Add number concentration tendencies to YOG

[jatkinson1000]

This PR should close #18 by adding a calculation for number concentration tendency to the YOG code using the updated cloud liquid and ice tendencies.

• The number concentration calculation is taken from the clubb routines.
• Number concentration tendency from YOG is allowed to be negative, but cannot reduce total number concentration below zero.
• Number concentration tendency from YOG is added as an optional output to the statistics files.
• Perform a check to ensure that the tendency will not generate negative number concentration and limit if necessary.

Note this is a reimplementation of #23 that was removed from main when resolving issues with moist-dry conversion

[jatkinson1000]

This has been rebased on top of the current CAM-ML branch.

TOGA II when run with and without cloud number tend comparing PRECC + PRECL:

Same plot but with observations and ZM:

Both start similarly, but there is an increase in precipitation when cloud number tendencies are included.
Tendencies lead to an increase in droplets which leads to longer-lasting precipitation?

[jatkinson1000]

What we are really interested in is what the clouds are doing:

• Plot specifically the number concentration of Ice and Liq, and compare to the ZM (and also the no number concentration CAM-ML). Check that this reasonable. Also the number concentration tendencies.
• Plot relative humidity as a more general check.

Did this quickly in the meeting using ncview:

• Seems we are forming large anvil clouds with ice build up at the top of the troposphere.
• This would explain why the precipitation is sustained at a higher level in the number-conc run.
• But the relative humidity remains very low in upper troposphere (200-400 hPa) and we see ice is not produced here.
  • ice tendency always tends to be negative.
  • The issue is that something forces the relative humidity to drop low early on, and then we will struggle to raise it back up as ice will immediately sublimate if it forms here.
  • Looking early in Toga we see that rel. humidity drops in the first 8 days in this region

Other updates to consider:

• check that number tendency will not reduce below 1 rather than 0.
  • i.e. if we have ANY water there should always be at least 1 droplet!
• Code to check is also verbose - could be simplified

Discussion:

• No number tendency means we don't get clouds
• number tendency in current form gives us too much
• Double check that the equation we have for droplets matches that in ZM
• try scaling number tendency by 0.5 to see if we can get "just enough" and improve behaviour
  • Looking at DICE tendency suggests and when ther eis too much suggests that this will likely not resolve the humidity issue, however

Tagging @paogorman in case there is anything I missed that he wants to add.