your name On the specification of the Background Error Covariance Matrix for Wave Data Assimilation Systems • Jesús Portilla
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- 1. your name On the specification of the Background Error Covariance Matrix for Wave Data Assimilation Systems Jess Portilla
- 2. your name Introduction Motivation for Data Assimilation Model and observations usually dont match Users tend to trust more in observations Some situations are simply too difficult to model Some areas have dense monitoring networks that is a pity not to use to improve model results
- 3. your name Introduction Background errors determine the extent and the magnitude in which observations get introduced into the model wave field
- 4. your name Objective DA Statistical DA a b o bx x K x x 2 2 2 b o b K Statistical DA concept pdf
- 5. your name 1 2 , , i o m i j j i j J Q x x Optimization problem The DA scheme Variational (3DVAR, 4DVAR) Optimal interpolation Kalman Filtering Adjoint modelling Neural Networks . . . error covariance matrix 0J 2 0J 3DVAR
- 6. your name Background error covariance matrix (BECM) Covariance (Target) Variances (can be estimated, e.g., triple co-location)Correlation coefficient (can be estimated, e.g., via the R2) i j ij i i w w w w Greenslade, D.J.M. and I.R. Young, 2005: The impact of Altimeter Sampling Patterns on Estimates of Background Errors in a Global Wave Model, J. Atmos. Oc. Tech., 22, No. 12 pp 1895 1917.
- 7. your name The North Sea Voorrips A.C., V.K. Makin, and S. Hasselmann., 1997: Assimilation of wave spectra from pitch-and-roll buoys in a North Sea wave model, J. Geophys. Res., 102 (C3), 5829-5849 Parametric error correlation length (using wave height) exp a d L 3/ 2 200( ) a L km Background errors (parametric) K13
- 8. your name Some remarks about Background errors Our current knowledge about the structure (shape and dimensions) of Background Errors is very poor. For consistent DA, wave conditions must be homogeneous, isotropic, and ergodic over the assimilation domain. The computation of the Background Errors should consider the wave spectrum as the reference variable and not integral parameters like Hs. Background Errors depend on wave climate, which in turn might be characterized by the existence of different regimes. For a proper specification of the BECM each wave system has to be considered independently. The wave climate and therefore the BECM is point specific and season dependent.
- 9. your name Wave climate MODEL BUOY wind sea wind sea swell swell Buoy Hs = 4.2 m Model Hs = 2.7 m Matching observations and model spectra
- 10. your name is the partition spectrum The truth is emulated from WWIII model output Computation of the BECM i j ij i i w w w w 2 2 2 1 analyzed true ij true true S S R S S ,S S f
- 11. your name The spectral correction model @ @, * * ,analysis remote o true obs o oS f S f energy correction frequency correction direction correction Each wave system is corrected individually No assumptions are made about the wind-sea or swell condition
- 12. your name Calculating for two main wave systems (e.g., North Sea)
- 13. your name Calculating for two main wave systems (e.g., North Sea)
- 14. your name Northerly system K13 Southwesterly system K13 Parametric (general) Calculating for two main wave systems (e.g., North Sea)
- 15. your name Summary A method for the computation of the BECM has been developed This method considers explicitly: a) The local spectral wave climate b) The spectral correction model to be applied Assumptions about the wind-sea or swell condition are not used Conclusions The developed method allows calculating the BECM objectively on statistical bases The computed BECMs implicitly define the spatial domain where the conditions of isotropy and homogeneity are fulfilled The condition of ergodicity can be included for instance by computing BECMs for each season
- 16. your name References Voorrips A.C., V.K. Makin, and S. Hasselmann., 1997: Assimilation of wave spectra from pitch-and-roll buoys in a North Sea wave model, J. Geophys. Res., 102 (C3), 5829-5849 Greenslade, D.J.M. and I.R. Young, 2005: The impact of Altimeter Sampling Patterns on Estimates of Background Errors in a Global Wave Model, J. Atmos. Oc. Tech., 22, No. 12 pp 1895 1917. Thanks for your attention!
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