# Towards Urban Sustainability: Developing Noise Prediction Model in an Informal Setting
## 2 Materials and Methods
Three additional samples were also selected, one sample from each of institutional (Audu Bako Secretariat), educational (Bayero University), recreational (Race Course). In each sampling location three sites were selected. To develop a model for noise level, a spatial multiple regression was applied using the geographic weighted regression tool in ArcGIS 10.3. The model is based on Tobler's First Law of geography and allows for estimation of dependent variable using a set of one or more dependent variables which are measured at a point whose location(s) is/are known. Six sets of variables: population density, land use and land cover, traffic volume, distance from road, and residential subdivision data were used as independents in the model. The choice was based their effect on noise level as identified from the literature, and availability of data on the variable. The model used is an adoption and modification of [PERSON] et al. [33] and is given as:  
\[ \begin{split} y_{i}\left(u\right)=\beta_{0i}(u)+\beta_{1i}\left(u \right)x_{1i}+\beta_{2i}\left(u\right)x_{2i}+\beta_{3i}\left(u\right)x_{3i}+ \beta_{4i}\left(u\right)x_{4i}+\\ \beta_{5i}\left(u\right)x_{5i}+\beta_{6i}\left(u\right)x_{6i}+ \varepsilon\end{split}  \tag{1}\]  
where \(\beta\_0i}\left(u\right)\) is a parameter that describes a relationship around location \(u\) and is specific to that location, \(y\) is the noise level dependent variable, \(x\_1\), \(x\_2\), \(x\_3\), \(x\_4\), \(x\_5\) and \(x\_6\) represent the independent variables as listed in Table 1, and \(\varepsilon\) the error term, describing the account factors that were not captured by this study. These variables were chosen because of their significant effects in noise prediction as explained [33]. Population determines the level of noise produce, because noise is largely human in nature especially in urban environment. The type of land use generally dictates the activity in the area. Trees are known to attenuate noise, and as such noise studies generally include vegetation cover in their predictions. In a city, areas have different traffic volumes and are located at different distance from the road, hence it is important to include \begin{table}
\begin{tabular}{c c} \hline \hline
**Independent Variable Name** & **Symbol** \\ \hline x\_1 & land cover \\ x\_2 & distance from road \\ x\_3 & population density \\ x\_4 & residential subdivision \\ x\_5 & land use \\ x\_6 & traffic volume \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of independent variables used in Equation (1). these variables in noise prediction. Noise is likely to vary between formal and informal areas. In Kano Metropolis, almost half of the city has no planning footprint [24]. Population was obtained from the National Population Commission which was based on the 2006 census, and the population cluster was created based on [32] and then projected using the geometric projection method and based on the inter-census growth rates (ICGRs) of different LGAs. The projected population data were used to compute population density and vector map was produced. The results were ranked and then rasterized. The land use map was produced based on [34]. The map was updated using most recent Google Earth pro data. The land uses were ranked based on intensity of usage and the ability to generate high noise levels. The final vector map was equally rasterized. For land cover data, a Landsat 8 image of the area for year 2018 was downloaded from the Glovis land cover facility site. The image was used to compute normalized differential vegetation index (_NDVI_). The _NDVI_ is computed as shown in Equation (2):  
\[NDVI=(NIR-Red)/(NIR+Red) \tag{2}\]  
where _NDVI_ is the most commonly used image indices for land cover [35; 36], _NIR_ is the near infrared region of the electromagnetic spectrum corresponding to band 5 and _Red_ is the red region corresponding to band 4 in Landsat image. The final _NDVI_ product is a value ranging from \(-1\) through 0 to \(+1\) with more positive values indicating vegetation cover.