Journal of Marine Science and Technology

, Volume 23, Issue 2, pp 319–332 | Cite as

Estimation of spatially varying parameters in three-dimensional cohesive sediment transport models by assimilating remote sensing data

  • Jicai Zhang
  • Dongdong Chu
  • Daosheng Wang
  • Anzhou Cao
  • Xianqing Lv
  • Daidu Fan
Original article
  • 153 Downloads

Abstract

Based on a three-dimensional cohesive sediment transport model with the adjoint data assimilation, the spatially varying parameters are estimated by assimilating satellite-retrieved suspended sediment concentrations (SSCs) in the Hangzhou Bay, China. To reduce the ill-posedness of the inverse problem, an independent point scheme is developed and a combined independent point and Tikhonov regularization scheme (CIPTRS) is presented. The CIPTRS is calibrated in ideal twin experiments and the results reveal that the CIPTRS can restrict the influence of ill-posedness and improve the accuracy of parameter estimation. In practical experiments, the spatially varying settling velocity is estimated by assimilating the satellite-retrieved SSCs using different strategies, and the best modeling results are obtained when the CIPTRS is used. To further improve the modeling results, the spatially varying settling velocity and initial conditions are estimated simultaneously using the CIPTRS. The data misfit between observed and simulated SSCs is largely decreased and the simulated SSCs can reproduce the spatial and temporal features of observed SSCs. The experimental results indicate that the adjoint method is a useful method to estimate the poorly known parameters in practical applications and the CIPTRS can effectively improve the results of data assimilation and parameter estimation.

Keywords

Cohesive sediment transport Data assimilation Adjoint method Parameter estimation Remote sensing data 

Notes

Acknowledgements

The authors would like to thank the reviewers for the constructive suggestions to greatly improve the manuscript. Thanks are extended to Professor Xianqiang He at Second Institute of Oceanography, State Oceanic Administration, China for providing the GOCI-retrieved SSCs data and Professor Jorge Nocedal at Northwestern University for sharing the source code of L-BFGS. Financial support to the study is provided by the national key research and development plan of China [Grant numbers 2017YFC1404000, 2017YFA0604100 and 2016YFC1402304], the Natural Science Foundation of Zhejiang Province [Grant number LY15D060001], the key research and development plan of Shandong Province [Grant number 2016ZDJS09A02], and the National Natural Science Foundation of China [Grant number 41206001].

References

  1. 1.
    Yang Z, Hamrick JM (2003) Variational inverse parameter estimation in a cohesive sediment transport model: an adjoint approach. J Geophys Res Oceans 1978–2012:108Google Scholar
  2. 2.
    Guan WB, Kot SC, Wolanski E (2005) 3-D fluid-mud dynamics in the Jiaojiang Estuary, China. Estuar Coast Shelf Sci 65:747–762CrossRefGoogle Scholar
  3. 3.
    Wang XH, Pinardi N (2002) Modeling the dynamics of sediment transport and resuspension in the northern Adriatic Sea. J Geophys Res Atmos 107:18-11–18-23Google Scholar
  4. 4.
    Dyer KR (1986) Coastal and estuarine sediment dynamics. Wiley, Oxford, p 173Google Scholar
  5. 5.
    Wang YP, Voulgaris G, Li Y, Yang Y, Gao J, Chen J, Gao S (2013) Sediment resuspension, flocculation, and settling in a macrotidal estuary. J Geophys Res Oceans 118:5591–5608CrossRefGoogle Scholar
  6. 6.
    Zhang J, Wang YP (2014) A method for inversion of periodic open boundary conditions in two-dimensional tidal models. Comput Methods Appl Mech Eng 275:20–38MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Lu X, Zhang J (2006) Numerical study on spatially varying bottom friction coefficient of a 2D tidal model with adjoint method. Cont Shelf Res 26:1905–1923CrossRefGoogle Scholar
  8. 8.
    Ullman DS, Wilson RE (1998) Model parameter estimation from data assimilation modeling: temporal and spatial variability of the bottom drag coefficient. J Geophys Res Atmos 103:5531–5549CrossRefGoogle Scholar
  9. 9.
    Chen H, Cao A, Zhang J, Miao C, Lv X (2014) Estimation of spatially varying open boundary conditions for a numerical internal tidal model with adjoint method. Math Comput Simul 97:14–38MathSciNetCrossRefGoogle Scholar
  10. 10.
    Fan W, Lv X (2009) Data assimilation in a simple marine ecosystem model based on spatial biological parameterizations. Ecol Model 220:1997–2008CrossRefGoogle Scholar
  11. 11.
    Navon IM (1998) Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography. Dyn Atmos Oceans 27(Special Issue in honor of Richard Pfeffer):55–79CrossRefGoogle Scholar
  12. 12.
    Hakami A, Henze D, Seinfeld J, Chai T, Tang Y, Carmichael G, Sandu A (2005) Adjoint inverse modeling of black carbon during the Asian Pacific Regional Aerosol Characterization Experiment. J Geophys Res Atmos 1984–2012:110Google Scholar
  13. 13.
    Tber MH, Talibi MEA, Ouazar D (2008) Parameters identification in a seawater intrusion model using adjoint sensitive method. Math Comput Simul 77:301–312MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Zhang J, Lu X (2008) Parameter estimation for a three-dimensional numerical barotropic tidal model with adjoint method. Int J Numer Methods Fluids 57:47–92MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Wang D, Cao A, Zhang J, Fan D, Liu Y, Zhang Y (2016) A three-dimensional cohesive sediment transport model with data assimilation: model development, sensitivity analysis and parameter estimation. Estuar Coast Shelf Sci. doi: 10.1016/j.ecss.2016.08.027 (in press) Google Scholar
  16. 16.
    Yeh WWG (1986) Review of parameter identification procedures in groundwater hydrology: the inverse problem. Water Resour Res 22:95–108CrossRefGoogle Scholar
  17. 17.
    Heemink A, Mouthaan E, Roest M, Vollebregt E, Robaczewska K, Verlaan M (2002) Inverse 3D shallow water flow modelling of the continental shelf. Cont Shelf Res 22:465–484CrossRefGoogle Scholar
  18. 18.
    Alekseev AK, Navon IM (2001) The analysis of an ill-posed problem using multi-scale resolution and second-order adjoint techniques. Comput Methods Appl Mech Eng 190:1937–1953MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Das S, Lardner R (1991) On the estimation of parameters of hydraulic models by assimilation of periodic tidal data. J Geophys Res Oceans 1978–2012(96):15187–15196CrossRefGoogle Scholar
  20. 20.
    Partheniades E (1965) Erosion and deposition of cohesive soils. J Hydraul Div 91:105–139Google Scholar
  21. 21.
    Thacker WC, Long RB (1988) Fitting dynamics to data. J Geophys Res Atmos 93:1227–1240CrossRefGoogle Scholar
  22. 22.
    Elbern H, Strunk A, Schmidt H, Talagrand O (2007) Emission rate and chemical state estimation by 4-dimensional variational inversion. Atmos Chem Phys 7:3749–3769CrossRefGoogle Scholar
  23. 23.
    Zhang J, Chen H (2013) Semi-idealized study on estimation of partly and fully space varying open boundary conditions for tidal models. Abstract and applied analysis. Hindawi Publishing Corporation, CairoMATHGoogle Scholar
  24. 24.
    Zhang J, Lu X (2010) Inversion of three-dimensional tidal currents in marginal seas by assimilating satellite altimetry. Comput Methods Appl Mech Eng 199:3125–3136MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    He X, Bai Y, Pan D, Huang N, Dong X, Chen J, Chen CTA, Cui Q (2013) Using geostationary satellite ocean color data to map the diurnal dynamics of suspended particulate matter in coastal waters. Remote Sens Environ 133:225–239CrossRefGoogle Scholar
  26. 26.
    Ryu JH, Choi JK, Eom J, Ahn JH, Ryu JH, Choi JK, Eom J, Ahn JH (2011) Temporal variation in Korean coastal waters using Geostationary Ocean Color Imager. J Coast Res:1731–1735Google Scholar
  27. 27.
    Chen C, Liu H, Beardsley RC (2003) An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: application to coastal ocean and estuaries. J Atmos Ocean Technol 20:159–186CrossRefGoogle Scholar
  28. 28.
    Du P, Ding P, Hu K (2010) Simulation of three-dimensional cohesive sediment transport in Hangzhou Bay, China. Acta Oceanol Sin 29:98–106CrossRefGoogle Scholar
  29. 29.
    MWRPRC (the Ministry of Water Resource of the People’s Republic of China) (2011) Bulletin of Chinese rivers and sediments 2011. China Water Power Press, Beijing (in Chinese) Google Scholar
  30. 30.
    Tang J (2007) Characteristics of fine cohesive sediment’s flocculation in the Changjiang estuary and its adjacent sea area, East China Normal University (in Chinese with English abstract)Google Scholar
  31. 31.
    Hu K, Ding P, Wang Z, Yang S (2009) A 2D/3D hydrodynamic and sediment transport model for the Yangtze Estuary, China. J Mar Syst 77:114–136CrossRefGoogle Scholar
  32. 32.
    Tikhonov A (1962) Solution of incorrectly formulated problems and the regularization method. Soviet Math Dokl 5Google Scholar
  33. 33.
    Terzopoulos D (1986) Regularization of inverse visual problems involving discontinuities. IEEE Trans Pattern Anal Mach Intell 8:413–424CrossRefGoogle Scholar
  34. 34.
    Cressman GP (1959) An operational objective analysis system. Mon Weather Rev 87:367–374CrossRefGoogle Scholar
  35. 35.
    Cai L, Tang DL, Li X, Zheng H, Shao W (2015) Remote sensing of spatial-temporal distribution of suspended sediment and analysis of related environmental factors in Hangzhou Bay, China. Remote Sens Lett 6:597–603CrossRefGoogle Scholar
  36. 36.
    Liu DC, Nocedal J (1989) On the limited memory BFGS method for large scale optimization. Math Program 45:503–528MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Zou X, Navon IM, Berger M, Phua KH, Schlick T, Dimet FXL (1992) Numerical experience with limited-memory quasi-Newton and truncated Newton methods. SIAM J Optim 3:582–608MathSciNetCrossRefMATHGoogle Scholar
  38. 38.
    Navon IM, Zou X, Derber J, Sela J (1992) Variational data assimilation with an adiabatic version of the NMC spectral model. Mon Weather Rev 120:1433CrossRefGoogle Scholar
  39. 39.
    Zou X, Navon IM, Sela J (1993) Control of gravitational oscillations in variational data assimilation. Mon Weather Rev 121:272–289CrossRefGoogle Scholar
  40. 40.
    Yang Z, Hamrick JM (2005) Optimal control of salinity boundary condition in a tidal model using a variational inverse method. Estuar Coast Shelf Sci 62:13–24CrossRefGoogle Scholar
  41. 41.
    Xie D, Wang Z, Gao S, Vriend HJD (2009) Modeling the tidal channel morphodynamics in a macro-tidal embayment, Hangzhou Bay, China. Cont Shelf Res 29:1757–1767CrossRefGoogle Scholar

Copyright information

© JASNAOE 2017

Authors and Affiliations

  • Jicai Zhang
    • 1
    • 2
  • Dongdong Chu
    • 1
  • Daosheng Wang
    • 3
    • 5
  • Anzhou Cao
    • 1
  • Xianqing Lv
    • 3
  • Daidu Fan
    • 4
  1. 1.Institute of Physical Oceanography, Ocean CollegeZhejiang UniversityZhoushanChina
  2. 2.State Key Laboratory of Satellite Ocean Environment DynamicsSecond Institute of Oceanography, State Oceanic AdministrationHangzhouChina
  3. 3.Physical Oceanography Laboratory/CIMSTOcean University of China and Qingdao National Laboratory for Marine Science and TechnologyQingdaoChina
  4. 4.State Key Laboratory of Marine GeologyTongji UniversityShanghaiChina
  5. 5.College of Oceanic and Atmospheric SciencesOcean University of ChinaQingdaoChina

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