Observation Impact Using a Variational Adjoint System

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NRL 6.2 New Start Proposal 73-P110-10
Observation Impact Using a Variational Adjoint
System
PI Dr. James Cummings, Code 7323 james.cummings_at_n
rlmry.navy.mil 831-656-5021 Co-PIs Dr. Hans
Ngodock, Dr. Alan Wallcraft, Dr. Scott Smith, Dr.
Nancy Baker (code 7531)
Approved! Funding Cycle Oct 2009 Sep 2012
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Objective Routine Assessment of Data Impacts

• Develop a system for assessing the impact of any
  and all observations assimilated in Navy ocean
  forecast models.
• System must be computationally efficient and
  capable of being run in near-real-time for
  routine observation monitoring.
• Impacts of observation subsets must be easily
  quantifiable
• instrument type (platform)
• measurement variable
• geographic region
• vertical depth level

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Motivation Need for Optimal Use of Observations

• Ocean predictions require very fine spatial
  scales
• model resolutions greatly exceed observation
  density
• ocean models are not well constrained by
  observations
• accurate forecasts on fine spatial scales depend
  on optimal use of the relatively sparse ocean
  observations
• All observations do not have equal value
• in terms of reducing forecasting error
• how can we quantify the impact of each
  observation?
• Ocean observing and forecast systems are in
  continuous evolution
• how can we provide routine assessments of data
  impact?

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Approach Methods for Estimating Data Impacts

• Conventional observing system experiments (OSE)
  withhold (deny) observations from the
  assimilation
• shows impact on all forecast parameters
• difficult to systematically evaluate all
  observation data types
• computationally expensive cannot be performed
  routinely
• removal (or addition) of an observation changes
  the analysis constraints on the remaining data
• this by itself can alter the outcome of the
  assimilation and the forecast

• Adjoint Technique
• shows impact on all observation data types
• equivalent to an OSE for short forecast periods
• computationally inexpensive same cost as a
  single run of the forecast model and the data
  assimilation
• can easily be implemented in operations
• provides routine generation of data impact
  statistics

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Analysis Forecast System
Observation (y)
Data Assimilation System
Forecast Model
Forecast (xf)
Analysis (xa)
Background (xb)
Adjoint System
Adjoint of the Forecast Model Tangent Propagator
Adjoint of the Data Assimilation System
Gradient of Cost Function J (?J/ ?xf)
Observation Sensitivity (?J/ ?y)
Analysis Sensitivity (?J/ ?xa)
Observation Impact lty-H(xb)gt (?J/ ?y)
What is the impact of observations on measures of
forecast error (J) ?
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Observation Impact Concept -
Observations move the forecast from the
background trajectory (Xb) to the trajectory
starting from the new analysis (Xa)
Observation impact is the combined effect of
all of the observations on the difference in
forecast error (ef - eg)
Xg
?
OBSERVATIONS ASSIMILATED
eg
Xf
?
Forecast Error
Xb
ef
?
?
VERIFYING ANALYSIS
Xa
?
t-24 t0
t24
Forecast Lead Time
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Observation Impact Equation
Langland and Baker (2004)
Forecast error difference for each observation
Adjoint sensitivity gradients in model grid-point
space
Observations assimilated
Adjoint of assimilation

• Forecasts are made with HYCOM/NCOM using NCODA
  3DVar/4DVar assimilation
• Adjoint versions of HYCOM/NCOM and NCODA
  3DVar/4DVar are used to calculate the observation
  impact
• Impacts of observation subsets can be computed
  based on instrument type, measurement
  variable, geographic region, etc

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Observation impact interpretation -
For any observation assimilated, if ...
lt 0.0 the observation is BENEFICIAL gt
0.0 the observation is NON-BENEFICIAL
forecast errors decrease
the effect
of the observation is to make the error of the
forecast started from xa less than the error of
the forecast started from xb
forecast errors increase
the effect of the
observation is to make the error of the forecast
started from xa greater than the error of the
forecast started from xb
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Identify observation impacts -

• Beneficial impacts
• associated with observations more accurate than
  the background in regions where adjoint
  sensitivity gradients are large
• extreme beneficial impacts from isolated
  observations indicate the need for greater
  observation density
• Non-beneficial impacts
• not expected, all observations should decrease
  forecast error
• if occurs, look for problems in data QC,
  instrument accuracy, model error, specification
  of assimilation error statistics

• Best Outcome
• - many observations that produce equal or similar
  impacts, not few, isolated observations that
  produce large impacts

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Science issues in data impact calculations -

• Three science issues need to be considered
• Observation data impacts are relevant only for
  the selected forecast error cost function.
• Observation data impacts depend strongly on the
  assimilation method and the forecast model.
• Accuracy of observation data impact equation
  subject to same limitations that apply to the
  adjoint of the forecast model simplified
  physics, TLM assumptions

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Issue 1 Data Impacts Relevant only for Selected
Forecast Error Cost Function

• cost function can be any differentiable scalar
  measure of forecast model accuracy
• single model variable (temperature, salinity,
  velocity)
• derived variable (sound speed)
• or some combination (integral energy norm as in
  NWP systems)
• impact of observations on all aspects of the
  forecast may not be directly estimated unless
  multiple cost functions are used.
• this project will develop and evaluate multiple
  ocean forecast error cost functions of Navy
  interest, for example
• errors in position and strength of oceanographic
  features (fronts and eddies)
• acoustic prediction errors derived from forecast
  ocean state

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Issue 2 Impacts Depend on Assimilation Method
and Forecast Model

• quality of the forecast, assimilation statistics,
  and other issues with different models and
  assimilation systems may lead to quantitative
  differences in estimates of observation impact.
• in this project, data impact systems will be
  developed for
• multiple ocean models (HYCOM and NCOM), and
• multiple data assimilation procedures (3DVar and
  4DVar)
• this will allow determination of robustness of
  impact results when model domains and assimilated
  observations overlap
• global HYCOM vs. regional NCOM
• both systems use same ocean data quality control
  system

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Issue 3 Accuracy of Data Impacts Subject to
Forecast Model Adjoint Limitations

• tangent linear assumptions and approximated
  physics affect accuracy of forecast model
  adjoint.
• observation innovation vector metric can be used
  as a check

is an approximation of the
full non-linear model error (ef - eg)

NOGAPS
Metric can be used as a check on accuracy of
tangent linear assumptions in forecast model
adjoint. Metric can be used to determine forecast
lengths over which tangent linear assumptions are
valid.
Langland and Baker (2004)
NOGAPS adjoint errors 75 full model error
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Payoff Project will address major challenges in
ocean observing and prediction

• by routine monitoring and assessment of the
  value of observations assimilated in HYCOM and
  NCOM.
• by immediate feedback on the impact of new
  observing systems deployed in support of Navy
  exercises.
• by providing locations (adjoint sensitivity
  gradients) where forecast errors are sensitive to
  the initial conditions.
• by providing guidance on where additional
  observations, or better use of existing data
  (data selection, data thinning, quality control),
  may have the greatest potential to reduce
  forecast error.

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Applications Multiple Uses of Adjoint-based
System
focus of this new start proposal
Hypothetical Observations and Targeted Observing
are variants of core Observation Impact system
Langland and Baker (2004) NRL/MR/7530-04-8746
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Summary System Components
Data Assimilation Adjoint
Forecast Model Adjoint

• NCOM developed at NRL SSC in 6.2 project
• HYCOM developed at French SHOM

• 3DVar and 4DVar
• Developed directly from analysis codes

System Integration NCOM with 3DVar and 4DVar
HYCOM with 3DVar
Service Hydrographique Oceanographique de la
Maritime
Develop Forecast Error Cost Functions
System Evaluation Navy Exercise Areas
Ocean Sampling Experiments
Global HYCOM Forecasts
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• END

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Adjoint sensitivity maps -
COAMPS forecast error adjoint sensitivities to
NCODA SST lower boundary conditions
sensitivities evolve over time with changing
weather patterns
Kuroshio
24 hrs
Convective Complexes
Adjoint sensitivity gradients indicate where
observations are likely to impact forecast error
From Amerault and Doyle (2008)
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NOGAPS Radiosonde Profile Observation Impact
1 Jan 28 Feb 2006
Most beneficial (04320)
Least beneficial (84401)
Many moderately beneficial Radiosonde impacts in
CONUS and Europe best outcome
criteria Langland and Baker (2004)
Most beneficial (lt - 0.1 J kg-1)
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Argo Oceanographic Analog to Radiosonde Network
Floats profile from 2000 m to the surface every
10 days, measuring temperature and salinity as a
function of depth. Adjoint-based system will
determine impact of T,S data from each float
cycle on reducing HYCOM and NCOM forecast errors.