Systematic errors in estimation of insolation by empirical formulas

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Systematic errors in the estimation of surface insolation, Q, by two popular empirical formulas are investigated statistically by using coincident measurements of the global solar radiation and the total cloud cover at JMA observatories over Japan. The results show that Reed's (1977) widely-accepted formula remarkably overestimates Q under overcast conditions. The overestimation is particularly evident in the summer months. The formula also overestimates Q in cloud-free conditions, which may be due to an overestimation of the clear-sky transmittance by Seckel and Beaudry (1973). By contrast, Kondo and Miura's (1985) formula underestimates Q under overcast conditions, whereas it slightly overestimates in partially cloudy conditions. It is shown that these systematic errors can explain some of the published differences between the estimation of Q by the two formulas. The users of these formulas should be careful since these cloudiness-dependent errors can contaminate not only the absolute values but also the temporal anomalies or the spatial variability of the insolation predicted by them. In particular, it can be serious in regions of dense cloud cover such as the northern North Pacific, the northern North Atlantic and the Southern Ocean. It is also shown that the ratio of Q to the insolation at the top of the atmosphere, QTOA, takes on a range of values, particularly under dense cloud cover. This implies an inherent difficulty in estimation of Q by a simple empirical formula utilizing only readily-available observables such as cloudiness.

Original languageEnglish
Pages (from-to)165-177
Number of pages13
JournalJournal of Oceanography
Issue number2
Publication statusPublished - 1998 Apr


  • Bulk formula
  • Cloud amount
  • Cloudiness
  • Empirical formula
  • Surface heat budget
  • Surface insolation


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