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Estimation of diffuse from measured global solar radiation

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Page 1: Estimation of diffuse from measured global solar radiation

Solar Energy Vol. 47, No. 2, pp. 75-82, 1991 00384)92X/91 $3.00 + .00 Printed in the U.S.A. Copyrighl © 1991 Pergamon Press plc

ESTIMATION OF DIFFUSE FROM MEASURED GLOBAL SOLAR RADIATION

W. W. MOR1ARTY Moriarty Meteorological Services, Sunbury, Victoria 3429, Australia

Abstract--A data set of quality controlled radiation observations from stations scattered throughout Australia was formed and further screened to remove residual doubtful observations. It was then divided into groups by solar elevation, and used to find average relationships for each elevation group between relative global radiation ( "clearness index"--the measured global radiation expressed as a proportion of the radiation on a horizontal surface at the top of the atmosphere) and relative diffuse radiation. Clear-cut relationships were found, which were then fitted by polynomial expressions giving the relative diffuse radiation as a function of relative global radiation and solar elevation. When these expressions were used to estimate the diffuse radiation from the global, the results had a slightly smaller spread of errors than those from an earlier technique given by Spencer. It was found that the errors were related to cloud amount, and further relationships were developed giving the errors as functions of global radiation, solar elevation, and the fraction of sky obscured by high cloud and by opaque (low and middle level) cloud. When these relationships were used to adjust the first estimates of diffuse radiation, there was a considerable reduction in the number of large errors .

I. I N T R O D U C F I O N

Information about the climatology of broad band solar radiation is required for many purposes, and for some of these purposes (building design and air conditioning, surface water and energy budgets and snow melt cal- culations in hilly terrain, solar power installations with tilted or moving collectors) it is necessary to break up the total or global radiation into direct and diffuse components. Measurements are now available covering many years at a considerable number of localities, but the gaps in the measuring network are still much too wide to allow simple spatial interpolation between ob- serving stations. Accordingly, workers have developed techniques for estimating global and direct/diffuse solar radiation from commonly made surface meteorological observations. Such techniques may not provide ac- curate results on individual occasions, especially when there are no observations of the hourly duration of direct sunlight, as there is then no way of distinguishing between occasions when the direct solar beam is blocked out by cloud and occasions when it shines through gaps in the cloud; but it is held that errors will tend to average out over many occasions, and the re- sults will give information which is useful climatolog-

ica l ly at places where no direct measurements are available. Moriarty [ 1,2 ] will present such a technique applicable to Australian localities.

There are many localities where global radiation on a horizontal surface has been measured over a number of years, but not direct or diffuse radiation. For such localities estimates o f diffuse or direct radiation may be made using the techniques based on meteorological observations, but it would clearly be preferable to use the extra information provided by the global mea- surements.

A number of investigators have devised techniques for estimating hourly or daily diffuse (or direct) radia- tion from measured global radiation, mostly using av-

75

erage relationships. Spencer[3] used Australian ob- servations to compare four such techniques, consid- ering hourly values. He found that one due to Orgill and Hollands [4 ] was much the best, provided that it was adapted to suit Australian data.

The method exploited a relationship between cor- responding averages of relative global radiation (global radiation expressed as a proportion of the radiation on a horizontal surface at the top of the a tmosphere - - sometimes referred to as the "clearness index") and the ratio of diffuse to global radiation (the "diffuse fract ion") . If the available observations of relative global radiation were divided into ranges of 0.05, and the mean diffuse fraction for each range was plotted against the mean relative global radiation, there re- suited a curve which could be approximated by three straight lines. These straight lines could then be used to estimate the diffuse radiation when it was not mea- sured. Spencer found the best results were obtained when the coefficients for these straight lines were cal- culated independently for each Australian station, but the results were still quite good when the coefficients took values averaged for all Australian stations. He noted a dependance of the coefficients on latitude, but considered this was probably due to changing average air mass with latitude i.e. to solar elevations being higher at lower latitudes.

A recent study of the diffuse fraction employing a similar approach was undertaken by Suehrcke and McCormick [ 5 ]. They made accurate measurements of global and beam radiation, and derived the diffuse radiation on a horizontal surface. They plotted the dif- fuse fraction, averaged over relative global radiation intervals of 0.02, against the relative global radiation, and fitted equations, based partly on theoretical con- siderations, to the resulting curves. We may note three particular ways their conclusions differed from those of the earlier workers: ( i) they noted, and took some

Page 2: Estimation of diffuse from measured global solar radiation

76 W. W. MORIARTY

account of, a dependance of the shape of the curves on solar elevation; (ii) they gave credence to an increase of the diffuse fraction for high values of relative global radiation, attributing it to the effect of reflections from the sides of clouds--the workers cited above had found such an increase, but ignored it; (iii) they found that the instantaneous diffuse fraction correlates with the instantaneous relative global radiation in a way that differs considerably from correlations obtained for daily or monthly values, so that instantaneous (or short- term) values should be used for radiation estimations relevant to nonlinear solar processes.

Iqbal[6] developed a slightly different approach originally put forward by Bugler[7]. He chose obser- vations from high quality observing stations with solar elevations within 1 ° of selected values ranging up to 40 ° , and then for each solar elevation he plotted relative diffuse radiation against relative global radiation. The values for plotting were averages taken for observations in ranges of relative global radiation of 0.05. He found curves whose shape varied quite strongly with solar elevation, but agreed in showing relative diffuse radia- tion increasing with relative global radiation up to a maximum, then decreasing to a minimum, and then increasing again.

Many more Australian radiation data have become available since Spencer's work. Some of these have been used, following the approach of Bugler and Iqbal, to develop relationships for the estimation of diffuse from global radiation anywhere in Australia. It was found possible to improve the accuracy of the results by taking account of the types and amount of cloud present. This paper describes the development of the technique and gives some results.

2. THE DATA SET

Half-hourly totals of global and diffuse radiation on a horizontal surface from twelve observing stations maintained by the Australian Bureau of Meteorology were used, covering a period of five years ( 1981-1985 ). The stations were the same as those used by Spencer except that Kalgoorlie replaced Melbourne, though the period was different. The locations of the stations, which are shown in Fig. 1, were spread out over most of Australia. The observations, kept in the Bureau's files, had been subjected to a range of quality control procedures, but they were further edited to remove all observations from periods when there was reason to suspect misalignment of the occulting disc, or when negative values of direct radiation suggested there might be an instrumental fault. To avoid complications due to shading by objects on the horizon, occasions when the solar elevation was less than 5 ° were deleted from the data set, and so were occasions when either global or diffuse observations were missing. Details of the ed- iting procedure will be described by Moriarty [ 1 ].

The half-hourly totals used were, subject to the above restrictions, those for the half-hours ending be- tween 0700 hours and 1730 hours local apparent time, except that those for the half-hour ending 1330 hours

were omitted. Limitations on the availability of com- puter space prevented use of the complete half-hourly data set.

The final edited data set contained 307 981 paired observations of global and diffuse radiation on a hor- izontal surface. These were divided by the radiation on a horizontal surface at the top of the atmosphere, calculated using a solar constant of 1368 w/m -2 and the solar elevation at the midpoint of the appropriate half-hour, to give paired values of relative global ra- diation (G) and relative diffuse radiation (D).

3. THE RELATIONSHIP BETWEEN DIFFUSE

AND GLOBAL RADIATION

The observations were first formed into groups by solar elevation, using groups consisting of all obser- vations within 5 ° greater or less than 5 °, 10 °, 15 °, 20 °, 30 ° , 40 ° , 50 ° , 60 ° , 70 ° , and 80 ° . Since there were no observations in the data set with solar elevation less than 5 ° , the first group consisted effectively of obser- vations with elevation between 5 ° and l0 °.

The observations in each solar elevation group were then divided into subgroups according to the value of relative global radiation G, and average values of G and relative diffuse radiation D were found for each subgroup. For forming the subgroups the values of G were divided into ranges of 0.05, up to a maximum of 1.0, except that the first subgroup included all cases with G less than 0.1. The number of observations in the top few subgroups of each solar elevation group was small, less than 60 for G groups with average values of 0.9 or more.

The average value of D for each subgroup was then plotted against the average value of G. The results are shown in Fig. 2. The curves were quite similar to those given by Iqbal [ 6 ], though higher solar elevations were included, and the values of D corresponding to values of G greater than about 0.4 were slightly less than he found. His observations were all from the northern hemisphere, so the smaller values of D in this study may be due to a hemispherical difference in atmo- spheric aerosol concentrations.

For each solar elevation group the curve began with a section in which D was approximately equal to G. This section would correspond to situations when the direct sunlight was blocked out by cloud. This does not necessarily imply overcast skies, as there might be clear skies in directions away from the sun. The fact that the average D was not exactly equal to G, but marginally less, may be attributed to a small number of cases in each averaging subgroup when the sun shone briefly, perhaps through thin cloud, during the half- hour of a measurement, with the additional global ra- diation for this small part of the half-hour being bal- anced during the remainder by darker skies and less diffuse radiation than usual.

As G increased beyond about 0.25, D increased more slowly than before until it reached a maximum, and then it decreased to a minimum for values of G between about 0.65 (for low solar elevations) and 0.8.

Page 3: Estimation of diffuse from measured global solar radiation

Estimation of diffuse from measured global solar radiation

~tZ;9 / '

/I ,ALICE SPRINGS ~ ' t ~ OCKHAMPTON

~ BRISBANE

W@ERALDTON

• KALGOORLIE /

' MILDURA WASGA [ ~ Y ~ ' ~ " ~ C ~ , ~ D E L,~I D E WAG GA BERRA

_ LAVERTON LEGEND MT G A M B I E ~

• Stations for d~i'o set A(BQsic set) o S~cli'ions for dora set B(Temperclfe zone comporison set) 0~.

~]~HOBART

Fig. 1. Locations of the Australian radiation measuring stations used in this study.

77

This part of the relationship curve varied strongly with solar elevation. The shape of the curve in this region would be due to the concurrence of (i) an increasing amount of direct radiation in the half-hourly totals due to decreasing interception of the solar beam by cloud, and/or decreasing scattering during its passage through the atmosphere; and (ii) a slower increase and then a decrease of diffuse radiation, due to decreasing reflection from the sides of clouds and/or decreasing scattering by clouds and/or by clear sky.

As G increased further, beyond the minimum in the curve, there was again an increase in the average value of D. Such an increase was also noted by Iqbal[6], and a similar one by Suehrcke and McCormick[5]. Other writers (e.g., Spencer[ 3 ]) found experimental evidence for a similar increase, but discounted it. The

high values of G, with increasing D, would be a result mainly of increasing diffuse radiation, due to reflections from the sides of clouds, combining with large values of direct radiation. It should be noted that, as the high- est few G subgroups contained only a few observations, the average values found for D were not dependable. The lines joining the plotted points in this region were in fact irregular, and the curves given in Fig. 2 have been smoothed.

4. ESTIMATING DIFFUSE RADIATION

To facilitate their use in estimating diffuse radiation, the curves in Fig. 2 were fitted by combinations of polynomials in relative global radiation (G) and solar elevation. The curve for each solar elevation group was

0 " 6 ' i ' ' ' ' ' ' '

¢-

o.~

0.3 u. G) ~J _> 0.2 i==

0 . 1

/:.:." / " .,'" i

i . . ' 1 . , . I . . . ' / . , ,

.......... / • , ~\, . . . . . . ,_ /

0:1 0:2 0:3 o~ 0:5 0:6 0:7 0:8 0;9 1.0 RELATIVE GLOBAL RADIATION

Fig. 2. Variation of average relative diffuse radiation (D) with relative global radiation (G) for various solar elevations (where X = solar elevation).

Page 4: Estimation of diffuse from measured global solar radiation

78 W. W. MORIARTY

broken into four segments, and the segments were fitted by straight lines or quadratics in G. Except for the last section (with increasing values of D) it was possible to fit the observations quite accurately. The relationships found for the various solar elevation groups were then combined by fitting the coefficients to quadratic and cubic expressions in solar elevation. The resulting sys- tem of equations for estimating D from G was com- plicated, but did not present a problem for computer calculation.

The accuracy of the system was checked against two data sets. The first one (data set A) was almost a subset of the basic set used to derive the system. It consisted of the observations for those half-hours which included the synoptic observation times of 0900, 1200, 1500, and 1800 hours local time, for the 12 stations used in the study, and over the same five year period, provided the solar elevation at the midpoint of the half-hour was 5 ° or more. Most of these observations would be included in the basic set, but some of those for the half-hour around 1800 hours local time would not. The data set A was subjected to the same editing procedure as the basic set. In its final form it contained 53 255 observations.

The second comparison data set (data set B) was a completely independent one. It consisted of the ob- servations for the half-hours including the synoptic observation times of 0600, 0900, 1200, 1500, and 1800

hours local time for the stations Adelaide, Brisbane, and Canberra (Fig. 1 ), and for the period (so far as the observations were available) from December 1982 to the end of 1986. Apart from the requirement that the solar elevation at the midpoint of the half-hour should be at least 5 ° , this data set was not subjected to any special editing. It contained 7441 observations.

So that any dependance of the results on solar ele- vation might be easily examined, the solar elevation groups already described were set up for each data set, and recombined to form modified sets. The relative diffuse radiation (D) was then estimated for each global observation, and subtracted from the measured value to give the error. These were averaged for various ways of subdividing each data set. The proportion of absolute errors greater than 0. l MJ m -2 in the half-hour radia- tion totals was also calculated, this giving an idea of the usefulness of the results for many applications[ 3].

Table 1 gives the results, with all the solar elevation groups added together, for each of the observing sta- tions in both test data sets. It should be noted that the overlapping of the solar elevation groups implies that, in Table l, errors corresponding to solar elevations less than 20 ° were given double weight. In the case of data set A, this would offset the fact that there were no early morning (0600 hours) observations. Table 2 shows the results for each of the test data sets by solar elevation group. It may be seen, as might have been expected,

Table 1. Errors (observation-estimation) in estimated diffuse radiation on a horizontal surface by observing station, for the basic data set (data set A), and a smaller independent data set of three temperate zone stations (data set B). The table compares errors when the estimation was done using only cloud and me- teorological data, when it was done using only global radiation measurements, and when it was done using Spencer's method. The figures for the number of observations apply to the estimations using global radiation. The corresponding figures for the estimations using cloud were slightly smaller, and those for Spencer's results, which referred to a different time period from the data set A, were unavailable. The table shows the percentage mean errors (%ME) in relative radiation (except for Spencer's method), and the percentage of

large absolute errors (%LAE), i.e. errors greater than 0. l MJ m -2, in the estimated half-hourly totals of radiation. The relative radiation is the radiation at the ground expressed as a proportion of the

radiation at the top of the atmosphere.

Observing No. of station obs.

Diffuse radiation estimated by cld.+ met.data Global radn. Spencer Rel. 1/2 hr. Rel. 1/2 hr. 1/2 hr. radn. total radn. total total %ME %LAE %ME %LAE %LAE

Data set A. Albany 3917 5.6 Guildford 5986 0.8 Kalgoorlie 4889 - 4.6 Geraldton 5226 5.1 Port Hedland 5010 - 4.6 Mt. Gambler 4823 4.2 Alice Springs 5739 -11.3 Hobart 5307 - 3.4 Laverton 4893 I.I Mildura 5539 2.5 Wagga Wagga 5432 1.5 Rockhampton 4465 -I0.I All stations 61226 - 0.7

23.8 2.8 17.7 21 15,5 - 2.2 13.9 17 19.6 1.3 12.8 18.4 6.8 14.0 19 15.0 - 4.3 12.2 15 24.0 3.9 16.7 17 15.7 -10.2 13.0 13 19.7 2.8 13.0 16 24.9 6.4 18.1 14 17.7 3.7 12.1 16 21.1 4.2 15.5 15 33.4 - 9.9 27.7 20 20.3 0.7 15.3

Data set B. Adelaide 3460 5.0 24.2 8.5 23.7 Brisbane 3490 i.i 22.3 2.8 17.4 Canberra 1479 20.0 29.6 25.2 34.0 All stations 8429 6.3 24.4 9.4 22.9

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Estimation of diffuse from measured global solar radiation

Table 2. Errors (observation-estimation) in estimated diffuse radiation on a horizontal surface by solar elevation group, for the same data sets and the same estimation techniques as in Table 1, except that there are no results for Spencer's method which could not distinguish between solar elevations. The table shows

the percentage mean errors (%ME) in relative radiation, and the percentage of large absolute errors (%LAE) in the estimated half-hourly totals of radiation in the same way as Table 1.

Diffuse radiation estimated by Solar cloud + met.data Global radiation elevation No. of Rel. 1/2 hr. Rel. 1/2 hr. group obs. radn. total radn. total (degrees) %ME %LAE %ME %LAE

Data set A. 5-10 1934 i.i 5-15 4264 1.4

10-20 6145 1.4 15-25 8794 0.7 25-35 12864 0,2 35-45 9761 -1.8 45-55 7332 -3.8 55-65 5221 -2,8 65-75 3018 -2,3 75-85 1893 -4,0

Data set B. 5-10 379 5.8 5-15 575 5.5

10-20 550 8.5 15-25 1141 9.4 25-35 1931 6.0 35-45 1399 5.3 45-55 791 4.8 55-65 874 5.0 65-75 543 8.3 75-85 246 1.4

0 2 0 8 3 7 8 3

19 3 27 4 31 5 38 8 38 7 41 1

0 8 1 6 5 5

I0 8 21 3 31 8 39 3 39 1 47 0 49 8

5.5 0.I 5.1 1.3 3.7 3.5 1.4 6.0

-i .8 13.0 0.5 19.5

-0.9 24.3 - 0 . 1 30 .8 -0 .6 32. i -2 .2 33.5

16.6 12.9 8.9 9 9 6 8 9 2 8 8 9 7

119 3 6

1.3 2.3 5.5

10.5 14.9 24.7 34.1 51 .5 57.3 39.4

79

that the large errors were concentrated in the higher solar elevation groups, where the largest absolute values of radiation occurred.

Tables 1 and 2 also show some statistics of the errors when diffuse radiation was estimated using a technique based only on cloud and other meteorological obser- vations, i.e., making no use of the global radiation ob- servations[l]. The mean errors in relative radiation from the two techniques were comparable. The pro- portion of large absolute errors was smaller when the global observations were used, though sometimes not much smaller, for all the observing stations except Canberra.

Canberra appears to be an atypical station. The large mean error in the estimates of relative diffuse radiation (D) made from cloud and other meteorological ob- servations will be noted in another paper[ 1 ], and will suggest that at least some of this might be due to er- roneously large diffuse radiation measurements. How- ever, something additional would be needed to explain the greater mean error and the higher proportion of large absolute errors when estimates were based on the global radiation measurements. A more detailed ex- amination of the results showed that the additional large errors tended to occur in the summer months during the middle of the day. A possible explanation is that the mountains surrounding Canberra gave rise to preferred development of cumulus clouds in posi- tions where their sides would reflect a large amount of radiation towards the measuring site.

In Table 1 some figures for the frequency of large

errors derived from Spencer's published results are given for comparison. The figures are not precisely comparable with those from this study, due to differ- ences in the way the estimates have been made and differences in the way the data sets have been assem- bled. The figures quoted from Spencer are the errors when the estimating relations are calculated for each station individually, while those for the procedure de- scribed in this paper are errors when a single set of relations is used for all stations. Also, Spencer's data set included a higher proportion of observations with low solar elevation than data set A. For his set included all available observations with hourly global radiation totals above 18 kJ m -2, a lower limit which would have allowed inclusion of many observations with solar elevation lower than the 5 ° which was the lower limit for data set A. Again, the data set A omitted obser- vations earlier (effectively) than 0600 hours or later than 1800 hours in summer, and earlier than 0900 hours or later than 1500 hours in winter, while Spencer used all the half-hourly observations (added together to give hourly totals). Table 2 shows that large errors were rare for low solar elevations, so Spencer's larger proportion of low solar elevations should correspond to a lower proportion of large errors.

Table 1 shows that, despite the differences which should disadvantage the procedure described in the present paper, Spencer's technique produced propor- tionately fewer large errors for only two stations, about the same proportion for three stations, and more for six stations.

Page 6: Estimation of diffuse from measured global solar radiation

80 W. W. MORIARTY

5. THE EFFECT OF CLOUD

For a given value of global radiation there are vari- ations in the contributions of direct and diffuse radia- tion, leading to a scatter in the observed diffuse radia- tion. Part of this is due to variations in the amount, type, and distribution of cloud cover. Routine mete- orological observations show the amount and type of cloud cover (though not its distribution across the sky), so it was decided to examine whether these observations could be used to reduce the frequency of large errors when diffuse radiation is estimated from global radia- tion. The approach adopted was to seek a relation be- tween the observed cloud and errors in the estimated diffuse radiation, and use this relation to improve the estimates. The data set A, described in the last section, was used for this, as it provided a set of half-hourly values of diffuse and global radiation with cloud ob- servations available within each half-hourly period. In general cloud cover changes fairly slowly, so the cloud observations were assumed representative of the whole half-hour [ 8 ].

Observations of low, middle and high cloud made by the Australian Bureau of Meteorology are the ob- server's estimates of the amount of sky which would be obscured by the layers in question if there were no lower clouds, rather than the amount of the layer visible to a ground based observer. The probability that the cloud layer will have an effect on the amount of solar radiation received at the ground, however, especially the amount of direct radiation, is dependent on the amount of sky obscured by the layer as viewed from the ground. For low cloud there was no problem, but it was necessary to adapt the reported amount of sky cover by middle and high cloud. When only two of the three layers were present, the reported cover by the lower layer was the amount visible from the ground, and the visible amount of the higher layer could be deduced using the reported total cloud cover. When there were three cloud layers present it was assumed that the difference between the low cloud and the total cloud amount was evenly divided between the middle and high layers, and adjustments were made if the es- timated cloud cover by either layer exceeded the re- ported cover [ I ].

Middle and low cloud have a similar effect on in- coming solar radiation in that they totally obstruct di- rect radiation (except for brief periods when the direct solar beam passes near the edge of such clouds), while high cloud differs in that it only partially blocks direct radiation. In this study, since it was a first examination of the effect of clouds on the relation between global and diffuse radiation, the situation was simplified by treating low and middle cloud in the same way, adding their sky coverage to give the cover of "opaque" cloud. High cloud was considered separately.

A second difficulty arising from Australian observ- ing practice related to almost overcast and almost clear skies. If there is less than ~ of blue sky visible the con- vention is to report i of cloud; and if there is less than

of cloud visible the convention is to report ~ cloud. Thus, on average, the effect on radiation of a reported cloud cover of 7 would correspond to an actual cloud

cover of more than ~; and the effect of a reported cloud cover of ~ would correspond to an actual cover of less than ~. A study, to be published at a future date, con- siders this matter and finds that no modification is needed for the reported amounts of high cloud, but a reported ~ of opaque cloud should be changed to 0.1, and a reported 7 should be changed to 0.936 [ 1 ]. These adjustments were made to all the cloud reports in this study.

The data set A was divided into solar elevation groups and relative global radiation (G) subgroups in the same way as described earlier for the basic data set. The first estimates of relative diffuse radiation on a horizontal surface (D) were then calculated from each observation of G using the relationships already de- scribed, and the error found by subtracting the esti- mated from the observed value. Next, for each G subgroup of each solar elevation group, a linear com- bination of the high and the opaque cloud cover was fitted to the errors.

Within each solar elevation group the three coeffi- cients in the fitted relationships showed regular vari- ations with G, and the form of the variations followed a fairly clear cut trend as solar elevation increased. By dividing the total range of G into three, and the range of solar elevation into two, it was found possible to fit the coefficients by polynomials which were cubic in G and linear or quadratic in solar elevation. The resulting system was complicated but did not present a problem for computer calculation, and it could be used to find corrections to the first estimates of D.

Table 3 shows the average residual errors, and the proportion of absolute errors greater than 0.1 MJ m -2, by observing station when this technique was applied to data sets A and B, and compares these results with those using the global-diffuse relationship without the cloud correction. Table 4 gives similar results by solar elevation group. It may be seen that the addition of the cloud correction produced a considerable reduction in the proportion of large errors for every station and for every solar elevation group. For Canberra, which we have seen to be an atypical station, there was an improvement as with the other stations, but the results were still not better than when the estimates were made using just cloud and other meteorological information.

6. CONCLUSIONS

A data set of global and diffuse radiation measure- ments was formed from quality controlled material held by the Australian Bureau of Meteorology, and further screened for doubtful observations. It was then used to develop relationships for different solar ele- vations between relative global radiation (G) and the average of corresponding relative diffuse radiation measurements (D). The curves expressing these rela- tionships were quite similar to some developed earlier by Iqbal, but extended to higher solar elevations.

From the curves polynomial expressions were found giving D as a function of G and solar elevation, and these were used to estimate diffuse radiation from the global measurements. The frequency of large absolute errors (greater than 0.1 MJ m -2) in the results was

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Estimation of diffuse from measured global solar radiation

Table 3. Errors (observation-estimation) in estimated diffuse radiation on a horizontal surface by observing station, for the basic data set (data set A), and a smaller independent data set of three temperate zone stations (data set B). The table compares errors when the estimation was done using only global radiation measurements, and when it was done using global radiation measurements together with cloud observations. The figures given for number of observations apply to the estimations using global radiation only, the corresponding figures for the estimations using cloud being slightly smaller. The table shows the percentage mean errors (%ME) in relative radiation and the percentage of large absolute errors (%LAE), i.e. errors

greater than 0.1 MJ m -2 in the estimated half-hourly totals of radiation. The relative radiation is the radiation at the ground expressed as a proportion of the radiation at the top of the atmosphere.

81

Diffuse radiation estimated by Glob.radn. only Glob.radn.+ cloud

Observing No. of Rel. 1/2 hr. Rel. 1/2 hr. station obs. radn. total radn. total

%ME %LAE %ME %LAE

Data set A. Albany 3917 2.8 17.7 0.7 9.7 Guildford 5986 - 2.2 13.9 -0.3 7.4 Kalgoorlie 4889 - 1.3 12.8 -2.4 9.1 Geraldton 5226 6.8 14.0 7.9 9.9 Port Hedland 5010 - 4.3 12,2 -1.3 7.8 Mt. Gambier 4823 3.9 16.7 -2.6 8.5 Alice Springs 5739 -10.2 13.0 -5.1 9.3 Hobart 5307 2.8 13,0 -2.4 7.2 Laverton 4893 6.4 18.1 0.9 11.2 Mi!dura 5539 3.7 12,1 4.2 8.6 Wagga Wagga 5432 4.2 15.5 3.3 9.7 Rockhampton 4465 - 9.9 27.7 -9.3 20.4 All stations 61226 0.7 15.3 -0.3 9.7

Data set B. Adelaide 3460 8.5 23.7 2.3 17.0 Brisbane 3490 2.8 17.4 3.0 11.6 Canberra 1479 25.2 34.0 21.7 29.3 All stations 8429 9.4 22.9 6.3 16.9

found to compare favourably with that from a tech- nique given previously by Spencer.

Next the effect o f c loud on the relationship between

G and D was examined. For this purpose c loud was considered in two layers, high c loud and opaque cloud ( low and middle level c loud) . The errors in the first

Table 4. Errors (observation-estimation) in estimated diffuse radiation on a horizontal surface by solar elevation group, for the same data sets and the same estimation techniques as in Table 3. The table shows

the percentage mean errors (%ME) in relative radiation, and the percentage of large absolute errors (%LAE) in the estimated half-hourly totals of radiation in the same way as Table 3.

Diffuse radiation estimated by Solar Glob,radn. only Glob. Radn.+ cloud elevation No. of Rel. 1/2 hr. Rel. i/2 hr. group obs. radn. total radn. total (degrees} %ME %LAE %ME %LAE

Data set A. 5-10 1934 5.5 0.I 0.6 0.0 5-15 4264 5.1 1.3 0.i 0.2

10-20 6145 3.7 3.5 -0.8 0.9 15-25 8794 1.4 6.0 -1.5 2.4 25-35 12864 -1.8 13.0 -0.5 6.8 35-45 9761 0.5 19.5 1.0 12.4 45-55 7332 -0.9 24.3 0.3 16.7 55-65 5221 -0,i 30.8 -0.9 21.7 65-75 3018 -0.6 32,1 -0.2 23.5 75-85 1893 -2.2 33.5 -i.0 27.5

Data set B. 5-10 379 16.6 1.3 i0.0 0.3 5-15 575 12.9 2.3 7.6 0.3

10-20 550 8.9 5.5 5.2 2.7 15-25 1141 9,9 10.5 6.0 6.2 25-35 1931 6.8 14.9 6.5 I0.8 35-45 1399 9.2 24.7 8.2 16.4 45-55 791 8.8 34.1 7.8 23.6 55-65 874 9.7 51.5 3.8 40.5 65- 75 543 11 . 9 57.3 3.2 50.9 75- 85 246 3.6 39.4 -i . 0 33.5

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82 W. W. MORIARTY

estimates of D from G were calculated, and it was found possible to relate them to the amount of cloud present in the two layers. Polynomial expressions in G and solar elevation were derived setting out the relationship, and these expressions were used to refine the first es- t imates o f diffuse radiation.

It was found that the second estimates were a con- siderable improvement over the first in that there was a considerably smaller number of large errors. Since the t reatment of cloud effects was rather clumsy, it is likely that a more refined approach would result in a further improvement in the results.

For Canberra the results were not as good as for other stations, possibly because of the effects of the surrounding mountains on the summer t ime cloud dis- tributions in the area. In other areas where the topog- raphy might similarly produce preferred areas for cloud development, the technique should be used with cau- tion. Apart from this, it should provide a useful method for estimating diffuse ( a n d / o r direct) radiation when only global measurements are available.

Acknowledgments--This work was commenced while the au- thor was working in the Australian Bureau of Meteorology, and the author is indebted to various of his former colleagues

for assistance and helpful discussions, particularly Mr. F. A. Callus and Ms. C. J. Skinner.

REFERENCES

1. W. W. Moriarty, Estimation of solar radiation from Aus- tralian meteorological observations, Solar Energy (to be published).

2. W. W. Moriarty, Cloud cover as derived from surface observations, sunshine duration, and satellite observa- tions, Solar Energy (to be published).

3. J. W. Spencer, A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation, Solar Energy 29, 19 (1982).

4. J. F. Orgill and K. G. T. Hollands, Correlation equation for hourly diffuse radiation on a horizontal surface, Solar Energy 19, 357 (1977).

5. H. Suehrcke and P. G. McCormick, The diffuse fraction of instantaneous solar radiation, Solar Energy 40, 423 (1988).

6. M. lqbal, Prediction of hourly diffuse solar radiation from measured hourly global radiation on a horizontal surface, Solar Energy 24, 491 (1980).

7. J. M. Bugler, The determination of hourly insolation on an inclined plane using a diffuse irradiance model based on hourly measured global horizontal insolation, Solar Energy 19, 477 (1977).

8. J.A. Davies and D. C. McKay, Estimating solar radiation from incomplete cloud data, Solar Energy 41, 15 ( 1988 ).