Correlation Between Clear Day Horizontal Diffuse and Beam Indices

Ever since the publication of the pioneering work by Liu and Jordan (1960) there have been persistent efforts to develop correlations between global, direct and dif­fuse irradiation. We have previously developed (Ianetz et al. 2001) empirical regres­sion equations that expressed Kd the ratio of the daily diffuse on a horizontal surface to the daily extraterrestrial irradiation on a horizontal surface, as a function of Kb, the ratio of the daily beam on a horizontal surface to the daily extraterrestrial on a horizontal surface, irrespective of day type, as presented graphically by Liu and Jordan (1960). The regression equations that gave the best fit to the data were found to be non-linear and exponential inform, viz., Kd = a[exp(bKb + cKb2)]. When this analysis was applied to a database consisting of solar horizontal diffuse and beam irradiation on clear days, i. e., the present discussion, it was observed that linear regression equations gave the best fit to the data. It can be concluded that the non­linearity observed in the previous analysis is caused by inclusion of both cloudy and partially cloudy days within the database.

The results of this analysis, i. e., the slope ‘a’ and intercept ‘b’ of the monthly linear regression curve and the corresponding correlation coefficient are reported in Table 4.7 for Beer Sheva. InFigs. 4.6 (a) and (b) the data and linear regression curves

Table 4.7 Monthly regression equation coefficients and correlation coefficient for Kd>c = aKb>c + b

Month (data)

a

b

R2

January (56)

-1.1787

0.7899

0.9131

February (104)

-0.9128

0.6427

0.9518

March (62)

-0.8712

0.6449

0.9396

April (96)

-0.9128

0.6427

0.9518

May (147)

-0.8324

0.6248

0.9379

June(278)

-0.7860

0.5961

0.9115

July (198)

-0.8730

0.6435

0.9282

August (91)

-0.7772

0.5833

0.9234

September (41)

-0.9292

0.6712

0.9827

October (60)

-0.8254

0.5928

0.8810

November (32)

-0.8132

0.5683

0.8950

December (28)

-0.9301

0.6279

0.9084

Fig. 4.6 Linear regression analysis of Kd>c as a function of Kb>c for (a) January, (b) July

for January and July, which are representative of those obtained for all months, are shown.

It is apparent from the magnitude of the coefficients of correlation reported in Table 4.7 for the monthly regression equations that, with the exception of October and November, more than 90% of the variation in Kd c is accounted for by the vari­ation in Kb_c, i. e., R2 exceeds 0.90 except for October and November, for which it slightly less than 0.90. It is also observed that the coefficients of the regression equations vary from month-to-month.

In the accompanying CD-ROM the reader will find a ReadMe file containing a step-by-step description of the procedure the authors used to produce the results described in this chapter.

Updated: August 1, 2015 — 4:49 pm