Singular Vectors for Moisture-Measuring Norms

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Singular Vectors for Moisture-Measuring Norms

Dr. Ronald M. Errico Goddard Earth Sciences
and Technology Center (UMBC) Global
Modeling and Assimilation Office
(NASA) Acknowledgements Kevin Raeder, Martin
Ehrendorfer,
Luc Fillion
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Outline 1. Questions posed 2.
Description of experiments 3. Range of results 4.
TLM verification 5. Related adjoint
experiments 6. Summary
Errico, Raeder, Ehrendorfer 2004, QJRMS Errico,
Raeder, Fillion 2003, Tellus
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Questions
Curiosity--driven science We have this
great tool What results will we obtain if we
use moisture-measuring norms
to compute SVs?
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• 
  Questions
• Practical
  Science
• What do these results imply about the relative
  effects
• of initial perturbations or errors in the
  dynamical fields
• versus in the moisture field?
• Are similar structures optimal for affecting both
  
• perturbation energy and precipitation?
• How sensitive is precipitation to initial
  specification of
• the divergent wind?
• 4. Is convective or nonconvective precipitation
  generally
• more sensitive to initial perturbations?
• Some obvious applications to data assimilation
  and predictability

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MAMS2
Description 1. Primitive equations with
water vapor 2. Bulk PBL (Deardorff )
3. Stability-dependent vertical diffusion
(CCM3) 4. RAS moist convection scheme
(Moorthi and Suarez) 5. Stratiform
precipitation (but no evaporation below)
6. Delta x 80 km 7. 20-levels, equally
spaced in sigma, ptop100 or 10 mb 8. 12
(or 24 hour) forecasts for 4 synoptic cases
9. Vertical mode initialization (Bourke and
McGregor) 10. Complete TLM and adjoint
versions 11. Well-tested code for
meaningful perturbations
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The Singular Vector Problem
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Norms Examined
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Weights based on analysis differences
ECMWF NCEP Re-Analysis Averaged DJF 90-91,
JJA 90, No. Amer.
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Precipitation Rates at Hour 12
W1
W2
Contour intervals 1, 3.2, 10, 32, 100 mm/day
S2
S1
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Leading Squared Singular Values
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Locations of first 4 leading SVs
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Fraction of E or Em contributed by fields at
each vertical level for 1st leading SV for each
case for each set of norms
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Examples of initially correlated SVs for
different norms
Maximize E
Maximize P
Maximize E
Maximize P
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Examples of finally correlated SVs for different
norms
V-moist initial SV final v field
V-dry initial SV final v field
V-dry initial SV final v field
V-dry initial SV final R field
V-moist initial SV final R field
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The Balance of Singular Vectors
Contour 2 units
Initial GPV mode
Initial Grav mode
Contour 1 unit
Errico 2000
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A peculiar SV Case S1, Vd to P.
u at t0
v at t0
u at t12
R at t12
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Linear vs. Nonlinear results
24-hour SV1 from case W1 Initialized with
T1K Final ps field shown
Errico and Raeder 1999 QJRMS
Contour interval 0.5 hPa
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Non-Conv Precip. ci0.5mm
Non-Conv Precip. ci0.5mm
Convective Precip. ci2mm
Convective Precip. ci2mm
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Linear vs. Nonlinear Results 12-hour SV
Linear
Nonlinear
Non-Convective Precip.
Convective Precip.
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Linear vs. Nonlinear Results 12-hour SV
Linear
Nonlinear
Non-Convective Precip.
Convective Precip.
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The ratio of non-convective to convective
precipitation rates for SV-1 of each of
the experiments.
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Motivation Key result from Errico, and Fillion,
2003 Tellus
Adjoint-derived, optimal perturbations (not SVs)
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Non-Conv. Precipitation Rate at Forecast Hour 24
Contour interval 2 cm/day
Errico et al. 2001 Tellus
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Jvorticity
Impacts for adjoint- derived optimal perturbations
for forecasts starting indicated hours in the
past.
Errico et al. 2003 Tellus
Jnon-conv. R
Jconv. R
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Conclusions I

• The effect of optimal moisture perturbations
  can be as
• great as optimal perturbations of wind or
  temperature,
• even regarding their effects on wind and
  temperature.
• The geographic locations of leading SVs can be
  very
• dependent on the specific norms considered.
• The vertical structures of leading SVs can vary
  greatly
• from case to case, even when the same norms
  are
• considered.
• In some (few) cases, the SV that optimizes
  perturbation
• energy is very similar to that which
  optimizes pertur-
• bation precipitation, implying that the same
  physics is
• responsible for both solutions.
• 5. In some cases, leading SVs having only
  initial pertur-
• bations of wind and temperature produce
  nearly identical
• final-time SVs as those produced by leading
  SVs having
• only initial moisture perturbations.

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Conclusions II

• An example of an initial-time SV dominated by
  wind
• divergence above the tropopause was
  obtained.
• 7. Sensitivities to non-convective
  precipitation have not been
• shown to always dominate sensitivities to
  convection.
• 8. Forecast precipitation does not seem more
  sensitive to
• initial perturbations of divergence than to
  other fields.
• 9. TLM analysis of precipitation processes can
  be useful,
• but can also be misleading.
• 10. The effects of possible moisture errors and
  of appropriately
• linearized moist physics should not be
  neglected or treated
• as secondorder.

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Balance of SVs Errico 2000 QJRMS
v field GPV norm
v field E norm
T field E norm
T field GPV norm
Contour intervals vary
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Bred Modes (LVs) And SVs
Results for Leading 10 SVs
Gelaro et al. QJRMS 2002