Review Hourly and daily clearness index and diffuse fraction at a tropical station, Ile-Ife, Nigeria

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 29: (2009) Published online 5 January 2009 in Wiley InterScience ( DOI: 1002/joc.1849 Review Hourly and daily clearness index and diffuse fraction at a tropical station, Ile-Ife, Nigeria E. C. Okogbue, a * J. A. Adedokun b and B. Holmgren c a Department of Meteorology, Federal University of Technology, Akure, Nigeria b Departments of Physics, Obafemi Awolowo University, Ile-Ife, Nigeria c Meteorological Institute, Uppsala University, S Uppsala, Sweden ABSTRACT: Dataset consisting of hourly global and diffuse solar radiation measured over the period February 1992 and December 2002 have been utilized to investigate the diurnal and 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 LST) monthly mean hourly diffuse fraction, M d (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 2, 4 and 0 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 1 and 5 (being generally greater than 5) with the corresponding values of the monthly mean hourly clearness index, M T, ranging between 3 and 5. 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 predominantly 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 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 needed in general circulation * Correspondence to: E. C. Okogbue, Department of Meteorology, Federal University of Technology, Akure, Nigeria. emokogbue@yahoo.co.uk models (GCMs) (Stokes and Schwartz, 19) 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, hydrology, ecology and energy development programmes and utilization, among others. Lack of adequate observations on solar radiation has been a persistent problem in studies of land-surface processes and a major limitation in the validation of crop growth simulation models (Thornton and Running, 1999; Liu and Scott, 2001) and photosynthesis models since the decomposition of solar irradiance into its various components is now a key feature of several canopy-scale models of photosynthesis (De Pury and Farquhar, 19). 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 systems within a particular region require information on the Copyright 2009 Royal Meteorological Society

2 1036 E. C. OKOGBUE ET AL. variation characteristics and distribution of the amount of solar energy received at the location (Duffie and Beckman, 1991; Coppolino, 19; and Ali et al., 2003). The separation of solar irradiance into the various components is also necessary for a wide range of these solar engineering tasks (Iqbal, 13). 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 required in assessing the climatological potential of a locality for solar energy utilization and in estimating the expected values of the output of concentrating solar collectors (Iziomon and Aro (19). 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 classification of sky types) over a particular locality (Ideriah and Suleman, 19; Kuye and Jagtap, 1992; Okogbue and Adedokun, 2002b). Synoptic cloud observations, though very subjective, have remained the only source of information on sky conditions for most parts of tropical Africa, Nigeria inclusive, since there are no ground-based instrumentation systems to monitor them routinely and objectively, and estimation procedures have only been established 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 compared to other variables such as temperature and rainfall (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, 19) 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 measurements are the least common. This is probably due to the high cost of purchasing and maintaining the necessary equipment, and the dearth of skilled personnel. A number of studies have however, been reported in Nigeria, notable among which are: Bamiro (13) and Ideriah and Suleman (19); Adeyefa and Adedokun (1991); Kuye and Jagtap (1992); Adedokun et al. (19); Maduekwe and Chendo (1995); Iziomon and Aro (19, 1999); Adeyewa et al. (1995, 19, 2002); Okogbue and Adedokun (2002a,b, 2003); Okogbue et al. (2002) and Jegede (19a,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 diffuse 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 investigated. 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 2 ) measured at Ile-Ife, Nigeria (7.5 N, 4.57 E) during the period March 1992 to December 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 campus of Obafemi Awolowo University, Ile-Ife, Nigeria comprised of two Kipp and Zonen pyranometers models CM11 for the global radiation and CM11/121 (incorporating a shadow ring) for diffuse radiation and a LICOR LI-210SA photometric sensor for the photometric illuminance. The altitude of the Physics building is about 275 m above sea level. The measuring site is, therefore, 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 improvised 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 values. 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 d (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 Station on the rooftop of the Physics Department Building at Obafemi Awolowo University, Ile-Ife, Nigeria. This figure is available in colour online at com/ijoc DOI: 1002/joc

3 ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1037 and the clearness index K T (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 d > 1 4. K d > 0, when K T > 0 (clear sky). 5. K d < 0 when K T < 0 (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 seasons occurs in association with the north south (meridional) 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, 16). At about the latitudinal belt 7 N (representative of the position at Ile-Ife), there frequently occur thunderstorm activities characteristic of the wet season beginning from mid-march/april (maximum about July/August) and extending till late October during the Northern Hemisphere summer. During this period, the presence of thick clouds (e.g. cumulus/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, 14) is a regular atmospheric phenomenon. The wet season is also generally characterized by high moisture content of the air. Consequently, the most important attenuators of solar radiation during this period are clouds and water vapour (Kyle, 1991; Jegede, 19a,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, 18; Balogun, 11). 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, 18; Adedokun et al., 19) 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 characteristics (background harmattan) and periods with intensive dust spells that could last 3 4 days or more (Kalu, 18 and Adebayo, 19). The high aerosol loading of the atmosphere during this season attenuates the solar radiation 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, 18, Jegede, 19a,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 0 ) and one day (H 0 ) (required for calculation of the hourly clearness index (M T ) and daily clearness index (K T ) are respectively estimated analytically by the familiar expressions according to Iqbal (13) with the solar constant I SC = 1367 Wm 2. The diurnal and annual patterns of M T, K T, the hourly diffuse fraction, (M d ), and the daily diffuse fraction, (K d ), 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 (10) and those of Li et al., For instance, Liu and Jordan (10) had shown that the information on the daily clearness index, (K T ), could also be presented as cumulative frequency, f (K T ), in percentage as follows: f = number of days with K T K T (f ixed value) number of days in the month 100% (1) Using data from a network of 27 stations, each with approximately 5 years of data, Liu and Jordan (10) proposed, based on Equation (1), a set of generalized K T 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 (10) has been queried by typical results obtained by Hawas and Muneer (14); Saunier et al. (17); Ideriah and Suleman (19); 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 clearness index is a widely used index since it depends only on global solar irradiance (i.e. one measured parameter) (Muneer, 1995, 19; Li et al., 2004). Low clearness index means low global solar radiation, which usually represents a cloudy sky with a high portion of diffuse DOI: 1002/joc

4 1038 E. C. OKOGBUE ET AL. component. Large clearness index means high global solar radiation, which is dominated by the direct component. There are however, no clear-cut K T values to define the sky conditions. Different researchers have therefore adopted different values. For instance, Reindl et al. (1990) have proposed K T > andk T < for clear sky and cloudy sky, respectively. Li and Lam (2001) and Li et al. (2004) used K T values of 0 5, >5 and > to define overcast, partly cloudy and clear skies respectively in Hong Kong and Kuye and Jagtap (1992) used K T > 5 and 2 K T 5, respectively, for very clear skies and cloudy skies, to classify the sky conditions at Port Harcourt, Nigeria. For this work, K T (or M T )valuesof0 K T (M T ) 5, 5 K T (M T ) 0, K T (M T ) 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 9 and 3. The diffuse fraction on the other hand, has rather very high values during such hours (ranging between 7 and 9) 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 dependence 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 to 7, 7 to 2, and 8 to 0 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 5 to 4, 4 to 5, and 9 to 4 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 Clearness Index (M T ) Diffuse Fraction (M d ) January 0 1 January Figure 2. Diurnal Variation of monthly means of: hourly clearness index, and 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, M d, has values, which are most of the time less than 2, 4 and 0 respectively for January, February and March, indicating that the direct (beam) irradiance constitutes a relatively significant proportion of the global solar irradiance reaching the ground during these months. Molecular scattering due to atmospheric constituents prevalent during this period which Adeyefa et al. (1995) have described as the harmattan period with moderate characteristics (background harmattan) 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 performance 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 season in the area), the radiation scattered by these clouds and reflected by the underlying surface would DOI: 1002/joc

5 ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1039 Clearness Index (M T ) 0 February 95 Clearness Index (M T ) March Diffuse Fraction (M d ) 1 February 95 Diffuse Fraction (M d ) 1 March Figure 3. Diurnal Variation of monthly means of: hourly clearness index, and diffuse fraction for the month of February in the dry season. cause a notable rise in the incoming diffuse radiation (Okogbue, 2007). Iziomon and Aro, 19 have reported daytime values of K d with values generally lower than 0 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, M T has very low values for both months during the hours close to sunrise and sunset, with values ranging between 0 and 2 for July and 1 and 8 for August. The cloudiness index (or diffuse fraction), M d on the other hand, has values ranging between 7 and 9 for July and 0 and 9 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, M d has values ranging between 1 and 5 over the period hours for July and August (being generally greater than 5) with the corresponding values of monthly mean hourly clearness index, M T, ranging Figure 4. Diurnal Variation of monthly means of: hourly clearness index, and diffuse fraction for the month of March in the dry season. between 3 and 5 (Figures 5 and 6) during the day. This again signifies the high proportion of diffuse component of the total irradiance arriving on the ground during these months, which are typical of the wet season. Iziomon and Aro (19) who reported similar values for Ilorin (M T values ranging between 5 and 8, and M d values generally greater than 2 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 scattering of beam radiation by altocumulus and altostratus clouds. Under a cloudy sky, the magnitude of the diffuse radiation flux reaching the ground depends essentially 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, 19). The value of solar radiation components received at the ground surface depends, therefore, on the clarity (transparency) or cloudiness (turbidity) of the atmosphere, and hence the clearness index (M T = I I ) and the diffuse ratio (or cloudiness index) (M d = o I I ) can respectively be used to define or quantify the clearness or d the turbidity/cloudiness of the atmosphere (Biga and Rosa, 11; Ideriah and Suleman, 19 and Iziomon and Aro, 1999; Babatunde and Aro, ; Babatunde, 2005). DOI: 1002/joc

6 1040 E. C. OKOGBUE ET AL. Clearness Index (M T ) Diffuse Fraction (M d ) July July Figure 5. Diurnal Variation of monthly means of: hourly clearness index, and diffuse fraction for the month of July in the wet season 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 radiation measured at Ile-Ife, Nigeria averaged over the 11- year period of data ( ) are presented as time series in Figure 7. For the period, the mean of the daily global and diffuse solar radiation are ± W m 2 day 1 and ± W m 2 day 1, 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 values of about 499 W m 2 day 1 and 471, with 80 W m 2 day 1 in March/early April and November respectively and a minima of about 1.24 W m 2 day 1 about July/August which is at the peak of the monsoon. The diffuse solar radiation followed a similar pattern. Figure 8 depicts the annual pattern of the daily clearness 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 parameters, K T and K d, have an almost regular bell-shaped Clearness Index (M T ) Diffuse Fraction (M d ) August August Figure 6. Diurnal Variation of monthly means of: hourly clearness index, and diffuse fraction for the month of August in the wet season. Solar radiation fluxes (W m -2 ) Global Diffuse Day of the Year (DOY) Figure 7. Daily averaged global and diffuse solar radiation at Ile-Ife (7.5 N, 4.57 E), Nigeria, 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, 19). The daily diffuse fraction and the monthly mean daily diffuse fraction both had their peak values of about 9 and 4, respectively, in August during the wet season. The daily and monthly average daily clearness index had their minimum values of 3 and 1 in July and August respectively. DOI: 1002/joc

7 ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION Data Period () Table I. Average monthly diffuse ratios for months with relatively similar atmospheric and sky conditions ( ). Values in parenthesis are values obtained for Ilorin, Nigeria, (Iziomon and Aro, 19) inserted for comparison. K T = H/H0, K d = Hd/H H/Ho Hd/H Day Number ( ) Dust-haze months K d Values Individual (%) Average (%) December, January 60, (58) Partly hazy, partly cloudy and partly clear-sky months February, March, November 61, 62, (53) a Less Cloudy Sky Months April, May, June, October 64, 61, 63, (60) Very Cloudy Sky Months July, August, September 75, 84, (72) KT, Kd 0 Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec Months Figure 8. Annual Pattern of: daily clearness index (K T ), and diffuse fraction (K d ) for the period 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 (19) have also been inserted in Table I for comparison. The monthly mean daily K d 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 (19) reported for Ilorin, Nigeria and for the period 19 and 19, mean K d 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 (19) 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, 19). KT Kd Note: Values in parenthesis are values obtained for Ilorin, Nigeria, (Iziomon and Aro, 19). a Clear sky Frequency and commutative frequency distribution of hourly clearness index M T The frequency of occurrence and cumulative frequency distributions for every 5 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 frequency of occurrence of different sky conditions. From Figures 9, 10, 11 and Table II, the distribution of hourly clearness index, M T, has a marked peak value at the 5 M T interval, and there are more data at the M T values between and (above 88% of the time), which represents cloudy sky with high diffuse radiation. From the cumulative frequency distribution (Figures 9 10 and 11) at M T >, the cumulative frequencies are.4, 99.7 and.1% for the annual, wet and dry seasons, 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 cumulative frequencies at M T = 5 (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 such 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 DOI: 1002/joc

8 1042 E. C. OKOGBUE ET AL. Frequency of Occurrence (%) Cumulative Frequency (%) N = >5 Hourly Clearness Index (M T ) Hourly Clearness Index (M T ) Figure 9. Frequency of occurrence, and cumulative frequency of hourly clearness index (M T ) at Ile-Ife for the period (N represents total number of hours considered). actually also refer to sky conditions under very intense dust spells and not just cloudiness Frequency and commutative frequency distribution of daily clearness index K T Frequency tables for every 5 interval of daily clearness index, K T, have also been similarly established as shown in Table III and the daily frequency of occurrence and cumulative frequency distributions plotted also on annual, wet and dry seasons basis as depicted in Figures 12, 13 and 14 respectively. Clearly, the pattern of daily K T is fairly evenly distributed, with peaks about the 5 K T interval for the annual and wet season distributions, respectively, and 5 for the dry season. There are also more data at the K T values between and (about 89% of the time) as was the case with the hourly clearness index M T, which represents cloudy sky with high diffuse solar radiation. Similarly, the cumulative frequencies at K T = 5 are 1.5, 2.3 and %, respectively, for the annual, wet and dry seasons (Figures 12, 13 and 14). This again implies that the local sky over Ile-Ife is overcast only for about 1.5% 5 5 Frequency of Occurrence (%) Cumulative Frequency (%) N = >5 Hourly Clearness Index (M T ) Hourly Clearness Index (M T ) Figure 10. Frequency of occurrence, and cumulative frequency of hourly clearness index (M T ) at Ile-Ife for the period (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 T =, the cumulative frequencies are 95.0,.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 Monthly K T Cumulative Distribution Curves Following the work of Liu and Jordan (10), the cumulative frequency, f (in percentage) of daily K T 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 (November March/April) and wet season (April/May October). If we define our cloudy days by K T 5 and very clear days by K T 5 as was done by Kuye 5 5 DOI: 1002/joc

9 ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1043 Frequency of occurrence (%) Cumulative Frequency (%) (Dry season) N = >5 Hourly Clearness Index (M T ) (Dry season) Table II. Frequency Distribution of Hourly Clearness Index (M T ) over Ile-Ife for the period M T interval Frequency of occurrence Percentage frequency (%) Annual Wet Dry Annual Wet Dry > Total Table III. Frequency distribution of daily clearness index (K T ) over Ile-Ife for the period Hourly Clearness Index (M T ) 5 5 > 5 Figure 11. Frequency of occurrence, and cumulative frequency of hourly clearness index (M T ) at Ile-Ife for the period (dry season) (N represents the number of hours considered). and Jagtap (1992) and Ideriah and Suleman (19), 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 T 5) 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 characterise the wet season and dust which are characteristics of the dry season). Based on the calculated monthly average clearness index K T, the monthly variations of f and the prevalent climatic conditions, six seasonal patterns can be identified at Ile-Ife. These consist of two distinct dry season K T interval Frequency of occurrence Percentage frequency (%) Annual Wet Dry Annual Wet Dry > Total patterns and four rainy season patterns, namely: November, 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 (19) and Kuye and Jagtap (1992) have identified similar seasonal patterns for Ibadan and Port Harcourt respectively. The monthly K T values for the different months and the average value for each of the identified seasonal patterns DOI: 1002/joc

10 1044 E. C. OKOGBUE ET AL. Frequency of occurrence (%) Cumulative Frequency (%) N = Daily Clearness Index (K T ) >5 5 Daily clearness index (K T ) Figure 12. Frequency of occurrence, and cumulative frequency of daily clearness index (K T ) at Ile-Ife for the period (N represents total number of days considered). are shown in Table V, with the corresponding values calculated for Ibadan for the period (15 10) (Ideriah and Suleman, 19) and Port Harcourt for the period (17 19) (Kuye and Jagtap, 1992) also included for comparison. Kuye and Jagtap (1992) identified five instead of the six seasonal K T patterns, since for Port Harcourt, the average K T 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 (10) termed monthly CDCs are shown in Figure 15. For comparison, the JS curves of K T = 9 and 6 for Ibadan (Ideriah and Suleman, 19) 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 T CDC though distinct, one from the other, are in agreement. The curves are orderly from K T = 1 to 0 and the present pattern, which also agrees with results obtained at other tropical locations like Ibadan (Ideriah and Suleman, 19), Port Harcourt 5 5 Frequency of Occurrence (%) Cumulative Frequency (%) (Wet Season) N = Daily Clearness Index (K T ) (Wet Season) >5 5 Daily Clearness Index (K T ) Figure 13. Frequency of occurrence, and cumulative frequency of daily clearness index (K T ) at Ile-Ife for the period (wet season) (N represents total number of days considered). (Kuye and Jagtap, 1992) and Ilorin (Udoh, ) and are different from those obtained for twenty-seven cities in the USA and Canada by Liu and Jordan (10). The results obtained by Liu and Jordan (10) gave much higher values of K T (usually up to or more) for each of the monthly average K T, which indicates the abundance of very clear skies in 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 (14); Saunier et al. (17); Ideriah and Suleman (19); Kuye and Jagtap (1992) and Udoh () 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 (10). Consequently, the use of such solar devices that are designed based on the CDCs of Liu and Jordan in 5 5 DOI: 1002/joc

11 ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1045 Frequency of Occurrence (%) Cumulative Frequency (%) (Dry Season) N = (Dry Season) 5 5 Daily Clearness Index (K T ) >5 5 Daily Clearness Index (K T ) 5 5 >5 Figure 14. Frequency of occurrence, and cumulative frequency of daily clearness index (K T ) at Ile-Ife for the period (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 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, M d, has values, which are, most of the time, less than 2, 4 and 0, respectively, for January, February and March indicating that the direct (beam) irradiance constitute 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, M d, has values ranging between 1 and 5 over the period LST (being generally greater than 5) with the corresponding values of M T ranging between 3 and 5 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 T and monthly average values of the clearness index, K T over Ile-Ife for the period (f is computed using Equation (1)). Values of f for K T K T (fixed value) Monthly Average K T Jan. (257) Feb. (213) March (266) April (235) May (257) June (269) July (2) Aug. (279) Sept. (270) Oct. (234) Nov. (262) Dec. (237) DOI: 1002/joc

12 1046 E. C. OKOGBUE ET AL. Table V. Average monthly/seasonal clearness index (K T ) values for Ile-Ife for the period , compared with similar results for Port Harcourt and Ibadan inserted for comparison. Port Harcourt a Ibadan b Ile-Ife c Individual Average Individual Avereage Individual Average Dry Season Nov, Dec, Jan 2, 5, 3 4 3, 1, 9 1 3, 0, 6 0 Feb, Mar, Apr 3, 1, 2 2 3, 3, 2 3 1, 9, Wet Season Aug Jul, Sep 5, 7 6 9, 0 9 3, 8 6 (c) Jun, Oct 9, 9 9 7, 7 7 4, 5 5 (d) May a Kuye and Jagtap (1992). b Ideriah and Suleman (19). c This study. Cumulative Frequency, f (%) Clearness Index (K T ) NDJ (0) FMA (9) A (1) JS (6) JO (5) M (8) JS (9;I deriah & Suleman) JS (6;Kuye & Jagtap) crop simulation and soil-vegetation-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 discussions 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. Figure 15. Monthly K T cumulative distribution curves for Ile-Ife over various periods with some of the results obtained by Ideriah and Suleman (19) 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 T 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 scattering by clouds (especially altocumulus and altostratus clouds) is more intense resulting in more diffuse component of the total solar radiation reaching the surface during the wet season than the dry season. The implication 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 implications for the much-talked-about climate variability and its impact on food production, numerical weather modelling and dependable weather forecast as global circulation, Appendix Symbols, definitions and notations used K d Daily diffuse fraction; K T Daily clearness index; K T Monthly average clearness index; I 0 Hourly extraterrestrial radiation; H 0 Daily extraterrestrial radiation; M T Hourly clearness index; M d Hourly diffuse fraction; M T Monthly average hourly clearness index; M d Monthly average hourly diffuse fraction; I SC Monthly average hourly diffuse fraction; f Percentage cumulative frequency of the average daily clearness index; References Adebayo SI. 19. Pronounced haze spell over Nigeria, 2 nd 11 th March 17. In Proceedings of the Pre-WAMEX Symposium on the West African Monsoon, Adefolalu DO (ed.). Leo Express Printers: Lagos; Adedokun JA. 18. West African Precipitation and dominant atmospheric mechanisms. Archives for Meteorology Geophysics and Bioclimatology A, 27: DOI: 1002/joc

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