A Shape-Aware Mass–Diameter Parameterization for Ice Crystals Constrained by Glaciogenic Seeding Experiments

Accurate estimates of ice crystal mass are essential for reducing uncertainties in cloud radiative forcing and precipitation forecasts. Ice crystal mass can be derived from imaging cloud probes using power-law mass–diameter (m-D) relationships. However, these often do not account for variability in crystal habit, leading to significant biases in ice water content (IWC) retrievals and complicating the comparison between in-situ observations and numerical models.

To address this, we developed a shape-aware m-D parameterization by explicitly incorporating the aspect ratio (AR) into a power-law framework. The parametrization is fitted using data from the CLOUDLAB campaigns, which use glaciogenic seeding to induce ice formation in supercooled stratus clouds. This experimental setup allows for two total water content (TWC) conservation assumptions: (i) the temporal stability of the stratus clouds allows to use the TWC of the unseeded cloud as a reliable baseline for the seeded section., and (ii) the introduction of ice crystals via seeding does not alter the TWC, even as the Wegener–Bergeron–Findeisen process redistributes mass from the liquid to the ice phase. Using data from 20 seeding experiments, we optimized the m-D parameters by minimizing the difference between seeded and the baseline TWC using a loss function based on the Wasserstein distance to ensure that the probability distribution of the derived TWC match the observed variability of the background cloud.

The resulting parameterization m = 0.0487 D^2.045 / AR² aligns well with existing m-D relationships but predicts lower ice crystal masses for high aspect ratios. When applied to the CLOUDLAB data, the formula successfully removes systematic overestimations in ice mass across various temperatures and growth stages. While riming and aggregation were only weakly present in our dataset, they did not lead to significant deviations. This study provides a shape-aware m-D formulation suitable for bulk microphysics schemes and demonstrates a robust, data-driven framework for constraining cloud parameters using field measurement from cloud seeding experiments.