Omar A Guerrero, Daniele Guariso, Theresa Liebig, 
Ony Minoarivelo, Alessandro Craparo, and Ashleigh Basel
Authors 
Omar A Guerrero1, Daniele Guariso1, Theresa Liebig2, Ony Minoarivelo2, Alessandro Craparo2, and 
Ashleigh Basel2 
1The Alan Turing Institute 
2CGIAR Focus Climate Security 
This work is licensed under Creative Commons License CC BY-4.0. 
Disclaimer
The views expressed in this document cannot be taken to reflect the official position of the CGIAR or its 
donor agencies. The designations employed and the presentation of material in this report do not imply 
the expression of any opinion on the part of CGIAR concerning the legal status of any country, territory, 
area, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries.
Acknowledgments 
This work was carried out with support from the CGIAR Initiative on Climate Resilience, ClimBeR. 
We would like to thank all funders who supported this research through their contributions to the 
CGIAR Trust Fund. 
1
Table of Contents 
1 Introduction ..................................................................................................................................................................................... 3  
2 CSI concept ....................................................................................................................................................................................... 4 
2.1 Connectivity ......................................................................................................................................................................... 4 
2.2 Synchronicity ....................................................................................................................................................................... 6 
2.3 Conceptual illustration .................................................................................................................................................... 7 
2.4 Data .......................................................................................................................................................................................... 8 
3 Methods .......................................................................................................................................................................................... 10 
3.1 Extreme events likelihood .......................................................................................................................................... 10 
3.2 Institutional fragility ..................................................................................................................................................... 12 
3.3 Connectivity ...................................................................................................................................................................... 13 
3.3.1 Conditional dependencies ..................................................................................................................................... 13 
3.3.2 Compounded conditional dependency network ......................................................................................... 14 
3.3.3 Modularity .................................................................................................................................................................... 16 
3.4 Synchronicity .................................................................................................................................................................... 17 
3.5        Computing the CSI ........................................................................................................................................................... 18 
4 An application to Kenya ........................................................................................................................................................... 19 
5 Conclusions ................................................................................................................................................................................... 21 
References ................................................................................................................................................................................................ 22 
A Development indicators by CSN dimension ................................................................................................................... 27 
2
Methodological Note for the Climate and Security Index
Omar A Guerrero1, Daniele Guariso1, Theresa Liebig2, Ony Minoarivelo2, Alessandro
Craparo2, and Ashleigh Basel2
1The Alan Turing Institute
2CGIAR Focus Climate Security
1 Introduction
There exists a large body of evidence showing how climate variability is widely impacting natural and
human systems. One of these many impacts is the potential threat to human security. The role of climate
variability as a possible cause of violent conflict has come to the forefront of public and scientific debates. In
this so-called Climate Security Nexus (CSN), climate variability acts as a multidirectional threat multiplier,
aggravating existing vulnerabilities of people of communities suffering from high levels of poverty, political
inequality, and dependence on renewable resources (e.g., agricultural production); especially in regions that
lack resilience and coping mechanisms to absorb, adapt, and recover from climate-related shocks.
Despite increasing attention towards the CSN, systematic and timely evidence about which geographies
might be at risk for climate-related insecurity is scarce. This is partly due to a lack of data, but also
to methodological challenges. Yet, data and analytical tools considering the complex interplay of climate,
socioeconomic vulnerabilities, and conflict are crucial in understanding the CSN (Madurga Lopez et al.,
2021). Composite indicators often used for ranking and benchmarking, while highly popular in several
domains (Greco et al., 2019), do not allow for modelling the underlying relationships among the indicators.
Hence, they are unable to fully account for complex interlinkages (Sharpe, 2004), as in the case of the
CSN. Similarly, indicators built using regression-based approaches (e.g., the Global Conflict Risk Index of
Halkia et al. (2020)) share the same limitations, mostly focusing on linear relationships and imposing severe
constraints on data structures. On the other hand, fashionable AI methods demand large-scale data that
do not exist in vulnerable countries and regions. Moreover, the most appealing feature of machine learning
3
approaches, their predictive power, has been severely questioned in the context of conflict studies (Bazzi
et al., 2022; Cederman and Weidmann, 2017; Muggah and Whitlock, 2022), with implications for the design
of early warning systems and decision-making support (O’Brien, 2010; Muggah and Whitlock, 2022).
The systematic quantification of climate security demands a novel approach that carefully considers the
complexity of socioeconomic systems and the empirical limitations of coarse-grained datasets. The proposed
Climate and Security Index (CSI) diagnoses climate security vulnerability by including a broad range of
drivers of the Climate Security Nexus from climatic, conflict, socioeconomic, agricultural, and institutional
dimensions. The CSI incorporates analytical tools and metrics from diverse disciplines, hardly combined
by researchers from the same field (e.g., signal processing, complex network analysis, Bayesian inference,
extreme value theory, stakeholder validation, etc.), supporting policymakers by informing contextualised
and climate-security-sensitive decisions for policies, programs, or finance. Its modular design allows users to
analyse key structural features of a socioeconomic system (e.g., its connectivity and synchronicity) and assess
the propagation of diverse climate shocks across several development dimensions. Our framework produces
intuitive graphical representations of a “vulnerability space”, facilitating the identification and comparison
of geographies that may be at risk of climate-driven instability.
2 CSI concept
When thinking about the connection between climate-related events and human security, two fundamental
dimensions come into mind: (1) how extreme are climate events and (2) how well-prepared is a society
to deal with them. These are the first two modules of the CSI, and they are in line with the relevant
literature (Meierding, 2013; Vivekananda et al., 2014). On the one hand, extreme events are shocks that
test the resilience of a system. On the other, institutional frameworks to mitigate the impact of such shocks
(e.g., evacuation plans, reallocation policies, support income programmes, reconstruction strategies, etc.)
act as the resilience buffers of societies. While both of these components are important to understanding
climate security, their interaction is much more nuanced than what one could disentangle from reduced
analysis such as regressions. The CSI tries to account for such nuances by borrowing concepts stemming
from the literature on complex adaptive systems (Simon, 1962; Gell-Mann, 1994; Miller and Page, 2009).
More specifically: connectivity and synchronicity.
2.1 Connectivity
To understand the nuanced relationship between climate events and the resilience provided by institutional
buffers, it is important to understand certain structural features of a country or socioeconomic system. Often,
4
structure relates to the way different components of a system interconnect. Such interconnections capture
how a change in part of the system may reach another part. In the context of the CSI, we can think of a
system as a country or region, and of its components as the different development dimensions that society
pays attention to. One prominent example of such a multidimensional view is the United Nations Sustainable
Development Goals (SDGs), which divide socioeconomic systems into 17 broad dimensions, covering topics
such as poverty, food security, public health, clean aquatic environments, the economy, and public governance
to mention a few. In the CSI, one could consider any set of dimensions that may be relevant to a particular
country or region.
The relevance of connectivity comes into play when thinking about the potential reach of shocks pro-
duced by extreme environmental events. For example, suppose that most of the food supply of a country
is domestically produced. Assuming such a country lacks instruments to diversify its food sources (e.g.,
international trade agreements), one would expect a more direct impact of climate events such as extended
droughts on food scarcity and prices. If much of this society allocates a significant portion of its income to
food consumption, one would expect poverty-related indicators to be affected by the droughts through the
aliment channel. This type of indirect dependencies between different development dimensions such as food
security and poverty are key to understanding the breadth and depth of climate-event impacts. They create
additional pressures on the institutional buffers, so it is crucial to quantify such structures of conditional
dependencies between different development dimensions.
A natural language to formalise the idea of connectivity is networks. Network analysis is a well-established
field that overlaps across different scientific communities (e.g., sociology, applied mathematics, economics,
physics, etc.). In fact, network studies have recently become popular to analyse the structure connecting
the SDGs (Ospina-Forero et al., 2022). Thus, one could exploit some of these methods to quantify the
structure that characterises a particular country or region. Here, the idea is to infer the network structure
of conditional dependencies between development indicators and to obtain an index of how interconnected
are the different development dimensions of a system. In a country like the one described in our previous
example, such a measure would indicate a strong connection between the dimension of food security and
poverty. Thus, the aim of the connectivity module is to quantify the ease with which a shock in a specific
development dimension may reach other ones. Arguably, a highly connected structure imposes an additional
burden on the institutional buffers as the government would need to implement coordinated responses across
various policy domains.
5
2.2 Synchronicity
Synchronicity or synchronisation is a phenomenon that has been documented in physical systems since
the 17th century when Dutch physicist Christiaan Huygens observed that two pendulum clocks hanging
from a common support would, after some time, exhibit a certain degree of coordination (Pikovsky et al.,
2001). Since then, the phenomenon of synchronisation has been documented across numerous physical and
biological systems (e.g., birds flocking, circadian rhythms, menstrual cycles, groups of running mammals,
predator-prey cycles, neurological activity, etc.). According to Pikovsky et al. (2001, p.8), we can understand
synchronisation as ‘an adjustment of rhythms of oscillating objects due to their weak interaction’. In the
context of the CSI, the different development dimensions can be understood as oscillating objects (with ups
and downs) as it is possible to track their dynamic levels through indicators. Furthermore, if such data are
processed through signal-processing techniques (such as the ones discussed in subsection 3.4), it is possible
to transform development indicators into wave data that can be used to measure synchronicity.
Why is synchronisation important in the CSI? With the development of complexity sciences, many studies
on physical and biological systems have shown that synchronicity often facilitates what is known as phase
transitions. In a nutshell, a phase transition is a qualitative change in the (often aggregate) properties of
a system; and such changes happens in a non-smooth nor gradual fashion.1 For example, certain types
of neural synchronisation relate to brain seizures (see Pikovsky et al. (2001) for various examples across
different domains). While the early findings about synchronisation were made in the physical and biological
domains, the recent availability of large-scale data and computer simulations has enabled the discovery of
various situations in social systems in which synchronicity enables major shifts in collective behaviour. A
case that is particularly relevant to the CSI is conflict.
In a study on worldwide protests and the “Arab spring”, Akaev et al. (2017) show that major historical
upraises have followed a high degree of synchronisation between changes in communications technology and
media openness. In a landmark model on the emergence of civil violence, Epstein (2002) shows that the
coordinated perception of hardships (from a repressive authority) in an agent population gives rise to local
or even global outbursts of violence. Ormazábal et al. (2022) show, more formally, that this type of civil
violence models exhibit clear phase transitions under which the entire system may switch from a peaceful
state to one overtaken by violence. Furthermore, Fonoberova et al. (2019) analyse how these dynamics may
be influenced by network connectivity, finding that small-world networks facilitate synchronised behaviours.
Synchronicity, thus, captures how coordinated would be the responses of different societal sectors should
there be a climate event. Societies that exhibit high levels of synchronicity are expected to experience faster
1In complexity science, synchronisation is often seen as a catalyst for the emergence of spontaneous order in chaotic systems
(Boccaletti et al., 2002).
6
and stronger responses, potentially increasing the risk of security threats such as civil violence. Under a
synchronised reaction, the institutional buffers are subjected to further pressures in terms of generating
timely responses.
Note that synchronicity is different from connectivity. In fact, in its original conception, synchronisation
was a way to measure rhythmic similarities between weakly coupled objects. Connectivity, in contrast, is
about strongly coupled components. Thus, two development dimensions that are not structurally connected
(in a network sense), may still exhibit high levels of synchronicity. This also implies that synchronisation is
different from correlation and that the former does not imply the latter, and the other way around. While
correlation focuses on co-movements that preserve certain change-magnitudes or order, synchronisation does
not consider the magnitude or amplitude of wave signals, but rather their coordination in terms of completing
their cycles (their phase). Thus, a system that may exhibit high synchronicity will not necessarily experience
high correlation levels.
2.3 Conceptual illustration
Together, connectivity and synchronicity provide information on the nuanced interaction between the dif-
ferent dimensions of the CSN. All the components of the CSI constitute four modules that diagnose climate
security vulnerability in a given country or region. In Figure 1, we provide an illustration of the CSI diag-
nostic tool. Given that the types of climate events are conditional on geography, the CSI allows to introduce
any type of events that may be relevant to the geographical unit under study. In this example, we denote
three types of climate events as I, II, and III. In the lower part of the plot, we have the remaining three
modules of the CSI. In this chart, higher values (outer rings) in any module represent a worse outcome. For
example, higher levels in extreme events type I mean that it is more likely to observe an extreme event of
such type in the near future; in terms of connectivity, it means that shocks to a development dimension
are more likely to propagate to other dimensions; for synchronicity, it means that the different parts of this
hypothetical society tend to respond with fewer delays from each other’s responses. Consequently, the area
described by the polygon can be considered a first measure of climate security vulnerability, so an index can
be constructed using this information. Nevertheless, the disaggregate version of the CSI provides a richer
diagnostic tool to understand where are the main weaknesses, strengths, and threats.
In the rest of this methodological note, we explain the type of data that needs to be collected to construct
the CSI diagnostic tool and the specific methods used to quantify each of its four modules.
7
Figure 1: Conceptual illustration of the CSI
extreme events
 type II
1.00
0.75
0.50
extreme events
 type I 0.25 extreme events
0.00  type III
0.25
0.50
0.75
connectivity synchronicity
institutional
fragility
Notes: Outer rings represent worse levels in each module.
2.4 Data
The modular structure of the CSI implies a variety of data sources and structures that need to match the
requirements of its methodological components. However, such diversity reflects the ability of the framework
to incorporate the multidimensional nature of the CSN, while allowing users to flexibly adapt the CSI to
the specific context under analysis. To measure extreme climate events likelihood, the framework relies on
time-series data of climate variables, measured on a monthly basis and aggregated at the national level.2
Users can define the type of weather events that they are interested in (e.g., droughts, heavy rainfall, heat
waves) and multiple climate variables can be considered at the same time (as shown by Figure 1).
The estimation of both the connectivity and synchronicity of the system requires time-series data on
development indicators. Critically, these indicators should be grouped into the dimensions of the CSN that
users have identified as relevant for their application. While some dimensions of the CSN are common
across different institutional settings (e.g., environment, conflict, institutional buffers), others might be more
context-specific (e.g., food systems, natural resources). As such, the choice of the dimensions (and the
corresponding indicators) is a crucial component of the CSI. It allows shaping the framework to the context
under analysis by incorporating the expertise of relevant knowledge holders within a co-production process,
which reflects the users’ needs.
2Given the moment estimator presented in subsection 3.1, the time-series of extreme climate events should extend over a
decade at least (i.e., n > 100).
8
The CSN dimensions (or policy domains) can then be tracked through multiple development indicators,
that capture the performance of the natural, social, and economic system. While in the case study presented
in section 4 we rely on development indicators measured for the whole country, the methods themselves do
not impose limitations on the geographical units considered, and more disaggregate analysis can be conducted
if information on the relevant CSN dimensions is available at the sub-national level. Development indicators
used for cross-country comparisons are usually measured on a yearly basis (e.g., see the World Development
Indicators database of the World Bank),3 which often results in short time-series. The methods proposed
in subsection 3.3 and subsection 3.4 are well-suited to deal with coarse-grained data, however, a minimum
number of observations is still necessary (i.e., n > 10). In addition, as a standard pre-processing procedure
in the development literature, indicators should be normalised to lie in the [0, 1] interval.4 They should
also be inverted whenever lower values represent better outcomes (e.g., the prevalence of stunting among
children).5 As an example, Figure 2 shows the average time trend of the development indicators used for
the application presented in section 4, grouped by the CSN dimensions considered. Interestingly, while both
socioeconomic and buffer indicators appear to exhibit a positive trend over time, conflict variables clearly
show (on average) erratic behaviour.
Figure 2: Average trend of indicators by CSN dimension for Kenya
Notes: Time-series data are normalized to the [0, 1] range.
Finally, institutional quality is proxied by a relevant index (measured at the national level), sourced from
The Bertelsmann Stiftung’s Transformation Index (BTI) project (more details in subsection 3.2)6 Users may
use the average of the indicator over the time period considered, its minimum or maximum values (to get
lower/upper bounds estimates of institutional quality), or the latest available data point (according to their
3World Development Indicators: https://datatopics.worldbank.org/world-development-indicators.
4Time-series data can be normalised to the [0, 1] range by using the formula (value−minV alue)/(maxV alue−minV alue).
5Indicators can be inverted through the operation 1− normalizedV alues
6The Transformation Index : https://bti-project.org/en/?&cb=00000.
9
needs). Table 1 summarises the data requirements for the different components of the CSI.
Table 1: CSI data structure
CSI component Data type Data points Geographical unit CSN dimensions
Extreme events likelihood Time-series n > 100 National No
Institutional fragility Time-series n = 1 National No
Connectivity Time-series n > 10 National/sub-national Yes
Synchronicity Time-series n > 10 National/sub-national Yes
3 Methods
In this section, we provide technical details on the methods used in each of the CSI modules. Something
important to keep in mind is that, within each module, there exist numerous quantitative methods coming
from various disciplines that try to capture conceptually similar phenomena. However, when working with
development data, the reality is that most of such methods cannot be used. The reason has to do with
the fact that development indicators tend to be coarse-grained, so they do not fulfil the data-demanding
requirements of frameworks such as machine learning. In fact, the development of the CSI is the result of
carefully considered analytic tools that (1) are conceptually meaningful to each module and (2) can be used
with small data. Thus, while the reader may be aware of alternative methods for one or more modules, they
should consider whether they are empirically viable in this context.
Let us explain the different methods module by module. In each case, we provide the general intuition
of the approach and refer to the original publications that developed the respective framework. Once these
details have been explained, we proceed to demonstrate the CSI with a real-world application.
3.1 Extreme events likelihood
A ubiquitous feature of complex adaptive systems is the prevalence of extreme events. Statistically speaking,
this characteristic is often described through a probability distribution with a heavy tail. That is, a distri-
bution where the likelihood of extremely large events is higher than under the assumption of exponentially-
decaying tails such as those from a normal distribution. If one assumes that the size of a climate event of a
certain type can be modelled as a random variable, then the presence of heavy tails in its distribution would
be a warning of potential shocks to the system.
When studying empirical data on event sizes, one would like to establish whether this information is
generated from a heavy-tailed distribution. In the literature of extreme value theory, various tail indices
10
Figure 3: An illustration of the likelihood of extreme events under heavy tails
0.10
exponential tail
heavy tail
0.08
0.06
0.04
0.02
0.00
5 10 15 20 25 30
event size
have been created for this purpose, for example, the Hill (Hill, 1975) and the Pickands (Pickands, 1975)
indices. In essence, these metrics measure the excess of probability mass for observations that lie beyond
the starting point of the tail.7 More excess means that there is more mass accumulated in extreme events,
making them more likely to occur. Figure 3 shows an example comparing a heavy-tailed distribution against
one with an exponentially decaying tail. The stripped region contains much more mass than the grey one,
suggesting that extreme events are more likely to occur under the dashed distribution. Tail indices such as
Hill’s and Pickand’s quantify this heavy-tailness.
Resnick (1997) points out that, while both the Hill and the Pickands (and other similar) indices are useful
to compare datasets coming from heavy-tailed distributions, one needs to have ex-ante knowledge or other
types of evidence suggesting heavy-tails. Thus, if the data come from a distribution with exponential tails,
these diagnostic tools are not expected to perform well. Thus, when one has different types of event-size data,
Resnick (1997) suggests employing the moment estimator developed by Dekkers et al. (1989). This metric is
sensitive to both thin and heavy tails and, while it is not bounded, negative values suggest exponential-like
tails, while positive ones indicate heavy tails. Thus, in terms of assessing climate security vulnerability, one
could say that a higher moment estimator denotes higher vulnerability as extreme events are more likely to
occur.
Next, let us provide the formal definition of the moment estimator as introduced by Dekkers et al. (1989).
Let X denote a random variable on climate event sizes with order statistics X(1) ≥ X(2) ≥ · · · ≥ X(n), where
n denotes the sample size. For the kth order statistic defining the beginning of the upper tail, and for
r = 1, 2, define
7The starting point of the tail of a distribution is often determined by choosing an order statistic that lies beyond the 66th
percentile.
11
probability of occurence
∑k ( )
(r) 1 X r
(i)
H(k,n) = log . (1)
k X
i=1 (k+i)
Then, the moment statistic is defined as
(1)
γ̂n = (k,n) + 1− 1/2
H . (2)
1− (1) (2)
(H(k,n))
2/H(k,n)
(1)
Note thatH(k,n) corresponds to the Hill index. Effectively, the moment estimator estimates the parameter
γ of the extreme value distribution Pr(x) = exp{−(1+γx)−γ−1}. Parameter γ determines the heavy-tailness
of the distribution. Dekkers et al. (1989) show that γ̂n converges in probability to γ as n → ∞. As we have
mentioned previously, a non-negative γ̂n indicates heavy tails, while negative values suggest thin ones.8
Thus, the CSI uses this index to assess the extreme-event component in each type of event.
Note that an empirical challenge of estimating heavy-tail indices tends to be the scarce availability of
large-scale data, as extreme events usually ‘show up’ in large datasets. Hence, to address this, we produce
a bootstrap sample of size nb >> n of the event-size dataset and compute γ̂n . We repeat this procedure
b
several times and report the average value of γ̂n obtained from the ensemble of bootstrapped samples. While
b
the moment estimator is not bounded below or above, in empirical studies it typically tends to hover in the
range of -1 to 1 (see Brooks et al. (2005) for applications using financial data). Therefore, one can use this
range as the reference space to assess the likelihood of experiencing extreme events. Furthermore, from a
qualitative point of view, the zero value provides an intuitive threshold to know if a particular type of event
is governed by a heavy or light-tailed distribution.
3.2 Institutional fragility
The quality of institutions plays a prominent role in the literature of conflict studies, especially in relation
to the recurrence of civil wars (e.g., see Walter (2004, 2015)). For the CSI, we are interested in the ability
of a government to adapt and respond to climate shocks and their consequences within the wider ecological,
social, and economic systems. To capture that, we rely on the Governance dimension of The Bertelsmann
Stiftung’s Transformation Index (BTI), an index based on expert assessment that has been widely used by
both international organizations (e.g., Fabra and Ziaja (2009)) and scholars (e.g., Hanson and Sigman (2021);
Knox (2021)). More specifically, we employ the indicator Steering Capacity, which measures three critical
features of governments’ institutional capacity 1) prioritisation, 2) implementation, and 3) learning. The
first aspect represents the capability of keeping strategic priorities during crises or stalemates, maintaining a
8In fact, γ = 0 yields a Gumbel distribution, which is another heavy-tailed one.
12
long-term perspective that goes beyond immediate electoral concerns and an effective organisation of policy
measures. The second is the ability to achieve its strategic priorities and declared objectives. Finally, the
third aspect captures innovation and flexibility in policymaking, both in terms of policy outputs and guiding
principles for policy formulation.
3.3 Connectivity
Let us recall that the aim of measuring the connectivity of a system in the context of the CSI is to assess
the “easiness” with which a shock in a particular policy domain or development dimension may reach one
or more different ones. As explained in subsection 2.4, by dimension or policy domain we mean broad
categories that encompass multiple development indicators as their target populations or policy instruments
can be considered somehow close or related. In network parlance, these dimensions are known as labels
that define communities of nodes. Here, nodes represent indicators, and the links between them capture
the potential that a shock starting in one indicator reaches another one. Thus, the end goal of this module
is to measure how much node connectivity takes place between communities (development dimensions) in
relation to how much happens within them. To achieve this, we need to break down our methodology into
three steps: (1) estimating conditional dependencies, (2) constructing a compounded conditional dependency
(CCD) network, and (3) estimating the modularity of the CCD network. Let us explain one step at a time.
3.3.1 Conditional dependencies
First, we measure the interdependencies between indicators using the information contained in their time-
series. While there exists a large number of methods to estimate networks from sets of time-series, the vast
majority rely on long series, at least of the order of hundreds of observations. Ospina-Forero et al. (2022)
provide a comprehensive overview of different classes of methods and assess the most adequate ones when
dealing with short time-series such as those from development indicators. From these potential methods, the
most suitable one for our application is one of sparse Bayesian networks (sparsebn) developed by Aragam
et al. (2019).
The method sparsebn is part of a larger family of so-called graphical models that construct a directed
acyclic graph of conditional dependencies between indicators.9 Usually, these methods start with a proposed
directed graph and, then, perform conditional independence tests across all the indicators to discard edges.
This process is repeated until one achieves the acyclical property. What makes sparsebn particularly well-
suited for development indicators is that it was designed to work with short time-series and a large number
9In network analysis, directedness means that the network edges point in one direction. Acyclicality means that, if one starts
a walk on a network, it is impossible to return to the initial node of the walk (there are no cycles).
13
of variables. It achieves this by sacrificing network density in the underlying graphical model, hence the
sparsity term in its name.10
It is important to mention that, while these models estimate links in terms of conditional dependencies
that are often interpreted as causal, in the context of the CSI, these relationships cannot be considered
causal; only conditional dependencies. Generally speaking, this is because development indicators are the
result of vertical causal chains. In other words, causal inference methods such as graphical models are
designed to study systems that operate roughly at the same level of aggregation (e.g., clinical studies), but
complex adaptive systems, such as an economy, differ from such configurations as interventions take place
at the micro-level while their outcomes are measured at the macro one. This is extensively discussed by
Guerrero and Castañeda (2020, 2021); Guerrero et al. (2023) in the context of the SDGs. To provide a brief
explanation of why one should not make causal claims from these estimates, consider an arrow i → j that
represents a change in indicator j conditioned by a change in indicator i, not a causal link. That is, the
existence of i → j means that, if we observe a change in j, a change in i was likely to have taken place.
However, a change in i does not necessarily trigger a change in j; otherwise it would be a causal link.11 In
terms of the model, a positive edge i → j indicates a higher likelihood of j growing, while a negative one
translates into a lower likelihood.
The resulting object from this step is an adjacency matrix A representing the acyclical network structure
of conditional dependencies between indicators. This network, however, does not allow us yet to measure
connectivity. The reason for this is that we are interested in indirect dependencies, as these are informative
about structural relations within the system. Thus, in the next step, we explain how to construct a denser
network that captures these indirect connections.
3.3.2 Compounded conditional dependency network
To motivate this step, let us use a theoretical example of a network where each node belongs to a community
or development dimension. Recall that the aim of the connectivity module is to quantify how different
communities facilitate the reach of shocks. Thus, for this example, let us assume that we are trying to
count the links between and within communities using the directed acyclic graph obtained from sparsebn.
Figure 4 shows a hypothetical example of a network of conditional dependencies. Here, we can see that
community A has direct links to communities B and C, but not to D. Nevertheless, it is clear that, should
10A virtue of Bayesian approaches such as sparsebn is that they allow the use of ex-ante knowledge through priors. Hence,
the user can provide a “white list” of edges that should be part of the estimated network, as well as a “black list” of edges
that should not, as they would mean false positives. This capability facilitates co-production with relevant stakeholders by
incorporating their expert knowledge in these estimates.
11Conditional dependencies are not plain correlations either. A correlation is just a co-movement of two variables, which
could be produced by a third variable, so that no conditioning between i and j would be necessary.
14
there be a shock in any node in A, it is possible that its effects could reach community D through indirect
channels. For example, one potential path for a shock in A2 is A2 → B3 → B5 → C1 → D1. Like this,
there are many potential paths through which a shock in community A could impact D. It is precisely the
implied structure of these indirect impacts that we aim to quantify to capture the connectivity of the system
across development dimensions.
Figure 4: Example of a network of conditional dependencies
A2 B3 C2 D5
D2
A1 B1 B2 B5 C1 D1 D4
D3
A3 B4 C3 D6
Notes: Nodes represent development indicators. They are coloured according to hypothetical development dimensions or policy
areas.
If one were to directly assess connectivity using the network presented in Figure 4, the community-level
connectivity structure would be the one shown in Figure 5. Clearly, this network leaves out several indirect
channels, as community D is only connected to C; not to A nor B. Thus, it is necessary to construct a dense
network that captures the implied structure of indirect paths. Such a network is denser than the one of
conditional dependencies, and provides the information needed to assess how “contained” would a shock to
a particular community be.
Figure 5: Connectivity between development dimensions implied by the network of conditional dependencies
A B
C
D
Notes: Colours represent hypothetical development dimensions or policy areas.
We construct a second network by compounding the conditional dependencies across the paths connecting
two given nodes i and j. Given the adjacency matrix A it is possible to find all the possible paths from i
15
to j through algorithms such as breadth-first search or depth-first search.12 Let the n-tuple P = (i, . . . , j)
denote a path from i to j, and P(i,j) the set of all paths from i to j. Then, the compounded conditional
dependency from i to j is
1 ∑ |P∏|−1
Ci,j = A .
|P(i,j)| P (3)
k,k+1
P∈P(i,j) k=1
Essentially, what Equation 3 does is to multiply all the weights along a path from i to j–the compounded
conditional dependency (CCD)–and, then, obtain the average CCD across all the possible paths from i to j.
Finally, to construct the CCD network, we need to filter only those values Cij > 0. The reason is that, given
the normalisation of the development indicators–where higher values denote better outcomes–a negative
shock (the relevant one for the CSI) comes in the form of a reduction in the value of an indicator, so the
CCD needs to be positive to reflect an indirect negative impact. Thus, by collecting all positive CCDs, we
construct an adjacency matrix C that encodes the network of compounded conditional dependencies.
3.3.3 Modularity
Once we have constructed the CCD network, we can compute a popular metric known in network science
as modularity. In a nutshell, modularity measures the structural balance between links within and between
communities in a network. In the context of the CSI, recall that communities are given by the development
dimensions. Hence, a high modularity would indicate a tendency to exhibit more within-community edges
than between them. Thus, in highly modular systems, a shock to a particular community is more likely to
be contained in that community.
The specific modularity measure that we employ is des∑igned for directed weighted networks, and was
developed by Leicht and ∑Newman (2008). First, let m = i,j Ci,j denote the total weight∑s in the CCD
network. Then, souti = j Ci,j is the total ‘outgoing strength’ of node i, while sini = j Cj,i is the
‘incoming’ one. Finally, modularity is defined as
1 ∑[ ]
sout
Q = C i sin
i,j − j
δc c , (4)
m m i j
i,j
where δc i d c t r u c i n
ic is an n i a o f n t o returning 1 if i and j belong to the same community, and 0 otherwise.
j
In its original form, the modularity score ranges from -1 to 1, with negative values indicating a low
modular structure and positive ones a high one. To be consistent with the direction of the extreme-events
module, let us define the connectivity index as
12Note that this task is efficient in the CSI because the network of conditional dependencies is acyclic.
16
C = −Q. (5)
Higher levels of connectivity indicate less modular structure and, hence, a higher risk of shock propagation
outside the community that originally experienced it. A value of C = 0 indicates that the structure is as
modular as a random network would be. Thus, one could interpret that negative values of connectivity would
tend to contain shocks to specific development dimensions and generate less pressure on the institutional
buffers.
3.4 Synchronicity
There exist various methods to quantify the synchronisation of two time-series. In the CSI, we use an
approach that has become a standard in the study of neuroscience, pioneered by Lachaux et al. (1999), and
that is well suited to work with short time-series. This method takes a signal and extracts information on its
instantaneous phase (the position of a waveform within its cycle at any given moment in time) of two time-
series and calculates its angular difference, i.e., the phase locking value (PLV). By computing the PLV over
all pairs of signals, we obtain the average PLV of the system that describes its degree of synchronisation.
The original PLV goes from 0 to 1, where 1 is full synchronisation and 0 is none. To make this module
consistent with the rest of the CSI, we re-normalise the PLV to be between -1 and 1, such that 1 means
full synchronisation and -1 none. Thus, the interpretation of the PLV is that larger values mean a higher
vulnerability as the various responses to extreme events across a country or region may happen at a similar
rhythm, imposing additional pressures on institutional buffers.
Next, let us provide further details on how to transform development indicators into waveform signals
and, then, compute the PLV. Let X = x1, x2, . . . , xT denote a time-series with T observations. To detrend
this series, we take its first differences and obtain Xd = (x2 − x1), (x3 − x2), . . . , (xT − xT−1). Next, take
differences with respect to the mean and normalise by the standard deviation, so we obtain
xd
xn t − µ̂
t = Xd
, (6)
ρ̂Xd
where µ̂Xd and ρ̂Xd are the sample mean and standard deviation of the detrended time-series respectively.
Once the time-series has been pre-processed to focus on its wave features, we need to transform the
normalised series into an analytical signal by applying the Hilbert transform.13 From this transformation,
we obtain the phase ϕx(t) (which is the imaginary part resulting from the Hilbert transformation), so the
13The Hilbert transform is a signal-processing method with a certain technical depth. We refer the reader to more specialised
readings in signal processing as the method is very standard in this domain.
17
PLV between two time-series X and Y as defined by Lachaux et al. (1999) is
∣ ∣
1 ∣∣T∑−
PLVx,y = ej( x
T − ∣ 1
ϕ (
1 ∣ ∣
t)−ϕy(t))∣∣∣ , (7)
t=1
where j reverts the angular difference to an imaginary number.
Finally, averaging over a dataset with N time-series and re-normalising the PLV, we obtain our syn-
chronicity module index
2 ∑
S = PLVi,j − 1. (8)
N
i,j
3.5 Computing the CSI
In summary, we have discussed the different methods used to quantify the four modules of the CSI: (1)
extreme events likelihood, (2) institutional fragility, (3) connectivity, and (4) synchronicity. Each of these
modules yields an index that hovers in the -1 to 1 space, where larger values can be interpreted as a higher
vulnerability in the corresponding module. Thus, if one considers these values as coordinates in the space
of climate security vulnerability, then the area within these points provides a reduced quantification of the
degree of such vulnerability. In Figure 6 we show the same polygon from Figure 1 overlaid on the maximum
area that could be produced by setting each module to its worst value. The CSI is the area of the inner
polygon as a fraction of the area defined by the outer one. Thus, higher values for the CSI denote more
climate security vulnerability. Since the extreme events modules are not bound by 1, the CSI goes from 0
to infinity, but it is unlikely to expect values beyond 1.
The Python package accessible in https://github.com/oguerrer/CSI provides all the necessary func-
tions to compute the CSI, as well as a tutorial to walk the reader through the data preparation. In the next
section, we show an application of the CSI to the case of Kenya.
18
Figure 6: Quantification of the CSI
CSI: 0.32
extreme events
 type II
1.00
0.75
extreme events 0.50
 type I 0.25 extreme events
0.00  type III
0.25
0.50
0.75
connectivity synchronicity
institutional
fragility
Notes: Outer rings represent worse levels in each module.
4 An application to Kenya
The institutional setting that we choose as the first implementation of the CSI is Kenya. This country
represents an interesting case study to analyse the effectiveness of the CSI in assessing the CSN. In fact,
according to Germanwatch, the country is at high risk of extreme weather events, scoring 19.67 in the
2018 Climate Risk Index, which places Kenya in the top ten countries most threatened by natural disasters
(Eckstein et al., 2019). At the same time, conflict severity is only limited in the country, as shown by the
2022 Conflict Severity Index provided by ACLED. This multifaceted index incorporates the complex nature
of conflicts by assessing their deadliness, danger, diffusion, and fragmentation.14
Our exercise starts by selecting five policy domains relevant to the CSN in this specific context: Conflict,
Environment and Climate, Natural Resources, Resilience/Buffer, and Socio-economy. This choice is informed
by domain experts from CGIAR, who helped identify the CSN dimensions and the corresponding indicators
(proxies), showing how the CSI can incorporate knowledge co-production processes in its framing. Table 2
reports the number of indicators, their average, and standard deviation by CSN dimension. In Table 3 of
Appendix A we list all 65 indicators, with their source and corresponding CSN dimension.
Since many indicators present time-series with a significant number of missing values, we impute them
using Gaussian Processes (GPs) (Rasmussen and Williams, 2005). GPs are a family of highly flexible machine
14ACLED Conflict Severity Index : https://acleddata.com/conflict-severity-index/#s5.
19
Table 2: Descriptive statistics of development indicators by CSN dimension
CSN dimension N Mean Std Dev
Conflict 4 0.657 0.294
Environment and Climate 14 0.481 0.258
Natural Resources 6 0.501 0.307
Resilience/Buffer 9 0.522 0.304
Socio-economy 32 0.532 0.359
Notes: All indicators have been normalised between 0 and 1, and higher values represent better outcomes. The table reports
(at the level of each CSN dimension) the number of indicators, together with their mean values and standard deviations over
the time period considered (2000-2022).
learning algorithms that have proven to be effective in modelling complex non-linear dynamics. GPs have
already been employed in the context of development indicators to study composite indices (Becker et al.,
2017) and to impute missing data in SDG indicator time-series (e.g., see Guerrero and Castañeda (2022);
Guerrero et al. (2021); Guariso et al. (2023)).
Once the missing values are imputed and the series normalised,15 we apply the methods presented in
subsection 3.3 and subsection 3.4 to measure connectivity and synchronicity in the case of Kenya. For
institutional fragility, we take the maximum value of the BTI’s indicator Steering Capacity over the period
considered.16 For the likelihood of extreme events, we compute the metrics discussed in subsection 3.1 using
simulated data drawn from two arbitrary distributions.17
Figure 7 shows the results of this exercise. The value of the CSI for Kenya is just slightly above the
0 threshold (0.21), meaning that the country exhibits only limited climate security vulnerability, a result
that is in line with Kenya’s score on the ACLED Conflict Severity Index. Arguably, the relatively low value
of the CSI is driven by the negative scores in connectivity, synchronicity, and institutional fragility, which
counterbalance and mitigate the adverse effect of the high likelihood of extreme weather events.
15After the imputation procedures, all time-series cover the period 2000-2022.
16The value was normalised using the theoretical boundaries of the score (i.e., [1, 10]), and inverted to be in the range [−1, 1],
as the other metrics included in the CSI.
17More specifically, we randomly drew 1000 observations from a generalised normal distribution (with shape parameter
β = 0.95) and a Pareto distribution (with shape parameter b = 2).
20
Figure 7: An application to Kenya
CSI: 0.21
extreme events
 type II
1.00
0.75
0.50
0.25
extreme events 0.00
 type I 0.25 synchronicity
0.50
0.75
connectivity institutional
fragility
Notes: Outer rings represent worse levels in each module.
5 Conclusions
In this methodological note, we propose the Climate and Security Index (CSI), an innovative and scalable
framework to understand the impact of climate shocks on the wider ecological, social, and economic envi-
ronment. Our approach incorporates multiple drivers of the Climate Security Nexus (CSN) from climatic,
conflict, socio-economic, agricultural, and institutional dimensions. The structural features of the system
described by these dimensions are assessed through a combination of different analytical tools and metrics
from diverse disciplines. Such methods are suitable to deal with the coarse-grained nature of development
indicators, which are often used to measure these policy domains. While the framework results in a single
metric that can be intuitively depicted through a graphical representation of a “vulnerability space”, its
modular design allows users to narrow down the analysis to individual structural features of the system,
which is key for further investigation with complementary methods and the design of long-term resilience
interventions. The methodology is applied for a specific case-study using national-level data for Kenya,
finding results that are consistent with other measures of conflict severity, while allowing for a deeper under-
standing of the underlying structural features characterising the CSN in the country. Further research will
extend the analysis by identifying a set of common CSN dimensions and development indicators, to conduct
cross-country comparisons and assess climate security at the regional level.
21
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Methodological Note for the Climate and Security Index
Appendix
Omar A Guerrero1, Daniele Guariso1, Theresa Liebig2, Ony Minoarivelo2, Alessandro
Craparo2, and Ashleigh Basel2
1The Alan Turing Institute
2CGIAR Focus Climate Security
26
A Development indicators by CSN dimension
Table 3: List of indicators
CSN dimension Source Name
Environment and Climate ECMWF Average annual rainfall
Environment and Climate CHIRPS Coefficient of variation of rainfall (Season: Jan-June)
Environment and Climate CHIRPS Coefficient of variation of rainfall (Season: Jul-December)
Environment and Climate CHIRPS Days with evapotranspiration ratio below 0.5 (Season: Jan-June)
Environment and Climate CHIRPS Days with evapotranspiration ratio below 0.5 (Season: Jul-December)
Environment and Climate CHIRPS Days with max temp above 30 degrees (Season: Jan-June)
Environment and Climate CHIRPS Days with max temp above 30 degrees (Season: Jul-December)
Environment and Climate CHIRPS Days with waterlogging (Season: Jan-June)
Environment and Climate CHIRPS Days with waterlogging (Season: Jul-December)
Environment and Climate CHIRPS Heat stress on cattle (Season: Jan-June)
Environment and Climate CHIRPS Heat stress on cattle (Season: Jul-December)
Environment and Climate CHIRPS Total annual rainfall
Environment and Climate The Climatology Lab Actual evapotranspiration
Environment and Climate The Climatology Lab Climate water deficit
Resilience-Buffer World Bank Open Data Agriculture VA
Resilience-Buffer Worldwide Governance Indicators Control of corruption
Resilience-Buffer World Bank Open Data GDP per capita, PPP
Resilience-Buffer Worldwide Governance Indicators Government effectiveness
Resilience-Buffer World Bank Open Data Industry VA
Resilience-Buffer Worldwide Governance Indicators Political stability-No violence
Resilience-Buffer Worldwide Governance Indicators Regulatory quality
Resilience-Buffer Worldwide Governance Indicators Rule of law
Resilience-Buffer Worldwide Governance Indicators Voice and accountability
Conflict ACLED Total number of conflict events
Conflict ACLED Total number of conflict fatalities
Conflict ACLED Total number of unique conflict subtype events
Conflict ACLED Total number of unique conflict type events
Socio-economy Varieties of Democracy Gender equality in respect for civil liberties
Socio-economy Varieties of Democracy Urban-rural location equality in respect for civil liberties
Socio-economy Varieties of Democracy Political group equality in respect for civil liberties
Socio-economy Varieties of Democracy Access to public services distributed by urban-rural location
Socio-economy Varieties of Democracy Access to state business opportunities by urban-rural location
Socio-economy Varieties of Democracy Access to state business opportunities by political group
Socio-economy Varieties of Democracy Access to state business opportunities by gender
Socio-economy Varieties of Democracy Access to state jobs by social group
Socio-economy Varieties of Democracy Health equality
Socio-economy Varieties of Democracy Power distributed by urban-rural location
Socio-economy World Bank Open Data Prevalence of stunting, height for age (modeled estimate, % of children under 5)
Socio-economy World Bank Open Data People using at least basic drinking water services, urban (% of urban population)
Socio-economy World Bank Open Data People using at least basic drinking water services, rural (% of rural population)
Socio-economy The Global Health Observatory (WHO) Prevalence of underweight among adults, BMI < 18 (age-standardized estimate) (%) Female
Socio-economy The Global Health Observatory (WHO) Prevalence of underweight among adults, BMI < 18 (age-standardized estimate) (%) Male
Socio-economy IDMC Conflict stock displacement
Socio-economy IDMC Disaster internal displacements
Socio-economy UNHCR Asylum-seekers
Socio-economy UNHCR IDPs of concern to UNHCR
Socio-economy UNHCR Others of concern
Socio-economy UNHCR Refugees under UNHCR’s mandate
Socio-economy KNOMAD Migrant remittance inflows (US$ million)
Socio-economy World Bank Open Data Employment in agriculture (% of total employment) (modeled ILO estimate)
Socio-economy World Bank Open Data Individuals using the Internet (% of population)
Socio-economy World Bank Open Data Rural population (% of total population)
Socio-economy World Bank Open Data Unemployment, total (% of total labor force) (modeled ILO estimate)
Socio-economy World Bank Open Data Age dependency ratio (% of working-age population)
Socio-economy IHME Difference of years of education (male - female)
Socio-economy IHME Piped water (% access)
Socio-economy IHME Sanitation facilities (% access)
Socio-economy IHME Years of education female
Socio-economy IHME Years of education male
Natural Resources World Bank Open Data Agricultural land (% of land area)
Natural Resources World Bank Open Data Forest area (% of land area)
Natural Resources World Bank Open Data Crop production index (2014-2016 = 100)
Natural Resources World Bank Open Data Food production index (2014-2016 = 100)
Natural Resources World Bank Open Data Livestock production index (2014-2016 = 100)
Natural Resources USGS Net primary production
27