1. ATOC 4720 class31
1. Coordinate systems
2. Forces

2. 1. Coordinate systems Dynamics: equations govern atmosphere motion
Fundamental law: Newton’s second law of motion
: net forces (N)
:mass (kg)
: acceleration ( )

3. Fixed frame in space:
Rotational frame: on earth: convenient
Newton’s second law: real forces
Convert from fixed fram to rotational frame:
see handout
During the process of conversion, an additional
force appears: Coriolis force, due to the earth’s
rotation

4. Horizontal coordinates
Spherical coordinate system rotating with the earth
Longitude
Latitude

5. the distance from earth’s center to the location of motion
For motion below 50km:
Error <1%

6. Vertical coordinate Geopotential height: Geopotential at
mean sea level
Average acceleration of gravity at sea level
With this choice, horizontal planes coincide with
with constant geopotential surface, and gravitational force does
not have horizontal component (below 50km, close to be
geometric height)

7. In this coordinate system, velocity components are:
Total velocity vector:

8. P and vertical coordinates
P coordinate: some equations are simpler using
P instead of Z coordinate
Convertion from Z to P: hydrostatic equation
Scientific basis: prompt class
Vertical velocity: ( )

9. Coordinate: terrain following
Since both Z and P coordinates sometimes intersect
topography at lower level, making PGF term difficult
to calculate P Z
We often use
Coordinate: terrain following
Surface pressure
at surface

10. Hybrid coordinate: NCAR CCSM
Lower levels:
Higher levels P

11. 2. Forces
PGF
Gravity
Friction-important in PBL (planetary boundary layer)
Coriolis force (apparent force, due to the earth’s rotation)

12. PGF: see blackboard