Validation Simulation Result
(2024 Validation Dataset)
RMSE Improvement & Analysis Increment
To verify the generalizability of the proposed framework, the adaptive matrix was applied to independent typhoon cases from 2024.
Fig. 4. Comparison of quadrant-specific SST RMSE improvement rates (left) and mean analysis increments (right) for the independent 2024 validation dataset. Even in the independent 2024 cases, the Adaptive R framework comprehensively outperforms the Fixed R baseline in error reduction across all quadrants, proving the system's generalizability through conservative increment constraints in the RR sector and robust corrections in the remaining quadrants.
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Comprehensive RMSE Improvement Across All Sectors (Left Plot): Compared to the Fixed R, the proposed Adaptive R framework consistently improved the RMSE reduction rate across all four quadrants (FR, FL, RR, RL). This overall improvement indicates that the quadrant-specific uncertainty characteristics derived from historical data remain stable and valid when applied to independent typhoon cases.
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Reduced Increment via Conservative Weighting in the RR Quadrant (Right Plot): In the Right-Rear (RR) quadrant, the mean analysis increment under Adaptive R decreased to 0.056 K (from 0.066 K under Fixed R), representing the lowest value among all sectors. This quantitatively confirms that assigning a larger observation error covariance (R) in the highly unstable RR quadrant effectively reduces the Kalman gain. Notably, despite assimilating fewer observations to avoid over-correction from convective noise, the RMSE reduction in the RR quadrant increased from 3.13% to 3.52%, demonstrating improved data assimilation performance.
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Enhanced Increments in the Remaining Quadrants (FR, FL, RL) (Right Plot): Conversely, quadrants with higher observational reliability exhibited larger analysis increments under the Adaptive R configuration compared to the Fixed R: FR (0.078 ⇒ 0.089 K), FL (0.077 ⇒ 0.096 K), and RL (0.061 ⇒ 0.067 K). By assigning greater weights to reliable observations, the system more effectively corrected the model field.
In validation experiments, the Adaptive R framework consistently improves RMSE by applying quadrant-dependent weighting that reduces over-correction in the RR quadrant and strengthens updates in more reliable regions.
Representative Error Case Study for Validation: TC 2418
To evaluate the physical and statistical consistency of the proposed adaptive data assimilation system on independent data, a spatial distribution and increment analysis was conducted on Typhoon 2418 (2024-09-26 12:00:00) from the independent 2024 validation dataset.
Spatial Distribution Analysis in Geographic Coordinates
The geographic coordinate maps show the data assimilation process in the context of the full typhoon track and sea surface temperature (SST) distribution over the Northwest Pacific.
Fig. 5. Spatial distribution of data assimilation fields for TC 2418 in geographical coordinates (2024-09-26 12:00:00). Panels (a) and (c) display the spatial distribution of DA increments cooling the model field, while panels (b) and (d) show the post-assimilation analysis biases responding to the widespread initial warm bias (red) along the typhoon track.
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Typhoon Track and Warm Bias Concentration: As Typhoon 2418 moved across the Northwest Pacific, a widespread warm bias (Fig. 5-(b), (d), red regions) in the ERA5 reanalysis was observed extensively along and around the storm's track. This reflects a systematic tendency of the model to underestimate typhoon-induced sea surface cooling (cold wake) effects.
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Physical Consistency of the Assimilation:To correct this warm bias, both the Fixed and Adaptive frameworks produced negative increments (Fig. 5-(a), (c), purple regions) surrounding the storm, effectively cooling the background field. Consequently, this case provides a suitable test case to evaluate the performance of quadrant-specific adaptive weighting, given the pronounced baseline error structure of the model.
Typhoon 2418 exhibits a widespread ERA5 warm bias along the storm track, which is effectively corrected by negative SST increments from both assimilation schemes, providing a strong test case for evaluating quadrant-specific adaptive weighting under large background errors.
Quantitative Analysis in Typhoon-Centric Local Coordinates
The local coordinate maps standardize the storm domain into a 500-km rectangular grid by aligning the typhoon's heading with the positive y-axis (along-track direction), thereby isolating the error control mechanisms relative to the storm's asymmetric physical structure.
Fig. 6. Quantitative comparison between Fixed R and Adaptive R frameworks in a 500km typhoon-centric local coordinate system for TC 2418. Panels (a) and (b) present the increment and analysis bias for Fixed R (RMSE: 0.215 K), while panels (c) and (d) present those for Adaptive R (RMSE: 0.218 K).
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Drivers of Enhanced Total Increments (a vs c): The mean absolute analysis increment across the local domain increased from 0.084 K (Fixed R) to 0.093 K (Adaptive R), indicating that the system more strongly enhanced corrections in the highly reliable forward quadrants (FR, FL).
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Suppression of Increments in the RR Quadrant: In the highly unstable RR quadrant (bottom-right), the magnitude of increments is noticeably reduced under the Adaptive R framework (c). This reflects the effect of a larger observation error covariance (R), which reduces the Kalman gain, thereby limiting the influence of noise-contaminated observations and preventing over-correction.
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The RMSE Performance of the Analysis field: For TC 2418, the domain-wide RMSE under Adaptive R (0.218 K) is slightly higher than under Fixed R (0.215 K), a difference of 0.003 K. However, quadrant-level results support the benefit of the adaptive approach. With an initial RR bias of 0.1050 K, Adaptive R yields a positive net improvement of 0.0017 K, indicating effective error reduction in the RR region.
In validation experiments, the Adaptive R framework improves quadrant-wise error consistency by reducing RR-region bias, despite a slight increase in domain-mean RMSE.