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Occurrence of standard skies during typical daytime half-days
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Renewable Energy 33 (2008) 491–500 www.elsevier.com/locate/renene
Technical Note
Occurrence of standard skies during typical daytime half-days Stanislav Darula, Richard Kittler Institute of Construction and Architecture, Slovak Academy of Sciences, 9, Dubravska Road, SK-845 03 Bratislava, Slovak Republic Received 7 September 2006; accepted 30 March 2007 Available online 25 May 2007
Abstract The current trials to introduce new daylight assessment criteria for future building designs as well as for renewable energy simulations with the trend to implement annual daylight profiles for a specific locale or region need more detail information on the exterior daylight conditions. Bratislava is the only locality in Central Europe where a CIE-IDMP general station is recording 1-min regular daylight measurements since 1994 and 10-year data gathered can be used now to derive models valid for wider regions. In this paper, the analysis of measurements and sky-type occurrence is representing daylight conditions only for this single site. As the meteorological net of observatories register sunshine duration for longer periods worldwide, also this information may serve as the basis for modelling exterior daylight illuminance courses as well as typical sky conditions when no other measurements are available. Furthermore, the new General Sky Standard adopted by CIE in 2003 and by ISO in 2004 gives the possibility to study actual skies occurring under four characteristic daylight situations associated with sunshine duration during typical half-days. r 2007 Elsevier Ltd. All rights reserved. Keywords: Daylight climate; Standard skies; Sunshine duration; Skylight; Illuminance daytime courses
1. Introduction For a quite long time, regular sunshine duration measurements using the Campbell–Stokes glass sphere heliograph were registered in many locations and reported in several publications or yearly reports of meteorological stations worldwide. Therefore, these were utilized as the only trustworthy information of the availability of solar energy, sunlight or daylight changing in time and location. For instance, Soler [1] used sunshine duration data of 77 European stations to compare models for the monthly average daily global radiation and later Soler and Gopinathan [2] studied the possibility to derive hourly global radiation courses based on data from 26 locations with the latitude range from 11 to 811. Similarly sunshine duration data were used in daylighting either to find the occurrence probability of typical skies [3] or to predict annual daylight profiles [4]. Since 1992, when the International Commission on Illumination (CIE) initiated the International Daylight Corresponding author. Tel.: +421 2 59309267; fax: +421 2 5477 3548.
E-mail address: [email protected] (S. Darula). 0960-1481/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2007.03.029
Measuring Programme (IDMP), several IDMP stations started regular measurements of the local daylight climate taking instantaneous data every 1 min. The Bratislava IDMP general station was established in 1994 and nowadays 10 fluent years of data gathered during 1994–2003 can be used to specify daylight climate in Slovakia or even in Central Europe. Long-term sunshine duration can be applied to characterise specific conditions or differences in several locations in comparison with data available for Bratislava. The 1-min irradiance data simultaneously registered with the illuminance records at the Bratislava IDMP Station can be used to calculate measured relative sunshine duration representing the 10-year period of measurements, which will be analysed in this study. The basic assumption to calculate sunshine is the threshold intensity 120 W/m2 produced on a plane perpendicular to sunbeams. Thus half-day or daily sunshine duration in hours or relative sunshine duration normalised to astronomically possible daytime can be calculated as well as monthly or yearly averages or even a long term, e.g. 10-year mean value. In Fig. 1 is shown the relative sunshine duration in every month within the 10-year measurement period and their mean course
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Monthly relative sunshine duration, sm
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Fig. 1. Relative sunshine duration monthly changes, Bratislava 1994–2003.
(solid line) with the long-term yearly mean (dot-dashed horizontal line). It is evident that monthly sunshine in any particular year is representing specific weather conditions with seasonal characteristic increases and decreases but in a certain month the differences in some years are quite noticeable. For instance, the minimum 9% sunshine duration in December 1995 has risen to 23.7% in the next year 1996 or even to 30% in 2003, while the 10-year average is just under 20%. In contrary, in July 1995 occurred the maximal 72.2% sunshine duration and the minimal 41.5% in 2000, while in June and August 2000 duration over 73% of possible sunshine were present. The 10-year mean monthly variations with relations to the long-term average sy ¼ 0.42 valid for Bratislava IDMP Station can be fitted by a cosine function of arc angles after the approximation: sm ¼ 0:42 þ 0:173 cos ð0:52 M 3:285Þ þ 0:053 cos ð1:04 M 2:854Þ,
ð1Þ
which is shown in Fig. 1 by a dashed curve quite close to the full lines of 10-year means in any month M. This approximation is useful when absolutely no data are available. This situation applies to the vast territory of Central Europe from the German and Polish Baltic shores roughly from the 541 geographical latitude to the Southern borders of Switzerland, Austria and Hungary, i.e. to 461. However, according to map 2 in Kittler, 1995, [5] in these latitudes the distribution of the long-term average yearly relative sunshine duration approximates from 0.35 for j ¼ 541 to 0.45 for j ¼ 461. As monthly average sunshine duration is closely linked with the probability of half-day situations which characterise daily illuminance profiles there is a possibility to specify also sky types causing diffuse illuminance levels,
methods and procedures were published in [4]. The estimation of the occurrence probability and number of half-day situations within any month was derived up to now. However, relevant standard sky types have to be applied in accordance with long-term occurrence to simulate daylighting during the whole year. If in a specific location no sunshine duration data are available, then Eq. (1) can by used to approximate monthly averages with expected differences in the range of 720%. 2. Typical half-day illuminance courses and their corresponding sunshine duration The graphical images of actually measured illuminance courses and levels during any half-day has identified their possible sorting into four categories which were already described in [6]. These were already applied in the comparison study of the Daylight Reference Year for Bratislava and Athens [7]. The illuminance courses can be characterised in half-day situations with different sunshine durations as well as instability. Thus two selection criteria for each half-day category were applied:
the relative half-day sunshine duration s derived from 5-min instantaneous measurement data, the additional parameter of instability U defining the changeability of global illuminance levels Gv in consecutive time sequences as X U ¼ ln ½ð1=ðn 1ÞÞ jGvi Gviþ1 j, (2) where global illuminance Gv differences in time intervals i and the next i+1 are summarised and divided by their total number n within the half-day.
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These four categories were classified as:
Situation 1: Absolutely cloudless clear half-days when sky patterns and sun beams illuminate the site with either few clouds or with even a solid cloud blocking the sun position for only a short time during the half-day. This category is defined by the half-day relative sunshine duration sX0.75 and time stability expressed the low value of the parameter of instability Uo8.4. Situation 2: Cloudy half-days or foggy periods with a slight penetration of sun beams indicated by brighter spots in the place of the sun position characterised by more or less even bright skies either without any sunlight presence or sometimes also with very low sunlight influences. This category is defined by conditions in the range 0.03oso0.75 and Uo10–6 s. Situation 3: Dark overcast half-days with very low diffuse illuminance levels and permanent sunlight absence, i.e. so0.03. Situation 4: Dynamic, i.e. cloudy-clear half-days with cloud patches passing the sun position that are characterised by abrupt changes caused by frequent covering and uncovering the sun positions in short sequences under different cloudiness and turbidity, which suit the rest of data.
Of course, in all four categories there are different illuminance levels due to changes in solar positions as well as influenced by various atmospheric turbidity and cloudiness conditions resulting in a wide range of diffuse to extraterrestrial illuminance ratios (Dv/Ev) under any sky type as documented in Darula and Kittler trilogy [8]. This can be commented as follows:
In any category, several sky types can be present and the change from one standard sky type to another can be expected [9] or [10], but due to the ratio of the zenith luminance to diffuse illuminance (Lz/Dv) shown in [11] or [12] a similarity in luminance patterns can be identified. In previous studies, analysing 5-year data gathered in 15 sky types at Bratislava IDMP station the range as well as mean and mode values of Dv/Ev as well as Tv values when sunshine was presented. These indicate that in case of clear and cloudless skies with sunlight, it has to be expected that the gradual increase of Pv/Ev ratio is followed by a drop of Dv/Ev dependent on the rising solar altitude. However, simple approximations for all clear skies can be applied in the range of turbidities Tv from 2 to 6.5 for morning half-days which produce halfday courses During cloudy half-days the Dv/Ev ratio is occurring in the wide range 0.15–0.5 but when there is no exact information available the mean value 0.35 is quite acceptable. Similarly uncertain are Dv/Ev ratios during overcast half-days when rather dense cloud layers and often also
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fog are reducing the overall transmittance of the atmosphere. Thus the Dv/Ev range is usually in the range from 0.05 to 0.25 with the mean 0.15. In case of dynamic situations exist similar conditions as under clear skies but in more or less rapid changes in a sequence following the sunlight presence or absence. So in those periods when sunlight is absent Dv/Ev is quite constant around 0.3 while during longer sunny periods it follows the clear sky situations.
3. Sky types associated with the four typical half-day situations The diffuse horizontal illuminance is resulting from the scattering of sun beams within the atmosphere and analysing sky luminance scans the luminance gradation and the scattering indicatrix functions were recently adopted by CIE [9] and ISO [10]. Thus nowadays are standardised 15 sky types characterised by luminance distributions occurring often worldwide in the whole range between totally overcast, partly cloudy and cloudless skies. The identification or sorting the skies when Lz and Dv are simultaneously measured is thus easy when also the instantaneous solar altitude is known. From the Bratislava 5-min data gathered during the 10year measurements 1994–2003 are extracted those cases which are within the strip 72.5% around the appropriate theoretical Lz/Dv curves. Then these typical cases can be sorted by a special computer programme into four half-day situation groups once with sun present and once with sun absent. Thus each of the eight groups will show the number of cases covering any half-day situation and the prevailing number of sky types representing that situation can be identified. To find differences between morning and afternoon half-day situations, these were separately sorted and thus the number of tables was multiplied because for each daylight situation the morning and afternoon number of 5-min cases in a standard sky strip is listed in tables. For detail information are these available in [13], but the relevant results are summarised in the following graphs for only morning half-days. In Fig. 2 are shown sky types during sunny clear mornings in each month within the 5-year period 1994–1998. Although in each half-day situation almost the whole spectrum of sky types can occur the maximal cases found indicate clearly, the prevailing sky type relevant for that situation as well as its frequency related to relative sunshine duration that reflects the 5-year average in a particular month. So, e.g. as August months have the maximum sunshine in Fig. 2 appears the maximum number of 604 5-min cases of sky type 11. The next lower number of 430 cases in the sky type 12 or CIE blue sky while on the third place is the sky type 10 with 327 cases. It is interesting that in all summer months from April to August, the prevailing sky type during morning halfdays is sky type 11 while in all autumn, winter and spring months a shift to sky type 12 or even 13 (in September) is
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Fig. 2. Occurrence of standard skies during clear sunny mornings in Bratislava 1994–1998.
evident. Of course, during December and January there are only few half-days with clear skies and sunshine, therefore the number of cases is small and the spread is random and irregular. Quite similar should be the situation during sunny mornings in Fig. 3 where analysis results in the next 5 years, i.e. 1999–2003 is represented. However, although the relative sunshine duration has risen in the 5-year averages only slightly, i.e. from 0.402 to 0.439, the shift to the increasing number of sky type 13 is remarkable and probably caused by more turbid and often summer cloudless situations. Opposite to typical situations of clear half-days are usually cloudy situations connected with sunshine more often associated with longer sunless periods. Therefore, on Fig. 4 is documented this case during the first 5 years 1994–1998 derived from Bratislava measurements. It is evident that sunless cloudy mornings occur quite often in all five first sky types, which belong to the overcast group but with higher diffuse illuminance levels and brighter luminance. Sky type 3, i.e. overcast sky moderately graded with azimuth uniformity seems to be on the top except in wintertime when sky type 2 prevailed. An even more complicated set of all sky types was documented in the second 5 years 1999–2003 as shown in Fig. 5. It is quite interesting that the uniform sky type 5 seems to be the most often for all of the first five sky types. Of course, during totally overcast mornings especially in wintertime (Fig. 6) the first two overcast sky types are prevailing when the sky type 2 and the CIE Overcast Sky. Type 1 is the most frequent in November and December as well as in March during 1994–1998. A similar distribution of sky types with a lower frequency existed also in the years 1999–2003, but astonishingly sky type 5, i.e. Lambert’s Uniform Sky, prevailed from November to January in Fig. 7.
Dynamic half-days (Figs. 8 and 9) are characterised by quite many interperiods with and without sunbeam penetration in between moving cloud patches. Therefore, sky types 11–13 are the most often in both 5-year spans. It is very interesting that during both analysed 5-year periods the total number of cases found within the 2.5% sky-type strips were quite similar, i.e. in the 1994–1998 span there were 169,158 representative case sky types. While in the second period, 1999–2003 there were only a few more (434), totalling 169,592 cases. The distribution in the four half-day situations with morning and afternoon sunny and sunless conditions are summarised in Table 1. Furthermore, these are presented in the barchart diagram in Fig. 10 for sunny periods and in Fig. 11 for sunless periods. It is evident that the prevailing number of cases under situations 1 and 4 comprises of sunny mornings and afternoons, while situations 2 and 3 are associated mostly with sunless conditions as documented in Figs. 2–9. It is quite noticeable that due to higher sunshine duration especially in 2000 and 2003, the number of sunny cases in the Table 1999–2003 has risen considerably while sunless cases under situations 2 and 3 have decreased. These shifts are followed also by consequence shifts in the sky-type prevalence. The summary table also proves the overall similarity of strip sorted data with relation to independent relative sunshine duration in both 5-year spans as the sum of sunny days to all data in 1994–1998 is 0.423 relative to sunshine duration 0.4, while in 1999–2003 is the ratio of sunny to all cases 0.5 due to a higher sunshine duration in this period 0.44. 4. Conclusions The generally available data derived from long-term sunshine duration measurements worldwide characterise the overall frequency of daylight situations occurring
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Fig. 3. Monthly changes of sky types during clear morning half-days in Bratislava 1999–2003.
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Fig. 5. Cloudy mornings in the period 1999–2003 have a prevailing sky type 5.
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Fig. 4. Cloudy mornings are caused by overcast sky types with prevailing uniform skies.
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Fig. 6. Overcast morning half-days especially in winter and spring time are dominated by sky type 1 or 2.
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Fig. 7. Overcast mornings during 1999–2003 are characterised by brighter overcast sky types concentrated mainly in winter time.
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Fig. 8. During dynamic conditions in mornings with prevailing sunny periods the occurrence of different sky types 11–13 is typical.
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Fig. 9. During the measuring period 1999–2003, clear sky types were prevailing during morning dynamic half-days.
Table 1 Total number of cases found in the Lz/Dv strips from the whole set of Bratislava 5-min data gathered during the years Half-day situation
Sunny mornings
Sunless mornings
Sunny afternoons
Sunless afternoons
Sum
1994–1998 1 2 3 4 Sum
13,658 4628 2783 15,207 36,276
1010 13,356 26,031 9531 49,928
13,841 4177 2480 14,836 35,334
3112 10,406 23,150 10,952 47,620
169,158
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19,846 4032 1564 17,412 42,854
1265 11,362 23,127 7793 43,547
19,785 3821 1482 17,082 42,170
2153 9504 20,693 8671 41,021
169,592
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Fig. 10. Comparison of half-day situations during sunny periods.
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during typical morning and afternoon half-days. If monthly averages of relative sunshine duration are available or can be approximately predicted for any location, then annual daylight profiles, i.e. year-round exterior horizontal illuminance changes characterising the local daylight climate can be derived. The method already described in earlier papers was tested on the bases of two 5-year regular measured data gathered in Bratislava during 1994–1998 and 1999–2003. Due to the enormous number of 5-min averages derived from 1 min instantaneously measured global and diffuse illuminance values the frequency of standard sky types for only the most important situations were selected and documented in this paper. It was shown that a very good correlation exists between the overall sunshine duration characteristics and the frequency of occurrence of standard sky types within different months and cloudiness conditions in Bratislava, Slovakia. After a thorough analysis presented for the four basic half-day situations there is no doubt that the following sky types are important to simulate annual daylight profiles:
Situation 1: The clear morning half-day is certainly typical with the prolonged sunshine under cloudless blue sky type 12 during colder months, i.e. October to March, which are usually dry and therefore with lower turbidities Tv ¼ 2.5–3.5 and Dv/Ev ¼ 0.15–0.25. During the warmer months May to September with higher air humidity, then whitish and more turbid sky types 11 or 13 are prevailing with Tv ¼ 3.5–4.5 and Dv/Ev ¼ 0.2–0.3. Of course, during short periods without sunshine the sky type does not change. Situation 2: The cloudy mornings are usually in 71–75% sunless and therefore are covered by a wide spread of standard sky types 1–13, but the highest number of cases
is under sky type 3 or 5 with Dv/Ev ¼ 0.15–0.35, respectively. Situation 3: The overcast half-days are quite dull and almost sunless. The year-round occurrence of sky types 1–3 is prevailing especially in wintertime, i.e. from November to January, when Dv/Ev is very low, i.e. 0.1–0.2. However, during years with higher sunshine duration in wintertime sky types 4 and 5 can also prevail with Dv/Ev around 0.2. Situation 4: The dynamic half-days are associated with quite a lot of sunshine periods summing up to around 60% of any half-day therefore the most frequent are sky types 11–13 with a wide range of Tv ¼ 3–5 with Dv/Ev in the range 0.2–0.4.
These long-term information on sunshine presence or absence under relevant sky types can serve for the simulations of daily illuminance courses in short time steps respecting the local annual daylight profiles based on the available or assumed data of monthly relative sunshine duration. Acknowledgements This study is summarising partial results elaborated under the support of the Slovak Grant VEGA 2/5093/5. Thanks also for the support of the bilateral SlovakHungarian co-operation under the project SK-HU 1148 as well as the bilateral Slovak-Czech project SK- CZ11006. Appendix A See Tables A.1 and A.2.
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Table A.1 Nomenclature describing symbols, terms and used formulae after the TWIN system [14] Symbol
Description
Formula
a,b av a c, d, e Dv
Parameters for the gradation function j(Z) Extinction coefficient of the ideally clear (Rayleigh) atmosphere Azimuth angle Parameters for the indicatrix function f(w) Diffuse illuminance at ground level in lx
See Table A.2 1 av ¼ 9:9þ0:043 m
Dv/Ev gs d Evo Ev A f(w)
Diffuse clearness index or skylight transmission of the atmosphere/clouds Solar altitude Solar declination Luminous solar constant in lx Extraterrestrial illuminance on the horizontal surface in lx Ellipcity factor Indicatrix functions for any element for solar zenith angle
j j(Z) w Gv J Lv Lv/Lz
Geographical latitude Gradation functions for any element for zenith angular distance between sky element and solar position Global horizontal illuminance on ground level in lx Julian day number Luminance in any sky element in cd/m2 Relative sky luminance distribution
Z cos ZdZ da
Evo ¼ 133800 Ev ¼ Evo A sin gs A ¼ 1+0.034 cos(360/365(J–21)) f(w) ¼ 1+(c exp(dw)–exp(dp/2))+e cos2 w f(Zs) ¼ 1+(c exp(dZs)–exp(dp/2))+e cos2 Zs
Gv ¼ Pv+Dv
Lv Lz
ðwÞjðZÞ ¼ f fðZsÞjð0 Þ
2
Zenith luminance in cd/m Zenith fraction and sky classification parameter Relative optical air mass of the atmosphere
P?
s sm sy S Sa Tv
Parallel beam solar illuminance at the ground level on a normal plane in lx Parallel beam solar irradiance at the ground level on a normal plane in W/m2 Parallel beam solar illuminance at the ground level on a horizontal plane in lx Relative sunshine duration Monthly average relative sunshine duration Yearly average relative sunshine duration Sunshine duration in hours Astronomical sunshine duration in hours Luminous turbidity factor in the direction of sun beams
U Z Zs
Instability parameter Zenith angle Solar zenith angle
Pv
Z¼0 a¼0 ½jðZÞf ðwÞ sin
j(Z) ¼ 1+a exp(b/cos Z) j(01) ¼ 1+a expb
Lz Lz/Dv m
Pe
See Table A.2 R p=2 R 2p
Dv ¼
m¼
1 sin gsþ0:50572ðgsþ6:07995 Þ1:6364
P? ¼ Evo exp(av m Tv)
Pv ¼ P? sin gs s ¼ S/Sa
Measured if Pe4120 W/m2 Sa ¼ 7:51 arc cos ðtg j tg dÞ ðPv=EvÞ Tv ¼ lnav m
Table A.2 Standard sky types and their gradation and indicatrix parameter [9,10] Type
1 2 3 4 5 6 7 8
Description of luminance distribution
Gradation group
Indicatrix group
a
b
c
d
e
CIE Standard Overcast Sky, Steep luminance gradation towards zenith, azimuthal uniformity Overcast with steep luminance gradation and slight brightening toward the sun Overcast, moderately graded with azimuthal uniformity Overcast moderately graded and slight brightening toward the sun Sky of uniform luminance Partly cloudy sky, no gradation towards zenith, slight brightening towards the sun Partly cloudy sky, no gradation towards zenith, brighter circumsolar region Partly cloudy sky, no gradation towards zenith, distinct solar corona
I
1
4.0
0.70
0
1.0
0
I
2
4.0
0.70
2
1.5
0.15
II
1
1.1
0.80
0
1.0
0
II
2
1.1
0.80
2
1.5
0.15
III III
1 2
0 0
1.00 1.00
0 2
1.0 1.5
0 0.15
III
3
0
1.00
5
2.5
0.30
III
4
0
1.00
10
3.0
0.45
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500 Table A.2 (continued ) Type
Description of luminance distribution
Gradation group
Indicatrix group
a
b
c
d
e
9 10 11 12 13 14 15
Partly cloudy, with the obscured sun Partly cloudy, with brighter circumsolar region White—blue sky with distinct solar corona CIE Standard Clear Sky, low luminous turbidity CIE Standard Clear Sky, polluted atmosphere Cloudless turbid sky with broad solar corona White—blue turbid sky with broad solar corona
IV IV IV V V VI VI
2 3 4 4 5 5 5
1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.55 0.55 0.55 0.32 0.32 0.15 0.15
2 5 10 10 16 16 24
1.5 2.5 3.0 3.0 3.0 3.0 2.8
0.15 0.30 0.45 0.45 0.30 0.30 0.15
References [1] Soler A. Statistical comparison for 77 European stations of 7 sunshine-based models. Sol Energy 1990;45(6):365–70. [2] Soler A, Gopinathan KK. Estimation of monthly mean hourly global radiation for latitudes in the 11N–811N range. Sol Energy 1994;52(3):233–9. [3] Nakamura H, Oki M. Investigation on the relation between the probability of occurrence of the three skies and relative sunshine duration. In: Proceedings of the CIE 31st Session 1987;Vol. 1 (no. 1):228–9. [4] Darula S., Kittler R. Monthly sunshine duration as a trustworthy basis to predict annual daylight profiles. In: Proceedings of lux Europa conference, Berlin, 2005:p. 141–144. [5] Kittler R. Alternative possibilities to define the zonal daylight climates on the sunshine duration basis in Europe. In: Asimakopoulos D et al. Daylight II: availability of daylight in Europe and the design of a Daylight Atlas. Final Report JOU2 CT 92-0144, NOA Athens, 1995:2, contributions. [6] Darula S, Kittler R. Sunshine duration and daily courses of illuminance in Bratislava. Int J Climatol 2004;24:1777–83. [7] Darula S. Kittler R. Kambezidis H. Bartzokas A. Markou M. Generation of a daylight reference year for Greece and Slovakia.
[8]
[9]
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[11]
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Final rep of the GR-SK project. 004/01, ICA SAS Bratislava and NOA, Athens, 2004. Darula S, Kittler R. New trends in daylight theory based on ISO/CIE sky standards: 1–3. Build Res J, 2004:52(3):181-97, 2004:52(4):245-55, and 2005:53(1):9-31. Commission Internationale de l’E´clairage, CIE Spatial distribution of daylight—CIE Standard General Sky. CIE Standard S 011/E:2003, CIE Central Bureau, Vienna. International Standard Organisation ISO Spatial distribution of daylight—CIE Standard General Sky. ISO Standard 15469: 2004. Kittler R, Perez R, Darula S. A set of standard skies characterizing daylight conditions for computer and energy conscious design. 1998, Final rep.US-SK grant 92 052 and a set of standard skies. Polygrafia SAV Bratislava, 1998. Kittler R, Darula S. Parametric definition of the daylight climate. Renew Energy 2002;26:177–87. Kittler R, Darula S. Modelling possibilities for predicting annual daylight illuminance courses based on Bratislava data. Build Res J 2006;54:79–100. Darula S, Kittler R. TWIN system: descriptors for the evaluation of illuminance and irradiance availability. Build Res J 2006;54: 189–97.
Renewable Energy 33 (2008) 491–500 www.elsevier.com/locate/renene
Technical Note
Occurrence of standard skies during typical daytime half-days Stanislav Darula, Richard Kittler Institute of Construction and Architecture, Slovak Academy of Sciences, 9, Dubravska Road, SK-845 03 Bratislava, Slovak Republic Received 7 September 2006; accepted 30 March 2007 Available online 25 May 2007
Abstract The current trials to introduce new daylight assessment criteria for future building designs as well as for renewable energy simulations with the trend to implement annual daylight profiles for a specific locale or region need more detail information on the exterior daylight conditions. Bratislava is the only locality in Central Europe where a CIE-IDMP general station is recording 1-min regular daylight measurements since 1994 and 10-year data gathered can be used now to derive models valid for wider regions. In this paper, the analysis of measurements and sky-type occurrence is representing daylight conditions only for this single site. As the meteorological net of observatories register sunshine duration for longer periods worldwide, also this information may serve as the basis for modelling exterior daylight illuminance courses as well as typical sky conditions when no other measurements are available. Furthermore, the new General Sky Standard adopted by CIE in 2003 and by ISO in 2004 gives the possibility to study actual skies occurring under four characteristic daylight situations associated with sunshine duration during typical half-days. r 2007 Elsevier Ltd. All rights reserved. Keywords: Daylight climate; Standard skies; Sunshine duration; Skylight; Illuminance daytime courses
1. Introduction For a quite long time, regular sunshine duration measurements using the Campbell–Stokes glass sphere heliograph were registered in many locations and reported in several publications or yearly reports of meteorological stations worldwide. Therefore, these were utilized as the only trustworthy information of the availability of solar energy, sunlight or daylight changing in time and location. For instance, Soler [1] used sunshine duration data of 77 European stations to compare models for the monthly average daily global radiation and later Soler and Gopinathan [2] studied the possibility to derive hourly global radiation courses based on data from 26 locations with the latitude range from 11 to 811. Similarly sunshine duration data were used in daylighting either to find the occurrence probability of typical skies [3] or to predict annual daylight profiles [4]. Since 1992, when the International Commission on Illumination (CIE) initiated the International Daylight Corresponding author. Tel.: +421 2 59309267; fax: +421 2 5477 3548.
E-mail address: [email protected] (S. Darula). 0960-1481/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2007.03.029
Measuring Programme (IDMP), several IDMP stations started regular measurements of the local daylight climate taking instantaneous data every 1 min. The Bratislava IDMP general station was established in 1994 and nowadays 10 fluent years of data gathered during 1994–2003 can be used to specify daylight climate in Slovakia or even in Central Europe. Long-term sunshine duration can be applied to characterise specific conditions or differences in several locations in comparison with data available for Bratislava. The 1-min irradiance data simultaneously registered with the illuminance records at the Bratislava IDMP Station can be used to calculate measured relative sunshine duration representing the 10-year period of measurements, which will be analysed in this study. The basic assumption to calculate sunshine is the threshold intensity 120 W/m2 produced on a plane perpendicular to sunbeams. Thus half-day or daily sunshine duration in hours or relative sunshine duration normalised to astronomically possible daytime can be calculated as well as monthly or yearly averages or even a long term, e.g. 10-year mean value. In Fig. 1 is shown the relative sunshine duration in every month within the 10-year measurement period and their mean course
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Monthly relative sunshine duration, sm
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Fig. 1. Relative sunshine duration monthly changes, Bratislava 1994–2003.
(solid line) with the long-term yearly mean (dot-dashed horizontal line). It is evident that monthly sunshine in any particular year is representing specific weather conditions with seasonal characteristic increases and decreases but in a certain month the differences in some years are quite noticeable. For instance, the minimum 9% sunshine duration in December 1995 has risen to 23.7% in the next year 1996 or even to 30% in 2003, while the 10-year average is just under 20%. In contrary, in July 1995 occurred the maximal 72.2% sunshine duration and the minimal 41.5% in 2000, while in June and August 2000 duration over 73% of possible sunshine were present. The 10-year mean monthly variations with relations to the long-term average sy ¼ 0.42 valid for Bratislava IDMP Station can be fitted by a cosine function of arc angles after the approximation: sm ¼ 0:42 þ 0:173 cos ð0:52 M 3:285Þ þ 0:053 cos ð1:04 M 2:854Þ,
ð1Þ
which is shown in Fig. 1 by a dashed curve quite close to the full lines of 10-year means in any month M. This approximation is useful when absolutely no data are available. This situation applies to the vast territory of Central Europe from the German and Polish Baltic shores roughly from the 541 geographical latitude to the Southern borders of Switzerland, Austria and Hungary, i.e. to 461. However, according to map 2 in Kittler, 1995, [5] in these latitudes the distribution of the long-term average yearly relative sunshine duration approximates from 0.35 for j ¼ 541 to 0.45 for j ¼ 461. As monthly average sunshine duration is closely linked with the probability of half-day situations which characterise daily illuminance profiles there is a possibility to specify also sky types causing diffuse illuminance levels,
methods and procedures were published in [4]. The estimation of the occurrence probability and number of half-day situations within any month was derived up to now. However, relevant standard sky types have to be applied in accordance with long-term occurrence to simulate daylighting during the whole year. If in a specific location no sunshine duration data are available, then Eq. (1) can by used to approximate monthly averages with expected differences in the range of 720%. 2. Typical half-day illuminance courses and their corresponding sunshine duration The graphical images of actually measured illuminance courses and levels during any half-day has identified their possible sorting into four categories which were already described in [6]. These were already applied in the comparison study of the Daylight Reference Year for Bratislava and Athens [7]. The illuminance courses can be characterised in half-day situations with different sunshine durations as well as instability. Thus two selection criteria for each half-day category were applied:
the relative half-day sunshine duration s derived from 5-min instantaneous measurement data, the additional parameter of instability U defining the changeability of global illuminance levels Gv in consecutive time sequences as X U ¼ ln ½ð1=ðn 1ÞÞ jGvi Gviþ1 j, (2) where global illuminance Gv differences in time intervals i and the next i+1 are summarised and divided by their total number n within the half-day.
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These four categories were classified as:
Situation 1: Absolutely cloudless clear half-days when sky patterns and sun beams illuminate the site with either few clouds or with even a solid cloud blocking the sun position for only a short time during the half-day. This category is defined by the half-day relative sunshine duration sX0.75 and time stability expressed the low value of the parameter of instability Uo8.4. Situation 2: Cloudy half-days or foggy periods with a slight penetration of sun beams indicated by brighter spots in the place of the sun position characterised by more or less even bright skies either without any sunlight presence or sometimes also with very low sunlight influences. This category is defined by conditions in the range 0.03oso0.75 and Uo10–6 s. Situation 3: Dark overcast half-days with very low diffuse illuminance levels and permanent sunlight absence, i.e. so0.03. Situation 4: Dynamic, i.e. cloudy-clear half-days with cloud patches passing the sun position that are characterised by abrupt changes caused by frequent covering and uncovering the sun positions in short sequences under different cloudiness and turbidity, which suit the rest of data.
Of course, in all four categories there are different illuminance levels due to changes in solar positions as well as influenced by various atmospheric turbidity and cloudiness conditions resulting in a wide range of diffuse to extraterrestrial illuminance ratios (Dv/Ev) under any sky type as documented in Darula and Kittler trilogy [8]. This can be commented as follows:
In any category, several sky types can be present and the change from one standard sky type to another can be expected [9] or [10], but due to the ratio of the zenith luminance to diffuse illuminance (Lz/Dv) shown in [11] or [12] a similarity in luminance patterns can be identified. In previous studies, analysing 5-year data gathered in 15 sky types at Bratislava IDMP station the range as well as mean and mode values of Dv/Ev as well as Tv values when sunshine was presented. These indicate that in case of clear and cloudless skies with sunlight, it has to be expected that the gradual increase of Pv/Ev ratio is followed by a drop of Dv/Ev dependent on the rising solar altitude. However, simple approximations for all clear skies can be applied in the range of turbidities Tv from 2 to 6.5 for morning half-days which produce halfday courses During cloudy half-days the Dv/Ev ratio is occurring in the wide range 0.15–0.5 but when there is no exact information available the mean value 0.35 is quite acceptable. Similarly uncertain are Dv/Ev ratios during overcast half-days when rather dense cloud layers and often also
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fog are reducing the overall transmittance of the atmosphere. Thus the Dv/Ev range is usually in the range from 0.05 to 0.25 with the mean 0.15. In case of dynamic situations exist similar conditions as under clear skies but in more or less rapid changes in a sequence following the sunlight presence or absence. So in those periods when sunlight is absent Dv/Ev is quite constant around 0.3 while during longer sunny periods it follows the clear sky situations.
3. Sky types associated with the four typical half-day situations The diffuse horizontal illuminance is resulting from the scattering of sun beams within the atmosphere and analysing sky luminance scans the luminance gradation and the scattering indicatrix functions were recently adopted by CIE [9] and ISO [10]. Thus nowadays are standardised 15 sky types characterised by luminance distributions occurring often worldwide in the whole range between totally overcast, partly cloudy and cloudless skies. The identification or sorting the skies when Lz and Dv are simultaneously measured is thus easy when also the instantaneous solar altitude is known. From the Bratislava 5-min data gathered during the 10year measurements 1994–2003 are extracted those cases which are within the strip 72.5% around the appropriate theoretical Lz/Dv curves. Then these typical cases can be sorted by a special computer programme into four half-day situation groups once with sun present and once with sun absent. Thus each of the eight groups will show the number of cases covering any half-day situation and the prevailing number of sky types representing that situation can be identified. To find differences between morning and afternoon half-day situations, these were separately sorted and thus the number of tables was multiplied because for each daylight situation the morning and afternoon number of 5-min cases in a standard sky strip is listed in tables. For detail information are these available in [13], but the relevant results are summarised in the following graphs for only morning half-days. In Fig. 2 are shown sky types during sunny clear mornings in each month within the 5-year period 1994–1998. Although in each half-day situation almost the whole spectrum of sky types can occur the maximal cases found indicate clearly, the prevailing sky type relevant for that situation as well as its frequency related to relative sunshine duration that reflects the 5-year average in a particular month. So, e.g. as August months have the maximum sunshine in Fig. 2 appears the maximum number of 604 5-min cases of sky type 11. The next lower number of 430 cases in the sky type 12 or CIE blue sky while on the third place is the sky type 10 with 327 cases. It is interesting that in all summer months from April to August, the prevailing sky type during morning halfdays is sky type 11 while in all autumn, winter and spring months a shift to sky type 12 or even 13 (in September) is
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Fig. 2. Occurrence of standard skies during clear sunny mornings in Bratislava 1994–1998.
evident. Of course, during December and January there are only few half-days with clear skies and sunshine, therefore the number of cases is small and the spread is random and irregular. Quite similar should be the situation during sunny mornings in Fig. 3 where analysis results in the next 5 years, i.e. 1999–2003 is represented. However, although the relative sunshine duration has risen in the 5-year averages only slightly, i.e. from 0.402 to 0.439, the shift to the increasing number of sky type 13 is remarkable and probably caused by more turbid and often summer cloudless situations. Opposite to typical situations of clear half-days are usually cloudy situations connected with sunshine more often associated with longer sunless periods. Therefore, on Fig. 4 is documented this case during the first 5 years 1994–1998 derived from Bratislava measurements. It is evident that sunless cloudy mornings occur quite often in all five first sky types, which belong to the overcast group but with higher diffuse illuminance levels and brighter luminance. Sky type 3, i.e. overcast sky moderately graded with azimuth uniformity seems to be on the top except in wintertime when sky type 2 prevailed. An even more complicated set of all sky types was documented in the second 5 years 1999–2003 as shown in Fig. 5. It is quite interesting that the uniform sky type 5 seems to be the most often for all of the first five sky types. Of course, during totally overcast mornings especially in wintertime (Fig. 6) the first two overcast sky types are prevailing when the sky type 2 and the CIE Overcast Sky. Type 1 is the most frequent in November and December as well as in March during 1994–1998. A similar distribution of sky types with a lower frequency existed also in the years 1999–2003, but astonishingly sky type 5, i.e. Lambert’s Uniform Sky, prevailed from November to January in Fig. 7.
Dynamic half-days (Figs. 8 and 9) are characterised by quite many interperiods with and without sunbeam penetration in between moving cloud patches. Therefore, sky types 11–13 are the most often in both 5-year spans. It is very interesting that during both analysed 5-year periods the total number of cases found within the 2.5% sky-type strips were quite similar, i.e. in the 1994–1998 span there were 169,158 representative case sky types. While in the second period, 1999–2003 there were only a few more (434), totalling 169,592 cases. The distribution in the four half-day situations with morning and afternoon sunny and sunless conditions are summarised in Table 1. Furthermore, these are presented in the barchart diagram in Fig. 10 for sunny periods and in Fig. 11 for sunless periods. It is evident that the prevailing number of cases under situations 1 and 4 comprises of sunny mornings and afternoons, while situations 2 and 3 are associated mostly with sunless conditions as documented in Figs. 2–9. It is quite noticeable that due to higher sunshine duration especially in 2000 and 2003, the number of sunny cases in the Table 1999–2003 has risen considerably while sunless cases under situations 2 and 3 have decreased. These shifts are followed also by consequence shifts in the sky-type prevalence. The summary table also proves the overall similarity of strip sorted data with relation to independent relative sunshine duration in both 5-year spans as the sum of sunny days to all data in 1994–1998 is 0.423 relative to sunshine duration 0.4, while in 1999–2003 is the ratio of sunny to all cases 0.5 due to a higher sunshine duration in this period 0.44. 4. Conclusions The generally available data derived from long-term sunshine duration measurements worldwide characterise the overall frequency of daylight situations occurring
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Fig. 3. Monthly changes of sky types during clear morning half-days in Bratislava 1999–2003.
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Fig. 5. Cloudy mornings in the period 1999–2003 have a prevailing sky type 5.
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Fig. 4. Cloudy mornings are caused by overcast sky types with prevailing uniform skies.
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Fig. 6. Overcast morning half-days especially in winter and spring time are dominated by sky type 1 or 2.
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Fig. 7. Overcast mornings during 1999–2003 are characterised by brighter overcast sky types concentrated mainly in winter time.
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Fig. 8. During dynamic conditions in mornings with prevailing sunny periods the occurrence of different sky types 11–13 is typical.
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Fig. 9. During the measuring period 1999–2003, clear sky types were prevailing during morning dynamic half-days.
Table 1 Total number of cases found in the Lz/Dv strips from the whole set of Bratislava 5-min data gathered during the years Half-day situation
Sunny mornings
Sunless mornings
Sunny afternoons
Sunless afternoons
Sum
1994–1998 1 2 3 4 Sum
13,658 4628 2783 15,207 36,276
1010 13,356 26,031 9531 49,928
13,841 4177 2480 14,836 35,334
3112 10,406 23,150 10,952 47,620
169,158
1999–2003 1 2 3 4 Sum
19,846 4032 1564 17,412 42,854
1265 11,362 23,127 7793 43,547
19,785 3821 1482 17,082 42,170
2153 9504 20,693 8671 41,021
169,592
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Fig. 10. Comparison of half-day situations during sunny periods.
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during typical morning and afternoon half-days. If monthly averages of relative sunshine duration are available or can be approximately predicted for any location, then annual daylight profiles, i.e. year-round exterior horizontal illuminance changes characterising the local daylight climate can be derived. The method already described in earlier papers was tested on the bases of two 5-year regular measured data gathered in Bratislava during 1994–1998 and 1999–2003. Due to the enormous number of 5-min averages derived from 1 min instantaneously measured global and diffuse illuminance values the frequency of standard sky types for only the most important situations were selected and documented in this paper. It was shown that a very good correlation exists between the overall sunshine duration characteristics and the frequency of occurrence of standard sky types within different months and cloudiness conditions in Bratislava, Slovakia. After a thorough analysis presented for the four basic half-day situations there is no doubt that the following sky types are important to simulate annual daylight profiles:
Situation 1: The clear morning half-day is certainly typical with the prolonged sunshine under cloudless blue sky type 12 during colder months, i.e. October to March, which are usually dry and therefore with lower turbidities Tv ¼ 2.5–3.5 and Dv/Ev ¼ 0.15–0.25. During the warmer months May to September with higher air humidity, then whitish and more turbid sky types 11 or 13 are prevailing with Tv ¼ 3.5–4.5 and Dv/Ev ¼ 0.2–0.3. Of course, during short periods without sunshine the sky type does not change. Situation 2: The cloudy mornings are usually in 71–75% sunless and therefore are covered by a wide spread of standard sky types 1–13, but the highest number of cases
is under sky type 3 or 5 with Dv/Ev ¼ 0.15–0.35, respectively. Situation 3: The overcast half-days are quite dull and almost sunless. The year-round occurrence of sky types 1–3 is prevailing especially in wintertime, i.e. from November to January, when Dv/Ev is very low, i.e. 0.1–0.2. However, during years with higher sunshine duration in wintertime sky types 4 and 5 can also prevail with Dv/Ev around 0.2. Situation 4: The dynamic half-days are associated with quite a lot of sunshine periods summing up to around 60% of any half-day therefore the most frequent are sky types 11–13 with a wide range of Tv ¼ 3–5 with Dv/Ev in the range 0.2–0.4.
These long-term information on sunshine presence or absence under relevant sky types can serve for the simulations of daily illuminance courses in short time steps respecting the local annual daylight profiles based on the available or assumed data of monthly relative sunshine duration. Acknowledgements This study is summarising partial results elaborated under the support of the Slovak Grant VEGA 2/5093/5. Thanks also for the support of the bilateral SlovakHungarian co-operation under the project SK-HU 1148 as well as the bilateral Slovak-Czech project SK- CZ11006. Appendix A See Tables A.1 and A.2.
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Table A.1 Nomenclature describing symbols, terms and used formulae after the TWIN system [14] Symbol
Description
Formula
a,b av a c, d, e Dv
Parameters for the gradation function j(Z) Extinction coefficient of the ideally clear (Rayleigh) atmosphere Azimuth angle Parameters for the indicatrix function f(w) Diffuse illuminance at ground level in lx
See Table A.2 1 av ¼ 9:9þ0:043 m
Dv/Ev gs d Evo Ev A f(w)
Diffuse clearness index or skylight transmission of the atmosphere/clouds Solar altitude Solar declination Luminous solar constant in lx Extraterrestrial illuminance on the horizontal surface in lx Ellipcity factor Indicatrix functions for any element for solar zenith angle
j j(Z) w Gv J Lv Lv/Lz
Geographical latitude Gradation functions for any element for zenith angular distance between sky element and solar position Global horizontal illuminance on ground level in lx Julian day number Luminance in any sky element in cd/m2 Relative sky luminance distribution
Z cos ZdZ da
Evo ¼ 133800 Ev ¼ Evo A sin gs A ¼ 1+0.034 cos(360/365(J–21)) f(w) ¼ 1+(c exp(dw)–exp(dp/2))+e cos2 w f(Zs) ¼ 1+(c exp(dZs)–exp(dp/2))+e cos2 Zs
Gv ¼ Pv+Dv
Lv Lz
ðwÞjðZÞ ¼ f fðZsÞjð0 Þ
2
Zenith luminance in cd/m Zenith fraction and sky classification parameter Relative optical air mass of the atmosphere
P?
s sm sy S Sa Tv
Parallel beam solar illuminance at the ground level on a normal plane in lx Parallel beam solar irradiance at the ground level on a normal plane in W/m2 Parallel beam solar illuminance at the ground level on a horizontal plane in lx Relative sunshine duration Monthly average relative sunshine duration Yearly average relative sunshine duration Sunshine duration in hours Astronomical sunshine duration in hours Luminous turbidity factor in the direction of sun beams
U Z Zs
Instability parameter Zenith angle Solar zenith angle
Pv
Z¼0 a¼0 ½jðZÞf ðwÞ sin
j(Z) ¼ 1+a exp(b/cos Z) j(01) ¼ 1+a expb
Lz Lz/Dv m
Pe
See Table A.2 R p=2 R 2p
Dv ¼
m¼
1 sin gsþ0:50572ðgsþ6:07995 Þ1:6364
P? ¼ Evo exp(av m Tv)
Pv ¼ P? sin gs s ¼ S/Sa
Measured if Pe4120 W/m2 Sa ¼ 7:51 arc cos ðtg j tg dÞ ðPv=EvÞ Tv ¼ lnav m
Table A.2 Standard sky types and their gradation and indicatrix parameter [9,10] Type
1 2 3 4 5 6 7 8
Description of luminance distribution
Gradation group
Indicatrix group
a
b
c
d
e
CIE Standard Overcast Sky, Steep luminance gradation towards zenith, azimuthal uniformity Overcast with steep luminance gradation and slight brightening toward the sun Overcast, moderately graded with azimuthal uniformity Overcast moderately graded and slight brightening toward the sun Sky of uniform luminance Partly cloudy sky, no gradation towards zenith, slight brightening towards the sun Partly cloudy sky, no gradation towards zenith, brighter circumsolar region Partly cloudy sky, no gradation towards zenith, distinct solar corona
I
1
4.0
0.70
0
1.0
0
I
2
4.0
0.70
2
1.5
0.15
II
1
1.1
0.80
0
1.0
0
II
2
1.1
0.80
2
1.5
0.15
III III
1 2
0 0
1.00 1.00
0 2
1.0 1.5
0 0.15
III
3
0
1.00
5
2.5
0.30
III
4
0
1.00
10
3.0
0.45
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500 Table A.2 (continued ) Type
Description of luminance distribution
Gradation group
Indicatrix group
a
b
c
d
e
9 10 11 12 13 14 15
Partly cloudy, with the obscured sun Partly cloudy, with brighter circumsolar region White—blue sky with distinct solar corona CIE Standard Clear Sky, low luminous turbidity CIE Standard Clear Sky, polluted atmosphere Cloudless turbid sky with broad solar corona White—blue turbid sky with broad solar corona
IV IV IV V V VI VI
2 3 4 4 5 5 5
1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.55 0.55 0.55 0.32 0.32 0.15 0.15
2 5 10 10 16 16 24
1.5 2.5 3.0 3.0 3.0 3.0 2.8
0.15 0.30 0.45 0.45 0.30 0.30 0.15
References [1] Soler A. Statistical comparison for 77 European stations of 7 sunshine-based models. Sol Energy 1990;45(6):365–70. [2] Soler A, Gopinathan KK. Estimation of monthly mean hourly global radiation for latitudes in the 11N–811N range. Sol Energy 1994;52(3):233–9. [3] Nakamura H, Oki M. Investigation on the relation between the probability of occurrence of the three skies and relative sunshine duration. In: Proceedings of the CIE 31st Session 1987;Vol. 1 (no. 1):228–9. [4] Darula S., Kittler R. Monthly sunshine duration as a trustworthy basis to predict annual daylight profiles. In: Proceedings of lux Europa conference, Berlin, 2005:p. 141–144. [5] Kittler R. Alternative possibilities to define the zonal daylight climates on the sunshine duration basis in Europe. In: Asimakopoulos D et al. Daylight II: availability of daylight in Europe and the design of a Daylight Atlas. Final Report JOU2 CT 92-0144, NOA Athens, 1995:2, contributions. [6] Darula S, Kittler R. Sunshine duration and daily courses of illuminance in Bratislava. Int J Climatol 2004;24:1777–83. [7] Darula S. Kittler R. Kambezidis H. Bartzokas A. Markou M. Generation of a daylight reference year for Greece and Slovakia.
[8]
[9]
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[11]
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Final rep of the GR-SK project. 004/01, ICA SAS Bratislava and NOA, Athens, 2004. Darula S, Kittler R. New trends in daylight theory based on ISO/CIE sky standards: 1–3. Build Res J, 2004:52(3):181-97, 2004:52(4):245-55, and 2005:53(1):9-31. Commission Internationale de l’E´clairage, CIE Spatial distribution of daylight—CIE Standard General Sky. CIE Standard S 011/E:2003, CIE Central Bureau, Vienna. International Standard Organisation ISO Spatial distribution of daylight—CIE Standard General Sky. ISO Standard 15469: 2004. Kittler R, Perez R, Darula S. A set of standard skies characterizing daylight conditions for computer and energy conscious design. 1998, Final rep.US-SK grant 92 052 and a set of standard skies. Polygrafia SAV Bratislava, 1998. Kittler R, Darula S. Parametric definition of the daylight climate. Renew Energy 2002;26:177–87. Kittler R, Darula S. Modelling possibilities for predicting annual daylight illuminance courses based on Bratislava data. Build Res J 2006;54:79–100. Darula S, Kittler R. TWIN system: descriptors for the evaluation of illuminance and irradiance availability. Build Res J 2006;54: 189–97.