Gillian Baxter

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Multiscale Data Assimilation for High Resolution
Nested Models
Gillian Baxter University of Reading Departments
of Mathematics and Meteorology Supervisors N.
K. Nichols, S. L. Dance, A. S. Lawless, S. P.
Ballard Sponsored by NERC and CASE studentship
with the Met Office
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• Contents
• A brief introduction to Data Assimilation
• High resolution models
• The long wave problem
• A few numerical results
• Conclusions

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What is data assimilation?
In order to run a weather forecasting model we
need initial conditions. We want initial
conditions which most accurately describe the
observed reality. Data Assimilation allows us to
combine observational data with a previous model
forecast (background). The initial conditions
are known as the analysis.
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4D-Var
time
constrained by the numerical model
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High resolution models
Pictures from BBC website
Accurate forecasting of convective storms is
important because these storms can lead to
dangerous flooding events, such as the Boscastle
flood in 2004.
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Boscastle Flood Comparison of 00 UTC 12, 4 and
1 km forecasts
12-18 from 00 UTC 1km
12-18 from 00 UTC 12km
12-18 from 00 UTC 4km
Actual peak accumulations reached about 200 mm
(gauge), 130 mm (2 km radar)
Plots from the Met Office, slide provided by S.
L. Dance
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• If we want a model with high resolution it can
  only have a limited domain size due to
  restrictions in computer power.
• This can create some problems
• The long wave problem.
• A limited area model (LAM) needs boundary
  conditions.

Met Office HRTM domains
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The long wave problem
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Some numerical results Model set up
The 1D heat equation
with homogeneous boundary conditions
Discretisation
where
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The truth has twice the spatial resolution and 4
times the temporal resolution of the LAM
Truth
Parent model
domain is 0,1
Boundary conditions provided by the parent model
LAM
buffer zone
buffer zone
the LAM starts at the first internal grid point
of the parent model and covers exactly half of
its domain
the LAM has 4 times the spatial resolution and 16
times the temporal resolution of the parent model
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Model set up
The 1D heat equation
with homogeneous boundary conditions
Discretisation
where
Davies Relaxation scheme
where b is the width of the buffer
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Aim To consider and compare the treatment in
the parent model and the LAM of wavelengths which
are

• Shorter than the resolution of the parent model

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where
--- truth --- parent background __ parent
analysis observations
Parent model outputs
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where
--- truth --- parent analysis __ LAM analysis
observations
LAM domain
LAM model outputs
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The Discrete Fourier Transform of the function
is
__ LAM __ parent model __ truth
Wavenumber k
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Aim To consider and compare the treatment in
the parent model and the LAM of wavelengths which
are

• Shorter than the resolution of the parent model
• Longer than the domain of the LAM

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1
0
2
3
4
5
6
7
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Wavenumber k
__ LAM __ parent model __ truth
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Summary The LAM can represent wavelengths that
are missed by the parent model. However, the LAM
may actually be worse at reproducing the longer
wavelengths. When the wavelength is longer than
the domain of the LAM it cannot be correctly
reproduced.
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Future Work The long wave information is
important and the challenge is how to assimilate
observations of these long waves in order to
feed information from the large scales into the
analysis for the limited area model. One option
may be to split the scales. Take longer
wavenumbers from the parent model and shorter
wavenumbers from the LAM.
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Plot taken from Development of 1-4km Resolution
Data Assimilation for Nowcasting at the Met
Office. S. Ballard, Z. Li, M. Dixon, S.
Swarbrick, O. Stiller and H. Lean. WMO
Nowcasting Meeting Abstract 3.02
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where
--- truth --- parent background __ parent
analysis observations
Parent model outputs
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where
--- truth --- parent analysis __ LAM analysis
observations
LAM model outputs