Retrieval and sensitivity analysis of cloud microphysical parameters via dual-frequency radar using regularized optimal estimation

Abstract. This study proposes an adaptively regularized bidirectional retrieval framework for cloud microphysical parameters using dual-frequency radar, evaluated via multi-source error sensitivity analyses and observational validations. Key features include: (1) a forward operator library for equivalent radar reflectivity factor (Zₑ) and specific attenuation coefficient (k) across diverse hydrometeor states; (2) Twomey–Tikhonov regularization to stabilize the optimization by constraining state increments and preserving forward operator continuity; and (3) a joint inverse-forward iterative strategy utilizing path-integrated attenuation (PIA) as a soft prior constraint for simultaneous attenuation correction and parameter optimization. Using WRF-simulated marine cyclones as a benchmark, W-/Ka-band radar experiments isolate key error sources, including radar noise, PIA uncertainties, a priori fields, and hydrometeor variations. While sensitivity analyses demonstrate the algorithm's effectiveness in suppressing a priori perturbations and mitigating PIA biases, retrieval accuracy remains susceptible to hydrometeor misclassification and observation noise, particularly within low signal-to-noise ratio regimes. Under combined uncertainties from Gaussian reflectivity noise (σ = 2 dB) and 10 %–20 % random PIA errors, relative errors for retrieved mass-weighted mean diameter (Dₘ) and equivalent liquid mass content (Mₑ) remain within 26 % and 40 %, respectively. Collocated W- and Ka-band measurements from ground-based (CloudCube) and spaceborne (EarthCARE, GPM) platforms further confirm algorithm reliability. When validated using liquid water path (LWP), retrievals from ground-based W-/Ka-band marine stratocumulus observations achieve about 30% error reduction over single-frequency W-band approaches, yielding a normalized root-mean-square error of 0.57 and a mean absolute percentage error of 29.2% relative to microwave radiometer data. In spaceborne mixed-precipitation comparisons, the algorithm leverages W-/Ka-band complementarity, yielding a marginal positive Dₘ bias against EarthCARE (ME = 0.04 mm) and a negative bias relative to GPM (ME = −0.12 mm). This work offers valuable methodological insights for next-generation spaceborne dual-frequency cloud radar missions.