1. Virtual temperature
AMS glossary: (
virtual temperature—(Also called density temperature.) The virtual temperature is computed from Tv = T(1 + rv/ ε)/(1 + rv), where rv is the mixing ratio of water vapor and ε is the ratio of the gas constants of air and water vapor, ≈
Always warmer than the physical temperature (corresponds to decrease in density due to water vapor; biggest deviations in moist boundary layer).
The virtual temperature allows the use of the dry-air equation of state for moist air, except with T replaced by Tv.
The virtual temperature is the temperature that dry dry air would have if its pressure and density were equal to those of a given sample of moist air.
For typical observed values of rv, the virtual temperature may be approximated by Tv = ( rv) T.
Some authors incorporate the density increment due to liquid or solid water into virtual temperature, in which case the definition becomes Tv = T(1 + rv/ε)/(1 + rv + rl) ≈ T( rv − rl), where rl is the liquid or liquid plus solid water mixing ratio.

2. Mass-based Ideal Gas Law
“d” means dry air; “v” refers to water vapor
“qv” is commonly used notation for specific humidity, mass of water vapor per mass of dry air
(the variable on the skew-T diagram)

3. Virtual temperature, Tv = (1 + 0.61 qv) T

4. Why do we need virtual temperature?
cf: Chapter 5 in Lamb & Verlinde
When we calculate bouyancy forces, we are dealing with the net forces that arise because of density differences. To relate air density to measured quantities (e.g., T), we need the Ideal Gas Law to be written for variable average molecular weights that arise due to variable water vapor contents.
Net vertical force:
Bouyancy is expressed as a net force per unit mass (positive = upward):
Subscript p= parcel
Others = surrounding air
We must adjust soundings for Tv before we compute buoyancy or CAPE
We had to use virtual temperature, since we substituted from the mass-based Ideal Gas Law

5.
Figure 1. Schematic sounding, showing the processes with and without the virtual correction (see the key). The parcel ascent curve is for the surface parcel.
The process of making the virtual correction to the parcel ascent trace occurs only after having computed the uncorrected parcel ascent curve. Never use the corrected sounding profile to compute the parcel ascent curve! The virtual correction to the parcel ascent curve uses the dewpoint of the ascending parcel (which is along the mixing ratio line below the saturation point, and is equal to the temperature along the moist adiabat which the parcel ascends at and above the saturation point). The LCL is the same as that found using the uncorrected parcel ascent process, whereas the CAPE, CIN, LFC, and EL should be found from the corrected sounding and parcel ascent traces.

6. Convection and associated microphysics
Cartoons and writeup showing convective cloud life cycle (discuss briefly)
What’s a “cold pool”? Is it stable or unstable?
Unstable sounding
Review conditional instability
Use sounding that was used for simulation
Be sure we are dealing with adjusted curves (ie. virtual temperatures)
Contrast with a maritime sounding with similar CAPE but different structure?
Overcoming CIN
Show how to calculate CAPE
What does this mean, energy wise? Job of convection: redistribution in the vertical
Where will this energy go? (discuss)

8. Water-related variables used in models (from slide by Dudhia re WRF)
Scheme differences:
which water variables are carried;
whether bulk or binned are carried;
how rates between them are represented, e.g., Kessler is threshold type – when qc gets large enough, some converts to qr with a specified “rate” (specified amount in a timestep)

9. (slide from Wei-Kuo Tao)
Now we add in number and not just mass for some schemes
Why would mean size matter?
Note that RAMS is a hybrid bulk / binned.
while RAMS is a bulk scheme it makes use of many "bin" characteristics. For example, while many bulk schemes express the fall velocity of particles using some expression as V=aD^b where D is some mean diameter of the size distribution, RAMS actually "allows" the different drop sizes to fall at different velocities based on their size, calculates which grid level each drop falls to within a time step, and then recalculates mass and number at that level. It actually makes a huge difference to factors such as evaporation rates, precipitation rates and the development of the cold pool. This just points to the difference that the manner in which the microphysical processes are represented can make a big difference to the storm dynamics. 
Notice that some schemes add in a number concentration variable, and some use bins to represent the distribution within a water category (RAMS)
WHY would the size of hydrometeor matter?

10. RAMS
From Cotton, Anthes and van den Heever

11. Convection and associated microphysics
Cartoons and writeup showing convective cloud life cycle (discuss briefly)
What’s a “cold pool”? Is it stable or unstable?
Unstable sounding
Review conditional instability
Use sounding that was used for simulation
Be sure we are dealing with adjusted curves (ie. virtual temperatures)
Contrast with a maritime sounding with similar CAPE but different structure?
Overcoming CIN
Show how to calculate CAPE
What does this mean, energy wise? Job of convection: redistribution in the vertical
Where will this energy go? (discuss)
Warm bubble
Why do we need this to “get things going”?
What happens first – how does motion get started?
Animation:

15. Convection and associated microphysics
How are microphysical processes evolving?
When do we start to see cloud water converting into rain?
Where in the cloud is this occurring?
What are the associated heat releases?
Animation:

19. Sketch sounding at
40 min

20. Convection and associated microphysics
How are microphysical processes evolving?
When do we start to see cloud water converting into rain?
Where in the cloud is this occurring?
What are the associated heat releases?
Ice phase initiation
Animation:

22. Convection and associated microphysics
How are microphysical processes evolving?
When do we start to see cloud water converting into rain?
Where in the cloud is this occurring?
What are the associated heat releases?
Ice phase initiation
Animation:
Ice species evolution
What are the rates at which water is being transferred into other species?
Where in the cloud does this occur?
Animation:
Animation:

25. The cloud collapses What determines when the cloud collapses?
Sketch the environmental sounding at the end of the life cycle of the one convective cloud we followed
What is the CAPE now?
What’s happening at the sides of the domain and why?
Remember to discuss the waves generated at the tropopause!

26. Sketch sounding at
80 min

28. The cold pool What initiated the cold pool?
Where does the cold pool first form? Why?
What role does the cold pool play in subsequent convection?
When does the cold pool become ‘strongest’? How can we define cold pool ‘strength’?
Animation:

32. (Extra)