Numerical Weather Prediction and Data Assimilation

1
Numerical Weather Prediction and Data Assimilation

• David Schultz, Mohan Ramamurthy, Erik Gregow,
  John Horel

2
What is a model?

• Resource Kalnay, E., 2003 Atmospheric Modeling,
  Data Assimilation and Predictability
• model tool for simulating or predicting the
  behavior of a dynamical system such as the
  atmosphere
• Types of models include
• heuristic rule of thumb based on experience or
  common sense
• empirical prediction based on past behavior
• conceptual framework for understanding physical
  processes based on physical reasoning
• analytic exact solution to simplified
  equations that describe the dynamical system
• numerical integration of governing equations by
  numerical methods subject to specified initial
  and boundary conditions

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What is Numerical Weather Prediction?

• The technique used to obtain an objective
  forecast of the future weather (up to possibly
  two weeks) by solving a set of governing
  equations that describe the evolution of
  variables that define the present state of the
  atmosphere.
• Feasible only using computers

4
A Brief History

• Recognition by V. Bjerknes in 1904 that
  forecasting is fundamentally an initial-value
  problem and basic system of equations already
  known
• L. F. Richardsons (1922) attempt at practical
  NWP
• Radiosonde invention in 1930s made upper-air data
  available
• Late 1940s First successful dynamical-numerical
  forecast made by Charney, Fjortoft, and von
  Neumann
• 1960s Edward Lorenz shows the atmosphere is
  chaotic and its predictibility limit is about two
  weeks

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NWP System

• NWP entails not just the design and development
  of atmospheric models, but includes all the
  different components of an NWP system
• It is an integrated, end-to-end forecast process
  system

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Data Assimilation
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Components of an NWP model

• 1. Governing equations
• Fma, conservation of mass, moisture, and
  thermodynamic eqn., gas law
• 2. Numerical procedures
• approximations used to estimate each term
  (especially important for advection terms)
• approximations used to integrate model forward
  in time
• boundary conditions
• 3. Approximations of physical processes
  (parameterizations)
• 4. Initial conditions
• Observing systems, objective analysis,
  initialization, and data assimilation

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Model Physics

• Grid-scale precip. (large scale condensation)
• Deep and shallow convection
• Microphysics (increasingly becoming important)
• Evaporation
• PBL processes, including turbulence
• Radiation
• Cloud-radiation interaction
• Diffusion
• Gravity wave drag
• Chemistry (e.g., ozone, aerosols)

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Grid spacing (resolution) defines the scale of
the features you can simulate with the model.
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Good Numerical Forecasts Require

• Initial conditions that adequately represent the
  state of the atmosphere (three-dimensional wind,
  temperature, pressure, moisture and cloud
  parameters)
• Numerical weather prediction model that
  adequately represents the physical laws of the
  atmosphere over the whole globe

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Sources of error in NWP

• Errors in the initial conditions
• Errors in the model
• Intrinsic predictability limitations
• Errors can be random and/or systematic errors

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Sources of Errors - continued

• Initial Condition Errors
• Observational Data Coverage
• Spatial Density
• Temporal Frequency
• Errors in the Data
• Instrument Errors
• Representativeness Errors
• Errors in Quality Control
• Errors in Objective Analysis
• Errors in Data Assimilation
• Missing Variables

• Model Errors
• Equations of Motion Incomplete
• Errors in Numerical Approximations
• Horizontal Resolution
• Vertical Resolution
• Time Integration Procedure
• Boundary Conditions
• Horizontal
• Vertical
• Terrain
• Physical Processes

Source Fred Carr
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Given all these assumptions and limitations, we
have no right to do as well in forecasting the
weather as we do!
Dave sez

• What other disciplines forecast the future with
  as much success as meteorology?

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NWP in Finland

• Currently, NWP models are run by FMI (limited
  domain over Europe) and by the European Centre
  for Medium-Range Weather Forecasts (global)
• Currently the FMI model is run at about 9 22 km
  and the ECMWF model is run at 25 km grid spacing,
  meaning that these models can resolve features
  about 6 times those grid spacings.
• The new AROME experimental model is running at
  2.5 km grid spacing.

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22 km HIRLAM 9 km HIRLAM 2.5 km AROME
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9 km HIRLAM 2.5 km AROME observed radar
reflectivity
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9 km HIRLAM 2.5 km AROME
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The Hopes of the Testbed

• Higher-resolution observations will provide
  higher-resolution initial conditions, which could
  be put into a higher-resolution NWP model,
  producing higher-resolution forecasts.
• The hope is that precise forecasts of convection,
  the sea breeze, rain/snow forecasting, and winds
  could be made up to a few hours in advance.
• BUT

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Difficulties Lie Ahead

• The reality is often that you end up with a
  higher-resolution, less-accurate forecast.
• Results from forecasting/research experiments at
  the NOAA/Storm Prediction Center show value can
  be added sometimes with high-resolution
  forecasts.
• When that value can be added is a very important
  forecasting/research question!!!

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Difficulties Lie Ahead

• Producing the initial conditions from sparse
  resolution (in space and time) and incomplete
  observations is not easy.
• Creating a gridded 3-D/4-D dataset suitable for
  initializing a NWP model is called data
  assimilation.
• How it is proposed to be done in the Helsinki
  Testbed is described next

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Erik Gregow Project Manager LAPS
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• Numerical weather prediction model that
  adequately represents the physical laws of the
  atmosphere over the whole globe
• Initial conditions that adequately represent the
  state of the atmosphere (three-dimensional wind,
  temperature, pressure, moisture and cloud
  parameters)

23
Good Numerical Forecasts Require

• Numerical weather prediction model that
  adequately represents the physical laws of the
  atmosphere over the whole globe
• Initial conditions that adequately represent the
  state of the atmosphere (three-dimensional wind,
  temperature, pressure, moisture and cloud
  parameters)

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Monitoring Current Conditions
September 6 20GMT
A D A S
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Potential Discussion Points

• Why are analyses needed?
• Application driven data assimilation for NWP
  (forecasting) vs. objective analysis (specifying
  the present, or past)
• What are the goals of the analysis?
• Define microclimates?
• Requires attention to details of geospatial
  information (e.g., limit terrain smoothing)
• Resolve mesoscale/synoptic-scale weather
  features?
• Requires good prediction from previous analysis
• Whats the current state-of-the-art and whats
  likely to be available in the future?
• Deterministic analyses relative to ensembles of
  analyses (ensemble synoptic analysisGreg
  Hakim)
• How is analysis quality determined? What is
  truth?
• Why not rely on observations alone to verify
  model guidance?

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Observations vs. Truth

• Truth? You cant handle the truth!
• Truth is unknown and depends on application
  expected value for 5 x 5 km2 area
• Assumption average of many unbiased observations
  should be same as expected value of truth
• However, accurate observations may be biased or
  unrepresentative due to siting or other factors

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Whats an appropriate analysis given the
inequitable distribution of observations?
Case 3
Case 2
Case 1
?
?
x
?
x
x
grid cell
observation
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Whats an appropriate analysis given the variety
of weather phenomena?
Elevated Valley Inversions
Front
O
?
O
?
?
O
O
O
O
z
T
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Analyses vs. Truth
Analysis value Background value observation
Correction

• An analysis is more than spatial interpolation
• A good analysis requires
• a good background field supplied by a model
  forecast
• observations with sufficient density to resolve
  critical weather and climate features
• information on the error characteristics of the
  observations and background field
• good techniques (forward observation operators)
  to transform the background gridded values into
  pseudo observations
• Analysis error relative to unknown truth should
  be smaller than errors of observations and
  background field
• Ensemble average of analyses should be closer to
  truth than single deterministic approach IF the
  analyses are unbiased

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Truth Continuum vs. Discrete
Truth is unknown Truth depends on application
Temperature
Truth
West
East
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Discrete Analysis ErrorGoal of objective
analysis minimize error relative to Truth not
Truth!
Temperature
Truth
West
East
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ADAS

• Near-real time surface
• analysis of T, RH, V
• (Lazarus et al. 2002 WAF
• Myrick et al. 2005 WAF
• Myrick Horel 2006 WAF)
• Analyses on NWS GFE
• grid at 5 km spacing
• Background field RUC
• Horizontal, vertical anisotropic weighting

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Description In the following slides,
temperature results from LAPS/MM5 analysis are
shown. The objective is to compare a normal MM5
analysis with LAPS/MM5 analysis, also verify
against some observations that are not included
into the LAPS analysis Input to LAPS analysis is
here - MM5 9-km resolution (input to MM5 is
ECMWF 0.35 deg) - 52 surface observations from
HTB area
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MM5 analysis Temperature at 9 m height, with 1
km resolution The analysis is based on 0.35
degree boundary fields from ECMWF operational
analysis.
09 Aug 2005,15 UTC
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MM5 analysis Temperature at 9 m height, with 1
km resolution Verification The figures, within
the plot, are measurements from certain stations
not included in the LAPS analysis
09 Aug 2005,15 UTC
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LAPS/MM5 analysis Temperature at 9 m height,
with 3 km resolution Verification The figures,
within the plot, are measurements from certain
stations not included in the LAPS analysis
09 Aug 2005,15 UTC
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LAPS/MM5 analysis Temperature at 9 m height,
with 1 km resolution Verification The figures,
within the plot, are measurements from certain
stations not included in the LAPS analysis
09 Aug 2005,15 UTC
38
LAPS/MM5 analysis Temperature at 9 m height,
with 1 km resolution Verification The figures,
within the plot, are measurements from certain
stations which are not
included in the LAPS analysis
09 Aug 2005,15 UTC
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Data Assimilation Surprises

• Torn and Hakim (unpublished) have applied an
  ensemble Kalman filter for several hurricanes to
  determine the most sensitive regions for
  forecasts in the western Pacific Ocean. The
  largest sensitivities are associated with
  upper-level troughs upstream of the tropical
  cyclone. Observation impact calculations indicate
  that assimilating 40 key observations can have
  nearly the same impact on the forecast as
  assimilating all 12,000 available observations.
• Sensitivity of the 48 hour forecast of tropical
  cyclone minimum central pressure to the analysis
  of 500 hPa geopotential height (colors) for the
  forecast initialized 12 UTC 19 October 2004.
  Regions of warm (cold) colors indicate that
  increasing the analysis of 500 hPa height at that
  point will increase (decrease) the 48 hour
  forecast of minimum central pressure. The
  contours are the ensemble mean analysis of 500
  hPa height.

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More Data Assimilation Woes

• Adaptive observations collecting data where the
  forecast is most sensitive
• Sometimes assimilating more data produces a worse
  forecast (Morss and Emanuel)
• Heretical thought What if none of the hundreds
  of observations from the Helsinki Testbed made
  any difference to the forecast?

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Challenges Ahead for Testbed/LAPS

• The Testbed only samples the lower troposphere at
  best, not the mid and upper troposphere.
• Weather phenomena, even adequately sampled by the
  Testbed data, will move out of the Testbed domain
  within an hour or two.
• Weather phenomena inadequately sampled by the
  Testbed data will move into the domain and screw
  up your forecast.
• Predictability of mesoscale weather features is
  unknown.
• All of this assumes a perfect model.

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Challenges Ahead for Forecasters

• Determinism is deadlong live probabilistic
  forecasting!
• High-resolution model output cannot be
  interpreted the same way as a coarser-resolution
  model output.
• Forecasters need to be retrained.
• Communication of high-resolution forecasts to end
  users is not simple (i.e., you cannot just send
  raw model output to users and expect them to use
  it).
• This ensures jobs for good forecasters in the
  future.