Climate as complex networks
The field of complex networks has emerged as an important area of science to generate novel insights into nature of complex systems  The application of network theory to climate science is a young and emerging field   . To identify and analyze patterns in global climate, scientists model climate data as Complex Networks.
Unlike most real-world networks where nodes and edges are well defined. In nodes in climate networks, nodes are identified as the site in a spatial grid of underlying global climate data set, which can be represented at various resolutions. Two nodes are connected by an edge depending on the degree of statistical similarity (that may be related to dependence) between the corresponding pairs of time-series taken from climate records.  . The climate network approach enables novel insights into the dynamics of the climate system over different spatial and temporal scales  .
Construction of climate networks
Depending upon the choice of nodes and/or edges, climate networks may take many different forms, shapes, sizes and complexities. Tsonis et al. introduced the field of complex networks to climate. In their model, the nodes for the network were constituted by a single variable (500 hPa) from NCEP/NCAR Reanalysis datasets. In order to estimate the edges between nodes, correlation coefficient at zero time lag between all possible pairs of nodes were estimated. A pair of nodes was considered to be connected, if their correlation coefficient is above a threshold of 0.5.
The team of Havlin introduced the weighted links method which considers (i) the time delay of the link, (ii) the maximum of the cross-correlation at the time delay and (iii) the level of noise in the cross-correlation function.     
Steinhaeuser and team introduced the novel technique of multivariate networks in climate by constructing networks from several climate variables separately and capture their interaction in multivariate predictive model. It was demonstrated in their studies that in context of climate, extracting predictors based on cluster attributes yield informative precursors to improve predictive skills.
Imme et al. introduced a new type of network construction in climate based on temporal probabilistic graphical model, which provides an alternative viewpoint by focusing on information flow within network over time. 
Applications of climate networks
Climate networks enable insights into the dynamics of climate system over many spatial scales. The local degree centrality and related measures have been used to identify super-nodes and to associate them to known dynamical interrelations in the atmosphere, called teleconnection patterns. It was observed that climate networks possess “small world” properties owing to the long-range spatial connections.
The temperatures in different zones in the world do not show significant changes due to El Niño except when measured in a restricted area in the Pacific Ocean. Yamasaki et al. found, 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 Niño. During El Niño many links of the network are broken, and the number of surviving links comprises a specific and sensitive measure for El Niño events. While during non-El Niño periods these links which represent correlations between temperatures in different sites are more stable, fast fluctuations of the correlations observed during El Niño periods cause the links to break.
Moreover, Gozolchiani et al. presented the structure and evolution of the climate network in different geographical zones and find that the network responds in a unique way to El Niño events.They found that when El Niño events begin, the El Niño basin loses its influence on its surroundings almost all dependence on its surroundings and becomes autonomous. The formation of an autonomous basin is the missing link to understand the seemingly contradicting phenomena of the afore-noticed weakening of the interdependencies in the climate network during El Niño and the known impact of the anomalies inside the El Niño basin on the global climate system.
Steinhaeuser et al. applied complex networks to explore the multivariate and multi-scale dependence in climate data. Findings of the group suggested a close similarity of observed dependence patterns in multiple variables over multiple time and spatial scales. 
Tsonis and Roeber investigated the coupling architecture of the climate network. it was found that the overall network emerges from intertwined subnetworks. One subnetwork is operating at higher altitudes and other is operating in the tropics, while the equatorial subnetwork acts as an agent linking the 2 hemispheres . Though, both networks possess Small World Property, the 2 subnetworks are significantly different from each other in terms of network properties like degree distribution.
Donges et al. applied climate networks for physics and nonlinear dynamical interpretations in climate. The team used measure of node centrality, betweenness centrality (BC) to demonstrate the wave-like structures in the BC fields of climate networks constructed from monthly averaged reanalysis and atmosphere-ocean coupled general circulation model (AOGCM) surface air temperature (SAT) data.
The pattern of the local daily fluctuations of climate fields such as temperatures and geopotential heights is not stable and hard to predict. Surprisingly, Berezin et al. found that the observed relations between such fluctuations in different geographical regions yields a very robust network pattern that remains highly stable during time. 
Ludescher et al. found evidence that a large-scale cooperative mode—linking the El Niño basin (equatorial Pacific corridor) and the rest of the ocean—builds up in about the calendar year before the warming event. On this basis, they developed an efficient 12-month forecasting scheme for El Niño events. 
The connectivity pattern of networks based on ground level temperature records shows a dense stripe of links in the extra tropics of the southern hemisphere. Wang et al  . showed that statistical categorization of these links yields a clear association with the pattern of the atmospheric Rossby waves, one of the major mechanisms associated with the weather system and with planetary scale energy transport. It is shown that alternating densities of negative and positive links are arranged in half Rossby wave distances around 3500, 7000, and 10 000 km and are aligned with the expected direction of energy flow, distribution of time delays, and the seasonality of these waves. In addition, long distance links that are associated with Rossby waves are the most dominant links in the climate network.
Different definitions of links in climate networks may lead to considerably different network topologies. Utilizing detrended fluctuation analysis, shuffled surrogates, and separation analysis of maritime and continental records, Guez et al. found that one of the major influences on the structure of climate networks is the existence of strong autocorrelations in the records, which may introduce spurious links. This explains why different methods could lead to different climate network topologies.
Teleconnections play an important role in climate dynamics. A climate network method was developed to identify the direct paths on the globe of teleconnections.
Computational issues and challenges
There are numerous computational challenges that arise at various stages of the network construction and analysis process in field of climate networks:
- Calculating the pair-wise correlations between all grid points is a non-trivial task.
- Computational demands of network construction, which depends upon the resolution of spatial grid.
- Generation of predictive models from the data poses additional challenges.
- Inclusion of lag and lead effects over space and time is a non-trivial task.
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