Status and perspectives
of the TOPAZ system
[email protected]
An EC FP V project, Dec 2000-Nov 2003
http://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.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, Norway
2- ENSMP - Centre de Géostatistique, France
Work performed within the TOPAZ ECproject
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
State
X0 ( x)
f


Observations
stochastic model
– f, h: linear operators
– X, Y: Gaussian
– Linear estimation
optimal
f
X n ( x) 
 X n 1 ( x)
h
h
Yn
Yn 1
physical model
– f, h: nonlinear
– X, Y: not Gaussian
– … sub-optimal
“optimality” for non-physical criteria => post-processing
The multi-Gaussian model
underlying in linear estimation methods
Gaussian
histogram
s
Linear
relations
• state variables
• between all
variables
• and assimilated
data
• and all locations
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 EnKF
Monte-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 filter
basic algorithm (details in Evensen 2003)
State
X0 ( x)
Observations
f


f
X n ( x) 
 X n 1 ( x)
h
h
Yn
Yn 1
nonlinear propagation, linear
analysis
Aan = f(Aan-1) + Kn (Yn - HAfn )
Aan = Afn . X5
Kalman gain:
Kn = Anf A’fnT HT .
( H A’fn A’fnT HT + R ) 1
Notations: Ensemble A = {X1, X2,… X100}, A’ = A - Ā
Anamorphosis
A classical tool from geostatistics
Physical
variable
Cumulative
density
function
Statistical
variable
Example: phytoplankton
in-situ concentrations
More adequate for linear estimation and
Anamorphosis in sequential DA
separate the physics from statistics
Physical
operations:
Forecast
Anamorphosis
function
Statistical
operation: A and Y
transformed
Afn = f (Aan-1)
Analysis
Aan = Afn + Kn(Yn-HAfn)
Forecast
Afn+1 = f (Aan)
• Adjusted every time or once for all
• Polynomial fit, distribution tails by hand
The anamorphosis
Monte-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!
Illustration
Idealised case: 1-D ecological model
• Spring bloom model, yearly cycles in the ocean
• Evans & Parslow (1985), Eknes & Evensen (2002)
Characteristics
• Sensitive to initial
conditions
• Non-linear dynamics
Nutrients
Phytoplankton
time-depths plots
Herbivores
Anamorphosis
(logarithmic transform)
Original
histograms
asymmetric
N
P
H
Histograms
of logarithms
less
asymmetric
Arbitrary choice, possible refinements (polynomial fit)
EnKF assimilation results
Gaussian
N
Lognormal
• Gaussian
assumption
– Truncated H < 0
– Low H values
overestimated
– “False starts”
P
• Lognormal
assumption
– Only positive
values
H
– Errors dependent
on values
RMS errors
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 …