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

$Page 1: Hourly and daily clearness index and diffuse fraction at a tropical station, Ile-Ife, Nigeria$
INTERNATIONAL JOURNAL OF CLIMATOLOGYInt. 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 atropical station, Ile-Ife, Nigeria

E. C. Okogbue,a* J. A. Adedokunb and B. Holmgrenc

a Department of Meteorology, Federal University of Technology, Akure, Nigeriab Departments of Physics, Obafemi Awolowo University, Ile-Ife, Nigeria

c Meteorological Institute, Uppsala University, S-751 20 Uppsala, Sweden

ABSTRACT: Dataset consisting of hourly global and diffuse solar radiation measured over the period February 1992 andDecember 2002 have been utilized to investigate the diurnal and seasonal variations of hourly and daily clearness indextogether with the diffuse fraction at a tropical station Ile-Ife (7.5 °N, 4.57 °E), Nigeria. Statistical analysis (the frequencyand cumulative frequency distribution of the hourly and daily clearness index) and subsequent characterization of the skyconditions over the station based on these were also done, and their implications for solar energy utilization in the areadiscussed.

Daytime (11 : 00–15 : 00 LST) monthly mean hourly diffuse fraction, Md (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 and0.60 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 thecorresponding values of the monthly mean hourly clearness index, MT , 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 almostdevoid of clear skies and overcast skies (clear skies and overcast skies occurred for only about 3.5% and 4.8% of the timerespectively). The sky conditions were rather predominantly cloudy (cloudy skies occurred for about 88% of the time) allthe 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 underdifferent atmospheric conditions, which obviously affectthe amount and quality of radiation obtained at the groundduring the course of the day. Atmospheric conditionssuch as, turbidity and transparency, air mass, atmosphericwater vapour content and layers and distribution of cloudcover have been suggested to exert depleting influenceon solar radiation at the Earth’s surface, mainly byabsorption, scattering and reflection of the incoming solarradiation.

Solar irradiance data is essential for studies on thedescription of atmospheric phenomena and large-scaleweather analysis and prediction because the amount ofsolar global radiation received on the Earth’s surface isthe driving force for most meteorological processes. Forexample, solar radiation data is required in improving theparameterization of clouds needed in general circulation

* Correspondence to: E. C. Okogbue, Department of Meteorology,Federal University of Technology, Akure, Nigeria.E-mail: [email protected]

models (GCMs) (Stokes and Schwartz, 1994) and asa valuable resource for validating the GCMs (Hansen,1999; and Iziomon and Mayer, 2001). Information onthe geographical distribution and the changes with timeof the solar radiant energy on the Earth’s surface is arequirement not only in weather and climate studies butalso in agricultural practice and food production, hydrol-ogy, ecology and energy development programmes andutilization, among others. Lack of adequate observationson solar radiation has been a persistent problem in stud-ies of land-surface processes and a major limitation in thevalidation of crop growth simulation models (Thorntonand Running, 1999; Liu and Scott, 2001) and photosyn-thesis models since the decomposition of solar irradianceinto its various components is now a key feature of sev-eral canopy-scale models of photosynthesis (De Pury andFarquhar, 1997).

The design, development and application of solarenergy collection and conversion systems required forthe exploitation of the vast energy of the Sun, and theperformance evaluation of such energy conversion sys-tems within a particular region require information on the

Copyright 2009 Royal Meteorological Society

1036 E. C. OKOGBUE ET AL.

variation characteristics and distribution of the amount ofsolar energy received at the location (Duffie and Beck-man, 1991; Coppolino, 1994; and Ali et al., 2003). Theseparation of solar irradiance into the various componentsis also necessary for a wide range of these solar engineer-ing tasks (Iqbal, 1983). For example, the knowledge ofthe distribution of the diffuse fraction of solar radiation(the ratio of the diffuse solar radiation to the global solarradiation) is particularly required in assessing the climato-logical potential of a locality for solar energy utilizationand in estimating the expected values of the output ofconcentrating solar collectors (Iziomon and Aro (1998).

The clearness index (which is the ratio of the globalsolar radiation measured at the surface to the total solarradiation at the top of the atmosphere) is a veritable toolin the characterization of sky conditions (or classifica-tion of sky types) over a particular locality (Ideriah andSuleman, 1989; Kuye and Jagtap, 1992; Okogbue andAdedokun, 2002b). Synoptic cloud observations, thoughvery 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 ofthe needed solar radiation components for characterizingthe sky conditions.

In spite of its significance, solar radiation, especiallythe 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 dearthin solar radiation data has been reported in a numberof countries like USA (Hook and McClendon, 1992),Canada (De Jong and Stewart, 1993) and Australia (Liuand Scott, 2001), it is however, in those parts of theworld naturally endowed with abundant availability ofsolar 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 dueto 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 inNigeria, notable among which are: Bamiro (1983) andIderiah 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 andAdedokun (2002a,b, 2003); Okogbue et al. (2002) andJegede (1997a,b,c, 2003).

The present contribution investigates, with respect tothe prevailing atmospheric conditions over the station,the diurnal and seasonal patterns of both the hourly anddaily clearness index and the cloudiness index (or dif-fuse fraction) computed based on the measured hourlyfluxes of global and diffuse solar radiation at Ile-Ife,Nigeria. The characterization of sky conditions overthe station using the clearness index is also investi-gated.

2. Data and instrumentation

The solar radiation data reported in this work comprisedof hourly averaged values of both global and diffuseradiation flux densities in units of Watt-hour per metersquared (W h m−2) measured at Ile-Ife, Nigeria (7.5 °N,4.57 °E) during the period March 1992 to December2002. Since the collection of data relating to the aboveperiod was continuous (except for some interruptionswhen any of the instruments used was stopped for repairsor recalibrations) it can be expected that inter-seasonalvariations will be manifested in the datasets.

The solar radiation measurement station which islocated on the rooftop of the 20-meter-high 3-storeyedDepartment of Physics building located within the cam-pus of Obafemi Awolowo University, Ile-Ife, Nigeriacomprised of two Kipp and Zonen pyranometers modelsCM11 for the global radiation and CM11/121 (incorpo-rating a shadow ring) for diffuse radiation and a LICORLI-210SA photometric sensor for the photometric illu-minance. The altitude of the Physics building is about275 m above sea level. The measuring site is, there-fore, at about 300 m above sea level. The instrumentswere installed and levelled on a horizontal surface at aheight of 1.5 m above an improvised flat concrete baseon the rooftop (Figure 1). The leads for the pyranometerswere directly connected to a Campbell Scientific micrologger (model 21X) and data sampled every 1 min andthen subsequently averaged to produce the hourly val-ues. Both devices were initially factory calibrated beforeinstallation with measurement accuracy of about 2%.Subsequently, further recalibrations have been carriedout locally by comparing the pyranometers with a morerecently calibrated CM11 pyranometer (Okogbue, 2007).

Data quality assurance checks were carried out withreference to the diffuse fraction Kd (which is the ratio ofthe diffuse solar radiation incident on a horizontal surfaceto the global solar radiation incident on the same surface)

Figure 1. The Solar Radiation Station on the rooftop of the PhysicsDepartment 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

ON CLEARNESS INDEX AND DIFFUSE FRACTION OF SOLAR RADIATION 1037

and the clearness index KT (which is the ratio of theglobal solar radiation measured at the surface to the totalsolar radiation at the top of the atmosphere) as suggestedby Reindl et al. (1990) in order to ensure good diffusesolar radiation data. In that respect, the following datawere excluded:

1. A day with even one missing hourly data (global ordiffuse).

2. Global solar radiation exceeding the extraterrestrialradiation.

3. Diffuse fraction Kd > 14. Kd > 0.80, when KT > 0.60 (clear sky).5. Kd < 0.90 when KT < 0.20 (overcast sky).

Case (iv) places a limit on the diffuse fraction underclear-sky conditions, whereas case (v) places a limit onthe diffuse fraction under cloudy overcast sky conditionsas suggested in Reindl et al. (1990).

3. Meteorological features of the site

The area experiences tropical climate such that two majorseasons can be clearly identified which greatly influencethe 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 demarcationbetween the southwesterly and the northeasterly windsover 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 lateOctober during the Northern Hemisphere summer. Dur-ing this period, the presence of thick clouds (e.g. cumu-lus/cumulonimbus and nimbostratus clouds) and otherhigh water content clouds, which could average up to6–7 oktas at 0900 h, local time, in the month of Augustat the peak of the wet season (Griffiths, 1974) is a reg-ular atmospheric phenomenon. The wet season is alsogenerally characterized by high moisture content of theair. Consequently, the most important attenuators of solarradiation during this period are clouds and water vapour(Kyle, 1991; Jegede, 1997a,b; Okogbue and Adedokun,2002b).

During the Northern Hemisphere winter, the ITD ispositioned north of the equator attaining a position about4–6°N in January. During this time, the northeasterlywinds prevail to an elevation of about 3000 m and bringcold, dry and stable continental air masses from thedesert region over which they originate. These windsare locally called the ‘harmattan’ (Adedokun, 1978;Balogun, 1981). Having had a long trajectory overthe desert, the harmattan winds advect tonnes of finedust to the region. The Harmattan dusts bring aboutspells 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. Adeyefaet al. (1995) classified the harmattan period into periodswith ‘moderate’ characteristics (background harmattan)and periods with intensive dust spells that could last3–4 days or more (Kalu, 1978 and Adebayo, 1989).The high aerosol loading of the atmosphere during thisseason attenuates the solar radiation passing through theatmosphere mainly by scattering with effects on theheat budget of the Earth–atmosphere systems, which canbe very significant especially in the tropics where theradiation balance is positive (El-Fandy, 1953; Kalu, 1978,Jegede, 1997a,b).

4. Methodology

The flux of energy received from the Sun at the topof the atmosphere, per unit of area, and per interval ofone hour (I0) and one day (H0) (required for calculationof the hourly clearness index (MT ) and daily clearnessindex (KT ) are respectively estimated analytically by thefamiliar expressions according to Iqbal (1983) with thesolar constant ISC = 1367 Wm−2.

The diurnal and annual patterns of MT , KT , the hourlydiffuse fraction, (Md), and the daily diffuse fraction,(Kd), are presented and discussed with reference to theprevailing atmospheric conditions over the area.

Furthermore, statistical analysis (the frequency andcumulative frequency distribution of the hourly and dailyclearness index) and subsequent characterization of thesky conditions over the station based on these have beendone following the pioneering work of Liu and Jordan(1960) and those of Li et al., 2004. For instance, Liuand Jordan (1960) had shown that the information on thedaily clearness index, (KT), could also be presented ascumulative frequency, f (KT), in percentage as follows:

f = number of days with KT ≤ KT (f ixed value)

number of days in the month

× 100% (1)

Using data from a network of 27 stations, each withapproximately 5 years of data, Liu and Jordan (1960)proposed, based on Equation (1), a set of generalizedKT cumulative distribution curves (CDC), which havebeen used in many studies since then. The claim of theuniversal applicability of the generalized CDC by Liu andJordan (1960) has been queried by typical results obtainedby Hawas and Muneer (1984); Saunier et al. (1987);Ideriah and Suleman (1989); Kuye and Jagtap (1992) forsome 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 onlyon global solar irradiance (i.e. one measured parameter)(Muneer, 1995, 1998; Li et al., 2004). Low clearnessindex means low global solar radiation, which usuallyrepresents a cloudy sky with a high portion of diffuse



component. Large clearness index means high globalsolar radiation, which is dominated by the direct compo-nent. There are however, no clear-cut KT values to definethe sky conditions. Different researchers have there-fore adopted different values. For instance, Reindl et al.(1990) have proposed KT > 0.6 and KT < 0.2 for clearsky and cloudy sky, respectively. Li and Lam (2001) andLi et al. (2004) used KT values of 0–0.15, >0.15–0.7and >0.7 to define overcast, partly cloudy and clear skiesrespectively in Hong Kong and Kuye and Jagtap (1992)used KT > 0.65 and 0.12 ≤ KT ≤ 0.35, respectively, forvery clear skies and cloudy skies, to classify the sky con-ditions at Port Harcourt, Nigeria. For this work, KT (orMT) values of 0 ≤ KT (MT ) ≤ 0.15, 0.15 ≤ KT (MT ) ≤0.60, 0.6 ≤ KT (MT ) ≤ ∞ were used to define overcast,partly cloudy and clear-sky conditions based on our fieldexperiences.

5. Results and discussions

5.1. Diurnal variations of the clearness index anddiffuse fraction

In Figures 2, 3 and 4 are presented plots of the diurnalvariation of the monthly means of hourly clearnessindex and diffuse fraction (or cloudiness index) forthe months of January, February and March which arerepresentative of the dry season. It is obvious fromFigures 2, 3 and 4 that the clearness index has verylow values during the hours close to sunrise and sunset,with values ranging between 0.09 and 0.33. The diffusefraction on the other hand, has rather very high valuesduring such hours (ranging between 0.77 and 0.99) withthe obvious implication that the solar radiation receivedat the surface during the hours close to sunrise andsunset consist mainly of the diffuse component. This isconsistent with the dependence of diffuse solar radiationreaching the surface on solar elevation and atmosphericturbidity, air mass, atmospheric water vapour contentand layers and distribution of cloud cover (Iziomon andAro, 1999). During the hours close to sunset or sunrise,the angle between the incoming solar beam and thereceiving surface is rather large and hence the solarbeam must pass through a large amount of atmosphericmass with varying atmospheric constituents and hence issignificantly scattered and reflected (Okogbue, 2007).

During the period about local noon, when the sunis overhead or near-overhead, as the case may be, thevalues of clearness index rise to their maximum (rangingfrom 0.50 to 0.57, 0.57 to 0.62, and 0.48 to 0.60 for themonths of January, February and March, respectively)(Figures 2, 3 and 4). The diffuse fractions, on the otherhand, fall to their minimum values (ranging from 0.45to 0.54, 0.44 to 0.55, and 0.49 to 0.64 for the monthsof January, February and March, respectively). Again,this is because the solar beam passes through a singleor relatively thin atmospheric thickness, and therefore,encounters relatively less atmospheric constituents, andhence, experiences less scattering and reflection, resulting

January

0

0.1

0.2

0.3

0.4

0.5

0.6

7 8 9 10 11 12 13 14 15 16 17 18

Local Time (hours)

Cle

arn

ess

Ind

ex (

MT)

93

94

95

96

97

98

2000

2002

(a)

January

0.4

0.5

0.6

0.7

0.8

0.9

1

7 8 9 10 11 12 13 14 15 16 17 18

Local Time (hours)

Diff

use

Fra

ctio

n (M

d)

93

94

95

96

97

98

2000

2002

(b)

Figure 2. Diurnal Variation of monthly means of: (a) hourly clearnessindex, and (b) diffuse fraction for the month of January in the dry

season.

in less of the diffuse component of the solar radiationbeing incident on the surface.

Furthermore, during the daytime from about 1100 to1500 LST, the monthly mean hourly diffuse fraction,Md , has values, which are most of the time less than0.52, 0.54 and 0.60 respectively for January, Febru-ary and March, indicating that the direct (beam) irra-diance constitutes a relatively significant proportion ofthe global solar irradiance reaching the ground dur-ing these months. Molecular scattering due to atmo-spheric constituents prevalent during this period whichAdeyefa et al. (1995) have described as the harmattanperiod with ‘moderate’ characteristics (background har-mattan) and, to a lesser extent, surface albedo, are mainlyresponsible for diffuse irradiance reaching the ground atthese times, especially for the months of January andFebruary.

The implication of this for solar energy utilizationis that solar concentrators that make use of parabolicmirrors are expected to have relatively high perfor-mance during these months at Ile-Ife. However, inthe event of appreciable cloudiness or albedo, as isthe case sometimes in the month of March (whichis a transition month from the dry to the wet sea-son in the area), the radiation scattered by theseclouds and reflected by the underlying surface would



February

0

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)

Cle

arn

ess

Ind

ex (

MT)

93

94

95

96

98

2000

(a)

February

0.4

0.5

0.6

0.7

0.8

0.9

1

7 8 9 10 11 12 13 14 15 16 17 18

Local Time (hours)

Diff

use

Fra

ctio

n (M

d)

93

94

95

96

97

98

2000

(b)

Figure 3. Diurnal Variation of monthly means of: (a) hourly clearnessindex, 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 havereported daytime values of Kd with values generallylower than 0.50 for the months of February, Novemberand March for Ilorin, a tropical station in North CentralNigeria.

Figures 5 and 6 depict the diurnal variation of themonthly means of hourly clearness index and diffusefraction (or cloudiness index) for the months of Julyand August which are typical of the wet season. It isalso clear from Figures 5 and 6 that the clearness index,MT has very low values for both months during thehours close to sunrise and sunset, with values rangingbetween 0.10 and 0.32 for July and 0.11 and 0.28 forAugust. The cloudiness index (or diffuse fraction), Md

on the other hand, has values ranging between 0.87 and0.99 for July and 0.80 and 0.99 for August. This isthe same trend that was observed for the dry months(Figures 2–4) with the obvious implication that the solarradiation received at the surface during the hours closeto sunrise and sunset in both seasons consist mainly ofthe diffuse component.

The monthly mean hourly diffuse fraction, Md hasvalues ranging between 0.61 and 0.85 over the period1100–1500 hours for July and August (being gener-ally greater than 0.65) with the corresponding valuesof monthly mean hourly clearness index, MT , 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)

Cle

arne

ss In

dex

(MT)

92

93

95

96

97

98

2001

(a)

March

0.4

0.5

0.6

0.7

0.8

0.9

1

7 8 9 10 11 12 13 14 15 16 17 18

Local Time (hours)

Diff

use

Fra

ctio

n (M

d)

93

94

96

97

98

2000

(b)

Figure 4. Diurnal Variation of monthly means of: (a) hourly clearnessindex, and (b) diffuse fraction for the month of March in the dry season.

between 0.23 and 0.45 (Figures 5 and 6) during theday. This again signifies the high proportion of dif-fuse component of the total irradiance arriving on theground during these months, which are typical of thewet season. Iziomon and Aro (1998) who reported simi-lar values for Ilorin (MT values ranging between 0.35and 0.48, and Md values generally greater than 0.62during the day for the months of July and August)attributed the high proportion of the diffuse componentduring the wet season to the intense forward scatter-ing of beam radiation by altocumulus and altostratusclouds. Under a cloudy sky, the magnitude of the dif-fuse radiation flux reaching the ground depends essen-tially on the amount, type and distribution of clouds.In the presence of cirrus, altostratus and altocumulusclouds, diffuse irradiance has been reported to increasewith the increase in cloudiness (Kondratyev, 1969). Thevalue of solar radiation components received at theground surface depends, therefore, on the clarity (trans-parency) or cloudiness (turbidity) of the atmosphere,and hence the clearness index (MT = I

Io) and the dif-

fuse ratio (or cloudiness index) (Md = IId

) can respec-tively be used to define or quantify the clearness orthe turbidity/cloudiness of the atmosphere (Biga andRosa, 1981; Ideriah and Suleman, 1989 and Iziomonand Aro, 1999; Babatunde and Aro, 2000; Babatunde,2005).



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)

Cle

arne

ss In

dex

(MT)

92

93

94

96

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99

2000

(a)

July

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

7 8 9 10 11 12 13 14 15 16 17 18

Local Time (hours)

Diff

use

Fra

ctio

n (M

d)

92

93

94

96

97

98

99

2000

(b)

Figure 5. Diurnal Variation of monthly means of: (a) hourly clearnessindex, and (b) diffuse fraction for the month of July in the wet season.

5.2. Annual pattern of daily solar radiation fluxes andthe solar radiation ratios (clearness index and diffusefraction)

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 timeseries in Figure 7. For the period, the mean of thedaily global and diffuse solar radiation are 367.51 ±62.12 W m−2 day−1 and 232.66 ± 27.68 W m−2 day−1,respectively. From Figure 7, it can be observed that theannual variation of the global solar radiation for theperiod showed a bimodal distribution with peak val-ues of about 490.89 W m−2 day−1 and 471, with 80 Wm−2 day−1 in March/early April and November respec-tively and a minima of about 196.24 W m−2 day−1

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 correspondingmonthly averages respectively. It is clear from Figure 8that both the daily and monthly average daily clearnessindex and diffuse fractions follow the same annual patternwith the curve of the diffuse fraction being an inversion ofthe curve of the clearness index. An interesting feature isthat within the five months of June to October the param-eters, KT and Kd , 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)

Cle

arne

ss In

dex

(MT)

92

93

94

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99

2000

(a)

August

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

7 8 9 10 11 12 13 14 15 16 17 18

Local Time (hours)

Diff

use

Fra

ctio

n (M

d)

92

93

94

96

97

98

99

2000

(b)

Figure 6. Diurnal Variation of monthly means of: (a) hourly clearnessindex, 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)

So

lar

rad

iati

on

flu

xes

(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 occurringabout the month of July/August for both the daily andmonthly average cases as earlier observed by (Ideriahand Suleman, 1989). The daily diffuse fraction and themonthly mean daily diffuse fraction both had their peakvalues of about 0.99 and 0.84, respectively, in Augustduring the wet season. The daily and monthly averagedaily clearness index had their minimum values of 0.23and 0.31 in July and August respectively.



Data Period (1992 - 2002)

0

0.1

0.2

0.3

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0.9

1

1 31 61 91 121 151 181 211 241 271 301 331 361

Day Number

KT =

H/H

0, K

d =

Hd/

H

H/Ho Hd/H

(a)

(1992- 2002)

0

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 (KT), and(b) diffuse fraction (Kd) for the period 1992–2002 at Ile-Ife.

The mean monthly diffuse ratios for the set of monthswith relatively similar atmospheric and sky conditions atthis location have also been estimated and are presentedin Table I. Values obtained for Ilorin, Nigeria by Iziomonand Aro (1998) have also been inserted in Table I forcomparison. The monthly mean daily Kd values varyfrom 58% for relatively dust-haze months to 59% forthe set of partly cloudy, partly hazy and partly clear-skymonths to 62 and 78% for the set of less cloudy andcloudy and wet months, respectively (Table I). Iziomonand Aro (1998) reported for Ilorin, Nigeria and for theperiod 1993 and 1994, mean Kd values varying from 53%for a set of relatively clear months, to 58% for a set ofdust-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 cloudymonths 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 andNovember atmospheric conditions are partly hazy, partlycloudy and partly clear, these months being transitionmonths, whereas for Ilorin the conditions are relativelyclear (Iziomon and Aro, 1998).

Table I. Average monthly diffuse ratios for months withrelatively 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 Kd Values

Individual (%) Average (%)

December, January 60, 56 58(58)

Partly hazy, partlycloudy and partlyclear-sky monthsFebruary, March,November

61, 62, 53 59

(53)a

Less Cloudy Sky MonthsApril, May, June,October

64, 61, 63, 62 62

(60)Very Cloudy Sky MonthsJuly, August, September 75, 84, 75 78

(72)

Note: Values in parenthesis are values obtained for Ilorin, Nigeria,(Iziomon and Aro, 1998).a Clear sky.

5.3. Frequency and commutative frequencydistribution of hourly clearness index MT

The frequency of occurrence and cumulative frequencydistributions for every 0.05 interval of hourly and dailyclearness index have been plotted as column and linegraphs on annual and seasonal basis as shown inFigures 9, 10 and 11. The frequency table (Table II) isalso presented for ease of reference, and the cumulativefrequency distribution is shown to get a feel for the fre-quency of occurrence of different sky conditions. FromFigures 9(a), 10(a), 11(a) and Table II, the distribution ofhourly clearness index, MT, has a marked peak value atthe 0.5–0.55 MT interval, and there are more data at theMT 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 MT > 0.6, the cumulative frequenciesare 97.4, 99.7 and 94.1% for the annual, wet and dry sea-sons, respectively. These indicate that the local sky overIle-Ife is clear for only about 3% of the time, and thisoccurs mostly during the dry season. Also, the cumula-tive frequencies at MT = 0.15 (the condition for overcastsky) are 4.8, 5.5 and 4.8% for the annual, wet and dryseasons, respectively.

Apart from clouds, atmospheric turbidity due to thehigh loading of the atmosphere by aerosols, especiallythe harmattan dust and other pollutants resulting fromanthropogenic activities such as road construction andwood processing over the area could result in a largescattering of global solar irradiance resulting in a veryhigh proportion of it in the diffuse component, whichan overcast sky represents. So, an overcast sky could



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 (MT)

Fre

quen

cy o

f O

ccur

renc

e (%

)

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.

10.

15 0.2

0.25 0.

30.

35 0.4

0.45 0.

50.

55 0.6

0.65 0.

70.

75


Cum

ulat

ive

Fre

quen

cy (

%)

(b)

Figure 9. (a) Frequency of occurrence, and (b) cumulative frequencyof hourly clearness index (MT) at Ile-Ife for the period 1992–2002 (N

represents total number of hours considered).

actually also refer to sky conditions under very intensedust spells and not just cloudiness.

5.4. Frequency and commutative frequencydistribution of daily clearness index KT

Frequency tables for every 0.05 interval of daily clearnessindex, KT, have also been similarly established as shownin Table III and the daily frequency of occurrence andcumulative frequency distributions plotted also on annual,wet and dry seasons basis as depicted in Figures 12, 13and 14 respectively. Clearly, the pattern of daily KT isfairly evenly distributed, with peaks about the 0.45–0.5KT interval for the annual and wet season distributions,respectively, and 0.5–0.55 for the dry season. Thereare also more data at the KT values between 0.2 and0.6 (about 89% of the time) as was the case withthe hourly clearness index MT, which represents cloudysky with high diffuse solar radiation. Similarly, thecumulative frequencies at KT = 0.15 are 1.5, 2.3 and0.3%, respectively, for the annual, wet and dry seasons(Figures 12(a), 13(a) and 14(a)). This again implies thatthe 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


Fre

quen

cy o

f O

ccur

renc

e (%

) 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.

10.

15 0.2

0.25 0.

30.

35 0.4

0.45 0.

50.

55 0.6

0.65 0.

70.

75


Cum

ulat

ive

Fre

quen

cy (

%)

(b)

Figure 10. (a) Frequency of occurrence, and (b) cumulative frequencyof hourly clearness index (MT) 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-yearperiod of data). For KT = 0.6, the cumulative frequenciesare 95.0, 94.2 and 95.5%, respectively, for the annual,wet and dry seasons. Again, this implies that the localsky over Ile-Ife is clear only for about 5% (whichrepresents only 154 days out of the 3076 days underconsideration). It can therefore be inferred from bothhourly and daily clearness index classification of the skyconditions over Ile-Ife that clear and overcast skies arevery rare over the station, and that the local sky overIle-Ife is predominantly cloudy all the year round.

5.5. Monthly KT Cumulative Distribution Curves

Following the work of Liu and Jordan (1960), the cumu-lative frequency, f (in percentage) of daily KT within themonth, has also been computed using Equation (1) asshown in Table IV. The climate in Nigeria can be broadlydivided into two seasons, namely, dry season (Novem-ber–March/April) and wet season (April/May–October).

If we define our ‘cloudy’ days by KT ≤ 0.35 and‘very clear’ days by KT ≥ 0.65 as was done by Kuye



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


Fre

qu

ency

of

occ

urr

ence

(%

) 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.

10.

15 0.2

0.25 0.

30.

35 0.4

0.45 0.

50.

55 0.6

0.65 0.

70.

75

> 0.

75


Cu

mu

lati

ve F

req

uen

cy (

%)

(b)

Figure 11. (a) Frequency of occurrence, and (b) cumulative frequencyof hourly clearness index (MT) 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), thenit is also obvious from Table IV that the frequency ofcloudy days is quite high for Ile-Ife ranging from 12.5%in May to 64.5% in August with August as the mostcloudy of the months. Kuye and Jagtap (1992) using13 years data obtained similar results for Port Harcourtwith the frequency of cloudy days ranging from 31.8% inMay to 58.1% in August. This shows that Port Harcourtexperiences more cloudy days during the early part of thewet season in May than Ile-Ife, with Ile-Ife being morecloudy than Port Harcourt at the peak of the wet seasonin August.

We can also deduce from Table IV that ‘very clear’days (KT ≥ 0.65) are rare in Ile-Ife, ranging only from3.1% in May (the atmosphere having just been cleansedof the turbid harmattan dust by the rains) to 4.2% inNovember (being a transition month from the wet to thedry season is relatively devoid of clouds which charac-terise the wet season and dust which are characteristicsof the dry season).

Based on the calculated monthly average clearnessindex KT , the monthly variations of f and the prevalentclimatic conditions, six seasonal patterns can be identi-fied at Ile-Ife. These consist of two distinct dry season

Table II. Frequency Distribution of Hourly Clearness Index(MT) over Ile-Ife for the period 1992–2002.

MT interval Frequency ofoccurrence

Percentagefrequency (%)

Annual Wet Dry Annual Wet Dry

0.0–0.05 14 2 12 1.2 0.3 2.40.05–0.1 18 9 9 1.5 1.3 1.80.1–0.15 25 19 6 2.1 2.7 1.20.15–0.2 51 35 16 4.3 5.0 3.30.2–0.25 83 52 31 7.0 7.5 6.30.25–0.3 89 63 26 7.5 9.1 5.30.3–0.35 131 101 30 11.0 14.5 6.10.35–0.4 165 123 42 13.9 17.7 8.50.4–0.45 157 100 57 13.2 14.4 11.60.45–0.5 149 83 66 12.5 11.9 13.40.5–0.55 178 85 93 15.0 12.2 18.90.55–0.6 97 22 75 8.2 3.2 15.20.6–0.65 24 2 22 2.0 0.3 4.50.65–0.7 5 0 5 0.4 0.0 1.00.7–0.75 1 0 1 0.1 0.0 0.2>0.75 1 0 1 0.1 0.0 0.2Total 1188 696 492 100.0 100 100.0

Table III. Frequency distribution of daily clearness index (KT)over Ile-Ife for the period 1992–2002.

KT interval Frequency ofoccurrence

Percentagefrequency (%)

Annual Wet Dry Annual Wet Dry

0.0–0.05 0 0 0 0.0 0.0 0.00.05–0.1 7 1 6 0.2 0.1 0.30.1–0.15 40 3 37 1.3 0.2 2.00.15–0.2 68 1 67 2.2 0.1 3.60.2–0.25 118 5 113 3.8 0.4 6.10.25–0.3 199 13 186 6.5 1.1 10.10.3–0.35 245 32 213 8.0 2.6 11.60.35–0.4 294 76 218 9.6 6.2 11.80.4–0.45 435 171 264 14.1 13.8 14.30.45–0.5 553 296 257 18.0 24.0 14.00.5–0.55 546 322 224 17.8 26.1 12.20.55–0.6 417 243 174 13.6 19.7 9.50.6–0.65 128 61 67 4.2 4.9 3.60.65–0.7 26 11 15 0.8 0.9 0.80.7–0.75 0 0 0 0.0 0.0 0.0>0.75 0 0 0 0.0 0.0 0.0Total 3076 1235 1841 100.0 100.0 100.0

patterns and four rainy season patterns, namely: Novem-ber, December, January (NDJ) and February, March,April (FMA) for the dry season; and August (A); Julyand 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 KT values for the different months and theaverage value for each of the identified seasonal patterns



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 (KT)

Fre

qu

ency

of o

ccu

rren

ce (%

)

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.

20.

25 0.3

0.35 0.

40.

45 0.5

0.55 0.

60.

65 0.7

0.75

Daily clearness index (KT)

Cum

ulat

ive

Fre

quen

cy (

%)

0.05

(b)

Figure 12. (a) Frequency of occurrence, and (b) cumulative frequencyof daily clearness index (KT) 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) (Ideriahand Suleman, 1989) and Port Harcourt for the period(1977–1989) (Kuye and Jagtap, 1992) also included forcomparison.

Kuye and Jagtap (1992) identified five instead ofthe six seasonal KT patterns, since for Port Harcourt,the average KT value for M is equal to that of thesecond period in the dry season FMA. The plots of thecumulative frequency, f, corresponding to each of the sixseasonal, monthly clearness index patterns (NDJ, FMA,A, JS, JO and M), which Liu and Jordan (1960) termedmonthly CDCs are shown in Figure 15. For comparison,the JS curves of KT = 0.39 and 0.36 for Ibadan (Ideriahand 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 atPort Harcourt and Ibadan vary for the different monthsfrom that at Ile-Ife as shown in Table V, Figure 15 showsthat the shapes of the KT CDC though distinct, one fromthe other, are in agreement. The curves are orderly fromKT = 0.31 to 0.50 and the present pattern, which alsoagrees with results obtained at other tropical locationslike 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

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0.05

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0.45

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0.65

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0.7-

0.75>0

.75


Fre

qu

ency

of O

ccu

rren

ce (%

)

N =1841

(a)

1992 - 2002 (Wet Season)

0

10

20

30

40

50

60

70

80

90

100

0.05 0.

10.

15 0.2

0.25 0.

30.

35 0.4

0.45 0.

50.

55 0.6

0.65 0.

70.

75


Cu

mu

lati

ve F

req

uen

cy (%

)

(b)

Figure 13. (a) Frequency of occurrence, and (b) cumulative frequencyof daily clearness index (KT) 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 aredifferent from those obtained for twenty-seven cities inthe USA and Canada by Liu and Jordan (1960).

The results obtained by Liu and Jordan (1960) gavemuch higher values of KT (usually up to 0.8 or more)for each of the monthly average KT , which indicates theabundance of very clear skies in those cities they reportedon, whereas, it has been clearly shown in this study thatclear skies are rare in Ile-Ife which is a tropical location.The claim of the universal applicability of the Liu andJordan’s CDC curves has been questioned by earliertypical results obtained by Hawas and Muneer (1984);Saunier et al. (1987); Ideriah and Suleman (1989); Kuyeand Jagtap (1992) and Udoh (2000) for some tropicallocations in India, Bangkok in Thailand, Ibadan, PortHarcourt, and Ilorin in Nigeria, respectively. This studytherefore corroborates their findings.

One major implication of this is that solar energyconcentrating devices which make use of incident beamradiation whose availability at the surface depends onhow clear the sky is, will not be as effective (in fact willnot be effective) in Ile-Ife and similar tropical locationsas they would be at the cities studied by Liu and Jordan(1960). Consequently, the use of such solar devices thatare designed based on the CDCs of Liu and Jordan in



1992-2002 (Dry Season)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

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0.05

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0.1-

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0.35

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0.45

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0.55

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0.6-

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0.65

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0.7-

0.75>0

.75


Fre

qu

ency

of

Occ

urr

ence

(%

)

N = 1235

(a)

1992 - 2002 (Dry Season)

0

10

20

30

40

50

60

70

80

90

100

0.05 0.

10.

15 0.2

0.25 0.

30.

35 0.4

0.45 0.

50.

55 0.6

0.65 0.

70.

75>0

.75


Cu

mu

lati

ve F

req

uen

cy (%

)

(b)

Figure 14. (a) Frequency of occurrence, and (b) cumulative frequencyof daily clearness index (KT) 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 ofthis and other findings based on measurements from thearea.

6. Conclusions

Hourly global and diffuse solar radiation data measuredduring the period 1992–2002 on top of the PhysicsDepartment building at Obafemi Awolowo UniversityIle-Ife, Nigeria, have been used to calculate the hourlyand daily clearness index and diffuse fraction at thestation. It has been established that during the daytimefrom about 1100 to 1500 LST, the monthly mean hourlydiffuse fraction, Md , has values, which are, most ofthe time, less than 0.52, 0.54 and 0.60, respectively,for January, February and March indicating that thedirect (beam) irradiance constitute a relatively significantproportion of the global solar irradiance reaching theground during these months. Molecular scattering dueto the aerosol loading of the atmosphere prevalent duringthis period are mainly responsible for diffuse irradiancereaching the ground at these times, especially for themonths of January and February. Again, during themonths of July and August (which are typical of the wetseason), the monthly mean hourly diffuse fraction, Md ,has values ranging between 0.61 and 0.85 over the period1100–1500 LST (being generally greater than 0.65) withthe corresponding values of MT ranging between 0.23and 0.45 during the day. This again signifies the highproportion of diffuse component of the total irradiancearriving on the ground during these months, which is aresult of the intense forward scattering of beam radiationby altocumulus and altostratus clouds.

Statistical analysis of hourly and daily clearness indexshowed that the local sky conditions at the station werealmost devoid of clear skies (clear skies occurred for onlyabout 3.5% of the time). Overcast skies were also veryscarce (overcast skies occurred for only about 4.8% ofthe time). The sky conditions were rather predominantlycloudy (cloudy skies occurred for above 72% of the time)all the year round.

The study has, therefore, shown that there is highproportion of diffuse component of the total irradiancearriving on the ground at the station all the year round

Table IV. Monthly percentage cumulative frequency, f, of the daily clearness index KT and monthly average values of theclearness index, KT over Ile-Ife for the period 1992–2002 (f is computed using Equation (1)).

Values of f for KT ≤ KT (fixed value) Monthly Average KT

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 0.46Feb. (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 0.51March (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 0.49April (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 0.48May (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 0.48June (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 0.44July (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 0.33Aug. (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 0.31Sept. (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 0.38Oct. (234) 0.0 3.0 11.9 18.4 26.9 64.9 92.3 99.1 100.0 100.0 100.0 100.0 0.45Nov. (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 0.53Dec. (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



Table V. Average monthly/seasonal clearness index (KT ) values for Ile-Ife for the period 1992–2002, compared with similarresults for Port Harcourt and Ibadan inserted for comparison.

Port Harcourta Ibadanb Ile-Ifec

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

a Kuye and Jagtap (1992).b Ideriah and Suleman (1989).c 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 (KT)

Cum

ulat

ive

Fre

quen

cy, f

(%

)

NDJ (0.50)

FMA (0.49)

A (0.31)

JS (0.36)

JO (0.45)

M (0.48)

JS (0.39;Ideriah &Suleman)

JS (0.36;Kuye& Jagtap)

Figure 15. Monthly KT cumulative distribution curves for Ile-Ifeover various periods with some of the results obtained by Ideriahand Suleman (1989) and Kuye and Jagtap (1992) for Ibadan andPort Harcourt respectively inserted for comparison. The number inparenthesis in the legend indicates the average KT for the period.

Equation (1) defines f.

due to molecular scattering of beam radiation by aerosolsand clouds which keep the sky turbid and cloudy most ofthe time. Compared to the molecular scattering of beamradiation by aerosols during the dry season, forward scat-tering by clouds (especially altocumulus and altostratusclouds) is more intense resulting in more diffuse com-ponent of the total solar radiation reaching the surfaceduring the wet season than the dry season. The impli-cation is that solar devices that use radiation from sunand sky under changing atmospheric conditions shouldbe preferred to solar energy concentrating devices, suchas parabolic mirrors, which make use of incident beamradiation (whose availability at the surface depends onhow clear the sky is). The results also have implica-tions for the much-talked-about climate variability and itsimpact on food production, numerical weather modellingand dependable weather forecast as global circulation,

crop simulation and soil-vegetation-atmosphere transfermodels require information on the decomposition of solarirradiance into its various components.

Acknowledgements

The authors gratefully acknowledge the support of theInternational Program in the Physical Sciences (IPPS),Sweden, for the establishment of the Obafemi AwolowoUniversity (OAU) Ile-Ife solar radiation station. Theassistance of Professor L. Hasselgren and useful discus-sions with Profs. Z. D. Adeyewa and O.O. Jegede arequite appreciated. The support of Third World Academyof Sciences (TWAS) and Obafemi Awolowo University,Ile-Ife, Nigeria, are also acknowledged.

Appendix

Symbols, definitions and notations used

Kd – Daily diffuse fraction;KT – Daily clearness index;KT – Monthly average clearness index;I0 – Hourly extraterrestrial radiation;H0 – Daily extraterrestrial radiation;MT – Hourly clearness index;Md – Hourly diffuse fraction;MT – Monthly average hourly clearness index;Md – Monthly average hourly diffuse fraction;ISC – Monthly average hourly diffuse fraction;f – Percentage cumulative frequency of the aver-

age daily clearness index;

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Documents

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