~Extremely simple to express another matter to explain mathematically.
~Down past the skin, snow layers thermal profiles literally change with weather
~ One can estimate sky conditions by the thermal profile of a snow drift
Going back to the Horizon refraction discovery of a few years ago:
Tice<= Ts, which has never been disproved optically, but never been measured physically except from sea ice buoys during the sunless long nights. The temperature on top of sea ice (including snow) is always colder of equal to surface temperature, this discovery, prompted the question about snow on top of land, is it the same?
After many thousand observations with measurements, T***<= Ts (***= top of snow layer) was very very elusive to measure, the first problem was sunlight, some of my readers know , sunlight induces a temperature error to all surfaces with a snow layer. There are no easy, readily observable temperature readings with relatively inexpensive instruments. Temperature stratas in a column of snow vary with weather, which is amazing. On many occasions, optical observations suggested T***=Ts the top of snow temperature did not confirm so, when optical observation interpretation had an obvious inversion, the snow was warmer than air. Even in the thick of winter, when everything is more refracted, snow readings denied what was seen, in great conflict with horizon sea ice observations.
Turns out it was the measurement method, and the crucial understanding which is that snow temperature columns vary in tandem to weather , which broke the mystery.
What does this mean?
In particular, it is the build up formula for winter on planet Earth, albedo up to 90% renders sunlight heat practically irrelevant, but winter comes from a dark world, where the sun is forgotten only reminisced by a faint twilight. It is in this star lit world, where winter becomes fierce or faint. If winter starts earlier, it can only be by pervasive dark moisture rich clouds, which imprints a snow carpet, nullifying any warming by whatever sunlight gets through. In the days of anthropogenic enhanced Global Warming, this frozen moisture should be greater, therefore more snow should be expected, as it does happen yearly more often than not,
"As sea ice shrinks, the Arctic becomes warmer and wetter, study finds8 / 2015 - Present
http://www.adn.com/article/20150809/sea-ice-shrinks-arctic-gets-warmer-and-wetter-study-fi November saw the biggest increases in “skin temperature” (defined as temperature at the Earth’s surface), and air temperature, with an average annual rise of 0.42 degrees Celsius on the surface and 0.32 degrees Celsius in the air, said the study, by Linette Boisvert of the NASA-affiliated Earth System Science Interdisciplinary Center at the University of Maryland."
except for when major climate event, such as from ENSO which changes cloud formations. I recall in the fall of 1998, a lack of High Arctic snow carpet was ever present:
EL-Nino creates low stratospheric cloud seeds, which propagate easily throughout the world. 1998 was then the warmest year in history because of an unusualy strong El-Nino, warmest despite a rapid change to La-Nina within the same year. (as with this October 16 NOAA SST chart) . The Canadian High Arctic fall in 98 was sunny with hardly any snow on ground as late as early November, with Barrow Strait freezing the latest in 20 years. ENSO had a long distance impact. Just like in 2016, but in 16, the Arctic fall had more snow because La-Nina spring trending brutally stopped during summer. 2017 late spring ENSO had an upsurge towards warming, then now fast trending to La-Nina (with lesser clouds being created worldwide), therefore less snow on the ground than with autumn 2016 as it is at present. This late in the year less clouds trending has huge winter implications, particularly where there is less snow than normal.
The question is what happens when land areas exceed snow in pure darkness. The answer is faster cooling tempered by snow cover . Land surfaces are pretty much like water when it comes to snow or sea ice. In summer Arctic sea surface water is a near constant in temperature varying quite slowly one day to the next. In winter, top of permafrost becomes land surface, a constant which varies at a wider range than surface sea water temperature though, but varies day to day in similar ways to sea surface. Depth is key, in very early winter top of land is very much like open water, the optical readings suggest warmer land surface than surface temperatures:
T * >Ts
from a sun radiation
equality in temperatures morning and evening:
T * = Ts
with low to mid level clouds:
surface cooling at night:
T * < Ts
is like a snowflake in a wide field, like a bergy bit in wide open water, the predominance of land or water is nearly oblivious with scarce presence of snow. Ts
is part and parcel of the air to surface complex, if the surface changes Ts does likewise, a bit of snow on wide land approaches the nature of no snow at all, in darkness or sunshine, but it can still affect the surface temperature as it can still be measured optically
Then when snow starts to cover the surface more completely , the horizon shifts to more neutral heights
T* * --> = <-- Ts nearing 50% snow cover tends to make equality in temperatures
is near 50 50 area cover snow when we can literally judge whether the area of snow exceeds land cover or is less than, made more complex by land temperature differing from top of snow temperature, if land gains more exposure when warmer than snow, the horizon drops (the reverse applies). These small variations are only applicable till cold really sets in especially on top of ground. When snow carpet approaches 100%, the optics are all inclined to behave like if snow is the only thing which matters.
Then the easiest equation expressing a physical dominance of snow is T*** <= Ts,, with near or complete snow cover , even with sunshine and during Midwinter darkness T***<= Ts,
even during a cooling atmosphere event, however when low or mid level clouds overcast the sky T***=Ts in all other circumstances T*** is colder than Ts.