## 3 Methodology
### Calculation of Geometric Parameters  
The characterization of macro-texture in pavements can be described using geometric parameters. In this paper, five categories of geometric parameters were calculated to describe the pavement texture. These categories included profile parameters, height parameters, functional parameters, volume parameters, and hybrid parameters. In order to provide a thorough understanding of these categories, Table 1 outlines the nineteen parameters and the equations that belong to these five categories in a detailed manner. The surface profile can be characterized by profile parameters [39] as explained by ISO (ISO 1984). Profile parameters are related to the vertical and horizontal extensions of surface profile irregularities. Mean profile depth (MPD) is the distance between the highest point of the profile and the mean line. Roughness average (_Ra_) is the arithmetic average of the absolute values of the profile heights over the evaluation length. RMS roughness (_Ra_) is the root-mean-square average of the profile heights over the evaluation length. _Ra_ and _Rq_ provide for easy statistical handling and enable stable results as the parameter is not significantly influenced by measurement noise. _Da_ is the arithmetic mean slope of the surface profile. _Dq_ is the root-mean-square slope of the surface profile. _La_ is the average wavelength of the profile. _La_ is the root-mean-square wavelength of the surface profile. Height parameters [40] specifically pertain to height values along the _z_-axis and concern height distribution. Skewness of height distribution (_Ssk_) is a measure of the asymmetry of the profile about the mean line. A negative skewness indicates that a greater percentage of the profile is above the mean line, and a positive value indicates that a greater percentage is below the mean line. Kurtosis of height distribution (_Sku_) is the quotient  
Figure 7: Data pre\(-\)process to remove the outliers. of the mean quadratic value of z and the fourth power of \(Rq\) within a sampling length. \(Sku\) > 3 indicates that the height distribution is sharp, and \(Sku\) < 3 indicates that the height distribution is even. \(Sku\) relates to the tip geometry of peaks and valleys. Maximum profile peak height (\(Sp\)) represents the maximum peak height of a profile within the sampling length. Maximum profile valley height (\(Sv\)) represents the maximum valley height of a profile within the sampling length. Functional parameters [7] and volume parameters [41] expand the material ratio curve parameters of the profile parameter in three dimensions and are suitable for evaluating friction and abrasion. The material volume and void volume were calculated from a material ratio curve as indicated in Figure 8. The position that corresponds to a material ratio of 10% and 80% was regarded as the threshold segmenting the peak, core, and dale. Core height (\(Sk\)) is the difference between the upper and lower levels of the core. Reduced peak height (\(Spk\)) is the mean height of the protruding peaks above the core. Reduced valley height (\(Svk\)) is the mean height of the protruding dales beneath the core. Volume parameters include dale void volume (\(Vvv\)), core void volume (\(Vvc\)), peak material volume (\(Vmp\)), and core material volume (\(Vmc\)). Hybrid parameters [36] integrate both height and spacing characteristics. Developed interfacial area ratio (\(Sdr\)) signifies the rate of an increase in the surface area. \(Sdr\) values increase as the surface texture becomes rough.