So a relatively simple question motivated by seeing some new ice form...
Do we know what day is breakeven for heat flux, counting only radiation, at various latitudes? Assume clear skies (though I'd be curious for cloudy too), and open water at 0C for albedo/blackbody purposes.
That is - if we only look at heat gained from the sun and heat lost via longwave to space (ignore atmospheric interaction, upwelling, currents, etc), what day of the solar year does this breakeven occur at various latitudes?
The original question seems to be asking when is the sunshine strong enough to balance OLR on open water (leads, etc.) without drawing energy from other sources. From the graphs it this thread I would put OLR at about 220w/m2 from cold water (but someone will have an accurate figure?), agreeing with late March to mid April. It would only be theoretical because in practice this would be later than ice would form (as the seawater would need to cool to about -10°C for ice to form) unless a lot of 'cold' was imported from somewhere else.
OTOH because of the high albedo of ice/snow there still would not be enough energy absorbed to actually melt anything and the surface is likely to remain below 00C until the sunshine is considerably stronger (but OLR would also be lower and more variable). That makes for another interesting question?
That "-10C for ice to form" is just a rule of thumb, or a simplified way to say that there are other heat sources, as for example water warmed up during summer in the upper layer of the ocean, that keep ocean water surface above freezing point for some time even when atm temps plunge well over zero, and as long as there is some stirring and mixing.
That is all for the freezing season start. As for the melting season start, something similar happens, there are additional effects that (most probably) delay the persistence of open water.
An important factor is the effect of land masses. In fall, air advected from continents starts to have a cooling effect, whereas at some point of the Spring, air acvected from continents starts to have a warming effect. I believe the effect of transported heat this way is not totally accounted for in the OLR - incoming sw radiation balance approximation. That makes the problem very location-dependent. It also adds some inertia to the problem, (I think), since you need to have land snow cover meltout ongoing (or gone) in order to not receive spells of cold air advected from the continents, delaying the day of overall heat balance for some days.
By observing a few seasons as I said for me the 1st of May is when the bell rings for this particular problem, plus minus 10 days