I think there is no simple answer to your question, and the approach you take might depend on your needs. As far as I know there is not a standard definition for "mixed phase cloud fraction."
One important point is that the COSP cloud variables provide estimates of cloud quantities that are intended to be comparable to the respective satellite products. So the "CAL" cloud fields are retrieved from the model to mimic the CALIPSO retrievals, and the ISCCP variables do the same but for the ISCCP products. These estimates are distinct from the model's predicted cloud fraction and liquid and ice amounts. In particular, all the retrievals tend to emphasize cloud-top quantities because they are less effective at detecting clouds below thick clouds. The passive products (ISCCP, MODIS, MISR) only work on sunlit grid points.
The CALIPSO cloud by phase variables come from a data structure in COSP called calipso_cldlayerphase. You can see that in the CAM COSP interface:
Community Atmosphere Model. Contribute to ESCOMP/CAM development by creating an account on GitHub.
github.com
The COSP code is available in it's own GitHub repository (or is available in the CESM or CAM source code tree once checkout externals is done):
COSP - The CFMIP (Cloud Feedbacks Model Intercomparison Project) Observation Simulator Package - CFMIP/COSPv2.0
github.com
If you take a look at the CALIPSO simulator, you will see that the cloud phase determination is a multi-step process. The presence of clouds is determined first, and then the phase discrimination is run only on points where cloud is detected. For levels from 8 to 19 km, there is an attenuated backscatter threshold for ice clouds (the phase discrimination line), and there is a temperature check (ice can't occur for T > 273.15K), then cloud are put into layers based on pressure. At levels below 8km there is a similar set of steps.
Instantaneously in each subcolumn, these cloud fractions are binary (0 or 1), and then fractional values come from aggregating the subcolumns.
Code is here:
COSP - The CFMIP (Cloud Feedbacks Model Intercomparison Project) Observation Simulator Package - CFMIP/COSPv2.0
github.com
For the specific variables you asked about in #2:
- CLDTOT_CALCS = "Calipso and Radar Total Cloud Fraction" This uses both the lidar and radar (CloudSat) retrievals to make a combined cloud fraction
- CLDTOT_CAL = "Calipso Total Cloud Fraction" This is the total cloud fraction that would be observed by CALIPSO (lidar)
- CLDTOT_CS = "Radar total cloud amount" This is the total cloud amount from the CloudSat (CS) simulator
- CLDTOT_ISCCP = This is the total cloud amount from the ISCCP simulator
- CLDTOT = This is the total cloud amount diagnosed using the model's predicted CLOUD field using cloud overlap assumptions which I think still follows the description of Collins 2001
https://doi.org/10.1175/1520-0469(2001)058<3224:POGCOF>2.0.CO;2