# Networks of climate change: Connecting causes and consequences

Petter Holme  Department of Computer Science, Aalto University, Espoo, Finland
Center for Computational Social Science, Kobe University, Kobe, Japan  Juan C.
Rocha  Stockholm Resilience Centre, Stockholm University, Sweden

###### Abstract

Understanding the causes and consequences of, and devising countermeasures to,
global warming is a profoundly complex problem. Network representations are
sometimes the only way forward, and sometimes able to reduce the complexity of
the original problem. Networks are both necessary and natural elements of
climate science. Furthermore, networks form a mathematical foundation for a
multitude of computational and analytical techniques. We are only beginning to
see the benefits of this connection between the sciences of climate change and
network science. In this review, we cover the wide spectrum of network
applications in the climate-change literature—what they represent, how they
are analyzed, and what insights they bring. We also discuss network data,
tools, and problems yet to be explored.

Figure 1: Overview of topics related to climate change that have been studied
by networks. Most topics in the science of climate change are causally
coupled. Still, in the discourse, some have more the flavor of causes, some
are more consequences. Figure 2: The causal structure of a climate model. The
network in panel A, adapted from Ref. [57], illustrates some components and
their interdependencies in a typical large-scale climate simulation model. In
panel B we show the same network as a directed graph where we keep the color
coding of the initial illustration.

##  I Introduction

Stating the obvious, studying climate change is challenging because it is so
complicated. Not only are climatological factors coupled into a complex causal
web, but humanity’s response to this challenge also depends on a multitude of
entangled processes [76, 27, 93, 24]. Looking closer at any component of this
network of causes and consequences, there are yet more networks: The
photochemical reaction network of the atmosphere determines the concentration
of greenhouse gasses [21]. The in- and outflows to this system are affected by
the bio-, geo- and technospheres’ chemical networks [62]. The human
contribution of greenhouse gases depends on the opinion dynamics of climate
action propagating over a web of people [30, 37], and the global economy,
which is, of course, a network [95]. (See Fig. 1.)

From the above observations, it is fair to call the science of climate change
a network science. However, it is not the only such: From power grids to the
neural system; from the narrative structure of novels to subway systems; from
friendship contacts to money-flows in banks; all these systems can be
understood as networks [75]. The function of these systems is, to some extent,
determined by the way they are connected [75]. Thus, a first step to analyze
them is representing them as graphs—mathematical objects consisting of nodes
pairwise connected by edges. To extract meaningful information about a system
from a graph is a rapidly developing, interdisciplinary field [75, 4]. Once
you can represent a complex system by a network, you can choose from an
abundance of methods to analyze it. In this review, we will survey
applications of network theory to the science of climate change and discuss
the future of integrating network modeling into climate research.

On the one hand, as we will argue, network theoretical methods have entered
the study of climate change late and are yet to be employed to their full
potential. On the other hand, networks are close to the heart of climate
science. Today’s network science carries the legacy of 1970’s systems theory
[76, 39], which is also an antecedent of much of today’s climate modeling
[33]. The similarities are easy to see, starting from the emphasis on an
integrative, holistic view. The main difference is perhaps that network theory
stresses _how_ things are connected. In Fig. 2A, we show a diagram of the
components and interdependencies of a state-of-art climate model (adapted from
Ref. [57]). In Fig. 2B, we plot the same diagram by a force-directed algorithm
to highlight its network structure. This network will be a standing example of
our paper.

In the remainder of this review, we start with an exposé of the tools and
techniques of networks science and the questions they are designed to answer
that pertain to climate change. Then we will review how these tools have been
used in the science of climate change, organized by topics roughly sorted from
causal to consequential (even if we recognize that is not strictly meaningful,
cf. Fig. 1). We aim to cover all issues directly related to the causes and
consequences of climate change. The area just outside of our scope includes
network science of sustainability [91].

##  II Topics and tools of network science

The mathematics of networks is a common language to describe the large-scale
structure of vastly different systems throughout the natural, social, and
formal sciences. With a network representation of a system of interest at
hand, there is a multitude of analysis methods available [75, 4]. This section
will overview these methods, and explain how to adapt these methods to
specific needs. It is organized around four typical questions that network
science can help to answer. Code for the non-standard methods we use, and the
data, can be found at https://github.com/pholme/ncc.

###  II.1 Identifying important nodes and edges

Once we have represented a system as a network, one approach is to zoom into
individual nodes and edges and investigate their function. Often one would
seek a ranking of the nodes or edges in order of importance. These would then
be a priority list of what nodes to protect (in, e.g., an ecological network
[1]) or influence (in, e.g., a network of stakeholders in greenhouse-gas-
emitting industries [9, 68, 91]).

The meaning of importance ultimately depends on several factors: what the
network represents, what dynamics are coupled by the network, how one would
like to influence the system, and what kind of interventions are at hand.
However, even though there are innumerable answers to these questions, the
measures typically fall into a few different categories: centrality, vitality,
and controllability measures.

The simplest importance measure is the degree—the number of neighbors of a
node. As the name suggests, centrality measures interpret a network as a
geometric object and use distances and imaginary flows to rank the nodes. One
prominent example is PageRank—the approach to ranking webpages that became the
starting point for Google [4]. Assume a walker jumps from node to node across
the network. With a probability $\alpha$ (traditionally $\alpha$—the
“attenuation factor”—is set to 0.85), the walker follows a random link out
from the node where it is. Otherwise, the walker goes to any node of the
network at random. The PageRank of node $i$ is then proportional to how often
the walker visits $i$. PageRank has been applied to directed networks far
beyond web pages, such as identifying keystone species in foodwebs [1]. Fig.
3A shows the PageRank values of the network in Fig. 2.

Another common approach to centralities is to look at the shortest paths
between pairs of nodes in the network. The betweenness centrality of node $i$
is essentially the count of shortest paths between all pairs of nodes that
pass through $i$. Several works related to climate change have used this
measure to rank nodes [85, 37, 61, 28, 29].

To illustrate the kind of reasoning that goes into the development of new
centrality measures, let us modify betweenness to suit better the purpose of
climate models such as the one shown in Fig. 2. Such models have always
emphasized cycles [33]—closed paths, rather than shortest paths between
distinct node pairs. So, rather than counting the latter, we can consider all
the simple cycles of the graph—cycles where a node appears at most once. Fig.
3B shows the counts of simplest cycles passing through the nodes and edges of
our climate-model dependency graph.

Both PageRank and our cycle betweenness rank node 20 (fossil fuel use)
highest, but some other nodes are ranked remarkably differently. Node 15
(fossil fuel reserves) has a high PageRank but low cycle betweenness, whereas
the situation is reversed for node 16 (mitigation and adaptation). This shows
that one needs to be careful to choose a centrality measure that is readily
interpretable in one’s investigation. Better still would be to validate
centralities before picking one—i.e., to pick the measure with the highest
predictive or explanatory power regarding some observed or simulated outcome.

Figure 3: Some applications of network-science methods to the network in Fig.
2. Panel A shows the PageRank values of the nodes by color. Panel B shows
counts of simple cycles by size for both nodes and edges. Panel C illustrates
a motif analysis. We show all isomorphically distinct three-node subgraphs and
their Z-score with respect to a degree-preserving null model. A large Z-score
means that the subgraph is overrepresented in the original graph. Panel D uses
the community detection algorithm InfoMap [87] to split the network into well-
defined clusters.

###  II.2 Mesoscopic structures (modules, motifs, clusters, or communities)

If we zoom out from the node- and edge-centric perspective of importance
measures, we come to mesoscopic structures. At this scale, network methods
typically concern finding subgraphs that could represent functionally or
conceptually clear subsystems.

Methods to discover network motifs are a common mesoscopic analysis tool (see
Refs. [61, 69, 54] for applications to climate change). Motifs are
statistically overrepresented subgraphs compared to the average of a null
model [2]. Often one can interpret motifs analogously to components of
electronic circuitry. For example, the three-node subgraph of nodes 1 and 2
both pointing to 3 and 1 also pointing to 2, could function as a logical AND-
gate [72]. To keep the calculation fast and the result interpretable, motif
analysis is often restricted to subgraphs of just three or four nodes.

A crucial step when identifying motifs is to choose a relevant null model. To
make the motifs meaningful, the model should sample all graphs with the same
basic constraints as the original graph with equal probability. The most
common null model are graphs with the same number of nodes and edges and the
same degree profile (i.e., the same number of nodes with in-degree $k_{i}$ and
out-degree $k_{o}$) as in the original graph. Since our example graph
represents a circulation model constructed to be strongly connected (there is
a path from every node to every other node), we add the constraint of strong
connectivity to our null model. We display the result for three-node subgraphs
in Fig. 3C. The most overrepresented subgraph consists of two mutually
dependent nodes that both influence a third node. Even though there is only
one such subgraph—16 (mitigation and adaptation) and 17 (climate impacts)
influence each other while both pointing at 18 (GDP)—such a configuration is
so rare in the null model that the motif is highly unlikely to appear by
chance. Straight feedforward paths like 3 (atmospheric CO2 concentrations)
pointing to 4 (instantaneous radiative forcing) pointing to 5 (effective
radiative forcing) are so common in the null model that it comes out as an
anti-motif (a subgraph suppressed by the network-forming forces). Presumably,
this could be because the middle node could be merged with either of the end
nodes when building a climate model.

Another mesoscopic methodology in network science is to detect communities
[82, 81, 96]—loosely defined as subgraphs with an intricate inner circuitry
and relatively few in- and output terminals. There is a vast number of methods
for this purpose. The probably most common one, the Louvain method [11],
heuristically optimizes the Newman-Girvan modularity [75]—a measure of
partitions of graphs that increase if many links are within the partitions
rather than between them. In Fig. 3D, we show the result of another approach,
InfoMap [87], building on an information-theoretic idea that algorithms could
use relevant communities to compress the description of random walks on the
network. From the network structure alone, this method roughly recreates the
anthropogenic component of the original graph as one community (IV), whereas
it splits the rest of the network into three communities.

###  II.3 Mechanisms driving the network evolution

Real-world networks are rarely completely random. Instead, they have
regularities, network structure, that can tell us something about the system’s
evolution. We have already mentioned one such observation and explanation—that
the suppression of feed-forward chains in our example network might come from
typical considerations of model building.

A common approach is to look at quantities at a network-wide level—thus
completing our zooming out from node-centric analysis via mesoscopic
structures to global properties. The most common such inquiry is the study of
the probability distribution of degree [61, 96, 103, 107, 108, 97]. Such are
often is heavy-tailed in empirical networks [4], and there are several
mechanisms proposed generating such structures. Fat-tailed degree
distributions are only one example of an interesting global network measures;
see Refs. [75, 4] for more examples.

Finally, we note there are methods of going straight to inferring the growth
mechanisms of networks without trying to reproduce a known network structure
[79]. Such methods are yet unused in the climate change literature.

###  II.4 How network structure affects the system dynamics

Another common research question in network science is to relate the structure
of a network to some dynamics occurring on the network (like opinion
dynamics—to take an example from the climate change literature [54]). Social
networks typically have an overabundance of triangles [58] which tend to slow
down the spreading of opinions or information than spearing on a random
network of a similar size. Assume A spreads climate-denial sentiments to B and
C. Then, if B was connected to another node, D, the spreading would have been
more efficient since D would not necessarily have the same opinion as B.

###  II.5 Finding a method that suits your project

How network methods enter a research project depends both on the available
data and research questions. Often one is faced with a choice between using
simpler or more complex network representations. Suppose one decides to
include information about directionality, weights of nodes or edges, how these
vary in time, etc. Then the predictive and explanatory power should, in
principle, increase, but the number of available methods that can handle the
complexity of the data would be much fewer. Often, however, it is reasonably
straightforward to extend a concept to suit your needs—like our cycle
betweenness (Fig. 3B) or the specialized null-model when calculating motifs
(Fig. 3C).

Finally, network methods do not exclude other approaches)—regression analysis,
differential-equation modeling, machine learning, etc. One would often use
network methods to complement, or as a complement to, other methods.

Figure 4: Network structure of Earth’s atmospheric reaction system. Panel A
shows a minimal reaction system comprising of two reactions. Panel B
illustrates a representation with two types of reaction nodes (photochemical
and non-photochemical). Panel C shows the most common projection to a simple
graph. Panel D displays a higher-order network representation [7] where the
molecular species involved in one reaction form a hyperedge—a generalization
of edges to represent the interactions of arbitrary number of elements. Panel
E shows the atmospheric reaction network of Earth (data from Ref. [97]) in a
representation similar to panel B. Figure 5: Teleconnections in the Earth’s
climate. The figure is adapted from Figs. 1 and 7 of Ref. [49], and slightly
simplified. Panels A and B show regions where the ground temperatures are
highly correlated. The dots marking the most representative grid point. Panels
C and D show Granger causality links between these regions. I.e., an arrow
from region $i$ to $j$ means that the temperatures at $i$ are correlated to
those at $j$ if they are shifted forward in time. We omit regions without
arrows.

##  III Causes: Flows of matter, energy, and opinions

A simple explanation of the causes of global warming does not need more than a
sentence—gases injected by humans into the atmosphere shield the thermal
radiation into space, raising the Earth’s mean temperature. However, going
just one level deeper, we are hit by a wall of complexity, as alluded to
above. In this section, we will take a network view of these explanations.

###  III.1 Global circulation models

We start our discussion of concrete networks with large-scale climate models
that inform the Intergovernmental Panel on Climate Change (IPCC) and decision-
makers worldwide. These are primarily simulation models made with prediction
and scenario testing in mind. They are built around a dynamic simulation of
fluid motion across a physical model of the Earth [33]. This fluid simulation
is coupled with other physical feedback mechanisms and sometimes social
components (Fig. 2). These couplings are causal—changing a variable in one end
of a link can change the state of the node at the other end. The causation
could happen through meteorological flows (of matter, energy, or some other
thermodynamic entity), economic couplings, or political influence.

Some design principle of general circulation models are:

  * •

Increasing accuracy by adding missing components and increasing spatial and
temporal resolution.

  * •

Increasing computational performance and eliminating computational bottlenecks
[114].

  * •

Increasing extensibility and facilitating validation by standardizing the
components of the models.

Simplifying these models has never been a main objective, meaning that they
have, after over 60 years in the making, reached a degree of complexity beyond
what a single research group or even a single organization could handle [61].
This also means that they represent, relatively completely, our mechanistic
understanding of climate processes. Furthermore, since these models are
meticulously validated [38], they constitute proofs of concept that few other
theories, in all of science, can match [50].

Critics may say that general circulation models are so complicated that they
no longer represent a scientific explanation [24]. Understanding the models
(and thus climate) calls for a network analysis, which closes the loop to the
systems diagrams of yesteryear [76].

###  III.2 Chemical reaction systems

The primary cycles of atmospheric greenhouse gasses are part of much larger
chemical reaction systems [21]. To understand the organization of these larger
systems, one can use network approaches [96, 97].

Fig. 4 shows a chemical reaction network of the Earth’s atmosphere. Note that
this network is integrated with the chemical processes of the oceans and land.
When it comes to CO2 capture, these other global chemistries could aid the
biosphere [62]. Given the versatility of whole-system network modeling in the
‘omics disciplines and biochemical modeling [4, 75, 2], it would be
interesting to construct a database with all reactions on Earth, outside of
the biosphere.

There are several established ways of analyzing chemical reaction systems.
These can incorporate more chemical constraints than a pure network-science
approach. For instance, flux-mode analysis [77] is a technique assuming both
an underlying reaction network and additional restrictions from mass
conservation, but not reaction kinetics.

It is worth mentioning that chemical reactions lend themselves well to higher-
order network representations [7]—one of the hottest topics at the moment in
network science. In such abstractions, more than two nodes can interact at one
time. For chemical reactions, we can, e.g., use this to encode the restriction
that molecules of two different species need to meet at a point in space and
time for a reaction to occur. These directions are, at the time of writing,
largely unexplored.

###  III.3 Climatic teleconnections

The presence of long-distance correlations in weather patterns has been known
since the 19th century [44]—the emblematic example being the El Niño Southern
Oscillation (ENSO) that connects weather in the equatorial Pacific Ocean.
Rather than studying the full correlation patterns, one can reduce them to a
network [100]. A cell in such a network typically represents a region of
relatively cohesive weather patterns. Different cells are linked if the
condition in one cell predicts the weather (technically authors use pressure
[107, 108], temperature [35, 46, 118], rainfall [13], or sea currents [25]) in
the other [107]. Since we can expect the weather dependency patterns to change
because of global warming, understanding the dynamics of climate networks
could inform climate models and improve our forecasting of climate change
[36].

Once we have established the links of such a climate network, we can describe
the dynamics of a climatic episode [47]. For example, Gozolchiani et al.
characterized the El Niño phase of ENSO by the El Niño basin [46], at the
onset, losing its influence on the rest of the networks. After some months,
the situation reverses, so a large part of the weather network becomes
influenced by the El Niño basin.

In Fig. 5, we show an example of a network of Granger causality of weather
patterns from Hlinka et al. [49]. Several papers on this topic focused on how
to derive meaningful networks of weather dependencies [40, 31, 32, 28, 29, 49,
89, 88, 100], others showed that climate networks reflect well-known features
of synoptic scale meteorology [113, 118, 98], or that climate network can help
in predicting extreme events [12, 13, 70]. Fan et al. [35], took the weather
dependency network modeling one step further and considered a network where
nodes are El Niño events, linked by their similarity. Steinhaeuser et al.
[101] also presented a relatively unusual climate network study in that it
builds on multilayer networks—networks where there are different classes of
nodes and edges [75].

###  III.4 Managing common-pool resources

We can understand many kinds of climate decisions through game theory. Even
though humans are not necessarily well-informed and relentlessly selfish—as
typically assumed in economic modeling—game theory can clarify what is at
stake in a particular decision.

Many goods related to climate change are common-pool resources. This means
they are non-excludable (in principle, everyone has access to it) and
rivalrous (the used part of the resource becomes unusable or degraded for the
future). Most game-theoretical studies do not rely on networks, but some do.
When agents interact through a social network, the network structure can
substantially affect the dynamics. For example, Chung et al. [23] showed that
once the social network compels people to follow norms (like conserving
common-pool resources), more social interaction promotes cooperation. This
finding was explored in a dynamic setting by Sugiarto et al. [103] who found
that such norm-enforcing social interactions could create a hysteresis effect
and thus the possibility of sudden behavioral (and related ecological)
changes. On a positive note, social networks could be susceptible to
governmental interventions [104], even though they fail to manage a common
pool resource when operating in isolation. Furthermore, systems of
reinforcement learning agents could also sustain limited shared resources
[83].

##  IV Consequences: Impact on nature and society

Now we turn to studies focusing primarily on the consequences of climate
change. Such consequences are, of course, coupled back to the causative
factors, and all cited studies duly regard themselves as contributing to our
understanding of a minor part of this grand cycle.

###  IV.1 Impact on ecological network structure

Traditionally, ecologists have used networks to study species interactions
such as predation or mutualism (e.g. pollination). Network representations of
ecological systems have helped assess the potential impacts of climate change
on community assembly and its stability [74], both in modeled [90] and
empirical mutualistic networks [6], as well as foodwebs [42]. We can expect
climate change to affect the niche and geographical range of species
distributions and, with them, the strength of species relationships. Network
science has been useful to predict the probability of secondary extinctions
given climate disturbance [6] or the effect of warming in fitness depression
in host-associated microbiomes [48]. Climate change can cause a shift from
bottom-up to top-down regulation of herbivorous communities in Arctic foodwebs
[64], which implies tracking the change over time of link strength in
ecological networks. Furthermore, Gilman et al. [43] used a very detailed
model of ecosystem response to climate change and found that ecosystems with
more links were more robust to global warming. In a similar vein, Schleuning
et al. [94] studied pollination and seed-dispersal networks with over 700
species. In a hybrid approach—with climatic niche-breadth estimates coupled to
simulations—they concluded that ecological networks are more sensitive to
plant than to animal extinction under climate change.

###  IV.2 Tipping points in ecological networks

Networks have also been used to analyze tipping points in ecological systems,
their interactions with climate, and potential cascading effects.

Ecosystems at large scales can undergo pervasive and abrupt changes if they
transgress tipping points. We can expect climate change to increase the rate
of such critical transitions [14]. For example, the shift from rain forest to
savannas has been estimated from remote sensing data to have a tipping point
at around 1500 mm of precipitation per year [111] or reduction of more than
40% of area. Climate change projections for marine ecosystems predict
unprecedented abrupt changes in global oceans [8]. The climate system has at
least 15 of these tipping elements identified [67, 66], and the list readily
grows to over 30 types of critical transitions if we include local and
regional ecosystems [85]. While climate-related processes (e.g., temperature
increase, changes in precipitation, or drought) are one of the main causes of
irreversible change in ecosystems, it is seldom the only one. A network study
that exploited the bipartite structure of drivers and regime shifts showed
that climate-related variables often interact with food production (e.g.,
agriculture, fishing), changes in nutrients flow, and urbanization [86].

Some systems with tipping points have connectivity features where networks can
enrich the analysis. For example, shifts from rainforests to savannas are
mediated by moisture recycling feedbacks, i.e., rain transport dynamics from
one place to another. Networks have been used to make such connections
explicit in space and time. For example to assess how regime shifts in a
region of the Amazon can affect the likelihood of regime shifts in another
area [61].

Tipping points have also been hypothesized to be interconnected across
different climate [67] and ecological systems [52, 99]. The network literature
already offers some tools that might be adequate to address potentially
cascading tipping effects. For example, an increase in connectivity and a
decrease in modularity can amplify tipping cascades [17, 18]. Ref. [61] showed
that some network motifs can destabilize interconnected tipping elements, and
high clustering (many triangles) exacerbates the systemic vulnerability to
regime shifts. Feedforward loops can decrease the coupling strength necessary
to initiate cascades, a finding applied in models of the Amazon rainforest
[117] and some climate tipping points [116]. Yet, these models assume a small
number of systems and a known coupling mechanism. The analysis of high-order
motifs on causal networks, such as feedback cycles, has enabled the
exploration of alternative mechanisms that couple tipping elements [85].

We still lack empirical evidence of cascading tipping points [92], which is
thus one of the most pertinent open questions. Combining network-based causal
inference methods with climate simulations or Earth system observations are
likely fruitful avenues for future research.

###  IV.3 Impact on socio-ecological systems

Predicting anthropogenic responses is perhaps the most challenging task in
climate science. That much said, it is maybe not hopeless—sometimes humans
behave very predictably. Mitigating climate change is maybe not hopeless
either—sometimes humans collectively solve emergencies with exceptional
efficiency.

Models of human response to climate change are very diverse, but many focus on
feedback effects from the climate to human behavior. For example, Peter et al.
[81] studied how a warmer climate would affect biofuel production. They
construct a complex Bayesian model of South African agriculture, including
around a hundred variables (like “soybean water use”) and their dependencies.
Yletyinen et al. [120] used a simulation of ecological decision-makers to
argue that oversimplifying social interactions be gravely misleading about
environmental outcomes. A yet more complex simulation platform, including
networked human decision-makers and ecosystems alike, was presented by Donges
et al. [26]. We note that the authors call the model simple, and given all
components they seek to include, it is a fair description. Still, compared to,
e.g., the networked game-theoretical models discussed above, it is very
intricate.

Several studies concern the impact of global warming on the management of
limited resources. Prager and Pfeifer [82] took a network approach to
understand rainwater management among Ethiopian smallholders and its
resilience to climate change. The authors constructed a multilayer network
representation with separate nodes for people and plots. Links in the plot-
plot networks represented water flow from one field to another. The social
network of smallholders reflected the fields in that downstream farmers would
depend on their upstream neighbors. Mina et al. investigated the management of
forest by a combined spatial simulation and network analysis [73]. Many
studies used similar social-network approaches to understand the resilience of
governance of shared resources, but less directly related to climate change.
For example, Jansen et al. [53] used a network approach to analyzing
irrigation in Darwin, Australia, and Lubell, Robins, and Wang [69] employed
exponential-random graph models [110, 75] to understand water management in
the Bay Area, California.

A vastly different type of social impact are population displacements in
response to global warming [34]. Catteano [20] pointed at the role of exiting
social networks in the demographic changes from people seeking environmental
refuge likely ahead of us—a paper without explicit network analysis but
hinting at the need for such. Researchers have also studied the climate-change
impacts of networked infrastructures like roads [41, 22] and power grids [71].
However, so far, without explicitly quantifying the implications in terms of
network structure.

###  IV.4 Opinion dynamics

Climate action is a consequence of social information spreading, both in the
networks of stakeholders and politicians and among the general public. In
other contexts, social influence over networks of friendships is a well-
studied topic [65]. Typically, articles either present analyses of social
media data [19] or simulation studies [104, 103].

In network studies of social-media posts about climate change, the nodes are
individuals, and links represent information sharing from one person to
another. We will mention four examples all drawing data from Twitter. The
boundaries of the data set then define the scope of the study. For example,
Cann et al. analyzed a Twitter network to understand public sentiments around
the announcement of the US withdrawal from the Paris Agreement. Using
community detection [11], they discovered a binary split (although far from
complete) into supporters and antagonists of the US action. Vu et al. [112]
also used Twitter data, but (rather than gleaning tweets about a specific
topic within a particular time window) they gathered the follower network
within a set of NGOs in the climate change sector. Their analysis focused on
employing centrality measures to identify key actors. Tyagi and coworkers
[109], used a richer network representation—a so called “signed network” where
positive links represent agreement and negative represent antagonism. They
could characterize polarization by analyzing the boundary represented by
negative links. In our final example, Goritz et al. argue that one can use
network analysis of discussions on social media in teaching topics on climate
change [45].

###  IV.5 Policy networks

The study of policy networks is a well-established field within political
science. A policy network consists of actors—organizations or
individuals—linked by common interests or beliefs concerning policymaking [84,
56]. Whereas the actors are typically officially recognized entities, links
could be anything from informal to institutionalized.

How the scientific information about climate reaches decision-makers can be
staggeringly complex. Broadbent and Vaughter investigated how information the
IPCC enters the information flow of policy networks in New Zealand and Japan
[15]. In a similar study, but focusing on information spreading by climate
denialists, Farrell [37] used official statements, press releases, and news
articles to study the network of information spreading intended to hinder
climate action. Furthermore, by employing topical modeling techniques from
natural language processing and network centrality measures, Farrell concluded
that top corporate actors are the drivers of this movement. In addition, he
noted a trend of actors deliberately obscuring this network. A few papers
studied the network of information sharing among policy actors [54, 115].
Using motif analysis (presented above), they found evidence of echo chambers
that effectively align the information that reaches the actors. If the
communication happens between agents of different viewpoints, to could,
however, mitigate some environmental crises [5].

Researchers have also used questionnaires to map the connections between
policymakers. Howe et al.focused on the Canadian climate policy network [51].
Using an exponential random graph framework [75], they studied how the
position of actors in the network predicted their stance on specific issues
like oilsand exploitation. Lee and van de Meene used the same
approach—analyzing questionnaire data by exponential random graphs—to
elucidate how cities learn climate action from each other [63]. Ylä-Antilla et
al. argue for an international perspective for interorganizational policy
network research on climate change comparing Canadian and Finnish data [119].
Papin [80] and Bansard et al. [3] take an international perspective on
networks of cities and their policies with respect to climate change.

Policy networks are coupled to financial networks. Stolbova, Monasterolo, and
Battiston used economic theory and data to analyze how shocks of new climate
policies propagate through financial networks [102]. Brulle studied another
type of financial network—the network of money flow among organizations of the
climate change counter-movement in the USA [16]—concluding that the most
central companies are the drivers of this system. I.e., the same conclusion
reached by other methods by Farrell [37].

##  V Discussion

###  V.1 Summary

For over a decade, climate scientists have employed network methods—from
governance studies via ecological tipping points to the web of climatic
teleconnections. To network scientists from other backgrounds, this seems
obvious. The second of the Essential principles of climate literacy by the
U.S. Global Change Research Program states that “climate is regulated by
complex interactions among components of the Earth system.” [106] This almost
directly portraying the Earth system as a complex network, so naturally we
need complex-network methods to understand it.

To a mainstream climate-change or Earth-system scientist [93], network science
will feel like the familiar stranger you see on your commute every morning.
All these fields share a great deal of intellectual ancestry. All recognize
the failure of reductionist science to account for emergent phenomena like
global warming and the human response to it. They also differ from machine-
learning applications in that they rely on causal arguments rather than
learning from examples. The latter is, of course, challenging when it comes to
dealing with the current (and only known) anthropogenic global warming. On the
other hand, we need data science too, as it is arguably a powerful tool for
several questions related to climate change [105].

Climate science has had a strong causal grounding due to its mechanical
modeling tradition and comprehensive estimates of uncertainty [38]. Climate
data, whether Earth system observations or scenario modeling output, usually
comes as high dimensional arrays that lend themselves for further exploration
of causal interdependencies of the climate system [89], and its interaction
with the biosphere [60], technosphere [27], or social systems [78]. Modern
methods for causal inference offer new opportunities to explore causal
connections by reducing the high dimensional space to a directed network [105,
89, 60, 88]. Caution is needed, however, to ensure that observations are long
enough to capture the time scales of the dynamics or that the resolution
captures the fast and slow processes of the interactions of interest. The
interplay between climate and other spheres are fruitful areas of research,
where networks as boundary objects are likely to play an important role.
Networks can, thus, enter causal modeling in many ways: the input data could
be a network (e.g., networks of information flow), the output could be a
network of causal connections of the same types of units (e.g., climatic
teleconnections), or a causal network connecting model components to a greater
whole (cf. Fig. 2).

###  V.2 Limitations of network approaches

Network-based methods are tools in the toolbox, not an entire toolbox. The
problems that one could solve with a pure network approach are limited to
those where the only available data is a network of binary, possibly weighted,
interactions (e.g., policy networks). When other information is available, a
network approach would typically also involve different types of modeling. For
example, a differential equation system could be described by the network
(leading to systems dynamic type models), or the network could result from
spatial data (like meteorological teleconnections). Indeed there is a full
spectrum, from pure network problems to those where network methods only add a
marginal value.

###  V.3 Conclusions and future directions

Applications of network science to climate change are still far from mature,
and in all the topics mentioned in this review, there is more work to do.
Recognizing the social factors behind many of the processes in play [10], we
believe applications of social network analysis are particularly promising.
One understudied issue is the impact of climate change on vulnerable
populations [55]. Another interesting focus area is migration triggered by
environmental deterioration [34]. Social networks are thought to be a critical
determinant of the migration flow, where international migration, in
particular, is guided by existing social ties. Networked infrastructures could
also be sensitive to climate change [59, 41] and relatively rarely studied by
the methods of network science. Finally, we believe climate science itself and
our understanding of climate changes in all its complexity also would benefit
from network studies (cf. Fig. 2).

To summarize, network science has found its way into the toolbox of an
increasing number of climate scientists. We envision that network approaches
eventually become a network in itself, methodologically connecting different
areas of the science of climate change.

###### Acknowledgements.

The authors thank Onerva Korhonen and Milja Heikkinen for comments on the
manuscript. P.H. was supported by JSPS KAKENHI Grant Number JP 21H04595.
J.C.R. was supported by Formas grant no. 942-2015-731.

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