Influence of Temperature Fluctuations on Rainfall Variations Using Statistical and Machine Learning Approaches over Selected Stations in Nigeria

Temperature changes have been identified as a global challenge, with serious consequences for global rainfall distribution over decades, resulting in low water distribution by water distribution companies, most notably in African sub-regions, specifically Nigeria. Temperature and rainfall variability, as reported by Aweda and Samson [1], has become a serious challenge around the world as a result of researcher forecasts and predictions. According to Buishand and Brandsma [2], temperature changes have a significant impact on rainfall variation. According to Intergovernmental Panel on Climate Change (IPCC) [3], diplomatic groups on climate change lead to serious challenges on climate, which pose effects on water reservoirs as well as drought, which mostly affects all areas causing death and serious challenges over various governments at all levels in Africa sub-regions. According to the report, countries such as India have greatly improved the development and management of water resources as important on rainfall over temperature changes in the country, indicating that rainfall is a seasonal occurrence [4]. Aweda et al. [5], on the other hand, report that the government at all levels should create good rules for the utilization of rainfall collected during the period of heavy rainfall for the benefit of farmers and domestic usage during periods of high temperatures, whereby drainage, streams, and rivers may have dried across the country. IPCC [6] stated in the report that there are variations in the rise of temperature in the Indian subcontinent due to changes in the country’s weather conditions. This, however, applies to what has been observed in Nigerian stations, where air temperature has a significant effect on the rainfall observed. Rainfall varies in time with a large amount of value experienced on a monthly, annual, and seasonal basis; however, different authors such as Aweda et al. [1, 7, 8] reported that there is a significant decline in rainfall at various stations due to temperature variation. According to Parthasarathy et al. [9], there is a significant decline trend over some specific areas in India. However, it was discovered in the Nigeria region that some locations experienced a decrease in rainfall as a result of high-temperature variations that occurred during a specific period of the year [1]. It has been observed that there is a decrease in the trend of rainfall across some detachments [10, 11] except as a result of global warming which could increase the dryness in different areas of some locations in the monsoon rainfall which could be less than 2.4% during 1979-2009 as compared to what was observed during 1949-1978 in the India region [4, 12]. However, as reported by Aweda and Samson [1], an alternative is the case in the Nigeria sub-region. However, due to dynamic seasonal wet season flow, recurrent development in rainfall production of meteorological conditions in primary and secondary turbulences shaped the activities of the wet season across some selected areas [1, 4, 5]. According to Ranade et al. [13], there are approximately seventeen junctions established crosswise throughout Asia’s Pacific region. This, however, was not found in the African sub-region. Rainfall has been reported to be a major factor influencing water quality, hydrology, and vegetation, which contributes to the development of any region in terms of agricultural production and the quality of an individual’s livelihood. However, this could result in a global weather variation. Furthermore, the effect of rainfall on temperature across the African region has been observed to be a significant prerequisite in the preparation and organization of quality water possessions for agricultural use. Furthermore, according to the report, farmers in the northern part of Nigeria primarily practice irrigation farming for the production of their crops during the country’s dry season, which helps the country’s food production and reduces the importation of some food items. However, research has shown that rainfall and temperature have contributed to the growth of any environment, resulting in agricultural planning and management in various regions, which can lead to drought and food scarcity in any environment [14-17]. Researchers such as Gentilucci et al. [16-20] reported that floods cause economic losses, reducing the importance of food security in society. However, the effect of drought in any environment, as reported by various authors Fuwape et al. [15-20], demonstrates that there is a need in agriculture, irrigation, and energy for the development and implementation of appropriate mechanisms for predicting rainfall and temperature using machine learning algorithms. Water engineering management has been reported as one of the major activities in water management in Nigeria. Oloruntade et al. [21] conducted research on the principle of wet-water storage and dry-water extraction in rivers and, most likely, the ocean. Climate change has been observed to have a significant impact on rainfall and temperature variability, resulting in a long-term effect on some meteorological parameters [22]. Historically, the Nigeria sub-region has been observed to significantly contribute to the production of water for their nearby neighbouring countries [23-25]. This aids the development of those countries and food production for their development. According to the report, farming has played an important role in the development of Nigeria, with an increase in the production of agricultural products [1] as a result of Nigeria’s rainfall and temperature variability. This has met the increased demand for food by citizens through improved water quality and temperature variability, resulting in increased food production [26]. Several revisions to rainfall and temperature reported both positive and negative influences across any study region [5, 21, 27-29]. However, reclassification of rainfall and temperature variation revealed that the rising or gathering of rainwater depends on location [30]. As a result, this study focused on temperature fluctuations and their impact on rainfall variations in selected Nigerian stations using statistical tools and machine learning. The data for this study were obtained from the HelioClim satellite archive. Many authors have worked on the variability of rainfall and temperature in African sub-regions, both temporally and spatially [21]. Rainfall trends in Nigeria have been reported by various authors, according to a report [1, 31-33]. However, the objective of this study is: (1) to investigate the relationship between data-driven atmospheric practices and agricultural productivity in arid regions by determining the variation of rainfall and the effect of temperature on it; (2) to analyze the effectiveness of predictive models in forecasting atmospheric and agricultural outcomes by studying the similarities between air temperature and rainfall patterns in the study areas using statistical tools and machine learning algorithms; (3) to evaluate the potential of data science in reducing resource wastage in agriculture by checking the performance of the quadratic regression over all stations considered using the R², RMSE, MSE and MAE based on different models.

Figure 2 depicts the yearly correlation results of selected Nigerian stations labelled Osogbo, Ikeja, Ibadan, Akure, Ado-Ekiti, and Abeokuta. The Machine Learning Algorithm (MLA) method revealed that the minimum rainfall in Osogbo was recorded in 1984, while the minimum temperature was recorded in 1980, and the maximum rainfall was recorded in 2015, while the maximum temperature was recorded in 2018. This demonstrates that the outcome of machine learning can predict what will happen in the future. The rainfall and temperature findings show that almost every station studied has a nearly identical pattern. This demonstrates that all of the selected Nigerian stations are in the same climatic region. However, the results show that all of the Nigerian stations studied have nearly the same rainfall and temperature pattern. Furthermore, the results show that the rainfall and temperature patterns are nearly identical at each station, indicating that the rainfall and temperature at the chosen station move at a similar rate. Short-term rainfall and temperature predictions are critical when rainfall and temperature output are increasing. According to the results, the maximum rainfall and temperature for the stations ranged from 200 to 240 mm and 25.8 to 26.8℃, while the minimum rainfall and temperature ranged from 110 to 140 mm and 24.2 to 24.6℃. This shows that the rainfall at the reported stations will be beneficial to farmer production.

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Figure 2. Yearly correlation between rainfall and temperature for the stations considered

As shown in Figure 3, the heat map for air temperature and rainfall revealed that both parameters are in correlation with each other. The result shows that the more the air temperature the more the rainfall for the selected stations.

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Figure 3. The heat map for rainfall and temperature

The result as shown in Figure 4 and Figure 5 revealed the frequency distribution of rainfall and temperature for all the stations considered. It was observed that the highest frequency observed in all the stations is around 70. This shows that all the stations are located around the same climatic zone. However, the minimum value recorded across the station was observed in Ibadan (Frequency < 0.1) and Ikeja (Frequency < 0.1). This was due to the proximity of the two stations nearer to the ocean which could influence the temperature of the area. More so, the frequency distribution of rainfall in all the stations considered revealed that the highest frequency was observed in Ado-Eiti (Frequency > 110). While the lower frequency distribution observed is found in Abeokuta (Frequency < 1.0).

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Figure 4. Frequency distribution graph for temperature across the selected stations

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Figure 5. Frequency distribution graph for rainfall across the selected stations

3.1 Temperature and rainfall statistical analysis

The result in Table 2 shows the monthly mean temperature and rainfall in the selected six locations in Nigeria. The result shows that the maximum monthly temperature was reported in March in all locations while rainfall was at its peak in September in all locations. The lowest temperature in all locations was obtained in August while rainfall was at its lowest values in December in five of the locations (Osogbo, Ibadan, Akure, Ado-Ekiti and Abeokuta) while in Ikeja, the least rainfall was obtained in January (Table 2). This result indicates similarities in temperature and rainfall patterns in the study areas.

Table 2. Monthly mean temperature and rainfall in the selected six locations

The Kolmogorov-Smirnov test was used to test the normality of the variables and the result as presented in Table 3 reveals that rainfall was not normally distributed in all locations (p < 0.05) while temperature followed normal distribution in only Ibadan (p = 0.182, p > 0.05), Akure (p = 0.200, p > 0.05) and Abeokuta (p = 0.107, p > 0.05) while that obtained in other locations were not normally distributed (p < 0.05). Hence, the relationship between variables was determined using Spearman rank correlation which is non-parametric correlation and the result is as presented in Table 3. Result showed that in all locations, there was a significant negative relationship between temperature and rainfall (p < 0.05) indicating that as the temperature increases significantly, there is a significant decrease in rainfall. This negative relationship was more pronounced in Ikeja (r = -0.408, p = 0.000, p < 0.01) and Abeokuta (r = -0.408, p = 0.000, p < 0.01) compared with that obtained in other locations.

Table 3. Summary of the result of normality and rank correlation for the relationship between rainfall and temperature in the selected locations

**Significant at 1% (p < 0.01), *significant at 5% (p < 0.05).

Different functional forms of regression models (linear, logarithm, inverse, quadratic and cubic regression) were used to examine the relationship between rainfall as the dependent variable and temperature as the predictor variable and the result obtained is as presented in Table 4. The result shows that in all locations, different regression models were significant (p < 0.05) indicating that a regression relationship exists between rainfall as the response variable and temperature as the predictor variable. The result shows that the cubic regression model was found to be outperformed other models in Osogbo (R² = 0.1450, RMSE = 137.6308), Ikeja (R² = 0 .174, RMSE = 94.07199), Ibadan (R² = 0.152, RMSE = 130.4768), Akure (R² = 0.125, RMSE = 133.3977), Ado-Ekiti (R² = 0.144, RMSE = 133.8516) and Abeokuta (R² = 0.188, RMSE = 109.9167). The performance of the quadratic regression in Ikeja was better than that of other locations as the R² in this location was higher than others while the RMSE was lower than that obtained in other locations. Based on the best model among the competing regression models, the regression equation as shown in Eqs. (1)-(6) was written for each of the locations.

For Osogbo:

$\hat{R}_i=-6486.285+580.639 T_i-12.539 T_i^2$          (1)

Ikeja:

$\hat{R}_i=-8129.771+676.661 T_i-13.720 T_i^2$          (2)

Ibadan:

$\hat{R}_i=-9624.811+829.338 T_i-17.442 T_i^2$          (3)

Akure:

$\hat{R}_i=-15391.175+1296.119 T_i-26.868 T_i^2$          (4)

Ado-Ekiti:

$\hat{R}_i=-5763.411+518.90 T_i-11.263 T_i^2$          (5)

Abeokuta:

$\hat{R}_i=-6392.832+564.808 T_i-12.038 T_i^2$          (6)

Table 4. Summary of the result of different regression models for the relationship between rainfall and temperature

**Significant at 1% (p < 0 .01), *significant at 5% (p < 0 .05). Bolded values are the highest adjusted R² and least value of MSE and RMSE (MSE- Mean Square Error, RMSE- Root Mean Square Error).

Table 5. The average results of the Machine Learning Algorithm (MLA) for rainfall and temperature data for the selected stations used

Table 5 shows the average results of the performances of the different 24 Machine Learning Algorithms (MLA) of regression type for the selected stations used. For all the stations, it was observed that temperature has is highest R² (1.00) in 15 models as shown in the result. while the lowest temperature value was Ensemble Boosted Trees (R² = -0.41). This implies that these Machine Learning Algorithms (MLA) models with R² (1.00) performed better in terms of fitness as compared with other MLA models. In terms of the forecasting performance of these MLA based on RMSE, the best forecasting Machine Learning model was Ensemble Boosted Trees (RMSE = 1.0637). The result also reveals that Narrow Neural Network gave the least (MAE = 0.029318), while the lowest MSE for the station is (MSE = 0.0019088) meaning that these ML algorithms are less formed as compared with other MLA models. For the rainfall in all the observed stations, the MLA shows that the stations have their highest value in terms of R² (1.00) this can be observed in five models namely Interaction Linear, Robust Linear, Narrow Neural Network, Medium Neural Network, and Trilayered Neural Network. While other models as their value of less than 1.00. However, their values range between 0.98 and 0.99. The highest RMSE (28.761) value observed for the rainfall in all the observed stations is the Fine Gaussian SVM model while the lowest model value was observed in the Interaction Linear model with RMSE (9.3881). Furthermore, it was observed that the highest MLA model in terms of the rainfall for MAE (20.582) was the Coarse Tree model and the lowest value was observed in Ensemble Boosted Trees (1.639). The highest MSE value and the lowest value observed in the stations are as follows Fine Gaussian SVM (827.19) and Trilayered Neural Network (90.207) respectively. This shows that the models used for this study can be categorised as good models for the future forecast and prediction of temperature and rainfall.

The study's findings offer vital insights for improving climate and water resource management in Nigeria. By identifying key climate variables affecting water resources, the research guides policymakers in developing targeted interventions, such as enhancing infrastructure to improve resilience against climate change. The application of machine learning models enables more accurate predictions, supporting better early warning systems and resource allocation. These insights can also optimize water usage in agriculture, promote sustainable practices, and strengthen community-based climate education. Ultimately, integrating these findings into national strategies will bolster Nigeria's efforts to manage climate-related risks and ensure sustainable water resources.