Combining measurements and
models in atmospheric physics
Saroja Polavarapu
Data Assimilation and Satellite Meteorology Division
Meteorological Research Division
Environment Canada
U Toronto Physics Colloquium, 10 Jan. 2008
OUTLINE
1. What is data assimilation?
2. Recent advances in DA
3. A new application: data
assimilation with a climate
model
1. What is data assimilation?
Atmospheric Data Analysis
An analysis is a regular,
physically consistent,
representation of the
state of the atmosphere
Instruments sample
imperfectly and
irregularly in space
and time.
analysis
Why do people want analyses?
1.To obtain an initial state for launching
weather forecasts
2.To make consistent estimates of the
atmospheric state for diagnostic studies.
3.For an increasingly wide range of
applications (e.g. atmospheric chemistry)
4.To challenge models with data and vice
versa
The Global Observing System
http://www.wmo.ch/web/www/OSY/GOS.html
Data coverage examples
Some data used by CMC on Jan. 6, 2008 12 UT
Underdeterminacy
X = state vector
Z = observation vector
Model
Lat x long x lev x
variables
Data
Reports x items x
levels
CMC global oper.
800x600x58x4
=1x108 =N
Sondes,pibal
720x5x27
AMSU-A,B
12000x12
800x600x80x4
=1.5x108
SM, ships, buoys
6000x5
aircraft
20000x3x18
GOES
50000x1
Scatterometer
40000x2
Sat. winds
22000x2
TOTAL
1.6x106 =M
CMC meso-strato
N
 60
M
• Cannot do X=f(Z), must do Z=f(X)
• Problem is underdetermined
• Need more information!
Optimal Interpolation
N×1

N×1
N×M
M×1
M×N
N×1
x  x  K z  H (x )
a
Analysis
vector
b
Background or
model forecast
b
Observation
vector
Observation
operator
Weight matrix
NxM
NxN

MxM
K  BH HBH  R
T
T
Can’t invert!

1

x  x  Bv
a
b
Analysis increments (xa – xb) must lie
in the subspace spanned by the
columns of B
Properties of B determine filtering
properties of assimilation scheme!
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
Data assimilation cycle
Analysis step
assimil.
scheme
model
forecast step
2. Recent advances in data
assimilation at operational
weather forecasting centres
3D-Variational assimilation
Instead of solving this:

x  x  K z  H (x )
a
b

b
K  BH HBH  R
T
T

1

Optimal
Interpolation
Minimize this:
J (x)  (x  xb )T B 1 (x  xb )  (z  H (x))T R 1 (z  H (x))
• Obs and models can be nonlinearly related. To
assimilate radiances directly, H includes an
instrument-specific radiative transfer model.
• Matrix inverses can be avoided
4D-Variational assimilation
Analysis trajectory
Background trajectory
1
1 N
T
1
J (x 0 )  (x 0  x b ) B (x 0  x b )   (z k  H (x k ))T R 1 (z k  H (x k ))
2
2 k 0
Differences between 4D-Var and 3D-Var
RMS errors for day-1 forecasts
500 hPa GZ (dam), avg. over Jan 1998
Dark areas: 4D-Var
beats 3D-Var
4D-Var beats 3D-Var over
storm track areas
4D-Var is better at picking up
unstable initial conditions
Klinker et al. (2000)
Popular assimilation techniques in
weather forecasting centres
•
•
•
•
1980’s – Optimal interpolation
1990’s – 3D variational assimilation
2000’s – 4D variational assimilation
Future – ?
Advances are being driven by
improvements in computational power and
increase in amount of observations.
Why are the lids of operational
weather forecast models
moving up into the mesosphere
(>80 km)?
1mb
10mb
100mb
1000mb
• By raising forecast model lid,
satellite radiances are better
analysed
• Satellite radiances sense
deep layers of atmosphere
so analyses are improved in
troposphere as well as
stratosphere
• Improved analyses give
improved forecasts
• ECMWF, GMAO (NASA), UK
Met Office have lids ~80 km
• CMC system with model lid
at 65 km to be operational in
2008
Winter Polar vortex
• Westerly wind increasing
with height
• Dominant feature of
stratosphere in winter
• Occasional disruption of
polar vortex by sudden
warming events (in Arctic)
http://www.nasa.gov/images/content/113260main_arctic-vortex-447.jpg
Time
delay
Long timescale
The stratosphere and troposphere are dynamically
coupled. Low model lids compromise this coupling.
Baldwin and Dunkerton (2001)
3. A new application: Data
assimilation with a climate
model
Middle Atmosphere Dynamics
Ozone from OSIRIS
for March 2004
• Brewer-Dobson circulation
Shaw and Shepherd (2008)
– wave driven, thermally indirect
– affects temperature, transport of species
• Gravity waves also important
– Helps drive meridional circulation
– But normally seen as “noise” in assimilation process
Approximate mass-wind balance in mid-troposphere extra-tropics
Lars Isaksen (2007)
http://www.ecmwf.int/newsevents/training/meteorological_presentations/MET_DA.html
Balance in data assimilation
Time evolution of surface
pressure over 24 hours
Initialized
forecast
• Because of obs errors,
integrating a model from
an analysis leads to
motion on fast scales
– Noisy forecasts, e.g.
precipitation
– 6-h forecasts are used to
quality check obs
Raw forecast
Williamson and Temperton (1981)
• Extra-tropical troposphere
is largely balanced
• Historically, after the
analysis step, a separate
“initialization” step was
done to remove fast
motions
Gravity waves may be a nuisance in the troposphere, but they
are prevalent in the mesosphere and are part of the signal!
T profiles over one night from lidar
R.J. Sica (U Western Ontario)
http://pcl.physics.uwo.ca/science/temperature/
CMAM + 3DVar
CMAM = Canadian
Middle Atmosphere Model
How does information
propagate into the
mesosphere?
No obs
obs
AMSU
10-13
conventional
obs + sat.
Global mean temperature profiles at SABER locations
for various filtering options
Jan. 25, 2002
No obs
Sponge layer
SABER
DF12
DF6
IAUC
IAU6
IAU4
obs
Sankey et al. (2007)
There are more resolved waves in the upper mesosphere
with less filtering
More waves --> more damping
--> more heating
Sankey et al. (2007)
• Changing the assimilation scheme in the
stratosphere and troposphere has huge
impacts on the mesosphere!
• Waves (real or spurious) in the lower
atmosphere propagate up to the
mesosphere
• Small errors lower down can look big in
the mesosphere
Information from below
propagates to the
mesosphere. Is the
mesosphere improved?
70ºN zonal mean temperatures during 2006 SSW
Stratopause is above 0.01 hPa!
ECMWF
too low
too cold
GEOS-5
too low
too warm
Gloria Manney, JPL
• Low lids of operations models deterrent
to study of stratopause region
• Research models with higher lids show
improvement relative to operational
systems, in this region
– CMAM-DAS with no mesospheric DA
– NOGAPS-ALPHA with MLS, SABER data
• Compared to independent data, CMAMDAS looks reasonable
Climate models are extensively
validated statistically against
observations.
Data assimilation with a climate
model allows one to compare to
measurements on a specific
day.
Stratospheric Sudden Warming
(SSW)
•
•
•
Dramatic event: T increases near pole of
40-60 K in 1 week at 10 hPa
Every couple of years in NH (+2002 SH)
Major SSW (1+2), Minor SSW (1 only)
1. Poleward increase of zonal-mean temperature
between 60° and pole at 10 hPa
2. Zonal mean zonal wind reverses
•
Waves propagate up from troposphere,
interacts with mean flow (Matsuno 1971).
Total column ozone from Earth Probe Total
Ozone Mapping Spectrometer (EPTOMS)
August 15 – September 26, 2002
http://www.gsfc.nasa.gov/topstory/20020926ozonehole.html
Mesospheric Coolings
schematic diagram
NH winter 2005/06
Courtesy of Kirstin Krüger
C
W
C
(Labitzke 1972)
South Pole temperature in 2002
during stratospheric warming
10 hPa (30km)
0.1 hPa (65 km)
hits
1995-2005
Met Office
analyses
misses
Ren et al. (2008)
<“hits”> - <“misses”>
Zonal mean temperature difference (K)
No obs
obs
“hits” are
colder in the
mesosphere
“hits” are
warmer in the
stratosphere
Ren et al. (2008)
Averages over Sept. 25 – Oct. 1, 2002
Resolved
waves
misses
GWD
GWD
hits
All waves
Waves 1-5
Ren et al. (2008)
2002 Stratospheric Warming study
• Assimilation with a climate model allowed us to
understand what caused the mesospheric
cooling above the stratospheric warming in our
simulations
• Planetary waves responsible for mesospheric
cooling below 60 km
• Mesospheric cooling is mainly due to
parameterized GWs above 75 km
• Observations inserted in stratosphere and
troposphere indirectly impact the mesosphere
through a GWD scheme!
Summary
• The atmospheric data assimilation problem is
characterized by huge, nonlinear systems and
insufficient observations.
• Because the math is well known, the key to
progress is using atm physics to make the right
approximations
• Information from below propagates to the
mesosphere (through both resolved and
parameterized waves) during 6-h forecasts
Other areas of current research in
data assimilation
•
•
•
•
Chemical weather forecasting
Ensemble Kalman filtering
Inferring winds from tracer measurements
Improving climate models by determining
uncertain parameters
• Evolving 4D-Var covariances from one
cycle to the next
• Improving tropical analyses
The End