This study presents a novel methodology for extracting latent variables from high-dimensional sparse data, particularly emphasizing spatial distributions such as precipitation distribution. This approach utilizes multidimensional scaling with a distance matrix derived from a new similarity metric, the Unbalanced Optimal Transport Score (UOTS). UOTS effectively captures discrepancies in spatial distributions while preserving physical units. This is similar to mean absolute error, however it considers location errors, providing a more robust measure crucial for understanding differences between observations, forecasts, and ensembles. Probability distribution estimation of these latent variables enhances the analytical utility, quantifying ensemble characteristics. The adaptability of the method to spatiotemporal data and its ability to handle errors suggest its potential as a promising tool for diverse research applications.

Four-dimensional variational (4D-Var) data assimilation is an effective method for obtaining physically consistent time-varying states. In this study, a method using a neural network surrogate model obtained by machine learning is proposed to solve one of the most serious challenges in 4D-Var: to construct an adjoint model. The feasibility of the proposed method was demonstrated by a 4D-Var experiment using a surrogate model for the Lorenz 96 model. In the method, several effective procedures have been proposed to obtain an accurate surrogate model and the assimilated initial conditions, including two-stage learning (i.e., single- and multi-step learning) of neural networks, limiting the target states of the surrogate model to a small subspace of the state phase space, and updating the surrogate model during 4D-Var iterations.

The nature of convective organization remains elusive, despite its importance for understanding the role of clouds in climate systems. This study reports a new type of large-scale structure formed by the self-organization of deep moist atmospheric convection in radiative-convective equilibrium. To understand the natural behavior of convection unaffected by the computational domain, we conducted cloud-resolving simulations by systematically increasing the horizontal domain size to approximately 25,000 km. We found that if the domain side length exceeded 5,000 km, the domain-averaged thermodynamic fields and the horizontal characteristic length converged in quasi-equilibrium; the cloud aggregation area exhibited a mesh-like pattern, analogous to the shallow convective organizations despite their different scales. Its characteristic length is estimated to be approximately 3,000–4,000 km. The results suggest that this length scale is related to the upper-limit size of mesoscale convective systems or the scale of supercloud clusters in a real tropical atmosphere.