One Encoding, Continuous Lead Times: Coherent Atmospheric Representations with Compositional Finite-Time Flows

Weather forecasts are often required at lead times that do not coincide with the temporal cadence of available data or trained forecasters. Although atmospheric evolution is continuous, most data-driven models learn transitions on a predefined temporal grid. Forecasts away from that grid therefore rely on interpolation, repeated fixed-step rollout, or separately learned horizon mappings, which neither explicitly represent intermediate evolution nor ensure that predictions at different lead times belong to the same atmospheric trajectory. The central challenge is thus not simply to provide time as an additional input, but to couple queried horizons through a common atmospheric representation and evolution rule. We present PhiCast, a coherent latent atmospheric evolution model that addresses this challenge through two coupled mechanisms. PhiCast encodes the observed multivariate atmosphere once as a shared spatial latent, converts forecast duration into a smooth state-aware coordinate, and uses a solver-free finite-time flow to map that same encoding directly to each queried horizon. This structure makes intermediate lead times directly accessible without interpolation, autoregressive feedback, numerical integration, or repeated encoding. Because direct queryability alone does not ensure that separately requested horizons describe one trajectory, composition-aware learning further aligns direct and temporally decomposed paths in both latent and forecast spaces. At lead times without direct forecast supervision, PhiCast attains the best Root Mean Square Error (RMSE) and Anomaly Correlation Coefficient (ACC) for all four evaluated variables, reducing variable-wise RMSE by 4.4–20.4% relative to the strongest competing result for each variable. Representation diagnostics further demonstrate smooth latent trajectories and substantially lower composition inconsistency. By making forecast duration an intrinsic coordinate of one coherent atmospheric representation, PhiCast establishes a path toward weather models whose temporal resolution is decoupled from the observation and supervision cadences that produced their training data.