INTERNATIONAL JOURNAL OF CLIMATOLOGY Int
99K - views

INTERNATIONAL JOURNAL OF CLIMATOLOGY Int

J Climatol 29 10351047 2009 Published online 5 January 2009 in Wiley InterScience wwwintersciencewileycom DOI 101002joc1849 Review Hourly and daily clearness index and diffuse fraction at a tropical station IleIfe Nigeria E C Okogbue

Download Pdf

INTERNATIONAL JOURNAL OF CLIMATOLOGY Int




Download Pdf - The PPT/PDF document "INTERNATIONAL JOURNAL OF CLIMATOLOGY Int" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.



Presentation on theme: "INTERNATIONAL JOURNAL OF CLIMATOLOGY Int"β€” Presentation transcript:


Page 1
INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 29 : 1035–1047 (2009) Published online 5 January 2009 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/joc.1849 Review Hourly and daily clearness index and diffuse fraction at a tropical station, Ile-Ife, Nigeria E. C. Okogbue, * J. A. Adedokun and B. Holmgren Department of Meteorology, Federal University of Technology, Akure, Nigeria Departments of Physics, Obafemi Awolowo University, Ile-Ife, Nigeria Meteorological Institute, Uppsala Uni versity, S-751 20 Uppsala, Sweden ABSTRACT: Dataset consisting of

hourly global and diffuse solar ra diation measured over the period February 1992 and December 2002 have been utilized to investigate the diurnal a nd seasonal variations of hourly and daily clearness index together with the diffuse fraction at a tropical station Ile-Ife (7.5 N, 4.57 E), Nigeria. Statistical analysis (the frequency and cumulative frequency distribution of the hourly and daily clearness index) and subsequent characterization of the sky conditions over the station based on these were also done, and their implications for solar energy utilization in the area discussed. Daytime

(11 : 00–15 : 00 LST) monthly mean hourly diffuse fraction, (explained in a separate –List of Symbols provided, along with other symbols used in this article), have values, which are most of the time less than 0.52, 0.54 and 0.60 respectively for January, February and March in the dry season. However, during the months of July and August (which are typical of the wet season), the values range between 0.61 and 0.85 (being generally greater than 0.65) with the corresponding values of the monthly mean hourly clearness index, , ranging between 0.23 and 0.45. Statistical analysis of hourly and

daily clearness index showed that the local sky conditions at the station were almost devoid of clear skies and overcast skies (clear skies and overcast skies occurred for only about 3.5% and 4.8% of the time respectively). The sky conditions were rather predominan tly cloudy (cloudy skies occurred for about 88% of the time) all the year round. Copyright 2009 Royal Meteorological Society KEY WORDS clearness index; diffuse fraction; tropical station sky conditions; Ile-Ife Received 22 May 2007; Revised 26 November 2008; Accepted 1 December 2008 1. Introduction Solar radiation is received at the

Earth’s surface under different atmospheric conditions, which obviously affect the amount and quality of radiation obtained at the ground during the course of the day. Atmospheric conditions such as, turbidity and transparency, air mass, atmospheric water vapour content and layers and distribution of cloud cover have been suggested to exert depleting influence on solar radiation at the Earth’s surface, mainly by absorption, scattering and reflection of the incoming solar radiation. Solar irradiance data is essential for studies on the description of atmospheric phenomena and

large-scale weather analysis and prediction because the amount of solar global radiation received on the Earth’s surface is the driving force for most meteorological processes. For example, solar radiation data is required in improving the parameterization of clouds n eeded in general circulation * Correspondence to: E. C. Okogbue, Department of Meteorology, Federal University of Technology, Akure, Nigeria. E-mail: emokogbue@yahoo.co.uk models (GCMs) (Stokes and Schwartz, 1994) and as a valuable resource for validating the GCMs (Hansen, 1999; and Iziomon and Mayer, 2001). Information on the

geographical distribution and the changes with time of the solar radiant energy on the Earth’s surface is a requirement not only in weather and climate studies but also in agricultural practice and food production, hydrol- ogy, ecology and energy development programmes and utilization, among others. L ack of adequate observations on solar radiation has been a persistent problem in stud- ies of land-surface processe s and a major limitation in the validation of crop growth simulation models (Thornton and Running, 1999; Liu and Scott, 2001) and photosyn- thesis models since the decomposition of

solar irradiance into its various components is now a key feature of sev- eral canopy-scale models of photosynthesis (De Pury and Farquhar, 1997). The design, development and application of solar energy collection and conversion systems required for the exploitation of the vast energy of the Sun, and the performance evaluation of such energy conversion sys- tems within a particular region require information on the Copyright 2009 Royal Meteorological Society
Page 2
1036 E. C. OKOGBUE ET AL variation characteristics and distribution of the amount of solar energy received at the

location (Duffie and Beck- man, 1991; Coppolino, 1994; and Ali et al ., 2003). The separation of solar irradiance into the various components is also necessary for a wide range of these solar engineer- ing tasks (Iqbal, 1983). For example, the knowledge of the distribution of the diffuse fraction of solar radiation (the ratio of the diffuse solar radiation to the global solar radiation) is particularly re quired in assessing the climato- logical potential of a locality for solar energy utilization and in estimating the expected values of the output of concentrating solar collectors

(Iziomon and Aro (1998). The clearness index (which is the ratio of the global solar radiation measured at the surface to the total solar radiation at the top of the atmosphere) is a veritable tool in the characterization of sky conditions (or classifica- tion of sky types) over a particular locality (Ideriah and Suleman, 1989; Kuye and Jagtap, 1992; Okogbue and Adedokun, 2002b). Synoptic cloud observations, though very subjective, have remained the only source of infor- mation on sky conditions for most parts of tropical Africa, Nigeria inclusive, since there are no ground-based instru-

mentation systems to monitor them routinely and objec- tively, and estimation procedures have only been estab- lished for very few locations in the country due to lack of the needed solar radiation components for characterizing the sky conditions. In spite of its significance, solar radiation, especially the diffuse component, is infrequently measured com- pared to other variables such as temperature and rain- fall (Thornton and Running, 1999; Wilks and Wilby, 1999; Liu and Scott, 2001). Although, a prevailing dearth in solar radiation data has been reported in a number of countries like

USA (Hook and McClendon, 1992), Canada (De Jong and Stewart, 1993) and Australia (Liu and Scott, 2001), it is however, in those parts of the world naturally endowed with abundant availability of solar energy all the year round (e.g. tropical Africa, Nigeria inclusive) that its continuous and accurate mea- surements are the least common. This is probably due to the high cost of purchasing and maintaining the nec- essary equipment, and the dearth of skilled personnel. A number of studies have however, been reported in Nigeria, notable among which are: Bamiro (1983) and Ideriah and Suleman

(1989); Adeyefa and Adedokun (1991); Kuye and Jagtap (1992); Adedokun et al . (1994); Maduekwe and Chendo (1995); Iziomon and Aro (1998, 1999); Adeyewa et al . (1995, 1997, 2002); Okogbue and Adedokun (2002a,b, 2003); Okogbue et al . (2002) and Jegede (1997a,b,c, 2003). The present contribution investigates, with respect to the prevailing atmospheric conditions over the station, the diurnal and seasonal patterns of both the hourly and daily clearness index and the cloudiness index (or dif- fuse fraction) computed based on the measured hourly fluxes of global and diffuse solar radiation

at Ile-Ife, Nigeria. The characterization of sky conditions over the station using the clearness index is also investi- gated. 2. Data and instrumentation The solar radiation data reported in this work comprised of hourly averaged values of both global and diffuse radiation flux densities in units of Watt-hour per meter squared (W h m ) measured at Ile-Ife, Nigeria (7.5 N, 4.57 E) during the period March 1992 to December 2002. Since the collection of data relating to the above period was continuous (except for some interruptions when any of the instruments used was stopped for repairs or

recalibrations) it can be expected that inter-seasonal variations will be manifested in the datasets. The solar radiation measurement station which is located on the rooftop of the 20-meter-high 3-storeyed Department of Physics building located within the cam- pus of Obafemi Awolowo University, Ile-Ife, Nigeria comprised of two Kipp and Zonen pyranometers models CM11 for the global radiation and CM11/121 (incorpo- rating a shadow ring) for diffuse radiation and a LICOR LI-210SA photometric sensor for the photometric illu- minance. The altitude of the Physics building is about 275 m above sea

level. The measuring site is, there- fore, at about 300 m above sea level. The instruments were installed and levelled on a horizontal surface at a height of 1.5 m above an impr ovised flat concrete base on the rooftop (Figure 1). The leads for the pyranometers were directly connected to a Campbell Scientific micro logger (model 21X) and data sampled every 1 min and then subsequently averaged to produce the hourly val- ues. Both devices were initially factory calibrated before installation with measurement accuracy of about 2%. Subsequently, further recalibrations have been carried

out locally by comparing the pyranometers with a more recently calibrated CM11 pyranometer (Okogbue, 2007). Data quality assurance checks were carried out with reference to the diffuse fraction K (which is the ratio of the diffuse solar radiation incident on a horizontal surface to the global solar radiation incident on the same surface) Figure 1. The Solar Radiation Statio n on the rooftop of the Physics Department Building at Obafemi Awolowo University, Ile-Ife, Nigeria. This figure is available in colour online at www.interscience.wiley. com/ijoc Copyright 2009 Royal Meteorological

Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 3
ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1037 and the clearness index K (which is the ratio of the global solar radiation measured at the surface to the total solar radiation at the top of the atmosphere) as suggested by Reindl et al . (1990) in order to ensure good diffuse solar radiation data. In that respect, the following data were excluded: 1. A day with even one missing hourly data (global or diffuse). 2. Global solar radiation exceeding the extraterrestrial radiation. 3. Diffuse fraction

K 4. K 80, when K 60 (clear sky). 5. K 90 when K 20 (overcast sky). Case (iv) places a limit on the diffuse fraction under clear-sky conditions, whereas case (v) places a limit on the diffuse fraction under cloudy overcast sky conditions as suggested in Reindl et al . (1990). 3. Meteorological features of the site The area experiences tropical climate such that two major seasons can be clearly identified which greatly influence the daily weather patterns, namely: wet (April–October) and dry (November–March) seasons. This change of sea- sons occurs in association with the

north–south (merid- ional) movement of the Inter-Tropical Discontinuity (ITD), which represents, at the surface, the demarcation between the southwesterly and the northeasterly winds over the sub-continent (Adejokun, 1966). At about the lat- itudinal belt 7 N (representative of the position at Ile-Ife), there frequently occur thunderstorm activities character- istic of the wet season beginning from mid-March/April (maximum about July/August) and extending till late October during the Northern Hemisphere summer. Dur- ing this period, the presence of thick clouds (e.g. cumu- lus/cumulonimbus and

nimbostratus clouds) and other high water content clouds, which could average up to 6–7 oktas at 0900 h, local time, in the month of August at the peak of the wet season (Griffiths, 1974) is a reg- ular atmospheric phenomenon. The wet season is also generally characterized by high moisture content of the air. Consequently, the most im portant attenuators of solar radiation during this period are clouds and water vapour (Kyle, 1991; Jegede, 1997a,b; Okogbue and Adedokun, 2002b). During the Northern Hemisphere winter, the ITD is positioned north of the equator attaining a position about

4–6 N in January. During this time, the northeasterly winds prevail to an elevation of about 3000 m and bring cold, dry and stable continental air masses from the desert region over which they originate. These winds are locally called the –harmattan’ (Adedokun, 1978; Balogun, 1981). Having had a long trajectory over the desert, the harmattan winds advect tonnes of fine dust to the region. The Harmattan dusts bring about spells of hazy sky conditions (Kalu, 1978; Adedokun et al ., 1989) or –dense dust veil’ (Mauder et al ., 2007) characteristic of the dry season in Nigeria. Adeyefa et al

. (1995) classified the harmattan period into periods with –moderate’ characteris tics (background harmattan) and periods with intensive dust spells that could last 3–4 days or more (Kalu, 1978 and Adebayo, 1989). The high aerosol loading of the atmosphere during this season attenuates the solar r adiation passing through the atmosphere mainly by scattering with effects on the heat budget of the Earth–atmosphere systems, which can be very significant especially in the tropics where the radiation balance is positive (El-Fandy, 1953; Kalu, 1978, Jegede, 1997a,b). 4. Methodology The

flux of energy received from the Sun at the top of the atmosphere, per unit of area, and per interval of one hour (I ) and one day (H ) (required for calculation of the hourly clearness index ( ) and daily clearness index ( ) are respectively estimated analytically by the familiar expressions according to Iqbal (1983) with the solar constant SC 1367 Wm The diurnal and annual patterns of , the hourly diffuse fraction, ( ), and the daily diffuse fraction, ), are presented and discussed with reference to the prevailing atmospheric conditions over the area. Furthermore, statistical analysis

(the frequency and cumulative frequency distribution of the hourly and daily clearness index) and subsequent characterization of the sky conditions over the station based on these have been done following the pioneering work of Liu and Jordan (1960) and those of Li et al ., 2004. For instance, Liu and Jordan (1960) had shown that the information on the daily clearness index, (K ), could also be presented as cumulative frequency, f (K ), in percentage as follows: number of days with K (f ixed value) number of days in the month 100% Using data from a network of 27 stations, each with

approximately 5 years of data, Liu and Jordan (1960) proposed, based on Equation (1), a set of generalized cumulative distribution curves (CDC), which have been used in many studies since then. The claim of the universal applicability of the generalized CDC by Liu and Jordan (1960) has been queried by typical results obtained by Hawas and Muneer (1984); Saunier et al . (1987); Ideriah and Suleman (1989); Kuye and Jagtap (1992) for some tropical locations in India, Bangkok in Thailand, Ibadan and Port Harcourt, in Nigeria, respectively. In terms of sky conditions classification, the

clear- ness index is a widely used index since it depends only on global solar irradiance (i.e. one measured parameter) (Muneer, 1995, 1998; Li et al ., 2004). Low clearness index means low global solar radiation, which usually represents a cloudy sky with a high portion of diffuse Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 4
1038 E. C. OKOGBUE ET AL component. Large clearness index means high global solar radiation, which is dominated by the direct compo- nent. There are however, no clear-cut K values to define the

sky conditions. Different researchers have there- fore adopted different values. For instance, Reindl et al (1990) have proposed K 6andK 2 for clear sky and cloudy sky, respectively. Li and Lam (2001) and Li et al . (2004) used K values of 0–0.15, 15–0 and 7 to define overcast, partly cloudy and clear skies respectively in Hong Kong and Kuye and Jagtap (1992) used K 65 and 0 12 35, respectively, for very clear skies and cloudy skies, to classify the sky con- ditions at Port Harcourt, Nigeria. For this work, K (or )valuesof0 (M 15, 0 15 (M 60, 0 (M were used to define overcast,

partly cloudy and clear-sky conditions based on our field experiences. 5. Results and discussions 5.1. Diurnal variations of the clearness index and diffuse fraction In Figures 2, 3 and 4 are presented plots of the diurnal variation of the monthly means of hourly clearness index and diffuse fraction (or cloudiness index) for the months of January, February and March which are representative of the dry season. It is obvious from Figures 2, 3 and 4 that the clearness index has very low values during the hours close to sunrise and sunset, with values ranging between 0.09 and 0.33. The

diffuse fraction on the other hand, has rather very high values during such hours (ranging between 0.77 and 0.99) with the obvious implication that the solar radiation received at the surface during the hours close to sunrise and sunset consist mainly of the diffuse component. This is consistent with the dependenc e of diffuse solar radiation reaching the surface on solar elevation and atmospheric turbidity, air mass, atmospheric water vapour content and layers and distribution of cloud cover (Iziomon and Aro, 1999). During the hours close to sunset or sunrise, the angle between the incoming

solar beam and the receiving surface is rather large and hence the solar beam must pass through a large amount of atmospheric mass with varying atmospheric constituents and hence is significantly scattered and reflected (Okogbue, 2007). During the period about local noon, when the sun is overhead or near-overhead, as the case may be, the values of clearness index rise to their maximum (ranging from 0.50 to 0.57, 0.57 to 0.62, and 0.48 to 0.60 for the months of January, February and March, respectively) (Figures 2, 3 and 4). The diffuse fractions, on the other hand, fall to their

minimum values (ranging from 0.45 to 0.54, 0.44 to 0.55, and 0.49 to 0.64 for the months of January, February and March, respectively). Again, this is because the solar beam passes through a single or relatively thin atmospheric thickness, and therefore, encounters relatively less atmospheric constituents, and hence, experiences less scattering and reflection, resulting January 0.1 0.2 0.3 0.4 0.5 0.6 7 8 9 101112131415161718 Local Time (hours) Clearness Index (M 93 94 95 96 97 98 2000 2002 (a) January 0.4 0.5 0.6 0.7 0.8 0.9 7 8 9 10 11 12 13 14 15 16 17 18 Local Time (hours) Diffuse

Fraction (M 93 94 95 96 97 98 2000 2002 (b) Figure 2. Diurnal Variation of monthly means of: (a) hourly clearness index, and (b) diffuse fraction for the month of January in the dry season. in less of the diffuse component of the solar radiation being incident on the surface. Furthermore, during the daytime from about 1100 to 1500 LST, the monthly mean hourly diffuse fraction, , has values, which are most of the time less than 0.52, 0.54 and 0.60 respectively for January, Febru- ary and March, indicating that the direct (beam) irra- diance constitutes a relatively significant proportion

of the global solar irradiance reaching the ground dur- ing these months. Molecular scattering due to atmo- spheric constituents prevalent during this period which Adeyefa et al . (1995) have described as the harmattan period with –moderate’ chara cteristics (background har- mattan) and, to a lesser extent, surface albedo, are mainly responsible for diffuse irradiance reaching the ground at these times, especially for the months of January and February. The implication of this for solar energy utilization is that solar concentrators that make use of parabolic mirrors are expected to have

relatively high perfor- mance during these months at Ile-Ife. However, in the event of appreciable cloudiness or albedo, as is the case sometimes in the month of March (which is a transition month from the dry to the wet sea- soninthearea),theradiationscatteredbythese clouds and reflected by the underlying surface would Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 5
ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1039 February 0.1 0.2 0.3 0.4 0.5 0.6 0.7 7 8 9 101112131415161718 Local Time (hours) Clearness

Index (M 93 94 95 96 98 2000 (a) February 0.4 0.5 0.6 0.7 0.8 0.9 7 8 9 101112131415161718 Local Time (hours) Diffuse Fraction (M 93 94 95 96 97 98 2000 (b) Figure 3. Diurnal Variation of monthly means of: (a) hourly clearness index, and (b) diffuse fraction for the month of February in the dry season. cause a notable rise in the incoming diffuse radia- tion (Okogbue, 2007). Iziomon and Aro, 1998 have reported daytime values of K with values generally lower than 0.50 for the months of February, November and March for Ilorin, a tropical station in North Central Nigeria. Figures 5 and 6 depict

the diurnal variation of the monthly means of hourly clearness index and diffuse fraction (or cloudiness index) for the months of July and August which are typical of the wet season. It is also clear from Figures 5 and 6 that the clearness index, has very low values for both months during the hours close to sunrise and sunset, with values ranging between 0.10 and 0.32 for July and 0.11 and 0.28 for August. The cloudiness index (or diffuse fraction), on the other hand, has values ranging between 0.87 and 0.99 for July and 0.80 and 0.99 for August. This is the same trend that was observed for

the dry months (Figures 2–4) with the obvious implication that the solar radiation received at the surface during the hours close to sunrise and sunset in both seasons consist mainly of the diffuse component. The monthly mean hourly diffuse fraction, has values ranging between 0.61 and 0.85 over the period 1100–1500 hours for July and August (being gener- ally greater than 0.65) with the corresponding values of monthly mean hourly clearness index, , ranging March 0.1 0.2 0.3 0.4 0.5 0.6 0.7 7 8 9 10 11 12 13 14 15 16 17 18 Local Time (hours) Clearness Index (M 92 93 95 96 97 98 2001 (a) March

0.4 0.5 0.6 0.7 0.8 0.9 7 8 9 101112131415161718 Local Time (hours) Diffuse Fraction (M 93 94 96 97 98 2000 (b) Figure 4. Diurnal Variation of monthly means of: (a) hourly clearness index, and (b) diffuse fraction for the month of March in the dry season. between 0.23 and 0.45 (Figures 5 and 6) during the day. This again signifies the high proportion of dif- fuse component of the total irradiance arriving on the ground during these months, which are typical of the wet season. Iziomon and Aro (1998) who reported simi- lar values for Ilorin ( values ranging between 0.35 and 0.48, and

values generally greater than 0.62 during the day for the months of July and August) attributed the high proportion of the diffuse component during the wet season to the intense forward scatter- ing of beam radiation by altocumulus and altostratus clouds. Under a cloudy sky, the magnitude of the dif- fuse radiation flux reachi ng the ground depends essen- tially on the amount, type and distribution of clouds. In the presence of cirrus, altostratus and altocumulus clouds, diffuse irradiance has been reported to increase with the increase in cloudiness (Kondratyev, 1969). The value of

solar radiation components received at the ground surface depends, therefore, on the clarity (trans- parency) or cloudiness (turbidity) of the atmosphere, and hence the clearness index ( ) and the dif- fuse ratio (or cloudiness index) ( ) can respec- tively be used to define or quantify the clearness or the turbidity/cloudiness of the atmosphere (Biga and Rosa, 1981; Ideriah and Suleman, 1989 and Iziomon and Aro, 1999; Babatunde and Aro, 2000; Babatunde, 2005). Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 6
1040 E. C.

OKOGBUE ET AL July 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 7 8 9 10 11 12 13 14 15 16 17 18 Local Time (hours) Clearness Index (M 92 93 94 96 97 98 99 2000 (a) July 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 7 8 9 101112131415161718 Local Time (hours) Diffuse Fraction (M 92 93 94 96 97 98 99 2000 (b) Figure 5. Diurnal Variation of monthly means of: (a) hourly clearness index, and (b) diffuse fraction for the month of July in the wet season. 5.2. Annual pattern of daily solar radiation fluxes and the solar radiation ratios (clearness index and diffuse fraction) The daily means of global and

diffuse solar radia- tion measured at Ile-Ife, Nigeria averaged over the 11- year period of data (1992–2002) are presented as time series in Figure 7. For the period, the mean of the daily global and diffuse solar radiation are 367 51 62 12 W m day and 232 66 27 68 W m day respectively. From Figure 7, it can be observed that the annual variation of the global solar radiation for the period showed a bimodal distribution with peak val- ues of about 490.89 W m day and 471, with 80 W day in March/early April and November respec- tively and a minima of about 196.24 W m day about July/August which

is at the peak of the mon- soon. The diffuse solar radiation followed a similar pat- tern. Figure 8 depicts the annual pattern of the daily clear- ness index and diffuse fraction and the corresponding monthly averages respectively. It is clear from Figure 8 that both the daily and monthly average daily clearness index and diffuse fractions follow the same annual pattern with the curve of the diffuse fraction being an inversion of the curve of the clearness index. An interesting feature is that within the five months of June to October the param- eters, and , have an almost regular

bell-shaped August 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 7 8 9 10 11 12 13 14 15 16 17 18 Local Time (hours) Clearness Index (M 92 93 94 96 97 98 99 2000 (a) August 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 7 8 9 101112131415161718 Local Time (hours) Diffuse Fraction (M 92 93 94 96 97 98 99 2000 (b) Figure 6. Diurnal Variation of monthly means of: (a) hourly clearness index, and (b) diffuse fraction for the month of August in the wet season. 1992 - 2002 100.00 200.00 300.00 400.00 500.00 600.00 1 31 61 91 121 151 181 211 241 271 301 331 361 Day of the Year (DOY) Solar radiation fluxes (W m -2 Global

Diffuse Figure 7. Daily averaged global and diffuse solar radiation at Ile-Ife (7.5 N, 4.57 E), Nigeria, 1992–2002. distribution with a prominent peak/depression occurring about the month of July/August for both the daily and monthly average cases as earlier observed by (Ideriah and Suleman, 1989). The daily diffuse fraction and the monthly mean daily diffuse fraction both had their peak values of about 0.99 and 0.84, respectively, in August during the wet season. The daily and monthly average daily clearness index had their minimum values of 0.23 and 0.31 in July and August respectively.

Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 7
ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1041 Data Period (1992 - 2002) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 31 61 91 121 151 181 211 241 271 301 331 361 Day Number = H/H0, K = H /H H/Ho Hd/H (a) (1992- 2002) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec Months KT, Kd KT Kd (b) Figure 8. Annual Pattern of: (a) daily clearness index (K ), and (b) diffuse fraction (K ) for the period 1992–2002 at Ile-Ife. The mean monthly

diffuse ratios for the set of months with relatively similar atmospheric and sky conditions at this location have also been estimated and are presented in Table I. Values obtained for Ilorin, Nigeria by Iziomon and Aro (1998) have also been inserted in Table I for comparison. The monthly mean daily K values vary from 58% for relatively dust-haze months to 59% for the set of partly cloudy, partly hazy and partly clear-sky months to 62 and 78% for the set of less cloudy and cloudy and wet months, respectively (Table I). Iziomon and Aro (1998) reported for Ilorin, Nigeria and for the period 1993

and 1994, mean K values varying from 53% for a set of relatively clear months, to 58% for a set of dust-haze months, 60% for a set of less cloudy months, and 71% for mainly cloudy and wet months. Clearly, our observation at Ile-Ife revealed that the very cloudy months are July, August and September instead of June, July and August observed by Iziomon and Aro (1998) for Ilorin. Again, at Ile-Ife by February, March and November atmospheric conditions are partly hazy, partly cloudy and partly clear, these months being transition months, whereas for Ilorin the conditions are relatively clear

(Iziomon and Aro, 1998). Table I. Average monthly diffuse ratios for months with relatively similar atmospheric and sky conditions (1992–2002). Values in parenthesis are values obtained for Ilorin, Nigeria, (Iziomon and Aro, 1998) inserted for comparison. Dust-haze months K Values Individual (%) Average (%) December, January 60, 56 58 (58) Partly hazy, partly cloudy and partly clear-sky months February, March, November 61, 62, 53 59 (53) Less Cloudy Sky Months April, May, June, October 64, 61, 63, 62 62 (60) Very Cloudy Sky Months July, August, September 75, 84, 75 78 (72) Note: Values in

parenthesis are val ues obtained for Ilorin, Nigeria, (Iziomon and Aro, 1998). Clear sky. 5.3. Frequency and commutative frequency distribution of hourly clearness index M The frequency of occurrence and cumulative frequency distributions for every 0.05 interval of hourly and daily clearness index have been plotted as column and line graphs on annual and seasonal basis as shown in Figures 9, 10 and 11. The frequency table (Table II) is also presented for ease of reference, and the cumulative frequency distribution is shown to get a feel for the fre- quency of occurrence of different sky

conditions. From Figures 9(a), 10(a), 11(a) and Table II, the distribution of hourly clearness index, M , has a marked peak value at the 0.5–0.55 M interval, and there are more data at the values between 0.2 and 0.6 (above 88% of the time), which represents cloudy sky with high diffuse radiation. From the cumulative frequency distribution (Figures 9(b) 10(b) and 11(b)) at M 6, the cumulative frequencies are 97.4, 99.7 and 94.1% for the annual, wet and dry sea- sons, respectively. These indicate that the local sky over Ile-Ife is clear for only about 3% of the time, and this occurs mostly

during the dry season. Also, the cumula- tive frequencies at M 15 (the condition for overcast sky) are 4.8, 5.5 and 4.8% for the annual, wet and dry seasons, respectively. Apart from clouds, atmospheric turbidity due to the high loading of the atmosphere by aerosols, especially the harmattan dust and other pollutants resulting from anthropogenic activities suc h as road construction and wood processing over the area could result in a large scattering of global solar irradiance resulting in a very high proportion of it in the diffuse component, which an overcast sky represents. So, an overcast

sky could Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 8
1042 E. C. OKOGBUE ET AL 1992 - 2002 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 0.0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3 0.3-0.35 0.35-0.4 0.4-0.45 0.45-0.5 0.5-0.55 0.55-0.6 0.6-0.65 0.65-0.7 0.7-0.75 >0.75 Hourly Clearness Index (M Frequency of Occurrence (%) N = 1188 (a) 1992 - 2002 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 Hourly Clearness Index (M Cumulative Frequency (%)

(b) Figure 9. (a) Frequency of occurrence, and (b) cumulative frequency of hourly clearness index (M ) at Ile-Ife for the period 1992–2002 (N represents total number of hours considered). actually also refer to sky conditions under very intense dust spells and not just cloudiness. 5.4. Frequency and commutative frequency distribution of daily clearness index K Frequency tables for every 0.05 interval of daily clearness index, K , have also been similarly established as shown in Table III and the daily frequency of occurrence and cumulative frequency distri butions plotted also on annual, wet

and dry seasons basis as depicted in Figures 12, 13 and 14 respectively. Clearly, the pattern of daily K is fairly evenly distributed, with peaks about the 0.45–0.5 interval for the annual and wet season distributions, respectively, and 0.5–0.55 for the dry season. There are also more data at the K values between 0.2 and 0.6 (about 89% of the time) as was the case with the hourly clearness index M , which represents cloudy sky with high diffuse solar radiation. Similarly, the cumulative frequencies at K 15 are 1.5, 2.3 and 0.3%, respectively, for the annual, wet and dry seasons (Figures 12(a),

13(a) and 14(a)). This again implies that the local sky over Ile-Ife is overcast only for about 1.5% 1992 - 2002 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 0.0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3 0.3-0.35 0.35-0.4 0.4-0.45 0.45-0.5 0.5-0.55 0.55-0.6 0.6-0.65 0.65-0.7 0.7-0.75 >0.75 Hourly Clearness Index (M Frequency of Occurrence (%) N = 1188 (a) 1992 - 2002 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 Hourly Clearness Index (M Cumulative Frequency (%) (b) Figure 10. (a) Frequency of occurrence, and (b)

cumulative frequency of hourly clearness index (M ) at Ile-Ife for the period 1992–2002 (wet season) (N represents the number of hours considered). of the time (representing only 40 days in the 11-year period of data). For K 6, the cumulative frequencies are 95.0, 94.2 and 95.5%, respectively, for the annual, wet and dry seasons. Again, this implies that the local sky over Ile-Ife is clear only for about 5% (which represents only 154 days out of the 3076 days under consideration). It can therefore be inferred from both hourly and daily clearness index classification of the sky conditions

over Ile-Ife that clear and overcast skies are very rare over the station, and that the local sky over Ile-Ife is predominantly cloudy all the year round. 5.5. Monthly K Cumulative Distribution Curves Following the work of Liu and Jordan (1960), the cumu- lative frequency, f (in pe rcentage) of daily K within the month, has also been computed using Equation (1) as shown in Table IV. The climate in Nigeria can be broadly divided into two seasons, namely, dry season (Novem- ber–March/April) and wet season (April/May–October). If we define our –cloudy’ days by K 35 and –very clear’ days by

K 65 as was done by Kuye Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 9
ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1043 1992- 2002 (Dry season) 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 0.0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3 0.3-0.35 0.35-0.4 0.4-0.45 0.45-0.5 0.5-0.55 0.55-0.6 0.6-0.65 0.65-0.7 0.7-0.75 >0.75 Hourly Clearness Index (M Frequency of occurrence (%) N = 492 (a) 1992- 2002 (Dry season) 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 > 0.75 Hourly Clearness Index (M Cumulative Frequency (%) (b) Figure 11. (a) Frequency of occurrence, and (b) cumulative frequency of hourly clearness index (M ) at Ile-Ife for the period 1992–2002 (dry season) (N represents the number of hours considered). and Jagtap (1992) and Ideriah and Suleman (1989), then it is also obvious from Table IV that the frequency of cloudy days is quite high for Ile-Ife ranging from 12.5% in May to 64.5% in August with August as the most cloudy of the months. Kuye and Jagtap (1992) using 13 years data obtained similar results

for Port Harcourt with the frequency of cloudy days ranging from 31.8% in May to 58.1% in August. This shows that Port Harcourt experiences more cloudy days during the early part of the wet season in May than Ile-Ife, with Ile-Ife being more cloudy than Port Harcourt at the peak of the wet season in August. We can also deduce from Table IV that –very clear days (K 65) are rare in Ile-Ife, ranging only from 3.1% in May (the atmosphere having just been cleansed of the turbid harmattan dust by the rains) to 4.2% in November (being a transition month from the wet to the dry season is relatively

devoid of clouds which charac- terise the wet season and dust which are characteristics of the dry season). Based on the calculated monthly average clearness index , the monthly variations of f and the prevalent climatic conditions, six seas onal patterns can be identi- fied at Ile-Ife. These consist of two distinct dry season Table II. Frequency Distribution of Hourly Clearness Index (M ) over Ile-Ife for the period 1992–2002. interval Frequency of occurrence Percentage frequency (%) Annual Wet Dry Annual Wet Dry 0.0–0.05 14 2 12 1.2 0.3 2.4 0.05–0.1 18 9 9 1.5 1.3 1.8 0.1–0.15 25 19 6

2.1 2.7 1.2 0.15–0.2 51 35 16 4.3 5.0 3.3 0.2–0.25 83 52 31 7.0 7.5 6.3 0.25–0.3 89 63 26 7.5 9.1 5.3 0.3–0.35 131 101 30 11.0 14.5 6.1 0.35–0.4 165 123 42 13.9 17.7 8.5 0.4–0.45 157 100 57 13.2 14.4 11.6 0.45–0.5 149 83 66 12.5 11.9 13.4 0.5–0.55 178 85 93 15.0 12.2 18.9 0.55–0.6 97 22 75 8.2 3.2 15.2 0.6–0.65 24 2 22 2.0 0.3 4.5 0.65–0.7 5 0 5 0.4 0.0 1.0 0.7–0.75 1 0 1 0.1 0.0 0.2 0.75 1 0 1 0.1 0.0 0.2 Total 1188 696 492 100.0 100 100.0 Table III. Frequency distribution of daily clearness index (K over Ile-Ife for the period 1992–2002. interval Frequency of occurrence Percentage frequency

(%) Annual Wet Dry Annual Wet Dry 0.0–0.05 0 0 0 0.0 0.0 0.0 0.05–0.1 7 1 6 0.2 0.1 0.3 0.1–0.15 40 3 37 1.3 0.2 2.0 0.15–0.2 68 1 67 2.2 0.1 3.6 0.2–0.25 118 5 113 3.8 0.4 6.1 0.25–0.3 199 13 186 6.5 1.1 10.1 0.3–0.35 245 32 213 8.0 2.6 11.6 0.35–0.4 294 76 218 9.6 6.2 11.8 0.4–0.45 435 171 264 14.1 13.8 14.3 0.45–0.5 553 296 257 18.0 24.0 14.0 0.5–0.55 546 322 224 17.8 26.1 12.2 0.55–0.6 417 243 174 13.6 19.7 9.5 0.6–0.65 128 61 67 4.2 4.9 3.6 0.65–0.7 26 11 15 0.8 0.9 0.8 0.7–0.75 0 0 0 0.0 0.0 0.0 0.75 0 0 0 0.0 0.0 0.0 Total 3076 1235 1841 100.0 100.0 100.0 patterns and four rainy seas on

patterns, namely: Novem- ber, December, January (NDJ) and February, March, April (FMA) for the dry season; and August (A); July and September (JS); June and October (JO); and May (M) for the rainy season. Ideriah and Suleman (1989) and Kuye and Jagtap (1992) have identified similar sea- sonal patterns for Ibadan and Port Harcourt respectively. The monthly K values for the different months and the average value for each of the identified seasonal patterns Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 10
1044 E. C.

OKOGBUE ET AL 1992 - 2002 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 0.0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3 0.3-0.35 0.35-0.4 0.4-0.45 0.45-0.5 0.5-0.55 0.55-0.6 0.6-0.65 0.65-0.7 0.7-0.75 >0.75 Daily Clearness Index (K Frequency of occurrence (%) N = 3076 (a) 1992 - 2002 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 Daily clearness index (K Cumulative Frequency (%) 0.05 (b) Figure 12. (a) Frequency of occurrence, and (b) cumulative frequency of daily clearness index (K ) at Ile-Ife for the period

1992–2002 (N represents total number of days considered). are shown in Table V, with the corresponding values cal- culated for Ibadan for the period (1975–1980) (Ideriah and Suleman, 1989) and Port Harcourt for the period (1977–1989) (Kuye and Jagtap, 1992) also included for comparison. Kuye and Jagtap (1992) identified five instead of the six seasonal patterns, since for Port Harcourt, the average value for M is equal to that of the second period in the dry season FMA. The plots of the cumulative frequency, f, corresponding to each of the six seasonal, monthly clearness index

patterns (NDJ, FMA, A, JS, JO and M), which Liu and Jordan (1960) termed monthly CDCs are shown in Figure 15. For comparison, the JS curves of 39 and 0.36 for Ibadan (Ideriah and Suleman, 1989) and Port Harcourt (Kuye and Jagtap, 1992), respectively, have also been inserted in Figure 15. Though the degree of cloudiness of the local sky at Port Harcourt and Ibadan vary for the different months from that at Ile-Ife as shown in Table V, Figure 15 shows that the shapes of the K CDC though distinct, one from the other, are in agreement. The curves are orderly from 31 to 0.50 and the present

pattern, which also agrees with results obtained at other tropical locations like Ibadan (Ideriah and Suleman, 1989), Port Harcourt 1992 - 2002 (Wet Season) 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 0.0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3 0.3-0.35 0.35-0.4 0.4-0.45 0.45-0.5 0.5-0.55 0.55-0.6 0.6-0.65 0.65-0.7 0.7-0.75 >0.75 Daily Clearness Index (K Frequency of Occurrence (%) N =1841 (a) 1992 - 2002 (Wet Season) 10 20 30 40 50 60 70 80 90 100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 Daily Clearness Index (K Cumulative Frequency (%) (b) Figure 13. (a)

Frequency of occurrence, and (b) cumulative frequency of daily clearness index (K ) at Ile-Ife for the period 1992–2002 (wet season) (N represents total number of days considered). (Kuye and Jagtap, 1992) and Ilorin (Udoh, 2000) and are different from those obtained for twenty-seven cities in the USA and Canada by Liu and Jordan (1960). The results obtained by Liu and Jordan (1960) gave much higher values of K (usually up to 0.8 or more) for each of the monthly average , which indicates the abundance of very clear skies i n those cities they reported on, whereas, it has been clearly shown in

this study that clear skies are rare in Ile-Ife which is a tropical location. The claim of the universal applicability of the Liu and Jordan’s CDC curves has been questioned by earlier typical results obtained by Hawas and Muneer (1984); Saunier et al . (1987); Ideriah and Suleman (1989); Kuye and Jagtap (1992) and Udoh (2000) for some tropical locations in India, Bangkok in Thailand, Ibadan, Port Harcourt, and Ilorin in Nigeria, respectively. This study therefore corroborates their findings. One major implication of this is that solar energy concentrating devices which make use of

incident beam radiation whose availability at the surface depends on how clear the sky is, will not be as effective (in fact will not be effective) in Ile-Ife and similar tropical locations as they would be at the cities studied by Liu and Jordan (1960). Consequently, the use of such solar devices that are designed based on the CDCs of Liu and Jordan in Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 11
ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1045 1992-2002 (Dry Season) 0.0 5.0 10.0 15.0 20.0 25.0 30.0

0.0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3 0.3-0.35 0.35-0.4 0.4-0.45 0.45-0.5 0.5-0.55 0.55-0.6 0.6-0.65 0.65-0.7 0.7-0.75 >0.75 Daily Clearness Index (K Frequency of Occurrence (%) N = 1235 (a) 1992 - 2002 (Dry Season) 10 20 30 40 50 60 70 80 90 100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 >0.75 Daily Clearness Index (K Cumulative Frequency (%) (b) Figure 14. (a) Frequency of occurrence, and (b) cumulative frequency of daily clearness index (K ) at Ile-Ife for the period 1992–2002 (dry season) (N represents total number of days considered). tropical

locations need to be reconsidered in the light of this and other findings based on measurements from the area. 6. Conclusions Hourly global and diffuse solar radiation data measured during the period 1992–2002 on top of the Physics Department building at Obafemi Awolowo University Ile-Ife, Nigeria, have been used to calculate the hourly and daily clearness index and diffuse fraction at the station. It has been established that during the daytime from about 1100 to 1500 LST, the monthly mean hourly diffuse fraction, , has values, which are, most of the time, less than 0.52, 0.54 and 0.60,

respectively, for January, February and March indicating that the direct (beam) irradiance constitu te a relatively significant proportion of the global solar irradiance reaching the ground during these months. Molecular scattering due to the aerosol loading of the atmosphere prevalent during this period are mainly responsible for diffuse irradiance reaching the ground at these times, especially for the months of January and February. Again, during the months of July and August (which are typical of the wet season), the monthly mean hourly diffuse fraction, has values ranging between

0.61 and 0.85 over the period 1100–1500 LST (being generally greater than 0.65) with the corresponding values of ranging between 0.23 and 0.45 during the day. This again signifies the high proportion of diffuse component of the total irradiance arriving on the ground during these months, which is a result of the intense forward scattering of beam radiation by altocumulus and altostratus clouds. Statistical analysis of hourly and daily clearness index showed that the local sky conditions at the station were almost devoid of clear skies (clear skies occurred for only about 3.5% of the

time). Overcast skies were also very scarce (overcast skies occurred for only about 4.8% of the time). The sky conditions were rather predominantly cloudy (cloudy skies occurred for above 72% of the time) all the year round. The study has, therefore, shown that there is high proportion of diffuse component of the total irradiance arriving on the ground at the station all the year round Table IV. Monthly percentage cumulative frequency, f, of the daily clearness index K and monthly average values of the clearness index, over Ile-Ife for the period 1992–2002 (f is computed using Equation (1)).

Values of f for K (fixed value) Monthly Average 0.1 0.2 0.3 0.35 0.4 0.5 0.6 0.65 0.7 0.8 0.9 1 Jan. (257) 0.0 0.0 1.6 5.8 20.6 78.2 99.6 100.0 100.0 100.0 100.0 100.0 0.46 Feb. (213) 0.0 0.0 0.0 1.4 3.8 39.4 95.8 100.0 100.0 100.0 100.0 100.0 0.51 March (266) 0.0 1.1 3.8 6.4 11.3 52.6 95.1 100.0 100.0 100.0 100.0 100.0 0.49 April (235) 0.0 4.3 8.1 10.2 14.5 47.2 95.3 98.7 100.0 100.0 100.0 100.0 0.48 May (257) 0.0 2.3 5.8 12.5 23.0 49.8 86.0 96.9 100.0 100.0 100.0 100.0 0.48 June (269) 0.0 3.3 11.2 20.1 33.8 66.2 96.7 99.6 100.0 100.0 100.0 100.0 0.44 July (297) 0.0 11.4 40.4 59.3 74.4

93.9 99.3 100.0 100.0 100.0 100.0 100.0 0.33 Aug. (279) 1.0 11.5 45.8 64.5 78.5 97.5 99.3 100.0 100.0 100.0 100.0 100.0 0.31 Sept. (270) 0.0 4.4 25.9 41.9 56.3 88.5 99.3 99.6 100.0 100.0 100.0 100.0 0.38 Oct. (234) 0.0 3.0 11.9 18.4 26.9 64.9 9 2.3 99.1 100.0 100.0 100.0 100.0 0.45 Nov. (262) 0.0 0.7 1.5 3.8 7.6 25.6 82.1 95.8 100.0 100.0 100.0 100.0 0.53 Dec. (237) 0.0 0.0 1.3 4.2 8.4 45.6 99.2 100.0 100.0 100.0 100.0 100.0 0.50 Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 12
1046 E. C. OKOGBUE ET AL Table V. Average

monthly/seasonal clearness index ( ) values for Ile-Ife for the period 1992–2002, compared with similar results for Port Harcourt and Ibadan inserted for comparison. Port Harcourt Ibadan Ile-Ife Individual Average Individual Avereage Individual Average 1.1.1 Dry Season (a) Nov, Dec, Jan 0.42, 0.45, 0.43 0.44 0. 53, 0.51, 0.49 0.51 0.53, 0.50, 0.46 0.50 (b) Feb, Mar, Apr 0.43, 0.41, 0.42 0.42 0. 53, 0.53, 0.52 0.53 0.51, 0.49, 0.48 0.49 1.1.2 Wet Season (a) Aug 0.33 0.33 0.35 0.35 0.31 0.31 (b) Jul, Sep 0.35, 0.37 0.36 0. 39, 0.40 0.39 0.33, 0.38 0.36 (c) Jun, Oct 0.39, 0.39 0.39 0. 47, 0.47

0.47 0.44, 0.45 0.45 (d) May 0.42 0.42 0.50 0.50 0.48 0.48 Kuye and Jagtap (1992). Ideriah and Suleman (1989). This study. 1992 - 2002 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Clearness Index (K Cumulative Frequency, f (%) NDJ (0.50) FMA (0.49) A (0.31) JS (0.36) JO (0.45) M (0.48) JS (0.39;I deriah & Suleman) JS (0.36;Kuye & Jagtap) Figure 15. Monthly cumulative distribution curves for Ile-Ife over various periods with some of the results obtained by Ideriah and Suleman (1989) and Kuye and Jagtap (1992) for Ibadan and Port Harcourt

respectively inserted for comparison. The number in parenthesis in the legend indicates the average K for the period. Equation (1) defines f. due to molecular scattering of beam radiation by aerosols and clouds which keep the sky turbid and cloudy most of the time. Compared to the molecular scattering of beam radiation by aerosols during the dry season, forward scat- tering by clouds (especially altocumulus and altostratus clouds) is more intense resulting in more diffuse com- ponent of the total solar radiation reaching the surface during the wet season than the dry season. The impli-

cation is that solar devices that use radiation from sun and sky under changing atmospheric conditions should be preferred to solar energy concentrating devices, such as parabolic mirrors, which make use of incident beam radiation (whose availability at the surface depends on how clear the sky is). The results also have implica- tions for the much-talked-about climate variability and its impact on food production, numerical weather modelling and dependable weather forecast as global circulation, crop simulation and soil-vege tation-atmosphere transfer models require information on the

decomposition of solar irradiance into its various components. Acknowledgements The authors gratefully acknowledge the support of the International Program in the Physical Sciences (IPPS), Sweden, for the establishment of the Obafemi Awolowo University (OAU) Ile-Ife solar radiation station. The assistance of Professor L. Hasselgren and useful discus- sions with Profs. Z. D. Adeyewa and O.O. Jegede are quite appreciated. The support of Third World Academy of Sciences (TWAS) and Obafemi Awolowo University, Ile-Ife, Nigeria, are also acknowledged. Appendix Symbols, definitions and notations

used – Daily diffuse fraction; – Daily clearness index; – Monthly average clearness index; – Hourly extraterrestrial radiation; – Daily extraterrestrial radiation; – Hourly clearness index; – Hourly diffuse fraction; – Monthly average hourly clearness index; – Monthly average hourly diffuse fraction; SC – Monthly average hourly diffuse fraction; f – Percentage cumulative frequency of the aver- age daily clearness index; References Adebayo SI. 1989. Pronounced haze spell over Nigeria, 2 nd –11 th March 1977. In Proceedings of the Pre-WAMEX Symposium on the West African Monsoon , Adefolalu DO

(ed.). Leo Express Printers: Lagos; 270–300. Adedokun JA. 1978. West African Precipitation and dominant atmospheric mechanisms. Archives for Meteorology Geophysics and Bioclimatology A, 27 : 289–310. Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc
Page 13
ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1047 Adedokun JA, Adeyefa ZD, Okogbue E, Holmgren B. 1994. Measure- ment of Solar and Longwave Radia tion Fluxes over Ile-Ife, Nige- ria. In American Institute of Physics ( AIP) Conference Proceedings Haubold HJ, Onuora LI

(eds). New York AIP Press No. 320: New York; 179–190. Adedokun JA, Emofurieta WO, Adedeji OA. 1989. Physical, miner- alogical and chemical properties of Harmattan dust at Ile-Ife, Nigeria. Theoretical and Applied Climatology 40 : 161–169. Adejokun JA. 1966. The three dimensional structure of Inter-Tropical Discontinuity Over Nigeria. Ni geria Meteorological Services Technical Note. No.39, Lagos, Nigeria, 9. Adeyefa ZD, Adedokun JA. 1991. Pyheliometric Determination of Atmospheric Turbidity in Harmattan season over Ile-Ife. Renewable Energy (14): 555–566. Adeyefa ZD, Holmgren B, Adedokun JA.

1995. Spectral solar irradiance under harmattan conditions. Renewable Energy (8): 989–996. Adeyefa ZD, Holmgren B, Adedokun JA. 1997. Spectral solar radiation measurement and turbid ity: Comparative studies within a tropical and a sub-Arctic environment. Solar Energy 60 (1): 17–24. Adeyewa ZD, Holmgren B, Adedokun JA. 2002. Specttroradiometric investigations of atmospheric turbidity parameters. Journal of African Meteorological Society (1): 15–29. Ali A-L, Atsu SSD, Jervase JA. 2003. Monthly Average Daily Solar Radiation and Clearness Index Contour Maps Over Oman Energy Conversion and

Management 44 : 691–705. Babatunde EB. 2005. Some solar radiation ratios and their interpretations with regards to rad iation transfer in the atmosphere. Nigeria Journal of Pure and Applied Physics : 41–45. Babatunde EB, Aro TA. 2000. Variation Characteristics of diffuse solar radiation at a tropical station (Ilorin, Nigeria). Nigerian Journal of Physics 12 : 20–24. Balogun EE. 1981. Convective Activity over Nigeria during the Monsoon season. In Proceedings of the International Conference on Early Results of FGGE and Large-scale Aspects of its Monsoon Experiment , Tallahassee, Florida, January

12-17, 8, 22–27. Bamiro OA. 1983. Empirical Relations for the determination of solar radiation in Ibadan, Nigeria. Solar Energy 31 (1): 85–94. Biga AJ, Rosa R. 1981. Statistical be haviour of solar radiation over consecutive days. Solar Energy 27 : 149–157. Coppolino S. 1994. A new correlation between clearness index and relative sunshine. Renewable Energy (4): 417–423. De Jong R, Stewart DW. 1993. Estimating global solar radiation from common meteorological observations in western Canada. Canadian Journal of Plant Science 73 : 509–518. De Pury DGG, Farquhar GD. 1997. Simple scaling of

photosynthesis from leaves to canopies without the errors of big-leaf models. Plant Cell and Environment 20 : 537–557. Duffie JA, Beckman WA. 1991. Solar Engineering of Thermal Processes . John Wiley and Sons: New York. El-Fandy MG. 1953. On the physics of dust atmosphere. Quarterly Journal of the Royal Me teorological Society 79 : 284–287. Griffiths JF (ed.). 1974. Climate of Africa. In World Survey of Climatology , Vol. 10, Landsberg HE (ed.). Elsevier Publishing Company: Amsterdam; 167–187. Hansen JW. 1999. Stochastic daily solar irradiance for biological modeling applications.

Agricultural Meteorology 94 : 53–63. Hawas M, Muneer T. 1984. Study of diffuse and global radiation characteristics in India. Energy Conversion and Management 24 143. Hook JE, McClendon RW. 1992. Estimation of solar radiation data missing from long-term meteorological records. Agronomy Journal 88 : 739–742. Ideriah FJK, Suleman SO. 1989. Sky conditions at Ibadan during 1975–1980. Solar Energy 43 (6): 325–330. Iqbal M. 1983. An Introduction to Solar Radiation . Academic Press: New York; 59–67. Iziomon MG, Aro TO. 1998. The diffuse fraction of global solar irradiance at a tropical location.

Theoretical and Applied Climatology 61 : 77–84. Iziomon MG, Aro TO. 1999. On the annual and monthly mean diurnal variations of diffuse solar radiation at a meteorological station in West Africa. Meteorology and Atmospheric Physics 69 : 223–230. Iziomon MG, Mayer H. 2001. Performance of solar radiation models – a case study. Agricultural Meteorology 110 : 1–11. Jegede OO. 1997a. Diurnal variations of the net radiation at a tropical station – Osu, Nigeria. Theoretical and Applied Climatology 58 161–168. Jegede OO. 1997b. Daily averages of net radiation measured at Osu, Nigeria in 1995.

International Journal of Climatology 17 1357–1367. Jegede OO. 1997c. Estimating net radiation from air temperature for diffusion modelling applications in a tropical area. Boundary-Layer Meteorology 85 : 161–173. Jegede OO. 2003. A note on net radiation at Osu, Nigeria. Meteorologische Zeitschrift 12 : 269–271. Kalu AE. 1978. The African dust plume: Its characteristics and propa- gation across West Africa in winter. In Saharan Dust – Mobilisation, Transport, Deposition , Morales C (ed.). SCOPE 14 Publication, John Willey and Sons: New York; 95–118. Kondratyev KY. 1969. Radiation in the

Atmosphere . Academic Press: New York; 277–280. Kuye A, Jagtap SS. 1992. Analysis of solar radiation data for Port Harcourt, Nigeria. Solar Energy 49 (2): 139–145. Kyle TG. 1991. Atmospheric Transmission, Emission and Scattering Pergamon Press Ltd: Oxford; 288p. Li DHW, Lam JC. 2001. An analysis of climatic parameters and sky condition classification. Building and Environment 36 : 435–445. Li DHW, Lau CCS, Lam JC. 2004. Overcast sky conditions and luminance distribution in Hong Kong. Building and Environment 39 101–108. Liu BYH, Jordan RC. 1960. The interrelationship and characteristic

distribution of direct, diffuse and total solar radiation. Solar Energy : 1–19. Liu DL, Scott BJ. 2001. Estimation of solar radiation in Australia from rainfall and temperature observations. Agricultural Meteorology 106 41–59. Maduekwe AAL, Chendo MAC. 1995. Predicting the components of the total hemispherical solar radiation from sunshine duration measurements in Lagos, Nigeria. Renewable Energy (7): 807 812. Mauder M, Jegede OO, Okogbue EC, Wimmer F, Foken T. 2007. Surface nergy balance measurements at a tropical site in West Africa during the transition from dry to wet season. Theoretical

and Applied Climatology DOI 10.1007/s00704-006-0252-6. Muneer T. 1995. Solar irradiance an d illuminance models for Japan II: luminous efficacies. Lighting Research and Technology 27 : 223–230. Muneer T. 1998. Evaluation of the CIE overcast sky model against Japanese data. Energy and Buildings : Elsevier, Netherlands; 27 175–177. Okogbue EC. 2007. Broad-band solar irradiance and photometric illuminance at the tropical station . Ile-Ife, Nigeria. Unpublished PhD Thesis, Obafemi Awolowo University, Ile-Ife, Nigeria, 223. Okogbue EC, Adedokun JA. 2002a. On the estimation of solar radiation

at Ondo, Nigeria. Nigerian Journal of Physics 14 (1): 97–104. Okogbue EC, Adedokun JA. 2002b. Charact erization of sky conditions over Ile-Ife, Nigeria based on 1992–1998 Solar Radiation Observations. Meteorogische Zeitschrift, Germany 11 (6): 419–423. Okogbue EC, Adedokun JA, Jegede OO. 2002. Fourier series analysis of daily global and diffuse Irradiation for Ile-Ife, Nigeria. Journal of Applied Sciences (3): 3034–3045. Okogbue EC, Adedokun JA. 2003. Improvi ng the estimation of global solar radiation over Ondo in South Western Nigeria. Nigerian Journal of Physics 15 (1): 20–31. Reindl DT,

Beckman WA, Duffie JA. 1990. Diffuse fraction correla- tions. Solar Energy 45 : 1–7. Saunier GY, Reddy TA, Kumar S. 1987. On the monthly probability distribution function of daily global i rradiation values appropriate for both tropical and temperate locations. Solar Energy 38 : 169–177. Stokes GM, Schwartz SE. 1994. The Atmospheric Radiation Mea- surement (ARM) Program: Programmatic background design of the cloud and radiation test bed. Bulletin of the American Meteorological Society 75 : 1201–1221. Thornton PE, Running SW. 1999. An improved algorithm for estimating incident daily sola

r radiation from measurements of temperature, humidity, and precipitation. Agricultural Meteorology 93 : 211–228. Udoh SO. 2000. Sky conditions at Ilor in as characterized by clearness index and relative sunshine. Solar Energy 69 : 45–53. Wilks DS, Wilby RL. 1999. The weather generation game: a review of stochastic weather models. Progress in Physical Geography 23 329–357. Copyright 2009 Royal Meteorological Society Int. J. Climatol. 29 : 1035–1047 (2009) DOI: 10.1002/joc