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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.
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