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Feiyu Lu, Zhengyu Liu, Shaoqing Zhang, and Yun Liu


This paper studies a new leading averaged coupled covariance (LACC) method for the strongly coupled data assimilation (SCDA). The SCDA not only uses the coupled model to generate the forecast and assimilate observations into multiple model components like the weakly coupled version (WCDA), but also applies a cross update using the coupled covariance between variables from different model components. The cross update could potentially improve the balance and quality of the analysis, but its implementation has remained a great challenge in practice because of different time scales between model components. In a typical extratropical coupled system, the ocean–atmosphere correlation shows a strong asymmetry with the maximum correlation occurring when the atmosphere leads the ocean by about the decorrelation time of the atmosphere. The LACC method utilizes such asymmetric structure by using the leading forecasts and observations of the fast atmospheric variable for cross update, therefore, increasing the coupled correlation and enhancing the signal-to-noise ratio in calculating the coupled covariance. Here it is applied to a simple coupled model with the ensemble Kalman filter (EnKF). With the LACC method, the SCDA reduces the analysis error of the oceanic variable by over 20% compared to the WCDA and 10% compared to the SCDA using simultaneous coupled covariance. The advantage of the LACC method is more notable when the system contains larger errors, such as in the cases with smaller ensemble size, bigger time-scale difference, or model biases.

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Feiyu Lu, Zhengyu Liu, Shaoqing Zhang, Yun Liu, and Robert Jacob


This paper uses a fully coupled general circulation model (CGCM) to study the leading averaged coupled covariance (LACC) method in a strongly coupled data assimilation (SCDA) system. The previous study in a simple coupled climate model has shown that, by calculating the coupled covariance using the leading averaged atmospheric states, the LACC method enhances the signal-to-noise ratio and improves the analysis quality of the slow model component compared to both the traditional weakly coupled data assimilation without cross-component adjustments (WCDA) and the regular SCDA using the simultaneous coupled covariance (SimCC).

Here in Part II, the LACC method is tested with a CGCM in a perfect-model framework. By adding the observational adjustments from the low-level atmosphere temperature to the sea surface temperature (SST), the SCDA using LACC significantly reduces the SST error compared to WCDA over the globe; it also improves from the SCDA using SimCC, which performs better than the WCDA only in the deep tropics. The improvement in SST analysis is a result of the enhanced signal-to-noise ratio in the LACC method, especially in the extratropical regions. The improved SST analysis also benefits the subsurface ocean temperature and low-level atmosphere temperature analyses through dynamic and statistical processes.

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Yuchu Zhao, Zhengyu Liu, Fei Zheng, and Yishuai Jin


We performed parameter estimation in the Zebiak–Cane model for the real-world scenario using the approach of ensemble Kalman filter (EnKF) data assimilation and the observational data of sea surface temperature and wind stress analyses. With real-world data assimilation in the coupled model, our study shows that model parameters converge toward stable values. Furthermore, the new parameters improve the real-world ENSO prediction skill, with the skill improved most by the parameter of the highest climate sensitivity (gam2), which controls the strength of anomalous upwelling advection term in the SST equation. The improved prediction skill is found to be contributed mainly by the improvement in the model dynamics, and second by the improvement in the initial field. Finally, geographic-dependent parameter optimization further improves the prediction skill across all the regions. Our study suggests that parameter optimization using ensemble data assimilation may provide an effective strategy to improve climate models and their real-world climate predictions in the future.

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Jingzhe Sun, Zhengyu Liu, Feiyu Lu, Weimin Zhang, and Shaoqing Zhang


Recent studies proposed leading averaged coupled covariance (LACC) as an effective strongly coupled data assimilation (SCDA) method to improve the coupled state estimation over weakly coupled data assimilation (WCDA) in a coupled general circulation model (CGCM). This SCDA method, however, has been previously evaluated only in the perfect model scenario. Here, as a further step toward evaluating LACC for real world data assimilation, LACC is evaluated for the assimilation of reanalysis data in a CGCM. Several criteria are used to evaluate LACC against the benchmark WCDA. It is shown that despite significant model bias, LACC can improve the coupled state estimation over WCDA. Compared to WCDA, LACC increases the globally averaged anomaly correlation coefficients (ACCs) of sea surface temperature (SST) by 0.036 and atmosphere temperature at the bottom level (T s) by 0.058. However, there also exist regions where WCDA outperforms LACC. Although the reduction in the anomaly root-mean-square error (RMSE) is not as consistently clear as the increase in ACC, LACC can largely correct the biased model climatology.

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Xinrong Wu, Shaoqing Zhang, Zhengyu Liu, Anthony Rosati, Thomas L. Delworth, and Yun Liu


Because of the geographic dependence of model sensitivities and observing systems, allowing optimized parameter values to vary geographically may significantly enhance the signal in parameter estimation. Using an intermediate atmosphere–ocean–land coupled model, the impact of geographic dependence of model sensitivities on parameter optimization is explored within a twin-experiment framework. The coupled model consists of a 1-layer global barotropic atmosphere model, a 1.5-layer baroclinic ocean including a slab mixed layer with simulated upwelling by a streamfunction equation, and a simple land model. The assimilation model is biased by erroneously setting the values of all model parameters. The four most sensitive parameters identified by sensitivity studies are used to perform traditional single-value parameter estimation and new geographic-dependent parameter optimization. Results show that the new parameter optimization significantly improves the quality of state estimates compared to the traditional scheme, with reductions of root-mean-square errors as 41%, 23%, 62%, and 59% for the atmospheric streamfunction, the oceanic streamfunction, sea surface temperature, and land surface temperature, respectively. Consistently, the new parameter optimization greatly improves the model predictability as a result of the improvement of initial conditions and the enhancement of observational signals in optimized parameters. These results suggest that the proposed geographic-dependent parameter optimization scheme may provide a new perspective when a coupled general circulation model is used for climate estimation and prediction.

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