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DA-1

Method of Simulation

This section describes the simulation design and workflow used to develop and evaluate the adaptive covariance framework within the Optimal Interpolation (OI) data assimilation system. First, we define the control experiment with the Fixed R and the experimental configuration employing the Adaptive R. Next, we describe the assimilation procedure used to derive quadrant-specific observation error variances from the 2014–2023 test dataset, thereby constructing the Adaptive R matrix. Finally, we evaluate the resulting analysis fields (x_a) against independent 2024 validation cases and OISST reference data using RMSE improvement rate and analysis increment.

1. Experimental Structure

The primary objective of this experiment is to quantify the performance difference between a traditional Data Assimilation (DA) approach—which applies uniform error weights across the entire domain—and our proposed adaptive DA approach, which assimilates quadrant-specific observation uncertainties derived from 10 years of historical data. We aim to demonstrate how accounting for the physical asymmetry of typhoons significantly improves the accuracy of the analysis field.

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  • Data Sources and Role​​

    • To ensure a robust DA process, three distinct SST products were assigned specific roles based on their physical characteristics.​

    • For the implementation of Optimal Interpolation (OI), the datasets are defined as follows:

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We designed the experimental framework to assimilate quadrant-specific observation uncertainties while accounting for the physical asymmetry of typhoons.

2. Methodology

Since the regridding during preprocessing renders the observation operator H as an identity matrix, the data assimilation equation simplifies to equation-(1). To isolate the sensitivity of the observation error covariance (R), the background error covariance (B) is strictly controlled as a global constant.

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Equation-(1)

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A 1D Optimal Interpolation (OI) scheme was applied to estimate the Analysis field.

Step1: We compare two distinct configurations

  • Control Group (Case1: Fixed R)

    • Static Observation Error Covariance: A conventional approach that assigns a uniform, static observation error covariance across all quadrants and grid points within the 500-km domain.

    • Spatial Domain Restriction to a 500-km Radius (Common Condition): To eliminate ambient noise from surrounding ocean areas outside the storm's dynamic influence and to focus strictly on typhoon-induced SST responses (e.g., Cold Wake) and quadrant structures, the spatial domain for all data assimilation and error calculations was strictly masked within a 500-km radius from the typhoon center.

    • Background Error Control: To independently analyze the sensitivity of the observation error covariance (R), the background error covariance (B) was tightly controlled as a global constant.

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  • Experimental Group (Case2: Adaptive R)

    • A dynamic approach that allocates R values based on the quadrant-specific standard deviations of MW errors calculated from 10 years (2014–2023) of historical data. Notably, for regions with extreme observational uncertainty, such as the Rear-Right (RR) quadrant, a significantly larger R value is assigned. This conservatively modulates the Kalman Gain, equation-(2), effectively preventing over-correction driven by noisy observations.

    • Equation-(2)

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The Kalman Gain (K) is determined by the relative weight of the background error covariance (B) and the observation error covariance (R).

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Adaptive R

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Step2: Validation

The performance of each case is evaluated by calculating the RMSE between the resulting analysis fields and the truth proxy (OISST).

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  1. We quantify the error reduction (Improvement) across different quadrants—focusing specifically on the highly unstable RR quadrant—when moving from the Fixed R to the Adaptive R framework.

  2. The "Net Advantage" between the two experiments is calculated, followed by a Paired T-test to statistically prove the significance of the Adaptive R algorithm.

  3. Cross-Validation on 2024 Independent Data: The established adaptive R matrix is applied to typhoon cases from the year 2024 (out-of-sample data). By analyzing the actual error improvement and the spatial distribution of the DA increments, we verify that the proposed system effectively captures the physical asymmetry of typhoons and produces robust correction performance in independent real-world cases.

Go

This study compares Fixed R and quadrant-dependent Adaptive R within a 500-km typhoon centered domain and validates their performance using RMSE against OISST, showing improved error reduction—especially in the RR quadrant—through uncertainty based Kalman gain modulation, with consistent performance further confirmed on independent 2024 typhoon cases.

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