Can total insolation integrated over a day with clouds ever be greater than total insolation integrated over a clear day? If so, what is the cause of this phenomenon? Is this phenomenon more likely to be seen at certain sites and/or times of the year?
It seems logical to conclude, based just on a "thought experiment," that total insolation integrated over the day on a clear
day will always be greater than total insolation
integrated over a day with some clouds. After all, even thin clouds reflect some sunlight and the sun is often not even visible behind thicker clouds.
Patterns of pyranometer data clearly show "spikes" in insolation from sunlight scattered and reflected by the sides of thick clouds,
but these spikes are always accompanied
by lower values of insolation when clouds cover the sun.
However, hourly insolation data from NOAA's Climate Reference Network (CRN) sites show that it is not uncommon for the measured insolation
summed over a day to be greater than summed insolation calculated from a clear-sky model for that site and date. Consider, for example, these data
from 2007 at the CRN site at Avondale, Pennsylvania. On January 2, 3, 11, and 17, the measured insolation is greater than the daily insolation calculated from
a clear sky model (highlighted in red).
Date kWhr/day MJ/day Clear sky kWhr/day Clear sky MJ/day 1, 1, 2007, 0.13, 0.46, 2.45, 8.82 1, 2, 2007, 2.70, 9.73, 2.46, 8.86 1, 3, 2007, 2.54, 9.14, 2.48, 8.91 1, 4, 2007, 2.46, 8.87, 2.49, 8.97 1, 5, 2007, 0.27, 0.98, 2.51, 9.02 1, 6, 2007, 2.29, 8.26, 2.52, 9.08 1, 7, 2007, 1.71, 6.16, 2.54, 9.15 1, 8, 2007, 1.06, 3.81, 2.56, 9.22 1, 9, 2007, 1.51, 5.42, 2.58, 9.29 1, 10, 2007, 2.49, 8.96, 2.60, 9.36 1, 11, 2007, 2.72, 9.78, 2.62, 9.44 1, 12, 2007, 0.82, 2.94, 2.65, 9.53 1, 13, 2007, 1.26, 4.54, 2.67, 9.61 1, 14, 2007, 0.91, 3.29, 2.70, 9.71 1, 15, 2007, 0.57, 2.05, 2.72, 9.80 1, 16, 2007, 0.62, 2.22, 2.75, 9.90 1, 17, 2007, 3.04, 10.94, 2.78, 10.00
There are several possible concerns about these data, typical of concerns which always must be considered when analyzing data where measurements are involved and the differences of interest between two data sets are expected to be small; for this research investigation, we would not expect the "excess" insolation as a result of clouds ever to be large. The calibration for the CRN pyranometer at this site might not be right. The clear sky model could be inadequate for representing sky conditions at this site. Or, this phenomenon could be real and have a reasonable physical explanation that will become clear only when many more sites are examined. It is certainly possible that there might be problems with the CRN pyranometer calibrations, although these instruments are recalibrated every year. It is possible that the clear sky model is inadequate — this possibility could be examined by comparing model data against data from a site with a high-quality research-grade pyranometer.
The NOAA CRN data are available online. Software for processing these data can be adapted from software already written by David Brooks. There is a discussion of the clear sky model here.