1. 1. The geostrophic wind: scale analysis 2. Effects of friction 3. The gradient wind ATOC 4720 class33

2. 1. The geostrophic winds: scale analysis Scale analysis: estimate the order of magnitude for each term, using the observed values. Very useful tool to identify the most important processes For unit mass, HORIZONTAL equation of motion:

3. Observed scales: Velocity V: 10-30 m/s; Time t (1 day): S; /S (Mid Latitude) Above from atmospheric Planetary boundary layer (PBL), friction is small (a=0).

4. Acceleration term: Coriolis term: The Coriolis term is one order of magnitude larger Than the acceleration term. In free atmosphere, friction is negligible. Therefore, to the lowest order: 0 0

5. Geostrophic balance: PGF is balanced by CF:

6. Horizontal equations of motion in component form In the above, we discussed the Vector form: In real situation, we often use component form:

7. Horizontal equation of motion in “x” direction, with a Unit vector “i”: (for simplicity, we look at local Cartesian coordinate:) x y z Similarly, In “y”:

8. Exercise: Perform scale analysis for each equation, to obtain geostrophy for each velocity component, using the observed scales provided earlier. Geostrophic winds: (P-vertical coordinate) (Z-vertical coordinate) Gestrophic winds:

9. H L Northern Hemisphere (NH): P1 P2 P3 P4 P5 x y PGF CF

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

12. 3. The gradient wind