A Global Data-Driven Weather Emulator for Temperature and Precipitation Based on Higher-Order Linear Inverse Modeling

Empirical, data-driven models provide a complementary approach to dynamical models for simulating and forecasting weather and climate variability across daily to subseasonal timescales. We present ongoing work toward the development of a global, data-driven weather emulator for temperature and precipitation based on higher-order Linear Inverse Models (LIMs) formulated within the Empirical Model Reduction (EMR) framework. This formulation enables the representation of effective low-order dynamics, memory effects, and scale-dependent variability embedded in high-dimensional atmospheric fields. Rather than relying on a fixed EOF-based spatial decomposition, we explore a state-space approach in which the spatial basis is parameterized and optimized using Kalman filtering, thereby learning an optimal dynamical representation directly from the data.

The model is trained using a combination of NASA satellite observations and atmospheric reanalysis products. Near-surface temperature is modeled directly, while precipitation is represented using a pseudo-precipitation variable: precipitation equals observed rainfall where it occurs and otherwise corresponds to the negative air-column integrated water-vapor saturation deficit, defined as the amount of water vapor required to bring the atmospheric column to saturation at each vertical level. This formulation yields a continuous and dynamically meaningful representation of moist processes that facilitates the analysis of variability statistics across scales.

Model performance is evaluated in terms of its ability to reproduce observed variability statistics, temporal persistence, and subseasonal prediction skill, while dynamical diagnostics will be used to investigate the underlying sources of forecast skill. By focusing on the statistical and dynamical representation of variability, this work contributes to ongoing efforts to bridge data-driven modeling and theoretical perspectives on weather to climate variability across scales.