an introduction to data assimilation xiang-yu huang danish meteorological institute, denmark
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2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 1Introduction to data assimilation
An introduction to data assimilation
Xiang-Yu HuangDanish Meteorological Institute, Denmark
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 2Introduction to data assimilation
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.
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 3Introduction to data assimilation
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 4Introduction to data assimilation
Numerical Weather Prediction: models and initial values
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 5Introduction to data assimilation
DMI-HIRLAM
The operational system consists of three nested models named "G", "E" and "D".
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 6Introduction to data assimilation
Data assimilation cycles
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 7Introduction to data assimilation
SYNOPSHIPBUOY
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 8Introduction to data assimilation
AIREPAMDARACARS
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 9Introduction to data assimilation
TEMPPILOT
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 10Introduction to data assimilation
ATOVS
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 11Introduction to data assimilation
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.
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 12Introduction to data assimilation
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
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 13Introduction to data assimilation
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 14Introduction to data assimilation
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 15Introduction to data assimilation
Received
Assimilated
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 16Introduction to data assimilation
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.
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 17Introduction to data assimilation
Routine monitoring
Short-range forecasts - observations
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 18Introduction to data assimilation
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)
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 19Introduction to data assimilation
Variational methods
(old forecast)
(new)
(initial condition for NWP)
x
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 20Introduction to data assimilation
Algorithms
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 21Introduction to data assimilation
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).
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 22Introduction to data assimilation
Observation operator H: from model state x to observations y
This is mainly for conventional “point” observations.Horizontal and vertical integration (not interpolation)may be needed for most remote sensing data.
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 23Introduction to data assimilation
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).
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 24Introduction to data assimilation
Level of preprocessing and the observation operator
Phase and amplitude
Ionosphere correctedobservables
Refractivity profiles
Bending angle profiles
Temperature profiles
Raw data:Frequency relations
Geometry
Abel trasformor ray tracing
Hydrostatic equlibriumand equation of state
Hspec=I
Hspec=HN
Hspec=HRHN
Hspec=HGHRHN
Hspec=HFHGHRHN
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 25Introduction to data assimilation
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.
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 26Introduction to data assimilation
Observation errors, computed for GPS/MET geopotential data(using ECMWF analyses as “TRUTH”)
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 27Introduction to data assimilation
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.
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 28Introduction to data assimilation
The Hollingsworth-Lönnberg method.(Estimate both B and R without “TRUTH”)
B:R:
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 29Introduction to data assimilation
ZZ
VZ
UZ
Horizontal multivariate correlation: spread the informationZV
VV
ZU
VU
UVUU
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 30Introduction to data assimilation
Wave number
Pres
sure
(hPa
)
Vertical correlation (spread the information)for the temperature at 500 hPa
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 31Introduction to data assimilation
Analysis increments due to 5 GPS/MET Z profiles
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 32Introduction to data assimilation
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.)
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 33Introduction to data assimilation
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.)
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 34Introduction to data assimilation
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)
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 35Introduction to data assimilation
Observationverification againstEWGLAMstation list
Jan 2003
NOA (No ATOVS)
WIA (With ATOVS)
MSLP
T02M
V10M
V850
V500
V200
T850
T500
T200
Z850
Z500
Z200
RH500 RH850
ATOVS into DMI OPR since 2002.(A) TOVS work started in 1988 (Gustafsson and Svensson)
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 36Introduction to data assimilation
Observed and predicted (+12h) precipitation
Observed Without ZTD With ZTD
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 37Introduction to data assimilation
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
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 38Introduction to data assimilation
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.
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 39Introduction to data assimilation
Other important aspects
• Balanced motion• Adjustment and initialisation• Flow dependent B• Non-Gaussian statistics
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 40Introduction to data assimilation
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
2nd GRAS SAF User Workshop, 11-13 June 2003, Helsingør, Denmark. 41Introduction to data assimilation
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!
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