Potential use of radar slant-linear depolarization for measuring rainfall microphysics

Abstract. Single-transmit, dual-receive millimeter-wave radars can be attractive for compact and scanning precipitation observations, but they do not necessarily provide the conventional horizontal/vertical dual-polarization variables used to constrain raindrop size distributions. This study evaluates whether a fixed slant-linear basis can turn the weak backscattering anisotropy of oblate raindrops into a useful liquid-rain observable. In the proposed geometry, a +45° transmitted polarization and co-/cross-slant receive channels project the difference between horizontal and vertical co-polar backscattering amplitudes into an orthogonal-slant return. We use explicit T-matrix scattering calculations, normalized-gamma and observed drop size distributions, and controlled neural-regression diagnostics to quantify the information content and observability of the resulting slant-linear depolarization ratio (SLDR). For the baseline Ka-band gamma ensemble, the reflectivity (Z₊)–SLDR space separates characteristic drop size and concentration that are ambiguous under reflectivity alone. With 1 dB SLDR uncertainty, adding SLDR reduces the independent-test RMSE of mass-weighted mean diameter (D_m) from 0.672 to 0.243 mm and reduces the RMSE of log-transformed rain rate (log₁₀R) from 0.163 to 0.055. The same sign of improvement persists for Nanjing 2DVD, EPFL HyMeX, NASA IFLOODS, and variable-shape gamma checks. Sensitivity tests show that random SLDR uncertainty degrades retrievals gradually, whereas relative co-/cross-slant gain bias and polarization leakage define stronger practical constraints. Through the controlled forward-simulation information-content tests, SLDR is identified as a physically distinct measurement coordinate for liquid-rain microphysics. The calibration and detectability conditions are also defined for a field test with suitable single-transmit, dual-receive radars.