I was not planning to reply to Bill’s questions, for some of the reasons Lucia stated. But since you seem concerned, here is a brief reply:
“– How much time does the energy represented by a photon from the Sun spend in the Earth system before it is lost to space?”
That depends. If a photon is reflected from a cloud (or other surface) back into space, then the time is a small fraction of a millisecond. If it is absorbed (converted to thermal energy), then the question strikes me as meaningless, since thermal energy is fungible… you can’t say what specific photos contributed to the heat content of anything on Earth.
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“- How many individual molecules does that energy represented by a photon from the Sun spend time in before it is lost to space?”
The time is indeterminate and meaningless, for the reasons outlined above.
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“- Why does the surface only warm by 0.017 joules/m2/second during the height of the day when the sunshine is beating down at 960.000 joules/m2/second.”
If I understand the question correctly (and I am not sure if I do), the net heat accumulation in any system is the energy inflow minus energy outflow. If the surface energy balance is close to zero, it just means inflow and outflow are close to balanced… over whatever the period of measurement is.
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“- Why is there no “time” component in any of the greenhouse radiation physics equations.”
Yikes! No idea what this question means.