1. Lecture 4 Effects of Cumulus on Large Scale Heat Budgets
Yanai, Esbensen and Chu (1972) The key paper outlining a framework for diagnostic studies of convective scale interaction

2. Why? We can take observations at scales of 100’s of km only
We can notice that dynamic and thermodynamic evolution of the flow is occurring due to the impacts of cumulus scale features that we cannot directly see
We need a consistent framework to assess this “apparent” effect

3. Define energy

4. Relationship with 1st Law

5. Mean Governing Equations
condensation
Average product => includes subgrid scale correlations, i.e. convection effects
evaporation
radiation

6. We can separate convection effects from effects of mena flow
Apparent Heat Source
Apparent Moisture Sink
Large Scale Response
Convective Scale Forcing
Can be Measured
Can be inferred

7. Apparent Moist Static Energy Source

8. Integrate Q1

9. Integrate Q2

10. Check on Accuracy

11. Cloud Model (Use Top Hat Averaging)

12. Average includes cloud and environment

13. Average includes cloud and environment

14. Diagnose vertical mass flux

15. Generalize a bit more

16. Note the observable Q1, Q2 and QR imply effect of cloud ensemble

17. Cloud Model

18. Idealization of Clouds

19. Conservation Eqs. for individual cloud “i”

20. Saturation Moist Static Energy

21. Simplify

22. Assumptions

23. Assumptions

24. Assumptions

25. Summary

26. Schematic of Model

27. Relationship between clouds and Q1, Q2

29. Total Ensemble Effect

30. Conditions at Cloud Base

31. Cloud Base (Continued)

32. Iterative Solution

33. Diagnostic flow from data

34. Subgrid scale forcing Implied from large scale flow

35. Subgrid scale forcing Implied from large scale flow