Comparative Analysis of Trigonometric and Polynomial Models in Meteorological Parameter Prediction for Sub-Saharan West African Stations

Energy's role in global development has been increasingly recognized as pivotal, as evidenced by extant research. Its significance extends beyond environmental improvement to encompass worldwide comfort and wellbeing [1]. The environmental performance of systems, particularly in the realms of heating, air conditioning, and ventilating of buildings, is influenced by solar cells and collectors, green power plants, and cooling towers. These systems depend on meteorological parameters such as air temperature, wind speed, wind direction, air pressure, and relative humidity, each contributing variably to the cooling and heating of the environment [2], [3], [4], [5].

Research has shown that atmospheric energy consumption calculations, particularly in regions with high wind speeds, can be enhanced by incorporating wind speed parameters into energy generation models [6], [7], [8], [9], [10], [11]. Precise planning, optimization, and performance forecasting of solar technology and environmental system control are fundamentally grounded in weather modeling [3], [4], [12], [13], [14]. However, the accessibility of meteorological data in Africa is hampered by several challenges. Financial constraints, mismanagement of funds by political office holders, and population migration are notable factors impeding energy production in African nations. The development of meteorological data characteristics for African energy production studies is based on these varied challenges. Additionally, various mathematical and statistical methods have been employed to determine data for forecasting and weather modeling in diverse settings. The creation of weather data modeling utilizes these methods [15], [16], [17]. Several studies have highlighted the influence of climatic factors on solar energy and the implications for energy concerns, particularly wind energy, in different global regions.

Calculations of Global Solar Radiation (GSR) have been undertaken by numerous researchers [18], [19], [20], yet these estimates often exhibit variations from the results reported by Kasten and Czeplak [21] and Poudyal et al. [22]. Such variations encompass factors like air pressure and air temperature [23], and the positioning of rainfall [24], [25], [26], [27]. It has been noted that weather limitations, including relative humidity, air temperature, air pressure, wind speed and direction, as well as environmental elements like sand and haze, show tendencies to fluctuate over the years [28]. Research conducted by various authors [3], [28], [29], [30],[31], [32] indicates that climatic disparities in urban areas are significantly influenced by suburban activities due to environmental factors.

In studies focusing on correlation models for global diffuse and slanted irradiation [33], it was found that air temperature notably influences other weather variables, including sunshine hours and relative humidity, as observed in Valencia, Italy. The coefficient of determination for these models was reported to range between 0.75 and 0.85 [34]. Research has also been conducted to establish polynomial relationships between relative sunshine and the clearness index in various environments [35]. Over a span of 15 years, statistical analyses of worldwide insolation data were performed at six locations in Pakistan [36]. Additionally, Aweda et al. [3] have contributed to environmental awareness by modeling weather characteristics in selected African sub-stations. Regression models based on weather data collected in Oman between 1987 and 1992 have been developed for predicting future environmental developments [15], [37], [38].

The impact of climate change on national development has been acknowledged as either positive or negative, presenting a range of challenges. This variability can significantly influence global energy growth and development. Notably, there has been limited research on climatic studies in the African sub-region and Asian countries [17], [39], [40]. Consequently, this study aims to model meteorological parameters in selected Sub-Saharan West African stations through the comparison of trigonometric and polynomial functions. This approach intends to enhance occupant awareness by providing more accurate predictive models for meteorological parameters.

For the purpose of this study, a range of meteorological variables was sourced from the HelioClim-1 Solar Radiation Data, as delineated in previous research [41]. These variables included air pressure, relative humidity, air temperature, rainfall, wind speed, and wind direction. Data retrieval occurred on March 5, 2023, and encompassed a time frame from January 1980 to December 2022, spanning 42 years. The data, in CSV format, were downloaded following protocols outlined in prior studies [37], [42].

The study was conducted across selected locations within the West African sub-region, as indicated in Figure 1. Six sites were specifically chosen for their distinct geographic and climatic characteristics: Abidjan, Abuja, Bamako, Conakry, Dakar, and Niamey. Data spanning from 1980 to 2022 were utilized for all these stations. Distinctions between hinterland and coastal regions at each station were systematically tabulated (Table 1), providing a clear differentiation of the geographical context of each location.

The collected data were subjected to descriptive statistical analysis, specifically employing mean and standard deviation, to evaluate the meteorological parameters. Subsequently, these parameters were modeled using both polynomial and trigonometric functions. To compare the efficacy of these models, the adjusted coefficient of determination and RMSE were utilized. The preference for the adjusted coefficient of determination over the standard coefficient of determination (R²) was to mitigate biases arising from the differences in the number of parameters in the polynomial and trigonometric models. In instances where a contradiction between the adjusted R² and RMSE was observed, the RMSE was given precedence. This was due to its focus on measuring the agreement between actual and predicted values, which is crucial for this study.

The parameters of these functions were estimated using the Econometric View (E-view 7.0) software. Statistical significance was determined at a 5% threshold, with a p-value of less than 0.05 deemed to indicate statistical significance. Table 2 provides a comprehensive summary of the functions employed in this study, with 'm' representing the month in all equations.

Table 3 delineates the results from the comparative analysis of polynomial and trigonometric functions in modeling meteorological parameters across six African capital cities. It was observed that the trigonometric function exhibited superior performance over the polynomial function in modeling temperature for Abidjan (Adj. R² = 0.98 7627, RMSE = 0.110032), Abuja (Adj. R² = 0.569552, RMSE = 0.761431), Bamako (Adj. R² = 0.854366, RMSE = 0.940537), Conakry (Adj. R² = 0.964589, RMSE = 0.098281), and Niamey (Adj. R² = 0.876062, RMSE = 0.999433). However, in Dakar (Adj. R² = 0.937577, RMSE = 1.0258864), the polynomial function outperformed the trigonometric model (Table 2). In the cases of Abidjan, Abuja, and Bamako, the trigonometric function yielded more accurate predictions for atmospheric pressure compared to the polynomial function, whereas in other locations, the polynomial model provided superior results. Regarding wind speed, the trigonometric function was found to be more effective in Abidjan, Abuja, Bamako, and Niamey, while in Conakry and Dakar, the polynomial function demonstrated better performance (Table 3). Additionally, the trigonometric function consistently resulted in lower RMSE for rainfall across all locations compared to the polynomial function (Table 2).

In the subgraph (A) of Figure 2 illustrates the trend in mean monthly temperature, showing a consistent decrease in Abidjan and Abuja, while in Bamako, Conakry, Dakar, and Niamey, a decline was observed between July and August (Figure 2). Mean monthly relative humidity across all locations was found to increase consistently from January to August in the subgraph (D) of Figure 2). Air pressure remained relatively constant throughout the year with minor variations month-to-month in the subgraph (C) of Figure 2. From January to April, a consistent decrease in monthly mean wind speed was recorded in Bamako, Dakar, and Niamey, whereas in Abidjan, an increase was noted from February to March, followed by a decrease towards year-end (in the subgraph (D) of Figure 2). A rise in monthly mean rainfall was observed in all locations from January to mid-year, followed by a consistent decrease towards year-end (in the subgraph (E) Figure 2).

The analysis of the monthly variations in meteorological parameters across the studied stations, as depicted in Figure 1, revealed distinct patterns. Air temperature exhibited a sinusoidal trend, peaking around April, May, and June, as shown in the subgraph (A) of Figure 2. This period represents the hottest months across all observed stations. Notably, Dakar and Abidjan recorded the highest temperatures, ranging between 34.5℃ and 34.7℃. The cooler months, specifically January and December, were characterized by lower temperatures in Dakar, approximately 20℃. August, typically the wettest month in Africa, marked a significant temperature decline at all stations. It has been observed that Dakar, influenced by the country's distinctive natural characteristics and the implications of human activities, exhibits a notable range in temperature extremes.

Air temperature and relative humidity are interconnected meteorological parameters. The study found that air temperature significantly influences relative humidity, which varied between 15% to 80% across the different study areas, as shown in the subgraph (B) of Figure 2. The highest relative humidity levels, around 80%, were recorded in Abidjan, Conakry, and Abuja. Dakar exhibited the lowest relative humidity, indicating a wetter climate possibly influenced by the city's topography. It is established that meteorological factors such as cloud cover, wind speed, and rainfall impact relative humidity. A notable decrease in relative humidity was observed in January at all stations, potentially due to the onset of winter conditions.

It was observed from the subgraph (C) of Figure 2 that Conakry and Abidjan registered the highest air pressure readings, each measuring 1005 hPa, predominantly in July. While these peak values were recorded during this month, the average pressure for both locations typically fluctuated around 1000 hPa. The investigation further revealed a gradual increase in atmospheric pressure, culminating in the highest recorded values in July. Conversely, the lowest temperature readings across all the observed stations were recorded in the same month, indicating a significant correlation between air pressure and temperature. Specifically, higher air temperatures were associated with elevated air pressure. Abuja, in contrast, exhibited the lowest air pressure, approximately 960 hPa, noted in March. An increase in air pressure was observed in December, following a consistent decline in November. Notably, November emerged as the month with the second-highest temperatures across all study locations.

Further analysis, as depicted in the subgraph (D) of Figure 2, focused on wind speed measurements in selected West African sites. The highest wind speed was recorded in Dakar, reaching 5.3 m/s, while Bamako reported the lowest at 0.56 m/s. The average minimum wind speed across all stations was identified as 1.5 m/s. These findings suggest that the wind speeds in West African stations are generally low, rendering these locations less suitable for wind energy production.

Rainfall patterns, as shown in the subgraph (E) of Figure 2, revealed that rainfall was relatively low during January, February, March, April, October, November, and December. Conakry experienced the highest rainfall in July, indicating favorable climatic conditions for its inhabitants. A gradual increase in rainfall was observed across all locations, peaking in July. This indicates that July is the month of highest rainfall. In contrast, Abuja experienced its heaviest rainfall in August, approximately 500 mm. Other locations like Abidjan, Bamako, and Dakar also recorded significant rainfall values. Notably, the values highlighted in bold represent the highest adjusted R² and the lowest RMSE, indicating the most effective model for each parameter and city.

Table 3, Table 4, and Table 5 encompass monthly parameter estimates from 1980 to 2022 for air temperature, air pressure, wind speed, rainfall, and relative humidity across the West African stations. These meteorological characteristics were derived from the HelioClim satellite's archive and modeled using specifically developed polynomial and trigonometric models. The models' parameters (a, b, c, d, and e) were determined based on the predictor variable for the 12 calendar months. Figure 3, Figure 4, Figure 5, Figure 6, and Figure 7 graphically represent the outcomes of the data under investigation, offering visual insights into the temporal patterns and variations of these meteorological parameters.

In Table 4, the comparative analysis of the best models for temperature and relative humidity across various African cities is presented. For Abidjan, the trigonometric model was identified as the most effective for temperature, evidenced by an adjusted R² of 0.987627 and RMSE of 0.110032 (Table 3), and a significant p-value of less than 0.01. In contrast, the polynomial model was found to be superior for relative humidity in Abidjan, as indicated by an adjusted R² of 0.965789 and RMSE of 0.633172 (Table 3), with a p-value signifying significance at the 5% level (Table 4). Similarly, in Abuja, Bamako, and Conakry, the trigonometric model showed better performance for temperature, while for Dakar, the polynomial regression model was more effective (adjusted R² = 0.937577, RMSE = 1.0258864) as outlined in Table 3.

In the analysis presented in Table 4, trigonometric models were identified as the most effective for relative humidity in Abuja, Bamako, Dakar, and Niamey, as indicated by high adjusted R² values and low RMSEs. Conversely, in Abidjan and Conakry, polynomial models demonstrated superior performance (Table 3). Table 4 summarizes the best model estimates for temperature and relative humidity, with all study locations showing significant p-values, ranging between 0.0000 and 0.02045 for pressure, and between 0.000577 and 0.432696 for wind speed. The regression results were significant at all stations for pressure (p<.05), except for wind speed in Niamey, where the regression did not reach significance (p>.05) as shown in Table 5.

Regarding wind speed, polynomial functions were determined to be the best model for Abidjan, Abuja, and Bamako, while trigonometric models were more suitable for Conakry, Dakar, and Niamey (Table 3). For rainfall, trigonometric functions consistently outperformed polynomial functions across all considered stations (Table 3), with p-values below 0.05, indicating a well-fitting model (Table 6).

The range of wind speed values across the studied stations was determined to be between 2.538059 and 3.707578 m/s. The p-values for these stations varied from 0.003827 to 0.432696. When these results were compared with those documented in source [5], it was evident that the models used in this study yielded improved performance. This enhancement in predictive accuracy can be ascribed to the specific climatic conditions prevailing at the examined stations. Furthermore, it was ascertained that the polynomial function exhibited superior performance over the trigonometric function in modeling both air pressure and wind speed. As presented in Table 6, the significance of the models was affirmed by p-values less than 0.05 (p<.05) at all stations, validating the statistical significance of the models in these contexts.

The results were further validated by plotting graphs of the actual versus predicted monthly mean for each meteorological parameter in each of the six African capital cities. These visual representations, as illustrated in Figure 3, Figure 4, Figure 5, Figure 6, and Figure 7, revealed a general agreement between actual and predicted values for all meteorological parameters, except for rainfall, where some discrepancies were observed in certain months (Figure 7).

This format is consistent across Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, facilitating easy comparison between actual observations and model predictions for each city.

This study, utilizing data from the HelioClim satellite archive, analyzed meteorological variables including air temperature, air pressure, wind speed, relative humidity, and rainfall in selected Sub-Saharan West African stations. The study employed five-parameter models (a, b, c, d, and e) and concluded that trigonometric and polynomial functions were the most suitable for modeling these meteorological parameters. Notably, Dakar was observed to experience both the highest and lowest temperatures, while Abidjan and Dakar recorded the highest and lowest relative humidity, respectively. Conakry exhibited the highest air pressure, with Abuja having the lowest. In terms of wind speed, Dakar reported the highest values, whereas Bamako had the lowest. Furthermore, Conakry experienced the highest rainfall, contrasting with Dakar's minimal precipitation.

The regression analysis of the weather data indicated that air temperature had a higher RMSE than other factors, with the polynomial function generally outperforming the trigonometric function. However, for air pressure predictions, the trigonometric function was more accurate in Abidjan, Abuja, and Bamako, while the polynomial function was preferable in other locations. For wind speed, the trigonometric function surpassed the polynomial model in Abidjan, Abuja, Bamako, and Niamey, whereas the opposite was true for Conakry and Dakar. Moreover, the trigonometric function consistently yielded the lowest RMSE for rainfall across all locations. The study posits that the developed models can serve as effective tools in climatic studies, enhancing understanding of weather conditions in various regions.

Therefore, this study concludes that the trigonometric function generally demonstrates superior performance in modeling meteorological parameters in most West African stations assessed. This work could guide further research and development in Africa's meteorological studies.

It is recommended that African governments prioritize the establishment of more research centers dedicated to data collection for research and application. This initiative is crucial for raising awareness about environmental cleanliness and the urgent need to curb deforestation and bush burning across the continent. Such practices contribute to ozone depletion, potentially leading to increased solar radiation and adversely affecting agricultural productivity. Furthermore, it is imperative that African governments formulate and implement policies to mitigate environmental pollution and disruptions, which have significantly contributed to the continent's ecological challenges.