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FUTA Journal of Research in Sciences, 2014 (1): 120-136 Empirical Models for the Prediction of Global Solar Radiation in Arid and

Coastal/Rainforest Regions of Nigeria

E. O. Ogolo*1 and O. B. Daramola2

1Department of Physics, Federal University of Technology, Akure, Nigeria. 2Department of Physics, Bowen University, Iwo. Osun State, Nigeria

*Corresponding author e-mail address: emogolo@gmail.com ___________________________________________________________________________________ Abstract In this study eight empirical models were developed for the simulation of global solar radiation (GSR) (both linear and multilinear) using multilinear regression technique for nine stations drawn from two regions of Nigeria; namely Arid and Coastal/Rainfall regions. The developed empirical models as functions of meteorological variables are M1 (sunshine hour), M2 (cloud cover), M3 (precipitation), M4 (sunshine hour and cloud cover), M5 (sunshine hour and precipitation), M6 (sunshine hour, relative humidity and cloud cover), M7 (sunshine hour, relative humidity and precipitation) and M8 (sunshine hour, air temperature, relative humidity, cloud cover and precipitation) for the simulation of GSR. The performance and the efficiency of the developed models in terms of the simulated and observed GSR was carried out, using some statistical indicators which include coefficient of determination (R2), mean bias error (MBE), root mean square error (RMSE) and standard error of estimate (SEE). Generally, all the models show the tendency of overestimation as the calculated MBE was positive for both regions. In Arid region, the highest coefficient of determination (R2 = 0.61) was recorded by model 4, a sunshine hour and cloud cover based model, while model 8 which combined all the parameters recorded the lowest MBE(2.08), RMSE(3.08) and SEE(1.83). For the Coastal/Rainfall region, model 8 is found to be more suitable compared with other empirical model as it has the highest R2 (= 0.74), lowest RMSE (= 1.47), MBE (0.80) and SEE (1.25). It is further observed that while all the sunshine hour and precipitation based models (M3, M5, M7 and M8) are characterized with tendency to perform better when compared with the sunshine hour and cloud cover based models (M2, M4 and M6) in Coastal/Rainforest region the reverse is the case in Arid region of the country . It was also discovered that the two schemes found to exhibit best performance for each region also perform better than Angstrom-Prescott and are hence recommended for the estimation of GSR in the arid and coastal regions of Nigeria ____________________________________________________________________________________________

Introduction Solar energy is a natural energy source that is infinite and its applications unending. It is an ancient renewable energy that exists in abundance daily but little is exploited for human needs especially in Africa where it is available in large quantity. Among the renewable resources, only the solar energy has the greatest potentiality, availability and is free from environmental hazards (Isikwue et al., 2012). Solar radiation is a principal driver for many processes (physical, chemical and biological) on the earth’s surface, and complete and accurate solar radiation data at a specific region are of

considerable significance for such research and application fields as architecture, agriculture, industry, environment, hydrology, meteorology, oceanography and ecology. Besides, solar radiation data are a fundamental input for solar energy applications such as photovoltaic systems for electricity generation, solar collectors for heating, solar air conditioning climate control in buildings and passive solar devices (Sopian et al., 2009). In spite of its significance, data on the direct measurement of solar radiation is scares and not readily available when compared with other meteorological variables (Thornton and

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Running, 1999). This observation is due to the cost and maintenance and calibration requirements of the expensive measuring equipment. Lack of adequate observations on solar radiation is not limited to any particular region or to an environment but a worldwide problem (Iziomon and Mayer, 2002). Hence, the need to develop some empirical relations for the estimation of the mean monthly solar radiation from other meteorological variables. Several empirical formulas have been developed to calculate the global solar radiation using various measurable atmospheric variables. These variables includes the sunshine hours (Angstrom, 1924, Black et al., 1954, Glove et al., 1958), the relative humidity and sunshine hours (Gopi Nathan 1988), the declination angle and the latitude (Liu et al., 1960), the number of rainy days, sunshine hours, latitude and locations (Ready, 1977), sunshine duration, relative humidity, maximum and minimum temperature, latitude, altitude and location (Sabbagh et al., 1977) and the total precipitation, water, turbidity and surface albedo (Hoyt, 1978). Besides the above, other related studies have also been reported on the estimation of Global and Diffuse solar radiation employing various climatological variables (Abdullah et al., 1988; Chandel et al., 2005; Ahmad et al., 2004; Udo, 2002, Togrul, 2002). In the continent of Africa, Nigeria in particular, efforts have been made by researchers in estimating solar radiation in some tropical stations (Awachie, 1988, Fagbenle, 1992, Akpabio, 2004, Augustine and Nnabuchi, 2009, Ogolo, 2010). In this study, an empirical method based on regressional techniques shall be developed involving some measurable atmospheric variables to estimate total solar radiation alongside with the standard Angstrom-

Prescott model for some tropical stations located at Arid and Coastal/Rainforest regions in Nigeria. It is anticipated that the outcome of this study would remove the usual constraints placed on related researches due to dart of data on global solar radiation. Site Description and Data Aqcuisition Site Description According to Olaniran (1983), Nigeria has been classified into four different climatic regions which are Arid, Midland, Guinea Savannah and Coastal/Rainforest regions out of which two regions (Arid and Coastal/Rainforest) of extreme and diverse climates shall be involved in this study. Nine tropical stations have been carefully selected from the above-named regions and based on the availability of relevant dataset. The stations selected within the two regions for study are respectively Sokoto, Kano, Katsina and Maiduguri in the Arid region and Lagos, Benin-City, Enugu, Calabar and Port-Harcourt in the Coastal/Rainforest region (see Figure1). The Arid region is well known for its wide annual and diurnal temperature ranges of about 150C and 200C, respectively. It is characterized with a total annual precipitation of less than 75cm. According to Iloeje (1965) as it was reported by Ogolo (2010), the dry season is excessively dry and long (up to 8 to 10 months) and desert-like conditions prevail. Coastal/rainforest region is found along the coastlines and extends hinterland up to some 100 to 150 kilometers inland. Temperatures are up to 270C to 300C most of the year and both the daily and annual ranges are as little as 100C and 50C, respectively. Relative humidity is around 80% and over 300cm of annual rainfall has the double maxima rainfall. This region has a long wet season from 7 – 10 months.

Table 1: Geographical location of stations in Nigeria

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Figure 1: Map of Nigeria showing the Data Collection Stations and Geographical Region Acquisition and Treatment of Data The data used in this study include monthly mean daily timescale on solar radiation, sunshine hour, maximum and minimum temperature, precipitation, cloud cover and relative humidity, extracted from the archives of Nigeria Meteorological Agency (NIMET), Oshodi, Lagos. The data obtained cover a period of twenty-five years (1975 – 1999) and have been treated for the removal of outliers due to compilation of the data from the source. Table 1 presents geographical information on the tropical stations classified into the two climatic regions under study. The observed solar radiation data obtained from the stations were measured by Gun Bellani distillate and recorded in millimetres. This unit was converted according to Afolayan (1988) by using a conversion factor of 1.357±0.176 MJ/m2 Methodology. The empirical models were developed by means of linear and multiple regression techniques in which various atmospheric variable data mentioned above were related to global solar radiation using a twenty year period (1975 –1994) monthly mean daily data set. The regression technique which is the method of linear least square, a procedure used to determine the best fit curve for a given data by minimizing squared error in each predicted

value. For a given data with k independent variables x1,x2,…, xk and one dependent variable, y, a linear/multiple regression model is developed and given according to Rajesh Kumar et al.,(2013) and defined as: Y = bo +b1x1 +b2x2+ ...+bkxk (1) Where bo, b1, …,bk are regression coefficients to be determined; x1,x2,…, xk are the input variables which are the atmospheric variables and Y is the ratio of global solar radiation to extraterrestrial radiation(Gr/Go). Following the above procedure, eight different empirical models are proposed for the estimation of global solar radiation for both Arid region and Coastal/Rainforest regions of Nigeria whose basic requirements (besides measured global solar radiation) utilize sunshine duration, air temperature, relative humidity, cloud cover and precipitation. The simplest model (which is considered as model one in this study) is the well-known Angstrom correlation (Angstrom, 1924) and later modified by Prescott (1940): Model 1: (2) The rest of the models are stated as follows:

Nnba

RsRo

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Model 2: )(Cba

RR

S

O (3)

Model 3: )(PbaRR

S

O (4)

Model 4: )()( Cc

Nnba

RR

S

O (5)

Model 5: )()( Pc

Nnba

RR

S

O (6)

Model 6:

)()()( CdRHc

Nnba

RR

S

O (7)

Model 7:

)()()( PdRHc

Nnba

RR

S

O (8)

Model 8:

)()()()()( PfCeRHdTcNnba

RR

airS

O

(9) where a, b, c, d, e and f are regression constants, Ro is the monthly mean daily global radiation on a horizontal surface (MJm−2 day−1), Tair, RH, C, and P are air temperature (0C), relative humidity (%), cloud cover and precipitation (mm) respectively, n is the monthly mean daily number of hours of bright sunshine (h), N is the monthly mean daily maximum number of hours of possible sunshine (or day length) (h), n/N is the relative sunshine duration and Rs is the monthly mean daily extraterrestrial radiation on a horizontal surface (MJm−2 day−1) given by Iqbal (1983) as follows:

ssscS wwER sin cos cossin sin 180

I24o

(10)

where Isc = 1367 Wm−2 is the solar constant, Eo is the eccentricity correction factor, Ø is the latitude of the location, δ is the solar declination angle and ws is the sunset hour angle. The expressions for EO, δ and ws are given by Iqbal (1983):

365360cos033.01EO

D

(11)

365

284360sin45.23 D

(12) where D is the Julian day number for each month and ws is given as

tantancos 1 sw (13)

The maximum possible sunshine duration N from equation (2) can be calculated as (Duffie and Beckman, 1991):

swN

152

(14)

The developed empirical models (equations 2-9) were validated using a five-year (1995-1999) of measured monthly mean weather data. The performance of the proposed model was evaluated using the standard error of estimate (SEE), Mean Bias Error (MBE) and Root Mean Square Error (RMSE). The expressions for the MBE (MJm-2day-1) and RMSE (MJm-2day-1) defined as (Ogolo, 2010):

21

2),,(

nRiRiRMSE obsest

(15) (16)

where Rest and Robs are respectively the estimated and observed values of global solar radiation and n is the number of observations used. It has been recommended by Che et al. (2007) that a zero value for MBE is ideal and a low RMSE is desirable. The lower the MBE and RMSE, the better the model. A positive MBE indicates overestimation, while a negative MBE shows

n

RiRiMBE obsest ),,(

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the underestimation of the observed values by the model. The RMSE test provides information on the short- term performance of the studied model as it allows a term by term comparism of the actual deviation between the estimated values and the measured values. A larger value of the Standard Error of Estimate (SEE) is undesirable and is stated by Irmak et al. (2003) as:

5.0

11

2

12

2

1 112

1

2

21

n

in

i

n

i ii

n

i

n

i in

i iiin

iii

xxn

yxyxnyyn

nnSEE

(17) The results of these estimated errors calculated are presented on Table (2-3) for the two regions under consideration. Boxplot Analysis of the Models

In the quest to further determine and evaluate the distribution of the developed models, the estimated values of solar radiation from the models compared with the measured values had been displayed graphically by the method of data display known as boxplot. Boxplot (also known as box and whisker plot), originally published by John Tukey (1977) is an efficient method for presenting a five sample statistics and potential outliers namely, the minimum, the lower quartile, the median, the upper quartile and the maximum - in a visual display. In this study, box plot of the predictive and measured solar radiation values have been lined up side by side (parallel boxplot) on a common scale and the various attributes of the samples compared at a glance for the comparative view of the distribution of GSR by the method when compared with the observed (see Figure 6-7). Result and Discussion.

The relationship between the atmospheric variables and global solar radiation was investigated by calculating the Pearson’s correlations coefficients of global solar radiation with other meteorological parameters for each station representing the two regions under consideration. The results are presented on Table 2. It is observed that correlations of GSR with other whether parameters for Arid stations are generally low except for the correlation of GSR and air temperature (Tair). The correlation of GSR with air temperature in all the stations under consideration in Arid region is high and positive. The correlations vary between 0.66 and 0.84 and statistically significant at 95% (see Table 2). The results on the table also show that correlation of GSR between relative humidity (RH) and precipitation (P) is low and negatively correlated. A very high correlation (mostly 99% significant) occurred between GSR and all the parameters employed in this study in all the stations classified under Coastal/Rainforest region. The only exception occurred in GSR correlation with precipitation in Lagos where the correlation coefficient is -0.49. Like other regions, negative correlation values are recorded between GSR and relative humidity, cloud cover and precipitation in this region. Regression coefficients were determined for the two selected regions of Nigeria namely, arid region and coastal/rainforest region. The regression coefficient values for all of the models and the corresponding input parameters are shown in Tables (3-4). From the tables, it is found that the regression coefficient values vary from one model to another and also from one region to another region. These differences have been attributed to the latitude and altitude of the region and the atmospheric conditions of the environment (Wang and Zhang, 2010, Ogolo, 2010).

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Table 2: Pearson’s Correlations of Global Solar Radiation and other Meteorological Parameters in Arid and Coastal/Rainforest Region.

NOTE: **. Correlation is significant at the 0.01 level (1-tailed). *. Correlation is significant at the 0.05 level (1-tailed). SUN – Sunshine Hour, RH – Relative Humidity, Tair – Air Temperature- CC – Cloud Cover, P - Precipitation.

Figure (2-3) shows the comparisons between the monthly mean of the estimated for all the models developed for Arid and Coastal/Rainforest region and the observed global solar radiation. It could be seen from the figures that the predictive values by the entire models exhibit a good variation trend alongside with the observed global radiation for the two regions. However, there is an irregular variation observed in the seasonal distribution of the models in the two regions. Generally models for Arid regions appear to behave differently between April and May. During this period, it was observed that, while observed GSR starts defining a trough in February, all the models delayed till April and May (see Figure 2). From the figure, it could also be seen that model 2 had a delay in making its major trough in relation to observed solar radiation. The trough should have occurred in August but delayed till the month of October. The case of irregular variation in the seasonal distribution of the models for Coastal/Rainforest region is found generally between the month of March and June. During this period, it was observed that, while observed GSR starts defining a crest in April, most of the models delayed till June (see Figure 3). Performance of the Models Based on Weather Parameters The results of the statistical indicators employed to test the suitability of the empirical models in predicting global solar radiation in two selected regions of Nigeria have been presented on Table 3-4. The correlation of monthly global solar radiation values estimated using model equations for the two regions with the measured values for the validation years were displayed in a scatter plot (see Figure 4-5) along with the slope, s; intercept, I and coefficient of determination, R2. In Arid region, the coefficient of determination, R2 which is an indication of the amount of variability in the one variable that is explained by the other (Sumari O’Neil, 2009) ranges from 0.17 – 0.6, the lowest value (0.17) is recorded by model 5 while the highest value (0.61) is recorded by model 4 (see Table 3). On the table, the MBE values obtained from the models are positive for all the models (ranges from 2.08-2.98) signifying overestimation in the prediction of GSR. The value of RMSE and SEE for the models ranges from 3.08-6.10 and 1.83-5.30 respectively. It is also readily seen that model 8 which combined all the meteorological parameters with R2 of 0.26 recorded the lowest MBE, RMSE and SEE (2.08, 3.08 and 1.83 respectively. The results on the table 3 also show that R2 value of all the cloud cover and relative humidity based models (see M2, M4, and M6) is higher than the rest of the models in this region (except for model 8). Likewise, on the average the error values (MBE, RMSE and SEE) of the former models are lower than the latter models. The results of the statistical comparison on the model performance showed that the most suitable model for the prediction of global solar radiation in Arid region is Model 8

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because of its lowest records in terms of MBE (2.08), RMSE (3.08) and SEE (1.83) (see Table 4). In addition, Models 2, 4 and 6 have good statistical performance based on the high correlation coefficient and low standard error of estimate (SEE). It is observed that all these models (i.e. 2, 4, 6 and 8) had two weather parameters in common (sunshine duration and cloud cover). From the box plot chart for Arid region (see Figure 6), it would be observed that the medians of the estimated global solar radiation distribution from the figures (the line in the middle of each box) differ within the interquartile range, IQR (50% of the ranked data) from one model to the other and in comparison with observed solar radiation (RO). By contrast, distribution of all the models shows clearly a bit higher global solar radiation values than the measured ones in Arid region.

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Table 3: Regression Coefficients of Model Equations and the values of the Statistical Indicators in Arid region.

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Table 4: Regression Coefficients of Model Equations and the values of the Statistical Indicators in Coastal/Rainforest region.

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Figure 4: Scatter plot between the observed and estimated solar radiation for model 1-8 in

Arid region

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Figure 5: Scatter plot between the observed and estimated solar radiation for model 1-8 in

Coatal/Rainforest region

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When looking at the model distribution, it is noticeable that the range values (difference between the minimum and maximum values in the data set) on Table 6 for the global solar radiation are higher than in the observed solar radiation except for model 8 with a lower value of global solar radiation range (7.28). There the boxplots of sunshine hour and cloud cover based models (i.e. M2, M4, M6 and M8) in comparison to the measured solar radiation have similar range, IQR and similar whiskers. The median values of the model box plot are all close to the measured global solar radiation especially the cloud cover based model i.e. M2 (23.81). Other models (MI, M3 and M7) are varying more, have larger IQR, some have larger ranges and some higher whiskers (see Table 6). But in all, sunshine hour and cloud cover based models have greater performance in predicting global solar radiation than any other parameter combinations in this region. For Coastal/Rainforest region, all the models exhibit good performance for the prediction of GSR based on their statistical indicators. The coefficient of determination, R2 ranges from 0.17-0.74, the lowest value (0.17) is recorded by model 2 while the highest value (0.74) is recorded by model 8. Base on the model estimated errors on Table 4; MBE like in Arid region is positive for all the models (ranges from 0.80 - 0.95) signifying overestimation in the prediction of GSR. From the table, the value of RMSE and SEE for the models ranges from 1.47-2.22 and 1.25-1.60 respectively. The standard error of estimate (SEE) for all the models recorded a considerable low values (1.25-1.60) with the lowest record from M1 (Angstrom-Prescott model) and M8 having the same value of 1.25. Critical observations on the model performance at this region indicate that

all the sunshine hour and precipitation based models (M3, M5, M7 and M8) performed better than the sunshine hour and cloud cover based models (M2, M4 and M6, see Table 5). Based on the results of the statistical indicators on Table 4, Model 8 which combines all the atmospheric variables for modeling is strongly recommended for simulating GSR for the stations in the Coastal/Rainforest region in Nigeria. The model had the highest correlation coefficient (0.74) and has lowest RMSE (1.47) and SEE (1.25) and considerably low value for MBE (0.80) as shown on Table 5 and also confirmed in scatterplot in Figure 3. Furthermore, Model 3, 5 and 7 which are sunshine hour and precipitation based models have better performance than the rest of the models and can stand as the second class model for the simulation of monthly GSR for the region under consideration. Almost all the boxplots developed for the models for this region are skewed to the right just like RO performance particularly for M4 and M6 (Figure 7). As a result of this skewness in the box plot of the models, their medians (see Table 7), ranging from 17.25-18.52 are slightly higher than the measured solar radiation box plot (17.22). On the table, the box plot of Angstrom-Prescott model has its range value a little bit higher (10.17) than the RO (8.01). The range values of model 4, 5, 6 and 7 are significantly closer in relation to RO. On the chart (Figure 4-5), the boxplots of model 2, 3, 4 and 6 and the measured solar radiation have similar IQR. Based on the box plot statistics on Table 7, all the eight models with different meteorological inputs are closer in performance in relation to measured solar radiation and may be consider fit to predict global solar radiation in this region.

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Figure 6: Box plot analysis for Global Solar Radiation in Arid Region

Figure 7: Box plot analysis for Global Solar Radiation in Coastal/Rainforest region.

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Table 5: Box plot Statistical Summaries for Arid region

Table 6: Box plot Statistical Summaries for Coastal/Rainforest region.

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Conclusion Eight different empirical models (both linear and multilinear) were developed and investigated in this work for the estimation of global solar radiation from climatologically data for nine stations in Nigeria namely, Sokoto, Kano, Katsina, Maiduguri, Lagos, Enugu, Calabar, Benin-City and Port-Harcourt. These stations were further categorized into two climatic regions of Nigeria namely, Arid and Coastal/Rainforest regions. The results from the study can be summarized thus:

1. It was observed that the regression coefficient values determined for all the two regions of Nigeria vary from one model to another and also from one region to another region.

2. The best performing and suitable models for the prediction of global solar radiation in Arid region were observed to have two weather parameters in common which are sunshine duration and cloud cover. The models are M2, M4, M6 and M8. The best performing model among them based on estimated error indicators is model 8.

3. The model performance at Coastal/Rainforest region indicates that all the sunshine hour and precipitation based models (M3, M5, M7 and M8) performed better than the sunshine hour and cloud cover based models (M2, M4 and M6, see Table 5). But in all, M8 which combined all the parameters is highly significant in terms of statistical indicators employed and therefore strongly recommended for simulating global solar radiation for the stations in the Coastal/Rainforest region in Nigeria.

4. It was also discovered that the best performing models for each region also perform better than Angstrom-Prescott and are hence recommended for the estimation of GSR in the arid and coastal regions of Nigeria.

5. While developing these models, none of the weather parameters had zero correlation coefficient. This indicates that all these weather parameters influence global solar radiation available at the earth’s surface. Hence, a multiple regression model correlating

all these parameters simultaneously with global radiation may give a better result.

6. Data generated from the recommended models is a major input in the production of solar electric (photovoltaic PV) modules which have the potential to supply a significant portion of the industrialized and developing countries electric energy particularly in Nigeria. Hence, the recommended models for the two regions can be employed for the estimation of monthly mean daily global solar radiation on a horizontal surface in the remaining stations within these regions and places with similar climatic conditions as the two regions in Nigeria.

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