Application and interpretation of adjointderived sensitivities in synopticcase studies

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Application and interpretation of
adjoint-derived sensitivities in
synoptic-case studies

• Michael C. Morgan
• University of Wisconsin-Madison

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Acknowledgements

• Linda Keller
• Kate La Casse
• Dr. Hyun Mee Kim (KMA)
• Daryl T. Kleist (NCEP/NOAA)

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Goals

• Describe what an adjoint model is
• Demonstrate adjoint applications to
• Synoptic case studies
• Diagnosis of key analysis errors
• Data assimilation
• Discuss interesting research problems for which
  adjoint-based tools might have some utility

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Goals

• Provide synoptic interpretations for selected
  forecast sensitivity gradients
• Describe the evolution of sensitivities with
  respect to the forecast trajectory
• Present a useful technique to display
  sensitivities with respect to vector quantities
• Discuss interesting research problems for which
  adjoint-based tools might have some utility

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Relationship between the nonlinear model and its
adjoint
Nonlinear Model
Linear Model
Adjoint Model
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How might adjoints be used?
adjoint model
input perturbation
An adjoint model is useful in the estimation of
a change in response function associated with
arbitrary, but small changes in the input to the
linearized model.
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Application 1 Synoptic case studies

• Impact studies
• vs.
• Sensitivity studies

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Impact studies or what if? experiments

• Impact studies involve studying the effects a
  specific initial and/or boundary perturbation
  (x0) to an NWP model has on some aspect of a
  forecast.
• While these perturbations are often chosen based
  on synoptic intuition, typically the precise
  choice of the location and structure of the
  imposed initial perturbations is not known.
• The chosen perturbations may have very little
  impact on the weather system of interest.
• As these studies are performed to assess the
  importance of a particular synoptic feature, many
  integrations are needed to yield useful results.

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Modeling System Used

• MM5 Adjoint Modeling System (Zou et al. 1997)
  with non-linear model state vector

• All sensitivities were calculated by integrating
  the adjoint model backwards using dry dynamics,
  about a moist basic state.

• The corresponding adjoint model state vector is

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Description of Case 1 and response functions

• Cold frontal passage over the upper midwest
  during the 36h period beginning 1200 UTC 10 April
  2003
• Sensitivity gradients were calculated for the 36
  hour MM5 forecast from Eta model initial
  conditions at 1200 UTC 10 April 2003 for three
  response functions
• 1) average temperature over WI
• 2) average north-south temperature difference
  over northern WI
• 3) average zonal wind over WI

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Mean sea level pressure and temperature (s0.85)
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Sensitivity with respect to initial conditions at
1200 UTC 10 April 2003
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36h temperature sensitivity evolution
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700 hPa sensitivities with respect to u and v
valid at 1200 UTC 11 April 2003 (f24)
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700 hPa sensitivities with respect to u and v
valid at 1200 UTC 11 April 2003 (f24)
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Sensitivity with respect to derived variables
Inversion
Adjoint of Inversion
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700 hPa sensitivity gradients valid at 1200 UTC
11 April 2003 (f24)
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Description of Case 2 and response function
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Impact study of McTaggart-Cowan (2002)
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Initial state (MSLP and 925hPa q)
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Initial state (250300 hPa PV)
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Forecast evolution
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Final state
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Sensitivity of 48h KE to vorticity
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Application 2 Identification of key analysis
errors
If the response function chosen is a (quadratic)
measure of forecast error, the output of the
adjoint model provides a means of changing the
initial conditions to determine an initial
condition which will minimize the forecast error
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VERIFYING ANALYSIS
11 April 1994 ECMWF forecast bust
DAY-5 FORECAST
Rabier et al. (1996)
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Control and perturbed analyses
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Evolution of key analysis errors
Rabier et al. (1996)
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VERIFYING ANALYSIS
DAY-5 FORECAST
OPTIMAL FORECAST
Rabier et al. (1996)
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Application 3 4DVAR data assimilation
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Application 3 4DVAR data assimilation
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Application 3 4DVAR data assimilation
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La CASsE STUDY
1200 UTC 13 February 2001
NCEP final analysis (mslp) and ship and buoy
observations of wind (ms-1) and mean sea level
pressure
NCEP final analysis (blue) and 36 hour MM5
forecast (red) mslp
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Water vapor image andsatellite-derived wind
vectors (ms-1)
0600 UTC 12 February 2001 300 hPa (yellow) and
400 hPa (blue)
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Assimilation in sensitive regions
1200 UTC 13 February 2001
NCEP final analysis (blue) and 36 hour MM5
forecast (red) mslp
Observations in sensitive regions assimilated at
0600 UTC
All observations assimilated at 0600 UTC
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Assimilation in insensitive regions
1200 UTC 13 February 2001
36 hour forecast mslp (cont. assim.)
25,000
20,000
15,000
Number of observations
10,000
5,000
0
Observations in insensitive regions assimilated
at 0600 UTC
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Questions?
Real-time forecast sensitivities may be found at
http//helios.aos.wisc.edu