Angular Momentum Cycle

1. Angular Momentum Cycle Balance Equations Angular Momentum in the Climatic System Observations Closing the Cycle of Angular Momentum

2. Angular momentum of a parcel with unit mass Balance Equations The total angular momentum of the Earth remains constant is the moment of force (torque). If the total torque vanishes M Mr rR Eq.:

3. 1. Earth Angular Momentum in the Climatic System sphere 2a. Atmosphere (solid rotation) spherical shell me= ma~106 2b. Atmosphere (zonal wind, the relative angular momentum) • Mr Mr (DJF-JJA) • NH~5.31025kg m2 s-1NH~9.41025kg m2 s-1 • SH ~7.61025kg m2 s-1SH ~-4.6 1025kg m2 s-1

4. NP 3. Ocean (very coarse estimate, no reliable measurements exist) • Zonal circulation 450 -0.51025kg m2 s-1 100Sv 00

5. b) Meridional shift of air and water masses + + + 300 z=2cm 0.81025kg m2 s-1 Patm=2mb 00 The observed changes of the angular momentum of atmosphere are 51025kg m2 s-1, Oceanic ones are< 11025kg m2 s-1  600 -600 Conclusion: Adjustment of the solid Earth‘s rotation to the rotation of fluid

6. Because MrDJF > MrJJA , JJA > DJF LOD[ms ]=0.168 Mr[1025kg m2 s-1] If Mr=5x1025kg m2 s-1LOD=0.8ms The relative angular momentum can be computed actronomically, as well as from the observed velocities: Mr =5x1025kg m2 s-1 correponds to u=2m s-1. Because the angular momentum is conserved

10. Angular Momentum in the Atmosphere Multiply the equation of momentum with Have in mind: Pressure, Friction Torques } Tropics-source Mid-latitudes-sink Meridional Transportt of angular momentum

12. Observations Ship reports Sink Source

15. Closing the Cycle of Angular Momentum Wind~10ms-1 Currents~ 10-2ms-1 -10-1ms-1 Small contribution of the oceanic transport