The application of ensemble Kalman filter in adaptive observation and information content

estimation studies

Junjie Liu and Eugenia Kalnay

July 13th, 2007

Question to address in adaptive observation study

Adaptive observation: temporarily adjust observation locations

• Common question: how to allocate the limited observation resources to maximize effectiveness of observations (improve the analysis and forecast as much as possible)?

• Question in hand: how to allocate 10% Doppler Wind Lidar (DWL) scanning range? (Future DWL will operate in adaptive targeting mode (NPOESS P3I science team) (observation locations change with time)

LETKF-based ensemble spread adaptive observation strategy

• It is the square root difference between ensemble members and ensemble mean state.

• Ensemble spread estimated from ensemble Kalman filter (EnKF) reflects the dynamical uncertainties related with background dynamic flow..

• In EnKF the ensemble spread strategy is very simple: we add the adaptive observations where the ensemble spread is large.

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Rawinsonde observation locations and simulated satellite winds scanning range

00z and 12z 00z and 12z06z and 18z 06z and 18z The “orbit” allows simulated DWL observations potentially scanning each location twice a day. Purpose: 10% adaptive observations: 10% of half global grid points.

Sampling strategies• Ensemble spread strategy (from Local Ensemble Transform Kalman Filter)

Adaptive observations are at locations with large ensemble wind spread at 500hPa.

3D-Var and LETKF have the same adaptive observation points

• Random picking Randomly pick locations from potential locations.

• Uniform distribution Uniformly distributed.

• Climatology ensemble spread Adaptive observations are at locations with large climatological

average ensemble wind spread from rawinsonde assimilation. Constant with time, and same for 3D-Var and LETKF.

• “Ideal” sampling

Adaptive observations are at locations with large background error obtained from the “truth”.

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500hPa zonal wind RMS error

4.04 2.36 0.92 0.74 0.43 0.36 0.30

3D-Var LETKF

RMSE

Rawinsonde; climatology; uniform; random; ensemble spread; “ideal”; 100%

With 10% adaptive observations, the analysis accuracy is significantly improved for both 3D-Var and LETKF.

3D-Var is more sensitive to adaptive strategies than LETKF. Ensemble spread strategy gets best result among operational possible strategies

1.18 0.38 0.36 0.33 0.32 0.29 0.23

500hPa zonal wind RMS error (2% adaptive obs)

3D-Var LETKF

With fewer (2%) adaptive observations, ensemble spread sampling strategy outperforms the other methods in LETKF

For 3D-Var, 2% adaptive observations are not enough to make significant improvement with any method

Rawinsonde; climatology; uniform; random; ensemble spread; “ideal”; 100%

Analysis sensitivity study within LETKF

S=∂Hxa

∂y=K THT =R−1HPaHT

• It can also show the cross sensitivity by exploring the off diagonal term.

• No cost in LETKF assimilation framework.

• Reflects the observation impact in the analysis.

• Show the analysis sensitivity to different type of observations (rawinsonde, different type of satellite observations etc.)

xa =xb + K (yo −h(xb))Analysis mean state:

The analysis sensitivity:

Degree of Freedom of Signal (DFS): the trace of the matrix S

Control experiment: rawinsonde only

All the dynamical variables (winds, temperature, specific humidity and surface pressure) are observed in the observation locations

Exp_uv (winds are observed in both rawinsonde and dense network, 30%)

Dense wind network

Contour: RMS error (zonal wind) difference between rawinsonde and exp_uv;

Shaded: DFS of zonal wind in dense network

Winds have large impact over the region that does not have much rawinsonde, especially over Southern Hemisphere and the Tropics.

The DFS reflects the wind impact

Possible applications to Carbon problem

• Observation system design: ensemble spread method; Using the posterior uncertainty estimation.

• Evaluate the significance of the carbon observations: based on the sensitivity study (impact of the carbon concentration data on the flux estimation)

• Will address the essential problem: uncertainty estimation