Machine-learning based estimates of mass-dimensional relations from simulated in situ imaging probes

Retrievals of ice precipitation from remote sensing measurements rely on a priori assumptions about particle mass and size within the sampling volume. Such a priori information typically includes a particle size distribution (PSD) and a mass-dimensional relation, m-D, where m is mass and D is the maximum dimension (or diameter). In situ measurements of ice particles from either airborne or ground-based imaging probes inform these assumptions. Owing to limited information about a particle‘s three-dimensional structure from probes with few independent view angles, estimates of the particle’s mass and size (D) based on these instruments are highly uncertain and systematically biased in D. Quantification of the uncertainty in the derived m-D relations is also challenging due to the lack of direct mass and D measurements, making it difficult to quantify the uncertainty of remote-sensing precipitation retrievals.Using a database of physically plausible three-dimensional ice particle structures, we develop a framework to estimate particle size, mass, and other physical properties from a variety of different imaging probe configurations. The simulated probe configurations we use include those containing a single projection, two orthogonal projections, three orthogonal projections, and up to 13 projections at the nodes of a Lebedev spherical quadrature scheme. We simulate two-dimensional binary images of the particles at each projection and train machine-learning models to estimate the particle size and mass. To provide direct estimates of the uncertainty for each probe configuration, the machine learning models are trained to predict distributions of the size and mass.The predictions of mean mass and size from the machine learning models increase in accuracy as the number of view angles increases, with greater improvements between the single-view and two-view configurations then between that and the three-orthogonal-view configuration. The uncertainty in mass decreases between the single and three-view models but remains relatively constant for the configurations using more than three views. Calculations of the spherical effective density based on the model predictions show favorable correspondence with the true spherical effective density of the particles, suggesting that the models largely capture the covariance between mass and size of the true particle shapes.These probabilistic estimates of mass and size are then used to retrieve samples of m-D relation coefficients for a subset of particles corresponding to a known m-D relation. To estimate the impact of the uncertainty in the retrieved m-D relation has on precipitation retrievals, we compare the ice water content (IWC) for the known m-D relation using a variety of PSDs and the retrieved m-D relation samples from each probe configuration. The errors in IWC decrease with increasing numbers of view angles, with smaller reductions in error for configurations with more than three view angles. Future areas of improvement in the machine-learning models, as well as how the errors in m-D retrievals from imaging probes impact the downstream uncertainty in remote sensing retrievals will also be discussed.