Yes, Th(ice) needs tp be fixed at a stable value derived from winter. This represents a physical attribute of the buoy installation. Since ice does not grow from the top, once installed Th(ice) remains the same. It just need to be discovered once for each buoy, using the various algorithms.
This, combined with limited time invested, has been hindering me from the start. I can't concentrate enough to decide once and for all on this Th(ice)(installed) for each buoy, as each algorithm gives a slightly different number. IMHO the installers should have published this number as part of buoy data, but oh well, never mind.
As for top melt, this can be identified by temperatures below Th(ice)(installed) being equal to air temperatures above that. Air temps fluctuate. Ice is an insulator. If a thermistor is in ice, it will fluctuate less and remain more rangebound than air temp. (The same is even truer for snow). In addition when air temps are extreme in any direction, the ice (and snow) should show a rather smooth gradient. Thus whether each thermistor is exposed to air or not can be calculated from the data, and no need for formulas which really cannot give a true answer as ice melt depends on more than just air temps - sunlight or clouds, wind speed, humidity, drainage, ice salinity, and more.