A periodical of the Faculty of Natural and Applied Sciences, UMYU, Katsina
ISSN: 2955 – 1145 (print); 2955 – 1153 (online)
ORIGINAL RESEARCH ARTICLE
1*Emmanuel Vezua Tikyaa, 1Titus Nyitar, 2Terver Sombo, 1Tertsea Igbawua
1Department of Physics, Joseph Sarwuan Tarka University, PMB 2373 Makurdi, Nigeria
2Department of Industrial Physics, Joseph Sarwuan Tarka University, PMB 2373 Makurdi, Nigeria
*Corresponding author: evtikyaa@uam.edu.ng.
The acknowledgement of road traffic noise as a major environmental pollutant has spurred the formulation of models to predict road traffic noise using fundamental variables. This study aims to modify and assess the efficacy of certain empirical models in predicting equivalent continuous noise levels in Makurdi metropolis, utilizing specific traffic flow and meteorological parameters. Measurements were conducted at two roundabouts and two junctions within Makurdi metropolis from November to December, 2022. The traffic flow and meteorological parameters were fitted to the continuous noise level data using a nonlinear multivariate regression technique, and the validation metrics were computed to determine which model performed best. The results of noise levels indicated that the mean Leq values across the study locations ranged from 68.65 ± 1.67 to 70.72 ± 0.90 dBA. These noise levels surpassed the National Environmental Standards and Regulations Enforcement Agency’s recommended threshold of 60 dBA by 8.65 to 10.72 dBA. Modelling results revealed that all the models performed well; however, Model-Leq3 exhibited an outstanding performance with the highest R2 value of 0.9999 at Wurukum Roundabout. Model-Leq3 is therefore recommended for predicting road traffic noise in Makurdi metropolis and other Nigerian cities.
Keywords: Empirical models, Traffic flow, Equivalent continuous noise level, Makurdi metropolis, Road traffic noise.
Noise refers to unpleasant, undesirable or annoying sound (Igbokwe and Adindu, 2023; Haruna et al., 2024). It is unavoidable and can impact us even when we are not actively aware of it. While our eyes can be deliberately closed, our ears are always open, making it impossible to intentionally shut out unwanted sounds. Our hearing system is constantly active even when we are sleeping, making us subconsciously aware of sounds around us (Goines and Hagler, 2007). Noise has become a growing health threat and if left unchecked could lead to hazardous health conditions (Balashanmugan et al., 2013). The World Health Organization (WHO) ranks noise pollution as the third major environmental threat after air and water pollution (Oyedepo, 2014; Karthik and Partheeban, 2015; Haruna et al., 2024). Noise is a widespread problem in Nigeria, yet it receives minimal attention from environmental authorities tasked with protecting the country’s ecosystem. The impact of noise on human health depends on exposure duration and volume (Naser, 2021). The World Health Organization has recognized seven harmful health effects of noise on humans. These are: hearing impairment, interference with spoken communication, impaired task performance, negative social behavior and annoyance reactions, sleep disturbance, mental health disturbance, and cardiovascular disturbances (Goines and Hagler, 2007).
Road traffic noise originates from various vehicle components, including engines, tires, exhaust systems, and brakes (Haruna et al., 2023). Many cities in developing countries face serious health issues due to noise pollution (Ede et al., 2024). Recent growth in the transportation sector has increased noise levels, accounting for 70 to 80% of urban noise pollution (Yadav et al., 2023). Several studies have shown that road traffic noise is the primary source of noise in cities (Igbokwe and Adindu, 2023). Fast-growing cities with poor planning and weak regulations suffer from excessive levels of road traffic noise (Nwobi-Okoye et al., 2015; Igbokwe and Adindu, 2023).
Models that predict road traffic noise are crucial for designing roads and assessing potential changes to existing roads, enabling the anticipation and mitigation of traffic noise. Several road traffic noise models have been developed by researchers worldwide. However, these models are not universally applicable, as they depend on the factors specific to the environment in which they were developed. Consequently, there is a need to modify some of these models to suit our environmental setting. Furthermore, several traffic noise models have continued to evolve with the hope of getting more accurate ones. Anila and Bino (2013) developed a statistical regression model in their study to predict road traffic noise under Indian conditions, using the average speed of light vehicles, the percentage of three-wheelers, the percentage of heavy vehicles, and traffic volume as variables. The model yielded a satisfactory result, with a coefficient of determination (R²) value of 0.804. The drawback of this model is the negligence of meteorological parameters and the consideration of the average speed of light vehicles instead of considering the average speed of all vehicle types. Kumar and Srinivas (2014) assessed the ambient noise levels produced by traffic in an urban area of Secunderabad. The average equivalent noise levels (Leq) were measured at various spots in commercial and residential areas. The predicted Leq was obtained using the Calixto model, and the correlation between the measured and predicted Leq showed good R² values of 0.733 and 0.750, respectively, for both study locations. The variables used in the model were vehicle flow and the percentage of heavy vehicles. The drawback of this model is the negligence of vehicle speed and meteorological variables. Kaushal and Rampal (2017) measured the traffic noise in Jammu city, India, across different seasons and formulated a mathematical model to predict noise levels at various intersections. The researchers used data on atmospheric temperature, surface temperature, relative humidity, vehicle count and vehicular speed to calculate noise levels through regression analysis. The model had a coefficient of determination (R2) value of 0.56. Heavy vehicles produce noise levels 5 to 10 dB higher than those of light vehicles (Nikolić et al., 2014). Consequently, the percentage of heavy vehicles needs to be included in the model to obtain a better result.
Similarly, the authors neglected meteorological parameters, which have a significant influence on road traffic noise. In another study, Ibili and Owolabi (2019) investigated traffic noise and related factors, including traffic composition, volume, and speed, in Ondo town’s Central Business District. The collected data was fed into the Calculation of Road Traffic Noise (CRTN) model. Results showed that the measured Leq for the study locations were above the World Health Organization (WHO) and Federal Highway Administration (FHWA) permissible limits. The CRTN model demonstrated strong predictive power, with an R² value of 0.943, indicating a reliable and accurate prediction of road traffic noise. Again, this model neglected meteorological parameters and lacked the use of a large sample size. The present study aims to modify and assess the effectiveness of various road traffic noise prediction models to determine the best fit for Makurdi metropolis.
2.1 Measurement of Sound Pressure Level
Sound levels are usually measured on a decibel (dB) scale. The decibel is a logarithmic measure comparing two pressures (Enda and Eoin, 2014). The sound pressure level (Lp) in decibels is calculated thus (Akinkuade and Fasae, 2015; Jhanwar, 2016):
\(L_{p}(dB) = 10{\log_{10}\left( \frac{p}{p_{o}} \right)}^{2} = 20\log_{10}\left( \frac{p}{p_{o}} \right)\) \((1)\)
where p is the root-mean-square sound pressure in Newton per square meter and po is the standard reference sound pressure with a value of \(2 \times 10^{- 5}Nm^{- 2}\) or \(20\mu Pa\)which is equivalent to the threshold of human hearing. The sound level meter, which utilizes the above equation, is designed to measure the sound pressure level.
2.2 Equivalent Continuous Noise Level
The equivalent continuous noise level (Leq), expressed in A-weighted decibels (dBA) is a parameter universally used in environmental noise measurement. It is the average sound energy the human ear receives over a certain time frame (Alam et al., 2001) and is given by (Thattai et al., 2017; Alani et al., 2020):
\(L_{eq} = 10\log_{10}\frac{1}{n}\left\lbrack \sum_{i = 1}^{n}{10^{\frac{L_{pi}}{10}}} \right\rbrack\) (2)
where Lpi is the ith sound pressure level reading in dBA and n is the number of measurements in the assessed time. The A-weighted decibels (Leq) is a widely accepted measure for describing traffic noise levels (Nwaogazie and Ofem, 2014; Sukeerth et al., 2017).
2.3 Traffic Density
Traffic density, K is the total number of vehicles per unit length of a roadway. It is given by (Ogunlade et al., 2021; Odiakose and Iyeke, 2024):
\(K = \frac{N_{t}}{L}\) (3)
where Nt is the total number of vehicles and L is the length of the roadway in kilometers (km).
2.4 Traffic Flow Rate
The traffic flow rate, Q, is the total number of vehicles traversing a certain cross-section during a given period of time and is expressed as (Ugwuanyi et al., 2017; Ogunlade et al., 2021):
\(Q = \frac{N_{t}}{T}\) (4)
where T is the time interval in hours (hrs). The flow rate is analogous to the discharge or the flux of a stream. The maximum possible flow rate of any road is called its capacity.
2.5 Space Mean Speed
The space mean speed, Vs is the average speed of vehicles over a given road segment (Ugwuanyi et al., 2017). This definition of space mean speed is also known as the fundamental relation of traffic flow theory (Ugwuanyi et al., 2017; Odiakose and Iyeke, 2024):
\(Q = V_{s}K\) (5)
When vehicles travel the same road length, that is, L = L1 = L2 = L3 = … = Ln, then Vs is given by (Ugwuanyi et al., 2017; Ogunlade et al., 2021; Odiakose and Iyeke, 2024):
\(V_{s} = \frac{L}{\left( \frac{1}{N_{t}}\sum_{i = 1}^{n}\left( \frac{L}{T_{i}} \right)^{- 1} \right)}\) (6)
where Ti is the time interval of the ith vehicle in hours (hrs).
2.6 Annual Average Daily Traffic
Annual Average Daily Traffic (AADT) is the total number of vehicles traveling across a roadway in a year, divided by 365 days. It is a metric generally applied in transportation planning and engineering. In 1992, the American Association of Highway and Transport Officials (AASHTO) introduced a method of calculating AADT without biases from seasons or days of the week by using an “average of averages” approach in their Traffic Data Programs. Recent innovations from traffic data providers now offer more detailed AADT data, broken down by roadside, day of the week, and time of day (Ugwuanyi et al., 2017).
This study was conducted in Makurdi, the capital of Benue State. Makurdi is located in the central part of Nigeria between Latitudes 7° 38ʹ and 7° 50ʹ N, and Longitudes 8° 24ʹ and 8° 38ʹ E (Abah, 2013). It is traversed by the country's second-largest river, the River Benue. The town sits on a major transportation route connecting Nasarawa State in the North and Enugu State in the South by road and rail (Shabu and Tyonum, 2013), with a landmass of approximately 800 km² and a population of about 367,588, based on the 2006 National Population Census data (Adeke et al., 2018). The area has two distinct seasons; the dry and wet seasons. The dry season typically begins in November and lasts until March, while the wet season commences in April and terminates in October, with an average annual rainfall of between 1200 and 2000 mm (Akaahan et al., 2016). Makurdi typically experiences high temperatures throughout the year (Abah, 2013), with average daily temperatures varying between 21 °C and 37 °C (Hula, 2010; Odoh and Jidauna, 2013). The relative humidity of the area fluctuates with the seasons, reaching its mean monthly peak of approximately 92% during the wet season (Onah et al., 2020). Two major roundabouts (i.e., Wurukum and High Level Roundabouts) and two busy junctions (i.e., SRS and Ankpa Ward Junctions) were selected for this study.
The road traffic sound pressure level was measured using a microprocessor digital sound level meter, model SL-5858. The meter was mounted on a stand 1.5 m above ground and 0.5 m from the operator to minimize the echoing of sound waves from the body. In order to avoid the effect of sound reverberation, measurements were taken at a distance of at least 3.5 m from any reflecting surface. The meter was positioned at a distance of 1.5 m from the edge of road shoulder. Readings from the meter were recorded every 10 minutes from 7:00 am to 6:00 pm each day at each study location, and the hourly equivalent continuous noise levels were computed for each location. Ambient temperature and relative humidity were measured at the study sites using a digital thermo-hygrometer, whereas the wind speed was measured with the aid of a digital thermo-anemometer. The instruments were mounted on a stand 1.5 m above the ground, and readings from the instruments were recorded every 10 minutes from 7:00 am to 6:00 pm each day at each study location.
A traffic count was conducted using Closed-Circuit Televisions (CCTVs), commonly known as CCTV cameras. The CCTVs were mounted on separate stands and positioned alongside the road at the study locations to capture moving vehicles from 7:00 am to 6:00 pm each day. The devices were positioned in areas with a free flow of traffic. The CCTVs were linked to mobile phones through Wi-Fi for monitoring. A 20000 mAh power bank powered each CCTV. A 4 m length of road section was marked on each roadway, and the number of vehicles crossing the marked sections was recorded. The CCTVs were positioned at each leg of the roundabouts and junctions to record only the incoming vehicles. The hourly number of vehicles for each day was later extracted by replaying the videos from the CCTVs on laptops, and the hourly average number of vehicles for each study location was computed in accordance with the American Association of State Highway and Transportation Officials (AASHTO) guidelines for calculating Annual Average Daily Traffic (AADT). The vehicles were counted and grouped into three (3) categories as motorcycles/tricycles (MT), cars/buses/vans (CBV) and heavy vehicles (HV). The road traffic sound pressure measurements, meteorological parameter measurements, and traffic counts were carried out at two major roundabouts and two busy junctions (cross intersections) within Makurdi metropolis for five days (i.e., Mondays, Wednesdays, Fridays, Saturdays, and Sundays) at each study location. All measurements at a particular location were carried out concurrently.
The modified multivariate models are presented in Table 1. The empirical model equations are labelled: Model-Leq1, Model-Leq2, Model-Leq3, Model-Leq4, and Model-Leq5. The table also highlights the modifications made to the original model equations.
Table 1: The Modified Multivariate Models
| Model | Model Name | Model Parameters | Modified Model Equation | Modification |
|---|---|---|---|---|
| Model-Leq1 | Mod. CRTN | \[PHV,Q,V_{s},T_{in}\] | \(L_{eq} = a_{1}\log Q + a_{2}\log\left\lbrack a_{3} + V_{s} + \frac{500}{V_{s}} \right\rbrack + a_{4}\log\left\lbrack 1 + a_{5}\frac{PHV}{V_{s}} \right\rbrack + a_{6}T_{in} + a_{7}\) | Tin added to the original model equation. |
| Model-Leq2 | Mod. Kaushal and Rampal | \(T_{a},RH,N_{t},V_{s}\) | \(L_{eq} = a_{1} + a_{2}T_{a} + a_{3}RH + a_{4}N_{t} + a_{5}V_{s} + a_{6}T_{in}\) | Tin added, while Ts is expunged from the original model equation. |
| Model-Leq3 | Mod. Anila and Bino | \[{RH,T_{a},V_{w},MT,CBV, }{HV,N_{t},PHV,K,Q,T_{in}}\] | \(L_{eq} = a_{1} + a_{2}RH + a_{3}T_{a} + a_{4}V_{w} + a_{5}MT + a_{6}CBV + a_{7}HV + a_{8}N_{t} + a_{9}PHV + a_{10}K + a_{11}Q + a_{12}T_{in}\) | RH, Ta, Vw, MT, CBV, HV, K, Q and Tin added, while S and T are expunged from the original model equation. |
| Model-Leq4 | Mod. Calixto | \[PHV,Q,T_{in}\] | \(L_{eq} = a_{1} + a_{2}\log\left\lbrack Q \times \left( 1 + a_{3}\frac{PHV}{100} \right) \right\rbrack + a_{4}T_{in}\) | Tin added to the original model equation. |
| Model-Leq5 | Mod. Anila and Bino quad. | \[{RH,T_{a},V_{w},MT,CBV, }{HV,N_{t},PHV,K,Q,T_{in}}\] | \(L_{eq} = a_{1} + a_{2}RH^{2} + a_{3}T_{a}^{2} + a_{4}V_{w}^{2} + a_{5}MT^{2} + a_{6}CBV^{2} + a_{7}HV^{2} + a_{8}N_{t}^{2} + a_{9}PHV^{2} + a_{10}K^{2} + a_{11}Q^{2} + a_{12}T_{in}\) | S and T are expunged from the original model equation and the remaining variables are squared, while Tin and square of RH, Ta, Vw, MT, CBV, HV, K and Q are added to the equation. |
where RH is the relative humidity in %, Ta is the ambient temperature in oC, Vw is the wind speed in km/hr, MT is the number of motorcycles and tricycles, CBV is the number of cars, buses and vans, HV is the number of heavy vehicles, Nt is the total number of vehicles, PHV is the percentage of heavy vehicles, K is the traffic density in veh/m, Q is the traffic flow rate in veh/hr, Vs is the space mean speed in km/hr, Ts is the average surface temperature in oC, T is the percentage of three wheelers, S is the average speed of light vehicles in km/hr, Tin is the time index and a1, a2, a3, …, a12 are regression constants. The time index Tin is a continuous count over the 24 hr period of the day beginning from 00:00 to 1:00 hr assigned index 1, 1:00 to 2:00 hrs assigned index 2, …, 7:00 to 8:00 hrs assigned index 8, 8:00 to 9:00 hrs assigned index 9, 9:00 to 10:00 hrs assigned index 10, … and 17:00 to 18:00 hrs assigned index 18.
The modified model equations are presented in Table 1. Figures 5 to 8 (5, 6, 7, & 8) presents a display of the model performance for the prediction of equivalent continuous noise level (Leq) using some traffic and meteorological parameters as exogenous variables for the different study locations, while the correlation between predicted and measured Leq across the study locations is illustrated in Figure 9 to 12. It can be observed from the graphs that all the models performed well, as there is only a slight variation between the measured and predicted Leq. The models were validated using performance functions such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Coefficient of determination (R2) (Tikyaa et al., 2018; Patel et al., 2024):
\(\mathbf{RMSE =}\sqrt{\frac{\sum_{\mathbf{i = 1}}^{\mathbf{n}}\left( \mathbf{L}_{\mathbf{eqm}}\mathbf{-}\mathbf{L}_{\mathbf{eqp}} \right)^{\mathbf{2}}}{\mathbf{n}}}\) (7)
\(\mathbf{MAE =}\frac{\mathbf{1}}{\mathbf{n}}\sum_{\mathbf{i = 1}}^{\mathbf{n}}\left| \mathbf{L}_{\mathbf{eqm}}\mathbf{-}\mathbf{L}_{\mathbf{eqp}} \right|\) (8)
\(\mathbf{MAPE =}\frac{\mathbf{1}}{\mathbf{n}}\sum_{\mathbf{i = 1}}^{\mathbf{n}}\frac{\left| \mathbf{L}_{\mathbf{eqm}}\mathbf{-}\mathbf{L}_{\mathbf{eqp}} \right|}{\mathbf{L}_{\mathbf{eqm}}}\mathbf{\times 100}\) (9)
\(R^{2} = 1 - \frac{\sum_{i = 1}^{n}{(L_{eqm} - L_{eqp})^{2}}}{\sum_{i = 1}^{n}{(L_{eqm} - {\overline{L}}_{eqm})^{2}}}\) (10)
where Leqm is the measured equivalent continuous noise level, Leqp is the predicted equivalent continuous noise level, \({\overline{L}}_{eqm}\)is the mean of the measured Leq and n is the number of measurements.
The measured values of road traffic sound pressure level (Lp) from the field survey were used to compute the equivalent continuous noise level (Leq) at each study location using equation 2. Similarly, the total number of vehicles (Nt) was used to calculate the traffic density (K), traffic flow rate (Q), and space mean speed (Vs) using Equations 3, 4, and 6, respectively. Results of diurnal variation of equivalent continuous noise level (Leq), total number of vehicles (Nt), traffic density (K), traffic flow rate (Q), and space mean speed (Vs) across the study locations are presented in Figures 1(a-e) to 4(a-e).
Figure 1: Diurnal Variation of: (a) Leq, (b) Nt, (c) K, (d) Q and (e) Vs at Wurukum Roundabout
Figure 2: Diurnal Variation of: (a) Leq, (b) Nt, (c) K, (d) Q and (e) Vs at High Level Roundabout
Figure 3: Diurnal Variation of: (a) Leq, (b) Nt, (c) K, (d) Q and (e) Vs at SRS Junction
Figure 4: Diurnal Variation of: (a) Leq, (b) Nt, (c) K, (d) Q and (e) Vs at Ankpa Ward Junction
The hourly variation of Leq, Nt, K, Q and Vs across the study locations is represented in Figure 1(a-e) to 4(a-e). Figure 1a indicates that a minimum Leq of 65.59 dBA occurred between 7 and 8 am, whereas a maximum Leq of 72.56 dBA occurred between 1 and 2 pm at Wurukum Roundabout. The Wurukum market and most of the motor parks in Makurdi's metropolis are located close to the Wurukum Roundabout. The low noise level recorded in the morning at this location may be attributed to the low traffic and commercial activities, while the high noise level recorded in the afternoon could be due to the high traffic and commercial activities. This could also be attributed to temperature variation at the location. Sound level increases as the temperature increases (Loonkar, 2023). Temperatures in Makurdi metropolis are usually low in the morning and high in the afternoon. In Figure 2a, a minimum Leq value of 67.54 dBA was recorded between 8 and 9 am, whereas a maximum Leq of 69.88 dBA was recorded between 12 noon and 1 pm at High Level Roundabout. The High Level Roundabout is situated close to the motor park and High Level market. Again, the low noise level experienced in the morning could be due to the low traffic and commercial activities, whereas the high noise level observed at this location in the afternoon could be attributed to the high traffic and commercial activities. It could also be due to temperature variation at the location. At SRS Junction (Figure 3(a)), the Leq reached a minimum value of 65.87 dBA from 7 to 8 am and a maximum value of 70.98 dBA from 11 am to 12 noon. The road to Akawe Torkula Polytechnic, Special Science Senior Secondary School and Joseph Sarwuan Tarka University, Markurdi is linked to SRS Junction. The road leading to the Northern part of the country is also linked to this junction. The morning’s varying noise levels may be due to lighter traffic early on and heavier traffic later, as travelers head to the northern part of the country and workers commute to their workplaces. Figure 4(a) shows that a minimum Leq of 68.96 dBA and a maximum Leq of 72.00 dBA were obtained from 12 noon to 1 pm and from 2 to 3 pm, respectively, at Ankpa Ward Junction. The road to Makurdi modern market is linked to this junction. There is also an Event Centre located close to this junction. The low noise levels recorded between 12 noon to 1 pm could be attributed to low traffic and low commercial activities at the Event Center and other places around this junction, while the high noise level experience between 2 and 3 pm could be due to high traffic and high commercial activities as customers rush to Modern market and music is played to entertain customers at the Event Centre. The diurnal mean Leq of 69.31, 68.98, 68.65, and 70.72 dBA were found at Wurukum Roundabout, High Level Roundabout, SRS Junction, and Ankpa Ward Junction respectively. SRS Junction and Ankpa Ward Junction recorded the minimum and maximum mean Leq of 68.65 and 70.72 dBA, respectively. These noise levels are above the safety threshold of 60 dBA prescribed by the National Environmental Standards and Regulations Enforcement Agency (NESREA). This implies that those who reside or spend most of their time around these areas are consistently exposed to harmful noise levels. The Leq at the study sites is comparable to that reported for other towns, such as Abeokuta metropolis, Port Harcourt, and the Federal Capital Territory (FCT) Abuja, by Oguntoke et al. (2019), Amah and Udeh (2023), and Ekom et al. (2024), respectively.
Similarly, the results of traffic parameters revealed that at Wurukum Roundabout, the minimum values of Nt, K, Q and Vs were obtained from 7 to 8 am, while the maximum values were recorded from 9 to 10 am as illustrated in Figure 1(b-e). The high values of traffic parameters recorded between 9 and 10 am could be due to heavy traffic flow as travelers leave the motor parks, traders and workers rush to Wurukum market and work respectively, while the low values of traffic parameters recorded between 7 and 8 am could be attributed to low traffic flow due to low number of vehicles taking off from the parks and low number of vehicles conveying traders to Wurukum market. The High Level Roundabout had minimum values of Nt, K, Q, and Vs from 7 to 8 am and maximum values from 3 to 4 pm, as illustrated in Figure 2(b-e). The low traffic parameters at this location in the morning could be a result of low traffic flow due to a low number of vehicles leaving High Level park or conveying traders to High Level market, while the high evening traffic parameters values likely resulted from increased traffic flow as travelers, traders and workers headed home after the day’s activities. In the same light, minimum values of Nt, K, Q, and Vs were recorded from 7 to 8 am, while the maximum values occurred from 5 to 6 pm at SRS Junction, as shown in Figure 3(b-e). The low traffic parameters recorded in the morning at this location could be a result of low traffic flow due to a low number of vehicles leaving Makurdi to Northern Nigeria, while the significant levels of traffic parameters obtained in the evening could be attributed to high traffic flow as travelers, students and workers return from the day’s activities. In Figure 4(b-e), minimum values of Nt, K, Q and Vs were found between 7 and 8 am, whereas the maximum values were obtained between 3 and 4 pm at Ankpa Ward Junction. Again, the low traffic parameters recorded at this location in the morning could be as a result of low traffic flow due to low number of vehicles conveying traders and customers to the Modern market, while the elevated levels of traffic parameters obtained in the evening could be linked to high traffic flow as traders and customers return from the market. In general, the results indicated substantial variation in noise levels and traffic flow across various locations and times of the day, confirming the trend of inconsistent variation in noise levels and traffic flow. These results align with those of Oguntoke et al. (2019) and Alani et al. (2020).
The results displayed in Tables 2 to 5 show the regression coefficients and model validation statistics, whereas Figures 5 to 8 present a display of the model performance for the prediction of the equivalent continuous noise level, Leq. Similarly, Figures 9 to 12 show the regression plots of measured and predicted Leq for the four study locations, demonstrating the goodness-of-fit of the five empirical models.
Table 2: Regression Constants and Validation Parameters of Model-Leq1-5 for Wurukum Roundabout
| Model | Regression Constants | Validation Parameters | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| a1 | a2 | a3 | a4 | a5 | a6 | a7 | a8 | a9 | a10 | a11 | a12 | RMSE | MAE | MAPE | R2 | |
| Model-Leq1 | 5131.66 | 2308.5102 | -40.168 | 9.5836 | -6.9777 | -0.3489 | 17492.321 | 0.2114 | 0.1777 | 0.2545 | 0.9866 | |||||
| Model-Leq2 | 67.5977 | 0.2899 | -0.1205 | 0.4853 | -92.6303 | -0.4841 | 0.2217 | 0.1781 | 0.2538 | 0.9853 | ||||||
| Model-Leq3 | 33.249 | 0.8016 | 3.2934 | -0.0227 | -0.185 | -0.1784 | 1.5083 | -0.1438 | 136.1216 | 1.8197 | -0.1438 | 0.9459 | 0.0056 | 0.0044 | 0.0063 | 0.9999 |
| Model-Leq4 | 24.7778 | 23.1597 | 2.998 | 0.2794 | 0.3850 | 0.2913 | 0.4170 | 0.9690 | ||||||||
| Model-Leq5 | 14.3847 | 0.0046 | 0.0419 | -0.1112 | -0.000002 | -0.00001 | 0.0019 | 0.00001 | -13.4287 | 0.0004 | -0.00001 | 0.5956 | 0.0186 | 0.0129 | 0.0186 | 0.9999 |
Table 3: Regression Constants and Validation Parameters of Model-Leq1-5 for High Level Roundabout
| Model | Regression Constants | Validation Parameters | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| a1 | a2 | a3 | a4 | a5 | a6 | a7 | a8 | a9 | a10 | a11 | a12 | RMSE | MAE | MAPE | R2 | |
| Model-Leq1 | 13.9222 | 13.5919 | 62.9845 | 2.094 | 3.1452 | -0.0142 | -9.539 | 0.2730 | 0.2217 | 0.3221 | 0.8658 | |||||
| Model-Leq2 | 12.1582 | 0.9651 | 0.3472 | -1.8428 | 352.098 | 0.814 | 0.1151 | 0.0955 | 0.1384 | 0.9783 | ||||||
| Model-Leq3 | 70.6538 | 0.0861 | 0.1932 | 0.0282 | 13.6886 | 13.6853 | 15.9601 | -7.1502 | 108.6603 | 0.9916 | -6.7893 | 0.5115 | 0.0827 | 0.0654 | 0.0951 | 0.9876 |
| Model-Leq4 | 67.2612 | 0.1717 | 303.0303 | 0.1008 | 0.1804 | 0.1412 | 0.2051 | 0.9759 | ||||||||
| Model-Leq5 | 18.5096 | 0.0042 | 0.0449 | -0.1095 | -0.0001 | -0.0002 | -0.046 | 0.00002 | 10.6129 | 0.0001 | 0.00002 | 0.1216 | 0.0745 | 0.0616 | 0.0893 | 0.9892 |
Table 4: Regression Constants and Validation Parameters of Model-Leq1-5 for SRS Junction
| Model | Regression Constants | Validation Parameters | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| a1 | a2 | a3 | a4 | a5 | a6 | a7 | a8 | a9 | a10 | a11 | a12 | RMSE | MAE | MAPE | R2 | |
| Model-Leq1 | 15.7107 | 3.3740 | -40.5063 | 37843.2033 | 0.0011 | 0.4399 | 4.0439 | 0.4559 | 0.3726 | 0.5386 | 0.9306 | |||||
| Model-Leq2 | 44.8353 | 0.3626 | 0.1201 | -0.9976 | 190.6507 | 0.4136 | 0.3397 | 0.2879 | 0.4180 | 0.9696 | ||||||
| Model-Leq3 | 17.5302 | 0.2525 | 0.8596 | -4.5057 | 0.6244 | 0.6337 | 0.5998 | -0.1420 | -2.4544 | -1.3464 | -0.1420 | 0.3775 | 0.2989 | 0.2347 | 0.3413 | 0.9730 |
| Model-Leq4 | 44.0653 | 7.8259 | -43.0953 | -0.0252 | 0.3653 | 0.3044 | 0.4446 | 0.9688 | ||||||||
| Model-Leq5 | 44.645 | -0.0027 | 0.0023 | 27.1442 | 0.0001 | 0.0003 | -0.0288 | -0.0001 | 33.2993 | 0.0002 | -0.00005 | 1.6217 | 0.1101 | 0.0782 | 0.1150 | 0.9958 |
Table 5: Regression Constants and Validation Parameters of Model-Leq1-5 for Ankpa Ward Junction
| Model | Regression Constants | Validation Parameters | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| a1 | a2 | a3 | a4 | a5 | a6 | a7 | a8 | a9 | a10 | a11 | a12 | RMSE | MAE | MAPE | R2 | |
| Model-Leq1 | 16.0972 | 2.3652 | -41.8816 | 240.0453 | -0.0079 | -0.1100 | 11.4963 | 0.3212 | 0.2627 | 0.3746 | 0.8677 | |||||
| Model-Leq2 | 102.9222 | -0.4659 | -0.2477 | 0.5273 | -100.7159 | -0.4535 | 0.1881 | 0.1455 | 0.2068 | 0.9692 | ||||||
| Model-Leq3 | 73.2995 | -0.0828 | -0.2543 | 1.2473 | 0.1169 | 0.1121 | -2.7002 | 2.6289 | 127.3174 | -2.5645 | 0.2629 | 0.3486 | 0.0551 | 0.0445 | 0.0634 | 0.9960 |
| Model-Leq4 | 62.1695 | 1.9019 | -175.383 | 0.0973 | 0.2251 | 0.1781 | 0.2531 | 0.9732 | ||||||||
| Model-Leq5 | 21.8594 | 0.0044 | 0.0252 | 0.0587 | 0.00001 | 0.00004 | 0.0071 | 0.00002 | 5.969 | -0.0009 | 0.00003 | 0.5502 | 0.1622 | 0.1397 | 0.1982 | 0.9645 |
Figure 5: Prediction Results of Leq using the five Models with Exogenous Variables for Wurukum Roundabout
Figure 6: Predicted Results of Leq using the five Models with Exogenous Variables for High Level Roundabout
Figure 7: Prediction Results of Leq using the five Models with Exogenous Variables for SRS Junction
Figure 8: Prediction Results of Leq using the five Models with Exogenous Variables for Ankpa Ward Junction
Figure 9: Predicted Leq Versus Measured Leq for Wurukum Roundabout
Figure 10: Predicted Leq Versus Measured Leq for High Level Roundabout
Figure 11: Predicted Leq Versus Measured Leq for SRS Junction
Figure 12: Predicted Leq Versus Measured Leq for Ankpa Ward Junction
The regression coefficients and model validation statistics of the four (4) study locations are presented in Table 2 to 5. Table 2 (Wurukum Roundabout) revealed that Model-Leq1 had RMSE, MAE, MAPE and R2 values of 0.2114, 0.1777, 0.2545 and 0.9866 respectively, whereas Model-Leq2 recorded RMSE, MAE, MAPE and R2 values of 0.2217, 0.1781, 0.2538 and 0.9853 respectively. The RMSE, MAE, MAPE, and R² values of 0.0056, 0.0044, 0.0063, and 0.9999 were recorded for Model-Leq3, while Model-Leq4 had RMSE, MAE, MAPE, and R² values of 0.3850, 0.2913, 0.4170, and 0.9690, respectively. Model-Leq5 recorded 0.0186, 0.0129, 0.0186, and 0.9999 values for RMSE, MAE, MAPE, and R², respectively. The results indicate that Model-Leq4 has the least performance, as it has the highest values of RMSE, MAE, and MAPE, and the lowest R2 value. In contrast, Model-Leq3 performed best, with the lowest values of RMSE, MAE, and MAPE and the highest R2 value. At High Level Roundabout (Table 3), RMSE, MAE, MAPE and R2 values of 0.2730, 0.2217, 0.3221 and 0.8658 were respectively recorded for Model-Leq1, while Model-Leq2 had RMSE, MAE, MAPE and R2 values of 0.1151, 0.0955, 0.1384, and 0.9783 respectively. Model-Leq3 recorded 0.0827, 0.0654, 0.0951 and 0.9876 for RMSE, MAE, MAPE and R2 respectively, while Model-Leq4 had 0.1804, 0.1412, 0.2051 and 0.9759 values for RMSE, MAE, MAPE and R2 respectively. Model-Leq5 had RMSE, MAE, MAPE and R2 values of 0.0745, 0.0616, 0.0893 and 0.9892 respectively. The model with the least performance in this location is Model-Leq1, whereas the one with the best performance is model Model-Leq5. RMSE, MAE, MAPE and R2 values of 0.4559, 0.3726, 0.5386 and 0.9306 were respectively obtained for Model-Leq1 at SRS Junction (Table 4), whereas Model-Leq2 had 0.3397, 0.2879, 0.4180 and 0.9696 for RMSE, MAE, MAPE and R2 respectively. Model-Leq3 recorded RMSE, MAE, MAPE and R2 values of 0.2989, 0.2347, 0.3413 and 0.9730 respectively, while RMSE, MAE, MAPE and R2 values of 0.3653, 0.3044, 0.4446 and 0.9688 were respectively obtained for Model-Leq4. RMSE, MAE, MAPE and R2 values of 0.1101, 0.0782, 0.1150 and 0.9958 were respectively recorded for Model-Leq5. Again, Model-Leq1 is the model with the least performance, whereas Model-Leq5 performed best. In the same light, at Ankpa Ward Junction (Table 5), Model-Leq1 recorded RMSE, MAE, MAPE and R2 values of 0.3212, 0.2627, 0.3746 and 0.8677 respectively, however, 0.1881, 0.1455, 0.2068 and 0.9692 values of RMSE, MAE, MAPE and R2 were respectively obtained for Model-Leq2. Model-Leq3 had RMSE, MAE, MAPE and R2 values of 0.0551, 0.0445, 0.0634 and 0.9960 respectively, whereas Model-Leq4 recorded 0.2251, 0.1781, 0.2531 and 0.9732 for RMSE, MAE, MAPE and R2 respectively. RMSE, MAE, MAPE and R2 values of 0.1622, 0.1397, 0.1982 and 0.9645 were respectively obtained from Model-Leq5. Model-Leq1 and Model-Leq3 have shown the least and best performance respectively.
The above analysis revealed that the coefficient of determination (R2) of Model-Leq1, Model-Leq2, Model-Leq3, Model-Leq4 and Model-Leq5 ranged from 0.8658 to 0.9866, 0.9692 to 0.9853, 0.9730 to 0.9999, 0.9685 to 0.9759 and 0.9685 to 0.9999 respectively across the study locations, with Model-Leq3 having the highest R2 range of 0.9730 to 0.9999. These R2 values are higher than those obtained by Akpen et al. (2018), Ibili and Owolabi (2019) and Amah and Udeh (2023) in Makurdi metropolis, Ondo town and Port Harcourt metropolis respectively.
In this study, measurement and modelling of diurnal road traffic noise was carried out within Makurdi metropolis. Measurements were conducted at 2 roundabouts and 2 junctions (cross intersections) for 20 days within the metropolis. These locations were selected on the basis that they are critical to traffic flow. The results of noise levels showed that the mean Leq values across the study locations ranged from 68.65 to 70.72 dBA. These noise levels were 8.65 to 10.72 dBA above NESREA’s 60 dBA set limit. This implies that residents and workers in these areas are likely to experience health issues associated with noise pollution. Modelling results revealed that all the models performed well, with Model-Leq1 having the least performance, as it had the highest values of RMSE, MAE, and MAPE, and the lowest R² value of 0.8658 at the High Level Roundabout. Model-Leq3 exhibited an outstanding performance, as it had the lowest values of RMSE, MAE, and MAPE, and the highest R2 value of 0.9999 at Wurukum Roundabout. Model-Leq3 is therefore recommended for predicting road traffic noise in Makurdi metropolis and other Nigerian cities.
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