I've watched the discussion and would like to make a few comments.
I have noticed that when there are passing clouds, as noted here before, the readings I get spike by at least 10% in some situations, especially 5-12,000 foot rapidly passing clouds in the summer.
When I have a perfectly cloudless day, my solar max curve fits so close to my measured values all day long, I wonder if I am having one of those days where all my temperature sensors are within a few tenths of a degree of one another. It happens reliably, so I trust it.
One thing that hasn't been discussed much is the type of sensor one uses. I have a variety of them, mostly off the popular Li-Cor or Apogee type. One is a Kipp-Zonen that is a somewhat different technology, but shows a blunted spike and is not totally immune to it.
In response to the huge number at sunrise, unless some mirror is shining it on the sensor, I'm not sure I can explain it. I have a couple that I have hooked up to data loggers with readouts just to watch the values, and they fall gradually and according to predictions for my location and elevation and are up high enough to have no interference from trees. In the morning they 'wake up' and begin to follow the predicted maximum. I never have had a problem with a surge in values. Maybe I'm just lucky but things behave well and are in close agreement (usually within 10 watts/m/m all day long with my best pyranometers). The logger outputs show a tenth of a watt (I don't know if that is achievable, but I wanted to show the best I could) and again there are often times that the lower values are dead on with each other, once I set the amplification factors from the factory calibration and haven't touched them since.
I use Brian Hamilton's Weather Display to generate the plot of theoretical maximum, which is code at least 10 years old I'm told, and it seems in agreement with other algorithms once I base it on atmospheric attenuation for my elevation. I have not used any local humidity scores, nor air quality to tweak it any further, since the numbers have been so good.
I have noted when a pesky tree branch grew near one sensor that what I call the cloud-edge phenomenon will slightly spike the readings on a bright day.
I also have noted that the spiking is much more likely to occur, not exclusively, in the summer with far higher radiation values than winter months when the max is quite feeble here at 45 latitude.
I'm sure there is some bunch of Master's Degree candidates just hoping for a project to do, and if their advisors don't think that too many papers have already been written, we might see something by nosing around for more scholarly works by those with far more mathematics ability than I to help sort this out. But like flickering picket fences, I'm thinking this is just what the type of sensors we use (which I blame mostly for this) is seeing.
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