I snapped this picture when I saw it on the way out today. In December I sprayed an inch of closed cell spray foam under the roof deck but the 2x8 framing is not coated yet. The heat loss through the 2x8 is enough to melt the snow.

How cold was it outside?

It's been below freezing since Tuesday mid day. The snow fell Tuesday night. High in low 20s and about single digits f at night. Today hit 33 this afternoon after the photo was taken Damon cold for va.

You may be right that it is the thermal bridging, however I wonder if it is just the residual heat in the rafter that melted some of the snow as it fell. If the rest of the snow over the rafter and not the rest of snow on the roof, melted right down to the shingles, they I would think it is thermal bridging but if it did not melt more then the picture shows, it was probably just residual heat that is now used up.

A 2x8 on the x8 dimension has an R value of between R7-R9 for most species (R7 for douglas fir, R8.7 for hemlock and several species of pine.)

But with only and inch of foam on the the roof deck, with no other cavity insulation the ful dimension of the rafter doesn't matter, only the depth that's INSULATED does. So with only an inch of the rafter being insulted on both sides you're looking at a thermal bridge of about R1-R1.2. The section of rafter on the interior side is fully exposed to the interior air temperature, making the temperature of the rafter wood 1" in from the roof deck pretty much the same temperature as the attic space.

Freshly sprayed 2lb foam is runs around R8-9, but will drop to R6 ish in some number of months. So right now you're looking at about a full order of magnitude difference in center-cavity R to thermal-bridge R.

Very cool illistration either way. I will also end up insulating the stud with one inch of foam as well and add another inch on top of the inch that is already there. After that I will fill the remaining few inches with fiberglass batt insulation. If I ma not mistaken there is enough space for a R19 batt in there on top of two inches of foam without being compressed. In that case it should have a value of R31. Should make a big difference this summer.