1. ATOC 4720: class 10 1. The hydrostatic equation; 1. The hydrostatic equation; 2. Geopotential; 2. Geopotential; 3. Scale height, hypsometric eqn; 3. Scale height, hypsometric eqn; 4. Thickness & height of constant pressure surfaces; 4. Thickness & height of constant pressure surfaces; 5. Reduction of pressure to sea level 5. Reduction of pressure to sea level

2. 1. The hydrostatic equation

3. Hydrostatic equation:

4. Pressure at any level z:

5. Physics: P(z) is equal to the weight of the air In the vertial column of unit cross-sectional Area lying above that level.

6. 2. Geopotential at z: work Unit:

7. Depend only on z, not on the route Geopotential height z:

8. Geopotential height Z is used as the vertial Coordinate in most atmospheric applications. (e.g., weather map). Hydrostatic equation can be written as: : not directly measured.

9. We know: So, Can be written as:

11. 3. Scale height and the hypsometric equation Assume an isothermal and dry atmosphere, Eqn: and thus, Hypsometric eqn.

12. Where, For Tv=288K, we obtain H=8.5km. However, T(z) varies with z, so we define:

13. 4. Thickness and heights of constant pressure surfaces Estimate: Using measurement of P,T, humidity at (z) radiosonde data. Example: Hurricane warm core.

14. 5. Reduction of pressure to sea level Mountainous regions, P1 and P2, due to elevation; In order to isolate P change due to weather, we reduce P to sea level. Z=0 sea level;