This study revisits the parametric modeling of the hurricane surface wind field composed of the storm vortex and the environmental background flow. First, we investigate the parametric representation of the surface background wind by analyzing its empirical relationship with storm movement. A marked deceleration and counter-clockwise rotation of the surface background wind from the storm translation vector is detected, a result predicted by the Ekman theory but rarely applied in wind and surge modeling. Then, we examine the various parameters used to model the wind field and, through numerical simulations, quantify their induced uncertainties in the extreme wind and surge estimates at two coastal sites. Our analyses show that, over the range of accepted values and methods in the literature, the local wind and surge estimates are most sensitive to uncertainties in the surface wind reduction factor and storm wind profile but less sensitive to uncertainties in other wind parameters, such as inflow angle and surface background wind (varying in the observed range). The surge is more sensitive than the wind to uncertainties in the wind parameters, and these sensitivities are comparable to the sensitivity of the surge to the uncertainty in the sea surface drag coefficient. We also find that some commonly used wind parameters unsupported by theory or observations can induce significant errors in the wind and surge estimates. The results of this study provide new insights and references for future hurricane wind and surge analysis.