Integrating GNSS-Derived Zenith Wet Delay into a Weather Foundation Model Improves Precipitation Forecasting

Technical Summary: Integrating GNSS-Derived Zenith Wet Delay into a Weather Foundation Model

Problem Statement
Despite the rapid advancement of machine learning weather models (MLWMs) and weather foundation models (WFMs) like Aurora, which rival traditional Numerical Weather Prediction (NWP) in computational efficiency, these models share a critical deficiency: the systematic underestimation of severe precipitation. This limitation stems partly from their reliance on training datasets derived from gridded reanalysis products (e.g., ERA5). Reanalysis fields often smooth out fine-scale spatial and temporal variations in column moisture due to assimilation cycles, leading to a filtered representation of water vapor that fails to capture the convective-scale variability necessary for accurate extreme event forecasting. Furthermore, while Global Navigation Satellite System (GNSS) signals have been assimilated into operational NWP for decades to measure atmospheric water vapor, leading MLWMs have not yet integrated GNSS-derived Zenith Wet Delay (ZWD) as an input variable.

Methodology
The authors present the first integration of GNSS-derived ZWD into Aurora, a state-of-the-art weather foundation model pretrained on ERA5, CMIP6, and operational forecasts. The study employs a two-stage fine-tuning protocol using the 1.3 billion-parameter "large" variant of Aurora:

1. Data Preparation: The study utilizes ZWDX, a global gridded ZWD product generated by an XGBoost model trained on over 19,000 GNSS stations. This product maps ERA5 inputs and station coordinates to GNSS-derived ZWD, providing spatially complete fields on a 0.25° grid aligned with Aurora's native resolution.
2. Step 1 (Learning Capability): The pretrained Aurora model is fine-tuned to predict ZWD as an auxiliary output variable alongside standard surface and pressure-level variables. This step verifies that the model's architecture can learn ZWD with skill comparable to its existing variables without structural modifications.
3. Step 2 (Precipitation Forecasting): Two parallel fine-tuning experiments are conducted to forecast six-hour accumulated precipitation (a task not present in pretraining):
   • Model A ("With ZWD"): Includes ZWD as an additional input and output variable.
   • Model B (Baseline, "Without ZWD"): Uses only standard variables.
   • Both models are initialized from the same pretrained checkpoint and trained with identical hyperparameters and data. The difference in performance isolates the specific contribution of GNSS-derived ZWD.
4. Evaluation: Models are evaluated on a held-out test set (April–December 2020) using deterministic metrics (MAE, RMSE, MSE, Pearson correlation), spatial structure metrics (Fractions Skill Score), threshold-based skill (Equitable Threat Score at various percentiles), and spectral fidelity (Log Spectral Distance across planetary, synoptic, and mesoscale bands).

Key Contributions

• First Integration: This work demonstrates the successful integration of GNSS-derived ZWD into a weather foundation model, establishing a new paradigm for incorporating geodetic observations into MLWMs.
• Learning Parity: The study proves that Aurora can learn ZWD as a new variable with skill levels comparable to its pretrained variables (e.g., specific humidity, wind, temperature) using standard variable-embedding mechanisms, requiring no bespoke modules.
• Systematic Improvement: The inclusion of ZWD systematically improves precipitation forecasts, with the most significant gains observed for extreme events.
• Spectral Realism: The integration results in a more realistic precipitation power spectrum at synoptic and planetary scales, indicating that ZWD helps correct the over-smoothing typical of deterministic forecasts.

Results

• ZWD Learning: In Step 1, ZWD was predicted with a correlation coefficient ($R$) of 0.998 and a relative MAE of 1.92%, performing on par with specific humidity and other standard surface variables.
• Deterministic Skill: In Step 2, adding ZWD reduced precipitation RMSE by 1.8% and MSE by 3.7% globally. The largest improvements occurred in the tropics and mid-latitude storm tracks, regions characterized by strong moisture-flux convergence.
• Extreme Event Skill: The Equitable Threat Score (ETS) for precipitation increased with event severity. At the 99th percentile (most extreme events), the ETS improved by 8.8%. This gain was consistent across individual high-impact events, including the South Asian monsoon, Typhoon Bavi, and Hurricane Delta.
• Spectral Fidelity: The Log Spectral Distance (LSD) decreased by 6.2% overall, with substantial improvements in the planetary (−39.9%) and synoptic (−33.6%) bands. This suggests ZWD provides structural information that sharpens the spatial organization of precipitation fields.
• Robustness: The improvements were statistically significant across ten training checkpoints and were not achieved at the expense of the model's performance on standard pretrained variables, which remained largely unchanged.

Significance and Claims
The authors claim that this study provides evidence that variables absent from standard reanalysis products, such as GNSS-derived ZWD, contain physical information critical for improving weather foundation models, particularly for high-impact precipitation forecasting. The results suggest that ZWD acts as a direct, unfiltered observable of column moisture that complements the smoothed humidity fields of reanalysis, allowing the model to better constrain moisture flux convergence and convective triggering.

The paper posits that these findings represent a "conservative lower bound," as the current implementation uses a gridded product (ZWDX) that still relies partially on ERA5 inputs. The authors suggest that future work utilizing raw, independent station data could yield even greater benefits. Ultimately, the study establishes a pathway for leveraging dense geodetic observing networks to enhance the reliability of AI weather forecasts in the situations where accuracy is most critical: extreme weather events.