Ingen diastitel

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An introduction to data assimilation Xiang-Yu
Huang Danish Meteorological Institute, Denmark
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Outline of the presentation

• Operational NWP activities
• Observations and preprocessing
• There are still many observations we are not able
  to assimilate.
• We have to prepare for new observations to come.
• Observation operators H
• Error covariances B and R
• They determine the assimilation quality.
• We can only guess what they should be.
• Data impact
• It can take decades of hard work just to
  assimilate one data type.
• How to assess data impact is application
  dependent.
• Summary and our near future plan.

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Numerical Weather Prediction models and initial
values
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DMI-HIRLAM The operational system consists of
three nested models named "G", "E" and "D".
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Data assimilation cycles
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Comments (I)Observations alone are not enough.

• Observations only cover part of the model domain
  (for limited area models they could also be
  outside of the model domain).
• Some observations provide incomplete model state
  at given locations (e.g. only wind).
• Some observations are not NWP model variables
  (e.g. radiance).
• NWP is not the only purpose of making
  observations.

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Quality control Observing systems have problems.

• Bad reporting practice check
• Blacklist check
• Gross check (against some limits)
• Background (short-range forecasts) check
• Buddy check (against nearby observations)
• Redundancy check
• Analysis check OI check or VarQC

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Comments (II)We are far from using all the
observations.

• Data quality dependent.
• Observing system dependent.
• NWP model (resolution) dependent.
• Assimilation method dependent.

At the same time, we have to prepare for the new
data like RO to come.
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Routine monitoring
Short-range forecasts - observations
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Analysis methods

• Empirical methods
• Successive Correction Method (SCM)
• Nudging
• Physical Initialisation (PI), Latent Heat Nudging
  (LHN)
• Statistical methods
• Optimal Interpolation (OI)
• 3-Dimensional VARiational data assimilation
  (3DVAR)
• 4-Dimensional VARiational data assimilation
  (4DVAR)
• Advanced methods
• Extended Kalman Filter (EKF)
• Ensemble Kalman Filter (EnFK)

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Variational methods
dx
(new)
(initial condition for NWP)
(old forecast)
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Important issues

• H observation operator, including the tangent
  linear operator H and the adjoint operator HT.
• M forecast model, including the tangent linear
  model M and adjoint model MT.
• B background error covariance (NxN matrix).
• R observation error covariance which includes the
  representative error (MxM matrix).

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This is mainly for conventional point
observations. Horizontal and vertical integration
(not interpolation) may be needed for most remote
sensing data.
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Examples of specific observation operators

• For direct model variable observations, Hspec
  I.
• Radial winds
• Integrated water vapour
• Refractivity
• For radiance data, RTTOV-7 (a complicated
  software).

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Level of preprocessing and the observation
operator
HspecHFHGHRHN
Raw data
Phase and amplitude
Frequency relations
Ionosphere corrected observables
HspecHGHRHN
Geometry
HspecHRHN
Bending angle profiles
Abel trasform or ray tracing
HspecHN
Refractivity profiles
Hydrostatic equlibrium and equation of state
HspecI
Temperature profiles
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Basic assumptions

• Observations are unbiased. (Bias removed.)
• Background is unbiased. (Bias removed?)
• Observation error covariance matrix is known. R
• Background error covariance matrix is known. B
• Observation errors and background errors are not
  correlated.

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Observation errors, computed for GPS/MET
geopotential data (using ECMWF analyses as
TRUTH)
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Estimate B without TRUTH

• The NMC method
• Background error covariances are proportional to
  correlations of differences between 48 h and 24 h
  forecasts valid at the same time.
• The analysis ensemble method
• Several analyses are performed with perturbed
  observations. Differences between background
  fields are used to estimate background error
  covariances.

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The Hollingsworth-Lönnberg method. (Estimate both
B and R without TRUTH)
B
R
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Horizontal multivariate correlation spread the
information
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Vertical correlation (spread the information) for
the temperature at 500 hPa
Pressure (hPa)
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Comments (III)We need to estimate observation
errors now and then.

• Observation errors include representative errors.
• Observation errors should be estimated for each
  model system.
• Observation errors may need to be re-estimated
  for each model refinement and instrument
  improvement.
• (It is believed that it is more important to get
  ?o /?b right than to estimate ?o and ?b.)

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Comments (IV)We need to estimate the background
errors again and again.

• Spread information (but could also cause
  problems)
• horizontally
• vertically
• to other variables
• Impose balances to the analysis.
• Background errors should be estimated for each
  model system and be re-estimated for each model
  improvement.
• (It is believed that it is more important to get
  ?o /?b right than to estimate ?o and ?b.)

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From research to operations

• Development and simple checks
• Coding
• Analysis increments
• Case studies
• Extensive experiments (e.g. one month for each
  season)
• Standard scores bias, rms, correlation, etc.
• Special scores precipitation, surface fluxes,
  etc.
• Special aspects noise, spin-up, etc.
• Pre-operational tests
• Operational use (feedback to further research)

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Observation verification against EWGLAM station
list Jan 2003 NOA (No ATOVS) WIA (With ATOVS)
ATOVS into DMI OPR since 2002. (A) TOVS work
started in 1988 (Gustafsson and Svensson)
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Observed
Without ZTD
With ZTD
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Recent HIRLAM impact studies

• 1. EWP minor positive impact blacklisting and
  bias correction may be needed.
• 2. MODIS wind slightly negative obs errors,
  screening procedures and level assignment need to
  be investigated.
• 3. MODIS IWV neutral obsver, but positive on
  heavy precip cases.
• 4. GPS ZTD neutral impact on most meteorological
  parameters, but positive impact on heavy
  precipitation cases.
• 5. AMSU-A positive impact for the recent
  two-month experiment. The firstguess check is
  important.
• 6. Quikscat positive impact

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Comments (V)We need to assess data impact
regularly.

• It can take years and decades for an observing
  system to reach the operational status.
• An observing system in operational use may also
  become redundant due to advances in assimilation
  techniques, new observing systems and
  improvements in other components.
• Continuous monitoring and further tuning are
  necessary to keep an observing system in the
  operational use.

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Other important aspects

• Balanced motion
• Adjustment and initialisation
• Flow dependent B
• Non-Gaussian statistics

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Summary

• Observations alone are not enough.
• We are far from using all the available
  observations, and at the same time we have to
  prepare for the new data to come.
• The statistics is evolving
• Observational errors
• Background errors
• It is getting more difficult for a new observing
  system to have a positive impact, as
• NWP models become better
• Other existing observing systems become better

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Assimilating Radio Occultation data

• Global data coverage.
• Good vertical resolution (in contrast to most
  other satellite data).
• Insensitive to cloud and precipitation.
• Positive impact from real data collected from a
  single LEO has already been found on one of the
  most advanced data assimilation systems.
• We will start soon after this workshop - next
  week!