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Article

A Geographic-Dependent Coupled Parameter Optimization Scheme Based on A-4DEnVar

by
Jianxin He
1,
Lige Cao
1,*,
Wei Li
1,
Guijun Han
1,
Xuan Wang
1,
Hong Li
1,
Kangzhuang Liang
2,
Gongfu Zhou
1,
Haowen Wu
1,
Qingyu Zheng
1,
Yang Zhang
1 and
Yicong Tong
1
1
Tianjin Key Laboratory for Marine Environmental Research and Service, School of Marine Science and Technology, Tianjin University, Tianjin 300072, China
2
Tianjin Institute of Meteorological Science, Tianjin 300074, China
*
Author to whom correspondence should be addressed.
J. Mar. Sci. Eng. 2026, 14(5), 418; https://doi.org/10.3390/jmse14050418
Submission received: 31 January 2026 / Revised: 23 February 2026 / Accepted: 24 February 2026 / Published: 25 February 2026
(This article belongs to the Special Issue Ocean Climate: Deep Learning, Statistical Methods and Dynamical Modeling)
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Abstract

Coupled climate models integrate atmospheric, oceanic, and land submodels, while the uncertainty of model parameters from different parameterization schemes or empirically derived parameters inevitably introduces systematic biases. Coupled parameter optimization (CPO) can reduce these biases to improve weather forecast and climate prediction, but must address strong nonlinearities inherent in coupled models. The analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation method retains the nonlinear processing capability of the four-dimensional variational (4D-Var) data assimilation method but gets rid of the dependence on the adjoint model. In this study, a novel dynamic independent point (DIP) scheme is introduced to the improved A-4DEnVar, which reduces computational dimensionality and further explores a broader parameter space of dimensionality reduction through the outer loop. Based on the improved A-4DEnVar, a series of geographic-dependent CPO experiments with an idealized 2D coupled model are carried out. Results show that A-4DEnVar accurately captures the geographical characteristics of parameters and effectively optimizes cross-component parameters despite strong nonlinearity. Additionally, the DIP scheme presents significant advantages compared to the static independent point scheme, especially with fewer independent points. This work is offering a new perspective for parameter optimization in coupled general circulation models used for climate estimation and prediction.
Keywords: A-4DEnVar; coupled parameter optimization; geographic-dependent parameter optimization; independent point scheme A-4DEnVar; coupled parameter optimization; geographic-dependent parameter optimization; independent point scheme

Share and Cite

MDPI and ACS Style

He, J.; Cao, L.; Li, W.; Han, G.; Wang, X.; Li, H.; Liang, K.; Zhou, G.; Wu, H.; Zheng, Q.; et al. A Geographic-Dependent Coupled Parameter Optimization Scheme Based on A-4DEnVar. J. Mar. Sci. Eng. 2026, 14, 418. https://doi.org/10.3390/jmse14050418

AMA Style

He J, Cao L, Li W, Han G, Wang X, Li H, Liang K, Zhou G, Wu H, Zheng Q, et al. A Geographic-Dependent Coupled Parameter Optimization Scheme Based on A-4DEnVar. Journal of Marine Science and Engineering. 2026; 14(5):418. https://doi.org/10.3390/jmse14050418

Chicago/Turabian Style

He, Jianxin, Lige Cao, Wei Li, Guijun Han, Xuan Wang, Hong Li, Kangzhuang Liang, Gongfu Zhou, Haowen Wu, Qingyu Zheng, and et al. 2026. "A Geographic-Dependent Coupled Parameter Optimization Scheme Based on A-4DEnVar" Journal of Marine Science and Engineering 14, no. 5: 418. https://doi.org/10.3390/jmse14050418

APA Style

He, J., Cao, L., Li, W., Han, G., Wang, X., Li, H., Liang, K., Zhou, G., Wu, H., Zheng, Q., Zhang, Y., & Tong, Y. (2026). A Geographic-Dependent Coupled Parameter Optimization Scheme Based on A-4DEnVar. Journal of Marine Science and Engineering, 14(5), 418. https://doi.org/10.3390/jmse14050418

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