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. The campaign was designed primarily as a testbed for ice-cloud scattering and radiative transfer models across the microwave and sub-millimetre spectrum. A key requirement for such closure tests is a near one-to-one relationship between the ice particle size distributions (PSDs) that enter the radiative transfer model and the radiometric measurements. Owing to the FAAM BAe-146 aircraft being unable to perform simultaneously above-cloud radiometric measurements and in-situ sampling within the same volume of cloud, we retrieve PSDs from the ground-based zenith-pointing radars at the time of the radiometric overpasses and then use the aircraft in-situ PSDs as an independent validation dataset.

We present a novel hybrid retrieval framework for mid-latitude ice PSD parameters (slope λ, intercept N_o, 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 N_o and λ, using a randomly oriented rosette-aggregate scattering model, to enforce simultaneous agreement with the observed 35 and 94 GHz reflectivities. In this way, the ML ensemble acts as a compact, data-driven representation of the prior information, this being an alternative approach to the Bayesian optimal-estimation framework.

We apply the retrieval to three of the CCREST-M cases with co-incident in-situ aircraft data. We 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 PICASSO derived in-situ measurements of IWC, and exponential (μ=0) and gamma PSD assumptions show comparable performance overall. Retrieved mean and median PSDs show generally good agreement with in-situ PSDs as a function of temperature, although systematic biases remain in one case, likely due to temporal cloud evolution between radar and in-situ sampling. The IWCs derived from the retrieved PSDs are generally within about 50 % of the in-situ measured IWCs over much of the –50 to –10^o C temperature range, with near-unity agreement between the estimated and in-situ IWCs for one of the cases. Independent validation using 200 GHz radar reflectivity profiles confirms retrieval consistency where ML predictions are reliable and for a well constrained case, reinforcing the robustness of the retrieval approach and ice crystal scattering model. The retrieved PSDs provide radar-constrained inputs for forthcoming radiative transfer closure studies using collocated mm-wave and sub-mm-wave radiometer observations.