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There's not a variable that is just "CTH". I'm assuming that is cloud-top height.
There are a few that might be useful:
see, for example: CAM History Fields
PCLDTOP: "Pressure of cloud top" -- I think this comes from the microphysics
If you run with COSP turned on, you also have access to:
MEANPTOP_ISCCP: Mean cloud top pressure*CLDTOT_ISCCP
PCTMODIS: MODIS Cloud Top Pressure*CLTMODIS
And of course the CALIPSO cloud detection could be used to make an estimate of cloud-top height.
The MISR cloud is reported on a cloud-top-height by optical depth grid.
The MODIS and ISCCP cloud are reported on cloud-top-pressure by optical depth grids.
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