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