Neural network modelling and classification of lithofacies ...
Approaches to climate change study and neural network modelling
description
Transcript of Approaches to climate change study and neural network modelling
Summer School on Climate Change
UniKore, 6-10 September 2008 1
Approaches to climate change study and neural network
modelling
Antonello PasiniCNR - Institute of Atmospheric Pollution
Rome, Italy
Summer School on Climate Change
UniKore, 6-10 September 2008 2
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 3
Climate scientists as grown-up babies
If you give a child a toy, he will eventually open it up.
Let’s open it up!
Summer School on Climate Change
UniKore, 6-10 September 2008 4
Climate scientists as grown-up babies
Let’s understand how it works...
… and let’s reassemble it!
Summer School on Climate Change
UniKore, 6-10 September 2008 5
Decomposing the system
Summer School on Climate Change
UniKore, 6-10 September 2008 6
Theoretical knowledgeWe possess theoretical knowledge of single sub-systems from experiments in “real laboratories” (e.g., laws from fluid-dynamics and thermodynamics of oceans and atmosphere).
In order to recompose the complexity of the system, we need a “virtual laboratory”...
Summer School on Climate Change
UniKore, 6-10 September 2008 7
Recomposing in a model
Summer School on Climate Change
UniKore, 6-10 September 2008 8
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 9
From dynamical modelling...
Summer School on Climate Change
UniKore, 6-10 September 2008 10
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 parameter-ization 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.
Summer School on Climate Change
UniKore, 6-10 September 2008 11
… 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!
Summer School on Climate Change
UniKore, 6-10 September 2008 12
A biological “inspiration”
… to a different strategy
Summer School on Climate Change
UniKore, 6-10 September 2008 13
Natural inputs
Anthropogenic inputs
Climatic behaviour
… to a different strategy
Summer School on Climate Change
UniKore, 6-10 September 2008 14
hl
j
jj
n
hhg
exp1
1
0
0.2
0.4
0.6
0.8
1
-10 -8 -6 -4 -2 0 2 4 6 8 10
weighted sum
sigm
oid
outp
ut n=3
n=8
n=20
n=50
A neural network model
Summer School on Climate Change
UniKore, 6-10 September 2008 15
i
ii OTE2
2
1
j kkjkjijii IwgWgO
A neural network model
Summer School on Climate Change
UniKore, 6-10 September 2008 16
1=
11
tWtWmVOThgtW
tWtWmtW
EtWtW
ijijjiiiiij
ijijij
ijij
A neural network model
Summer School on Climate Change
UniKore, 6-10 September 2008 17
1
11
twtwmIOThgWhg +tw
twtwmtw
Etwtw
jkjkki
iiiiijjjjk
jkjkjk
jkjk
A neural network model
Summer School on Climate Change
UniKore, 6-10 September 2008 18
A neural network model
• Tool for short historical time series of data (“all-frame” or “leave-one-out” procedure);
• early stopping method.
Summer School on Climate Change
UniKore, 6-10 September 2008 19
Assessment on the past
Global case study;
regional case study.
Summer School on Climate Change
UniKore, 6-10 September 2008 20
Global case studyInput 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 inter-annual temperature variability.
Summer School on Climate Change
UniKore, 6-10 September 2008 21
Global case study4 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).
Summer School on Climate Change
UniKore, 6-10 September 2008 22
Global case studyNatural forcings
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1860 1880 1900 1920 1940 1960 1980 2000
Years
Te
mp
era
ture
an
om
ali
es
[°C
]
Anthropogenic forcings
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1860 1880 1900 1920 1940 1960 1980 2000
Years
Te
mp
era
ture
an
om
ali
es
[°C
]
Summer School on Climate Change
UniKore, 6-10 September 2008 23
Global case studyNatural + anthropogenic forcings
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1860 1880 1900 1920 1940 1960 1980 2000
Years
Te
mp
era
ture
an
om
ali
es
[°C
]
Natural + anthropogenic forcings + ENSO
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1860 1880 1900 1920 1940 1960 1980 2000
Years
Te
mp
era
ture
an
om
ali
es
[°C
]
Summer School on Climate Change
UniKore, 6-10 September 2008 24
Remarks• Anthropogenic forcings appear as a main
probable cause of the changes in T;• the input related to ENSO acts as a 2nd-
order 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
Summer School on Climate Change
UniKore, 6-10 September 2008 25
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).
Summer School on Climate Change
UniKore, 6-10 September 2008 26
The residualsNo 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.
Summer School on Climate Change
UniKore, 6-10 September 2008 27
The residualsThe auto-correlation function is almost completely confined inside the white noise limits;
some oscillations are visible but more uncoupled than in previous results.
Summer School on Climate Change
UniKore, 6-10 September 2008 28
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 29
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 30
Regional case studyWe 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.
Summer School on Climate Change
UniKore, 6-10 September 2008 31
Regional case study NAO - NAO +
Summer School on Climate Change
UniKore, 6-10 September 2008 32
Regional case study (CET)
3 case studies and input data:a) global (natural + anthropogenic) forcings;b) NAO only;c) global forcings + NAO.
CET series in extended winters
1
2
3
4
5
6
7
1860 1880 1900 1920 1940 1960 1980 2000
Years
Te
mp
era
ture
[°C
]
Summer School on Climate Change
UniKore, 6-10 September 2008 33
Regional case study (CET)
Case Bias [°C] MAE [°C](a) -0.002 0.995(b) 0.117 0.601(c) -0.037 0.651
(a)
-4
-3
-2
-1
0
1
2
3
4
5
1860 1880 1900 1920 1940 1960 1980 2000
Years
Re
sid
ua
ls [
°C]
(b)
-4
-3
-2
-1
0
1
2
3
4
5
1860 1880 1900 1920 1940 1960 1980 2000
Years
Re
sid
ua
ls [
°C]
(c)
-4
-3
-2
-1
0
1
2
3
4
5
1860 1880 1900 1920 1940 1960 1980 2000
Years
Re
sid
ua
ls [
°C]
Summer School on Climate Change
UniKore, 6-10 September 2008 34
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 inter-annual variability of climate at regional scale.
Summer School on Climate Change
UniKore, 6-10 September 2008 35
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 36
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 37
DiscussionWe 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.
Summer School on Climate Change
UniKore, 6-10 September 2008 38
Impact studies (animals)
How rainfall, snow cover and temperature affect them?
Summer School on Climate Change
UniKore, 6-10 September 2008 39
From Pasini et al. (submitted)
Bivariate linear and nonlinear analyses (meteo-climatic forcings vs. rodent density)
Impact studies (animals)
Summer School on Climate Change
UniKore, 6-10 September 2008 40
From Pasini et al. (submitted)
Neural reconstruction of rodent density in the Apennines starting from data of meteo-climatic forcings
Impact studies (animals)
Summer School on Climate Change
UniKore, 6-10 September 2008 41
From Pasini et al. (submitted)
Neural “backcast” of rodent density in the Apennines starting from data of meteo-climatic forcings
Impact studies (animals)
Summer School on Climate Change
UniKore, 6-10 September 2008 42
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 43
Preliminary considerations
Deterministic
Ensemble
0
5
10
15
20
25
TIME (12 - hours interval)
10m
WIN
D S
PE
ED
(K
TS
)
Summer School on Climate Change
UniKore, 6-10 September 2008 44
Preliminary considerationsIs 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).
Summer School on Climate Change
UniKore, 6-10 September 2008 45
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 46
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 47
The forced Lorenz system
dx/dt = (y-x) + f0 cos dy/dt = rx - y - xz + f0 sin
dz/dt = xy - bz
Toy simulation of an increase of anthropogenic forcings in the climate system
Our choice of the parameters:f0 = 2.5 5, = /2 still chaotic solutions.
Summer School on Climate Change
UniKore, 6-10 September 2008 48
The Lorenz system
Summer School on Climate Change
UniKore, 6-10 September 2008 49
Unforced vs. forced
Summer School on Climate Change
UniKore, 6-10 September 2008 50
Predictability (dynamics)
Summer School on Climate Change
UniKore, 6-10 September 2008 51
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 52
Predictability (dynamics)
n = 8
Blue: g < 0
Green: 0 g < 0.04
Yellow: 0.04 g < 0.064
Red: g 0.064
Summer School on Climate Change
UniKore, 6-10 September 2008 53
Predictability (dynamics)
Unforced Forced
Summer School on Climate Change
UniKore, 6-10 September 2008 54
Predictability (dynamics)
Summer School on Climate Change
UniKore, 6-10 September 2008 55
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 56
Predictability studies by NNsHere, 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%);
Summer School on Climate Change
UniKore, 6-10 September 2008 57
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 58
Predictability studies by NNs
Distributions of distance errors for each class
Blue class
0
2
4
6
8
10
12
14
16
18
20
1 5 9 13 17 21 25 29 33 37 41 45
NN forecast error (distance)
Fre
qu
ency
(%
)
Yellow class
0
2
4
6
8
10
12
14
16
18
20
1 5 9 13 17 21 25 29 33 37 41 45
NN forecast error (distance)
Fre
qu
ency
(%
)
Summer School on Climate Change
UniKore, 6-10 September 2008 59
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?
Summer School on Climate Change
UniKore, 6-10 September 2008 60
Predictability studies by NNsSome 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).
Summer School on Climate Change
UniKore, 6-10 September 2008 61
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.
Predictability studies by NNs
Summer School on Climate Change
UniKore, 6-10 September 2008 62
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.
Predictability studies by NNs
Related to the forecast of g
Summer School on Climate Change
UniKore, 6-10 September 2008 63
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).
Summer School on Climate Change
UniKore, 6-10 September 2008 64
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 65
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).
Summer School on Climate Change
UniKore, 6-10 September 2008 66
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!
Summer School on Climate Change
UniKore, 6-10 September 2008 67
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 68
The rationale
Summer School on Climate Change
UniKore, 6-10 September 2008 69
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).
Summer School on Climate Change
UniKore, 6-10 September 2008 70
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).
Summer School on Climate Change
UniKore, 6-10 September 2008 71
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 72
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 73
Pros and ConsA 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.
Summer School on Climate Change
UniKore, 6-10 September 2008 74
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 75
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 76
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 77
A simple example
Predictor 500hPa SLP24 h mean (nearest grid point) *24 h north-south gradient * *24 h east-west gradient * *24 h geostrophic vorticity *
6 variables + values of the same variables for the
previous day + sin and cos (Julian day)
Summer School on Climate Change
UniKore, 6-10 September 2008 78
A simple exampleValidation
Summer School on Climate Change
UniKore, 6-10 September 2008 79
A simple exampleFuture scenarios
Summer School on Climate Change
UniKore, 6-10 September 2008 80
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).
Summer School on Climate Change
UniKore, 6-10 September 2008 81
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).
Summer School on Climate Change
UniKore, 6-10 September 2008 82
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.
Summer School on Climate Change
UniKore, 6-10 September 2008 83
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
Summer School on Climate Change
UniKore, 6-10 September 2008 84
Essential references
• Assessment on the past: A. Pasini, M. Lorè, F. Ameli (2006), Ecological Modelling 191, 58-67.
• 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.
Summer School on Climate Change
UniKore, 6-10 September 2008 85
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://ipcc-ddc.cru.uea.ac.uk/guidelines/StatDown_Guide.pdf (and references therein).
• R.M. Trigo & J.P. Palutikof (1999), Climate Research 13, 45-59.
Summer School on Climate Change
UniKore, 6-10 September 2008 86
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).
Summer School on Climate Change
UniKore, 6-10 September 2008 87
For Italian readers...