STIPP: Space-time in situ postprocessing over the French Alps using proper scoring rules

TL;DR

STIPP introduces a probabilistic, space-time in situ postprocessing framework that generates joint hourly ensembles for multiple weather variables from a six-hourly deterministic NWP input over a French Alpine station network. It uses a transformer-based encoder–processor–decoder architecture and trains with multivariate proper scoring rules, notably the Energy Score $ES$ and the marginal $CRPS$, to preserve spatio-temporal dependencies while maintaining sharpness. The approach outperforms baselines in both marginal accuracy and correlation structures, with variants illustrating the benefits of joint spatio-temporal training over time-step-wise predictions. Case studies and spectral analyses demonstrate improved temporal continuity and plausible cross-station correlations, suggesting practical value for hybrid gridded–in situ forecasting pipelines. Overall, STIPP advances data-driven atmospheric modeling by integrating postprocessing with temporal interpolation under a principled probabilistic training regime.

Abstract

We propose Space-time in situ postprocessing (STIPP), a machine learning model that generates spatio-temporally consistent weather forecasts for a network of station locations. Gridded forecasts from classical numerical weather prediction or data-driven models often lack the necessary precision due to unresolved local effects. Typical statistical postprocessing methods correct these biases, but often degrade spatio-temporal correlation structures in doing so. Recent works based on generative modeling successfully improve spatial correlation structures but have to forecast every lead time independently. In contrast, STIPP makes joint spatio-temporal forecasts which have increased accuracy for surface temperature, wind, relative humidity and precipitation when compared to baseline methods. It makes hourly ensemble predictions given only a six-hourly deterministic forecast, blending the boundaries of postprocessing and temporal interpolation. By leveraging a multivariate proper scoring rule for training, STIPP contributes to ongoing work data-driven atmospheric models supervised only with distribution marginals.

Figures (11)

• Figure 1: STIPP system diagram. The model makes joint probabilistic time series forecasts for a set of station locations, given a gridded NWP forecast and recent observations at these locations.
• Figure 2: The STIPP architecture. Top left. The NWP data encoder is used in conjunction with the station data encoder (not depicted) to build the input sequence. Bottom left. The input sequence contains tokens representing past and future states for each station, as well as tokens representing the NWP forecast. The forecast station tokens are placeholders which will be populated by the processor. Right. The processor is a self-attention transformer. It treats the encoded token sequences after relevant spatial, temporal and semantic embeddings are added. Stochasticity is injected through its conditional layer norm modules to enable generative forecasting.
• Figure 3: Skill scores for in situ weather forecasting according to lead time. The score are computed against the Schaake Shuffle baseline. The upward arrow (↑) indicates that lower is better for all metrics.
• Figure 4: Power spectrum density of STIPP variants forecasts in the lead time dimension. The spectra are represented as a ratio over the spectrum of the observations. A value of one indicates the same energy signature as the observations for that period.
• Figure 5: Spread-error ratios of STIPP variants.