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Status and perspectives
of the TOPAZ system
An EC FP V project, Dec 2000-Nov 2003http://topaz.nersc.no
NERSC/LEGI/CLS/AWI
Continued development of DIADEM system…
Continuing with the MerSea Str.1 and MerSea IP EC-projects
The monitoring and prediction system
From DIADEM to TOPAZ
• Model upgrades– MICOM upgraded to HYCOM– 2 Sea-Ice models– 3 ecosystem models (1 simple, 2 complex)– Nesting: Gulf of Mexico, North Sea
(MONCOZE)
From DIADEM to TOPAZ
• Assimilation already in Real-time– SST ¼ degree from CLS, with clouds.– SLA ¼ degree from CLS.
• Assimilation tested– SeaWIFs Ocean Colour data (ready)– Ice parameters from SSMI, Cryosat (ready) – In situ observations: ARGO floats and XBT (ready)– Temperature brightness from SMOS (ready)
Assimilation methods
• Kalman filters: full Atlantic domain
– Ensemble Kalman Filter (EnKF)
– Singular Evolutive Extended Kalman Filter (SEEK)
• Optimal Interpolation: Nested models
– Ensemble Optimal Interpolation (EnOI)
Grid size: from 20 to 40 km
SSH from assimilation and data
EnKF: local assimilation of SST
Perspectives
• EnKF: one generic assimilation scheme (global/local)
• Possibilities for specific schemes – using methodology from geostatistics– Estimation under constraints (conservation)– Estimation of transformed Gaussian variables
(Anamorphosis)
Thus TOPAZ is
• Extension and utilization of DIADEM system
• Product and user oriented with strong link to off shore industry
• Contribution to GODAE and EuroGOOS task teams
• To be continued with Mersea IP EC-project.
• CUSTOMERS <=> TOPAZ <=> GODAE
Summary
• HYCOM model system completed and validated
• Assimilation capability for in situ and ice observations ready
• Development of forecasting capability for regional nested model (cf Winther & al.)
• Operational demonstration phase started
• Results on the web http://topaz.nersc.nohttp://topaz.nersc.no
Assimilating ice concentrations
• Assimilation of ice concentration controls the location of the ice edge
• Correlation changes sign dependent on season
• A fully multivariate approach is needed
• Largest impact along the ice edge
Ice concentration update
Temperature update
Assimilating TB data
• Brightness temperature TB will be available from SMOS (2006)
• Assimilation of TB data controls SSS and impacts SST
• TB (SST, SSS, Wind speed, Incidence, Azimuth, Polarization)
• Results are promising using the EnKF
TB data SST SSS TB
TB Assimilation SST impact SSS impact
Bibliography
• The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation,
Geir Evensen, in print, Ocean Dynamics, 2003.
• About the anamorphosis:
Sequential data assimilation techniques in oceanography,
L. Bertino, G. Evensen, H. Wackernagel, (2003)
International Statistical Review, (71), 1, pp. 223-242.
An Ensemble Kalman Filter for non-Gaussian variables
L. Bertino1, A. Hollard2, G. Evensen1, H. Wackernagel2
1- NERSC, Norway2- ENSMP - Centre de Géostatistique, France
Work performed within the TOPAZ EC-project
Overview
• “Optimality” in Data Assimilation– Simple stochastic models, complex physical
models→ Difficulty: feeding models with estimates
• The anamorphosis: – Suggestion for an easier model-data interface
• Illustration – A simple ecological model
Data assimilation at the interface between statistics and physics
f f0 1
h h
1
( ) ( ) ( )n n
n n
x x x
X X X
Y Y
State
Observations
stochastic model– f, h: linear operators– X, Y: Gaussian – Linear estimation
optimal
“optimality” for non-physical criteria => post-processing
physical model– f, h: nonlinear – X, Y: not Gaussian – … sub-optimal
The multi-Gaussian modelunderlying in linear estimation methods
• state variables• and assimilated data
• between all variables• and all locations
Gaussian histogram
s
Linear relations
The world does not need to look like this ...
Why Monte Carlo sampling?
• Non-linear estimation: no direct method– The mean does not commute with nonlinear
functions:
E(f(X)) f(E(X))
• With random sampling A={X1, … X100}
E(f(X)) 1/100 i f(Xi)
• EnKF: Monte-Carlo in propagation step
• Present work: Monte-Carlo in analysis step
The EnKFMonte-Carlo in model propagation
• Advantage 1: a general tool– No model linearization– Valid for a large class of nonlinear physical models– Models evaluated via the choice of model errors.
• Advantage 2: practical to implement– Short portable code, separate from the model code– Perturb the states in a physically understandable way– Little engineering: results easy to interpret
• Inconvenient: CPU-hungry
Ensemble Kalman filterbasic algorithm (details in Evensen 2003)
f f0 1
h h
1
( ) ( ) ( )n n
n n
x x x
X X X
Y Y
State
Observations
nonlinear propagation, linear analysis
Aan = f(Aa
n-1) + Kn (Yn - HAfn )
Aan = Af
n . X5
Notations: Ensemble A = {X1, X2,… X100}, A’ = A - Ā
Kalman gain:
Kn = Anf A’f
nT HT .
( H A’fn A’f
nT HT + R ) -
1
AnamorphosisA classical tool from geostatistics
More adequate for linear estimation and simulations
Physicalvariable
Cumulative density function
Statistical variable
Example: phytoplankton in-situ
concentrations
Anamorphosis in sequential DAseparate the physics from statistics
Physical operations: Anamorphosis
function
Statistical operation: A and Y
transformedForecast
Afn = f (Aa
n-1)
Forecast
Afn+1 = f (Aa
n)
Analysis
Aan = Af
n + Kn(Yn-HAfn)
• Adjusted every time or once for all
• Polynomial fit, distribution tails by hand
The anamorphosisMonte-Carlo in statistical analysis
• Advantage 1: a general tool– Valid for a larger class of variables and data– Applicable in any sequential DA (OI, EKF …)– Further use: probability of a risk variable
• Advantage 2: practical implementation– No truncation of unrealistic/negative values (no gravity
waves?)– No additional CPU cost– Simple to implement
• Inconvenient: handle with care!
Characteristics• Sensitive to initial
conditions• Non-linear dynamics
Nutrients
Phytoplankton Herbivores
0. 100. 200. 300.
0. 100. 200. 300.
Temps (j)
-200.
-100.
0. Profondeur (m)
9
6
3
0mM/m3
0. 100. 200. 300. -200.
-100.
0. >4
3
2
1
0mM/m3
Illustration Idealised case: 1-D ecological model
• Spring bloom model, yearly cycles in the ocean
• Evans & Parslow (1985), Eknes & Evensen (2002)
time-depths plots
Anamorphosis (logarithmic transform)
Original
histograms
asymmetric
Histograms of logarithms
less asymmetric
N P H
0.0 0.5 1.0
ref-H
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Frequencies
0. 5. 10.
ref-N
0.00
0.05
0.10
0.15
Frequencies
0. 1. 2. 3.
ref-P
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Frequencies
Isatis
-15. -10. -5. 0.
log ref-H
0.00
0.05
0.10
0.15
0.20
0.25
Frequencies
-3. -2. -1. 0. 1. 2.
log ref-N
0.00
0.05
0.10
0.15
0.20
Frequencies
-10. -5. 0.
log ref-P
0.00
0.05
0.10
0.15
0.20
Frequencies
Arbitrary choice, possible refinements (polynomial fit)
EnKF assimilation results
• Gaussian assumption
– Truncated H < 0
– Low H values overestimated
– “False starts”
• Lognormal assumption
– Only positive values
– Errors dependent on values
RMS errors
Gaussian Lognormal
N
P
H
0. 100. 200. 300.
0. 100. 200. 300. 0. 100. 200. 300.
0. 100. 200. 300.
>=0.036
0.018
0
-0.018
<-0.036mM/m3
0. 100. 200. 300.
0. 100. 200. 300.
>=0.08
0.04
0
-0.04
<-0.08mM/m3
Conclusions
• An “Optimal estimate” is not an absolute concept– “Optimality” refers to a given stochastic model
– Monte-Carlo methods for complex stochastic models
• The anamorphosis and linear estimation– Handles a more general class of variables
– Applications in marine ecology (positive variables)
• Can be used with OI, EKF and EnKF.• Next: combination of EnKF with SIR …