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Ensemble Kalman Filter Junjie, Jeremy, Nir,
Kazuyuki, Ji-Sun, Jun. H
IntroductionSPEEDY model and data assimilationThe implementation of EnKF for the
carbon problem
Why are we here? What’s the main concern?
Prediction of CO2 concentration in the atmosphere for a better life on the earth
How to couple the CO2 with the climate? What we know now
The effect of CO2 on the global climate
Budget of CO2 exchange through the interface between land/ocean and atmosphere
General sense of transport through the atmospheric wind
Why are we here?
What we don’t know now The distribution of CO2 exchange between Land/Ocean and
the atmosphere [Source/Sink of CO2] Things that effect the variation of land/ocean CO2 uptakes
If we know the distribution of CO2 source/sink well, we may also be able to reduce atmospheric CO2 with a mechanism of land/ocean CO2 uptake.
Data assimilationVariational methods
t0 t1
Ensemble Kalman filter methods
Truth
forecast of t0 = background of t1
observation at t1
forecast of t1Require linear and adjoint modelProvides the initial condition of the ensemble forecast
assimilation window
corrected forecastJo
t0 tntiyo
yo
yo
yoprevious forecast
xbJb
Jo
Jo
Jo
xa
3D-V
ar
EnKF types
Perturbed ensemble Kalman filter
Square root ensemble Kalman filter
t0 t1
Truth
forecast of t0 = background of t1
observation at t1
forecast of t1
Background of t1
ObservationPerturbed ObservationsForecast of t1
t1t0
Local Ensemble Transform Kalman Fitler (LETKF)
One kind of Square root EnKF
SPEEDY
LETKF
observations
Ensemble forecast
Ensemble analysis
Use observation only in the local patch
Very parallel
Highly independent of the model
Initial perturbation: zonal wind (t=1,z=3) Stdev.=1
Difference in zonal wind (t=40,z=3)
Model integration(Perturbation becomes larger and propagates
around the world)
CHAOTIC SYSTEM
Time evolutions of zonal wind and these difference (z=1, global average)
Difference rapidly increases (after 2 weeks)
(m/s)
RMSE
CHAOTIC SYSTEM
w/ perturbation
w/o/ perturbation
Analysis increment (t=200, 500 hPa)
Analysis increment (t=2, 500 hPa)
RMS (zonal wind)Analysis becomes similar to “truth”
3D-VAR
Model integration
Background error (shaded) & analysis increment (contours)
(flow-independent) (flow-dependent)
“errors of the day”
3D-VAR LETKF
3D-VAR vs LETKF
LETKF analysis increment captures bkgd error patterns
Zonal wind
RMSE (zonal wind, 500hPa, global average)
LETKF provides better analysis(even with 10 ensemble members)
13 m/s11 m/s
3 m/s4.5 m/s
3D-VAR LETKF
3D-VAR vs LETKF
RMSE (zonal wind, pressure-longitude cross section)
Latitude
Pre
ssur
e
3D-VAR LETKF
Blue (small RMSE), Red (large RMSE: 8m/s-)
LETKF provides better analysis everywhereHemispheric asymmetry is coming from abundance of OBS data
1m/s
3m/s5m/s
1m/s
3m/s
5m/s
8m/s
3D-VAR vs LETKF
3D-VAR LETKF
Time
Pre
ssur
e
Blue (small RMSE), Red (large RMSE: 8m/s-)
RMSE (zonal wind, pressure-time cross section, global mean)
LETKF provides better analysis everywhereAnalysis error of zonal wind is large in the upper troposphere probably
because of a strong and stable subtropical jet stream
5m/s
3m/s2m/s
4m/s
3D-VAR vs LETKF
Summary for SPEEDY exercises
• Chaos is a significant difficulty when modeling physical systems
• Initial condition and model imperfections strongly favor the use of data assimilation
• Updating background error covariance using the forecast model results in significant improvements
• Even with a simple model such as SPEEDY, certain DA techniques may be hard to use (4DVar)
Prospects for using the ensemble Kalman filter for C data assimilation
Setting up carbon data assimilation: major issues
• Need a predictive model for C fluxes (~CASA land biosphere, ocean biogeochemistry+transport model) – simpler alternatives? (e.g. Sipnet)
• Atmospheric transport models are available and tried (e.g. NCEP/ECMWF reanalysis)
• Prior-uncertainty estimation probably feasible (cf. Anna's talk)
• Can we express everything as current state variables? (desirable not to need a lag)
Advantages of EnKF for this application
• Linearization of model nonlinearity not required• Derivatives, adjoints of messy models not required• Direct propagation of uncertainties• Large parts of the problem are inherently local
(forests don't move)
The challenges:carbon vs. weather
• Can we model the evolution of C fluxes? Our large-scale biology models are semiquantitative, at best – no simple laws.
• Variability on wide range of spatial and temporal scales – “log-linear” autocorrelograms– Model skill at different scales may not correlate well (cf.
Dave's talk)– Will running at synoptic timescales tell us anything about
long-term sinks and climate-change response?
Finis