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Climate network papers

Here I'll mention some papers I want to understand before December 1st. If you'd like to help me, you can read them and comment on them. I can email you copies if you want.

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edited November 2014

This paper pointed out by Nathan Urban is freely available, as are all papers where I create a link on the paper title instead of the journal name.

Abstract. Complex network theory has been successfully applied to understand the structural and functional topology of many dynamical systems from nature, society and technology. Many properties of these systems change over time, and, consequently, networks reconstructed from them will, too. However, although static and temporally changing networks have been studied extensively, methods to quantify their robustness as they evolve in time are lacking. In this paper we develop a theory to investigate how networks are changing within time based on the quantitative analysis of dissimilarities in the network structure.

Our main result is the common component evolution function (CCEF) which characterizes network development over time. To test our approach we apply it to several model systems, Erdős–Rényi networks, analytically derived flow-based networks, and transient simulations from the START model for which we control the change of single parameters over time. Then we construct annual climate networks from NCEP/NCAR reanalysis data for the Asian monsoon domain for the time period of 1970–2011 CE and use the CCEF to characterize the temporal evolution in this region. While this real-world CCEF displays a high degree of network persistence over large time lags, there are distinct time periods when common links break down. This phasing of these events coincides with years of strong El Niño/Southern Oscillation phenomena, confirming previous studies. The proposed method can be applied for any type of evolving network where the link but not the node set is changing, and may be particularly useful to characterize nonstationary evolving systems using complex networks.

Note the idea that the El Niño breaks links elsewhere in the world. We've seen another paper espousing this idea. It's different than the idea that we can predict an El Niño by increased link strength in the Pacific, but not in contradiction.

They have a useful literature review:

Complex network techniques, based on statistical associations between climate parameter time series at different points on Earth, have yielded new insights in the investigation of climate dynamics (Tsonis and Swanson, 2008; Donges et al., 2009; Paluš et al., 2011). Such climate networks have been used for detecting long-range correlations, or teleconnections (Martin et al., 2013; Barreiro et al., 2011), and studying such phenomena such as the El Niño/Southern Oscillation (ENSO, Gozolchiani et al., 2008; Deza et al., 2013) and the IndianMonsoon system (Rehfeld et al., 2013; Malik et al., 2011; Stolbova et al., 2014). In particular, Tsonis and Swanson (2008) found changes in the global network topology during El Niño events, with significantly fewer links and lower clustering coefficients, and inferred a lower predictability for El Niño over La Niña years. Using climate networks, Yamasaki et al. (2008) and Gozolchiani et al. (2008) also found ENSO influence on regional atmospheric processes in non-ENSO regions. Temporal and spatial variability of climate, and thus climate network structure, are of increasing interest considering ongoing environmental changes, and climate networks as evolving in time are still an open subject. The spatial-temporal developments in a given network set can be too complex to be captured by eye, and systematic approaches to quantify changes are needed. While Berezin et al. (2012) investigated the origins of the climate network stability such as the spatial embedding and physical coupling between climate in different locations using the correlation between correlation matrices, other studies describe how the network graph is changing over time to understand the behaviour of the underlying dynamical system (e.g. Rehfeld et al., 2013).

Comment Source:This paper pointed out by [[Nathan Urban]] is freely available, as are all papers where I create a link on the paper title instead of the journal name. * L. Tupikina, K. Rehfeld, N. Molkenthin, V. Stolbova, N. Marwan, and J. Kurths, [Characterizing the evolution of climate networks](http://www.nonlin-processes-geophys.net/21/705/2014/npg-21-705-2014.html), _Nonlin. Processes Geophys._ **21** (2014), 705-711. > **Abstract.** Complex network theory has been successfully applied to understand the structural and functional topology of many dynamical systems from nature, society and technology. Many properties of these systems change over time, and, consequently, networks reconstructed from them will, too. However, although static and temporally changing networks have been studied extensively, methods to quantify their robustness as they evolve in time are lacking. In this paper we develop a theory to investigate how networks are changing within time based on the quantitative analysis of dissimilarities in the network structure. > Our main result is the common component evolution function (CCEF) which characterizes network development over time. To test our approach we apply it to several model systems, Erdős–Rényi networks, analytically derived flow-based networks, and transient simulations from the START model for which we control the change of single parameters over time. Then we construct annual climate networks from NCEP/NCAR reanalysis data for the Asian monsoon domain for the time period of 1970–2011 CE and use the CCEF to characterize the temporal evolution in this region. While this real-world CCEF displays a high degree of network persistence over large time lags, there are distinct time periods when common links break down. This phasing of these events coincides with years of strong El Niño/Southern Oscillation phenomena, confirming previous studies. The proposed method can be applied for any type of evolving network where the link but not the node set is changing, and may be particularly useful to characterize nonstationary evolving systems using complex networks. Note the idea that the El Niño breaks links elsewhere in the world. We've seen another paper espousing this idea. It's different than the idea that we can _predict_ an El Niño by _increased_ link strength in the Pacific, but not in contradiction. They have a useful literature review: > Complex network techniques, based on statistical associations between climate parameter time series at different points on Earth, have yielded new insights in the investigation of climate dynamics (Tsonis and Swanson, 2008; Donges et al., 2009; Paluš et al., 2011). Such climate networks have been used for detecting long-range correlations, or teleconnections (Martin et al., 2013; Barreiro et al., 2011), and studying such phenomena such as the El Niño/Southern Oscillation (ENSO, Gozolchiani et al., 2008; Deza et al., 2013) and the IndianMonsoon system (Rehfeld et al., 2013; Malik et al., 2011; Stolbova et al., 2014). In particular, Tsonis and Swanson (2008) found changes in the global network topology during El Niño events, with significantly fewer links and lower clustering coefficients, and inferred a lower predictability for El Niño over La Niña years. Using climate networks, Yamasaki et al. (2008) and Gozolchiani et al. (2008) also found ENSO influence on regional atmospheric processes in non-ENSO regions. Temporal and spatial variability of climate, and thus climate network structure, are of increasing interest considering ongoing environmental changes, and climate networks as evolving in time are still an open subject. The spatial-temporal developments in a given network set can be too complex to be captured by eye, and systematic approaches to quantify changes are needed. While Berezin et al. (2012) investigated the origins of the climate network stability such as the spatial embedding and physical coupling between climate in different locations using the correlation between correlation matrices, other studies describe how the network graph is changing over time to understand the behaviour of the underlying dynamical system (e.g. Rehfeld et al., 2013).
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edited November 2014

Let me look at those "new insights" papers mentioned above. Here's the first:

Abstract. We construct the networks of the surface temperature field for El Niño and for La Niña years and investigate their structure. We find that the El Niño network possesses significantly fewer links and lower clustering coefficient and characteristic path length than the La Niña network, which indicates that the former network is less communicative and less stable than the latter. We conjecture that because of this, predictability of temperature should decrease during El Niño years. Here we verify that indeed during El Niño years predictability is lower compared to La Niña years

Comment Source:Let me look at those "new insights" papers mentioned above. Here's the first: * A. Tsonis and K. L. Swanson, [Topology and predictability of El Niño and La Niña networks](https://pantherfile.uwm.edu/aatsonis/www/publications/2008-06_Tsonis-AA_TopologyandPredictabilityofElNinoandLaNinaNetworks-2.pdf), _[Phys. Rev. Lett.](http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.228502)_ **100** (2008) 228502. > **Abstract.** We construct the networks of the surface temperature field for El Niño and for La Niña years and investigate their structure. We find that the El Niño network possesses significantly fewer links and lower clustering coefficient and characteristic path length than the La Niña network, which indicates that the former network is less communicative and less stable than the latter. We conjecture that because of this, predictability of temperature should decrease during El Niño years. Here we verify that indeed during El Niño years predictability is lower compared to La Niña years <img src = "http://math.ucr.edu/home/baez/ecological/el_nino/tsonis_swanson_topology_and_predictability_of_el_nino_and_la_nina_climate_networks.jpg" alt = ""/>
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edited November 2014
• J. Donges, Y. Zou, N. Marwan and J. Kurths, Complex networks in climate dynamics, European Physical Journal Special Topics 174 (2009), 157-179. A version of this is freely available on the arXiv.

This seems somewhat related to the following 149-page thesis:

Here are some small samples from the latter:

We have performed an extensive and detailed graph theoretical analysis of climate networks on the global topological scale focussing on the flow and centrality measure betweenness which is locally defined at each vertex, but includes global topological information by relying on the distribution of shortest paths between all pairs of vertices in the network. The betweenness centrality field reveals a rich internal structure in complex climate networks constructed from reanalysis and atmosphere-ocean coupled general circulation model (AOGCM) surface air temperature data. Our novel approach uncovers an elaborately woven meta-network of highly localized channels of strong dynamical information flow, that we relate to global surface ocean currents and dub the backbone of the climate network in analogy to the homonymous data highways of the internet. This finding points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long term mean (140 years for the model run and 60 years for reanalysis data). Carefully comparing the backbone structures detected in climate networks constructed using linear Pearson correlation and nonlinear mutual information, we argue that the high sensitivity of betweenness with respect to small changes in network structure may allow to detect the footprints of strongly nonlinear physical interactions in the climate system.

Pearson correlation is just what we usually call correlation around here: it detects linear correlations. Mutual information detects nonlinear correlations.

We give brief climatological interpretations of the network properties unveiled by our approach, since the main aim of this study is the comparison of linear and nonlinear climate network construction methods (Sect. 3.2). Super-nodes found in the AWC field (Fig. 3.5) over the tropics and locally the mid-latitudes, were shown to be related to major atmospheric teleconnection patterns (Tsonis et al. (2008b)). For example, the region of increased AWC in the North East Pacific is associated to the well-known Pacific North-American (PNA) pattern (Wallace and Gutzler (1981)). The El Niño cold tongue in the tropical East Pacific is clearly visible in the AWC field, as well as in all other fields considered (Fig. 3.6, 3.7 and 3.8).

AWC is "area weighted connectivity" is defined on page 15. It's similar to degree centrality, which is simply the degree of a vertex in a graph: the number of its nearest neighbors. Area weighted connectivity corrects for the fact that in a typical grid on the globe, grid rectangles near the poles are smaller than those near the equator.

The Pacific North-American pattern is discussed here, and there's data on it. Quoting:

The Pacific/ North American teleconnection pattern (PNA) is one of the most prominent modes of low-frequency variability in the Northern Hemisphere extratropics. The positive phase of the PNA pattern features above-average heights in the vicinity of Hawaii and over the intermountain region of North America, and below-average heights located south of the Aleutian Islands and over the southeastern United States. The PNA pattern is associated with strong fluctuations in the strength and location of the East Asian jet stream. The positive phase is associated with an enhanced East Asian jet stream and with an eastward shift in the jet exit region toward the western United States. The negative phase is associated with a westward retraction of that jet stream toward eastern Asia, blocking activity over the high latitudes of the North Pacific, and a strong split-flow configuration over the central North Pacific.

The positive phase of the PNA pattern is associated with above-average temperatures over western Canada and the extreme western United States, and below-average temperatures across the south-central and southeastern U.S. The PNA tends to have little impact on surface temperature variability over North America during summer. The associated precipitation anomalies include above-average totals in the Gulf of Alaska extending into the Pacific Northwestern United States, and below-average totals over the upper Midwestern United States.

Although the PNA pattern is a natural internal mode of climate variability, it is also strongly influenced by the El Niño/ Southern Oscillation (ENSO) phenomenon. The positive phase of the PNA pattern tends to be associated with Pacific warm episodes (El Niño), and the negative phase tends to be associated with Pacific cold episodes (La Niña).

Comment Source:* J. Donges, Y. Zou, N. Marwan and J. Kurths, Complex networks in climate dynamics, _European Physical Journal Special Topics_ **174** (2009), 157-179. A version of this is [freely available on the arXiv](http://arxiv.org/abs/0907.4359). This seems somewhat related to the following 149-page thesis: * J. Donges, _[Complex Networks in the Climate System](http://opus.kobv.de/ubp/volltexte/2011/4977/pdf/donges_diplom.pdf)_ Here are some small samples from the latter: > We have performed an extensive and detailed graph theoretical analysis of climate networks on the global topological scale focussing on the flow and centrality measure betweenness which is locally defined at each vertex, but includes global topological information by relying on the distribution of shortest paths between all pairs of vertices in the network. The betweenness centrality field reveals a rich internal structure in complex climate networks constructed from reanalysis and atmosphere-ocean coupled general circulation model (AOGCM) surface air temperature data. Our novel approach uncovers an elaborately woven meta-network of highly localized channels of strong dynamical information flow, that we relate to global surface ocean currents and dub the **backbone of the climate network** in analogy to the homonymous data highways of the internet. This finding points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long term mean (140 years for the model run and 60 years for reanalysis data). Carefully comparing the backbone structures detected in climate networks constructed using linear Pearson correlation and nonlinear mutual information, we argue that the high sensitivity of betweenness with respect to small changes in network structure may allow to detect the footprints of strongly nonlinear physical interactions in the climate system. [Pearson correlation](https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient#For_a_population) is just what we usually call correlation around here: it detects linear correlations. Mutual information detects nonlinear correlations. > We give brief climatological interpretations of the network properties unveiled by our approach, since the main aim of this study is the comparison of linear and nonlinear climate network construction methods (Sect. 3.2). Super-nodes found in the AWC field (Fig. 3.5) over the tropics and locally the mid-latitudes, were shown to be related to major atmospheric teleconnection patterns (Tsonis et al. (2008b)). For example, the region of increased AWC in the North East Pacific is associated to the well-known Pacific North-American (PNA) pattern (Wallace and Gutzler (1981)). The El Niño cold tongue in the tropical East Pacific is clearly visible in the AWC field, as well as in all other fields considered (Fig. 3.6, 3.7 and 3.8). AWC is "area weighted connectivity" is defined on page 15. It's similar to **degree centrality**, which is simply the degree of a vertex in a graph: the number of its nearest neighbors. Area weighted connectivity corrects for the fact that in a typical grid on the globe, grid rectangles near the poles are smaller than those near the equator. The Pacific North-American pattern is discussed [here](http://www.cpc.ncep.noaa.gov/data/teledoc/pna.shtml), and there's data on it. Quoting: > The Pacific/ North American teleconnection pattern (PNA) is one of the most prominent modes of low-frequency variability in the Northern Hemisphere extratropics. The positive phase of the PNA pattern features above-average heights in the vicinity of Hawaii and over the intermountain region of North America, and below-average heights located south of the Aleutian Islands and over the southeastern United States. The PNA pattern is associated with strong fluctuations in the strength and location of the East Asian jet stream. The positive phase is associated with an enhanced East Asian jet stream and with an eastward shift in the jet exit region toward the western United States. The negative phase is associated with a westward retraction of that jet stream toward eastern Asia, blocking activity over the high latitudes of the North Pacific, and a strong split-flow configuration over the central North Pacific. > The positive phase of the PNA pattern is associated with above-average temperatures over western Canada and the extreme western United States, and below-average temperatures across the south-central and southeastern U.S. The PNA tends to have little impact on surface temperature variability over North America during summer. The associated precipitation anomalies include above-average totals in the Gulf of Alaska extending into the Pacific Northwestern United States, and below-average totals over the upper Midwestern United States. > Although the PNA pattern is a natural internal mode of climate variability, it is also strongly influenced by the El Ni&ntilde;o/ Southern Oscillation (ENSO) phenomenon. The positive phase of the PNA pattern tends to be associated with Pacific warm episodes (El Ni&ntilde;o), and the negative phase tends to be associated with Pacific cold episodes (La Ni&ntilde;a).
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Here's the last of the "new insights" papers:

Abstract. The bias due to dynamical memory (serial correlations) in an association/dependence measure (absolute cross-correlation) is demonstrated in model data and identified in time series of meteorological variables used for construction of climate networks. Accounting for such bias in inferring links of the climate network markedly changes the network topology and allows to observe previously hidden phenomena in climate network evolution.

Comment Source:Here's the last of the "new insights" papers: * M. Paluš, D. Hartman, J. Hlinka and M. Vejmelka, [Discerning connectivity from dynamics in climate networks](http://www.nonlin-processes-geophys.net/18/751/2011/npg-18-751-2011.html), _Nonlin. Processes Geophys._ **18** (2011), 751–763. > **Abstract.** The bias due to dynamical memory (serial correlations) in an association/dependence measure (absolute cross-correlation) is demonstrated in model data and identified in time series of meteorological variables used for construction of climate networks. Accounting for such bias in inferring links of the climate network markedly changes the network topology and allows to observe previously hidden phenomena in climate network evolution.
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Thanks for the cut down reading lists from you and Paul. I'm afraid the PhysRevLett link to the Tsonis paper is paywalled. Sorry to refer the pain.

Comment Source:Thanks for the cut down reading lists from you and Paul. I'm afraid the PhysRevLett [link](http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.228502) to the Tsonis paper is paywalled. Sorry to refer the pain.
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I found the Tsonis paper on his website here.

Comment Source:I found the Tsonis paper on his website [here](https://pantherfile.uwm.edu/aatsonis/www/publications/2008-06_Tsonis-AA_TopologyandPredictabilityofElNinoandLaNinaNetworks-2.pdf).
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edited November 2014

I’m afraid the PhysRevLett link to the Tsonis paper is paywalled.

Yes, that's why I put the link on the journal name instead of the paper title! This is our official convention for links, which makes it easy for people to know ahead of time if the paper is free or not.

(I mention this not mainly to scold you, but to make sure the newbies learn the rules here. These are discussed in more detail on the wiki.)

But more importantly, thanks for finding a free version! I'll update my comment to include that!

Comment Source:> I’m afraid the PhysRevLett link to the Tsonis paper is paywalled. Yes, that's why I put the link on the journal name instead of the paper title! This is our official convention for links, which makes it easy for people to know ahead of time if the paper is free or not. (I mention this not mainly to scold you, but to make sure the newbies learn the rules here. These are discussed in more detail [on the wiki](http://www.azimuthproject.org/azimuth/show/How+to#referring_to_a_paper_in_a_journal).) But more importantly, _thanks for finding a free version!_ I'll update my comment to include that!
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Is it possible to get hold of:

J. Donges, Y. Zou, N. Marwan and J. Kurths, Complex networks in the climate system, Eur. Phys. J.-Spec. Top. 174 (2009), 157–179.

Also, thanks John for getting me to look at the right-hand column of the ResearchGate subscription page which I'd zoomed off-screen where I found a box saying that if you don't have an institutional email apply to have a personal email address recognised.

Comment Source:Is it possible to get hold of: > J. Donges, Y. Zou, N. Marwan and J. Kurths, Complex networks in the climate system, Eur. Phys. J.-Spec. Top. 174 (2009), 157–179. Also, thanks John for getting me to look at the right-hand column of the ResearchGate subscription page which I'd zoomed off-screen where I found a box saying that if you don't have an institutional email apply to have a personal email address recognised. I applied but didn't get an answer. I'll try their sysadmin.
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edited November 2014

Jim wrote:

Is it possible to get ahold of:

J. Donges, Y. Zou, N. Marwan and J. Kurths, Complex networks in the climate system, Eur. Phys. J.-Spec. Top. 174 (2009), 157–179.

Donges lists this paper on his webpage and says it's freely available on the arXiv. The paper on the arXiv has a somewhat longer title! However, it lists the paper as being published in the same pages of the same issue of the same journal. So, I think it's the same paper.

Again, I think Donges' thesis is good to read for a thorough introduction.

Comment Source:Jim wrote: > Is it possible to get ahold of: > > J. Donges, Y. Zou, N. Marwan and J. Kurths, Complex networks in the climate system, Eur. Phys. J.-Spec. Top. 174 (2009), 157–179. Donges lists this paper [on his webpage](https://www.pik-potsdam.de/members/donges/publications) and says it's [freely available on the arXiv](http://arxiv.org/abs/0907.4359). The paper on the arXiv has a somewhat longer title! However, it lists the paper as being published in the same pages of the same issue of the same journal. So, I think it's the same paper. Again, I think Donges' [thesis](http://opus.kobv.de/ubp/volltexte/2011/4977/pdf/donges_diplom.pdf) is good to read for a thorough introduction.
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edited November 2014

Thanks as always John. I managed to find the paper and his thesis on his webpage. I've decided to write some literate code and have got as far as a working toy implementions of degree centrality, AWC, Hamming distance etc. I have to mentality reconcile this with some common component evolution (Stills, Tishby ,Nemenman) code and the information bottleneck approach. I like the classification into Pearson correlation and mutual information climate networks. Perhaps, as is being discussed elsewhere for SOI and link strengths, the statistical and mutual information contribute independent information?

Comment Source:Thanks as always John. I managed to find the paper and his thesis on his webpage. I've decided to write some literate code and have got as far as a working toy implementions of degree centrality, AWC, Hamming distance etc. I have to mentality reconcile this with some common component evolution (Stills, Tishby ,Nemenman) code and the information bottleneck approach. I like the classification into Pearson correlation and mutual information climate networks. Perhaps, as is being discussed elsewhere for SOI and link strengths, the statistical and mutual information contribute independent information?