ATOC 4720: class 10ATOC 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 4. Thickness & height of constant

pressure surfaces;pressure surfaces; 5. Reduction of pressure to sea 5. Reduction of pressure to sea

levellevel

1. The hydrostatic equation1. The hydrostatic equation

Hydrostatic equation:

Pressure at any level z:

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

2. Geopotential2. Geopotential

at z: work

Unit:

Depend only on z, not on the routeGeopotential height z:

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.

We know:

So,

Can be written as:

3. Scale height and the 3. Scale height and the hypsometric equationhypsometric equation

Assume an isothermal and dry atmosphere, Eqn:

and thus,

Hypsometric eqn.

Where,

For Tv=288K, we obtain H=8.5km.

However, T(z) varies with z, so we define:

4. Thickness and heights of 4. Thickness and heights of constant pressure surfacesconstant pressure surfaces

Estimate: Using measurement of P,T, humidity at (z) radiosonde data.

Example: Hurricane warm core.

5. Reduction of pressure to 5. Reduction of pressure to sea levelsea 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;