1. Angular Momentum Cycle 1.Balance Equations 2.Angular Momentum in the Climatic System 3.Observations 4.Closing the Cycle of Angular Momentum

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

3. Angular Momentum in the Climatic System 1. Earth 2a. Atmosphere (solid rotation) sphere spherical shell 2b. Atmosphere (zonal wind, the relative angular momentum) M r  M r (DJF-JJA) NH~5.3  10 25 kg m 2 s -1 NH~9.4  10 25 kg m 2 s -1 SH ~7.6  10 25 kg m 2 s -1 SH ~-4.6  10 25 kg m 2 s -1 m e = m a ~10 6

4. 3. Ocean (very coarse estimate, no reliable measurements exist) a)Zonal circulation 45 0 0 100Sv NP -0. 5  10 25 kg m 2 s -1

5. The observed changes of the angular momentum of atmosphere are  5  10 25 kg m 2 s -1, Oceanic ones are< 1  10 25 kg m 2 s -1 -60 0 60 0 b) Meridional shift of air and water masses 30 0 0 + + +   z=2cm  P atm =2mb 0. 8  10 25 kg m 2 s -1 Conclusion: Adjustment of the solid Earth‘s rotation to the rotation of fluid Conclusion: Adjustment of the solid Earth‘s rotation to the rotation of fluid

6. Because the angular momentum is conserved Because M r DJF > M r JJA,  JJA >  DJF  LOD[ms ]=0.168  M r [10 25 kg m 2 s -1 ] If  M r =5x10 25 kg m 2 s -1  LOD=0.8ms The relative angular momentum can be computed actronomically, as well as from the observed velocities:  M r =5x10 25 kg m 2 s -1 correponds to  u=2m s -1.

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

12. Observations Ship reports Source Sink

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