Ensemble Kalman Filter Applications: StormScale Analysis and Forecasting

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Ensemble Kalman Filter ApplicationsStorm-Scale
Analysis and Forecasting

• David Dowell

Cooperative Institute for Mesoscale
Meteorological Studies, Norman, Oklahoma National
Center for Atmospheric Research, Boulder, Colorado
2
Acknowledgments

• Severe Weather Analysis and Prediction group at
  National Severe Storms Laboratory
• Mike Coniglio Kim Elmore
• Ted Mansell David Stensrud
• Lou Wicker Qin Xu
• Nusrat Yussouf
• Collaborators at NCAR, OU, and elsewhere
• Altug Aksoy Jeff Anderson
• Don Burgess Mike French
• Tadashi Fujita Glen Romine
• Bill Skamarock Chris Snyder
• Jenny Sun

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Atmospheric Data Assimilation (DA)

• using all available information -- observations
  physical laws numerical model to estimate as
  accurately as possible the state of the
  atmosphere

4
Goals of DA

• Case studies
• optimal analysis of data from multiple sensors
• Initializing numerical forecast models

t0
t0-2Dt
t1
t2
t0-4Dt
forecast
assimilate obs
assimilate obs
assimilate obs
assimilate obs
assimilate obs
assimilate obs
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Background-Error Covariance Matrix

• Provides information on
• magnitude of error in current atmospheric state
  estimate (large variance?large error)
• how errors are related spatially and between
  different variables (correlation)

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Kalman Filter vs. Ensemble Kalman Filter (EnKF)

• Kalman filter -- explicitly evolve entire
  background-error covariance matrix
• Large matrices for our problems
• (100)3 grid points ? 10 variables2 1014
  matrix elements
• Even if feasible to store matrix, have to deal
  with numerical instability in advancing the
  matrix
• Ensemble Kalman filter -- when needed, estimate
  an individual covariance matrix element from
  ensemble statistics

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Favorable Aspects of Ensemble Kalman Filter (EnKF)

• Scheme is relatively easy to implement
• Information about forecast uncertainty provided
  by the ensemble can be useful
• Ensemble forecasting and data assimilation are
  conducive to parallel computing

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How the EnKF Method Works
Snyder and Zhang 2003
observed quantity
state variable
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Error Covariances from Ensemble2D Cold Bubble
height
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Error Covariances from Ensemble2D Cold Bubble
height
L
H

• correlation between temperature field
• and eastward velocity component at point shown

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EnKF Equations

• computation of Kalman gain

adjustment of ensemble mean
N number of ensemble members xf,
xa forecast/analysis of a particular model
field at a particular location H(xf) model
state mapped to the observation type and
location yob observation s2ob observation error
variance _ ensemble mean deviation from
ensemble mean
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Ensemble Data AssimilationGood Model and Good
Observations
initial ensemble
truth
t0
forecast
before assimilation
after assimilation
t0 Dt
forecast
t0 2Dt
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Ensemble Forecasting and DASynoptic Scale

• First attempts to use EnKF method dry,
  quasi-geostrophic flows (Evensen 1994, Houtekamer
  Mitchell 1998)
• State variables observed (u, v, p, T from
  soundings), but at sparse locations
• Numerical model believed to be a reasonably
  accurate representation of the atmosphere
• O(100) members in ensemble
• Ensemble variability (mostly) from initial and
  boundary-condition perturbations
• Representing uncertainty in positions and
  strengths of weather systems

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Convective Storm-Scale Ensemble Forecasting and
DA Challenges

• Isolated, small, and unbalanced phenomena
• Multiple scales
• Influence of larger scale systems on storm
  initiation and evolution
• Larger scale response to heating and cooling by
  deep, moist convection

Trier et al. 2000
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Challenges of Storm-Scale Ensemble Forecasting
and DA

• Sensitivity to model parameterizations (e.g.,
  precipitation microphysics)

varied parameters in supercell simulations inter
cept parameter and density of hail/graupel
Gilmore et al. 2004
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Challenges of Storm-Scale Ensemble Forecasting
and DA

• Unobserved fields
• Most of the model state variables are unobserved
  on these scales (L1 km, T1 min), so
  assimilation must retrieve these fields.
• Storm-scale observations Doppler radar
• Environmental data surface, satellite,
  sounding, etc.
• Relatively little information is available for
  diagnosing errors in storm-scale analyses.

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Radar Observations

• Doppler velocity
• power-weighted mean over sampling volume of
  component of scatterer (rain, hail, etc.) motion
  toward or away from radar
• reflectivity
• function of scatterer sizes and number
  concentrations

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WSR-88D Network (central plains)
Alexander and Wurman 2004
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Variables in a Typical Cloud Model

• u eastward wind component
• v northward wind component
• w upward wind component
• p pressure
• T temperature
• qv water vapor mixing ratio
• qc cloud water mixing ratio
• qr rain mixing ratio
• qi ice crystal mixing ratio
• qs snow mixing ratio
• qh hail/graupel mixing ratio

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Challenges of Storm-Scale DAUnobserved Fields

• Model variables
• u, v, w, p, T, qv, qc, qr, qi, qs, qh
• Radar observations
• Doppler velocity -- single velocity component
• reflectivity -- complicated function of qr, qi,
  qs, qh
• Unobserved quantities
• two velocity components
• p, T, qv, qc
• individual hydrometeor categories

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Brief History of Storm-Scale DA

• Static initialization and/or data insertion
• Ziegler (1985) -- first time radar observations
  were used in a numerical cloud model (?)
• 4DVar
• Since 1990
• Discussed by Jenny Sun tomorrow
• 3DVar
• Since 2004 (?)
• Discussed in Part 2 this morning
• EnKF
• Since 2001

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EnKF Assimilation of Radar DataExperiments with
Synthetic Data(Snyder and Zhang 2003)

• Produce a reference simulation (truth)
• Splitting supercell
• Create synthetic Doppler velocity observations
• Volumetric observations every 5 min
• Random error added to point value of model
  velocity component in direction of radar beam
• Initialize 50-member ensemble
• Advance ensemble to time of first synthetic
  observations, assimilate them, advance ensemble
  to time of next observations, etc.

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Synthetic DA Experiments Initialization

• Each ensemble member has the same base state
• Random perturbations are added to the model
  fields
• Gaussian noise (Snyder and Zhang 2003), or
  coherent blobs in random locations (Dowell et al.
  2004)
• Entire domain, or localized region where storms
  develop
• Before the first ob. is assimilated, the ensemble
  is advanced for a few 10s of min, during which
  time some random perturbations initiate
  convective storms

localized temperature blobs
vertical velocity 30 min later (first assim. time)
north
east
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EnKF Assimilation of Synthetic Radar Data (Snyder
and Zhang 2003)
Vertical velocity at 6 km AGL
truth
EnKF analysis
3 volumes assimilated
13 volumes assimilated
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EnKF Assimilation of Synthetic Radar Data (Tong
and Xue 2005)
RMS errors in model fields over a 100-min period
black line both Doppler velocity and
reflectivity assimilated
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EnKF Assimilation of Synthetic Radar Data (Tong
and Xue 2005)
Correlation between model fields and refl. at
point shown at t80 min
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EnKF Assimilation of Synthetic Radar Data (Tong
and Xue 2005)
Forecast from ensemble-mean analysis at 80 min
truth
forecast
20-min forecast
100-min forecast
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Conclusions EnKF Experiments with Synthetic
Radar Data

• The model state in the reference simulation is
  reproduced well after several volumes of radar
  data are assimilated over 30 minutes
• Ensemble covariances between observed and
  unobserved quantities are necessary for efficient
  retrieval of the atmospheric state
• Tested by comparing control assimilation
  experiment to assimilation experiment with filter
  update of some model variables turned off

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Limitations ofExperiments with Synthetic Data

• These experiments are perfect model experiments
• Same model that produces the reference simulation
  is used to assimilate observations
• With only a little help from the assimilation,
  the model wants to proceed along the correct
  trajectory
• More realistic experiments must consider the
  impact of model error and how to ameliorate it

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Real-Data Storm-ScaleEnKF Experiments

• 17 May 1981 Arcadia, OK supercell (Dowell et al.
  2004a)
• 8 May 2003 Oklahoma City, OK supercell (Dowell et
  al. 2004b, Wicker et al. 2007)
• 11 June 2003 southwest OK multicell and squall
  line (Coniglio et al. 2007)
• 15 May 2003 Shamrock, TX supercell (M.
  French)
• 29 May 2004 Geary, OK supercell (K.
  Kuhlman)

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EnKF Assimilation of Radar Data17 May 1981
Arcadia, OK Storm

• Idealized model (VDRAS)
• Horizontally homogeneous initial environment
• Warm-rain precipitation microphysics scheme
• Grid spacing Dx1 km
• 50-member ensemble
• Randomness in locations of warm
  bubbles that initiate storms
• Assimilation
• Cimarron vel. and reflectivity
• Verification
• Dual-Doppler analysis
• Tower measurements

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Arcadia StormEnKF Analysis vs. Dual-Doppler
Analysis
Vertical velocity (4.0 m s-1 contour
interval) and horizontal wind at 4.25 km AGL
EnKF analysis (5 radar-data volumes assimilated)
Dual-Doppler analysis
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Arcadia StormEnKF Analysis vs. Instrumented
Tower
Vertical velocity (m s-1)
Perturbation temperature (K)
EnKF analysis Tower data
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NCOMMAS Assimilation Experiments8 May 2003
Oklahoma City Supercell

• NCOMMAS forecast model
• Grid spacing Dx2.0 to 0.5 km
• LFO/Gilmore precip. microphysics (rain,
  hail/graupel, snow, ice crystals)
• 50-member ensemble
• Assimilation of KOUN Doppler velocity and
  reflectivity data
• Verification with independent dual-Doppler
  analysis
• Sensitivity experiments
• Model resolution
• Observation resolution
• Precipitation microphysics

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8 May 2003 Oklahoma City SupercellSingle-Radar
Assimilationvs. Independent Dual-Doppler Analysis
Reflectivity and Wind at 300 m AGL
Dual-Doppler Analysis
90-min Assimilation
image provided by Arthur Witt
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8 May 2003 Oklahoma City SupercellForecast from
Ensemble Mean(55 min assimilation 26 min
forecast)
Reflectivity at 500 m AGL
Observations
Forecast
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Computing Effective Reflectivity Factor
(Reflectivity) from Model Fields
For spherical raindrops,
Assume inverse exponential drop-size distribution
in model
For typically assumed n0 value (Marshall-Palmer)
,
Reflectivity computations for ice species
(hail/graupel, snow, ice crystals) are more
complicated and less certain. For now, use
method developed by Smith et al. 1975.
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Time-Height Diagrams Differences between
Reflectivity Observations and Forecasts
Mean of (ob. - prior ensemble mean) reflectivity,
in dBZ
11 June 2003 multicell (experiments by M.
Coniglio)
8 May 2003 supercell
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Ensemble Data AssimilationModel Error (Bias)
initial ensemble
truth
t0
forecast
t0 Dt
before assimilation
forecast
after assimilation
t0 2Dt
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Reflectivity Difference8 May 2003 storm, 1.5
deg elevation angle
Forecast (ensemble mean)
Observations
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8 May 2003 SupercellSensitivity to
Precipitation Microphysics

• Assume all hail/graupel is dry.
• Vary intercept parameter for rain category
• n08?106 m-4 (default -- Marshall-Palmer)
• n08?105 m-4 (fewer drops, larger mean size)

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8 May 2003 SupercellSensitivity to
Precipitation Microphysics
Mean of (ob. - prior ensemble mean) reflectivity,
in dBZ
LFO/Gilmore
fewer and larger raindrops
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8 May 2003 SupercellSensitivity to
Precipitation Microphysics
Pert. Temperature at 250 m AGL (after
assimilation for 85 min)
LFO/Gilmore
fewer and larger raindrops
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8 May 2003 SupercellRadar and Oklahoma Mesonet
Data
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Conclusions Storm-Scale DA Experimentswith
Real Data

• Current experiments indicate that we are handling
  well the initial uncertainty in storm location
  and strength
• Storm dynamical characteristics determined by
  random initialization assimilating several
  radar-data volumes
• However, analyses of thermodynamical and
  microphysical fields, and forecasts of all
  fields, are sensitive to model parameterizations
  and other characteristics
• precipitation microphysics
• resolution
• surface fluxes?
• Limited evidence (e.g., reflectivity analysis)
  suggests we are dealing with significant model
  error (bias).

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Storm-Scale DA Experiments with Real DataHow to
Proceed?

• Since the only operational storm-scale obs. are
  from the WSR-88D, we need special observations to
  assess model errors on the storm scale
• Time is right for a field program with a
  storm-scale DA focus
• Design ensembles to account for typical model
  errors
• more sophisticated microphysics schemes?
  microphysics ensembles?
• higher (and variable) resolution?
• If successful, can start having more confidence
  in probabilistic information provided by the
  ensemble

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Storm-Scale DA Experiments with Real DataHow to
Proceed?

• Learn how to take advantage of future obs. that
  will be available in the operational network
• dual-polarization radar
• additional information about hydrometeor type and
  concentration
• satellite
• high-resolution thermodynamic information

Ryzhkov et al. 2005
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National Severe Storms Laboratory
VisionProbabilistic Numerical Forecasts of
Severe Weather
J. Kimpel 2003
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You should consider data assimilation for your
convective storm research if

• Complete 4D analyses (particularly of wind
  fields) in storms are useful to you
• You are ready to tackle some of the modeling
  challenges in simulating realistic convective
  storms
• You have lots of storage and CPU time available
• You want to increase your chance of a job after
  graduation

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You should not consider data assimilation for
your convective storm research if

• You dont have a good computer with lots of
  storage
• You dont want to analyze gigabytes and terabytes
  of data
• You are happy in a world of only observations

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Ensemble Forecasting and DAMesocale

• Improve mesoscale analyses through ensemble
  forecasting and data assimilation
• ensemble variability from
• perturbations in initial and boundary conditions
• diversity in model parameterizations
• observations surface, radar,
• Produce forecasts (up to 12 hr) of mesoscale
  features
• Provide initial and boundary conditions for
  high-resolution (convective) numerical forecasts

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EnKF Assimilation of Surface Observationsinto a
Mesoscale Model

• Penn State-NCAR mesoscale model (MM5) with Dx30
  km grid centered over central U.S.
• Ensemble 25 members, initial and boundary
  condition perturbations, physics-scheme diversity
• Land surface, PBL, convection, radiation
• Data assimilation 1500 surface observations
  (u, v, T, Td) per hour
• Experiment 6-hour assimilation followed by
  18-hour forecast (emphasis on 6-hour forecast)

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Ensemble of Model Parameterizations

• Land surface NOAAH, 5 layer, Force Restore
• PBL MRF, Blackadar, Burk-Thompson, Eta
• convection Grell, Kain-Fritsch, Betts-Miller
• radiation Cloud, CCM2, RRTM

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EnKF Assimilation of Surface Observations8 May
2003 (tornado outbreak) Case
Ensemble standard deviation of dewpoint (K) at 2
m AGL
parameterization diversity only
i.c. and b.c. perturbations only
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EnKF Assimilation of Surface Observations8 May
2003 Case

• (Fujita, Stensrud, and Dowell 2006)

Temperature (thick lines) and dewpoint (thin
lines) at 2 m AGL
forecast, no assimilation
observations
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EnKF Assimilation of Surface Observations8 May
2003 Case

• (Fujita, Stensrud, and Dowell 2006)

Temperature (thick lines) and dewpoint (thin
lines) at 2 m AGL
6-hour EnKF assimilation 6-hour forecast
observations
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EnKF Assimilation of Surface Observations8 May
2003 Case

• (Fujita, Stensrud, and Dowell 2006)

0Z Norman sounding
observed
6-hour assimilation 6-hour forecast
forecast, no assimilation
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EnKF Assimilation of Surface ObservationsConclus
ions

• Assimilating surface observations for 6 hours
  improves subsequent forecasts for 6 hours.
• Improved forecast of storm environment
  (boundaries, thermodynamic profiles, etc.)
• Improved precipitation forecast (not shown)
• Ensemble design is important.
• Errors in locations of weather systems are
  handled by initial and boundary condition
  perturbations data assimilation.
• Physics-scheme diversity accounts for uncertainty
  in processes sensitive to terrain, radiation, etc.