Climate Networks around the Globe are Significantly Effected by El Nino

Abstract

The temperatures in different zones in the world do not show significant changes due to El-Nino except when measured in a restricted area in the Pacific Ocean. We find, in contrast, that the dynamics of a climate network based on the same temperature records in various geographical zones in the world is significantly influenced by El-Nino. During El-Nino many links of the network are broken, and the number of surviving links comprises a specific and sensitive measure for El-Nino events. While during non El-Nino periods these links which represent correlations between temperatures in different sites are more stable, fast fluctuations of the correlations observed during El-Nino periods cause the links to break.

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Climate Networks around the Globe are Significantly Effected by
El Ni˜ no
K. Yamasaki,1A. Gozolchiani,2and S. Havlin2
1Tokyo University of Information Sciences, Chiba, Japan∗
2Minerva Center and Department of Physics,
Bar Ilan University, Ramat Gan, Israel.
(Dated: April 10, 2008)
Abstract
The temperatures in different zones in the world do not show significant changes due to El-
Ni˜ no except when measured in a restricted area in the Pacific Ocean. We find, in contrast, that
the dynamics of a climate network based on the same temperature records in various geographical
zones in the world is significantly influenced by El-Ni˜ no. During El-Ni˜ no many links of the network
are broken, and the number of surviving links comprises a specific and sensitive measure for El-
Ni˜ no events. While during non El-Ni˜ no periods these links which represent correlations between
temperatures in different sites are more stable, fast fluctuations of the correlations observed during
El-Ni˜ no periods cause the links to break.
∗Electronic address: yamasaki@rsch.tuis.ac.jp
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arXiv:0804.1374v1 [physics.ao-ph] 8 Apr 2008

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Networks are often used to formulate the dynamics of complex systems that are built
from many interacting components (see e.g. [1, 2]). While in some cases the representation
of the system as a network is obvious and the nodes and links are identified directly (e.g.
cables connecting computers in a computer network) [3], there are cases in which the process
that couples the individual interacting components is more complex and a link is guessed
by tracking similarities in the dynamical behavior of two nodes [4].
Even when the usual traces of dynamics of interacting nodes on a network, such as
partial synchronization, clusters with correlated dynamics, oscillatory synchronization [5],
and phase slips [6], are evident, the mission of designing a generic tool that reliably extracts
information about the network structure from measurements of the dynamics of nodes is
still far from being accomplished.
In this Letter we develop a method for generating climate networks, which is suitable
for tracking structural changes in these networks (dynamics of a network). These changes
correspond, in our case, to strong climate changes due to El-Ni˜ no. We find that networks
constructed from temperature measurements on different sites in the world are changed
dramatically during El-Ni˜ no events in a similar way. These structural changes are seen even
for geographical zones where the mean temperature is not affected by El-Ni˜ no.
We analyze daily temperature records taken from a grid (available at [7]) in various
geographical zones (shown in Fig. 1). To avoid the trivial effect of seasonal trends we subtract
from each day’s temperature, the yearly mean temperature of that day. Specifically, if we
take the temperature signal of a given site in the grid to be?Ty(d), where y is the year and d
is the day (ranging from 1 to 365), the new filtered signal will be Ty(d) =?Ty(d)−1
(where N is the number of years available in the record) [8].
N
?
y?Ty(d)
We compute for a time shift τ ∈ [−τmax,τmax] days for each pair of sites l and r on the grid,
their cross correlation function Xy
l,r(τ > 0) ≡ ?Ty
l(d)Ty
r(d + τ)?dand Xy
l,r= MAX(Xy
l,r(τ ≤ 0) ≡ Xy
l,r)/STD(Xy
r,l(τ >
0). The correlation strength of the link is chosen to be Wy
l,r),
where MAX and STD are the maximal value and the standard deviation of the absolute
value of Xy
l,rin the range of τ, respectively [9]. The time shift at which Xy
l,ris maximal
is defined as the time delay. Up to here, the prescription is similar to other methods (see
e.g. [10] ).
From reasons that will become clear later, we are able to set a physical threshold Q so that
only pairs l,r that satisfy Wy
l,r> Q, are regarded as significantly linked. Mathematically
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this can be represented by the Heaviside function Θ(x) as follows,
ρy
l,r= Θ(Wy
l,r− Q). (1)
Some of the elements of the matrix ρ may blink as a function of y, i.e., appear and
disappear. Thus, even though there are many pairs l,r that their correlation values Wy
l,rin
a specific year are above Q, some of these Wy
l,rare sensitive to the choice of the beginning of
the period y, and to noise . In the present work we choose to discard the question of which
pairs comprise the static network, and concentrate in the structural changes of the network
over time. Blinking links seem to be a signature of structural changes, so we distinguish
between them and the more robust links, that are stable during larger time periods.
In the next step we examine if a currently existing link ρy
l,rexisted in the earlier periods of
the network. To accomplish this we define a new matrix, which takes into account previous
states of the links in the last k states of the network. We define a new matrix My
l,rwhich
counts the number of times a link appeared before continuously (without a blink):
My
l,r=
y−1
?
n=0
y
?
m=y−n
ρm
l,r.(2)
A link (l,r) in the current network ρ appeared k times in a row before (including its
current appearance) iff My
l,r≥ k.These links represent long lasting relations between
temperature fluctuations in the zone. Counting them enables us to distinguish between the
two qualitatively different groups of links, blinking links which are removed, and robust links
which we include in the network. The number of links that exist in our network depends on
y,
nk(y) =
N
?
l=0
N
?
r=l+1
Θ
?
My
l,r− k + 1
?
. (3)
Where k is the number of times a link has to survive in order to be included in the network
(according to Eq. (2)), and N is the total number of links in the geographical zones. The
summand in the rhs of Eq. (3) represents the network matrix. In the current work we chose
the y resolution (the jumps between two subsequent dates represented by y) to be 50 days,
k = 5 and the threshold Q = 2.
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FIG. 1: The four geographical zones used for building the four climate networks studied. The dots
represent the nodes of the network. The rectangular geographical zone inside zone 1 shows the
standard basin for which El-Ni˜ no effects on temperature and pressure is significantly observed (see
Fig. 2a)
The results shown below are not sensitive to the choice of k. However, choosing too
large k values reduces the number of surviving links significantly, and therefore eliminates
much of the effect. Choosing too small values of k, on the other hand, does not enable the
elimination of blinking links, and therefore causes nk(y) to be more noisy, but the significant
effect of breaking links is still evident.
We chose four representative zones around the globe, as shown in Fig. 1. Our networks
are built from measurements of temperatures close to sea level (networks Aj), and from
measurements on a 500mb pressure level (networks Bj), on a grid of 7.5oresolution. The
measurements are taken for the years 1979-2006, for which 8 known El-Ni˜ no events have
occurred .
In Fig. 2a we show the effect of El-Ni˜ no as 8 main extreme values on the two standard El-
Ni˜ no indices (based on temperature and pressure measurements), measured in the standard
basin region inside zone 1 of Fig. 1 [13]. In the top of each of the eight panels in Fig. 2b,c we
show the mean temperature anomaly over the whole corresponding zone defined in Fig. 1.
It is clearly seen that compared to Fig. 2a the El-Ni˜ no effect on mean temperature in all
zones becomes very weak and almost cannot be detected except at zones A1and B1(which
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FIG. 2: (a) Mean sea surface temperature (left) in the standard basin shown in the rectangle inside
A1in Fig. 1 (NINO3), and the difference in sea level pressure (right) between Tahiti and Darwin
(SOI), both are standard indices for El-Ni˜ no (see e.g. [11]). (b) and (c) (color online) The upper
curves represent the temperature anomaly series in zones (b) A1,A2,A3,A4and (c) B1,B2,B3,B4.
The lower curves present nk(y), namely, the number of links that survives in the network as a
function of time, for these same zones. In zone B4, the graph for nk(y) is completely flat, when
Q = 2. For this zone we show the cases of Q = 2.4 (middle curve) and Q = 2.5 (lower curve) [12]
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