Reliability of smart noise pollution map

2.1 Study area

The city of Al-Sadr is located in the northeast of the Iraqi capital, Baghdad, and is a densely populated area with a population of 1,276,249 according to the latest statistics from the Iraqi Ministry of Planning for the year 2020. Al-Sadr city is connected to the center of Baghdad province by four main roads. To study traffic noise in Al-Sadr city, the most important of these main roads was selected. The study area included the two main roads for entering and leaving Al-Sadr city, which extend from Al-Muthaffar Square to Market Maridi, round-trip during the morning and afternoon periods. The study area included Al-Muthaffar street and Al-Jawader street as shown in Figure 1. As for the evening period, the study area included the two main roads from Al-Muthaffar Square to the intersection of Zayn al Qaws Street and Al-Jawader Street, because the road leading to Maridi market is closed at night and only allows pedestrian traffic. The two main roads selected for the study for entering and exiting Al-Sadr are busy and vibrant roads bordered by residential areas, parks, commercial and service areas, as well as government and industrial institutions. The transportation system in Al-Sadr relies on small buses, private transport vehicles, motorcycles, as well as tik tok (three-wheeled vehicles) that are widely spread throughout the city.

Figure 1

The study area’s geographical location and the measured noise point distribution for the main road to enter and exit from Al-Sadr city, Baghdad, Iraq.

2.2 Noise survey, processing data, and creating spatial database

First, the methodology of the study included a field survey of noise levels. After conducting a field reconnaissance of the main road leading in and out of the city of Al-Sadr, selected points were identified for measuring traffic noise levels. The measured traffic noise points on both entry and exit roads were opposite each other, and the distance between every two successive noise points on each road was 100 m, measured using a measuring tape. The spatial coordinates of each measured noise point were determined using Garmin GPS Map 64s. The noise levels were measured using a SVAN977 sound and vibration analyzer with an A-type filter, and the measurement duration at each point was 5 min. The device was installed at a distance of 1 m from the sidewalk, with a height of 1.5 m above the ground and a detector precision of 0.1 dB. Eighty points of traffic noise were measured for both the entry and exit roads of Al-Sadr city. Measurements were taken for each point during three periods: morning (7–9 am), midday (12–2 pm), and evening (4–6 pm). At each measurement point, three noise values (LAeq, Max, Min) were obtained. The statistical results, including the mean, standard deviation, minimum value, and maximum value, for the measured noise points for both the entry and exit roads of Al-Sadr city and for the three measurement periods, are presented in Tables 1 and 2. The environmental conditions for noise measurements were represented by a dry road surface, with the ambient air temperature within the moderate continental range, where the temperature did not fall below 5°C or exceed 35°C, and the wind speed did not exceed an average of 10 m/s. Second, the methodology of the study involved downloading field measured data and processing it using the software platform SvanPC++, where the extracted data included noise values (LAeq, Max, Min) for each measured traffic noise point. The data were exported from platform SvanPC++ to an Excel file that included the spatial coordinates of each measured noise point. Third, a spatial geodatabase was created using version 3.22 of the QGIS software, and processing was performed within the program to create feature class layers for the measured noise points for the main entry and exit roads, as well as for the three measurement periods.

2.3 Smart Map Plugin (OK)

The Smart Map Plugin is a software component developed and integrated with QGIS version 3.10 or higher [33]. The interpolation is performed using the Smart Map Plugin (OK) through an open-source Python library called PyKrige, which supports the 2D OK technique and includes variogram models [35]. The Smart Map Plugin simplifies the process of digital map drawing using OK interpolation without the need for programming knowledge [33]. Furthermore, it facilitates the examination of variations and the implementation of interpolation using the significant parameters of the OK method, such as the number of neighbors, search radius, semi-variogram, and its factors (range, sill, nugget, and fitting the mathematical models) [33,36]. The developed Smart Map Plugin (OK) was used to configure a suitable statistical semi-variogram for performing the interpolation, where the plugin allows the user to fit five models of the theoretical semi-variogram: exponential, spherical, Gaussian, linear, and linear with sill. The cross-validation method was used to choose the semi-variogram model. The search radius for kriging was set equal to the range obtained by the semi-variogram. The number of neighbors for the main entrances and exits during morning and afternoon periods were determined as 25 points, while for the evening period, the number of neighbors was set to 20 points. The maps produced by the plugin are exported to QGIS in raster format. In addition to that, Figure 2a represents the interface of the Smart Map plugin for selecting and entering the measured layers and Figure 2b includes the facilities provided by the plugin for selecting the appropriate semi-variogram.

Figure 2

Graphical User Interface for Smart Map. (a) Selection the traffic noise data value to be interpolated. (b) Determine the parameters and configuration semi-variograms for the Ordinary kriging interpolation method.

2.4 Moran’s I (index)

Moran’s I is a commonly used measure for assessing spatial autocorrelation and is also a useful indicator for analyzing spatial association of environmental variables [14]. It is available in the Smart Map Plugin of the QGIS software, where the spatial weight matrix (W) for Moran’s I is calculated in Smart Map using the PySAL Python library. The PySAL library provides a kernel function that determines weights for neighbors based on distances between sample points in the grid. The univariate Moran’s I is used to measure, compare, and test the degree of autocorrelation of the same variable that is interpolated at different distances. Therefore, the spatial autocorrelation degree was calculated for traffic noise attributes (LAeq, Max, Min) for three measurement periods in the morning, afternoon, and evening using Moran’s I, as shown in Figure 3. The mathematical formula for calculating the value of Moran’s I (Legendre & Fortin, 1989) is as follows:

where N is the number of observations, x ̅ is the mean of the variable, X i is the variable value at a particular location, X j is the variable value at another location, W ij is a weight indexing location of i relative to j, in the smart map plugin, and (W) represents the spatial weight matrix, the sum of all w _ij .

Figure 3

GUI of Smart Map. Moran’s I calculation of the spatial autocorrelation between noise points measured, for the entre main road at morning in Al-Sadr City using LAeq noise value.

When the value of univariate Moran’s I is zero, it indicates that the variable under study shows no spatial correlation and that the pattern is random. When the value of Moran’s I is closer to −1, it indicates that the variable tends to have more contrasting values, and as its value approaches 1, it indicates that the variable tends to have higher similarity values and that the pattern is clustered rather than random.

2.5 Generation scenarios for evaluating the interpolation methods

A comparison was conducted between the Smart Map Plugin (OK) and the IDW method to determine which method is better for producing traffic noise maps for the study area. The noise level value of LAeq was used as the interpolation attribute, representing the equivalent sound pressure level in decibels, and yielding a high level of Moran’s I during the three measurement periods. The comparison was performed by drawing an equal number of measured traffic noise points, located in the same spatial location for each interpolation method, with 18 points for both the main entry and exit roads of Al-Sadr city considered as check points. These points were represented as a feature class in the project’s geodatabase. While the remaining traffic noise points, which are also represented as a feature class in the project’s Geodatabase, have the same spatial location in both of the interpolation methods and consist of 62 points for the two main entry and exit roads of Al-Sadr city, they are used to perform interpolation in both comparison methods. Regarding the traffic noise points selected to check the interpolation methods, they were identified using the random selection algorithm that deals with vector data. The number of selected features method within the random selection algorithm was chosen to select the number of points to be drawn for the purpose of checking, and this method helped identify the nature of the check sample distribution. To have complete control over the checking process, some adjustments were made manually by the user in the point selection process. The noise points selected for check and evaluating the noise models were located in opposite directions of each other. The points for the entry road were located in the opposite direction of the exit road, and vice versa. Additionally, the check points were chosen in an organized manner, as illustrated in Figure 4. The identified traffic noise points for the examination process were exported to a new feature class within the project’s Geodatabase for use in comparing two interpolation methods. The remaining traffic noise points were utilized for the interpolation process using both the Smart Map Plugin (OK) and IDW methods, with each method producing a raster with the same number of points and for three measurement periods as shown in Figures 5 and 6. During the comparison between the two interpolation methods, the fundamental parameters for each method were determined. For the Smart Map Plugin (OK) method, the primary parameters were identified, represented by the search radius equal to the range, as well as the number of neighbors and the semi-variogram configuration. In the IDW method, the main parameters are represented by the distance coefficient P, in addition to defining the extent of the predicted raster layer. The resulting raster is then clipped along the boundaries of the study area. In both methods, the pixel size of the resulting raster is set to 1 m × 1 m. To evaluate and validate the spatial interpolation quality in the Smart Map Plugin (OK) and IDW methods, selected check points are used, in addition to the raster resulting from the interpolation of the remaining noisy points. First, it is verified whether the predictive raster resulting from the interpolation using both methods has been properly generated. This is done by using the raster pixel to point algorithm to convert the predictive raster to points, to ensure that individual pixel units within the raster do not contain null values in the output results. Then, the check points and raster resulting from the remaining traffic noise points are entered into the sample raster value logarithm to extract the values of the selected check points within the predictive raster and create a new vector layer. The new vector layer created by the sample raster value algorithm has the same properties as the input data, with knowledge of the corresponding raster values for the location of the specified check point. The logarithmic field calculator and its associated expression are used to create an error field and calculate its value by subtracting the interpolated value from the measured value of the specified check points. The mean prediction error is then calculated through the statistics panel available in the QGIS software. Finally, the logarithmic field calculator and its associated expression are used again to square the error value to find the RMSE value, which is calculated according to Eq. (2). Using this value, the best method for producing traffic noise maps for the entry and exit roads of Sadr City can be determined.

where x̂ _i represents the interpolated value of the noise attribute at point i, x _i is the observed value of the traffic noise attribute at point i, and n is the number of points.

Figure 4

The interface of the QGIS program and the algorithms used for the purpose of performing the validation to compare the raster generated by both methods, IDW and Smart Map Plugin (OK), using check points.

Figure 5

Comparison between the Smart Map Plugin (OK) and the IDW method, using the LAeq noise value, for three periods, morning, noon, and evening, for the main entry road to Al-Sadr City. (a) IDW method morning, (b) Smart Map (OK) method morning, (c) IDW method noon, (d) Smart Map (OK) method noon, (e) IDW method evening, and (f) Smart Map (OK) method evening.

Figure 6

Comparison between the Smart Map Plugin (OK) and the IDW method, using the (LAeq) noise value, for three periods, morning, noon, and evening, for the main exit road to Al-Sadr City. (a) IDW method morning, (b) Smart Map (OK) method morning, (c) IDW method noon, (d) Smart Map (OK) method noon, (e) IDW method evening, and (f) Smart Map (OK) method evening.

In addition, Figure 7 briefly illustrates the methodology used in this study.

Figure 7

Study methodology.

3.1 Interpolation by IDW method

IDW is a spatial interpolation method used to generate an overlay raster surface using the Z value of point attributes with known spatial coordinates [43]. Each cell derived using this method takes into account a distance factor, connecting the closest measured points, and estimates values between them [42,45]. This method is referred to as “inverse distance weighted” because the unknown point is influenced by all measured points, but the impact is greater when the distance between the unknown and known point is small, and decreases as the distance increases [46,47]. When the distance between the unknown point and each known point is weighted, the average weight of the measuring point is calculated, but this is not a direct increase in weight, rather an inverse increase, i.e., the weight is inverse [48]. In its simplest form, IDW is referred to as “linear interpolation,” where weights are calculated using the linear function of the distance between measured points and the interpolate point [43]. It is one of the deterministic methods based on the following mathematical law [38]:

where Z ˆ ( s 0 ) is the predictive value, N is the number of samples points measured and will be used in prediction, λ i is the measured point weight, and Z ( s i ) is the observed value.

where the weight is reduced by the p coefficient when the distance is large and d i 0 represents the distance between each measured point s_i and the prediction site s_o.

Interpolation is performed using the IDW method in the QGIS software by inputting the measured noise point layer and selecting the interpolation attribute field, which represents noise values (Min, Max, LAeq). The parameter of the distance coefficient weight was set to 2, and the pixel size of the resulting raster was adjusted to 1 × 1. The raster is created on the extent of the study area, and then a clip is made to create the raster on the boundaries of the main road for entry and exit from the city of Sadr. The raster is then classified and the interpolated noise values are displayed within the selected study area boundaries.

3.2 Interpolation by OK method

It is an advanced spatial statistical method [49]. It is a well interpolator that produces an estimator surface (raster) from a set of discrete measured points with Z values and uses kriging to verify the spatial behavior of the studied phenomenon [42]. The Kriging method is similar to the IDW method, where non-measured locations are interpolated by weighting the distance to surrounding measured points. However, the difference is that Kriging method not only relies on distance, but also on the arrangement of measured points and spatial autocorrelation [14,43,49]. In the Kriging method, there are statistical and mathematical steps, where the kriging algorithm requires a positivity spatial autocorrelation model, and the semi-variogram plot describes this relationship between measured samples of the studied phenomenon [49,46,43,42]. This statistical model is used to find mathematical functions of variables and an interpolation surface that is sought after [42,49]. However, appropriate mathematical models for the data must be selected, and there must be positivity during modeling to show and describe spatial continuity [43,49]. Among many unbiased estimates, Kriging is considered the “best linear unbiased estimator” (used in statistics to estimate random effects in linear mixed models) [46]. Kriging results indicate that interpolation takes into account gradual spatial changes, and predictions do not pass through known measured points but rather predict higher and lower values than the original measured values [43,44]. The most common and widely used method belonging to the Kriging family is OK, a flexible and simple univariate local method [42,46]. It estimates the local mean, i.e., the sample mean within the search window, and requires homogeneity and spatial autocorrelation among the measured samples [46]. OK uses the appropriate semi-variogram program to calculate interpolation weights, and the semi-variance is linked to the distance between measured sample points [49]. OK allows for transformations, removal of external directional bias from resulting statistical layers, and measurement of prediction errors [38]. The general equation for OK is as follows [38]:

where s is a location (X, Y), Z(s) is the measured value at that location, μ is the mean for data (no trend) on which the model is based, and ε(s) is random errors. The predictor is formed as a weighted sum of the data.

where Z ˆ ( s 0 ) is the predicted value at that location , s 0 is the prediction location, and λ i is an unknown weight for the measured value.

4.1 Spatial autocorrelation with Moran’s I

The spatial autocorrelation of traffic noise values (LAeq, Max, Min) measured along the two main roads entering and leaving the city of Al-Sadr was examined using Moran’s I for three measurement periods: morning, afternoon, and evening. The correlation analysis was conducted on a sample of traffic noise points measured along the main entrance and exit roads of the city, ranging from 5 to 40 points. Moran’s I was used to assess the degree to which traffic noise values were spatially clustered along the main roads. It was observed that Moran’s I tend to increase as the number of measured traffic noise points along the main roads increases. The average value of Moran’s I for the measured traffic noise values was calculated for the two main roads entering and exiting the city, and is depicted in black for the three measurement periods in Figure 8.

Figure 8

Computing Moran’s I for the spatial autocorrelation, between the measured traffic noise points, for the (LAeq), (Max), and (Min) values and measuring the average Moran’s I. (a) Morning enter, (b) Morning exit, (c) Noon enter, (d) Noon exit, (e) Evening enter, and (f) Evening exit.

Figure 8a and b depicts the spatial autocorrelation between traffic noise points measured on the main entrance and exit roads of Al-Sadr city during the morning rush hour. A weak autocorrelation was observed at a sample size of 5, which increases with an increasing number of points until it stabilizes at a high level. The values of Moran’s I for the traffic noise values (LAeq, Max, Min) on the main entrance road were 0.9, 0.893, and 0.828, respectively, while those for the main exit road were 0.888, 0.835, and 0.920, respectively. The Moran’s I value for the Min values on the entrance road in the morning was slightly lower than that for the LAeq and Max noise values. On the other hand, the Moran’s I value for the Max noise values on the exit road in the morning was slightly lower than that for the LAeq and Min noise values. It should also be noted that the Moran’s I values for the Max and LAeq noise values for the main entrance road in the morning and for the Min noise value for the main exit road in the morning were higher than the average Moran’s I.

In Figure 8c and d, which represents the spatial autocorrelation between traffic noise points measured for the main entrance and exit roads of Sadr city at noon, strong spatial autocorrelation was observed from the beginning for the LAeq and Min noise values, where Moran’s I was constant and stable for both roads, with values of 0.898 and 0.918 for the entrance road, and 0.883 and 0.947 for the exit road, respectively. However, the Moran’s I value for the max noise value decreased at the sample size of 5, then gradually increased to reach a stable value of 0.733 for the entrance road and 0.838 for the exit road, which is lower compared to the Moran’s I value for the LAeq and Min noise values. In addition, Moran’s I for noise values LAeq and Min appears to be higher than the average Moran’s I.

In addition, in Figure 8e and f, which represents the spatial autocorrelation between traffic noise measurements for the main entrance and exit roads of Al-Sadr city in the evening, Moran’s I values for LAeq noise levels show high correlation values until reaching a stable value of 0.886 for the entrance road, while showing initially moderate values for the exit road before increasing and continuing in this upward trend until reaching a stable value of 0.879. The values of Max traffic noise in the evening exhibit a high and stable spatial autocorrelation, which stabilizes with a Moran’s I value of 0.860 for the entrance road and 0.883 for the exit road. Additionally, the Min traffic noise values in the evening exhibit a low Moran’s I value at a sample size of 5, then begin to increase and stabilize at a value of 0.874 for the main entrance road and a value of 0.903 for the main exit road, which is higher than its value for LAeq and Max noise levels for the exit road in the evening. It is also noteworthy that the Moran’s I value for LAeq noise values for the entrance road in the evening was higher and very close to the average Moran’s I, while the Moran’s I value for the Min noise values for the exit road in the evening was higher than the average Moran’s I.

The decrease in Moran’s I is attributed to the variation among some of the measured traffic noise points value, which slightly reduces the spatial correlation between the samples. According to the spatial analysis of the areas surrounding the main entrance and exit roads of Al-Sadr City, the variation in some values of the traffic noise is a result of differences in traffic congestion in some parts of the studied main roads (Table 3).

4.2 Comparison between IDW and Smart Map (OK) methods

A comparison was made between the Smart Map Plugin (OK) method and the IDW method using the LAeq value for measured traffic noise points during three measurement periods in the morning, afternoon, and evening. Several processing steps were performed within the QGIS software to evaluate the interpolation methods. The comparison between the interpolation methods was conducted under similar conditions, using parameters that provided the best results for each method. The results of the comparison and check between the two interpolation methods showed that the Smart Map Plugin (OK) method outperformed the IDW method, as it gave the lowest standard deviation and RMSE. Additionally, the statistical results of the comparison and check showed that the mean prediction error obtained using the Smart Map Plugin (OK) method was lower than that obtained using the IDW method for the main entrance and exit roads of Al-Sadr city and for the three measurement periods. Except for the evening exit road, the mean prediction error resulting from using IDW was lower due to the decrease in Moran’s I value resulting from the decrease in spatial correlation between traffic noise points. When using the Smart Map Plugin (OK) and inputting all measured traffic noise points, the value of Moran’s I is high. However, it is noted that this value decreases after selecting a portion of the points for examination, as shown in Table 3. The statistical results of comparing the Smart Map Plugin (OK) method and the IDW method were displayed using Data Plotly (a plugin in QGIS that allows for creating graphs using Plotly library and Python API), as illustrated in Figures 9 and 10.

Figure 9

The statistical results of the check process using the Smart Map Plugin (OK) method and the IDW method, for the main road to enter Al-Sadr City, and for three measurement periods, morning, noon, and evening. (a) Check IDW morning, (b) Check Smart Map (OK) morning, (c) Check IDW noon, (d) Check Smart Map (OK) noon, (e) Check IDW evening, and (f) Check Smart Map (OK) evening.

Figure 10

The statistical results of the check process using the Smart Map Plugin (OK) method and the IDW method, for the main road to exit Al-Sadr City, and for three measurement periods, morning, noon and evening. (a) Check IDW morning, (b) Check Smart Map (OK) morning, (c) Check IDW noon, (d) Check Smart Map (OK) noon, (e) Check IDW evening, and (f) Check Smart Map (OK) evening.

4.3 Interpolated maps

The three noise attributes (LAeq, Max, Min) were interpolated for all measured traffic noise points on the main entry and exit roads of Al-Sadr City. The Smart Map Plugin (OK) was used for interpolating the traffic noise attributes, as shown in Figures 11–13, because it gave the lowest RMSE values for the three measurement periods, namely, morning, afternoon, and evening after comparing it with the IDW method. Grids with cell sizes of 1 m × 1 m were used. After the spatial interpolation process, areas of high and low noise levels were found along the surface of the main entry and exit roads of Al-Sadr City. Regarding the predictive maps that were created for the purpose of comparison and validation between the Smart Map plugin (OK) method and the IDW method, using the noise level value (LAeq) as the Z value, there was a noticeable difference between the spatial patterns of the maps produced by each interpolation method. The spatial distribution and arrangement of the data, as well as the spatial correlation between them, along with the quality of the data, can affect the performance of the spatial interpolation method and the accuracy of the resulting surface. This may be the reason why the OK method advanced with caution. Furthermore, the transitions between LAeq values were smoother in the prediction maps produced using OK.

Figure 11

The resulting interpolation maps using Smart Map Plugin (OK) for the noise values of LAeq, Max, Min for the main road to enter and exit from Al-Sadr City at the morning. (a) Enter Main Road Smart Map Morning LAeq, (b) Exit Main Road Smart Map Morning LAeq, (c) Enter Main Road Smart Map Morning Max, (d) Exit Main Road Smart Map Morning Max, (e) Enter Main Road Smart Map Morning Min, and (f) Exit Main Road Smart Map Morning Min.

Figure 12

The resulting interpolation maps using Smart Map Plugin (OK) for the noise values of LAeq, Max, Min for the main road to enter and exit from Al-Sadr City at the noon. (a) Enter Main Road Smart Map Noon LAeq, (b) Exit Main Road Smart Map Noon LAeq, (c) Enter Main Road Smart Map Noon Max, (d) Exit Main Road Smart Map Noon Max, (e) Enter Main Road Smart Map Noon Min, and (f) Exit Main Road Smart Map Noon Min.

Figure 13

The resulting interpolation maps using Smart Map Plugin (OK) for the noise values of LAeq, Max, Min for the main road to enter and exit from Al-Sadr City at the evening. (a) Enter Main Road Smart Map Evening LAeq, (b) Exit Main Road Smart Map Evening LAeq, (c) Enter Main Road Smart Map Evening Max, (d) Exit Main Road Smart Map Evening Max, (e) Enter Main Road Smart Map Evening Min, and (f) Exit Main Road Smart Map Evening Min.