The accurate estimation of atmospheric state variables from radar observation in rapidly growing deep convection, which causes heavy thunderstorms, is a major challenge. This study examines the advantage of incorporating radar observation data with very high frequency such as 30 s compared with the conventional case of 5 min, from a theoretical perspective.

Using a simple day-night thermodynamic model based on surface energy balance, this study explains key mechanisms of the urban heat island (UHI): reduced diurnal temperature range (DTR) due to high heat capacity and increased mean temperature from low albedo. The model captures the stronger nighttime UHI and reproduces observed patterns, showing its value in understanding UHI dynamics and urban effects.

This work extends the Mapping Particle Filter to account for local dependencies. Two localization methods are tested: a global particle flow with local kernels, and iterative local mappings based on correlation radius. Using a two-scale Lorenz-96 truth and a one-scale forecast model, experiments with full/partial and linear/nonlinear observations show Root Mean Square Error reductions using localized Gaussian mixture priors, achieving competitive performance against Gaussian filters.