×

zbMATH — the first resource for mathematics

A hybrid data assimilation scheme for model parameter estimation: application to morphodynamic modelling. (English) Zbl 1432.86005
Summary: We present a novel algorithm for joint state-parameter estimation using sequential three dimensional variational data assimilation (3D Var) and demonstrate its application in the context of morphodynamic modelling using an idealised two parameter 1D sediment transport model. The new scheme combines a static representation of the state background error covariances with a flow dependent approximation of the state-parameter cross-covariances. For the case presented here, this involves calculating a local finite difference approximation of the gradient of the model with respect to the parameters. The new method is easy to implement and computationally inexpensive to run. Experimental results are positive with the scheme able to recover the model parameters to a high level of accuracy. We expect that there is potential for successful application of this new methodology to larger, more realistic models with more complex parameterisations.
MSC:
86-08 Computational methods for problems pertaining to geophysics
86A05 Hydrology, hydrography, oceanography
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Soulsby, R., Dynamics of marine sands, (1997), Thomas Telford Publications
[2] Scott, T.R.; Mason, D.C., Data assimilation for a coastal area morphodynamic model: morecambe bay, Coastal eng, 54, 91-109, (2007)
[3] van Dongeren, A.; Plant, N.; Cohen, A.; Roelvink, D.; Haller, M.C.; Catalán, P., Beach wizard: nearshore bathymetry estimation through assimilation of model computations and remote observations, Coastal eng, 55, 1016-1027, (2008)
[4] Jazwinski, A.H., Stochastic processes and filtering theory, (1970), Academic Press · Zbl 0203.50101
[5] Navon, I.M., Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dyn atmos oceans, 27, 55-79, (1997)
[6] Evensen, G.; Dee, D.P.; Schröter, J., Parameter estimation in dynamical models, (), 373-398 · Zbl 0992.76075
[7] Bell, M.; Martin, M.; Nichols, N., Assimilation of data into an Ocean model with systematic errors near the equator, Quart J R meteorol soc, 130, 873-894, (2004)
[8] Martin M, Nichols N, Bell M. Treatment of systematic errors in sequential data assimilation. Technical Note No. 21. Meteorological Office, Ocean Applications Division; 1999.
[9] Griffith, A.K.; Nichols, N.K., Adjoint techniques in data assimilation for treating systematic model error, J flow, turb combust, 65, 469-488, (2000) · Zbl 1094.76556
[10] Trudinger, C.; Raupach, M.; Rayner, P.; Enting, I., Using the Kalman filter for parameter estimation in biogeochemical models, Environmetrics, 19, 8, (2008)
[11] Hansen, J.A.; Penland, C., On stochastic parameter estimation using data assimilation, Physica D, 230, 88-98, (2007) · Zbl 1113.62141
[12] Kondrashov, D.; Sun, C.; Ghil, M., Data assimilation for a coupled ocean – atmosphere model, Mon weather rev, 136, 5062-5076, (2008)
[13] Courtier, P.; Andersson, E.; Heckley, W.; Pailleux, J.; Vasiljevic, D.; Hamrud, M., The ECMWF implementation of three-dimensional variational assimilation (3D-var). I: formulation, Quart J R meteorol soc, 124, 1783-1807, (1998)
[14] Nichols, N.K., Mathematical concepts of data assimilation, () · Zbl 0633.65075
[15] Smith, P.J.; Baines, M.J.; Dance, S.L.; Nichols, N.K.; Scott, T.R., Variational data assimilation for parameter estimation: application to a simple morphodynamic model, Ocean dyn, 59, 5, 697-708, (2009)
[16] Smith PJ, Dance SL, Nichols NK. Data assimilation for morphodynamic model parameter estimation: a hybrid approach. Mathematics Report 2/2009. Department of Mathematics, University of Reading; 2009.
[17] Hamill, T.M.; Snyder, C., A hybrid ensemble Kalman filter-3D variational analysis scheme, Mon weather rev, 128, 2905-2919, (2000)
[18] Smith PJ, Baines MJ, Dance SL, Nichols NK, Scott TR. Data assimilation for parameter estimation with application to a simple morphodynamic model. Mathematics Report 2/2008. Department of Mathematics, University of Reading; 2008.
[19] Grass A. Sediment transport by waves and currents. Report No.: FL29. SERC London Centre for Marine Technology; 1981.
[20] Spiegelman, M.; Katz, R.F., A semi-Lagrangian crank – nicolson algorithm for the numerical solution of advection – diffusion problems, Geochem geophys geosyst, 7, 4, (2006)
[21] Rodgers, C.D., Inverse methods for atmospheric sounding: theory and practice, Series on atmospheric, oceanic and planetary physics, vol. 2, (2000), World Scientific · Zbl 0962.86002
[22] Smith PJ. Joint state and parameter estimation using data assimilation with application to morphodynamic modelling. Ph.D. Thesis, University of Reading; 2010.
[23] Gill, P.E.; Murray, W.; Wright, M.H., Practical optimization, (1981), Academic Press · Zbl 0503.90062
[24] Smith PJ, Dance SL, Nichols NK. A hybrid sequential data assimilation scheme for model state and parameter estimation. Mathematics Report 2/2010, Department of Mathematics, University of Reading; 2010. <http://www.reading.ac.uk/maths/research/>.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.