J. Nig. Soc. Phys. Sci. 4 (2022) 588 Journal of the Nigerian Society of Physical Sciences Statistical Analysis and Distribution of Global Solar Radiation and Temperature Over Southern Nigeria M. A. Okonoa, E. P. Agbob,∗, B. J. Ekaha, U. J. Ekahb, E. B. Ettahb, C. O. Edetb,c,d aDepartment of Physics, University of Calabar, Nigeria bCross River University of Technology, Calabar, Cross River State, Nigeria cFaculty of Applied and Human Sciences, Universiti Malaysia, Perlis, Malaysia dFaculty of Electronic Engineering Technology, Universiti Malaysia, Perlis, Malaysia Abstract The intensity of solar energy that is received by a particular location is affected by most meteorological conditions including, the solar irradiance received by the location, precipitation, extreme heat as a result of the surface or ambient temperature, etc. We obtain the monthly global solar irradiation and ambient temperature for the three (3) eco-climatic zones in the south of Nigeria (17 locations) for 12 years (2005 - 2016) from the Photovoltaic Geographical Information System (PVGIS) Satellite. The goal of this study is to understand how regional meteorological conditions affect radiation and temperature reception. Monthly and annual trends were plotted and compared for both variables in each region to show the similarity or dichotomy in their trends. The Mann-Kendall (M-K) trend test has been adopted to reveal the changes in the variations on an annual basis, and results showed that the trend were not significant for both variables. Box plots have been used to give a better description of the data, and compared to show similarities and differences. Finally, we adopted the Gaussian (normal) distribution to show, understand and compare the data distribution. Linear regression plots for each zone shows that the relationship between the solar irradiation and temperature is high. Results show that the climate and vegetation of a region contributes majorly to the variation of radiation and temperature. Inhomogeneity of data or results for locations in the same zones may be attributed to local meteorological conditions. The results obtained here will prove vital in decision making relating to the adoption of solar energy technologies in the region. Results show that the climate and vegetation of a region contributes majorly to the variation of radiation and temperature. Inhomogeneity of data or results for locations in the same zones may be attributed to local meteorological conditions. DOI:10.46481/jnsps.2022.588 Keywords: Global solar radiation, temperature, box plots, Mann-Kendall test, Sen’s slope estimate, Gaussian distribution, linear regression Article History: Received: 15 January 2022 Received in revised form: 24 June 2022 Accepted for publication: 12 July 2022 Published: 14 August 2022 c© 2022 The Author(s). Published by the Nigerian Society of Physical Sciences under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0). Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Communicated by: S. J. Adebiyi 1. Introduction Careful study of the world’s economy shows the impor- tance of solar energy (directly related to global solar radiation ∗Corresponding author tel. no: +234(0)7018774580 Email address: emmanuelpaulagbo@gmail.com (E. P. Agbo) and temperature) to economic growth [1, 2]. Many developing countries in Africa have this flaw of not being able to develop systems to put them in the position of producing enough less ex- pensive energy despite the potential of Africa as a continent [3]. This inefficiency in solar energy conversion causes the poverty and under development activities for low GDP countries [4]. 1 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 2 Usage of fossil fuels and wood for example, causes harm on a long term to these regions [5, 6]. This shows that global solar radiation is one of the environmentally friendly source of en- ergy for the climate system and has an amount that varies with respect to the geographical location, altitude, atmospheric con- ditions, among others [4]. This study seeks to unravel the ambiguity of the variation of these most important variables in solar energy. These are ar- guably the climatic variables with the most effect on a region’s solar energy variation [7–11]. A good understanding of climate change and projected trends of these two variables is very im- portant for policymakers and/or industry managers to undertake project planning and/or installing solar cells in a considered lo- cality. Many studies across the world have been carried out for highlighting the changes, trends and variability analysis of the solar irradiance and temperature. [12-18], but the problem is that little or no study has focused on the regional variations of a country, this study in particular is unique in that it focuses on all major cities (stations) in a country like Nigeria. The assump- tion is that locations in the same region have the same variation, but this may not be entirely so as latitudes, elevation, and other local meteorological factors vary. Abdulkarim et al. [19] analysed solar radiation and climate data’s effects generally (including on economics) on the devel- opment of solar photovoltaic (PV) systems in Nigeria. With one location for each radiation region, results showed that the southern station of Port Harcourt had the lowest viability for so- lar energy conversion when compared to Maiduguri and Minna. Their results also showed a positive relationship between so- lar radiation and temperature for all stations, while showing a negative linear relationship between solar radiation and relative humidity. The horizontal surface solar radiation (or Global Hor- izontal Radiation) and temperature levels for stations in south- ern Nigeria were evaluated using NASA SSE data by Dike et al. [20]. Results summarized that there is a potential for more adoption of solar energy in the region in spite of recorded lower levels. Ohunakin et al. [21] developed six (6) empirical models (linear and quadratic) based on ambient temperature and sun- shine parameters for the southern region of Osogbo. Results showed that the temperature based models had the lowest statis- tical error, and therefore showed the best agreement with mea- sured data, making it suitable for the estimation of global solar radiation. They went further to conclude that this is so for loca- tions with the same latitude. This clearly proves the connection between the two parameters. Another study which applied so- lar radiation models was that of Okundamiya et al. [22]. Using twenty-two (22) years data for Abuja, Sokoto and the south- ern station of Benin City, confirmed results by Ohunakin et al. [21] after applying the multivariate regression relationship de- duced after estimations has been made that air temperature ra- tio, maximum air temperature, among others performed better than other relationships. This study however is focused on analyzing the global so- lar radiation and temperature variations in 17 locations of the southern eco-climatic zones of Nigeria (The guinea savannah, the tropical rainforest and the mangrove swamp. Monthly trends for radiation and temperature for all locations (17) in each zone of the southern region will plotted and compared with each other, the same will be done for the annual trends. The Mann- Kendall (M-K) trend test has been applied to discern the signifi- cance of the increasing or decreasing radiation and temperature trends. Two-dimensional Gaussian distributions as well as box plots were used to show the nature of the distribution. Results can be applied to aid in the knowledge of these variables in the region to better understand its climate dynamics like un- derstanding the potential of global solar radiation reception for renewables and vegetation. 2. Methodology Various methods have been utilized to analyse the data ob- tained. These methods include the use of box plots to describe data and linear regression (LR) plots between radiation and temperature to give a better understanding of the relationship between the variations of both. Kernel density Estimation (KDE) plots have also been used to better explain the distribution of data. 2.1. Theoretical Review Box plots shows a graphical summarization of data. Unlike the KDE, it does not give a detailed representation of the data distribution, but gives an indication of the skewness of data. Box plots summarizes data in the following way; Lower extreme/minimum (Q1 − 1.5 × I QR), Lower quar- tile (Q1), median (Q2), upper quartile (Q3) and upper extreme (Q4 = Q3 + 1.5 × I QR). We use the (KDE) to examine the features and distributions of observations. The KDE takes into account the probability density function (PDF) for a normal distribution. For a univariate KDE, the PDF is given as [23]. f (x|µ, σ2) = 1 √ 2πσ2 ex p [ − 1 2σ2 (x −µ)2 ] (1) where, σ is the standard deviation and µ is the mean. From Equation (1), the ‘argument’ exponential function 12σ2 (x− µ)2 is a quadratic function of x. This can be seen as a parabola which points downward (as evident from Gaussian/normal dis- tributions); this is because the quadratic function has a negative coefficient [24]. The term in front of the exponential function 1√ 2πσ2 from equation (1) is the coefficient of the function (a constant) which does not depend on x. In simple terms, this is a normalization factor that warrants that; 1 √ 2πσ2 ∫ ∞ −∞ ex p [ − 1 2σ2 (x −µ)2 ] = 1. (2) We can simplify Equation (1) by assuming a standard deviation (σ) of 1 and a mean (µ) of 0. f (x) = 1 √ 2π ex p ( − x2 2 ) . (3) The Equation (3) is a simplification of the one-dimensional (1D) Gaussian kernel function which has been employed in this study. 2 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 3 The Linear regression function is used to show the relation- ship between two variables (dependent and independent). In the case of a simple linear regression we have one independent and one dependent variable [23]. It is given by Y = ±mX ± c + e, (4) where Y is the dependent variable, X is the independent vari- able, m is the value of the slope, c is the intercept and e is the residual error. 2.2. Test for Trend (The Mann-Kendall Trend Test) We use the M-K test when analysing time-series data. The test is non-parametric and does not require the data to conform to a particular distribution. [10, 25-26]. We apply this test when a given range of data x j agrees with the relation; x j = f (ti) + �i, (5) f (ti) here is a function of continuously increasing or decreasing monotonically, �i are the range residuals. In the M-K test, we test the null hypothesis Ho which says that there is no trend, and the alternative hypothesis H1 which means that there is a trend in the series. If the results gotten from the test agrees with the null hypothesis (meaning that there is no trend), it means that the given data xi is randomly ordered in time (t), while the alternative hypothesis says that there is either an increasing monotonic or a decreasing monotonic trend [27-29]. The M-K test uses the statistic S , calculated using; S = n−1∑ k=1 n∑ j=λ=1 sgn(x j − xk), (6) where; sgn(x j − xk) =  +1; if(x j − xk) > 0 0; if(x j − xk) = 0 −1; if(x j − xk) < 0 (7) The number of data values is represented by n. A positive S value indicates an upward variation, and a negative S value characterizes a downward variation. The normal approximation (Z statistic) is always used if the number of data values n is from 10 and above. We should also note that when there are tied/equal values, the accuracy of using the Z statistic will reduce if the data values are close to 10. To compute the value of the Z statistic, the variance of S ′V AR(S )′ is used [25] V AR(S ) = 1 18 n(n − 1)(2n + 5) − g∑ p=1 tp(tp − 1)(2tp + 5) (8) g represents the number of tied groups in the series (showing that the test takes the tied or equal values into consideration. The number of data values in the pth group is represented by tp. The test statistic Z is now obtained using the values of V AR(S ) and S [25]; Z =  S−1 √ V AR(S ) ; S > 0 0; S = 0 S +1 √ V AR(S ) ; S < 0 (9) The decreasing variation is discerned from a negative Kendall Z value, and an increasing trend is seen from a positive Z value. Both interpretations can be concluded to have a significant trend if and when the data’s p-value is lower than the significance level (< 5% = 0.05 in this case). The trend is not significant if the p-value is higher than the level of significance [30]. 3. Study Location Nigeria is lies between longitude 2 o E and 15 o E and lat- itude 4 o N and 14o N, having two major seasons, wet and dry [31]. The country is situated just above the geographical equa- tor and this results to high sunshine intensity. This study is focused on the analysis of temperature and global solar radia- tion for the southern eco-climatic region, and figure 1a shows all states in the southern region and 1b shows the eco-climatic region as well as the locations in study. The region is character- ized by her proximity to the Atlantic Ocean [32]. Table 1 gives more information about each location. 3.1. Data Source and Method of Analysis Monthly data for average ambient temperature in Celsius and the total monthly GSR (Global Global solar radiation) in kWh/m2/mo were obtained from the PVGIS (photovoltaic geo- graphical information system) for twelve years (2005-2016) at https://re.jrc.ec.europa.eu/pvg tools/en?tools.html#PVP. The total monthly GHI (kWh/m2/month) for all southern locations converted to average daily GHI in mega joules (M J/m2/day) and further analyzed with the average daily tem- perature (in Celsius). The analysis tool for this study is the Microsoft Excel soft- ware, which was used for the data conversion, storage and wran- gling. Data visualization was carried out by the Python pro- gramming language. All graphical representations and some statistical analysis were implemented. Packages in python pro- gramming like sklearn, seaborn, matplotlib, pandas, and numpy etc., were utilized for representations including box plots, linear regression, 1D KDE plots. All were compared for all locations in each zone. The 2D KDE employed the two (2) random variables (ra- diation and temperature) for its implementation. Temperature represented the x-axis and radiation represented the y-axis. 3 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 4 Figure 1. : (a) Map of Nigeria showing the southern region (b) Map of Nigeria showing the distribution of al eco-climatic zones, with the exact locations of the stations being studied. Table 1. Elevation and Location (coordinates) of all study locations. Location(State) Elevation Latitude Longitude (m) (o N) (o E) Abeokuta (Ogun) 30 7.155 3.339 Ado-Ekiti (Ekiti) 375 7.601 5.273 Akure (Ondo) 354 7.258 5.218 Ibadan (Oyo) 217 7.371 3.964 Ikeja (Lagos) 41 6.626 3.361 Osogbo (Osun) 352 7.754 4.581 Asaba (Delta) 44 6.025 6.693 Calabar (Cross River) 13 4.977 8.313 Benin City (Edo) 88 6.325 5.607 Port Harcourt (Rivers) 10 4.814 7.080 Uyo (Akwa Ibom) 73 5.048 7.907 Yenagoa (Bayelsa) 16 4.904 6.234 Abakiliki (Ebonyi) 46 6.312 8.107 Awka (Anambra) 103 6.218 7.083 Enugu (Enugu) 199 6.463 7.542 Owerri (Imo) 73 5.490 7.034 Umuahia (Abia) 154 5.525 7.517 4. Results and Discussion 4.1. Monthly trends Figures 2a, 2b, and 2c show the monthly variation of ra- diation for the Guinea savannah, mangrove swamp and tropi- cal rain forest regions respectively. They all have their lowest values between the months of July and August (July mostly). This variation corresponds approximately with the month (s) that have the lowest recorded temperature (Figures 2d, 2e, and 2f) in the study areas. The radiation trend steadily reduces from January till it reaches its minimum value in July, and then rises steadily between September and December. These radiation trends (Figures 2a, 2b, and 2c) correlates positively with that of the ambient temperature (Figures 2d, 2e, and 2f). The significant difference between the monthly trends of radiation and temperature for all locations is that while the peak radiation value for the locations are observed to be in Jan- uary (on average), the peak ambient temperatures are observed to be in the month of March (on average). This may be at- tributed to the inclusion or the increased longwave radiation around the months of March with in agreement with Soneye et al. [33]. The sky is clear and have no clouds from December through February, but the clouds begin to form in the month is March when rainfall begins. This increases the diffused radia- tion as the clouds acts as a greenhouse gas [34]. Figures 3 and 4 shows the mean radiation and temperature trends respectively for the 3 zones in study. They show that the mangrove swamp zone has lower values of temperature in the dry months (January - April), and relative to other zones, her temperature value is higher in the wet months. This could be attributed to the fact that the mangrove swamp zone has a closer proximity to the Ocean than other regions in the south. Figures 2b and 2e proves this as it shows that Calabar, Asaba, Yenegoa, and Uyo all have low values due to their close proximity to the Atlantic Ocean. The hottest locations from the monthly trends include Abak- iliki and Lagos, having monthly temperature trends that are far above others; this can be attributed to the industrial activities in those locations [35]. From Figure 4, we can see that the months with the lowest temperature values corresponds to months in the rainy/wet season which runs between the months of June and October approximately. 4.2. Annual Trends Results were gotten for the annual global solar radiation variations for the Guinea savannah, mangrove swamp and trop- ical rain forest regions in Figures 5a, 5b and 5c; and for the ambient temperature variations for the Guinea savannah, man- grove swamp and tropical rain forest regions in Figures 5d, 5e and 5f respectively. Sen’s slope is represented for all the afore- mentioned Figures in Table 2 and Table 3. From just mere observation, we can see from the figures that the annual radiation trends steeply increased in the latter parts of the trend. The trends for the average ambient temperature are relatively stable across all years. Figures 6 and 7 show the radiation and ambient tempera- ture trends respectively for all southern zones. From Figure 6, we can see that the radiation variation representation for the mangrove swamp zone is the lowest among all zones. If we compare this variation to that of ambient temperature in Figure 7, we will observe that all temperature trends for all zones are 4 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 5 Table 2. The M-K trend test results for global solar radiation showing the nature of each of their across all years (2005 - 2016). Mann p- Kendall’s Kendall’s Test value Sen’s Location Tau Statistic Statistic (Two- Intercept slope Test trend (S) (S) tailed) (Q) Interpretation Abakiliki -0.212 -14 -0.89 0.37 19.38 -0.008 FALSE NST (↓) Awka -0.212 -14 -0.89 0.37 18.95 -0.026 FALSE NST (↓) Enugu -0.273 -18 -1.17 0.24 19.24 -0.025 FALSE NST (↓) AdoEkiti -0.061 -4 -0.21 0.84 19.54 -0.005 FALSE NST (↓) Umuahia -0.273 -18 -1.17 0.24 18.49 -0.030 FALSE NST (↓) Owerri -0.212 -14 -0.89 0.37 18.44 -0.024 FALSE NST (↓) Port Harcourt -0.030 -2 -0.07 0.95 16.68 -0.009 FALSE NST (↓) Osogbo 0.061 4 0.21 0.84 18.92 0.019 FALSE NST (↑) Benin City 0.091 6 0.34 0.73 18.19 0.018 FALSE NST (↑) Abeokuta 0.182 12 0.75 0.45 18.47 0.036 FALSE NST (↑) Akure 0.091 6 0.34 0.73 19.06 0.014 FALSE NST (↑) Ibadan 0.061 4 0.21 0.84 18.79 0.018 FALSE NST (↑) Asaba -0.121 -8 -0.48 0.63 19.04 -0.016 FALSE NST (↓) Calabar 0.091 6 0.34 0.19 18.19 0.018 FALSE NST (↑) Ikeja -0.091 -6 -0.34 0.73 17.92 -0.029 FALSE NST (↓) Uyo -0.152 -10 -0.62 0.54 17.18 -0.009 FALSE NST (↓) Yenagoa -0.333 -22 -1.77 0.15 17.33 -0.050 FALSE NST (↓) *Note: Significance level = 5% (0.05); (↑) indicates an increasing variation and (↓) indicates a decreasing variation; NST - no significant trend Table 3. The M-K trend test results for average ambient temperature showing the nature of each of their across all years (2005 - 2016). Mann p- Kendall’s Kendall’s Test value Sen’s Location Tau Statistic Statistic (Two- Intercept slope Test trend (S) (S) tailed) (Q) Interpretation Abakiliki -0.20 -13 -0.82 0.41 26.45 -0.049 FALSE NST (↓) Awka -0.24 -16 -1.03 0.30 25.36 -0.038 FALSE NST (↓) Enugu -0.21 -14 -0.89 0.37 25.57 -0.052 FALSE NST (↓) AdoEkiti 0.02 1 0.00 1.00 24.16 2.22×−16 FALSE NST (↑) Umuahia -0.33 -22 -1.44 0.15 24.70 -0.036 FALSE NST (↓) Abeokuta 0.08 5 0.27 0.78 25.40 0.007 FALSE NST (↑) Port Harcourt -0.18 -12 -0.75 0.45 25.12 -0.018 FALSE NST (↓) Owerri -0.18 -12 -0.75 0.45 24.82 -0.020 FALSE NST (↓) Akure -0.08 -5 -0.27 0.78 24.91 -0.005 FALSE NST (↓) Ibadan 0.00 0 0.00 1.00 25.38 0.001 FALSE NST (↑) Benin City -0.30 -20 -1.30 0.19 25.17 -0.020 FALSE NST (↓) Osogbo 0.03 2 0.07 0.95 24.09 0.004 FALSE NST (↑) Asaba -0.27 -18 -1.17 0.24 25.86 -0.025 FALSE NST (↓) Calabar -0.29 -19 -1.24 0.22 25.59 -0.023 FALSE NST (↓) Ikeja -0.29 -19 -1.24 0.22 26.79 -0.017 FALSE NST (↓) Uyo -0.24 -16 -1.03 0.30 25.08 -0.025 FALSE NST (↓) Yenagoa -0.21 -14 -0.89 0.37 25.46 -0.023 FALSE NST (↓) *Note: Significance level = 5% (0.05); (↑) indicates an increasing variation and (↓) indicates a decreasing variation; NST - no significant trend relatively similar, with highest values for both the radiation and temperature observed in its most recent year (2016). The hottest locations in the mangrove swamp region for the annual trends from Figure 5e are Ikeja and Asaba, and this cor- responds to the locations with the highest radiation in Figure 5b. The same could be said for Abakiliki in Figures 5a and 5d for 5 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 6 Figure 2. Monthly trend of radiation for all eco-climatic locations (a) Guinea Savannah (b) Mangrove swamp and (c) Rainforest; average ambient tempera- ture trends (d) Guinea Savannah (e) Mangrove swamp and (f) Rainforest. Figure 3. Monthly trend of radiation for all eco-climatic zones in southern Nigeria. the guinea savannah zone, where the location of highest tem- perature corresponds to that of highest global solar radiation. The elevation height of the locations is a contributing factor to the temperature values as observed from the figures. It exten- sion, Ikeja shows that a low radiation value is contributed by a Figure 4. Monthly trend of temperature for all eco-climatic zones in southern Nigeria. Figure 5. Annual trend of radiation for all eco-climatic locations (a) Guinea Sa- vannah (b) Mangrove swamp and (c) Rainforest; average ambient temperature trends (d) Guinea Savannah (e) Mangrove swamp and (f) Rainforest. location’s proximity to a water body, directly related to the sea level. 6 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 7 Figure 6. Annual trends of radiation for all southern regions. Figure 7. Annual trends of average ambient temperature for all southern re- gions. Mann-Kendall trend test The M-K test has been adopted to analyze the significance of the trends of radiation and average ambient temperature along with Sen’s slope (Q). Results presented in Table 2 shows that the results for all locations in each vegetation zone for global solar radiation and in Table 3 for ambient temperature. Signifi- cance level of 5% (0.05) was used for the test. For the global solar radiation trends from Table 2, we can see that all locations in the Mangrove swamp vegetation region all have reducing trends apart from Calabar, characterized by their negative Sen’s slope. Apart from Calabar, they all have negative Sen’s slope value. The same reducing radiation trends can be observed in Ow- erri and Port Harcourt for the Rain Forest vegetation zone after showing negative Z values also. Five of the six locations that have increasing trends are in the Rain Forest vegetation region, these locations are characterized by their positive Sen’s slope and Kendall Z values. They include Abeokuta, Akure, Ibadan, Osogbo and Benin City for the SW region having Z values of 0.75, 0.34, 0.21, 0.21 and 0.34 respectively. This shows that the Rain forest vegetation region is majorly characterized by increased radiation trends. For the ambient temperature trends from table 3, as was similar with that of the radiation results, all locations in the Mangrove swamp vegetation region have reducing trends, char- acterized by their negative Sen’s slope. They have a Z-statistic value of -1.17, -1.24, -1.24, -1.03, -0.89 for Asaba, Calabar, Ikeja, Uyo, Yenagoa respectively. Figure 8. Box plots showing radiation distribution for all eco-climatic locations (a) Guinea Savannah (b) Mangrove swamp and (c) Rainforest; average ambient temperature distributions (d) Guinea Savannah (e) Mangrove swamp and (f) Rainforest. In the same way as the Mangrove vegetation region, the Guinea Savannah vegetation region also shows reducing tem- perature trends. This shows the similarity between the Man- grove vegetation region and the Guinea Savannah region. The Rain forest vegetation region has three (3) locations has increasing trends for ambient temperature, these locations are characterized by their positive Sen’s slope and Kendall Z values. They include Abeokuta, Ibadan and Osogbo of the Rain forest vegetation zone having Z values of 0.27, 0, and 0.07. The results for majority of these locations for temperature in table 3 approximately corresponds relatively to that of global solar radiation in Table 2. At 5% significance level, all radiation and temperature vari- ations accepted the null hypothesis Ho and rejected the alterna- tive hypothesis H1 after its probability value (p-value) of these series (increasing or decreasing) was found to be more than the significance level α = 0.05. This means that although most fig- ures reducing or increasing variations, this increase or decrease aren’t occurring with much significance. 4.3. Box Plots To discern the distribution of radiation and temperature for all locations, box plots have presented in Figures 8 (a – f) and 9 7 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 8 Table 4. Linear regression results for all Mangrove swamp locations. Asaba Calabar Ikeja Uyo Yenagoa Correlation (R) 0.95 0.92 0.89 0.92 0.88 Slope 1.75 2.65 1.87 2.46 2.36 Error in slope 0.19 0.36 0.30 0.34 0.40 R2 0.89 0.84 0.80 0.84 0.78 Intercept (C) -26.07 -50.53 -32.05 -44.30 -42.77 Error in C 4.89 9.32 7.90 8.51 10.13 SD 0.75 1.27 1.18 1.15 1.37 Figure 9. Box plots showing the average (a) radiation and (b) temperature dis- tribution over each southern eco-climatic zone. Table 5. Linear regression results for all Guinea savannah locations. Abakiliki Awka Enugu Ado-Ekiti Umuahia Correlation (R) 0.95 0.95 0.93 0.93 0.94 Slope 1.45 1.76 1.55 1.74 2.04 Error in slope 0.15 0.18 0.19 0.22 0.23 R2 0.91 0.90 0.86 0.86 0.89 Intercept (C) -18.59 -25.49 -20.08 -22.47 -31.82 Error in C 3.85 4.65 4.91 5.28 5.67 SD 0.72 0.79 0.89 0.93 0.86 Table 6. Linear regression results for all SW locations. Abeokuta Benin City Akure Ibadan Owerri Osogbo Port Harcourt Correlation (R) 0.91 0.96 0.93 0.94 0.95 0.95 0.90 Slope 1.94 1.96 1.61 2.13 2.18 2.17 2.55 Error in slope 0.29 0.18 0.20 0.25 0.23 0.21 0.38 R2 0.82 0.92 0.87 0.87 0.90 0.91 0.82 Intercept (C) -30.67 -30.71 -21.02 -35.19 -35.82 -33.22 -47.34 Error in C 7.33 4.57 4.94 6.47 5.62 5.15 9.63 SD 1.12 0.69 0.92 0.98 0.79 0.88 1.27 Figure 10. KDE plots showing radiation distribution in M J/m2/day for all locations in the Mangrove swamp zone (a) Asaba (b) Calabar (c) Ikeja (d) Uyo (e) Yenagoa. (a and b). A careful observation of the box plots show that their distribution for some locations is almost similar, characterized by a median that is almost uniform. Figures 8a and 8d shows the radiation and temperature dis- tribution respectively for all locations in the guinea savannah zone. Similar to that of locations in the mangrove swamp zone, all boxes representing radiation in the Guinea savannah zone (from Figure 8a), shows that the peak radiation value for all lo- cations is approximately equal. However, for the temperature distribution in Figure 8d, Abakiliki has the highest temperature value for all locations in the SE, with Umuahia and Ado-Ekiti having the lowest. The representation for the radiation and temperature in Fig- ures 8b and 8e respectively for the Mangrove swamp zone shows that Asaba has the highest radiation and temperature value; this corresponds to results of our monthly and annual line plots. The 8 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 9 Figure 11. KDE plots showing temperature distribution in Celsius for all loca- tions in the Mangrove swamp zone (a) Asaba (b) Calabar (c) Ikeja (d) Uyo (e) Yenagoa. Figure 12. KDE plots showing radiation distribution in M J/m2/day for all locations in the Guinea savannah zone (a) Abakiliki (b) Awka (c) Enugu (d) Ado-Ekiti (e) Umuahia. Figure 13. KDE plots showing temperature distribution in Celsius for all loca- tions in the Guinea savannah zone (a) Abakiliki (b) Awka (c) Enugu (d) Ado- Ekiti (e) Umuahia. temperature representations in the Figure 8e for each location has relatively smaller ranges than that of the radiation plot in Figure 8e. This could be attributed to the fact that it takes a certain threshold of temperature to bring about a notable shift in radiation [36]. All location in the mangrove swamp zone all have approximately the same peak radiation values from Fig- ure 8b, but the same cannot be said for the temperature plot in Figure 8e. Figures 8c and 8f represents the distribution of radiation and temperature for all locations in the rain forest zone. This region seems to have the widest range of radiation distribution for all her locations from figure 8e. The data distribution range for the temperature however, has some variations. As it was ear- lier explained in the monthly and annual line plots, Abeokuta in Ogun state has the highest temperature for all locations this region. The range of this box represented in Figure 8f is not also large; hence, the temperature is constantly high. Although scattered across different peak values, all locations in this zone have about the same distribution range from the highest to the lowest value. All plots in Figure 8 shows that the peak radiation is closely similar which is in contrast with that of the ambient tempera- ture. This observation shows that changes in the peak value of temperature to only results in a radiation peak value that cannot rise above a particular threshold value. This crystalizes the ar- gument that the radiation value of a location is affected by the geographical location (latitude, elevation height) also. Figure 9 shows the collation of radiation and temperature 9 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 10 Figure 14. KDE plots showing radiation distribution in M J/m2/day for all locations in the Rain Forest zone (a)Abeokuta (b)Awka (c) Ibadan (d) Osogbo (e) Owerri (f) Benin City (g)Port Harcourt. box plots respectively for all zones in the south. The average values of temperature and radiation are well represented in the figure. The global solar radiation representation from Figure 9a shows that the southern locations have between 14 and 20 M J/m2/day. Due to the fact that the global solar radiation variation depends majorly on the variation of ambient tempera- ture, we observe higher values of global solar radiation for the guineas savannah and rainforest regions. This is not so for the mangrove swamp zone. All southern regions had their values within the range of 23 oC to 26.5 oC from the temperature box plot in Figure 9b. Relating to the radiation plot in Figure 9, the mangrove swamp region’s close proximity to the Atlantic Ocean bring about the low temperature ranges, even though judging from the latitude of the region (closest to the equator), it should be slightly hotter. 4.4. Univariate KDE Distribution plots for temperature and global solar radiation for all locations being studied has been well represented (Fig- ures 10 - 16). The univariate Gaussian (normal) distribution was carried out to show the density of data distribution as well as to show the modal peaks and skewness of the distribution. The purpose of these plots is to show how the temperature and Figure 15. KDE plots showing temperature distribution in Celcuis for all loca- tions in the Rain Forest zone (a)Abeokuta (b)Awka (c) Ibadan (d) Osogbo (e) Owerri (f) Benin City (g)Port Harcourt. radiation data is being distributed across the data range, reveal- ing the median, modal peak(s)/densities, etc. Figures 10 show the radiation distribution for locations in the mangrove swamp zone. All locations seem to have at least a modal peak at about 20 M J/m2/day. Yenagoa have 2 modal peaks while Calabar and Uyo have the same distribution and density from the figure. The similarity between these pair of regions arises from the fact that they are in close proximity to each other. The temperature distributions for all locations in the man- grove swamp zone (Figure 11) all have the same Gaussian dis- tribution. Their densities peak at approximately 0.27 and they all have 2 modal peaks. The uniformity in the distributions of all temperature representations for the SS zone shows the uni- form climatic conditions in the region. From Figure 12, we see the radiation distributions for all locations in the guinea savannah locations. Similar to the man- grove swamp locations, the modal peak lies round 20 M J/m2/day, showing the similarity between the locations. In particular, the density/Gaussian distributions for Abakiliki, Enugu and Umuahia are more similar with each other, having a peak density value of about 0.15 around their modal peak. The temperature distribution locations in the guinea savan- nah zone (Figure 13) like that of the mangrove swamp zone. is 10 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 11 Figure 16. KDE plots showing distributions for all eco-climatic regions in the south for global solar radiation (a) Mangrove swamp (b) Rain Forest (c) Guniea savannah; and temperature (d) Mangrove swamp (e) Rain Forest (f) Guniea savannah. similar across all locations in the same zone. The distribution is the same with a Gaussian distribution that has 2 close modal peaks; this shows the data spread across range of values. The homogeneity in the distributions of all temperature representa- tions for the guinea savannah zone shows the uniform climatic conditions in the region just as was in that of the mangrove swamp. Figure 14 shows the radiation distribution for all locations in the rain forest region. Contrary to other zones (mangrove swamp and guinea savannah), the locations in the rain forest have a more similar density (Gaussian) distribution. The temperature distribution for all locations in the rainfor- est zone (Figure 15) is not a similar as of that for all locations in the mangrove swamp and guinea savannah zones. All locations show relatively similar Gaussian distributions. Figure 16 shows the combined distribution plots for tem- perature and radiation for all the southern zones. The density (KDE) plots for the global solar radiation for the Mangrove swamp, Rain Forest, and Guniea savannah (Figures 16a, 16b and 16c respectively) follows similar curves with that of the ambient temperature (Figures 16d, 16e and 16f respectively). This shows a strong positive coefficient of correlation between the global solar radiation and temperature for each zone. Figure 17. Regression plots showing the relationship between radiation and temperature for all locations in the Mangrove swamp zone. Figure 18. Regression plots showing the relationship between radiation and temperature for all locations in the Guinea savannah zone. 4.5. Linear Regression The goal of the linear regression to understand the relation- ship between the variation of ambient temperature and global11 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 12 Figure 19. Regression plots showing the relationship between radiation and temperature for all locations in the Rain Forest zone. solar radiation for all locations in each zone. The same scale was used for the plots to show the discrepancies in the trend lines. The independent variable was the temperature and the radiation was the dependent variable. Results from the regres- sion analysis have also be well represented in tables including the coefficient of correlation (R), Coefficient of determination (R2), slope, error in slope, intercept, error in intercept. standard deviation. From Figure 17, we can see the regression plots for all lo- cations in the mangrove swamp zone. Table 4 shows the re- sults from the regression. Asaba has the strongest relationship between radiation and temperature; characterized by its strong positive R value (the strongest for the zone), lowest error in slope and standard deviation from the mean. Other locations in the mangrove swamp zone from the figure all have strong positive values of R also. Since we used the same scale to plot for all locations in the region, we can see the differences in the radiation and temperature spread across the y and x axes re- spectively. This spread agrees with results from the box plots for the zone (Figures 8b and 8e). Yenagoa, although having a strong positive R value (0.88), represents the lowest in the man- grove swamp zone. Figure 18 represents the regression plots for all locations in the guinea savannah region. Table 5 shows the results from this regression. We can observe from the trend that all loca- tions have an almost similar relationship between radiation and temperature. This is characterized by the similar R value for all 5 locations in the region (R values ranges between 0.93 and 0.95). This very strong positive R value corresponds to lower errors in the slope and intercept of the trends, as well as the standard deviation (Table 5). This means that the guinea savan- nah zone constitutes the strongest relationship between global solar radiation and temperature for all zones. Figure 19 represents the regression plots for all locations in the SW region. Table 6 shows the results from this regression. From our results, Benin City has the strongest positive R value (0.96), followed by Owerri and Osogbo Ibadan (0.95 each). The lowest R value is observed in Port Harcourt (0.90). This is so because from our box plot results for radiation and temperature in figure 8c and 8f respectively, a high temperature value for Port Harcourt does not bring about a high radiation value for the same location in the region. In conclusion, all southern locations have strong positive re- lationships between radiation and temperature. This proves that for any change in the temperature variations in the region, there is a corresponding strong similar change in the global solar ra- diation variation [37, 38]. 5. Conclusion We have shown the relationship between the variation of so- lar irradiation and average ambient temperature for locations in the eco-climatic zones in the south of Nigeria. This region is made up of 17 locations and 2 eco-climatic zones (mangrove swamp, guinea savannah and tropical rainforest). The study was done to have a better understanding of the trends, distribu- tions and relationships between the two variables. The Mann- Kendall trend test has been used to study the significance of the variations of both variables in all regions and in general the following results and inferences were outlined. • The trends of solar irradiance and ambient temperature for all stations and eco-climatic zones are not increasing or decreasing annually with significance from the results of the MK test. • Linear regression, and distribution plots depict the posi- tive relationship between both variables (Global solar ra- diation and temperature) across all stations, albeit, some variations in the strong positive correlation for some loca- tions were observed. This may be attributed to the differ- ences in elevation height, climatic conditions, and local weather, etc. • Results show that the climate and vegetation of a region contributes majorly to the variation of radiation and tem- perature. Inhomogeneity of data or results for locations in the same zones may be attributed to local meteoro- logical conditions and effects like carbon emission from industries, proximity to major water bodies, etc. • Although 12 years’ data might not be sufficient to con- clude in terms of climatological conditions, the results show that meteorological conditions of the study loca- tions are almost uniform in variation. This proves that latitudinal locations are one of the major contributors to 12 Okono et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 588 13 global solar radiation and temperature variations, espe- cially for locations that are relatively close in geographi- cal proximity. Acknowledgments We thank the referees for the positive enlightening com- ments and suggestions, which have greatly helped us in making improvements to this paper. Code Availability: The code associated with this analysis can be assessed from https://github.com/Emmaestro001/JNSPS- Article-Analysis. 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