Using Diffusion Maps to Quantify DA-Induced Imbalances in Mixed-Phase Convective Clouds

In modeling mixed-phase convective clouds, we concern ourselves with states of the atmosphere that can be characterized by features such as temperature, pressure, and humidity, along with mixing ratios and number concentrations for various species of hydrometeors. Data assimilation (DA) uses observations to update these states, but sometimes produces non-physical estimates, resulting in spurious effects such as excess latent heating and gravity waves. Other symptoms, however, are not as easily detectable, particularly when it comes to cloud microphysics. In this context, there is a need for a succinct method of identifying unphysical DA-generated model states. We employ the diffusion map; a manifold-learning, nonlinear dimensionality reduction technique which embeds high-dimensional feature space points into a lower-dimensional eigenspace using the connectivity of the input data. We demonstrate this technique applied to mixed-phase convective clouds in a freerunning simulation of the Weather Research and Forecasting model. Furthermore, we introduce a method for quantifying the degree to which DA can adjust model states away from the manifold uncovered by diffusion maps, and then illustrate its utility for a holistic comparison between an ensemble Kalman filter (EnKF) and a localized particle filter, finding that the EnKF is more prone towards producing unphysical model states. The approach developed produces intelligible results, and is applicable not only to DA evaluation but potentially to direct enhancement of the DA itself.