Probabilistic Emulation of the Community Radiative Transfer Model Using Machine Learning

Technical Summary: Probabilistic Emulation of the Community Radiative Transfer Model Using Machine Learning

Problem Statement
Operational numerical weather prediction (NWP) systems rely heavily on the assimilation of satellite radiance observations to correct forecast drift and improve initial conditions. However, the computational cost of the observation operator—the radiative transfer model (RTM) used to map model state variables to expected observations—remains a significant bottleneck. Consequently, a vast majority of available satellite data, particularly from high-resolution sensors like the GOES Advanced Baseline Imager (ABI), goes unused in operational assimilation. While fast RTMs like the Community Radiative Transfer Model (CRTM) exist, they are still too slow to exploit the full volume of data, especially with the anticipated arrival of hyperspectral instruments. Furthermore, existing machine learning (ML) emulators of CRTM have been deterministic (producing point estimates) and instrument-specific, limiting their utility in data assimilation (DA) frameworks where explicit error characterization is required.

Methodology
The authors developed a neural network (NN) based probabilistic emulator to approximate the CRTM for the GOES-16 and GOES-17 ABI instruments, specifically targeting infrared channels 7–16.

• Data Generation: Training data was generated using the Global Forecast System Finite Volume Cubed Sphere (GFS FV3) model. Simulated ABI scans were created for a 30-day period (February 15 – March 15, 2022) at 6-hour intervals. CRTM was used to generate the target brightness temperatures and error characteristics for these inputs. The dataset was split into training (80%), validation (10%), and test (10%) sets.
• Model Architecture: The NN accepts 1,166 input variables, including 127 vertical levels of nine atmospheric profiles (e.g., temperature, water vapor, cloud properties), 16 surface variables, and seven metadata variables (sensor and solar angles). The architecture consists of three hidden fully connected layers with 512 nodes each, utilizing the SWISH activation function.
• Probabilistic Output: Unlike previous deterministic emulators, this model predicts a normal distribution for each channel. The output layer predicts both the mean brightness temperature (scaled between 180 K and 355 K) and the standard deviation of the error relative to CRTM.
• Training and Tuning: The model was trained using the Adam optimizer with a batch size of 32. The loss function employed was the Continuous Rank Probability Score (CRPS), which evaluates both the accuracy of the mean prediction and the reliability of the predicted uncertainty. Hyperparameters were tuned manually based on validation performance.
• Explainable AI (XAI): To ensure the model learned relevant physics rather than memorizing data, Shapely Additive Explanations (SHAP) were applied to analyze the impact of input variables on outputs for both clear-sky and cloudy conditions.

Key Results

• Predictive Accuracy: The emulator achieved a Root Mean Square Error (RMSE) of 0.3 K averaged across all channels. For clear-sky conditions, the RMSE was less than 0.1 K for 9 out of 10 infrared channels. Channel 7 exhibited higher errors due to its reflected short-wave IR component.
• Error Characterization: The model successfully predicted error standard deviations. The normalized RMSE (actual error divided by predicted standard deviation) was close to 1 for all channels, indicating the model slightly underestimates true errors but provides a reliable characterization of uncertainty. Calibration curves showed that predictions are well-calibrated for the vast majority of samples, with systematic underestimation occurring only for extreme error values.
• Computational Efficiency: On a single CPU, the ML emulator was approximately 5 times faster than CRTM. The authors note that CRTM is substantially slower for cloudy conditions, suggesting the speed advantage of the ML model would be even greater in those scenarios.
• Physical Consistency: SHAP analysis confirmed that the NN internalized relevant physical relationships. For water vapor channels, the model correctly identified the impact of water vapor at the expected atmospheric levels (upper, mid, and lower). The ozone channel was primarily driven by ozone mixing ratio, and Channel 7 was heavily influenced by solar zenith angle, consistent with radiative transfer physics. Jacobian comparisons showed good agreement with CRTM in the troposphere, though divergence occurred above 200 hPa due to a lack of stratospheric water vapor variability in the training data.

Significance and Claims
The paper claims that this work demonstrates the feasibility of using a probabilistic neural network to emulate CRTM for the ABI, a platform for which no ML operator previously existed. The primary significance lies in the model's ability to generate reliable probabilistic error estimates, a feature absent in prior deterministic emulators. This capability is crucial for operational DA, as it allows for a hybrid workflow where the fast ML emulator is used for assimilation when predicted errors are low, while the slower, physics-based CRTM can be reserved for cases where the emulator's uncertainty is high.

The authors assert that the model's accuracy (RMSE < 0.1 K for most clear-sky channels) is sufficient to support future DA experiments. The integration of XAI methods provides confidence that the model has learned the underlying physics, increasing the likelihood of robust performance on out-of-sample data. The study concludes that this approach offers a path to utilizing the currently unused fraction of ABI observations, potentially improving forecast skill, while acknowledging that further work is needed to refine performance for extreme error cases and to integrate the system into operational workflows.