1. ATOC 4720 class35 1. The thermodynamic energy equation
2. The continuity equation

2. Previous classes Horizontal: vector form: Components:
Vertical equation of motion:

3. Brief Review of previous a few classes:
Geostrophic wind value:
T- days
Mid-latitude

4. Cross-isobar flow due to friction

5. The gradient wind

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

7. Hydrostatic balance Hydrostatic balance is well satisfied even by
mesoscale convection.

8. Thermal wind relation

9. 1. Thermodynamic energy equation
Rewrite hydrostatic equation: (show math on blackboard)

10. Obviously, we have 3 equations, 4 unknowns
We need an equation for T. [Prompt]

11. The first law of thermodynamics says:
Denote as the heating rate:

12. Since
So,
Substituting into the above equation and denote
Where,

13. Physics: Temperature change is determined by:
[1] the rate of adiabatic heating or cooling due to
compression or expansion;
[2] the rate of diabetic heating.

14. Scale analysis: estimating the relative important of
adiabatic and diabetic heating:
[1]: Adiabatic heating:
Typical pressure change over the course of a day
following an air parcel
In mid latitude mid-troposphere,

15. [2] Diabetic heating: absorption of solar radiation,
absorption and emission of infrared radiation,
latent heat release, in upper atmosphere,heat absorbed
or liberated in chemical & photochemical reactions.
Diabetic mixing with environment (latent & sensible).
In lower atmosphere, sources and sinks tend to balance each
other. As a result,

16. Note that all time-dependent term we introduced so far is:
Time change following an individual air parcel. (Lagrangian)
In most cases, we wish to know time change at a
Specific location, say T change over Boulder.
Local change: Eularian change.

17. Since
We obtain
Because,
We have

18. 3-d advection
Local change
Individual change
Cold T
Warm T Tb Ta
Boulder
Mountain in the west