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Polarimetric variables such as differential phase Φ_DPand its range derivative, specific differential phaseK_DP, contain useful information for improving quantitative precipitation estimation (QPE) and microphysics retrieval. However, the usefulness of the current operationally utilized estimation method ofK_DPis limited by measurement error and artifacts resulting from the differential backscattering phaseδ. The contribution ofδcan significantly influence the Φ_DPmeasurements and therefore negatively affect theK_DPestimates. Neglecting the presence ofδwithin non-Rayleigh scattering regimes has also led to the adoption of incorrect terminology regarding signatures seen within current operationalK_DPestimates implying associated regions of unrealistic liquid water content. A new processing method is proposed and developed to estimate bothK_DPandδusing classification and linear programming (LP) to reduce bias inK_DPestimates caused by theδcomponent. It is shown that by applying the LP technique specifically to the rain regions of Rayleigh scattering along a radial profile, accurate estimates of differential propagation phase, specific differential phase, and differential backscattering phase can be retrieved within regions of both Rayleigh and non-Rayleigh scattering. This new estimation method is applied to cases of reported hail and tornado debris, and the LP results are compared to the operationally utilized least squares fit (LSF) estimates. The results show the potential use of the differential backscattering phase signature in the detection of hail and tornado debris.