Modeling the effects of rainfall intensity on the heteroscedastic traffic speed dispersion on urban roads

The heteroscedasticity refers to a collection of random variables with a subpopulation that have different dispersions from others. The variable dispersion could be quantified by measures of statistical dispersion such as standard deviation or coefficient of standard deviation. This study aims to model the effects of rainfall intensity on the heteroscedastic traffic speed dispersion on urban roads. The traffic and rainfall intensity data were collected by a selected video traffic detector and its nearest rainfall station in Hong Kong, respectively. The coefficient of variation of speed (CVS) was employed to measure the vehicular traffic speed dispersion. The analysis shows that the empirical values of CVS typically range from 0.05 to 0.2 at different traffic densities and rainfall intensities, and the exponential function provides a good fit to traffic speed data under both dry and rain conditions. A generalized function of CVS with the effects of rainfall intensity is proposed, calibrated, and validated with different sets of empirical data. The calibration and validation results show that the proposed generalized function of CVS fits well with the empirical data. The empirical findings and the generalized function of CVS proposed in this study may benefit for assessing and modeling the level-of-service performance of urban roads in Pacific Rim cities similar to Hong Kong with relatively high annual rainfall intensity.