AMSR-E Science Team Meeting

1
AMSR-E Science Team Meeting Missoula, MT Aug
14-16, 2007 An adaptive ensemble Kalman filter
for soil moisture data assimilation R.
Reichle1,2, W. Crow3, C. Keppenne2, and R.
Koster1,2 rolf.reichle_at_gmao.gsfc.nasa.gov
1 - Goddard Earth Sciences and Technology Center,
UMBC 2 - Global Modeling and Assimilation Office,
NASA-GSFC 3 - Hydrology and Remote Sensing Lab,
USDA-ARS
2
Introduction
Large-scale soil moisture is needed, for example,
for water cycle studies and for initializing
weather/climate models. It is available from
Catchment land surface model forced w/ observed
meteorology. Complete space-time coverage, incl.
root zone.
AMSR-E surface soil moisture Upper 1cm, 50km,
daily.
Weights based on respective uncertainties.
Soil moisture retrievals (subject to error)
Model soil moisture (subject to error)
Assimilation
Optimalsoil moisture
3
Global assimilation of AMSR-E soil moisture
retrievals
Assimilate AMSR-E surface soil moisture (2002-06)
into NASA Catchment model
Validate with USDA SCAN stations (only 23 of 103
suitable for validation)
Anomaly time series correlation coeff. with in situ data - (with 95 confidence interval) Anomaly time series correlation coeff. with in situ data - (with 95 confidence interval) Anomaly time series correlation coeff. with in situ data - (with 95 confidence interval) Confidence levels Improvement of assimilation over Confidence levels Improvement of assimilation over
N Satellite Model Assim. Satellite Model
Surface soil moisture 23 .38.02 .43.02 .50.02 gt99.99 gt99.99
Root zone soil moisture 22 n/a .40.02 .46.02 n/a gt99.99
Assimilation product agrees better with ground
data than satellite or model alone. Modest
increase may be close to maximum possible with
imperfect in situ data. Reichle et al., JGR, 2007
4
Input error parameters Q and R
Weights themselves are subject to error!!! Wrong
weights may lead to poor estimates.
5
Synthetic assimilation experiment
Investigate impact of wrong model and obs error
inputs on assimilation estimates
Precip., radiation, (subject to error)
True precip., radiation,
Repeat for many different sets of model and
retrieval error covs.
Land model (subject to error)
Retrieval error covariance R (subject to error)
Model error covariance Q (subject to error)
True land model
Soil moisture retrievals (subject to error)
Model soil moisture (subject to error)
True soil moisture
Assimilation (EnKF)
Optimalsoil moisture
compare
Reichle et al., WRR 2007 (in review)
6
Impact of Q and R on assimilation estimates
RMSE of assimilation estimates v. truth for
Surface soil moisture m3/m3
Each symbol represents one 19-year assim.
experiment over the Red-Arkansas with a unique
combination of input model and observation error
parameters.
Q model error (including errors in precip,
radiation, and soil moisture tendencies) P
P(Q) soil moisture error variance
forecast error std-dev
input obs error std-dev
Reichle et al., WRR 2007 (in review)
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Impact of Q and R on assimilation estimates
RMSE of assimilation estimates v. truth for
Surface soil moisture m3/m3

• True input error covariances yield minimum
  estimation errors.
• Wrong model and obs. error covariance inputs
  degrade assimilation estimates.
• In most cases, assimilation still better than
  open loop (OL).

Reichle et al., WRR 2007 (in review)
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Impact of Q and R on assimilation estimates
RMSE of assimilation estimates v. truth for
Root zone soil moisture m3/m3
Surface soil moisture m3/m3
sqrt(P(Q_true))

• Root zone more sensitive than surface soil
  moisture.

Reichle et al., WRR 2007 (in review)
9
Impact of Q and R on assimilation estimates
(fluxes)
RMSE of assimilation estimates v. truth for
Sensible heat flux W/m2
Latent heat flux W/m2
Runoff mm/d

• Fluxes more sensitive to wrong error parameters
  than soil moisture.
• Sensible/latent heat more sensitive to model
  error cov than obs error cov
• (probably related to ensemble propagation).

Reichle et al., WRR 2007 (in review)
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Diagnostics of filter performance and adaptive
filtering

• Find true Q, R by enumeration?
• RMSE plots require truth (not usually
  available).
• Too expensive computationally.
• Use diagnostics that are available within the
  assimilation system.

Filter update x x- K(y x-) K P (P
R)-1 Kalman gain Diagnostic E(y - x-) (y
x-)T P R
innovations obs model prediction (internal
diagnostic)
state err cov obs err cov (controlled by inputs)
Example Average obs. minus model prediction
distance is much larger than assumed input
uncertainties
soil moisture
time
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Diagnostics of filter performance and adaptive
filtering

• Find true Q, R by enumeration?
• RMSE plots require truth (not usually
  available).
• Too expensive computationally.
• Use diagnostics that are available within the
  assimilation system.

Filter update x x- K(y x-) K P (P
R)-1 Kalman gain Diagnostic E(y - x-) (y
x-)T P R
state err cov obs err cov (controlled by inputs)
innovations obs model prediction (internal
diagnostic)
Contours misfit between diagnostic and what it
should be. Adaptive filter Nudge input error
parameters (Q, R) during assimilation to minimize
misfit.
Reichle et al., WRR 2007 (in review)
12
Diagnostics of filter performance and adaptive
filtering

• Find true Q, R by enumeration?
• RMSE plots require truth (not usually
  available).
• Too expensive computationally.
• Use diagnostics that are available within the
  assimilation system.

Filter update x x- K(y x-) K P (P
R)-1 Kalman gain Diagnostic E(y - x-) (y
x-)T P R
state err cov obs err cov (controlled by inputs)
innovations obs model prediction (internal
diagnostic)
Contours misfit between diagnostic and what it
should be. Adaptive filter Nudge input error
parameters (Q, R) during assimilation to minimize
misfit.
Diagnostic 1 E(y - x) (y x-)T
R Diagnostic 2 E(x -x-) (y x-)T P(Q)
Reichle et al., WRR 2007 (in review)
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Adaptive v. non-adaptive EnKF (soil moisture)
Adaptive
Difference
Non-adaptive
Surface soil moisture m3/m3
Contours RMSE of assim. estimates v. truth
Root zone soil moisture m3/m3

• Adaptive filter Map experiment onto contour
  plot based on initial guess of R, P(Q).
• Adaptive filter yields improved assimilation
  estimates for initially wrong model and
  observation error inputs (except for R00).

Reichle et al., WRR 2007 (in review)
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Adaptive v. non-adaptive EnKF (fluxes)
Contours RMSE of assim. est. v. truth
Non-adaptive
Adaptive
Difference

• Adaptive filter generally yields improved flux
  estimates.
• Degradation when R is severely underestimated. ?
  Simply choose large R at the start and let the
  filter adapt it.

Sensible heat flux W/m2
Latent heat flux W/m2
Runoff mm/d
Reichle et al., WRR 2007 (in review)
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Adaptive v. non-adaptive EnKF (filter diagnostics)
Non-adaptive
Adaptive
Difference

• Adaptive filter (by design) improves innovations
  stats.
• Adaptive filter retrieves obs error std (except
  for R00).
• On balance, adaptive filter improves estimate of
  error bars on assimilation product (surface soil
  moisture).

Log10 of innov. misfit
Error in estimate of obs error std sqrt(R) m3/m3
Error in estimate of analysis error std
sqrt(P) m3/m3
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Adaptive filter summary
Wrong model and observation error inputs degrade
assimilation estimates. Degradation quantified
with synthetic experiment over Red-Arkansas river
basin. Adaptive EnKF Generally improves
assimilation estimates. Better at estimating
obs. error cov. R than model error cov. Q.
Cheap.
Try it out for AMSR-E...
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Variance of normalized innovations
from assimilation of AMSR-E soil moisture
(2002-06)
Non-adaptive
Adaptive
Reichle et al., JGR 2007
Variance of normalized innovations (ideally equal
to 1)
Variance deficiency in dry climates, excess
variance in wetter climates.
Improvement by (adaptively) tuning model error
parameters.
18
Mean of normalized innovations
from assimilation of AMSR-E soil moisture
(2002-06)
Non-adaptive
Adaptive
Reichle et al., JGR 2007
Mean of normalized innovations (ideally equal to
0)
Biases appear because adaptive tuning changes
strength of perturbations. Leads to changes in
model climate of soil moisture, which is then
inconsistent with a priori scaling.
No statistically significant biases detected
(after scaling of retrievals to model climate).
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Adaptive adjustments
from assimilation of AMSR-E soil moisture
(2002-06)
Obs. error variance
Model error variance
Blue Obs/model error in non-adaptive filter was
over-estimated. Red Obs/model error in
non-adaptive filter was under-estimated.
? Derive error estimates for AMSR-E soil
moisture retrievals.
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AMSR-E soil moisture retrievals errors
Non-adaptive (initial guess)
Adaptive
Adaptive filter yields error estimates for AMSR-E
soil moisture retrievals.
21
Global assimilation of AMSR-E soil moisture
retrievals
Assimilate AMSR-E surface soil moisture (2002-06)
into NASA Catchment model with adapative EnKF
Validate with USDA SCAN stations (only 23 of 103
suitable for validation)
Anomaly time series correlation coeff. with in situ data - (with 95 confidence interval) Anomaly time series correlation coeff. with in situ data - (with 95 confidence interval) Anomaly time series correlation coeff. with in situ data - (with 95 confidence interval) Confidence levels Improvement of assimilation over Confidence levels Improvement of assimilation over
N Satellite Model Assim. Satellite Model
Surface soil moisture 23 .38.02 .43.02 .50.02 gt99.99 gt99.99
Root zone soil moisture 22 n/a .40.02 .46.02 .47.02 n/a gt99.99
No significant change with adaptive filter
Assimilation product agrees better with ground
data than satellite or model alone. Modest
increase may be close to maximum possible with
imperfect in situ data.
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Soil moisture data assimilation OSSE
Adaptive filter useful for future mission
design How uncertain can retrievals be and still
add useful information in the assimilation
system?
Reichle et al., GRL 2007 (in prep)
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Previous work Soil moisture retrieval OSSE
Soil moisture retrieval Observing System
Simulation Experiment (OSSE) Can we achieve a
retrieval accuracy of 0.04 m3/m3 (4) in
absolute soil moisture with realistic errors in
brightness temperatures and retrieval
parameters? What is the impact of time-invariant
errors on retrieval accuracy?
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Soil moisture assimilation OSSE Design
True radiative transfer model
True brightness temp.
True soil moisture
True land model
True precip., radiation,
Precip., radiation, (subject to error)
compare
1.) Add data assimilation.
Land model (subject to error)
Optimalsoil moisture
Brightness temp. (subject to error)
Retrieval algorithm (subject to error)
Model soil moisture
Soil moisture retrievals
Assimilation
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Soil moisture assimilation OSSE Design
True radiative transfer model
True brightness temp.
True soil moisture
True land model
True precip., radiation,
compare
2.) Repeat for many different sets of model and
retrieval error characteristics to get contour
plots.
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Contribution of soil moisture retrievals to land
assimilation products
Skill (R) of assimilation product (surface soil
moisture)
Skill (R) of assimilation product (root zone soil
moisture)
Skill (R) of model (root zone soil moisture)
Skill (R) of model (surface soil moisture)
Skill (R) of retrievals (surface soil moisture)
Skill (R) of retrievals (surface soil moisture)
The skill of the assimilation product increases
with the skill of the retrievals and the skill of
the model. Published AMSR-E and SMMR
assimilation products are consistent with
expected skill levels for surface soil moisture,
to a lesser degree also for root zone soil
moisture.
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Contribution of soil moisture retrievals to land
assimilation products
Skill (R) added to assimilation product (surface
soil moisture)
Skill (R) added to assimilation product (root
zone soil moisture)
Skill (R) of model (root zone soil moisture)
Skill (R) of model (surface soil moisture)
Skill (R) of retrievals (surface soil moisture)
Skill (R) of retrievals (surface soil moisture)
Assimilation of soil moisture retrievals adds
skill (relative to model product). Even
retrieval data sets of poor quality contribute
valuable information to the assimilation product.
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New EOS project
Towards improved weather and sub-seasonal climate
forecasts through assimilation of NASA EOS land
surface products into the NASA GMAO seasonal
forecasting and weather prediction
systems PI/Co-Is Reichle, Bosilovich, Koster,
and Tedesco Phase 1 Add off-line/uncoupled
assimilation of - AMSR-E SWE (snow water
equivalent) - MODIS LST (land surface
temperature) Phase 2 Land surface assimilation
into coupled land-atmosphere system.
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THANK YOU FOR YOUR ATTENTION!
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Extra slides
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Soil moisture assimilation
Nonlinearly propagates ensemble of model
trajectories. Can account for wide range of
model errors (incl. non-additive). Approx.
Ensemble size. Linearized update.
xki state vector (eg soil moisture) Pk state
error covariance Rk observation error
covariance
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Introduction Retrieval errors
Soil moisture retrievals are subject to large
time-variant and time-invariant errors.
Example AMSR-E retrievals are much drier than
SMMR retrievals. Magnitude of differences is
comparable to dynamic range.
Time-invariant errors addressed with scaling
prior to data assimilation (assimilation of
percentiles). Time-variant errors addressed
with data assimilation.
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Introduction Time-invariant errors
An effective strategy Scale satellite
retrievals to the models climatology prior to
assimilation.
An effective strategy Scale satellite
retrievals to the models climatology prior to
assimilation.
An effective strategy Scale satellite
retrievals to the models climatology prior to
assimilation.
Step 1 Determine climatological PDF of satellite
retrievals
Step 2 Determine climatological PDF of modeled
quantity
Step 3 Convert a given satellite retrieval value
into the equivalent model value (e.g., using
standard normal deviates or CDF matching).
This satellite-based value
is equivalent to this model-based value
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Previous work Soil moisture retrieval OSSE
Time-invariant errors contribute to RMSE but do
not affect anomaly estimates.
For modeling and forecasting applications,
satellite retrievals might be useful (Rgt0.5) even
though their absolute errors exceed 0.04 m3/m3.
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Synthetic assimilation experiment

• NASA Catchment land surface model
• Red-Arkansas (308 catchments)
• Hourly forcing data (1981-2000)
• True model error Q_true (perturbations)
• standard deviation ?time
• Precipitation 50 of magnitude 1 day
• SW 30 of magnitude 1 day
• LW 50 W/m2 1 day
• Catchment deficit 0.05 mm 12 h
• Surface excess 0.02 mm 12 h
• Surface soil moisture (observation space)
• sqrt(P(Q_true))0.03 m3/m3 (no assimilation)
• sqrt(P(Q_true))0.02 m3/m3 (w/ assim, depends on
  R_true)
• Select one replicate of an ensemble integration
  as the truth.
• Add noise to generate synthetic obs. of surface
  soil moisture. sqrt(R_true) 0.02 0.05
  0.08 m3/m3
• Mask with space-time pattern from Hydros OSSE (up
  to 1 obs/day).

cross-corr.