Parameterisation of the Four Half-Day Daylight Situations

The International Commission on Illumination (C.I.E) in its Technical Committee TC 3-08 for Daylight initiated in 1983 the so called International Daylight Measurement Programme (IDMP). This programme was officially launched by the CIE President Bodmann (1991) and several CIE IDMP stations were established world-wide and now relatively long-term regular data are available for studies and analysis (Kittler et al., 1992). Although some daily courses served to characterise luminance sky patterns and local daylight climate, there are possible more detail analysis of half-day situations with relation to sunshine duration, cloudiness and turbidity influences parametrised. This chapter tries to show the theoretical basis with documented applications using examples of several parametrised evaluations of measurements taken at the Bratislava and Athens CIE IDMP general stations which can be taken as instructing samples to be imitated using local measured data. The aim is also to show how momentary illuminance values correspond with hourly averages under four different daylight situations and how these half-day situations can be simulated when only monthly relative sunshine duration is available and when monthly or year-round random daylight conditions are needed and could be approximated.


Introduction
The International Commission on Illumination (C.I.E) in its Technical Committee TC 3-08 for Daylight initiated in 1983 the so called International Daylight Measurement Programme (IDMP).This programme was officially launched by the CIE President Bodmann (1991) and several CIE IDMP stations were established world-wide and now relatively long-term regular data are available for studies and analysis (Kittler et al., 1992).Although some daily courses served to characterise luminance sky patterns and local daylight climate, there are possible more detail analysis of half-day situations with relation to sunshine duration, cloudiness and turbidity influences parametrised.This chapter tries to show the theoretical basis with documented applications using examples of several parametrised evaluations of measurements taken at the Bratislava and Athens CIE IDMP general stations which can be taken as instructing samples to be imitated using local measured data.The aim is also to show how momentary illuminance values correspond with hourly averages under four different daylight situations and how these half-day situations can be simulated when only monthly relative sunshine duration is available and when monthly or year-round random daylight conditions are needed and could be approximated.

Regular daylight measurements and their possible analysis
Since the CIE (2003) and ISO (2004) fifteen general homogeneous sky luminance patterns were standardised many CIE IDMP (International Daylight Measurement) stations recording regularly long-term daylight parameters try to evaluate the frequency of typical skies in their localities.Because the general CIE IDMP stations without sky luminance scanners sometimes do not record even zenith luminance vz L simultaneously with diffuse skylight illuminance measurements v D there are missing either sky scans or the classifying parameter / vz v LD , which could identify the momentary sky type.Thus, usually are only available data of regularly measured illuminance parameters in one minute steps during daytime, i.e.: -Global horizontal illuminance by an unshaded detector v G , -Diffuse skylight illuminance on a horizontal sun-shaded detector v D , -Parallel sunbeam illuminance is sometimes measured by a sun tracker with a skyshading cylinder and a detector placed perpendicularly to sunbeam flux v The station location is given by the geographical latitude  in deg., while date is specified by solar declination  and hour number H during daytime in TST .
Solar declination angle can be calculated for any day number within a year J (i.e. for 1 st January 1 J  and for 31 st December 365 J  ) using different approximate equations (e.g.Kittler & Mikler, 1986).The simplest is that introduced by Cooper (1969)   360 23.45 sin 284 365 and a more accurate approximation was recommended by EU after Gruter (1981)    The perpendicular parallel sunbeam illuminance at the ground level can be also calculated applying the Bouguer law, i.e.
  where LSC is the luminous solar constant (Darula et al., 2005), which is the normal extraterrestrial illuminance on the outer border of the atmosphere for the average distance between sun and earth, approximately 133800 LSC  lx., which is corrected for any date by the ellipticity factor  , which is often approximated by IESNA (1984)   m -relative optical air mass approximated by Kasten & Young (1989)   1.6364 1 sin 0.50572 6.07995 v a -luminous extinction coefficient of a clean and dry (Rayleigh) atmosphere after Clear (1982), later published by Navvab et al., (1984) 0.1 1 0.0045 or 1 9.9 0.043 v T -luminous turbidity factor, which defines the number of clean and dry atmospheres in the direction of sunbeams that reduces relatively its momentary penetration.In fact, if in eq. ( 8) v P  is measured by a sun tracker or v P is derived from measured vv GD  data, then the actual value v T can be determined as where vvv PGD  and the extraterrestrial horizontal Thus, once the momentary illuminance v P  or v P is determined the actual sunlight impact on any arbitrary plane can be calculated using the cosine of its incidence angle.However, for the vertical planes oriented either to direct East or West cardinal points this cosine function is simplified to

G
or vvW G respectively.So, when the direct sunlight using eq.( 15) can be subtracted only diffuse skylight components for these orientations can be determined, i.e. vvE D or vvW D .

Four typical half-day situations indicated by illuminance courses
In the previous paper (Darula & Kittler, 2004a) 1.Although the measurement registration is in the local clock time without the summertime shift it is evident that the courses follow the solar altitude changes, i.e. the sin s  tendency of the extraterrestrial horizontal illuminance after eq. ( 14).Therefore the efficiency parameters / vv GE and / vv PE should be rather stable and showing a large amount of the extraterrestrially available luminous flux reaching the ground level, therefore these parameters can markedly characterise situation 1 (Fig. 2).The momentary 1-minute measurements except some slight spreads on the April day show a steady rise with the solar altitude which is even better followed by the hourly averages in Fig. 3 with the stepwise rise of / vv GE from 0.45 to 0.75.In consequence, also the luminous turbidity factors v T follow the stable atmospheric conditions without abrupt changes, except when the sun position is shaded by crossing cloud patches and then can reach higher short time peaks as in Fig. 4 on 8 th April 2006.However, due to gradual evaporation during morning the turbidity might fluently rise with the formation of Cirrus or Cirrostartus veiling cloudiness as is shown by the trend of rising hourly average v T values in a small range 1.5 to 3 in Fig. 5.Such rising v T effects can be expected especially in equatorial regions with sometimes gradual cloud formation at noontime and in afternoon hours, which no longer belong to situation 1.   LD , can identify the momentary sky type with the fluent rising tendency dependent on the solar altitude.In Fig. 8 this tendency is shown using 1-minute data while in Fig. 9 the same is documented after hourly mean values.Due to rather constant and fluent trends during situation 1 besides the momentary one-minute recordings also hourly averages and appropriate parameters are quite satisfactorily reflecting clear half-days which might reduce the number of data considerably (Darula. & Kittler, 2005a This is an normalising amount to calculate relative sunshine duration during the halfday hd s if the true measured sunshine duration in hours hd S is available: In the half-day system relative sunshine duration during the morning half-day is hd m ss  while its afternoon relative duration is hd a ss  either in absolute values or % respectively.If regular minute recordings are measured, then hd S can be calculated as the sum of all data after the WMO (1983) andCIE 108 (1994) when the direct irradiance e P   120 W/m 2 taken in hours or their decimals.
Situation 2: Cloudy half-days with possible foggy short periods are characterised by scarce and lower sunlight influences under a range of relative sunshine durations ( 0.03 0.75 s  and 10 6 Us   ) and relatively higher diffuse illuminance levels.Such situations are caused by the prevailing area of the sky covered from almost homogeneous presence of clouds layers with different combinations of cloud type, turbidity and cloud cover overlayed in their height positions and movement drifts.Therefore, usually their v G courses are close to v D levels and so are also ratios / LD parameters in Fig. 17 and especially their averages in Fig. 18 with the data spread within the values 0.2 to 0.38 close to overcast sky (Darula & Kittler, 2004b).Due to cloudiness overlays and turbidity changes rather high values of v T factors have to be expected usually dependent on the solar altitude as shown in Fig. 15 or 16.However, within the half-day courses momentary unstable v P can occur, thus there are cases also with higher average relative sunshine durations during the half-day in the range 0.1 to 0.5, but seldom over 0.5 with lower sunlight intensities, which are usually indicated by smaller peaks within the half-day course.These drab sunlight influences are documented by the small differences between / LD are over 0.3 and stable during the half-day, i.e. without any dependence on the solar altitude (Darula & Kittler, 2004c).Under overcast sky conditions when sunbeam influences are absent the sky luminance patterns in all azimuth directions are uniform, so only gradation luminance distribution can cause the v D illuminance rise from sunrise to noon.29, but the former indicate a tendency of the background spring and summer clear skies.However, these background scene is also influenced by gradually increasing turbidity, which is low with lower solar altitude and considerably rising when the sunheight is over 35 degrees (Fig. 31 and 32).

LD and /
vv GE time-averaged ratios are capable to differentiate the halfday situations when data are summarised during a day, a week or month in these mixed groups.Therefore the first step to identify, select or classify the half-day situations is to check the overall courses of v G and v D illuminance trends and levels and their relative efficiencies compared to the momentary extraterrestrial availability levels expressed in / vv GE and / vv DE ratios.Of course the stable or discontinuous sunshine duration follows the changes in / vv GE and the momentary presence of / vv PE ratios indicating the penetration of available extraterrestrial sunshine intensity.These half-day courses roughly characterise also the range of prevailing sky luminance patterns that can be expected and principally belong to the particular half-day situation.While situation 1 and 3 and sometimes even 2 are approximately homogeneous with evenly distributed turbidities and cloudiness cover over the whole sky vault, the situation 4 is characteristic for its unstable dynamic illuminance changes caused by complex layers of different cloud types and distribution as well as patch movements.Thus under situation 4 can happen locally many accidental variations between quite low turbidity pockets with white-blue sky background through which direct sunshine temporarily can reach the ground while in other intervals the cloud patches cover and shade the sun beam penetration considerably.Under homogeneous atmospheric conditions the / vz v LD ratio is quite a safe indicator of the sky luminance pattern, but during the dynamic half-day the zenith luminance as well as the sun position are influenced by passing clouds or cloud patches in several following sequence intervals.However, for general practice and local characterisation of daylight conditions year-round longterm data are needed and should be locally available.Daylight data are also measured at the CIE IDMP stations or can be taken from the satellite database.In this respect besides global irradiation recorded in short-term variability or hourly averages at ground meteorological stations or recalculated from satellite measurements, only relative sunshine duration in daily or monthly averages have a very long tradition and are evaluated in many stations world-wide.When inspecting monthly graphs of daily illuminance courses it becomes obvious that especially during winter and summer seasons typical weather patterns last for several days with changes either during night-time or noon.Even during perfectly clear days the symmetry around noon seems to be broken by higher turbidity in afternoon hours caused by water vapour evaporated due to rising air temperature and sunshine.Furthermore, in equatorial climate have to be expected changes in cloud cover at around noon, i.e. frequent mostly clear mornings and hours before noon but rather cloudy afternoons.During the Slovak-Greek cooperation simultaneously collected data at the CIE IDMP stations in Bratislava and Athens could serve to compare four half-day situations occurring in the temperate climate of Central Europe to those in the Mediterranean region (Darula et al., 2004).Available data was gathered during relatively long period 1994-1999.
The whole set of measured data was used to analyse the relation between sunshine duration and daily courses of illuminance.Relative sunshine duration with standard deviation SD for four typical situations were investigated in number with respect to their sequence of occurrence and results are documented in Table 1.Symbol s is relative sunshine duration calculated for the whole day while sm is for the morning period when local clock time was less than 12 o´clock and sa for the afternoon relative sunshine duration when local clock time was from 12 hours to sunset.Except for the rapid change from overcast to clear all possible changes from morning to afternoon situations were found during the long-term of six years, i.e. 2182 days or 4364 half-days.The average relative sunshine duration corresponds perfectly with the change from the morning situation to the afternoon one respecting the tendency of the following situation change.Although the half-day characteristics and their sequences in one or few days can form a typical year simulation, within this span any time subdivision can be utilised, i.e.Bratislava 1-minute data or Bratislava and Athens 5-minute average data can serve for analysis and comparison studies of several descriptor interrelations.However, to reach an absolute symmetry in halfdays due to perfect noon time all measured momentary or average values are to be recalculated from local clock time in which these were recorded to true solar time.Of course, it has to be realised that because the daytime span between sunrise and sunset is changing during the year as well as with the local latitude the relative time of a half-day element is not constant., 1994 -1999 Anyhow it can be assumed that in simulation programs of a daylight reference year the halfday sequences or changes will allow to model in series of about sixty cases during a specific month either the fluent and gradual or sudden changes in weather or sky types corresponding to the probability of occurrence with its proportionality to monthly averages of relative sunshine duration.At least the mentioned four half-day daylight situations have to be foreseen for modelling the complex sun-sky coexistence with cloudiness patterns in any daylight climate, although typical cases were selected only from measurements collected in Athens and Bratislava.A research report (Darula et al., 2004) contains the detail analysis with proposals of several parameters to identify the four relevant situations from measured half-day illuminance courses and the daily average relative sunshine duration.It is evident that the stable and homogeneous situation 1 and situation 3 can be defined by the s instead of sm and sa.However, the dynamically changing illuminance courses had to be identified and classified or selected to situation 1, situation 2 or situation 4 by introducing an additional U parameter. where and i x and 1 i x  are consecutive illuminance values in the half-day course.

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Using these classification parameters all four daylight types are interrelated by a fluent course of half-day average / vv GE and / vv DE dependent on the half-day sunshine duration as documented in Fig. 33 and 34 containing all 1994 morning and afternoon data recorded in Bratislava and in Athens first.In the second step a more detail separation of half-day situations dependent on half-day relative sunshine duration was made for morning 1994 data (Fig. 35) and afternoon (Fig. 36) in relation to / vv GE parameter repeated for also / vv DE and / vv PE with the best fit simulation of their dependence on the half-day relative sunshine duration.However, as most frequently are available only monthly relative sunshine durations in meteorological station reports the probability of occurrence of the morning and afternoon halfday situations was sought first for 1994 data (example in Fig. 37 for situation 1) and checked for 1991-2001 data.Thus best fit probability for the monthly redistribution simulation of morning and afternoon situations 1 to 4 were predetermined solely dependent on the monthly relative sunshine duration using curves in Fig. 38 for morning half-days or in Fig. 39 for afternoons (Darula et al., 2004 andDarula &Kittler, 2005b).
  for the afternoon half-days by:   These probabilities of the occurrence of typical four daylight situations were derived from measurements in two different climate zones, i.e. in Bratislava as well as in Athens.So, it can be assumed that the dependence on monthly sunshine durations during morning and afternoon half-days could be valid not only in Central Europe and European Mediterranean regions but also world-wide. while the overall number of morning half-days in a particular month is Nm for mornings and Na for afternoons in Fig. 40 and 41.These document and confirm the redistribution model that approximates the participation of the main three situations on sunlight presence and monthly sunshine duration within the particular half-day assuming that the overcast halfday is absolutely without any sunshine, thus   sa ranges after eq. ( 34) and ( 35).During dynamic half-days both 4 sm and 4 sa should be in the range 0.3 to 0.75 to be related to the rise of / vv GE from 0.35 to 0.6 respectively.For an example of such a check can be taken the ten-year (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004) It is evident that the course distribution of illuminances is caused by the sine of the solar angle with either the momentary sine value for the moment or for the chosen time interval.
This sine of the solar altitude  s after eq. ( 2) for any hour number H during daytime in TST can be used.For a short time period a straight-line interpolation can be applied when

 
12 /2 HHH  or a value after eq. ( 16) is more precise.A further possible step to specify the site and situation dependent illuminance stimulated a study that would show the relation of the four situations on typical sky patterns or ISO (2004)/CIE (2003) standard general skies if possible.Originally these standards were derived with the specification of indicatrix and gradation function in Kittler (1995) and finally recommended for standardisation in Kittler et al., (1997).After a detail number of 5-minute measured cases in Bratislava specifying every year within the five year 1994 -1998 span all four daylight situations were analysed with the following results:  (Darula & Kittler, 2008a) was in coherence considerably also with the seasonal frequency of dominant sky types found in the seasonal distribution (Kitttler et al., 2001) with prevailing overcast skies in type 2 and 3 and clear sky types 12 and 11 in Bratislava, while in Athens the highest frequency of clear polluted sky type 13 was documented, while uniform cloudy skies 5 and 6 were the most often occurring in dull seasons.Of course, the seasonal changes in occurrence frequency of clear and overcast skies is linked with relative sunshine duration and therefore with the number of half-days in any locality.However, it is interesting that in any daylight climate there exists a number of (Lambert) overcast sky type 5 with uniform luminance sky patterns, e.g. in Bratislava five year long-term these represented 12.6 % whithin cloudy situation 2 during morning halfdays and over 14 % during afternoons whithin overcast situation 3 these were represented by morning 8.08 % and afternoon 7.74 % presence.More and further measurements in different locations are expected to demonstrate the sitespecific and short-term variability of illuminance levels (as recently was shown for irradiance by Perez et al., 2011).Due to dynamic situations it is important to evaluate shortterm (momentary 1 or 5-minute regular measurements) because estimations of using hourly insolation data from satellite-based sources can be problematic and less accurate when subhourly variability is uncertain and especially if irradiance data are recalculated via luminous efficacy into illuminances (Darula & Kittler, 2008b).Therefore long-term regular measurements in absolute illuminance values are so important to have site-specific fundamental data with the possibility to derive also half-day situations.When modelling year-round situation frequencies it is also important to randomly distribute also some sequential ocurrence of specific situations (Darula & Kittler 2002) which can occur several half-days or even days after each other as is documented in Table 4 and 5. Of course, one situation can last during the whole day, i.e. the morning situation is the same in the afternoon, but quite frequent are also changes from clear to dynamic or cloudy to dynamic and vice versa especially in summer as shown in Table 4.In winter are typical lasting same situations except dynamic in two adjacent days, while in summer all consecutive days with the same situation are quite often except overcast.

Conclusions
Architectural and building science tries to gather and apply available human knowledge for the complex, aesthetic and functional creation of sophisticated habitable and healthy spaces with best environmental qualities encompassing shelter for human live, relaxation and work activities.Of course, the urban and structural objects with different interior spaces in their architectural plans and building forms have to respect natural conditions in various geographical locations, topography, local life stile and culture with trials for optimal solutions according to requirements concerning human health and prosperity, investor tendencies, investment and maintenance costs.To satisfy a complex sum of conditions, needs, codes and standards summarised by inhabitants, investors and national institutions leads to relatively simple and realistic criteria with a reasonable and experience-based background including simplified scientifically sound knowledge.
In case of utilising insolation and daylight conditions the traditional daylight science and technology is facing novel approaches and more real enhancements.In this sense are questionable also some older daylight criteria that were still recently used since the first calculation simplifications derived in the 18 th Century.The Daylight Factor, Sky factor and Sky Component of the Daylight Factor used as basic criteria in various standards assume the existence of the unit uniform sky luminance after Lambert (1760).Although such Lambert uniform skies exist world-wide these do not represent typical sky luminance patterns in any site-specific conditions especially in subtropical, tropical and equatorial regions where mostly clear sky luminance distributions prevail that cause skylight illuminance conditions added frequently by sunlight.This study tries to show and document that site-dependent daylight illuminance levels and their changes have to be expected in short-term, half-day, monthly or yearly variations in a realistic range under four typical half-daily situations.These situations can be classified with respect to relevant parameters which are dependent on extraterrestrially available illuminance reduced by atmospheric optical depth and air mass, turbidity and cloudiness conditions in site-specific variability.For practical purposes the probability of occurrence frequency of a particular half-day situation is related to the half-day or monthly relative sunshine duration which in absence of special measurements is available from many meteorological records world-wide.These monthly relative sunshine duration data can serve to estimate the local number of morning and afternoon half-day situations in any month and model their year-round expectance.Following this aim all data and figures after Bratislava and Athens CIE IDMP regular measurements can be considered as examples documenting the parameterisation and applicability of the four half-day situation system.Current saving energy policies are also directed towards utilising renewable energy and in this respect also daylighting can serve to reduce electricity consumption in artificial illumination of interiors.A more precise determination of half-day illumination levels within year-round balance of supplementary electric lighting will enable to control it more effectively.Thus, daylight as natural source can be applied for interior illumination respecting local sunlight and skylight availability.

Acknowledgement
This chapter was written and partially supported under the Slovak grant project APVV-0177-10 using daylight measurements recorded by the Bratislava CIE IDMP gathered and evaluated under the Slovak VEGA grant 2/0029/11.

Fig
Fig. 6. / vv DE courses under situation 1: after 1-minute measurements situation 2. To document cloudy half-days were chosen from the Bratislava data again seasonally typical cases, i.e. a summer day 3 rd June 2007, an autumn day on 5 th September 2007, a cloudy winter morning on 20 th December 2006 and a spring morning on 5 th April 2006.The measured half-day courses of global horizontal illuminance v G and diffuse sky illuminance v D are recorded in local clock time again in Fig. 10.In early morning hours under cloudy conditions / vv GE and / vv DE are almost the same as is not so noticeable from the winter course of illuminances, but evident in Fig. 11 in 1-minute or in Fig. 12 in the hourly alternative compared with Fig. 13 and 14.In this cloudy case the / vv GE and / vv DE values is very high reaching 0.25 to 0.6 level indicating a very bright but sunless winter half-day which is indicated also by the v T lower values compared with all other cloudy samples (in Fig. 15 and 16) as well as in rather horizontal range of / vz v comparing Fig. 12 and 14 respectively.Situation 3: Overcast half-days are absolutely without any sunlight and are caused by either dense layers of Stratus or Altostratus cloudiness or inversion fog when the sun www.intechopen.composition is uncertain as it cannot be seen or guessed behind the overall dense clouds.Under such conditions v G low, usually in the range 0.02 -0.25, the ratios / vz v

Fig
Fig. 24.Illuminance courses during overcast morning situations 4 Fig. 33.Morning and afternoon / vv GE data after Bratislava and Athens measurements

FigFig. 36 .
Fig. 34.Morning and afternoon / vv DE data after Bratislava and Athens measurements

Fig. 37 .Fig. 39 .
Fig. 37. Relation of clear situation to monthly relative sunshine duration in Bratislava and Athens clock controling system starting every minute count has to be recorded too either in local clock time LCT or true solar time TST .These regular measurements can serve for the specification of daylight situations during the half-day or to the rough identification of the sky type in any minute, hour or date.In fact even in absence of the sun tracker the v P  illuminance can be derived from v G and A Except these few sunshaded events the clear sky is quite stable and all horizontal illuminance parameters v P , v G and v D follow a fluent increase in level during the morning hours and similar decrease during the afternoon due to solar altitude changes in different seasons.Examples of selected half-days with situation 1 are using recorded data from the Bratislava CIE IDMP general station (  = 48°10´N, L  = 17°05´E) with the Central European climatic influences, but these should be taken as instructional and illustrative examples characterising typical cases of situation 1.As examples of clear sky mornings in Bratislava, Slovakia, were chosen courses measured during a long summer day on the 20 th July 2006 followed by an autumn day on 22 nd September 2007, while a short winter day 26 th December 2006 represents one of the shortest days and the spring day 8 th April 2006 with slight veiling Cirro-Stratus influences is also documented.The measured half-day courses of global horizontal illuminance v G and diffuse sky illuminance v D are documented in Fig. ).

Table 1 .
Statistical parameters of typical courses in Bratislava This redistribution of half-day situations during mornings and afternoons was calculated for Bratislava and Athens data and as examples are shown in Table2and 3 only those for morning half-days.Although the verification of these redistributions for other localities is rather complicated it is evident that the ranges of mornings sm and those measured during afternoons sa can be in every month specific too.While during overcast situations the range of the spread 0.05 -0.35 (Fig.35and 36), the s ranges in dynamic situations are quite large i.e. 0.3 -0.76 while Gv/Ev spread is approximately within 0.32 -0.61.Thus eq.(34) and (35) characterise the redistribution of sm and sa due to four half-day situations simulating Central European and Mediterranean daylight conditions.In other climate regions (like maritime and equatorial) or during rainy (April or May) or during monsoon months more general relations might be valid as vv GE within

Table 4 .
Occurrence of daylight situations with typical sequences in one whole day

Table 5 .
Repetition of four half-day situations in conscutive two days www.intechopen.com