ESTIMATION OF DIRECT SOLAR BEAM IRRADIANCE FROM MEASUREMENTS OF THE DURATION OF BRIGHT SUNSHINE

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 18: (1998) ESTIMATION OF DIRECT SOLAR BEAM IRRADIANCE FROM MEASUREMENTS OF THE DURATION OF BRIGHT SUNSHINE G. STANHILL* Institute of Soils and Water, Agricultural Research Organization, Bet Dagan , Israel Recei ed 4 March 1997 Re ised 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 be highly correlated with those obtained using a normal incidence pyrheliometer to measure direct irradiance, I, at two sites in the very dissimilar radiation climates of Israel and Ireland. The statistical relationships are presented for a variety of time-scales, ranging from annual to hourly totals. For individual mean monthly values the common linear relationship was I=2.209 n MJ m 2 day 1, with a standard error of estimate of MJ m 2 day 1 and a coefficient of determination of r 2 = Analysis of long-term series of sunshine hour measurements indicate that reductions in direct irradiance have occurred at both measurement sites 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 of bright sunshine, n, measured with the Campbell-Stokes sunshine recorder have been published. A review of the extensive literature shows that it consists largely of studies of the relationship between global irradiance K, expressed as a fraction of the maximum possible, i.e. extra-terrestrial irradiance K, and duration of bright sunshine expressed as a fraction of the maximum possible duration, i.e. hours of daylight, N. The parameters of such relationships were found to depend on the local atmospheric characteristics 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-normalized values of direct solar beam irradiance, I, and n measured under two very different radiation climates and for 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-term series 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 high correlation between daily totals of I and the mass of sunshine card burnt by exposure to the sun and suggested that in view of the relative cheapness of the sunshine recorder, and the large numbers of this instrument already in service in many countries, its possible use as an integrating actinometer appears to be worthy of study. (Galindo Estrada and Fournier D Albe, 1960). * Correspondence to: Institute of Soils and Water, Agricultural Research Organization, Bet Dagan , Israel. Contract grant sponsor: Agricultural Research Organization (Israel); Contract grant number: 2065-E, 1997 Series CCC /98/ $ Royal Meteorological Society

2 348 G. STANHILL The results of such a study in the very different irradiance climates of Israel and Ireland are reported in 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 an equatorial mount and recorded continuously were used, with results expressed in units of MJ m 2 per day, year or hour and referred to the World Radiometric Reference Scale. Duration of bright sunshine was 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 Meteorological Organization 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 main observatories; in Israel at Bet Dagan in the central coastal plain, some 10 km downwind of the major coastal conurbation of Tel Aviv-Jaffa, and in Ireland at Valentia on the extreme western coast of the Iveragh 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 show that in Israel, annual totals of direct irradiance and hours of bright sunshine are more than double those in Ireland, and the mean daytime cloud cover is half. The interannual variation in all three parameters was 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 form of linear and quadratic relationships between I and n Monthly mean alues Daily totals of I and n measured at Valentia during 16 years were highly correlated. The standard error of estimates of I obtained with a linear regression fitted to mean daily values of 191 individual months was MJ m 2 day 1, or 12.1% of the mean value of I, MJ m 2 day 1. The standard error of the slope was 1.4% of the mean. The coefficient of determination of the linear regression, r 2 =0.961, was highly significant (p=0.001). Table I. Details of measurement sites and series Site Coordinates Mean sea-level Measurement Mean annual values and standard deviation (m) period I (GJ m 2 year 1 ) n (h year 1 ) cloud a (oktas) Bet Dagan, E Israel N Valentia, W Ireland N a Mean daytime cloud cover.

3 Period analysed Years: annual totals Site 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 of quadratic equation (Q) estimate Coefficient of determination r 2 Bet Dagan I=4.458 n 7727 L Valentia I=2.337 n 440 L Pooled data I=2.161 n 245 L Pooled data I= n n 2 Q Months: individual Bet Dagan I=2.146 n L months (mean daily totals) Valentia I=2.457 n L Pooled data I=2.209 n L Pooled data I= n n 2 Q mean months Bet Dagan I=2.408 n L (mean daily Valentia I=2.081 n L totals) Pooled data I=2.186 n L Pooled data I= n n 2 Q Days: individual days Bet Dagan I=2.498 n L (daily totals) Bet Dagan I= n n 2 Q Hours: individual hours Bet Dagan I=2.206 n L (hourly totals) Bet Dagan I= n n 2 Q n ESTIMATING DIRECT SOLAR BEAM IRRADIANCE 349

4 350 G. STANHILL Figure 1. The relationship between mean values of direct irradiance, I, MJm 2 day 1, and sunshine duration, n, h day 1, for individual 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 1.368, r 2 =0.969 Linear regressions calculated for mean monthly values during individual years showed small differences in the parameters of the equations; the mean value for the slopes of all 16 regressions, 2.133, had a standard deviation of 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 ( MJ m 2 per sunshine hour per year) and statistically non-significant (r 2 =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 r 2 =1.00 to a minimum of Although the offset values for regressions of both the pooled and individual years did not significantly differ from zero, the standard error of estimates of I obtained with an equation forced through zero was greater 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 of I using linear regression fitted to the mean daily values of 192 individual months was MJ m 2 day 1 or 9.1% of the mean value of I, which was MJ m 1 day 1 at Bet Dagan. The standard error of the slope was MJ m 2 per sunshine hour, 2.3% of the mean. The coefficient of determination (r 2 =0.911) was highly significant (p=0.001). Differences in the parameters of linear regressions calculated for individual years at Bet Dagan were not negligible; the mean value of the slopes of all 16 regressions 2.432, had a standard deviation of 0.25, with a trend to increase with year of measurement, although this increase was small ( MJ m 2 per sunshine hour per year) and not statistically significant (r 2 =0.12). The slopes for individual years ranged from a maximum of 3.20 MJ m 2 per sunshine hour to a minimum of The coefficients of determination for individual years were all highly significant (p=0.01) and ranged from a maximum of r 2 =0.98 to a minimum of At Bet Dagan the standard error of estimates of I obtained using a linear regression forced through zero 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 by linear regressions with and without an offset value and also by a quadratic, curvilinear equation. The parameters of the equations (Table II) show the quadratic equation had the lowest standard error of I estimates, 10.6% of the mean I value MJ m 2 day 1, and the highest coefficient of determination, r 2 = The better fit provided by a curvilinear relationship and the small, positive offset value of I when n=0, is to be expected on theoretical grounds, as sunshine is not recorded by the Campbell-Stokes apparatus until direct irradiance exceeds the burning threshold value of the sunshine cards, which has been standardized at 120 W m 2 or MJ m 2 h 1 (WMO, 1983). Thus, as n 0 the slope of daily values of I against n will decrease.

5 ESTIMATING DIRECT SOLAR BEAM IRRADIANCE 351 At the other extreme, under high sun, cloudless, dry air and non-turbid conditions, values of I will approach the above-atmosphere, solar constant values of 1367 W m 2 or MJ m 2 h 1 and the slope of daily values of I against n will increase Indi idual daily alues Empirically, the curvilinearity of the relationship was confirmed when the range of daily totals was increased by examining individual daily, rather than mean monthly values of I and n, as is shown in Figure 2 based on 110 daily totals measured at Bet Dagan and selected to cover the full annual range of values. The fitted quadratic equation has a marginally higher coefficient of determination, and a marginally lower standard error of estimate, which is 19.2% of the mean value of I, than the linear regression 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 Indi idual hourly alues A close relationship between I and n was even found for individual hourly values, suggesting that diurnal 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 Bet Dagan, selected to give a full range of hourly values of n (Table II) had a standard error of estimate of 48.4% and a coefficient of determination r 2 which was significant at p= The quadratic relationship fitted to the same data had a standard error of estimate of 44.6% I, and was statistically marginally superior to the linear relationship Annual alues Annual sums of I and n were highly significantly (p=0.001) correlated at both sites although the slope of the linear relationships differed considerably. At Bet Dagan the slope, MJ m 2 per sunshine hour, was much greater than at Valentia, where it was MJ m 2 h 1, again suggesting the curvilinear relationship over the full range of values Long-term trends At both sites, a decrease in the annual totals of sunshine hours was found. The statistically fitted linear trend at Valentia over the period was 4.53 h year 1 and was statistically highly significant, p= At Bet Dagan the linear trend over the shorter period of measurement available, , 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, MJm 2 day 1, and sunshine duration, n, h day 1, at Bet Dagan. The line represents the fitted quadratic equation

6 352 G. STANHILL The mean annual decreases in I corresponding to those in n are MJ m 2 at Valentia and MJ m 2 at Bet Dagan. To examine the relationship between the changes in annual sums of n at the two sites, these were expressed as normalized anomalies,a y =(n y n)/ where n y is the annual total of sun hours for the year y, and n and are, respectively, the mean and standard deviation of the measurement series. There was no significant correlation between the two non-parametric series at p= DISCUSSION The linear and near-linear relationship between I and n demonstrated in this study under the very different radiative regimes of Israel and Ireland, are surprising in that they imply that direct irradiance is constant for that portion of the day when I 120Wm 2, the burning threshold of the Campbell-Stokes sunshine recorder. This despite the fact that I varies markedly with the length of the solar path through the atmosphere, i.e. solar elevation h, and the scattering properties of the atmosphere, in particular its water content and aerosol load. The explanation of this paradox is probably the exponential relationship existing between I and h under clear-sky conditions. For example at Aspendale, a coastal site in South Australia, I increased five-fold between 2 and 20 h, but only 25% between 30 and 70 h (Paltridge and Pratt, 1976). This exponential relationship 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 of I during this period as well as changes in atmospheric turbidity and water content are, together with errors in measurements, primarily of n (Painter, 1981), the reasons for the standard errors of estimates of I based on measurements of n reported herein. In this study, the standard error of estimation varied inversely with the length of the period for which I was estimated. At Bet Dagan, the standard error, expressed as coefficients of variation relative to the mean values of I, was 3.8% for annual estimates, 9.1% for monthly estimates, 19.2% for daily estimates and 44.6% for estimates of hourly values. Corresponding coefficients of variation for the estimates at Valentia were somewhat higher, 6.5% for annual and 12.1% for monthly estimates. The error of estimation for individual daily sums of I at Bet Dagan using a linear regression, 2.93 MJ m 2 day 1,is comparable with the error of estimation at Mexico City, 2.61 MJ m 2 day 1, reported by Galindo Estrada 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 site and/or by the different measures of sunshine duration adopted. At Mexico City the mass of sun card burnt each day, measured as weight loss, was used to estimate I, whereas at Bet Dagan, the recommended standard measure of duration of sunburn was used. Even if it were demonstrated that the volume of sun card burnt provides a marginally superior estimate of direct irradiance, its use can hardly be recommended in view of the long duration of records of sunshine hour duration (at Valentia, for example, since 1869), their widespread availability (335 such records were reported in 1991 in the Monthly Bulletin, Solar Radiation and Radiation Balance Data (the World Network) published for the World Meteorological Organization by Voeikov Main Geophysical Observatory, 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 Bet Dagan and Valentia at other sites with different irradiance regimes. Where estimates of I are needed for diurnal or individual daily values, the relationships at new sites could be established relatively quickly by calibrations over the time and irradiance range of interest. However, the long period of calibration required to validate seasonal and year-to-year relationships makes this approach of limited utility. The year-to-year differences found at both sites suggests that more than 1 year of calibration would be needed to 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 means averaged over a 15 year period with those given below between normalized values of global irradiance and

7 ESTIMATING DIRECT SOLAR BEAM IRRADIANCE 353 sunshine hours, the standard method used to estimate solar irradiance from measurements of sunshine hours. Bet Dagan K =K (0.659 n/n+0.096), r 2 =0.864, p=0.01 Valentia K =K (0.737 n/n+0.180), r 2 =0.935, p=0.01 Pooled data K =K (0.466 n/n+0.242), r 2 =0.949, p=0.001 These standard equations show somewhat lower coefficients of determination and considerably greater between-site variation in the parameters of the equations, which at both sites differ considerably from those derived from the pooled data. The long-term decreases in I found at both sites are not surprising because larger, statistically significant reductions in global, i.e. direct plus diffuse irradiance on a horizontal surface, have been reported at both sites, which were unaccompanied by increases in the extent of cloud cover (Stanhill 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 and at Valentia, on the south-west coast of Ireland, direct solar beam irradiance was highly correlated and 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 with a standard error of less than 10% for both annual totals and mean monthly values. For individual daily totals the error of estimation was less than 20% and, for individual hourly estimates, just below 50%. At Valentia with greater cloud cover and lower solar elevations, the corresponding standard 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 determination, r 2 values, varying between 0.7 and 0.9 according to the period for which the estimation was made. 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 Bet Dagan. A marginally greater, 5%, proportion of the variation in I was explained by variations in n when the theoretically more appropriate quadratic relationship was used in place of a linear one. The use of a single, joint quadratic relationship to estimate I at both sites, resulted in slightly smaller error terms at Valentia and slightly larger ones at Bet Dagan, compared with estimates based on the local relationships. Long-term decreases in n were found at both sites, with trends of different magnitudes and statistical significances; the considerable year-to-year variations in the long-term trends at the two sites, expressed by their normalized anomalies, were only weakly correlated. At Valentia the annual decrease between 1940 and 1995 averaged 0.353% and was highly significant at p=0.01; at Bet Dagan the decrease between 1963 and 1995 averaged 0.092% per year and was only significant at p=0.10. ACKNOWLEDGEMENTS I wish to thank A. Ianetz of the Israel Meteorological Service and D. Fitzgerald of the Irish Meteorological Service for their kindness in providing unpublished data; also Etty Dadosh for assistance with computations and S. Moreshet for the preparation of the figures. Contribution from the Agricultural Research Organization, The Volcani Center, Bet-Dagan, Israel, No E, 1997 series.

8 354 G. STANHILL REFERENCES Galindo Estrada, I.G. and Fournier D Albe, E.M The use of the Campbell-Stokes sunshine recorder as an integrating actinometer, Q. J. R. Meteorol. Soc., 86, Martinez, J.A., Tena, F., Onrubia, J.E., and de la Rubia, J The historical evolution of the Ångstrom formula and its modifications, Agric. For. Meteorol., 33, Painter, H.E The performance of a Campbell-Stokes sunshine recorder compared with a simultaneous record of normal incidence irradiance, Meteorol. Mag., 110, Paltridge, G.W. and Pratt, C.M.R Radiati e Processes in Meteorology and Climatology, Elsevier, Amsterdam, p.117. Stanhill, G. and Moreshet, S Global radiation climate change at seven sites remote from surface sources of pollution, Climatic Change, 26, Stanhill, G. and Ianetz, A Long-term trends in, and the spatial variation of, global irradiance in Israel, Tellus, 49B, WMO, Measurement of radiation, in Guide to Meteorological Instrument and Obser ing Practice, 5th edn, World Meteorological Organization, Geneva, Chapter 9.