Transcript Approaches to climate change study and neural

Approaches to climate change study
and neural network modelling
Antonello Pasini
CNR - Institute of Atmospheric Pollution
Rome, Italy
Summer School on
Climate Change
UniKore, 6-10 September 2008
1
Outline
• Climate science and
dynamical modelling;
• neural network model;
• assessment on the past;
• about predictability in past
and future scenarios;
• NN downscaling;
• conclusions and prospects.
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Climate scientists as grown-up
babies
If you give a
child a toy, he
will eventually
open it up.
Let’s open it up!
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Climate scientists as grown-up
babies
Let’s understand how
it works...
… and let’s
reassemble it!
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Decomposing the system
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Theoretical knowledge
We possess theoretical knowledge of
single sub-systems from experiments in
“real laboratories” (e.g., laws from fluiddynamics and thermodynamics of oceans
and atmosphere).
In order to recompose
the complexity of the
system, we need a
“virtual laboratory”...
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Recomposing in a model
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From dynamical modelling...
• Physical characterization and
forecasting in the climate system is a
very difficult task, if we adopt an
approach with complete dynamics.
• Global Climate Models (GCMs) are the
standard tools for grasping this
complexity.
• They permit to recognize the role of
some cause-effect relationships.
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From dynamical modelling...
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From dynamical modelling...
• However, the results of GCMs could
crucially depend on the delicate balance
(fine tuning) among the relative strength
of feedbacks and the various parameterization routines  doubtful results .
• Furthermore, they show limits in
reconstruction and forecasting at
regional and local scales.
• So, an independent (more “holystic”)
analysis could be interesting.
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… to a different strategy
• The simplest idea: application of a
multivariate linear model to the analysis
of influence/causality:
forcings (which influence temperature)
vs.
temperature itself
• Bad results: the linear model is too
simple  neural networks!
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… to a different strategy
A biological “inspiration”
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… to a different strategy
Natural inputs
Climatic
behaviour
Anthropogenic
inputs
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A neural network model
1
sigmoid output
0.8
n=3
0.6
n=8
n=20
0.4
n=50
0.2
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
weighted sum
 

g j hj
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
 h j
1  exp  

nhl





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A neural network model

Oi  gi 




Wij g j 


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j

k

w jk I k  




1
E   Ti   Oi
2 i

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
2
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A neural network model




 W t 
= W t    g  h T  O V  mW  t   W t  1
Wij t  1  Wij t   
 E
 m Wij t  Wij t  1 
ij

ij
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i
i

i


i
j
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ij
ij
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A neural network model




 w t 
t + g  h W g  h T  O I  mw t   w
 E
w jk t  1  w jk t   
 m w jk t  w jk t  1 
jk
 w jk

j

j
ij i
i

i


i
k
jk
jk
t  1
i
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A neural network model
• Tool for short historical time series of data
(“all-frame” or “leave-one-out” procedure);
• early stopping method.
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Assessment on the past
Global case study;
regional case study.
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Global case study
Input data:
• solar irradiance and stratospheric optical
thickness as indices of natural forcings
coming from Sun and volcanoes;
• CO2 concentration and sulfate emissions as
anthropogenic forcings;
• SOI index (ENSO) as a circulation pattern
in ocean and atmosphere which can be
important for better catching the interannual temperature variability.
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Global case study
4 case studies:
a) natural forcings only;
b) anthropogenic forcings only;
c) natural + anthropogenic forcings;
d) natural + anthropogenic forcings + ENSO.
In cases when anthropogenic forcings are
considered, a strong improvement in the
reconstruction performance is achieved by
neural modelling (vs. linear modelling).
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Global case study
Anthropogenic forcings
0.6
0.6
0.4
0.4
Temperature anomalies [°C]
Temperature anomalies [°C]
Natural forcings
0.2
0
-0.2
-0.4
0.2
0
-0.2
-0.4
-0.6
1860
1880
1900
1920
1940
1960
1980
2000
-0.6
1860
1880
Years
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1900
1920
1940
1960
1980
Years
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2000
Global case study
Natural + anthropogenic forcings + ENSO
0.6
0.6
0.4
0.4
Temperature anomalies [°C]
Temperature anomalies [°C]
Natural + anthropogenic forcings
0.2
0
-0.2
-0.4
0.2
0
-0.2
-0.4
-0.6
1860
1880
1900
1920
1940
1960
1980
2000
-0.6
1860
1880
Years
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1900
1920
1940
1960
1980
Years
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2000
Remarks
• Anthropogenic forcings appear as a main
probable cause of the changes in T;
• the input related to ENSO acts as a 2ndorder corrector to the estimation obtained
by anthropogenic and natural forcings
(nevertheless, in a nonlinear system we
cannot separate the single contributions to
the final result);
• the amount of variance not explained by our
final model is low 
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Remarks
 Is this low amount due to the natural
variability of climate system or to some
hidden dynamics coming from one or more
neglected dynamical causes?
Look at the residuals!
Three tests:
•Fourier spectrum;
•autocorrelation function;
•MonteCarlo Singular Spectrum Analysis
(MCSSA).
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The residuals
No particular peak
and periodicity;
the spectrum
trend is almost
flat…
… but, decrease in
the amplitude
above 3 cycles per
10 years;
we cannot exclude
red or pink noise.
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The residuals
The autocorrelation
function is almost
completely
confined inside
the white noise
limits;
some oscillations
are visible but
more uncoupled
than in previous
results.
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The residuals
The plots show results obtained applying MCSSA: due
to some points exceeding the confidence limits
provided by an AR(1) process, the presence of
components different from red noise is suggested.
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The residuals
No undoubted conclusion can be reached by
our analysis of the residuals (besides, it is
well known how is difficult to distinguish
between noise and chaotic dynamical signals
in short time series).
Anyway, we can be confident that the major
causes of temperature change have been
considered and only 2nd-order dynamics
has been neglected in our study.
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Regional case study
We want to analyze the fundamental elements
that drive the temperature behaviour at a
regional scale, with the same strategy
adopted in the previous global case study.
It is well known that the North Atlantic
Oscillation (NAO) correlates quite well with
temperatures in a period called “extended
winter” (December to March).
We want to assess the relative influences of
global forcings and NAO on temperature in
Central England.
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Regional case study
NAO -
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NAO +
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Regional case study (CET)
CET series in extended winters
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Temperature [°C]
6
5
4
3
2
1
1860
1880
1900
1920
1940
1960
1980
2000
3 case studies and input data:
a) global (natural + anthropogenic) forcings;
b) NAO only;
c) global forcings + NAO.
Years
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Regional case study (CET)
Case
(a)
(b)
(c)
Bias [°C]
-0.002
0.117
-0.037
MAE [°C]
0.995
0.601
0.651
Residuals [°C]
(b)
5
4
3
2
1
0
-1
-2
-3
-4
1860 1880 1900 1920 1940 1960 1980 2000
Years
(c)
5
4
3
2
1
Residuals [°C]
Residuals [°C]
(a)
0
-1
-2
-3
-4
5
4
3
2
1
0
-1
-2
-3
-4
1860 1880 1900 1920 1940 1960 1980 2000
1860 1880 1900 1920 1940 1960 1980 2000
Years
Years
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Regional case study (CET)
Global forcings have a very little influence on
the behaviour of temperatures in the Central
England during extended winter.
NAO - driving force: when NAO is considered
the values of linear correlation coefficients
(estimated T vs. observed T) are about 0.72
 0.75 in the two cases. These values are
lower than in the analogous situations of the
previous global case study (about 0.88).
This is probably due to the enhanced interannual variability of climate at regional scale.
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Discussion
A non-dynamical approach allows us to obtain
simple assessments in a complex system.
At a global scale we are able to reconstruct
the global temperature behaviour only if we
take the anthropogenic forcings into account.
Furthermore, we are able to recognize the
influence of ENSO in better catching the
inter-annual variability of our global time
series of temperature.
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Discussion
At a regional scale, the recognition of the
major influence of NAO on the CET time
series appears very important (a further
discussion in the afternoon exercise session).
In general, our results can be used in order to
identify the fundamental elements for
obtaining both:
• successful dynamical regional models
• and reliable statistical downscaling of GCMs
in the past and for future scenarios.
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Discussion
We possess a phenomenological tool for
obtaining preliminary assessments on the
past in the climate system.
In particular it is worthwhile:
• to consider an extension to inputs related to
other kinds of forcings, circulation patterns
and oscillations;
• to apply our method to other regions of the
world;
• to extend our treatment to the
reconstruction of precipitation regimes.
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Impact studies (animals)
How rainfall,
snow cover and
temperature
affect them?
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Impact studies (animals)
Bivariate linear
and nonlinear
analyses
(meteo-climatic
forcings vs.
rodent density)
From Pasini et al. (submitted)
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Impact studies (animals)
Neural
reconstruction
of rodent
density in the
Apennines
starting from
data of meteoclimatic
forcings
From Pasini et al. (submitted)
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Impact studies (animals)
Neural
“backcast” of
rodent
density in the
Apennines
starting from
data of
meteoclimatic
forcings
From Pasini et al. (submitted)
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Predictability
• Paper by Lorenz (1963) and the
discovery of “deterministic chaos” in
meteo-climatic systems;
• predictability problem and change of
perspective in the forecasting activity
at medium- and long-range;
• ensemble integrations for estimating
the predictability horizon in different
meteorological situations.
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Preliminary considerations
Ensemble
25
10m WIND SPEED (KTS)
20
15
10
5
Deterministic
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0
TIME (12 - hours interval)
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Preliminary considerations
Is the Lorenz-63 model important only
for historical reasons?
In the present situation, we deal with
very complex meteo-climatic models
(107 degrees of freedom);
inside these models, their physical
behaviour can be obscured and also the
ensemble strategy cannot be fully
followed up (because of the large
amount of computer time needed).
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Preliminary considerations
In this framework, the Lorenz-63 model
represents a toy model which mimics
some features of both the atmosphere
and the climate system:
for instance, their chaotic behaviour …
… and the presence of preferred states
or “regimes”.
Furthermore, the local predictability on
the Lorenz attractor resembles the
predictability of single real states.
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The Lorenz system
dx/dt =  (y-x)
dy/dt = rx - y - xz
dz/dt = xy - bz
Our choice of the parameters:
 = 10, b = 8/3, r = 28 
 chaotic solutions.
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The forced Lorenz system
dx/dt =  (y-x) + f0 cos 
dy/dt = rx - y - xz + f0 sin 
dz/dt = xy - bz
Our choice of the parameters:
f0 = 2.5  5,  = /2 
 still chaotic solutions.
Toy simulation of an increase of anthropogenic
forcings in the climate system
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The Lorenz system
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Unforced vs. forced
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Predictability (dynamics)
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Predictability (dynamics)
The concept of bred vector:
• Bred vectors are simply the difference
v between two model runs after a
certain number (n) of time steps, if the
second run is originated from slightly
perturbed initial conditions v0.
• We define the bred-growth rate as:
g = 1/n ln(v/v0).
• g can be used to identify regions of
distinct predictability on the attractor.
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Predictability (dynamics)
n=8
Blue: g < 0
Green: 0  g < 0.04
Yellow: 0.04  g < 0.064
Red: g  0.064
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Predictability (dynamics)
Unforced
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Forced
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Predictability (dynamics)
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Predictability studies by NNs
The idea to forecast future states of the
Lorenz system by NN is not new…
… but previous works considered the prediction
of the time series for a single variable
(usually the x variable) in order to
reconstruct the complete dynamics under the
conditions of the Takens theorem;
this permits to mimic the reconstruction of an
unknown dynamics by observational data in a
complex system.
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Predictability studies by NNs
Here, we consider the full 3D dynamics of the
Lorenz system and try to estimate the
predictability on its attractor in several
regions (related to bred-growth classes), by
considering changes in NN forecasting
performance:
• network topology: 3 - 15 - 3;
• single-step forecast from t0 to t0+n (n=8);
• total set of Lorenz simulated data (20,000
input-target patterns) divided into a training
set (80%) and a validation/test set (20%);
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Predictability studies by NNs
• the 3D-Euclidean distance between output
and target points as a measure of our
forecast performance.
• The NN forecast performance “feels”
increased predictability in forced situations.
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Predictability studies by NNs
Distributions of distance errors for each class
Yellow class
20
18
18
16
16
14
14
NN forecast error (distance)
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41
37
33
29
25
21
45
41
37
33
0
29
0
25
2
21
2
17
4
13
4
9
6
5
6
17
8
13
8
10
9
10
12
5
12
1
Frequency (%)
20
1
Frequency (%)
Blue class
NN forecast error (distance)
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Predictability studies by NNs
In short, the average forecast error decreases
in the forecasting activity on the forced
system.
This can be obviously due to a more frequent
permanence of the system’s state in regions
of high predictability (blue points).
Can this be due to a change in local
predictability of single points in the Euclidean
3D-space, too?
Is this due to both of these factors?
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Predictability studies by NNs
Some points:
• Of course, the Lorenz system is only a toy
model of the atmosphere and the climate
system;
• operationally, we would like to obtain an
estimate of predictability for future times,
when observations are not still available, while
here the recognition of distinct predictability
regions are obtained by NN just in comparison
with the “observed” states in Lorenz models
(obtained after dynamical integration).
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Predictability studies by NNs
Thus, we obtain just an a posteriori recognition
of the predictability over the Lorenz
attractors  is it possible to obtain an
operational estimation of predictability?
Yes, by forecasting (via NNs) the bred-growth
rates directly (1 output).
Main result: NNs are able to forecast g and a
statistical significant increase of
performance is shown when the external
forcing is applied.
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Predictability studies by NNs
Related to
the forecast
of g
Thus, not only the presence of an external
forcing permits to better forecast the future
states over the attractors (as shown
previously), but also the NN estimation of the
predictability itself is improved in these
forced situations.
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Provisional conclusions
• Neural modelling is able to distinguish
regions of distinct predictability over Lorenz
attractors.
• Increased predictability has been found in
the forced case (confirmed by dynamical
quantities) and operational estimation of g
has been obtained (here, it is an exercise,
but it could become important as emulation
of dynamical computations for predictability
assessments in real dynamical models, where
ensemble runs are very time-consuming).
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Prospects
Our NN performance is not very good 
improvements can be envisaged by:
• obtaining extended data sets by prolonged
Runge-Kutta integrations;
• consideration of different input sets (e.g.,
truncated time series of delayed data);
• application of other NN architectures and
learning paradigms.
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NN downscaling
• Up to now we have considered NNs as a
strategy which is alternative to dynamical
modelling.
• In doing so we have obtained both results
comparable with those coming from GCMs (in
the case of influence analysis on the past)
and new results (e.g., in the predictability
case study on unforced and forced Lorenz
systems).
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NN downscaling
• As a matter of fact, these strategies are
based on two distinct view-points for the
analysis of a system: a dynamical
decomposition-recomposition approach vs. an
analysis of the system as a whole by learning
directly on data.
• The challenge of complexity is extremely
hard and different view-points (and the
associated strategies) are welcome!
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NN downscaling
• Probably, these strategies can be seen more
appropriately as complementary than as
alternative.
• A concrete example of “synergies” between
them is represented by the case of GCMs
downscaling via NNs.
• In what follows we will discuss this
complementary approach and the work in
progress about it.
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The rationale
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The rationale
GCMs are not able to determine climate at
regional/local scale.
So, there is a need for downscaling.
It can be achieved either dynamically or
statistically, so that we have two cases:
• dynamical downscaling (regional climate
models - RCMs);
• statistical downscaling (regression models,
weather classification, weather generators).
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The rationale
Here we do not discuss about weather
classification and weather generators: see
Wilby et al. (2004) in the references.
In short, statistical downscaling is based on
the view-point that the regional/local climate
is conditioned by two factors:
• the large scale climatic state;
• the regional/local physiographic features
(e.g., topography, land/sea distribution, land
use).
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The rationale
So the process for a statistical downscaling is
as follows:
• to establish a statistical model which is able
to link large-scale climate variables
(predictors) with regional/local variables
(predictands);
• to feed the large-scale output of a GCM to
the statistical model;
• to estimate the corresponding regional/local
climate characteristics.
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Pros and Cons
Advantages of a statistical downscaling:
• the techniques used for building and applying
the statistical model are usually quite
inexpensive from the computer-time point of
view;
• they can be used to provide site-specific
information, which can be critical for many
climate change impact studies.
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Pros and Cons
A major theoretical weakness:
• we are not able to verify the basic
assumption that underlies these models;
• that is to say, we cannot be sure that the
statistical relationships developed for the
present-day climate also hold under the
different forcing conditions of possible
future climates (“stationarity” assumption);
• however, this is a limitation that affects also
physical parameterizations of GCMs.
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Be aware...
• Predictors relevant to a regional/local
predictand should be adequately reproduced
by the GCM to be downloaded (e.g., remind
NAO as an important element to determine
European climate);
• therefore, predictors have to be chosen on
the balance of their relevance to the target
predictand and their accurate
representation by climate models.
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NNs in downscaling
• Among the regression models, NNs appear
particular for their characteristic feature
of achieving nonlinear relationships between
predictors and predictands.
• This feature is obviously important in the
nonlinear climate system and it becomes
increasingly crucial when dealing with
regional/local variables (predictands) which
are heterogeneous and discontinuous in space
and time, such as daily precipitation.
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A simple example
• I would like to present just a simple example
of application (by Trigo & Palutikof, 1999).
• Reconstruction on the past and future
scenarios for minimum and maximum daily
temperatures in Coimbra (Portugal).
• Feed-forward networks with one hidden
layer and backpropagation training.
• Training and validation on the past; test on
future scenarios.
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A simple example
6 variables + values of the same
variables for the previous day +
sin and cos (Julian day)
Predictor
24 h mean (nearest grid point)
24 h north-south gradient
24 h east-west gradient
24 h geostrophic vorticity
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500hPa
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SLP
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A simple example
Validation
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A simple example
Future scenarios
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Recent advances
• Recently, a particular attention has been
devoted to the combination of dynamical and
moisture variables as predictors;
• furthermore, some researchers stressed the
importance of a cross-validation of the
downscaling model from observational data
for periods that represent independent or
different climate regimes (thus somewhat
validating the “stationarity” assumption).
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Recent advances
• Recently, NNs used for downscaling were
extended to SOM (Kohonen networks);
• inter-comparisons of NNs and other methods
for a statistical downscaling show that neural
network modelling is one of the best
methods to do so (see more in Pasini (2008)).
• At present, in general the scores of methods
of statistical downscaling are comparable
with those coming from dynamical
downscaling (RCMs).
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Conclusions and prospects
• Modelling the dynamics of the climate
system is a difficult task.
• In this framework, neural network modelling
begins to help in grasping this complexity,
both as an alternative strategy to dynamical
modelling, and as a complementary technique
that may be used together with GCMs.
• Climate change studies represent a field in
which NNs (and, more generally, AI
techniques) can be applied successfully.
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Essential references
• Climate modelling: A.
Pasini (2005), From
Observations to
Simulations: a
conceptual introduction
to weather and climate
modelling, World
Scientific,
www.worldscibooks.com
/environsci/5930.html
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Essential references
• Assessment on the past: A. Pasini, M. Lorè, F.
Ameli (2006), Ecological Modelling 191, 5867.
• Predictability: A. Pasini (2007), Predictability
in past and future climate conditions: a
preliminary analysis by neural networks using
unforced and forced Lorenz systems as toy
models, in Proceedings of the 87th AMS
annual meeting (5th AI Conference), San
Antonio, AMS, CD-ROM.
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Essential references
• NN downscaling: R.L. Wilby et al. (2004),
Guidelines for use of climate scenarios
developed from statistical downscaling
methods. IPCC Task Group TGICA,
http://ipccddc.cru.uea.ac.uk/guidelines/StatDown_Guide
.pdf (and references therein).
• R.M. Trigo & J.P. Palutikof (1999), Climate
Research 13, 45-59.
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Essential references
• All these topics are now
reviewed in A. Pasini
(2008), Neural network
modeling in climate
change studies, in
Artificial Intelligence
Methods in the
Environmental Sciences
(S.E. Haupt, A. Pasini and
C. Marzban eds.),
Springer (in press).
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For Italian readers...
[email protected]
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