estimation of direct solar beam irradiance from measurements of the duration of bright sunshine

INTERNATIONAL JOURNAL OF CLIMATOLOGY

Int. J. Climatol. 18: 347–354 (1998)

ESTIMATION OF DIRECT SOLAR BEAM IRRADIANCE FROMMEASUREMENTS OF THE DURATION OF BRIGHT SUNSHINE

G. STANHILL*Institute of Soils and Water, Agricultural Research Organization, Bet Dagan 50-250, Israel

Recei6ed 4 March 1997Re6ised 1 August 1997

Accepted 2 August 1997

ABSTRACT

Measurements of the duration of bright sunshine, n, using the Campbell-Stokes sunshine recorder are shown to behighly correlated with those obtained using a normal incidence pyrheliometer to measure direct irradiance, I, at twosites in the very dissimilar radiation climates of Israel and Ireland. The statistical relationships are presented for avariety of time-scales, ranging from annual to hourly totals. For individual mean monthly values the common linearrelationship was I=2.209 n−0.955 MJ m−2 day−1, with a standard error of estimate of 91.368 MJ m−2 day−1

and a coefficient of determination of r2=0.969.Analysis of long-term series of sunshine hour measurements indicate that reductions in direct irradiance have

occurred at both measurement sites. © 1997 Royal Meteorological Society.

KEY WORDS: Israel; Ireland; direct beam irradiance; duration of bright sunshine; long-term trends

1. INTRODUCTION

During the last 70 years many studies of the relationship between solar irradiance and the duration ofbright sunshine, n, measured with the Campbell-Stokes sunshine recorder have been published. A reviewof the extensive literature shows that it consists largely of studies of the relationship between globalirradiance K¡, expressed as a fraction of the maximum possible, i.e. extra-terrestrial irradiance K¡¡, andduration of bright sunshine expressed as a fraction of the maximum possible duration, i.e. hours ofdaylight, N. The parameters of such relationships were found to depend on the local atmosphericcharacteristics as well as on the time intervals for which they were established (Martinez et al., 1984).

The innovative feature of this present study is that it examines the relationship between non-normalizedvalues of direct solar beam irradiance, I, and n measured under two very different radiation climates andfor a range of time intervals.

Estimates of I are required for the evaluation of the adsorptance of solar energy by the atmosphere,buildings, plant canopies, animal bodies and solar collection devices, and whereas very few long-termseries of such measurements are available, those of the duration of bright sunshine using the Campbell-Stokes sunshine recorder provide the most widely available and longest measures of solar radiation.

In 1960, Galindo Estrada and Fournier D’Albe showed that in Mexico City there was a highcorrelation between daily totals of I and the mass of sunshine card burnt by exposure to the sun andsuggested that ‘in view of the relative cheapness of the sunshine recorder, and the large numbers of thisinstrument already in service in many countries, its possible use as an integrating actinometer appears tobe worthy of study’. (Galindo Estrada and Fournier D’Albe, 1960).

* Correspondence to: Institute of Soils and Water, Agricultural Research Organization, Bet Dagan 50-250, Israel.

Contract grant sponsor: Agricultural Research Organization (Israel); Contract grant number: 2065-E, 1997 Series

CCC 0899–8418/98/030347–08$17.50© 1998 Royal Meteorological Society

G. STANHILL348

The results of such a study in the very different irradiance climates of Israel and Ireland are reportedin this paper and the relationships found were used to examine long-term trends in direct irradiance.

2. MEASUREMENTS

Direct irradiance measurements obtained with the Eppley normal incidence pyrheliometer mounted on anequatorial mount and recorded continuously were used, with results expressed in units of MJ m−2 perday, year or hour and referred to the World Radiometric Reference Scale. Duration of bright sunshinewas measured with the Campbell-Stokes sunshine recorder and expressed in hours and fraction of hours.Full descriptions of these instruments and their accuracies are given in the World MeteorologicalOrganization’s Guide to Meteorological Instrument and Observing Practices (WMO 1983).

The measurements of I and n were made by the Israel and Irish Meteorological Services at their mainobservatories; in Israel at Bet Dagan in the central coastal plain, some 10 km downwind of the majorcoastal conurbation of Tel Aviv-Jaffa, and in Ireland at Valentia on the extreme western coast of theIveragh peninsula, some 2 km south of the small town of Cahirsiveen. A description of the sites,instruments and their calibrations together with the results are published by the meteorological services,respectively, in the occasional publication ‘Solar radiation and radiation balance at Bet Dagan’ and in‘Solar radiation observations’, an annual publication of the Irish Meteorological Service, Glasnevin Hill,Dublin.

The coordinates of the sites are given in Table I with mean values of I, n and cloud cover. These showthat in Israel, annual totals of direct irradiance and hours of bright sunshine are more than double thosein Ireland, and the mean daytime cloud cover is half. The interannual variation in all three parameterswas much greater in Ireland than in Israel.

3. RESULTS

The results obtained at both sites and for a range of time intervals are presented in Table II in the formof linear and quadratic relationships between I and n.

3.1. Monthly mean 6alues

Daily totals of I and n measured at Valentia during 16 years were highly correlated. The standard errorof estimates of I obtained with a linear regression fitted to mean daily values of 191 individual months was90.761 MJ m−2 day−1, or 12.1% of the mean value of I, 6.307 MJ m−2 day−1. The standard error ofthe slope was 1.4% of the mean. The coefficient of determination of the linear regression, r2=0.961, washighly significant (p=0.001).

Table I. Details of measurement sites and series

Site Coordinates Mean sea-level Mean annual values and standard deviationMeasurementperiod(m)

n (h year−1) clouda (oktas)I (GJ m−2

year−1)

3.090.232489966.77390.4981967–199530Bet Dagan, 34°49%EIsrael 32°00%N

2.31790.268 1180997 6.190.210°15%WValentia, 20 1979–199551°56%NIreland

a Mean daytime cloud cover.

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Table II. Relationships between direct beam irradiance, I (MJ m−2), and duration of bright sunshine, n (h)

Regression equation Linear regression (L)/ Standard error ofSite Coefficient ofPeriod ndetermination r2quadratic equation (Q) estimateanalysed

Years:0.763 16258.9annual totals LI=4.458 n−7727Bet Dagan

150.6 0.708 15Valentia I=2.337 n−440 LL 265.5 0.987 31Pooled data I=2.161 n−245

0.989 31Pooled data 243.0QI=1982.5−0.416 n+0.581×10−4 n2

Months:0.761 0.961 191individual Bet Dagan I=2.146 n−0.582 L

months0.056 0.911 192I=2.457 n−3.333 LValentia(mean daily

totals)0.969 383Pooled data I=2.209 n−0.955 L 1.3680.972 3831.312Pooled data I=0.083+1.744 n+0.036 n2 Q

0.541mean months 0.990 12Bet Dagan I=2.408 n−2.933 LI=2.081 n−0.375 L 0.253 0.995 12(mean daily Valentia

totals)L 0.556 0.995 24Pooled data I=2.186 n−0.840

0.997 24Pooled data 0.421QI=0.191+1.741 n+0.035 n2

Days:L 2.929 0.908 110individual days Bet Dagan I=2.498 n−3.199

0.915 110Bet Dagan 2.837QI=−1.411+1.695 n+0.061 n2(daily totals)

Hours:0.742 109individual hours Bet Dagan I=2.206 n−0.130 L 0.5440.782 109Bet Dagan 0.503(hourly totals) QI=0.093−0.180 n+2.283 n2

G. STANHILL350

Figure 1. The relationship between mean values of direct irradiance, I, MJ m−2 day−1, and sunshine duration, n, h day−1, forindividual monthly values at Bet Dagan ( ) and Valentia (). The line represents the fitted linear regression with offset I=2.209

n−0.955, standard error of estimate 91.368, r2=0.969

Linear regressions calculated for mean monthly values during individual years showed small differencesin the parameters of the equations; the mean value for the slopes of all 16 regressions, 2.133, had astandard deviation of 90.14. The slopes for individual years ranged from a maximum of 2.42 MJ m−2

h−1 of bright sunshine to a minimum of 1.87, with a very small (−0.005 MJ m−2 per sunshine hour peryear) and statistically non-significant (r2=0.03) trend for the slope to decrease with year of measurement.The coefficients of determination of the linear regressions for individual years were highly significant(p=0.01) in all cases, ranging from a maximum of r2=1.00 to a minimum of 0.79.

Although the offset values for regressions of both the pooled and individual years did not significantlydiffer from zero, the standard error of estimates of I obtained with an equation forced through zero wasgreater that calculated with a linear regression including an offset term.

For a similar sized data base of measurements made at Bet Dagan the standard error of estimates ofI using linear regression fitted to the mean daily values of 192 individual months was 91.678 MJ m−2

day−1 or 9.1% of the mean value of I, which was 18.538 MJ m−1 day−1 at Bet Dagan. The standarderror of the slope was 90.056 MJ m−2 per sunshine hour, 2.3% of the mean. The coefficient ofdetermination (r2=0.911) was highly significant (p=0.001).

Differences in the parameters of linear regressions calculated for individual years at Bet Dagan were notnegligible; the mean value of the slopes of all 16 regressions −2.432, had a standard deviation of 90.25,with a trend to increase with year of measurement, although this increase was small (+0.011 MJ m−2 persunshine hour per year) and not statistically significant (r2=0.12). The slopes for individual years rangedfrom a maximum of 3.20 MJ m−2 per sunshine hour to a minimum of 2.10. The coefficients ofdetermination for individual years were all highly significant (p=0.01) and ranged from a maximum ofr2=0.98 to a minimum of 0.81.

At Bet Dagan the standard error of estimates of I obtained using a linear regression forced throughzero was 10% greater than when using the linear regression with a fitted offset value.

The pooled data from both Valentia, Ireland and Bet Dagan, Israel, shown in Figure 1, was fitted bylinear regressions with and without an offset value and also by a quadratic, curvilinear equation. Theparameters of the equations (Table II) show the quadratic equation had the lowest standard error of Iestimates, 10.6% of the mean I value 12.439 MJ m−2 day−1, and the highest coefficient of determination,r2=0.972. The better fit provided by a curvilinear relationship and the small, positive offset value of Iwhen n=0, is to be expected on theoretical grounds, as sunshine is not recorded by the Campbell-Stokesapparatus until direct irradiance exceeds the burning threshold value of the sunshine cards, which hasbeen standardized at 120 W m−2 or 0.432 MJ m−2 h−1 (WMO, 1983). Thus, as n�0 the slope of dailyvalues of I against n will decrease.


ESTIMATING DIRECT SOLAR BEAM IRRADIANCE 351

At the other extreme, under high sun, cloudless, dry air and non-turbid conditions, values of I willapproach the above-atmosphere, solar constant values of 1367 W m−2 or 4.921 MJ m−2 h−1 and theslope of daily values of I against n will increase.

3.2. Indi6idual daily 6alues

Empirically, the curvilinearity of the relationship was confirmed when the range of daily totals wasincreased by examining individual daily, rather than mean monthly values of I and n, as is shown inFigure 2 based on 110 daily totals measured at Bet Dagan and selected to cover the full annual range ofvalues. The fitted quadratic equation has a marginally higher coefficient of determination, and amarginally lower standard error of estimate, which is 19.2% of the mean value of I, than the linearregression with offset. Both of the above equations were superior to the linear correlation without offset,which had a standard error of estimate of 22.1% I( .

3.3. Indi6idual hourly 6alues

A close relationship between I and n was even found for individual hourly values, suggesting thatdiurnal variations in I could be estimated from those in n.

The linear relationship, fitted to 109 hourly values from ten complete days of measurement at BetDagan, selected to give a full range of hourly values of n (Table II) had a standard error of estimate of48.4% and a coefficient of determination r2 which was significant at p=0.001.

The quadratic relationship fitted to the same data had a standard error of estimate of 44.6% I( , and wasstatistically marginally superior to the linear relationship.

3.4. Annual 6alues

Annual sums of I and n were highly significantly (p=0.001) correlated at both sites although the slopeof the linear relationships differed considerably. At Bet Dagan the slope, 4.45890.664 MJ m−2 persunshine hour, was much greater than at Valentia, where it was 2.33790.416 MJ m−2 h−1, againsuggesting the curvilinear relationship over the full range of values.

3.5. Long-term trends

At both sites, a decrease in the annual totals of sunshine hours was found. The statistically fitted lineartrend at Valentia over the period 1940–1995 was −4.53 h year−1 and was statistically highly significant,p=0.001. At Bet Dagan the linear trend over the shorter period of measurement available, 1963–1995,was less, −2.99 h−1 year−1, and was only significant at p=0.10.

Figure 2. The relationship between individual daily values of direct irradiance, I, MJ m−2 day−1, and sunshine duration, n, hday−1, at Bet Dagan. The line represents the fitted quadratic equation


G. STANHILL352

The mean annual decreases in I corresponding to those in n are −10.58 MJ m−2 at Valentia and−13.32 MJ m−2 at Bet Dagan.

To examine the relationship between the changes in annual sums of n at the two sites, these wereexpressed as normalized anomalies,Ay= (ny−n)/swhere ny is the annual total of sun hours for the yeary, and n and s are, respectively, the mean and standard deviation of the measurement series. There wasno significant correlation between the two non-parametric series at p=0.05.

4. DISCUSSION

The linear and near-linear relationship between I and n demonstrated in this study under the verydifferent radiative regimes of Israel and Ireland, are surprising in that they imply that direct irradiance isconstant for that portion of the day when I\120 W m−2, the burning threshold of the Campbell-Stokessunshine recorder. This despite the fact that I varies markedly with the length of the solar path throughthe atmosphere, i.e. solar elevation h, and the scattering properties of the atmosphere, in particular itswater content and aerosol load.

The explanation of this paradox is probably the exponential relationship existing between I and h underclear-sky conditions. For example at Aspendale, a coastal site in South Australia, I increased five-foldbetween 2° and 20° h, but only 25% between 30° and 70° h (Paltridge and Pratt, 1976). This exponentialrelationship is the reason for the well-established flat topped diurnal curve of I under clear sky conditions,so that I varies markedly during only a relatively small proportion of the day’s length. The variations ofI during this period as well as changes in atmospheric turbidity and water content are, together witherrors in measurements, primarily of n (Painter, 1981), the reasons for the standard errors of estimates ofI based on measurements of n reported herein.

In this study, the standard error of estimation varied inversely with the length of the period for whichI was estimated. At Bet Dagan, the standard error, expressed as coefficients of variation relative to themean values of I, was 3.8% for annual estimates, 9.1% for monthly estimates, 19.2% for daily estimatesand 44.6% for estimates of hourly values. Corresponding coefficients of variation for the estimates atValentia were somewhat higher, 6.5% for annual and 12.1% for monthly estimates. The error ofestimation for individual daily sums of I at Bet Dagan using a linear regression, 2.93 MJ m−2 day−1, iscomparable with the error of estimation at Mexico City, 2.61 MJ m−2 day−1, reported by GalindoEstrada and Fournier D’Albe (1960) for a similar sized data base.

The slightly greater error term at Bet Dagan may have been caused by the higher values of I at this siteand/or by the different measures of sunshine duration adopted. At Mexico City the mass of sun cardburnt each day, measured as weight loss, was used to estimate I, whereas at Bet Dagan, the recommendedstandard measure of duration of sunburn was used.

Even if it were demonstrated that the volume of sun card burnt provides a marginally superior estimateof direct irradiance, its use can hardly be recommended in view of the long duration of records ofsunshine hour duration (at Valentia, for example, since 1869), their widespread availability (335 suchrecords were reported in 1991 in the Monthly Bulletin, Solar Radiation and Radiation Balance Data (theWorld Network) published for the World Meteorological Organization by Voeikov Main GeophysicalObservatory, St Petersburg, Russia), and the extra time and equipment needed to measure weight loss.

An important, practical question is the feasibility of using the joint relationships established at BetDagan and Valentia at other sites with different irradiance regimes. Where estimates of I are needed fordiurnal or individual daily values, the relationships at new sites could be established relatively quickly bycalibrations over the time and irradiance range of interest. However, the long period of calibrationrequired to validate seasonal and year-to-year relationships makes this approach of limited utility. Theyear-to-year differences found at both sites suggests that more than 1 year of calibration would be neededto establish the seasonal relationship between I and n.

It is of interest to compare the relationships between I and n tabulated in Table II for monthly meansaveraged over a 15 year period with those given below between normalized values of global irradiance and


ESTIMATING DIRECT SOLAR BEAM IRRADIANCE 353

sunshine hours, the standard method used to estimate solar irradiance from measurements of sun-shine hours.

Bet Dagan K¡=K¡¡ (0.659 n/N+0.096), r2=0.864, p=0.01

Valentia K¡=K¡¡ (0.737 n/N+0.180), r2=0.935, p=0.01

Pooled data K¡=K¡¡ (0.466 n/N+0.242), r2=0.949, p=0.001

These standard equations show somewhat lower coefficients of determination and considerablygreater between-site variation in the parameters of the equations, which at both sites differ consid-erably from those derived from the pooled data.

The long-term decreases in I found at both sites are not surprising because larger, statisticallysignificant reductions in global, i.e. direct plus diffuse irradiance on a horizontal surface, have beenreported at both sites, which were unaccompanied by increases in the extent of cloud cover (Stan-hill and Moreshet, 1994; Stanhill and Ianetz, 1997).

5. CONCLUSIONS

Under the very different radiation regimes of Bet Dagan, in the central coastal plain of Israel andat Valentia, on the south-west coast of Ireland, direct solar beam irradiance was highly correlatedand linearly related to standard measurements of the duration of bright sunshine.

In the largely cloud-free and high sun climate of Bet Dagan, I could be estimated from n witha standard error of less than 10% for both annual totals and mean monthly values. For individualdaily totals the error of estimation was less than 20% and, for individual hourly estimates, justbelow 50%. At Valentia with greater cloud cover and lower solar elevations, the correspondingstandard errors of estimates were slightly higher for both annual totals and mean monthly means.

At both sites linear relationships of I on n were highly significant, with coefficients of determina-tion, r2 values, varying between 0.7 and 0.9 according to the period for which the estimation wasmade. The slope of the relationship varied between 2.15 and 2.46 MJ m−2 (774 to 886 W m−2)per sunshine hour at both sites and for all periods except for the annual relationship at BetDagan. A marginally greater, B5%, proportion of the variation in I was explained by variationsin n when the theoretically more appropriate quadratic relationship was used in place of a linearone.

The use of a single, joint quadratic relationship to estimate I at both sites, resulted in slightlysmaller error terms at Valentia and slightly larger ones at Bet Dagan, compared with estimatesbased on the local relationships.

Long-term decreases in n were found at both sites, with trends of different magnitudes andstatistical significances; the considerable year-to-year variations in the long-term trends at the twosites, expressed by their normalized anomalies, were only weakly correlated. At Valentia the annualdecrease between 1940 and 1995 averaged −0.353% and was highly significant at p=0.01; at BetDagan the decrease between 1963 and 1995 averaged −0.092% per year and was only significantat p=0.10.

ACKNOWLEDGEMENTS

I wish to thank A. Ianetz of the Israel Meteorological Service and D. Fitzgerald of the Irish Me-teorological Service for their kindness in providing unpublished data; also Etty Dadosh for assis-tance with computations and S. Moreshet for the preparation of the figures.

Contribution from the Agricultural Research Organization, The Volcani Center, Bet-Dagan, Is-rael, No. 2065-E, 1997 series.


G. STANHILL354

REFERENCES

Galindo Estrada, I.G. and Fournier D’Albe, E.M. 1960. ‘The use of the Campbell-Stokes sunshine recorder as an integratingactinometer’, Q. J. R. Meteorol. Soc., 86, 270–272.

Martinez, J.A., Tena, F., Onrubia, J.E., and de la Rubia, J. 1984. ‘The historical evolution of the Angstrom formula and itsmodifications’, Agric. For. Meteorol., 33, 109–128.

Painter, H.E. 1981. ‘The performance of a Campbell-Stokes sunshine recorder compared with a simultaneous record of normalincidence irradiance’, Meteorol. Mag., 110, 102–109.

Paltridge, G.W. and Pratt, C.M.R. 1976. Radiati6e Processes in Meteorology and Climatology, Elsevier, Amsterdam, p.117.Stanhill, G. and Moreshet, S. 1994. ‘Global radiation climate change at seven sites remote from surface sources of pollution’,

Climatic Change, 26, 89–103.Stanhill, G. and Ianetz, A. 1997. ‘Long-term trends in, and the spatial variation of, global irradiance in Israel’, Tellus, 49B, 112–122.WMO, 1983. ‘Measurement of radiation’, in Guide to Meteorological Instrument and Obser6ing Practice, 5th edn, World

Meteorological Organization, Geneva, Chapter 9.


estimation of direct solar beam irradiance from measurements of the duration of bright sunshine

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