The Application of Observation Adjoint Sensitivity to Satellite Assimilation Problems Nancy L. Baker Naval Research Laboratory Monterey, CA

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The Application of Observation Adjoint
Sensitivity to Satellite Assimilation
ProblemsNancy L. BakerNaval Research
Laboratory Monterey, CA
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Outline

• Introduction and motivation
• Data assimilation adjoint theory what is
  observation sensitivity?
• Examples of observation sensitivity with NAVDAS
  adjoint
• 00 UTC 7 February 1999 for TOVS
• 00 UTC 10 February 2002 for ATOVS/AMSU-A
• Summary and conclusions

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Introduction to Observation Adjoint Sensitivity

• A significant component of the medium-range
  forecast error is due to errors in the initial
  conditions
• particularly true for relatively poorly sampled
  regions
• Classical adjoint sensitivity computes the
  sensitivity of a cost function J (e.g., 72-h
  forecast error) to the initial conditions for
  that forecast.
• highlights regions that are very sensitive to
  small errors in the initial conditions (e.g.,
  temperatures and winds).
• The complete NWP adjoint sensitivity to J must
  include the adjoint of the data assimilation
  system.
• sensitivity of J to the observations and
  background

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Motivation

• Research was originally motivated by preparations
  for FASTEX in late 1996
• targeting methods were not able to take into
  account how the data assimilation system would
  use the additional observations
• the presence of other observations in the area
• as such, could not provides guidance on where to
  place the adaptive observations in the sensitive
  region
• Observation sensitivity has applicability far
  beyond targeting applications
• help us to understand how observations are used
  by the assimilation system
• help us identify potential sources of forecast
  errors due to errors in the initial conditions

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What is observation sensitivity?
forward problem
Observations (y)
Data Assimilation System
Forecast Model
Forecast (xf)
Analysis (xa)
Background (xb)
adjoint problem
Observation Sensitivity (?J/ ?y)
Adjoint of the Data Assimilation System
Adjoint of the Forecast Model Tangent Propagator
Sensitivity to the Analysis (?J/ ?xa)
Gradient of Cost Function J (?J/ ?xf)
Background Sensitivity (?J/ ?xb)
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NAVDAS ADJOINT NRL Atmospheric Variational Data
Assimilation System

• NAVDAS adjoint computes the sensitivity of the
  forecast aspect J (such as forecast error) to the
  observations and background.
• The sensitivity of J to the observations is given
  by
• ?J/?xa - sensitivity of J to the initial
  conditions.

Compare to linear analysis equation
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Sensitivity of the 72-h energy-weighted NOGAPS
forecast error to the initial wind and height
fields at 00 UTC 07Feb 1999. Verification area
over west coast of U.S.
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t
Magnitude of the sensitivity of the 72-h NOGAPS
energy-weighted forecast error to the MSU-2
brightness temperatures. The t indicates
time-window discontinuities.
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Sensitivity to MSU-2 Brightness Temperatures

• Maximum MSU-2 sensitivity occurs when
• the observations are relatively isolated, or
• the observation density abrupt changes,
• coincident with large amplitude and spatial scale
  sensitivity to the initial fields.
• Large observation sensitivities near 45oN, 175oE
• occur in the middle of a large-scale sensitivity
  to the initial 700-hPa temperature field,
• and are associated with a time-window data
  discontinuity

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Sensitivity to TOVS Brightness Temperatures

• Other abrupt changes in TOVS brightness
  temperature density may be associated with larger
  observation errors.
• TOVS brightness temperatures over land and ice
  are more difficult to assimilate properly and are
  eliminated in the present NAVDAS configuration
• This creates an abrupt change in the observation
  density along the coastlines and ice-edge
  boundaries where the observations are less
  accurate (mixed field-of-view).
• Abrupt changes in the data density also occur for
  the less accurate observations along the edges of
  the satellite scan.

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Implications

• Sensitivity to the relatively inaccurate
  observations along the data discontinuity is
  larger than the sensitivity to the more accurate
  (data dense) observations.
• assuming identical observation errors are
  assigned
• This implies that the less accurate observations
  have greater potential to change the forecast
  aspect, and to influence the analysis.
• Increasing the assumed observation error variance
  will decrease both the observation sensitivity
  and the influence of the observation on the
  analysis.

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Estimate of the potential forecast impact due to
the observations

• Define the change in J as the projection of the
  analysis error (?a) onto the analysis sensitivity
  gradient
• The reduction in the expected variance of the
  change in J due to the observations is

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Sensitivity of NOGAPS 72-h forecast error to
the initial T,u,v,p fields10 UTC 09 February 2002
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for different observation types
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Discussion

• Are very large values of observation sensitivity
  desirable?
• implies that the analysis depends upon a few
  observations in highly sensitive regions
• even small errors in the observation may
  contribute to the forecast error
• the corresponding background sensitivity is large
• as observations are added, the analysis becomes
  less dependent upon individual observations and
  the background, and the observation and
  background sensitivities decrease
• intermediate values of observation sensitivity
  are desirable

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Conclusions and Future Work

• The observation sensitivity gives an estimate of
  the potential for an observation to make changes
  to the analysis with the amplitude and structure
  suggested by the analysis sensitivity.
• Actual impact cannot be determined until the
  observations have been taken and the forecast
  computed.
• Develop observation sensitivity techniques to
  diagnose sources of forecast error
• Investigate alternate impact functions

(Doerenbecher and Bergot, 2001)
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Supplemental Slides
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Summary

• The observation sensitivity is largest when
• the analysis sensitivity is large in amplitude
• the spatial scales of the analysis sensitivity
  and background error covariances are similar
  (i.e., large targets)
• the observation is assumed to be more accurate
  than the background
• the observations are relatively isolated or
  associated with an abrupt change in the
  observation density (e.g, along coastlines or
  edges of satellite swaths)
• The observation sensitivity is weak when
• the analysis sensitivity is weak amplitude or
  small-scale
• the length scales of the analysis sensitivity is
  shorter than the background error covariance
  length scales
• the observation is assumed to be less accurate
  than the background
• the observation density is high

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Understanding Observation Sensitivity

• For relatively isolated observations, K and KT
  are large in amplitude and spatial scale.
• When KT projects strongly onto the analysis
  sensitivity, both and the potential
  change to J will be large
• the observation has more independent information
• the observation will be given more weight in the
  analysis
• potential changes to the analysis due to the
  observation are large in amplitude and spatial
  scale

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Understanding Observation Sensitivity

• For high density observations, KT is small in
  amplitude and spatial scale.
• The projection of KT onto the analysis
  sensitivity will be weaker, and both
  and the potential change to J are small.
• Similarly, if the observations are more accurate
  than the background, the observations will be
  given more weight and the potential changes to J
  are larger.

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Observation Sensitivity for a Hypothetical Flight
Path
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Understanding Observation Sensitivity