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Solar radiation on sloping surfaces with different orientations in granada, Spain
Solar Energy Vol. 28, No. 3, pp. 257-262, 1982 Printed in Great Britain.
O0394192X/821030257.-O6503.001O © 1982 Pergamon Press Ltd.
SOLAR RADIATION ON SLOPING SURFACES WITH DIFFERENT ORIENTATIONS IN GRANADA, SPAIN J. I. JIMENEZand Y. CASTRO Department Fisica Fundamental, Facultad de Ciencias, Universidad de Granada, Granada, Spain
(Received 17 February 1981; accepted 18 August 1981) Abstract--Daily radiation on slopes is usually computed by the Liu and Jordan method. Measurements of the global and diffuse radiation fluxes at various tilt and azimuth angles have been made in clear days with a pyranometer equatorially mounted upon a modified theodolite system• The resulting data have been used to evaluate the validity of the Liu and Jordan model with the assumption of an isotropic distribution of diffuse radiation in the sky. It is concluded that the model yields significantlybetter results when the reception surface is oriented in the azimuth of the Sun, but not for other azimuthal orientations of the slope. Although an evident anisotropy has been found in the diffuse radiation distribution, the results obtained by this modeling approach are considered sufficient for flat-plate collector applications. I. INTRODUCTION The total radiation balance, i.e. direct, diffuse and reflected solar radiation received by a sloping surface has not been throughly worked out in the authors opinion. Because of the complexities associated to precise calculations of the flux of diffuse radiation incident upon slopes of different orientations many workers[I-5] assume an isotropic distribution for practical calculations of the skylight and reflected radiation on the slopes involved• In order to compute the radiation incident on a tilted and oriented plane, it is necessary to start with the hourly direct and diffuse radiation on a horizontal plane. If these are not available, it is possible to calculate the values from global irradiation by a suitable method [6, 7]. In the present paper, we investigate the dependence of the radiation fluxes with the slope and the azimuthal orientation from the south. Similarly, we consider also the validity of the Liu and Jordan model[8] based on the isotropic assumption by comparison with the measurements carried out in our laboratory.
Io incident upon a plane with a slope s and an azimuthal orientation y and the direct solar radiation on a horizontal plane/, can be expressed as [9]
Ro =~_=cos 0o cos 0z
where 0o is the angle of incidence of direct solar radiation on a plane of any slope and orientation and 0z is the Sun elevation, i.e. the angle of incidence of direct solar radiation on a horizontal plane• (ii) Diffuse sky radiation The correction factor for the diffuse radiation component depend on the distribution assumed of them over the sky. In this work the Liu and Jordan's hypothesis was assumed, taking into account that this component is uniformly distributed over the sky dome [8, 9]. Thus, a surface tilted a slope angle s from the horizontal "sees" a portion of the sky dome given by[3, 8, 9] /as
2. TltEORETICALREMARKS The flux of radiation upon a tilted flat surface consist of three contributions. (i) The flux of direct solar radiation, (ii) The flux of diffuse sky radiation and (iii) the part of reflected radiation (direct plus diffuse) by the ground underlying the atmosphere which is incident on the tilted surface. Each one of these contributions depends on the geographical coordinates, cloud coverage, the solar altitude and the optical properties of the atmosphere and underlying surface• We shall consider these fluxes separately• (i) Direct solar radiation The flux of direct solar radiation may be calculated by the evaluation of the factor Ro when we know this flux on a horizontal plane. The factor Ro which relates the direct solar radiation
(1)
l+coss .
• =
2
~d
(2)
being Id.s the flux of diffuse radiation incident on a plane tilted a slope angle s in any orientation and lathe one on a horizontal plane. (iii) Ground reflection Also with the assumed hypothesis, the sloped surface "see" a portion of the ground and the surface receives the radiation reflected from it. Assuming a diffuse reflectance p (the surface albedo) for the surroundings, the value of reflected radiation Ir.s incident on a tilted plane, is [3, 8, 9]
It., -
1 - cos s
2
(l + Ia)p.
(3)
The total irradiance I,.s upon a tilted surface of any 257
258
J. I. JIMC~NEZand Y. CASTRO
orientation is then
(4)
I,.s: Io + Ia.s + l,.s. Substituting the values of Io, Ia.s and It., we find - . l+coss l-coss .... I,.s = KN + - - - ~ Ia + - - - - - ~ 1 1 + la)p.
(5)
Liu and Jordan [6] considered that the diffuse radiation can be taken as about 20 per cent of the global flux on a horizontal surface. The validity of their assumption has been proved as well for Mediterranean towns as Barcelona with somewhat analogue climatologic conditions [7]. On the other hand, the diurnal distribution of the albedo of the underlying surface has been estimated by several workers[10, 11]. For the roof of the University's building (tar-macadam cover) we take p = 0.2. With these hypothesis the values of irradiance have been calculated with the formula
I,.s = 0.8I, Ro + 0.21,
+ 0.21,
1 - cos s 2
(6)
Thus a set of data can be used not only to assess the validity of the model described above but to check the equations of a regression model proposed by Munroe [12]. This regression model was described by two equations, the first for daily values Sn : Smin -'~ (Smax - Smin) exp
[
-
(7)
and the second for instantaneous values
It = I. { l -exp [ - ((ta/2)- Abs (12- t))2]} b
(8)
where n is the day of the year, Sn is the average daily total energy, Smax and Smi, are the maximum and the minimum average value of daily totals for the year, I, is the average irradiance in W/m2 at time t hours, In is the maximum value of the average irradiance for day n, ta is the length of the day and a and b are constants. 3. MATERIALSAND METHODOF MEASUREMENT
The data necessary for the computations concerning the angular distribution of the intensity of the direct, scattered and reflected radiation were obtained by means of direct measurements carried out with two KippZonen pyranometers. The view angle is 2 r and measures the global radiation (direct plus diffuse) over a horizontal surface. Both solarimeters were conveniently calibrated before the experiments according to the International Pyrheliometric Scale 1956. One of the pyranometers was mounted horizontally and measure the global radiation. The pyranometer used was mounted equatorially on a modified meteorological theodolite. With the theodolite we obtain slopes from 0 to 900 at 150 interval and measures at orientations from south from 0 to 3600 at 450
interval. The system was provided with a small shading disc (4 cm in diameter) mounted on a semicircular track (60cm in diameter) to obtain the measurements of diffuse radiation. The complete system used to carry out the measurements was installed on the flat roof of one of the University buildings where the exposure of the sensor was good, without appreciable obstacles for the incoming radiation and at a height of 2 m over the roof level. Outputs of the two sensors were recorded continuously on a Houston Omniscribe two channel chart recorder. The set of measurements studied here was taken under conditions of clear skies on a series that began 27 June and finished 23 July 1980. Similar conditions in the atmospheric characteristics were considered in the selection of the days that compose our data set; so that six days were selected for the study, that in which the solar radiation was greater than 60 per cent of the extraterrestrial solar radiation. For each day we analyzed a series of data with the pyranometers oriented as described above. The set of 49 points has been normalized for the changes in the Sun elevation during each series. Each measure was made once with the sensor shaded from direct solar radiation and once with the sensor completely exposed to the Sun, the time interval taken in both modes of observation being about 2 min. 4. DATAANALYSIS
The data obtained for the six days selected with the criteria mentioned above were used to construct maps of global and diffuse radiation for a solar elevation of 40°. The results of each experiment present great similarities and confirm the selection of the days studied. Figures 1 and 2 show the average results of all of the experiments. We can see in Fig. 1 that good symmetry exist around the principal axis. The change of flux from minimum to maximum is nearly of an order of magnitude as a consequence of the great dominance of the direct solar radiation over the sky radiation when the sensor is directly oriented to the Sun and related with the dependence with cos 0o. These results are consistent with the literature [13, 14]. The maximum of irradiance (900 W/m2) is presented between the slopes 45 and 600 and for an azimuthal orientation of 90°E (from south). In similar way the minimum of irradiance (90 W/m2) appear for slopes of 45--600 and for orientation from 225°E to near 315°E. Figure 2 shows the results from diffuse radiation data. The first characteristic that can be extracted from them is the evident anisotropy in the distribution of this component of the global radiation, coming from the sky and ground reflection. The anisotropy presented show an increase of diffuse radiation in the circumsolar region and near the horizon in accordance with many workers [2, 13, 14]. The contribution of diffuse component of the radiation field is about 17 per cent of global flux upon a horizontal surface, 13 per cent on a surface normal to the propagation of the solar beam, and, of course, 100 per cent for a surface oriented in such a way that the sensor is
259
Solar radiation on sloping surfaces with different orientations 180
~0
270
0 Fig. 1. Globalsolar radiation on a pyranometer oriented at various combinationsof slopes and azimuth angles from clear skies. Slope angle is distance from center; azimuth is with respect to the South. (Sun elevation 40; units are W/m2). 180
270
0 Fig. 2. Diffuse radiation from sky and ground on a pyranometer as in Fig. 1. completely shaded from the solar beam. The great increment presented near the horizon is due to the effect of "brightening" horizon in clear atmospheres, and to the ground reflection which contributes a significant amount for the case of a vertical wall (90° slope) due to the existence of a mirror effect in the sensor platform.
5, MODELCALCULATIONS The average radiation on a tilted surface with different orientations has been estimated with the model described above. First, we calculated the average daily irradiance 5'. from (7), and later, from (8) we obtained I, for the four minutes periods corresponding to the experimental
260
J. I. JIMENEZand Y. CASTRO
measurements for each slope and azimuthal orientation. Maps constructed for the average values of the global irradiation for the six days of the experiments, calculated from (6) are shown in Fig. 3 and for diffuse radiation in Fig. 4. The first characteristic observed for the global radiation (Fig. 3) is the great similarity with the experi-
mental results showed in Fig. 1. Note that the absolute values of maximum flux (800 W/m2) and minimum flux (100 W/m2), are nearly the same as those found experimentally. However, in Fig. 4 the estimate diffuse flux differs substantially of the experimental results shown in Fig. 2. 180
270
0 Fig. 3. Model calculations of global radiation as in Fig. 1. 180
90
2701
0 Fig. 4. Model calculations of diffuse radiation from sky and ground as in Fig. 1.
261
Solar radiation on sloping surfaces with different orientations Therefore, the hypothesis of isotropy of the diffuse radiation assumed by Liu and Jordan does not seem to be substained by our measurements. The anisotropy might be due to the well known brightening horizon exhibited by clear skies and the maximum of the diffuse flux in the circumsolar zone, as stated above. Anisotropy of the radiation reflected from the ground should play a part as well on the effect. The different behaviour of the global solar radiation and the diffuse radiation prompted us to study individually each component of the radiation field for three selected azimuthal orientations. For the sake of convenience we choose for this comparison the azimuths of maximum (90%) and minimum (270°E) and an intermediate value (180°E). The comparison of the observed and calculated values of the direct solar radiation are shown in Fig. 5 as a function of the tilt angle and for the above mentioned orientations. There is good agreement between the observed and calculated values, as the differences between them are always less than 15 per cent except for small values of direct solar radiation (azimuth of 270°E) but some of the difference in this last case might be due to the imperfect cosine response of the pyranometer itself [14]. The results for the diffuse radiation from the sky dome and ground are shown in Fig. 6. Here the discrepancies between the model calculations and the measurements are greater. Only for the 90eE azimuth exists a good agreement and the differences between calculated and observed values increase for the other azimuthal orientations. The magnitude of this diffuse flux is, of course, relatively small in comparison with the direct flux given above, except for 270°E azimuth from south. Figure 7 show the global flux of solar radiation. As the diffuse radiation is always less than 20 per cent, the model calculations and the experimental data present good agreement for the 90 and 180°E orientations. The observed values are below the estimated ones, specially
Tilt angles
zoo
y = 90*
~5o ~ ~oo ~: 50
~._
,~ ~o 4%-go }5 9o
o ,~ ~
8 ~ i5
, - i
y =
E
,
,
,
- -
800
,5o
too 5o o
;5 3 ' o A ~
900--~
,
- ,
Boo
/ y - 90
"~ 7 0 0 600 E
o
500
~400 300' ""-.
"~
0 200 I00
o
,;
~
~
500
400
200
do
-g
90
ongles
for those azimuthal positions where diffuse flux is the most important component of the global radiation. Summarizing, the model employed to estimate the global radiation upon tilted surfaces presents good agreement for normal surfaces whose normal direction is in the plane of propagation of the solar beam where the contribution of the diffuse radiation is small, but there are significant discrepancies for other orientations due to evident anisotropy in the distribution of the diffuse field of radiation. An improved model taking into account this anisotropy is actually in development in our laboratory.
" ' ' " " .....
"/"
2
£~
......
Calculated
_o
300
,
......... O b s e r v e d
600
4..
A 90
Fig 6. Diffuse radiation from sky and ground as a function of the flit angle of the surface sensor for three azimuthal orientations. Comparisonwith model calculations.
Fig, 7. Global solar radiation as a function of the tilt angle of the pyranometer according to measurements and model calculations for three azimuthal orientations.
- -
700
x~
270*
2c~
Tilt
900 ~
y = 180"
-."
".
I OQ
....'-..
f5
"'%.
30
45
60
76
90-
Tilt ongles
Fig. 5. Direct solar radiation as a function of the tilt angle of the pyranometer according to measurements and model calculations for three azimuthal orientations.
6. CONCLUSIONS
Munroe's regression model used for estimations of the global radiation from meteorological data available in many weather stations, can be used to predict success-
262
J. I. JIMI~NEZand Y. CASTRO
fully the radiation flux on a horizontal surface. Using Liu and Jordan's method it is then possible to predict the total radiation flux incident on a sloping surface of any orientation. Results are reasonable when the surface is in the direction of propagation of the solar beam. However, we have verified that the diffuse radiation field shows anisotropy in its distribution. In spite of this, the obtained results are still useful for planning passive systems utilizing solar energy. REFERENCES
1. K. J. A. Revfeim, Solar radiation at a site of known orientation on the earth surface. J.. Appl. Meteorol. 15, 651-656 (1976). 2. K. Ya. Kondratyev and M. P. Manolova, The radiation balance upon slopes. Solar Energy 4, 14-19 (i%0). 3. A. de Vos and G. de Mey, The solar energy incident on a plane at the earth surface: situation in Belgium. Arch. Met. Geoph. Biokl. Ser. B, 25, 135-150(1977). 4. J. C. Page, The estimation of monthly mean values of daily short wave irradiation on vertical and inclined surfaces from sunshine records for latitudes 60 N-40 S. Rep. No. BS 32, Dept. Bidg. Sc., Univ. of Sheffield (1976).
5. M. Villarrubia et aL, Solar radiation incident on tilted flat surfaces in Barcelona, Spain. Solar Energy 25(3), 25%264 (1980). 6. B. Y. H. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4(3), 1-19 (1%0). 7. J. I. Jim6nez et al. Solar and diffuse radiation at Barcelona. Solar Energy 19(6), 775-776 (1977). 8. B. Y. H. Liu and R. C. Jordan, The long term average performance of flat-plate solar energy collectors. Solar Energy 7, 53 (1%3). 9. J. A. Duffie and W. A. Beckman, Solar Energy Thermal Processes. Wiley, New York (1974). 10. K. Ya. Kondratyev, Radiation in the Atmosphere. Academic Press, New York (1%9). 11. J. I. Jim~nez, Ph.D. Thesis, Univ. Aut6noma of Barcelona (1976). 12. M. M. Munroe, Estimations of totals of irradiance on a horizontal surface from U.K. average meteorological data. Solar Energy 24(3), 235-238 (1980). 13. J. I. Jim6nez et al., Plane incident solar radiation. Effects of slope and orientation, Proc. International Work-Shop on Solar Energy, Solar Energy International Syrup., 1-13 (1978). 14. R. C. Temps and K. L. Coulson, Solar radiation incident upon slopes of different orientations. Solar Energy 19, 174184 (1977).
Resumen--La radiaci6n solar diaria sobre superficies inclinadas se calcula comfinmente por el m6todo de Liu y Jordan. Mediante un solar/metro montado ecuatorialmente sobre un teodolito modificadose han realizado medidas de la radiaci6n solar global y difusa en dfas claros para varias combinaciones de inclinaciones y orientaciones. Los datos obtenidos se ban usado para comprobar la validez del modelo de Liu y Jordan con la hip6tesis de distribuci6n isotr6pica de la radiaci6n difusa. Este modelo proporciona mucho mejores resultados cuando la superficie estfi orientada hacia el Sol que para otras orientaciones. Aunque se ha encontrado una evidente anisotropla en la distribuci6n de la radiaci6n difusa, los resultados obtenidos a partir de este modelo se revelan suficientes para suutilizati6n en el disefio de sistemas de approvechamiento de la energia solar, en particular, para colectores planos.
O0394192X/821030257.-O6503.001O © 1982 Pergamon Press Ltd.
SOLAR RADIATION ON SLOPING SURFACES WITH DIFFERENT ORIENTATIONS IN GRANADA, SPAIN J. I. JIMENEZand Y. CASTRO Department Fisica Fundamental, Facultad de Ciencias, Universidad de Granada, Granada, Spain
(Received 17 February 1981; accepted 18 August 1981) Abstract--Daily radiation on slopes is usually computed by the Liu and Jordan method. Measurements of the global and diffuse radiation fluxes at various tilt and azimuth angles have been made in clear days with a pyranometer equatorially mounted upon a modified theodolite system• The resulting data have been used to evaluate the validity of the Liu and Jordan model with the assumption of an isotropic distribution of diffuse radiation in the sky. It is concluded that the model yields significantlybetter results when the reception surface is oriented in the azimuth of the Sun, but not for other azimuthal orientations of the slope. Although an evident anisotropy has been found in the diffuse radiation distribution, the results obtained by this modeling approach are considered sufficient for flat-plate collector applications. I. INTRODUCTION The total radiation balance, i.e. direct, diffuse and reflected solar radiation received by a sloping surface has not been throughly worked out in the authors opinion. Because of the complexities associated to precise calculations of the flux of diffuse radiation incident upon slopes of different orientations many workers[I-5] assume an isotropic distribution for practical calculations of the skylight and reflected radiation on the slopes involved• In order to compute the radiation incident on a tilted and oriented plane, it is necessary to start with the hourly direct and diffuse radiation on a horizontal plane. If these are not available, it is possible to calculate the values from global irradiation by a suitable method [6, 7]. In the present paper, we investigate the dependence of the radiation fluxes with the slope and the azimuthal orientation from the south. Similarly, we consider also the validity of the Liu and Jordan model[8] based on the isotropic assumption by comparison with the measurements carried out in our laboratory.
Io incident upon a plane with a slope s and an azimuthal orientation y and the direct solar radiation on a horizontal plane/, can be expressed as [9]
Ro =~_=cos 0o cos 0z
where 0o is the angle of incidence of direct solar radiation on a plane of any slope and orientation and 0z is the Sun elevation, i.e. the angle of incidence of direct solar radiation on a horizontal plane• (ii) Diffuse sky radiation The correction factor for the diffuse radiation component depend on the distribution assumed of them over the sky. In this work the Liu and Jordan's hypothesis was assumed, taking into account that this component is uniformly distributed over the sky dome [8, 9]. Thus, a surface tilted a slope angle s from the horizontal "sees" a portion of the sky dome given by[3, 8, 9] /as
2. TltEORETICALREMARKS The flux of radiation upon a tilted flat surface consist of three contributions. (i) The flux of direct solar radiation, (ii) The flux of diffuse sky radiation and (iii) the part of reflected radiation (direct plus diffuse) by the ground underlying the atmosphere which is incident on the tilted surface. Each one of these contributions depends on the geographical coordinates, cloud coverage, the solar altitude and the optical properties of the atmosphere and underlying surface• We shall consider these fluxes separately• (i) Direct solar radiation The flux of direct solar radiation may be calculated by the evaluation of the factor Ro when we know this flux on a horizontal plane. The factor Ro which relates the direct solar radiation
(1)
l+coss .
• =
2
~d
(2)
being Id.s the flux of diffuse radiation incident on a plane tilted a slope angle s in any orientation and lathe one on a horizontal plane. (iii) Ground reflection Also with the assumed hypothesis, the sloped surface "see" a portion of the ground and the surface receives the radiation reflected from it. Assuming a diffuse reflectance p (the surface albedo) for the surroundings, the value of reflected radiation Ir.s incident on a tilted plane, is [3, 8, 9]
It., -
1 - cos s
2
(l + Ia)p.
(3)
The total irradiance I,.s upon a tilted surface of any 257
258
J. I. JIMC~NEZand Y. CASTRO
orientation is then
(4)
I,.s: Io + Ia.s + l,.s. Substituting the values of Io, Ia.s and It., we find - . l+coss l-coss .... I,.s = KN + - - - ~ Ia + - - - - - ~ 1 1 + la)p.
(5)
Liu and Jordan [6] considered that the diffuse radiation can be taken as about 20 per cent of the global flux on a horizontal surface. The validity of their assumption has been proved as well for Mediterranean towns as Barcelona with somewhat analogue climatologic conditions [7]. On the other hand, the diurnal distribution of the albedo of the underlying surface has been estimated by several workers[10, 11]. For the roof of the University's building (tar-macadam cover) we take p = 0.2. With these hypothesis the values of irradiance have been calculated with the formula
I,.s = 0.8I, Ro + 0.21,
+ 0.21,
1 - cos s 2
(6)
Thus a set of data can be used not only to assess the validity of the model described above but to check the equations of a regression model proposed by Munroe [12]. This regression model was described by two equations, the first for daily values Sn : Smin -'~ (Smax - Smin) exp
[
-
(7)
and the second for instantaneous values
It = I. { l -exp [ - ((ta/2)- Abs (12- t))2]} b
(8)
where n is the day of the year, Sn is the average daily total energy, Smax and Smi, are the maximum and the minimum average value of daily totals for the year, I, is the average irradiance in W/m2 at time t hours, In is the maximum value of the average irradiance for day n, ta is the length of the day and a and b are constants. 3. MATERIALSAND METHODOF MEASUREMENT
The data necessary for the computations concerning the angular distribution of the intensity of the direct, scattered and reflected radiation were obtained by means of direct measurements carried out with two KippZonen pyranometers. The view angle is 2 r and measures the global radiation (direct plus diffuse) over a horizontal surface. Both solarimeters were conveniently calibrated before the experiments according to the International Pyrheliometric Scale 1956. One of the pyranometers was mounted horizontally and measure the global radiation. The pyranometer used was mounted equatorially on a modified meteorological theodolite. With the theodolite we obtain slopes from 0 to 900 at 150 interval and measures at orientations from south from 0 to 3600 at 450
interval. The system was provided with a small shading disc (4 cm in diameter) mounted on a semicircular track (60cm in diameter) to obtain the measurements of diffuse radiation. The complete system used to carry out the measurements was installed on the flat roof of one of the University buildings where the exposure of the sensor was good, without appreciable obstacles for the incoming radiation and at a height of 2 m over the roof level. Outputs of the two sensors were recorded continuously on a Houston Omniscribe two channel chart recorder. The set of measurements studied here was taken under conditions of clear skies on a series that began 27 June and finished 23 July 1980. Similar conditions in the atmospheric characteristics were considered in the selection of the days that compose our data set; so that six days were selected for the study, that in which the solar radiation was greater than 60 per cent of the extraterrestrial solar radiation. For each day we analyzed a series of data with the pyranometers oriented as described above. The set of 49 points has been normalized for the changes in the Sun elevation during each series. Each measure was made once with the sensor shaded from direct solar radiation and once with the sensor completely exposed to the Sun, the time interval taken in both modes of observation being about 2 min. 4. DATAANALYSIS
The data obtained for the six days selected with the criteria mentioned above were used to construct maps of global and diffuse radiation for a solar elevation of 40°. The results of each experiment present great similarities and confirm the selection of the days studied. Figures 1 and 2 show the average results of all of the experiments. We can see in Fig. 1 that good symmetry exist around the principal axis. The change of flux from minimum to maximum is nearly of an order of magnitude as a consequence of the great dominance of the direct solar radiation over the sky radiation when the sensor is directly oriented to the Sun and related with the dependence with cos 0o. These results are consistent with the literature [13, 14]. The maximum of irradiance (900 W/m2) is presented between the slopes 45 and 600 and for an azimuthal orientation of 90°E (from south). In similar way the minimum of irradiance (90 W/m2) appear for slopes of 45--600 and for orientation from 225°E to near 315°E. Figure 2 shows the results from diffuse radiation data. The first characteristic that can be extracted from them is the evident anisotropy in the distribution of this component of the global radiation, coming from the sky and ground reflection. The anisotropy presented show an increase of diffuse radiation in the circumsolar region and near the horizon in accordance with many workers [2, 13, 14]. The contribution of diffuse component of the radiation field is about 17 per cent of global flux upon a horizontal surface, 13 per cent on a surface normal to the propagation of the solar beam, and, of course, 100 per cent for a surface oriented in such a way that the sensor is
259
Solar radiation on sloping surfaces with different orientations 180
~0
270
0 Fig. 1. Globalsolar radiation on a pyranometer oriented at various combinationsof slopes and azimuth angles from clear skies. Slope angle is distance from center; azimuth is with respect to the South. (Sun elevation 40; units are W/m2). 180
270
0 Fig. 2. Diffuse radiation from sky and ground on a pyranometer as in Fig. 1. completely shaded from the solar beam. The great increment presented near the horizon is due to the effect of "brightening" horizon in clear atmospheres, and to the ground reflection which contributes a significant amount for the case of a vertical wall (90° slope) due to the existence of a mirror effect in the sensor platform.
5, MODELCALCULATIONS The average radiation on a tilted surface with different orientations has been estimated with the model described above. First, we calculated the average daily irradiance 5'. from (7), and later, from (8) we obtained I, for the four minutes periods corresponding to the experimental
260
J. I. JIMENEZand Y. CASTRO
measurements for each slope and azimuthal orientation. Maps constructed for the average values of the global irradiation for the six days of the experiments, calculated from (6) are shown in Fig. 3 and for diffuse radiation in Fig. 4. The first characteristic observed for the global radiation (Fig. 3) is the great similarity with the experi-
mental results showed in Fig. 1. Note that the absolute values of maximum flux (800 W/m2) and minimum flux (100 W/m2), are nearly the same as those found experimentally. However, in Fig. 4 the estimate diffuse flux differs substantially of the experimental results shown in Fig. 2. 180
270
0 Fig. 3. Model calculations of global radiation as in Fig. 1. 180
90
2701
0 Fig. 4. Model calculations of diffuse radiation from sky and ground as in Fig. 1.
261
Solar radiation on sloping surfaces with different orientations Therefore, the hypothesis of isotropy of the diffuse radiation assumed by Liu and Jordan does not seem to be substained by our measurements. The anisotropy might be due to the well known brightening horizon exhibited by clear skies and the maximum of the diffuse flux in the circumsolar zone, as stated above. Anisotropy of the radiation reflected from the ground should play a part as well on the effect. The different behaviour of the global solar radiation and the diffuse radiation prompted us to study individually each component of the radiation field for three selected azimuthal orientations. For the sake of convenience we choose for this comparison the azimuths of maximum (90%) and minimum (270°E) and an intermediate value (180°E). The comparison of the observed and calculated values of the direct solar radiation are shown in Fig. 5 as a function of the tilt angle and for the above mentioned orientations. There is good agreement between the observed and calculated values, as the differences between them are always less than 15 per cent except for small values of direct solar radiation (azimuth of 270°E) but some of the difference in this last case might be due to the imperfect cosine response of the pyranometer itself [14]. The results for the diffuse radiation from the sky dome and ground are shown in Fig. 6. Here the discrepancies between the model calculations and the measurements are greater. Only for the 90eE azimuth exists a good agreement and the differences between calculated and observed values increase for the other azimuthal orientations. The magnitude of this diffuse flux is, of course, relatively small in comparison with the direct flux given above, except for 270°E azimuth from south. Figure 7 show the global flux of solar radiation. As the diffuse radiation is always less than 20 per cent, the model calculations and the experimental data present good agreement for the 90 and 180°E orientations. The observed values are below the estimated ones, specially
Tilt angles
zoo
y = 90*
~5o ~ ~oo ~: 50
~._
,~ ~o 4%-go }5 9o
o ,~ ~
8 ~ i5
, - i
y =
E
,
,
,
- -
800
,5o
too 5o o
;5 3 ' o A ~
900--~
,
- ,
Boo
/ y - 90
"~ 7 0 0 600 E
o
500
~400 300' ""-.
"~
0 200 I00
o
,;
~
~
500
400
200
do
-g
90
ongles
for those azimuthal positions where diffuse flux is the most important component of the global radiation. Summarizing, the model employed to estimate the global radiation upon tilted surfaces presents good agreement for normal surfaces whose normal direction is in the plane of propagation of the solar beam where the contribution of the diffuse radiation is small, but there are significant discrepancies for other orientations due to evident anisotropy in the distribution of the diffuse field of radiation. An improved model taking into account this anisotropy is actually in development in our laboratory.
" ' ' " " .....
"/"
2
£~
......
Calculated
_o
300
,
......... O b s e r v e d
600
4..
A 90
Fig 6. Diffuse radiation from sky and ground as a function of the flit angle of the surface sensor for three azimuthal orientations. Comparisonwith model calculations.
Fig, 7. Global solar radiation as a function of the tilt angle of the pyranometer according to measurements and model calculations for three azimuthal orientations.
- -
700
x~
270*
2c~
Tilt
900 ~
y = 180"
-."
".
I OQ
....'-..
f5
"'%.
30
45
60
76
90-
Tilt ongles
Fig. 5. Direct solar radiation as a function of the tilt angle of the pyranometer according to measurements and model calculations for three azimuthal orientations.
6. CONCLUSIONS
Munroe's regression model used for estimations of the global radiation from meteorological data available in many weather stations, can be used to predict success-
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fully the radiation flux on a horizontal surface. Using Liu and Jordan's method it is then possible to predict the total radiation flux incident on a sloping surface of any orientation. Results are reasonable when the surface is in the direction of propagation of the solar beam. However, we have verified that the diffuse radiation field shows anisotropy in its distribution. In spite of this, the obtained results are still useful for planning passive systems utilizing solar energy. REFERENCES
1. K. J. A. Revfeim, Solar radiation at a site of known orientation on the earth surface. J.. Appl. Meteorol. 15, 651-656 (1976). 2. K. Ya. Kondratyev and M. P. Manolova, The radiation balance upon slopes. Solar Energy 4, 14-19 (i%0). 3. A. de Vos and G. de Mey, The solar energy incident on a plane at the earth surface: situation in Belgium. Arch. Met. Geoph. Biokl. Ser. B, 25, 135-150(1977). 4. J. C. Page, The estimation of monthly mean values of daily short wave irradiation on vertical and inclined surfaces from sunshine records for latitudes 60 N-40 S. Rep. No. BS 32, Dept. Bidg. Sc., Univ. of Sheffield (1976).
5. M. Villarrubia et aL, Solar radiation incident on tilted flat surfaces in Barcelona, Spain. Solar Energy 25(3), 25%264 (1980). 6. B. Y. H. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4(3), 1-19 (1%0). 7. J. I. Jim6nez et al. Solar and diffuse radiation at Barcelona. Solar Energy 19(6), 775-776 (1977). 8. B. Y. H. Liu and R. C. Jordan, The long term average performance of flat-plate solar energy collectors. Solar Energy 7, 53 (1%3). 9. J. A. Duffie and W. A. Beckman, Solar Energy Thermal Processes. Wiley, New York (1974). 10. K. Ya. Kondratyev, Radiation in the Atmosphere. Academic Press, New York (1%9). 11. J. I. Jim~nez, Ph.D. Thesis, Univ. Aut6noma of Barcelona (1976). 12. M. M. Munroe, Estimations of totals of irradiance on a horizontal surface from U.K. average meteorological data. Solar Energy 24(3), 235-238 (1980). 13. J. I. Jim6nez et al., Plane incident solar radiation. Effects of slope and orientation, Proc. International Work-Shop on Solar Energy, Solar Energy International Syrup., 1-13 (1978). 14. R. C. Temps and K. L. Coulson, Solar radiation incident upon slopes of different orientations. Solar Energy 19, 174184 (1977).
Resumen--La radiaci6n solar diaria sobre superficies inclinadas se calcula comfinmente por el m6todo de Liu y Jordan. Mediante un solar/metro montado ecuatorialmente sobre un teodolito modificadose han realizado medidas de la radiaci6n solar global y difusa en dfas claros para varias combinaciones de inclinaciones y orientaciones. Los datos obtenidos se ban usado para comprobar la validez del modelo de Liu y Jordan con la hip6tesis de distribuci6n isotr6pica de la radiaci6n difusa. Este modelo proporciona mucho mejores resultados cuando la superficie estfi orientada hacia el Sol que para otras orientaciones. Aunque se ha encontrado una evidente anisotropla en la distribuci6n de la radiaci6n difusa, los resultados obtenidos a partir de este modelo se revelan suficientes para suutilizati6n en el disefio de sistemas de approvechamiento de la energia solar, en particular, para colectores planos.