Representing Model Uncertainty on Seasonal and Longer Timescales

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Representing Model Uncertainty on Seasonal and
Longer Timescales By Tim Palmer ECMWF With
thanks to Paco Doblas-Reyes, Renate Hagedorn,
Glenn Shutts
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South Reading in January 2001
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South Oxford in January 2003
Global Warming?
Photo courtesy of Dave Frame, AOPP
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MONDAY APRIL 16 2001
Ministers too simplistic on climate change
By Mark Henderson Science Correspondent and
James Landalle Political Correspondent
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Probability Analysis of Extreme Climate Change
based on 19-member CMIP2 Multi-model Ensemble.
DJF
Are these probabilities reliable? How can they be
validated?
From Palmer and Räisänen, Nature 2002
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DEMETER Multi-model ensemble system for seasonal
prediction

• 7 global coupled ocean-atmosphere climate
  models

9 member ensembles ERA-40 initial conditions
SST and wind perturbations 4 start dates per
year 6 months hindcasts
Hindcast production for 1987-1999 (1958-2001)
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Reliability 2m-Temp.gt0
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Conceptual Background
SST, Tropics, 1987
verification
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Conceptual background (probabilistic view)
SST, Tropics, 1987
MSLP, Tropics, 1988
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Reliability 2m-Temp.gt0
0.222 0.994 0.227
0.170 0.959 0.211
multi-model
single-model (54 members)
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Reliability 2m-Temp.gt0
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Reliability Precipgt0.43?
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Malaria predictions (0º,35ºE)
ERA-40 Multi-Model Terciles Ens-mean
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http//www.ecmwf.int
Retrieve NetCDF
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• Are there other ways of representing model
  uncertainty?
• Perturbed parameters
• Stochastic physics

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Why are models uncertain? We know the equations
of climate well as PDEs the uncertainties arise
in converting these PDEs to ODEs.
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(Deterministic) Parametrisations motivated by
statistical mechanics, but
Wavenumber spectra of zonal and meridional
velocity composited from three groups of flight
segments of different lengths. The three types of
symbols show results from each group. The
straight lines indicate slopes of 3 and 5/3.
The meridional wind spectra are shifted one
decade to the right.(after Nastrom et al, 1984).
shallow atmospheric spectra, no scale separation
between resolved and unresolved scales
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From Schertzer and Lovejoy, 1993
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Unconstrained pdf of P
lt...gt grid box average
Grid box
Pdf constrained by specific value of ltugt and lt?gt
if parametrisation concept was valid
In practice, however
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Actual vs Parametrised Tendency in a Large-Eddy
Simulation 1km resolution tendencies averaged
over 64x80km grid boxes (G.Shutts personal
communication)
Actual PDF
Parametrised PDF
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Could stochastically sampling the probability
distribution of the sub-grid tendency, rather
than always sampling the mode, make a difference?
Yes if atmosphere is nonlinear!! Eg ball bearing
in skewed potential well.
?
?
Mean state without noise
Mean state with noise
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Lorenz(1963) in an EOF basis (Selten 1995)
3rd EOF only explains 4 of variance. Parametrise
it?
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Lorenz(1963) in a truncated EOF basis with
parametrisation of a3
Good as a short-range forecast model (using L63
as truth), but exhibits major systematic errors
compared with L63, as, by Poincaré-Bendixon
theorem, the system cannot exhibit chaotic
variability system collapses onto a point
attractor.
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Stochastic-Lorenz(1963) in a truncated EOF basis
Stochastic noise
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Lorenz attractor
Truncated Stochastic-Lorenz attractor weak noise
Error in mean and variance
Truncated Stochastic-Lorenz attractor
Palmer, 2001 (acknowledgment to Frank Selten)
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ECMWF stochastic physics scheme(s)
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? is a stochastic variable, drawn from a
uniform distribution in -0.5, 0.5, constant
over time intervals of 6hrs and over 10x10
lat/long boxes
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Buizza, Miller and Palmer, 1999 Palmer 2001
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ENSO prediction skill and spread
No stochastic physics
persistence
With stochastic physics
ECMWF coupled model
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Stochastic physics has an impact on the mean
state of the ECMWF model
Impact of stochastic PD scheme
Systematic error
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A possible hybrid stochastic-dynamic
parametrisation cellular automaton
EG Probability of an oncell proportional to
CAPE and number of adjacent on cells on
cells feedback to the resolved flow
(Palmer 1997, 2001)
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T95 aquaplanet runs (left control, right with
stoch. phys.)
CA-based vorticity forcing in low moist Ri regions
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• Conclusions
• Based on seasonal prediction studies, forecast
  probability distributions from multi-model
  ensembles are intrinsically more reliable than
  those from single-model ensembles.
• Provides necessary (but not sufficient)
  justification for using a probabilistic analysis
  of climate change projections based on
  multi-model ensembles eg CMIP - in IPCC AR4
• Not all aspects of model uncertainty are well
  represented by state-of-the-art multi-model
  ensembles.
• It is possible that the effects of unresolved
  scales in Earth-system models are better
  represented using (computationally cheap)
  stochastic dynamical systems, than by
  conventional deterministic (bulk-formula)
  parametrisations.