Transcript Data Assimilation Cycle - Isaac Newton Institute for Mathematical

After Climategate
and Cancun….
…What next for
climate science?
By Tim Palmer
University of Oxford
University of Cambridge
From IPCC AR4 WG1
AR4
assessment
of likely
range
Potential Amplifiers of Climate
Change
Water Vapour
Water
Vapour
Aerosols
Clouds
Clouds
Carbon cycle
Ice albedo
Methane Clathrates
IPCC AR4 WG1
“…..there has been no apparent
narrowing of the uncertainty range
associated with cloud feedbacks in
current climate change simulations.
A straight-forward approach of
model validation is not sufficient to
constrain the models efficiently and
a more dedicated approach is
needed.”
Wilhelm Bjerknes (1862-1951)
Proposed weather
forecasting as a
deterministic
initial value
problem based on
the laws of
physics
ECMWF
Lewis Fry Richardson (1881-1953)
The first numerical
weather forecast
ECMWF
John von Neumann (1903-1957)
Integrating the
numerical weather
forecast on a digital
computer
ECMWF
Forecast Skill 1980-2010
ECMWF
Data Assimilation (DA)
Aim: to combine limited observations with our
Knowledge of the laws of physics for optimal state
estimation
PHYSICAL
LAWS
OBS
DATA
DA
MODEL
OPTIMAL STATE ESTIMATE
11
M.J. Rodwell
Data Assimilation Cycle: Unbiased Model
12
T
Schematic diagram of data assimilation / forecast cycle (perfect model)
Observations
Analysis
Analysis increment
Mean Analysis Increment = 0
First guess forecast
0
1
2
Time (cycles)
3
4
Data Assimilation
 Central tool for determining the initial state for a weather
forecast
Find the state x given
observations yi by minimising
1
J ( x)  ( x0  xb )T B 1 ( x0  xb )
2
T
1 n
+   H i ( xi )  yi  Ri1  H i ( xi )  yi 
2 i 0
•
•
•
•
Multiple time scales
High dimensions
Sparsity of data
Nonlinearity of climate
processes
• Model Uncertainty
Don’t worry.
No hurricane!
X   X   Y
Y   XZ  rX  Y
Z  XY  bZ
The Butterfly Effect
X   X   Y
Y   XZ  rX  Y
Ed Lorenz
Z  XY  bZ
Idealised model of
weather
AN 19871016, 06GMT
EPS Cont FC +66 h
956
979
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MLSP 66-hourWEATHER
forecasts, VT: FORECAST
16-Oct-1987, 6FOR
UTC
AN ENSEMBLE
TL399OCT
EPS with
TL95, moist SVs
1987
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984
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Probability of
hurricane-force
gusts on
October 16th
1987
In a nonlinear system, predictability is
flow dependent – and predictable
Very
predictable
part of the
model Z
X
Very
unpredictable
part of the
model. Oct 87!
“How can we trust
global climate
forecasts 100 years
into the future when
the same models can’t
demonstrate shorterrange forecasts?”
X   X   Y
Y   XZ  rX  Y
Z  XY  bZ
50%
50%
“climate change”
X   X   Y  f
Y   XZ  rX  Y
80%
Z  XY  bZ
20%
Flat calm!
Surface Pressure
Potential Vorticity on 315K
Rossby wave breaking
Policy Relevance
How much more
frequent will
persistent blocking
anticyclones be
under climate
change?
The weather forecast
problem is fundamentally
an initial value problem…..
….. whilst the climate
change problem is
fundamentally a forced
problem
MLSP 66-hour forecasts, VT: 16-Oct-1987, 6 UTC
TL399 EPS with TL95, moist SVs
In recent years, ensemble
prediction has also become
a standard tool for climate
forecasting….but for the
latter there are more
uncertainties than just
initial-condition
uncertainties
Why is there uncertainty in
climate predictions?
Chaos
Future
Emissions
Model
Uncertainty
Standard ansatz for “ab initio” weather/climate models
Eg


   u.  u   g  p  2u
 t

X1 X 2 X 3 ...
... X n
Increasing scale
Eg momentum“transport” by:
•Turbulent eddies in
boundary layer
•Orographic gravity wave
drag.
•Convective momentum
transport
Simplified deterministic
bulk-formula
parametrisations
P  X n ; 
IPCC AR4 WG1 Chapter 8
“…models still show significant errors. Although these are
generally greater at smaller scales, important large-scale
problems also remain. ……The ultimate source of most
such errors is that many important small-scale processes
cannot be represented explicitly in models, and so must
be included in approximate form as they interact with
larger-scale features.
…consequently models continue to display a substantial
range of global temperature change in response to
specified greenhouse gas forcing. “
..we do not know how to close the equations with
deterministic bulk formulae and produce a climate model
which has no significant biases against observations
.. Estimates of global warming also depend sensitively on the
parameters α….
“There are no
obvious
problems with
the high
temperature
models,
Stainforth
says…. The
uncertainty at
the upper end
has exploded,
says teammember
Myles Allen.”
Why is it so hard to
produce a bias free
climate model?
“Truth”
X  X  Y
Y   XZ  rX  Y
Z  XY  bZ
“Model”
“Model= Truth + Bias”
What is the origin of
this bias?
Let’s guess that the origin of the
bias lies in the model’s equation for
X, ie that the model equations are
X   X   Y  f
Y   XZ  rX  Y
Z  XY  bZ
Looks
reasonable.
“Model”
f
X   X   Y 
2
In fact
f
Y   XZ  rX  Y 
2
Z  XY  bZ
X   X   Y  f cos 
Y   XZ  rX  Y  f sin 
Z  XY  bZ
Direction of
response
Y
 0
•


4
•
Direction of f
X


2
•
3

4
•
Leading EOF (ie
leading eigenvector
of the covariance
matrix C of L63)
There is a tendency for systematic errors
in “biased models” of Lorenz 63 to
project onto the L63’s dominant mode of
internal variability, regardless of the “root”
cause of the error.
This makes it difficult to identify the “root”
cause of model error, by diagnosing the
model’s systematic bias
Is this true for comprehensive climate
models as well?
Northern Annular Mode
Z500 Difference eto4-er40 (12-3 1990-2005)
2
14
6
12
6
6
10
2
-2
8
2
2
-2
-2
-6
6
4
-2
-6
ECMWF
Seasonal
Forecast
Systematic Error
2
-2
-2
-6
-2
-6
-4
-6
-10
-2
-2
-2
2
-8
-10
-12
2
-14
What is the root
cause of this
bias?
CNTT511-CNTT95
CNTT95-ERA40
Z500 Difference f8o8-f18l (12-2 1962-2005)
-2
SPBST95-CNTT95
Z500 Difference eut3-eto4 (12-3 1990-2005)
14
Z500 Difference ezeu-eto4 (12-3 1990-2005)
14
-2
-2
-6
12
10
-2
2
-2
10
8
2
2
2
2
-2
2
-2
8
2
-2
12
6
4
2
-2
6
-6
6
-2
-8
-4
2
-2
2
-4
2
2
-2
4
2
2
6
2
2
6
2
-2
6
-6
2
2
-8
-2
-10
-10
-12
-12
-14
-14
-2
2
Impact of
changing P
Impact of
changing
resolution
Impact of adding
stochastic noise
Response to three very different model revisions
each lies in the direction of the system’s principal
mode of internal variability. So what is the
primary cause of the bias??
1905 - Annus Mirabilis
•Special Theory of Relativity
•Quantum explanation of the photoelectric
effect
•Brownian Motion
..the same random forces which cause the
erratic motion of a particle in Brownian
motion would also cause drag if the particle
were pulled through the fluid.
Fluctuation-Dissipation Theorem
A very general result in statistical
thermodynamics which links the
response of a system to external
forcing, to internal fluctuations of the
system in thermal equilibrium.
First applied to the climate system
by Chuck Leith
M.J. Rodwell
Data Assimilation Cycle: Unbiased Model
43
T
Schematic diagram of data assimilation / forecast cycle (perfect model)
Observations
Analysis
Analysis increment
Mean Analysis Increment = 0
First guess forecast
0
1
2
Time (cycles)
3
4
M.J. Rodwell
Data Assimilation Cycle: Biased Model
44
T
Schematic diagram of data assimilation / forecast cycle (imperfect model)
Observations
Analysis
Analysis increment
Mean Analysis Increment ≠ 0
First guess forecast
0
1
2
Time (cycles)
3
4
−Mean Analysis Increment = Mean Net Tendency
= Convective + Radiative + … + Dynamical Tendency
Can assess individual processes when acting on states close to the truth
(Klinker and Sardeshmukh 1992)
Climate Sensitivity and Model
Parameters (Stainforth et al, 2005)
Greater than three times
larger climate sensitivity
with perturbed cloud
parameter
Circles: AGCM + Mixed-Layer model results from Stainforth et al. (2005) show combined RMSE of 8 year
mean, annual mean T2m, SLP, precipitation and ocean-atmosphere sensible+latent heat fluxes (equally
weighted and normalised by the control).
Diamonds: AGCM results from Rodwell & Palmer (2006) show RMSE from 39 year mean, annual mean T850,
SLP and precipitation (equally weighted and normalised by the control).
Slide 45
ECMWF
Mean Temperature Analysis Increment
Tendencies
Rodwell and Palmer,
Quarterly Journal of the
CLOUD T bias at D+5. Tendencies at step 2 Royal Meteorological
Society, 2006
CONTROL T bias at D+5. Tendencies at step 2
CONTROL T bias at D+5. Tendencies at step 2
12
12
36
36
96
96
12
36
96
CONTROL
884
979
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-9
-6
-3
0
3
Kday-1 (K for bias)
6
9
ENTRAIN/5 T bias at D+5. Tendencies at step 2
Pressure (approx)
539
728
Vertical Diffusion
Cumulus Convection
Large Scale Precipitation
539
353
Total
D+5 Bias
728
Cloud Frac
884
539
979
1012
-9
728
12
36
96
ENTRAIN/5
202
-6
-3
0
3
Kday-1 (K for bias)
6
9
ENTRAINx3 T bias at D+5. Tendencies at step 2
ENTRAIN/5 and
ENTRAINx3 are out
of balance
ENTRAINx3
202
884
Pressure (approx)
Pressure (approx)
Radiative
202
353
353
12
36
96
CLOUD Dynamic
202
Pressure (approx)
Pressure (approx)
202
353
353
979
1012
539
539
-6
728
728
884
884
979
1012
979
1012
-9
-6
-3
0
3
Kday-1 (K for bias)
6
9
-9
-3
-6
-3
0
3
Kday-1 (K for bias)
0
Kday-1 (K for bias)
6
Slide 46
9
3
ECMWF
6
Can a 6hr weather forecast determine the
climate 100 years from now?
It can strongly constrain what the climate
will be like 100 years from now!
So why not use data assimilation today to
constrain climate predictions?
1950
2000
Weather
models
Climate
models
No IPCC AR4
model had data
assimilation
capability…climate
change is not
primarily an initial
value problem
Towards Comprehensive Earth System Models
1975
1970
1985
1992
1997
Atmosphere
Atmosphere
Atmosphere
Atmosphere
Atmosphere
Atmosphere
Land surface
Land surface
Land surface
Land surface
Land surface
Ocean & sea-ice
Ocean & sea-ice
Ocean & sea-ice
Sulphate
aerosol
Sulphate
aerosol
Non-sulphate
aerosol
Sulphate
aerosol
Non-sulphate
aerosol
Carbon cycle
Carbon cycle
Huge Demands on
Human resources
Ocean & sea-ice
Off-line
model
model
development
Strengthening colours
denote improvements
in models
Sulphur
cycle model
Land carbon
cycle model
Ocean carbon
cycle model
Atmospheric
chemistry
Atmospheric
chemistry
Non-sulphate
aerosols
Carbon
cycle model
Atmospheric
chemistry
The Met.Office Hadley Centre
Ocean & sea-ice
2000
Many Demands on Computing Power and on
Human Resources
Decadal, Centennial,
Paleo Integrations
Data Assimilation
Estimating
uncertainty
(ensembles)
Chemistry,
Aerosols,
Carbon Cycles…
Vertical structure (inc.
Stratosphere, Mesosphere)
Horizontal
resolution (eg
Rossby Wave
Breaking)
Could climate scientists do more to
reduce uncertainty in climate
predictions?
• Yes. I have given one example of how this could be
achieved in principle. However, the weather and climate
forecast communities are still not well integrated, and
hence not making enough one another’s expertise
• Moreover, many institutes around the world view their
climate models as matters of institutional (sometimes
national) pride. The downside is that these same
institutes individually have neither the human nor the
computational resources needed to make significant
inroads into the problem of reducing climate uncertainty –
eg when such resources are needed merely to try to
replicate developments made elsewhere.
A community-wide approach to
climate model development?
Could governments/ the private sector
do more to reduce uncertainty in
climate predictions?
• Current and planned high-performance
computing devoted to climate (especially in
Europe) is wholly inadequate to reduce
substantially the uncertainties in climate
change in the coming decade.
• Governments should work together to provide
dedicated leadership-scale computing facilities
for use by the climate community.
Conclusions
• Discussions on global emissions cuts appear to be
reaching stalemate.
• I believe we need to focus on reducing uncertainty in
climate predictions if we are to move policy forward.
This is not straightforward scientifically.
• Over the coming years we need a renewed effort by
scientists and by governments:
– By scientists to do all they can to focus on the problem of
reducing uncertainty – mathematical multidisciplinary
programmes like that at INI definitely help!!
– By governments to provide collectively, the technology to
enable new innovative methods to be implemented