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Mathematical Problems in Engineering
Volume 2013, Article ID 373540, 12 pages
Research Article

Optimization of the Spatiotemporal Parameters in a Dynamical Marine Ecosystem Model Based on the Adjoint Assimilation

1Laboratory of Physical Oceanography, Ocean University of China, Qingdao 266100, China
2Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
3Key Laboratory of Marine Spill Oil Identification and Damage Assessment Technology, The organaization of North China Sea Monitoring Center, Qingdao 266033, China
4Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China

Received 15 January 2013; Accepted 28 April 2013

Academic Editor: Ker-Wei Yu

Copyright © 2013 Xiaoyan Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By utilizing spatiotemporal biological parameterizations, the adjoint variational method was applied to a 3D marine ecosystem dynamical model. The results of twin experiments demonstrated that the mean absolute error (MAE) of phytoplankton in the surface layer and the reduced cost function (RCF) could be used to evaluate both the simulation results and parameter estimation. Spatiotemporal variation of key parameters (KPs) was optimized in real experiments. The RCF and MAE in each assimilation period (72 periods per year) decreased obviously. The spatially varying KP (KPS), temporally varying KP (KPT), and constant KP (KPC) were obtained by averaging KPs of spatiotemporal variation. Another type of spatiotemporal KP (KPST) was represented by KPS, KPT, and KPC. The correlation analysis of KPs, either KPS or KPT, accorded with the real ecological mechanism. Running the model with KPS, KPT, KPC, and KPST, respectively, we found that MAE was the minimum when KPs were spatiotemporal variation (KPST), while MAE reached its maximum when KPs were constant (KPC). Using spatiotemporal KPs could improve simulation precision compared with only using spatially varying KPs, temporally varying KPs, or constant KPs (these forms are the results in a previous study). KPST, a representation of spatiotemporal variation, reduces the variable number in calculation.