The WOCE Global Synthesis: How far have we come, how far might we get? (Ocean State Estimation)

1
The WOCE Global Synthesis How far have we come,
how far might we get?(Ocean State Estimation)
Detlef Stammer Center for Observations, Modeling
and Predictions Scripps Institution of
Oceanography In consultation with D.
Behringer, J. Carton, G. Egbert, B. Ferron, I.
Fukumori, A. Koehl, T. Lee, R. Schlitzer, J.
Schroeter and C. Wunsch
2
Observing System
Each element of an ocean observing system samples
a specific aspects of the time-varying flow field.
3
Synthesis Concept

The concept of a WOCE data synthesis through
ocean state estimation (data assimilation) is to
obtain a dynamically self-consistent solution of
the ocean circulation and its uncertainties by
combining those diverse observations with a
state-of-the-art ocean general circulation model
(GCM). Results will be used subsequently to
study the ocean and its interaction with the
atmosphere.
4
State Estimation Components

• Model -Data Comparison
• Prior Statistics
• Estimation
• Posteriori Statistics (hypothesis testing)
• Scientific Analysis

5
International Synthesis Activities

• OSU Global tide model
• NCEP Simple Initialization
• SODA Simple Analysis
• AWI Global LSG adjoint, low resolution
• IFREMER/SOC Indian Ocean Synthesis
• ECCO Global and regional activities

6
The Methodology
Cost Function
Model
Penalty-function type cost function

The model can be imposed upon the objective
function by using Lagrange multipliers
(constrained optimization), or in an
unconstrained optimization form with a
penalty-function type of formulation.
7
Physical Self-Consistency
Quantitative ocean studies need dynamically
self-consistent solutions. Most data assimilated
solutions (including Kalman Filter) are not
physically consistent. Estimations with a
smoother or an adjoint method are.
Filtered Estimate
Smoothed Estimate
Filter Correction
Time
Model Physics
(Fukumori et al, 2002)
8
Example The ECCO Synthesis

• NOPP funded consortium (involving MIT, JPL and
  SIO)
• To describe the global ocean circulation at time
  scales of days to decades.
• To employ rigorous methods of ocean/data
  syntheses in a sustained form in support of
  GODADE and CLIVAR.
• Two streams (adjoint and KalmanFilter-Smoother
  approaches)
• The global synthesis (reanalysis) 1 degree,
  10yrs
• (intended 50yrs with 1 degree resolution and
  15 yrs with 1.4 degree).
• Near-realtime estimates 1-1/3 degree
  (intended ¼ degree).
• Data used as constraints include the WOCE data
  set altimetry, SST, XBT, sections, PALACE/ARGO,
  drifter, ...

9
The Mean Ocean Circulation, global
Geoid Estimate and Geoid Error
10
SSH Anomalies from T/P and ECCO
11
Example Indian Ocean Synthesis
20
Estimate
Indian Ocean WOCE Synthesis on 1 degree spatial
resolution
0
10
0
14
18
-10
20
First guess
0
0
4
6
-10
(Ferron and Marotzke, 2002)
12
The Mean Circulation, Indian Ocean
ECCO, 1 degree
0
3
4
10
0
2
18
1
(Ferron and Marotzke, 2002)
13
The Mean Circulation, Atlantic
Velocity and temperature, 160 m
Constraint
Constraint - Ref.
24
4.5
10
0
-4
-4
14
The Mean Circulation, Atlantic
Velocity and temperature, 2000 m
Constraint
Constraint - Ref.
0.3
5
4
-0.3
3
15
The Mean Circulation, Atlantic Pre-WOCE
Wunsch, 1978
N
ECCO
N
Latitude
16
RMS Temperature Misfit 160 m Depth
WHP Temperature
PALACE and ARGO Temperature
5
1
0
0
Quality control is an important aspect of a
climate observing system.
17
What have we learned from synthesis efforts?

• Only a few examples can be discussed here
• Barotropic variability
• Mean and time-varying flow field.
• Transports of heat, freshwater and volume.
• Surface Fluxes.
• Regional budgets of heat and freshwater.
• Ocean Dynamics Vorticity dynamics and bottom
  torques.
• Secular Trends.
• Tides and dissipation.
• Earth Angular Momentum.
• CO_2 Cycle.

18
Global Ocean Heat and Freshwater Transports
Freshwater Transports
Heat Transport
GW
o
Global
IP
Atl
O
o
19
Ocean Volume Transports
Mean Volume Transports
Volume Transports
Year
20
Heat Trans.
(PW)
IO
Mada
Indo
Volume (Sv)
Year
21
Volume Drake
Heat Transp.
(PW)
Drake
Cape
NA
SA
Year
(Schroeter, Wenzel et al., 2002)
ECCO
22
Interannual mixed-layer heat balance El Nino,
IOD, PDO
(Lee et al., 2002)
23
Time-mean tropical-subtropical
exchange through STC Poleward Ekman flow
equatorward pycnocline flow both via western
boundary interior.
Adjoint tracer c' (19801997) using the ECCO
analysis.

• Water flows along several distinct pathways
  from the subtropics to the tropics that depend on
  intra-annual fluctuation in circulation.

(Lee et al., 2002)
(Fukumori et al, 2002)
24
Surface Flux Estimates
Net Heat Flux
Zonal Wind Stress
100
Eq, 170W
ECCO-NCEP
ECCO
-100
100
Large-NCEP
TAO
NCEP
-100
1992
1998
Year
(Stammer, et al., 2002)
25
Vorticity Balance below 2200m
The left field is mostly balanced by the bottom
pressure torque (BPT), especially near topography.
Beta V
BPTfw
(Lu and Stammer, 2002)
26

In the deep ocean the circulation is strongly
influenced by topography. This is also reflected
in the complicated structures of the vertical
motion. The simulated flow field and vertical
motion bear little or no resemblence with the
Stommel-Arons theory.
(Lu and Stammer, 2002)
27
Secular Trends in the Ocean
(Schroeter, Wenzel et al., 2002)
28
Long-term Heat Uptake
Levitus
(Stammer, Koehl and Cornuelle, 2002)
(Schroeter, Wenzel et al., 2002)
29
Tidal energy dissipation
Assimilation of TOPEX/Poseidon data for global
ocean tides
Allowed mapping of tidal energy dissipation

• Ocean state barotropic tidal elevations and
  currents
• Dynamics frequency domain shallow water
  equations
• Weights allow misfit in momentum equations,
  conserve mass exactly
• Minimize penalty functional with a modified
  representer approach

1 TW dissipated over rough topography in the
deep ocean possible source of mechanical energy
for vertical mixing
(Egbert et al., 1994 Egbert and Ray, 2000)
30
Tidal Energy Dissipation

(Egbert et al., 1994 Egbert and Ray, 2000)
31
Infrastructure Support

• Community Model Developments
• Adjoint model Compilers
• Data and Model Infrastructure
• Computational Support

32
Model Development

• Community models MOM, POP, HYCOM, MIT, ...
• Community models are moving to similar physics,
  grids, numerics, adjoints.
• Example MIT GCM
• Used to study atmospheric and oceanic
  circulation.
• Non-hydrostatic capability.
• Finite volume treatment (lopped cells).
• Wide range of physical parameterizations (KPP,
  GM).
• Compatible with tangent linear and adjoint
  compiler.
• Exploits parallel computers.
• Designed to address the estimation problem.

(Marshall et al, 1997a,b)
33
Adjoint Model Compiler

• Source-to-sources differentiation tool.
• Adjoint model from a FORTRAN forward model.
• Allows easy addition of model improvements and
  new data.
• Available tools are TAMC, TAF, ... (Giering and
  Kaminski, 1998)
• New open-source tool underway (NSF ITR project).
• Use of the MIT/ECCO adjoint model
• Optimization (e.g., Stammer et al., 2002a,b,c,d)
• Sensitivity studies (e.g., Marotzke et al.,
  1999 Lee et al. 2002)
• Observing system design. (e.g., Koehl and
  Stammer, 2002 Koehl, 2002)

34
http//www.usgodae.fnmoc.navy.mil
Live Access Server (LAS)
http//www.ecco-group.org/las
http//www.usgodae.fnmoc.navy.mil
http//www.ecco-group.org/las
35
Computational Support

• State estimation needs considerable dedicated
  computational resources.
• Supported through NSF, ONR and NASA
  resources in US.
• NCAR
  NPACI/SDCS SIO/COMPAS

Atlas
Black Forest
36
How far can we get?

• What are the pressing problems?
• Error statistics and smoothing
• Extending the control space
• Extending model resolution
• Improving models
• Understanding coupled model assimilations

• What are (current) limitation?
• Model and forcing errors (biases)
• Non-linearities
• Data distributions
• Computational requirements
• Manpower

• What are the prospects?
• Ocean energetics and transports
• Mixing and ventilation
• Sea level rise
• Coupled climate simulations

37
Extended Control Vector Ocean Mixing

• State estimation allows to estimate mixing
  coefficients

Delta Horiz. Viscosity, 610m
Delta Horiz. Diffusivity, 610m
(Stammer, 2002)
38
Extended Control Vector Ocean Topography

• State estimation allows to improve aspects of
  the topography

(Losch and Wunsch, 2002)
39
Ocean Energetics and Wind Work

• Questions about first principles of the ocean can
  be addressed from ocean state estimates. Examples
  are wind work on the ocean and energetics of the
  ocean.
• But significant work is required to understand
  model limitations and possible improve models

Both mass leakages and numerical approximations
make unclear the extent to which models can be
regarded as energy conserving in any of the three
main elements (kinetic, potential and internal
energies).
40

ECCO Estimate of Wind work put into the ocean
(CI1000 W/m2)

X1000 W/m2
(Wunsch, 2002)
41
High-Resolution Estimations
Eddy-permitting Estimation in Subduction region
(1/6 degree) nested into global results.
Subduction Rate
Maximum MLD

• Subduction box results.

(Gebbie and Wunsch, 2002)
42
Adjoint Sensitivities and Observing Strategies
(Marotzke, et al., 1999)

43
Observing System Design Optimal Observations
Where does SSH need to be observed to reproduce
the Febr. Heat Transport??
(Koehl and Stammer , 2002)
44
Predictions Using the Adjoint Method
Required dynamically-consistent initialization
of a coupled ocean-atmosphere system using ocean
data. Preliminary application of the adjoint
method to a coarse resolution Indo-Pacific
coupled ENSO prediction model. Results show a
potential for improving prediction over 3dvar and
nudging assimilation (Galanti Tziperman
Harrison, Rosati, Sirkes, 2002)
45
ENSO Prediction Using the Adjoint Method
Predicted Nino3 SST Correlation RMS
Correlation
RMS Error
46
Biological Modeling and Carbon

• Estimates of CO_2 surface fluxes obtained by
  driving a biogeochemical model with from ECCO
  flow fields.

mol/m2/yr
(McKinley et al., 2002)
47
How far have we come?

• A time-varying synthesis of the WOCE dataset has
  been performed.
• Results will quickly improve and can be used for
  quantitative studies.
• Results are being produced already in near-real
  time.
• Estimation machinery will be essential for
  CLIVAR, GODAE.
• Ocean data are being used to understand and
  estimate air-sea fluxes.
• First steps toward a climate observing system
  design are underway.
• Much has to be learned regarding data and model
  errors, new data types, and new approaches.
• A time-varying coupled ocean-atmosphere system is
  the ultimate goal, but much has to be learned
  regarding coupled climate model initialization
• Limits in resolution and length of estimations
  have yet to be determined.
• It remains a challenge to convince the community
  about the value of ocean state estimation and to
  secure resources required to perform ocean state
  estimation in a sustained manner.

48
How far might we get?

• In 5-10 years
• We will have a sustained ocean/climate observing
  system.
• 1/64 degree global multi-year simulations of the
  global ocean will be performed.
• ¼ degree rigorous optimizations will be routine
  and sustained on global scale.
• Regional approaches will go to much higher
  resolution (1/10 degree?) .
• Ocean syntheses/reanalyses will be a standard
  means to understand long-term changes in the
  ocean and atmosphere over the past decades.
• Global coupled models will be run in assimilation
  mode to initialize climate prediction runs (ENSO
  to inter-decadal).
• Ocean and coupled syntheses will be used as a
  basis for carbon cycle simulations, etc.
• They will be used in many other applications
  operationally and scientifically.

49
High-Resolution Estimations
ECCO ¼ degree Assimilation in NA noise in
adtaux
(Koehl and Stammer, 2002)
50
Kalman Filter-Smoother
Partitioned Kalman Filter Smoother (MWR 2002)
approximates model errors by a sum of those of
smaller independent components.

• Allows a practical means to conduct a physically
  consistent near-optimal data assimilation at
  ultra-high resolutions.

(Fukumori et al., 2002)
51
The Role of variable "w" in ECCO Results
.5m/d
.3
W' at 220 and 610 m
610m
T'
int(wd_zT)
-.4
-.5m/d
80S
80N
0.8
Corrlelation
Depth
0
5000m
-0.8
(Stammer et at., 2002)
Latitude