1. 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind ATOC 4720 class34

2. H L Northern Hemisphere (NH): P1 P2 P3 P4 P5 x y PGF CF Previous class: GEOSTROPHY:

3. Geostrophic wind value:

4. In PBL, friction is important. Frictional convergence toward the low pressure! Important! V cross the isobars!

5. Cross-isobar flow due to friction

6. The gradient wind

7. x y z 1.Smaller-scale convection : GEOSTROPHY BREAKS DOWN Observations for small-scale convection: Velocity U-V: 20 m/s; Time T (100-1000s)= S

8. Acceleration term: Coriolis term: Therefore, the Coriolis term can be NEGLECTED! Geostrophy breaks down! 0

9. 2. The vertical equation of motion In z direction: Newton’s second law of motion for unit mass: negligible Free atmosphere negligible Large-scale motion, T: 1day; W:10m/s: Even for T=1000s,

10. Hydrostatic balance Hydrostatic balance is well satisfied even by mesoscale convection. Exercise: find out for what scale convection (vertical velocity and timescale), hydrostatic balance can break down.

11. 3. Thermal wind relation Geostrophic wind speed: Perform vertical derivation: Between 2 layers:

12. Substitude (Z2-Z1) from the hypsometric equation (2.29) (for dry air)