In this study, a novel methodology for snow quantification based on the joint use of radar reflectivity Z and specific differential phase KDP is introduced. An extensive dataset of 2D video disdrometer measurements of snow in central Oklahoma is used to derive polarimetric relations for snow water equivalent rate (S) and ice water content (IWC) in the forms of bivariate power-law relations S = a1KDPb1Zc1 and IWC = a2KDPb2Zc2, along with similar relations for the intercept N0s and slope Λs of exponential snow size distribution. The polarimetric relations dramatically reduce the impact of the variability of snow particle size distributions on the S and IWC estimates. This novel approach is tested against the standard S(Z) relation using snow disdrometer measurements in three geographical regions (Oklahoma, Colorado, and Canada). It demonstrated significant improvement in snow estimates compared to the traditional Z-based methods.