Seamless prediction

Seamless
prediction
Prediction from days to
decades
Wilco Hazeleger

Seamless prediction

Seamless prediction

Seamless prediction
The science case:
Same physical principles for weather and climate (but different
processes acting on different scales)
Prediction problem with different role initial and boundary conditions
Seasonal to decadal prediction as focus
The modelling case:
Convergence of NWP-Climate model development
Seamless earth system prediction
The application case:
Calibration (weights) of climate predictions & projections
Seamless connection to impact studies

3 pillars of 21st century scientific method
Theory (since antiquity)
Combined with experiment
(since Galilei & Newton)
….and with simulation
(since 1940s, Teller, von Neumann, Fermi,..)

Sources and limits of
predictability

Natural variability, chaotic atmosphere
Lorentz limit ~15 days
Selten et al, Sterl et al 2008

Natural and `forced variability

Predicting natural variability: more than noise?
• 0-hypothesis: ocean integrates white noise (weather)
(Hasselmann 1976)
dX ( t)
dt
= −α X ( t)
+ζ ( t)
• With α damping coefficent and ζ(t) random variable (AR1 process à red noise)
• When variability stands out of red noise, e.g. oscillations due
to internal dynamics, dynamical predictions may be possible
• But… even red noise is a source of predictability (e.g. damped
persistence)

Spectra of global mean temperature: peaks?

Monthly: Soil moisture, Sea Surface temperatures,
Atmospheric composition
l Dry soils in spring can lead to high summer temperatures

Seasonal to interannual: El Niño
Sea surface temperature anomaly during El Niño

Seasonal to interannual: Coupled ocean-atmosphere
variability

El Nino – Southern Oscillation (ENSO)
" Predictable 3-9 month ahead (depending on the season)
" World-wide impact
Precipitation SON
Temperature DJF

Decadal: Atlantic Multidecadal Oscillation
Knight et al. 2005

Decadel: Pacific decadal variability

Multi-decadal: anthropogenically forced change

Modelling climate changes: uncertainties
Natural
fluctuations
GHG emission
uncertainty
Model uncertainty
Hawkins and Sutton, 2009

Predictability beyond the Lorentz-limiet
l
The atmospheric circulation is chaotic and unpredictable beyond
~15 days, the averaged weather is in some areas and in some
seasons predictable beyond the Lorentz limit
l
l
(damped) persistence beyond 15 days
Showly fluctuating patterns of variability (often involving slow
ocean responses): ENSO, Indian Ocean Zonal Mode, Pacific
Decadal Oscillation, Atlantic Multidecadal Oscillation,…,…
l
Initial conditions of the earth system provide memory: ocean,
ice, soil, atmospheric composition
l
Anthropogenic forcing (trends) predictable

The ideal case: potential
predictability

What to expect from predictions?
• Diagnostic potential predictability: ratio of variances in a long
control simulation
DPP
=
σ
σ
m
2
σ
2 − 1
v
2
• With σ v
2
variance of m-year means
(e.g. Boer et al, Pohlmann et al)

Diagnostic potential predictability in EC-Earth
10 yr

What to expect from predictions?
• Prognostic potential predictability: ensemble spread in relation
to total variance
PPP = 1−
1
N(
M
−1)
i=
1
2
• With X ij is the i th member of j th ensemble, N is number
ensembles, M number of ensemble members
N
∑
j=
1
M
∑
σ
[ X
ij
( t)
− X
j
( t)]
2
Griffies and Bryan 1997, Collins et al, Pohlmann et al

Atlantic MOC (30N)
MOC (Sv)
Collins et al 2006

Prognostic Potential predictability in EC-Earth (T2m, yr
1-10)
T. Koenigk, SMHI, pers. comm.

Prognostic potential predictability in EC-Earth (T2m, yr
1-10; without trend)
T. Koenigk, SMHI, pers. comm.

Making predictions

Prediction systems
l
Statistical
l
l
l
l
analyse 100 years of data for relationships
Easy to fool yourself (and others)
Much used in tropics: Monsoons India, Indonesia, West Africa,
hurricanes, seasonal prediction US
Often misused: summer and winter predictions for Europe

Statistical: Precipipation in Curaçao
l
Rain related to ENSO
4 months in advance

Prediction systems
l Dynamical
Use numerical weather prediction model, run it longer. Use climate
model, run it shorter
" Essential: good initial state of ocean, snow, soil, aerosols,
greenhouse gasses
" ECMWF, EC-Earth, Met Office, Météo France, NCEP, ...

Prediction experiment
Initialize atmosphere-ocean-sea ice-land models
from observed/analyzed ocean and sea ice state
Perturb initialized models to generate ensembles
Verify the results against own analyses and
independent observations

Complex Global Circulation Model
Based on laws of physics (F= m x a
and thermodynamics)
Forcing specified (Q= e.g. radiation)
Small scales not resolved
Big science: 2 million lines of code
and 10 variables on 10^9 gridpoints

Initialization, in particular the ocean:
Limited subsurface ocean observations
1960 1980
2007

Initialisation ocean: ocean analyses
A. Koehl, pers. comm.

Perturbing the ensemble
" Perturbations which grow most rapidly in slow component (e.g. in
ocean, for instance Kleeman et al. for ENSO, Hawkins and Sutton
for 3D ocean, bred vectors B. Kirtman etc.)
" Consistent with the observational uncertainties
" Can be useful for identifying regions where additional observations
would be most valuable to improve predictions

Perturbing ocean
• E.g. linear Inverse Modelling (Penland & Sardeshmukh 1995, Hawkins &
Sutton 2009)
dx
dt
x(
t
P
T
= Bx + ζ x represents
+ τ ) =
Px
0
= λx
P x(
t)
τ
0
leading EOFs
Eigenvectors are
optimal growing
perturbations
In practice, pragmatic approaches (perturbing
atmosphere, different ocean states, perturbing ocean
diffusivity)
Hawkins & Sutton 2009

Measures of skill

Measures of skill

Some simple deterministic measures of skill
N
• Mean error (additive
1
bias)
ME = ∑(
Fi
− O
N
i=
1
i
)
• Root mean square error
RMSE
=
1
N
N
∑
i=
1
(
−
F i Oi
)
2
• Anomaly correlation
• (F=forecast,
=observation,
C=climatology)
AC
( F −C)(
O −C)
= ∑
2
( F −C)
( O −C)
2

Skill weather prediction: 500hPa height

Skill dynamical seasonal predictions: temperature
Dec-Feb temperature, predicted from 1st of November
Note: bias correction always needed

Skill dynamical seasonal predictions: precipitation

Probabilistic scores
Reliability diagram: How well do the predicted probabilities of an
event correspond to their observed frequencies?
The range of forecast probabilities is divided into K bins (for example, 0-5%, 5-15%, 15-25%, etc.).
The sample size in each bin is often included as a histogram or values beside the data points.

Skill single and multi-model ensemble
From EU Demeter project (Doblas Reyes)

Probabilistic score
Relative Operation Characteristic: What is the ability of the forecast
to discriminate between events and non-events?
Plot hit rate (POD) vs false alarm rate (POFD), using a set of increasing probability thresholds
(for example, 0.05, 0.15, 0.25, etc.) to make the yes/no decision.
The area under the ROC curve is frequently used as a score.

Temperature
Precipitation

ROC score, 3 month lead time
Temperature
Sea level pressure

Probabilistic scores
Rank histogram: How well does the ensemble spread of the forecast
represent the true variability (uncertainty) of the observations?
1. At every observation (or analysis) point rank the N ensemble members from lowest to highest.
2. Identify which bin the observation falls into at each point
3. Tally over many observations to create a histogram of rank.
Flat - ensemble spread about right to represent forecast uncertainty
U-shaped - ensemble spread too small, many observations falling outside the extremes of the
ensemble
Dome-shaped - ensemble spread too large, most observations falling near the center of the ensemble
Asymmetric - ensemble contains bias

Always use a 0-hypothesis
• Verify against
simplest statistical
X ( t + τ )
model (AR1,
damped persistence, A(
τ ) = 0
or climatology) A(
τ ) = 1
=
A(
τ ) X ( t)
(climatology)
(persistence)

Skill dynamische verwachtingen
l
l
l
l
Temperatuur: trend + persistentie + ENSO
Neerslag: ENSO + beetje meer, beter dan puur statistische
modellen
Kan regionaal verbeterd worden met downscaling technieken (bv
SVD tussen waargenomen en verwachte velden om spatiële biases
te corrigeren)
Zal beter worden naarmate meer relevante processen goed
gecalibreerd maagenomen worden.

The model and bias

Based on ECMWF weather
and seasonal prediction
system
Regular merging with
operational ECMWF
NWP system
Resolution standard runs:
Atmosphere: T159 L62
(AMIP runs up to T799)
Hazeleger et al BAMS, October, 2010
Ocean: 1 degree L42 (with
equatorial refinement
and tripolar grid)

Low (T159) and high resolution (T799)

EC-Earth: temperature and bias

EC-Earth: precipitation and bias

EC-Earth: El Nino

EC-Earth: the North Atlantic Oscillation
Observations
EC-Earth

EC-Earth: the Atlantic Ocean overturning

EC-Earth: global mean temperature
EC-Earth
Observations

‘Weather’ predictions

Seasonal predictions

Seasonal predictions: mean bias
May
Nov
Bias of first month near-surface air temperature re-forecasts wrt ERA40/Int over 1976-2005.

Seasonal predictions: ENSO (2-4 month lead time)
EC-Earth
Ratio sd: 1.34
Corr: 0.82
RPSSd: 0.48
ECMWF System 3
Ratio sd: 0.84
Corr: 0.86
RPSSd: 0.68
Niño3.4 time series for ERA40/Int (red dots), ensemble range (green box-and-whisker)
and ensemble mean (blue dots) 2-4 month (JJA) re-forecasts over 1981-2005.
Doblas-Reyes, IC3-group

Correlation skill
1-month
lead time
JJA
DJF
7-month
lead time
Ensemble-mean correlation of EC-Earth near-surface air temperature re-forecasts
wrt ERA40/Int over 1976-2005. Dots for values statistically significant with 95% conf.

Seasonal forecast ENSO

Seasonal forecast July-Sept 2011 temperature
Left: prediction; anomalies probability above mean
Right: ROC skill (hit rate vs false alarm rate)

Seasonal predictions: tropical cyclones

Decadal predictions

Decadal predictions in EC-Earth: global mean SST
Wouters et al, in prep

Decadal predictions in EC-Earth, drift corrected
Wouters et al, in prep

Verification multi-model EU-ENSEMBLES decadal
predictions
van Oldenborgh, Doblas-Reyes, Wouters and Hazeleger, subm

Skill multiannual predictions
anomaly correlations ensemble mean – observations
lead time 2-5 years and 6-9 years averaged

Verification multi-model decadal predictions
van Oldenborgh, Doblas-Reyes, Wouters and Hazeleger, subm

Skill initialized predictions at multiannual lead times
• Trend, as defined by regression on global mean CO 2 concentrations,
removed
• Seasonal predictability comparable to ECMWF S3

Skill initialized predictions at multiannual lead times
R=0.77 R=0.80 R=0.19

Skill initialized predictions at multiannual lead times
• Trend, as defined by regression on global mean CO 2 concentrations,
removed
• Seasonal predictability comparable to ECMWF S3

Predicting Atlantic Multidecadal Oscillation
R=0.67 R=0.84 R=0.57

Skill of very simple statistical model

Final remarks
Predictability beyond the Lorenz limit: (damped) persistence &
(damped) oscillations
Memory provided by slow components of the earth system: soil
moisture, snow, ocean temperatures
à Challenge in initialization of dynamical models (atmosphere as in
weather prediction, but memory quickly lost. Ocean, snow, ice, land
surface relevant for longer time scales)
Statistical models perform well in tropics, dynamical models can
outperform: predictability at multiannual time scales found (AMO,
PDO)
Always verify! If possible probabilistically

http://www.cawcr.gov.au/projects/verification