These plots are based on:
The chi^2 tests were over 100 (even over a limited range) for single layer height distribution. Chi^2 about 25 for lower cloud height distribution for different thicknesses.
One layer ice cloud thickness (km) distribution:
Scale height: .9 (from fitted curve)
Scale height: .75 (from data)

One layer ice cloud height: mean 14.4 km std 1.97

Two layer ice clouds height (both layers): mean 15.6 km std 2.07 and 13.4 km std 2.4
. 
Lower cloud height distribution for .25 km gap mean height 14.8 km; std 1.74

Lower cloud height distribution for .50 km gap mean height 14.7 km; std 1.90

Lower cloud height distribution for .75 km gap mean height 14.3 km; std 1.76

Lower cloud height distribution for 1.0 km gap mean height 14.0 km; std 1.67

Lower cloud height distribution for 1.25km gap mean height 13.5 km; std 1.87

Lower cloud height distribution for .25 km cloud thickness mean height 14.1 km; std 2.11

Lower cloud height distribution for .50 km cloud thickness mean height 13.9 km; std 2.17

Lower cloud height distribution for .75 km cloud thickness mean height 13.7 km; std 2.05

Lower cloud height distribution for 1.0 km cloud thickness mean height 13.6 km; std 1.91

Lower cloud height distribution for 1.25 km cloud thickness mean height 13.7 km; std 1.95

Low cloud height vs high cloud height. 1,1 is 7.75km (30,30) is 15km