introduction to data assimilation: lecture 1
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Introduction to Data Assimilation: Lecture 1. Saroja Polavarapu Meteorological Research Division Environment Canada. PIMS Summer School, Victoria. July 14-18, 2008. Goals of these lectures. Basic idea of data assimilation (combining measurements and models) - PowerPoint PPT PresentationTRANSCRIPT
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Introduction to Data Assimilation: Lecture 1
Saroja Polavarapu
Meteorological Research Division Environment Canada
PIMS Summer School, Victoria. July 14-18, 2008
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Goals of these lectures
• Basic idea of data assimilation (combining measurements and models)
• Basic processes of assimilation (interpolation and filtering)
• How a weather forecasting system works
• Some common schemes (OI, 3D, 4D-Var)
• Progress over the past few decades
• Assumptions, drawbacks of schemes
• Advantages and limitations of DA
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ApproachApproach
• Can’t avoid equations– but there are only a few (repeated many times)
• Deriving equations is important to understanding key assumptions
• Introduce standard equations using common notation in meteorological DA literature
• Introduce concepts and terminology used by assimilators (e.g. forward model, adjoint model, tangent linear model…)
• Introduce topics using a historical timeline
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Outline of lectures 1-2• General idea
• Numerical weather prediction context
• Fundamental issues in atmospheric DA
• Simple examples of data assimilation
• Optimal Interpolation
• Covariance Modelling
• Initialization (Filtering of analyses)
• Basic estimation theory
• 3D-Variational Assimilation (3Dvar)
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Atmospheric Data AnalysisGoal: To produce a regular, physically consistent,
four-dimensional representation of the state of the atmosphere from a heterogeneous array of in-situ and remote instruments which sample imperfectly and irregularly in space and time. (Daley, 1991)
analysis
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• Approach: Combine information from past observations, brought forward in time by a model, with information from new observations, using – statistical information on model and observation errors– the physics captured in the model
• Observation errors– Instrument, calibration, coding, telecommunication errors
• Model errors– “representativeness”, numerical truncation, incorrect or missing
physical processes
Analysis = Interpolation + Filtering
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Why do people do data assimilation?
1. To obtain an initial state for launching NWP forecasts
2. To make consistent estimates of the atmospheric state for diagnostic studies.
• reanalyses (eg. ERA-15, ERA-40, NCEP, etc.)
3. For an increasingly wide range of applications (e.g. atmospheric chemistry)
4. To challenge models with data and vice versa
• UKMO analyses during UARS (1991-5) period
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Producing a Numerical Weather Forecast
1. Observation• Collect, receive, format and process the data• quality control the data
2. Analysis• Use data to obtain a spatial representation of the atmosphere
3. Initialization• Filter noise from analysis
4. Forecast • Integrate initial state in time with full PE model and
parameterized physical processes
Dat
a A
ssim
ilatio
n
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Data Assimilation Cycles
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http://www.wmo.ch/web/www/OSY/GOS.html
The Global Observing System
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Observations currently in use at CMC
Maps of data used in assimilation onJuly 1, 2008 12Z
Canadian Meteorological Centre – Centre Météorologique Canadien
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Radiosonde observations used
U,V,T,P,ES profiles at 27 levels
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Pilot balloon observations used
U,V profiles at 15 levels
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Wind profiler obs used
U,V (speed, dir) profiles at 20 levels
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SYNOP and SHIP obs used
U,V,T,P,ES at surface
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Buoy observations used
U,V,T,P,ES at surface
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Aircraft observations used
T,U,V single level (AIREP,ADS) or up to 18 levels (BUFR,AMDAR)
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Cloud motion wind obs used
U,V (speed, dir) cloud level
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AMSU-A observations used
Brightness temperatures ch. 3-10
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AMSU-B observations used
Brightness temperatures ch. 2-5
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GOES radiances used
Brightness temperature 1 vis, 4 IR
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Quikscat used
U,V surface
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SSM/I observations used
Related to integrated water vapour, sfc wind speed, cloud liquid water
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75Z
X
N
N
Underdeterminacy
• Cannot do X=f(Y), must do Y=f(X)• Problem is underdetermined, always will be• Need more information: prior knowledge, time evolution, nonlinear
coupling
Data Reports x items x levels
Sondes,pibal 720x5x27
AMSU-A,B 14000x12
SM, ships, buoys 7000x5
aircraft 19000x3x18
GOES 5000x1
Scatterometer 7000x2
Sat. winds 21000x2
TOTAL 1.3x106
Model Lat x long x lev x variables
CMC global oper. 800x600x58x4
=1x108
CMC meso-strato 800x600x80x4
=1.5x108
X = state vector Z = observation vector
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Optimal Interpolation
)( bba H xzKxx Analysis vector
Background or model forecast
Observation vector
Observation operator
Weight matrix
N×1 N×1 M×1N×M M×N N×1
1 RHBHBHK TT
NxN MxM
Can’t invert!
NxM
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Bvxx ba
Analysis increments (xa – xb) must lie in the subspace spanned by the columns of B
Properties of B determine filtering properties of assimilation scheme!
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The fundamental issues in atmospheric data assimilation
• Problem is under-determined: not enough observations to define the state
• Forecast error covariances cannot be determined from observations. They must be stat. modelled using only a few parameters.
• Forecast error covariances cannot be known exactly yet analysis increments are composed of linear combination of columns of this matrix
• Very large scale problem. State ~ O(108)• Nonlinear chaotic dynamics
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Simple examples of data assimilation
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Analysis errorBackground errorObservation error
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Obs 1 analysis
Daley (1991)
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m x 1n x 1
n x m
n x 1 m x 1
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representativeness measurement
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n x 1
m x 1n x 1
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OI was the standard assimilation method at weather centres from the early 1970’s to the early 1990’s.
Canada was the first to implement a multivariateOI scheme.
Gustafsson (1981)
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Summary (Lecture 1)• Data assimilation combines information of
observations and models and their errors to get a best estimate of atmospheric state (or other parameters)
• The atmospheric DA problem is underdetermined. There are far fewer observations than is needed to define a model state.
• Optimal Interpolation is a variance minimizing scheme which combines obs with a background field to obtain an analysis