Climate Dynamics

, Volume 53, Issue 9–10, pp 5349–5373 | Cite as

Sensitivity determined simultaneous estimation of multiple parameters in coupled models: part I—based on single model component sensitivities

  • Yuxin Zhao
  • Xiong Deng
  • Shaoqing ZhangEmail author
  • Zhengyu Liu
  • Chang Liu


While various data assimilation algorithms based on Bayes’ theorem have been developed for state estimation, some of these algorithms have also been applied to model parameter estimation. Coupled model parameter estimation (CPE) adjusts model parameters using available observations; then, the observation-adjusted parameters can greatly mitigate the model bias, which has great potential to reduce climate drift and enhance forecast skill in coupled climate models. However, given numerous model parameters that are associated with multiple time scales, how to conduct CPE with the simultaneous estimation of multiple parameters (SEMP) is still a popular research topic. With the aid of 3 coupled models, ranging from the conceptual coupled model to the intermediate coupled circulation model, this study has developed a systematic method to implement the SEMP–CPE. Linking coupled model sensitivities with the signal-to-noise ratio of the CPE, the SEMP–CPE method uses a timescale structure with coupled model sensitivities to determine which and how many parameters are estimated simultaneously in each CPE cycle to minimize the error of the coupled model simulation. Given that in a coupled model, the timescales by which different model components sensitively respond to a parameter perturbation can be quite different due to their different variabilities in their characteristic timescales, the first part of our study series focuses on the SEMP–CPE associated with single model component sensitivities. The results show that the quality of the model state analysis (in terms of assimilation) improves with the number of parameters being estimated by the order of sensitivities until the signal-to-noise ratio reaches a low threshold. Only when the most impactful physical parameters are estimated is the error of the state estimation consistently decreasing; as well as the signal-to-noise ratio in state-parameter covariance in SEMP scheme is enhanced. While only the signal extracted from the SEMP–CPE reaches saturated, the signal-to-noise ratio in the SEMP–CPE is maximized, and the state estimation error is minimized. Otherwise, if the parameters with low sensitivities are included in the CPE, the error of the state estimation increases instead. These results provide some insight into simultaneously estimating multiple parameters in a biased coupled general circulation model that assimilates real observations, which further improves climate analysis and prediction initialization.


Data assimilation Coupled parameter estimation Simultaneous estimation of multiple parameters Single model component sensitivities 



This research was funded by National CMOST Key Research & Development projects (Nos. 2017YFC1404100 and 2017YFC1404104), the NSFC (Nos. 51379049, 41676088, 41775100, and 41830964), the FRFCUC (Nos. HEUCFX41302, HEUCFD1505, and HEUCF160410), the YCAB of Heilongjiang Province (No. 1254G018), the SRFROCS of Heilongjiang Province (No. LC2013C21), and the HEU and CSC (which supported Xiong Deng studying abroad at GFDL/UW-Madison/OSU for two and a half years).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yuxin Zhao
    • 1
  • Xiong Deng
    • 1
    • 2
  • Shaoqing Zhang
    • 1
    • 3
    • 4
    Email author
  • Zhengyu Liu
    • 2
  • Chang Liu
    • 1
  1. 1.College of AutomationHarbin Engineering UniversityHarbinPeople’s Republic of China
  2. 2.Atmospheric Science Program, Department of GeographyOhio State UniversityColumbusUSA
  3. 3.Physical Oceanography Laboratory/CIMST, and College of Atmosphere and OceanOcean University of ChinaQingdaoPeople’s Republic of China
  4. 4.Qingdao National Laboratory for Marine Science and TechnologyQingdaoPeople’s Republic of China

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