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

Abstract

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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Xuefeng Zhang, Shaoqing Zhang, Zhengyu Liu, Xinrong Wu, and Guijun Han

Abstract

Imperfect physical parameterization schemes in a coupled climate model are an important source of model biases that adversely impact climate prediction. However, how observational information should be used to optimize physical parameterizations through parameter estimation has not been fully studied. Using an intermediate coupled ocean–atmosphere model, the authors investigate parameter optimization when the assimilation model contains biased physics within a biased assimilation experiment framework. Here, the biased physics is induced by using different outgoing longwave radiation schemes in the assimilation model and the “truth” model that is used to generate simulated observations. While the stochastic physics, implemented by initially perturbing the physical parameters, can significantly enhance the ensemble spread and improve the representation of the model ensemble, the parameter estimation is able to mitigate the model biases induced by the biased physics. Furthermore, better results for climate estimation and prediction can be obtained when only the most influential physical parameters are optimized and allowed to vary geographically. In addition, the parameter optimization with the biased model physics improves the performance of the climate estimation and prediction in the deep ocean significantly, even if there is no direct observational constraint on the low-frequency component of the state variables. These results provide some insight into decadal predictions in a coupled ocean–atmosphere general circulation model that includes imperfect physical schemes that are initialized from the climate observing system.

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Guijun Han, Xinrong Wu, Shaoqing Zhang, Zhengyu Liu, and Wei Li

Abstract

Coupled data assimilation uses a coupled model consisting of multiple time-scale media to extract information from observations that are available in one or more media. Because of the instantaneous exchanges of information among the coupled media, coupled data assimilation is expected to produce self-consistent and physically balanced coupled state estimates and optimal initialization for coupled model predictions. It is also expected that applying coupling error covariance between two media into observational adjustments in these media can provide direct observational impacts crossing the media and thereby improve the assimilation quality. However, because of the different time scales of variability in different media, accurately evaluating the error covariance between two variables residing in different media is usually very difficult. Using an ensemble filter together with a simple coupled model consisting of a Lorenz atmosphere and a pycnocline ocean model, which characterizes the interaction of multiple time-scale media in the climate system, the impact of the accuracy of coupling error covariance on the quality of coupled data assimilation is studied. Results show that it requires a large ensemble size to improve the assimilation quality by applying coupling error covariance in an ensemble coupled data assimilation system, and the poorly estimated coupling error covariance may otherwise degrade the assimilation quality. It is also found that a fast-varying medium has more difficulty being improved using observations in slow-varying media by applying coupling error covariance because the linear regression from the observational increment in slow-varying media has difficulty representing the high-frequency information of the fast-varying medium.

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Jeffrey L. Anderson, Bruce Wyman, Shaoqing Zhang, and Timothy Hoar

Abstract

An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held–Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model’s state at all levels when only observations of surface pressure (PS) are available. The impacts of varying the spatial density and temporal frequency of PS observations are examined. The error of the ensemble mean assimilation prior estimate appears to saturate at some point as the number of PS observations available once every 24 h is increased. However, increasing the frequency with which PS observations are available from a fixed network of 1800 randomly located stations results in an apparently unbounded decrease in the assimilation’s prior error for both PS and all other model state variables. The error reduces smoothly as a function of observation frequency except for a band with observation periods around 4 h. Assimilated states are found to display enhanced amplitude high-frequency gravity wave oscillations when observations are taken once every few hours, and this adversely impacts the assimilation quality. Assimilations of only surface temperature and only surface wind components are also examined.

The results indicate that, in a perfect model context, ensemble filters are able to extract surprising amounts of information from observations of only a small portion of a model’s spatial domain. This suggests that most of the remaining challenges for ensemble filter assimilation are confined to problems such as model error, observation representativeness error, and unknown instrument error characteristics that are outside the scope of perfect model experiments. While it is dangerous to extrapolate from these simple experiments to operational atmospheric assimilation, the results also suggest that exploring the frequency with which observations are used for assimilation may lead to significant enhancements to assimilated state estimates.

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

Abstract

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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Xiangbo Feng, Nicholas Klingaman, Shaoqing Zhang, and Liang Guo
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Feiyu Lu, Zhengyu Liu, Shaoqing Zhang, Yun Liu, and Robert Jacob

Abstract

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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Xinrong Wu, Wei Li, Guijun Han, Shaoqing Zhang, and Xidong Wang

Abstract

While fixed covariance localization can greatly increase the reliability of the background error covariance in filtering by suppressing the long-distance spurious correlations evaluated by a finite ensemble, it may degrade the assimilation quality in an ensemble Kalman filter (EnKF) as a result of restricted longwave information. Tuning an optimal cutoff distance is usually very expensive and time consuming, especially for a general circulation model (GCM). Here the authors present an approach to compensate the demerit in fixed localization. At each analysis step, after the standard EnKF is done, a multiple-scale analysis technique is used to extract longwave information from the observational residual (referred to the EnKF ensemble mean). Within a biased twin-experiment framework consisting of a global barotropical spectral model and an idealized observing system, the performance of the new method is examined. Compared to a standard EnKF, the hybrid method is superior when an overly small/large cutoff distance is used, and it has less dependence on cutoff distance. The new scheme is also able to improve short-term weather forecasts, especially when an overly large cutoff distance is used. Sensitivity studies show that caution should be taken when the new scheme is applied to a dense observing system with an overly small cutoff distance in filtering. In addition, the new scheme has a nearly equivalent computational cost to the standard EnKF; thus, it is particularly suitable for GCM applications.

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

Abstract

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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Shan Li, Shaoqing Zhang, Zhengyu Liu, Xiaosong Yang, Anthony Rosati, Jean-Christophe Golaz, and Ming Zhao

Abstract

Uncertainty in cumulus convection parameterization is one of the most important causes of model climate drift through interactions between large-scale background and local convection that use empirically set parameters. Without addressing the large-scale feedback, the calibrated parameter values within a convection scheme are usually not optimal for a climate model. This study first designs a multiple-column atmospheric model that includes large-scale feedbacks for cumulus convection and then explores the role of large-scale feedbacks in cumulus convection parameter estimation using an ensemble filter. The performance of convection parameter estimation with or without the presence of large-scale feedback is examined. It is found that including large-scale feedbacks in cumulus convection parameter estimation can significantly improve the estimation quality. This is because large-scale feedbacks help transform local convection uncertainties into global climate sensitivities, and including these feedbacks enhances the statistical representation of the relationship between parameters and state variables. The results of this study provide insights for further understanding of climate drift induced from imperfect cumulus convection parameterization, which may help improve climate modeling.

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