Status and perspectives

of the TOPAZ system

Laurent.Bertino@nersc.no

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 …