect to "fixed" stars. Earth's rotation in addition to the relative vorticity. [Zeta]a=[Zeta]r+fc The Coriolis parameter is a measure of the vorticity of the planet.
Potential Vorticity Absolute vorticity divided by depth of rotating column of air. [Zeta]p=([Zetar]r+fc)/dz=constant Conserved in the absence of turbulent drag and heating.
Vorticities Combined If rotating column of air is stretched vertically, then relative vorticity must increase or move further N where planetary vorticity is greater. Relative={Shear={-dM/dn} Curvature={M/R}} Planetary={fc} Stretching={[Zeta]p(dz)} -dM/dn+M/R+fc=[Zeta]p(dz
Planetary Waves The jet stream meanders N and S in a wavy pattern due to instabilities in the atmosphere as they circle the globe. average wavelength of 3000 km to 4000 km.
Created by: lawli