An ensemble machine-learning first-guess approach for physics-based retrieval of ice particle size distributions from multi-frequency radar, validated with CCREST-M aircraft observations

Abstract. The Characterising CiRrus and icE cloud acrosS the specTrum-Microwave (CCREST-M) aircraft campaign (February–March 2024) was based around the Chilbolton Observatory, UK, using the Facility for Airborne Atmospheric Measurements (FAAM) BAe-146 aircraft together with ground-based multi-frequency radars to provide a testbed for ice-cloud scattering and radiative transfer models across the microwave and sub-millimetre spectrum. Ice particle size distributions (PSDs) are retrieved from the ground-based zenith-pointing radars at the time of the radiometric overpasses, and the aircraft in-situ PSDs are used as an independent validation dataset. We present a novel hybrid retrieval framework for mid-latitude ice PSD parameters (slope λ, intercept No, and shape μ of the gamma size distribution) that combines a machine-learning (ML) ensemble with physics-based multi-frequency radar retrievals using 3, 35, and 94 GHz reflectivities. An ensemble of ML models is trained on observations from the Parameterising Ice Clouds using Airborne ObServationS and triple-frequency dOppler radar (PICASSO) campaign, also centred on Chilbolton Observatory. These models predict PSD moments from temperature, pressure, 3 GHz-retrieved ice water content (IWC), and the mean mass-weighted dimension. The ML predictions are converted into first guess gamma-PSD parameters at each height. A subsequent deterministic optimisation then adjusts No and λ, using a randomly oriented rosette-aggregate scattering model, to enforce simultaneous agreement with the observed 35 and 94 GHz reflectivities. Application of the above method to three CCREST-M cases show that the ML ensemble reproduces PSD moments well for two cases but fails when extrapolating beyond its trained temperature range in the third case. Retrieved IWCs from the 3 GHz radar compare favourably with in-situ measurements of IWC, and exponential (μ=0) and gamma PSD assumptions show comparable performance overall. Retrieved mean PSDs show generally good agreement with in-situ PSDs as a function of temperature for two of the cases, with IWCs within about 50 % of the in-situ measured IWCs over much of the −50 to −10 °C temperature range. The systematic biases seen in one case are attributed to temporal cloud evolution between radar and in-situ sampling. Independent validation using 200 GHz radar reflectivity profiles shows good agreement between the forward-modelled refllectivities and measurements above about 4.5 km. Below 4.5 km the agreement is more sparse owing to the likely presence of dendritic particles, which depart from the rosette-aggregate scattering assumption.