**3. Characteristic variation and atmospheric effects on albedo**

#### **3.1 Daily variations of H/Ho, Hd/H, Hr/Ho**

It is instructive and informative to compare the variations and characteristics of the reflection coefficient Hr/Ho, cloudiness index Hd/H and clearness index H/Ho as done in the graphs in Figs. 1 – 4 for February, April, August and November, months representing four periods of different atmospheric or sky conditions in the year. By the graphs the atmospheric conditions causing the variations could be discerned. The graphs represent daily and unequal fluctuations of the parameters in those months as shown in the figures. The fluctuations in the values of the parameters in turn indicate daily changes in the atmospheric conditions causing the variations.

In the graphs the reflectance, Hr/Ho and the cloudiness index, Hd/H have the same characteristics but show slight differences in magnitudes, while they both have opposite characteristics to H/Ho. Reflection coefficient, Hr/Ho, from this observation, may therefore be interpreted to be a sort of cloudiness index as Hd/H is (Prado et al, 2005), and confirmed by Eqns. 3 and 4.

The magnitude of the cloudiness index could be interpreted to mean the degree of cloudiness or turbidity in the sky and to imply the magnitude of the diffuse radiation in the global, while the magnitude of reflection co-efficient would indicate the degree of brightness of the surface and the amount of reflected radiation back to space.

It could be said by this, that if the sky was relatively cloudless, albedo, or reflection coefficient, Hr/Ho would be relatively small, thus, more radiation would be available to solar energy devices on the earth. On the other hand the variation of Hd/H which was simultaneously significant, was observed to be high in magnitude more than those of the others for the same changes in atmospheric conditions. This implies that it is more sensitive to the atmospheric condition changes responsible for the variations than the others.

Discussing specifically the variation of the parameters in each of the sampled months, and since H and Hr are each a fraction of the same quantity, Ho, it is plausible that, H/Ho and Hr/Ho are compared. In Fig.1, representing variation in February, the daily fluctuation of H/Ho and Hr/Ho were observed not to be significantly big, however the values of H/Ho were bigger than those of Hr/Ho practically throughout the month. This implies that since H is toward the ground surface and Hr is toward the space, the global radiation H, received on the Earth's surface was more than the reflected radiation, Hr lost to space in February at Ilorin.

Fig. 1. H/Ho, Hd/H, Hr/Ho for February 2000

be interpreted to be a sort of cloudiness index as Hd/H is (Prado et al, 2005), and confirmed

The magnitude of the cloudiness index could be interpreted to mean the degree of cloudiness or turbidity in the sky and to imply the magnitude of the diffuse radiation in the global, while the magnitude of reflection co-efficient would indicate the degree of brightness

It could be said by this, that if the sky was relatively cloudless, albedo, or reflection coefficient, Hr/Ho would be relatively small, thus, more radiation would be available to solar energy devices on the earth. On the other hand the variation of Hd/H which was simultaneously significant, was observed to be high in magnitude more than those of the others for the same changes in atmospheric conditions. This implies that it is more sensitive to the atmospheric condition changes responsible for the variations than the

Discussing specifically the variation of the parameters in each of the sampled months, and since H and Hr are each a fraction of the same quantity, Ho, it is plausible that, H/Ho and Hr/Ho are compared. In Fig.1, representing variation in February, the daily fluctuation of H/Ho and Hr/Ho were observed not to be significantly big, however the values of H/Ho were bigger than those of Hr/Ho practically throughout the month. This implies that since H is toward the ground surface and Hr is toward the space, the global radiation H, received on the Earth's surface was more than the reflected radiation, Hr lost to space in February at

of the surface and the amount of reflected radiation back to space.

Fig. 1. H/Ho, Hd/H, Hr/Ho for February 2000

by Eqns. 3 and 4.

others.

Ilorin.

Fig.2, presenting the variations or the fluctuations of the parameters in April, indicates very significant variations of the parameters. The high and frequent fluctuations of the parameters could indicate corresponding high, dynamic changes in the atmospheric conditions in the month. Again, H/Ho was higher than Hr/Ho on many days in the month, indicating that more radiation was available on the ground surface than lost to space in reflection. There is however a rise in the value of albedo, i.e. Hr/Ho, observed in this month. This could be due to the presence of some clouds in the sky and heavy hygroscopic particles replacing the harmattan dust particles in the sky.

Fig. 2. H/Ho, Hd/H, Hr/Ho Graphs for April 2000

In August, in fig.3, the variations of the parameters were very significant with bigger values of fluctuation. However Hr/Ho and Hd/H were much bigger than H/Ho for almost all the days in the month. This is a reversal of the case in February and November, and which could only imply that more radiation was reflected back to space than received on the Earth's surface. The high values of Hd/H at the period would indicate that the little global radiation received was mostly diffuse radiation. The high values of Hr/Ho, the reflectance, or albedo, would imply high brightness of the Earth's surface toward the space, and low surface temperature of the Earth in this month.

Fig. 3. H/Ho, Hd/H, Hr/Ho Graphs for August 2000

But in November (in Fig.4), the values of H/Ho were much higher than those of Hr/Ho and Hd/H for almost all the days in the month. The low values of Hr/Ho imply that little amount of radiation was reflected back to space, and large amount of radiation was received on the ground surface. They also imply low values of albedo, and therefore less brightness of the surface of the Earth but high surface temperature. All these, and the very low values of Hd/H could indicate that very little amount of diffuse radiation, little or no clouds and little or no dust particles in the sky are the characteristics of the November month in the year.

Fig. 4. H/Ho, Hd/H, Hr/Ho Graphs for November 2000

#### **3.2 Monthly average variations of H/Ho, Hd/H, Hr/Ho examined**

146 Solar Radiation

But in November (in Fig.4), the values of H/Ho were much higher than those of Hr/Ho and Hd/H for almost all the days in the month. The low values of Hr/Ho imply that little amount of radiation was reflected back to space, and large amount of radiation was received on the ground surface. They also imply low values of albedo, and therefore less brightness of the surface of the Earth but high surface temperature. All these, and the very low values of Hd/H could indicate that very little amount of diffuse radiation, little or no clouds and little or no dust particles in the sky are the characteristics of the November month in the year.

Fig. 3. H/Ho, Hd/H, Hr/Ho Graphs for August 2000

Fig. 4. H/Ho, Hd/H, Hr/Ho Graphs for November 2000

The graphs of the monthly averages of Hr/Ho, Hd/H and H/Ho in Fig.5, indicate high values of Hr/Ho in July, August and September with the highest in August, and relatively low values in October, November, December and January with the lowest in November. Similarly the graphs indicate high values of Hd/H in June, July and August with the highest in August, and low values of it in November, December and January with the lowest in November. The result, that the parameters, Hd/H and Hr/Ho, have their highest and lowest values occurring in the same months respectively confirm that the two parameters are twins of the same physical quantity, cloudiness and turbidity, but in the opposite directions, thus answering the question raised earlier on.

The results further show that the high values of Hr/Ho in July, August and September, with the highest in August, the peak of rainy season and a predominantly cloudy month, confirm the more, that the reflection of solar radiation by the planet Earth, in this region, is mostly by clouds. The lowest value of the parameter in November confirms also that November is relatively cloudless and dustless, that is, relatively clear and clean (Babatunde and Aro, 1990). A high value of reflectance observed in February, though a relatively cloudless month, would indicate that reflection of radiation at this period is by the dust particles in the atmosphere, and indicates that the atmosphere in February of that year was heavily laden with harmattan dust.

Fig. 5. Monthly average variation of H/H0 , Hd/H, Hr/H0 for year 2000


Table 1. The Monthly Average of the Radiation coefficients and Fluxes in (MJ/m^2 day) for year 2000

### **3.3 Seasonal variation and sky conditions by Hr/Ho, the albedo**

Table 1 and Fig.5 above, present the monthly average values of reflectivity, Hr/Ho, of the Earth and its atmosphere at this location. The reflectance or reflectivity of radiation or albedo property of the contemporary atmosphere is seen to vary from month to month at this location as in any other location on the earth's surface. The seasonal values can be inferred from the monthly average values. An interesting implication of this is that reflectance or albedo could be used as a radiation or atmospheric parameter to determine the sky conditions of a location or region. It may also be used to estimate the surface temperature of the Earth at the location. The following expression, though not very accurate, relates the surface temperature, T of the Earth to its albedo, i.e.

$$\mathbf{T} = \{ \text{ (1-a)S/4o} \}^{1/4} \text{ (McIluven/1992)}$$

where **a** is the albedo, **S** is the solar constant and **σ** is the universal Stefan-Boltzman constant. The expression indicates that the temperature T would decrease as albedo increases.

Nigeria, the case study, being in the tropics, experiences two main seasons: dry season and rainy season. While temporal demarcation between them is not rigid, the dry season is from about November to April and the rainy season is from about May to October. The two seasons may be divided into sub- seasons or periods with slightly different weather or atmospheric conditions (Falaiye et al, 2003). For the purpose of determining the sky conditions using seasonal variations of albedo in this work, the two seasons were subdivided into four divisions. For each period, the representative value of the albedo or reflectivity of the Earth was computed. The sub-divisions are presented in Table 2 below.


Table 2. Sub- Seasons with Albedo Values in Year 2000

However for the two main seasons, the sky conditions parameters are summarized as follow in Table 3.


\*1- Dry Season, \*2 - Rainy Season

148 Solar Radiation

Table 1. The Monthly Average of the Radiation coefficients and Fluxes in (MJ/m^2 day) for

Table 1 and Fig.5 above, present the monthly average values of reflectivity, Hr/Ho, of the Earth and its atmosphere at this location. The reflectance or reflectivity of radiation or albedo property of the contemporary atmosphere is seen to vary from month to month at this location as in any other location on the earth's surface. The seasonal values can be inferred from the monthly average values. An interesting implication of this is that reflectance or albedo could be used as a radiation or atmospheric parameter to determine the sky conditions of a location or region. It may also be used to estimate the surface temperature of the Earth at the location. The following expression, though not very accurate,

T = [ (1- a )S/4σ ]1/4 (McIIveen,1992) where **a** is the albedo, **S** is the solar constant and **σ** is the universal Stefan-Boltzman constant. The expression indicates that the temperature T would decrease as albedo

Nigeria, the case study, being in the tropics, experiences two main seasons: dry season and rainy season. While temporal demarcation between them is not rigid, the dry season is from about November to April and the rainy season is from about May to October. The two seasons may be divided into sub- seasons or periods with slightly different weather or atmospheric conditions (Falaiye et al, 2003). For the purpose of determining the sky conditions using seasonal variations of albedo in this work, the two seasons were subdivided into four divisions. For each period, the representative value of the albedo or reflectivity of the Earth was computed. The sub-divisions are presented in Table 2 below.

**3.3 Seasonal variation and sky conditions by Hr/Ho, the albedo** 

relates the surface temperature, T of the Earth to its albedo, i.e.

year 2000

increases.

**Mon Ho H Hd H/Ho Hd/H Hr/Ho Hr**  Jan 32.61 16.21 7.24 0.489 0.456 0.511 16.664 Feb 34.85 19.14 9.83 0.549 0.522 0.451 15.717 Mar 37.03 21.44 9.74 0.58 0.459 0.42 15.553 Apr 37.75 18.85 8.79 0.519 0.474 0.481 18.158 May 37.16 19.17 8.90 0.516 0.492 0.484 17.985 Jun 36.51 17.72 8.34 0.485 0.6 0.515 18.803 Jul 36.66 14.95 8.83 0.408 0.627 0.592 21.703 Aug 37.29 13.14 8.46 0.353 0.68 0.647 24.127 Sep 37.11 17.10 9.05 0.461 0.545 0.539 20.002 Oct. 35.44 17.67 8.01 0.498 0.47 0.502 17.791 Nov. 33.11 18.96 6.73 0.572 0.361 0.428 14.171 Dec. 31.18 17.26 6.47 0.543 0.384 0.457 14.537

Table 3. Seasonal sky conditions parameters for year 2000

For the dry season, the sky is generally and relatively cloudless as indicated by the relatively low average value of albedo, as seen in Table 3. More solar radiation is therefore expected to be available at the Earth's surface at this period, while in the rainy season the albedo is relatively high, and this is attributed to high cloudiness at this period, see Table 3. Hence, relatively little amount of radiation is expected on the Earth's surface, and the surface of the Earth-Atmosphere is expected to be brighter and cooler. A further analysis of these results shows that the sums of the ratios H/Ho + Hd/H and H/Ho + Hr/Ho are each approximately equal to unity, a deduction that these quantities are compliments of each other, in the two seasons. This confirms further that Hd/H and Hr/H0 are mirror images of one another. They are the same atmospheric or sky condition parameter, cloudiness index.
