**2. Methodology**

#### *2.1. Climate Change Modelling*

We implemented climate modelling in a GIS environment for reference as well as projected climates. Available monthly climate data were read and converted to variables required for subsequent calculations. We used time-series data from the Climate Research Unit (CRU) at the University of East Anglia, the Global Precipitation Climatology Centre (GPCC), and the EU WATCH Integrated Project. We obtained the CRU TS v3.21 (time-series) datasets from the British Atmospheric Data Centre (BADC), highlighting month-by-month climatic variations over the last century covering the period from January 1901 to December 2012. CRU TS v3.21 data were calculated on 0.25 × 0.25 degree grids. We downloaded the GPCC v6 full re-analysis data product and concluded the spatial interpolation to 5 arc-minutes resolution for the period 1981–2010. We obtained the daily data at 0.5-degree resolution from the WATCH Integrated Project data repository; we compiled within-month precipitation distribution and computed the deviation of daily temperatures from respective monthly means for each month for the period 1981–2010.

We used the results of the IPCC's AR5 climate model for two representative concentration pathways (RCPs: 2.6 and 8.5) to characterise a range of possible future climate distortions for the periods 2041-2070 (2050s) and 2071-2100 (2080s). The RCPs were developed and documented in a special issue of climate change [21]. We implemented climate model simulations based on RCPs as part of the Coupled Model Inter-comparison Project Phase 5 (CMIP5) [22] and extracted monthly mean temperature and precipitation data from the WorldClim 30 arc-second raster databases [23]. We analysed the multi-model ensembles for two climate forcing levels of the RCPs based on spatial data from the IPCC's AR5 CMIP5 process and corrected data bias, downscaling it 0.25-degree as in the Inter-sectoral Impact Model Inter-comparison Project (ISI-MIP) [24]. In order to calculate the ensemble mean, we used the ISI-MIP data at 0.25-degree resolution of five climate models (GFDLESM2M, HadGEM2-ES, IPSL-CM5A-LR, MIROC-ESM-CHEM, and NorESM1-M).

#### *2.2. Fuzzy Cognitive Mapping*

We conducted the perception mapping study aided by the fuzzy cognitive maps-based approach introduced by Kosko in 1986 [25] to document communities' perceptions about the direct and indirect impacts of climate variability and change on di fferent livelihood assets. The FCM approach captures the functioning of a complex system based on people's perceptions [26]. The process of data capture in the FCM approach is considered quasi-quantitative because the quantification of concepts and links can be interpreted in relative terms [27–29]. In order to generate data, the participants debated the cause-e ffect relations between the qualitative concepts and generated quantitative data based on their experiences, knowledge, and perceptions of inter-relationships between the concepts [26–28,30,31].

#### 2.2.1. Main Aspects of Fuzzy Cognitive Maps

FCMs are graph-based structures, describing signed weighted digraphs [25]. They can handle vagueness while being capable of incorporating and adapting human knowledge through fuzzy logic. They form a component of soft computing providing, thereby, a simple but powerful tool for analysing, representing, and simulating dynamic systems [32].

The structure of FCMs consists of concepts (i.e., nodes) *C*1, *C*2 ... *Ci*, and connections between them. All this is represented by the adjacency matrix W [ ]. The concepts are mapped to the real-valued activation level where *Ci* takes values in the interval [0,1], which is the degree to which the observation belongs to the concept (i.e., the value of the fuzzy membership function). As a consequence of the dynamic interactions of connected nodes, the concept's state changes over time. The reasoning is performed as the calculation of Equation (1), where *f* ( ) stands for a hyperbolic transformation function Equation (2), ensuring that the concept defined value falls within the interval [0,1] and *f* ( ) is given by Equation (2), where *C*—parameter, *C* > 0.

$$\mathbf{C}\_{i}^{(t+1)} = f \begin{cases} \mathbf{C}\_{i}^{(t)} + \sum\_{\substack{j=1 \\ j=1 \\ i \neq j}}^{n} \mathbf{C}\_{j}^{(t)} \times \mathbf{W}\_{ji} \\ \mathbf{i} \neq j \end{cases} \tag{1}$$

$$f(\mathbf{x}) = \frac{e^{\lambda x} - e^{-\lambda x}}{e^{\lambda x} + e^{-\lambda x}}, a \in \mathbb{R}^+ \tag{2}$$

The edges *Wij* displayed in the dimensions of the matrices denote the degrees of the causal relationship (i.e., the weight of the edge or influences between the connected nodes) and typically lie between [−1, 1]; whereas *Wij* > 0 implies that *Ci* increases *Cj*, *Wij* = 0 means no relation and *Wij* < 0 means *Ci* decreases <sup>C</sup>*j*. Therefore, the adjacency matrices are not symmetric as per definition. The diagonal entries (e.g., *Wii*, *Wjj*) in *W* reflect the effect on it. With increasing uncertainty, fuzzy rules, or fuzzy numbers may be used to describe the weights of the connections [25,32].

#### 2.2.2. Constructing Fuzzy Cognitive Maps

#### **Step 1: Obtaining fuzzy cognitive maps from community groups**

The majority of marginal and poor people across the globe rely on climate-sensitive livelihood activities that are highly susceptible to increase in temperature and variability in precipitation patterns, along with extreme climatic events, such as cyclones, floods, droughts, etc., making them highly vulnerable to climate change [33]. Hence, in order to obtain fuzzy cognitive maps, we selected marginal farmers possessing less than two acres of land and some livestock as our stakeholders. The steps of constructing fuzzy cognitive maps from stakeholders/farmers are given in Section 2.2.2.

A consensus of the local community was obtained with regard to the summer and winter temperatures, as well as precipitation variability increase over the last 10 to 15 years. We also sought community opinion in the context of increasing intensity and frequency of climatic extremes. The communities perceived an overall increase in temperatures and precipitation variability. The communities also perceived an increase in climate-related extremes, including cyclonic storms and floods. We divided the local community members, after the group discussion, into groups of four to five individuals. We formed the groups according to simple wealth-ranking allocating individuals with the same landholdings/ number of livestock within a single group while conducting gender-wise segregation. This helped in neutralising power dynamics within each group. We demonstrated the construction of fuzzy cognitive maps to the participants with the help of a disparate context. We asked the following questions from each of the 46 community groups:


The participants designed cognitive maps relevant to the central concept: Increased climate variability and change. They laid out concepts pertinent to the central concept, showing impacts of climate variability and change on their lives and livelihoods and adaptation practices adopted; they also assigned cause–effect interconnections between the concepts. Stakeholders assigned individual weights to each connection on a scale of 1–10, with 1 representing the minimum impact and 10 the maximum. Researchers scaled down these weights to a scale of 0.1–1, with 0.1 representing the minimum impact and 1 the maximum [26,27,30].

#### **Step 2: Coding of individual cognitive maps into adjacency matrices**

We coded individual cognitive maps into adjacency matrices listing the same concepts on the vertical and horizontal axes. Weights assigned by the stakeholders were coded into the adjacency matrix. A value is coded into the matrix if a connection exists between two concepts [26–28,34].

#### **Step 3: Quantitative aggregation of individual cognitive maps**

We aggregated each coded map to construct a social cognitive map (SCM) through matrix addition [26–28,30]. Thus, the SCM we obtained represents the perception of all the 46 community groups. SCM gives a better representation of system dynamics yielding a more accurate, reliable, and comprehensive understanding of a system [26,27,30].

#### **Step 4: Qualitative aggregation of the social cognitive map**

In order to organise the data and make it easier to understand, we condensed the concepts obtained from the SCM into broader categories based on their nature [26,27,30]. We followed it up with calculations for an arithmetic mean of the weights of concepts mentioned in the SCM. We did this to identify interconnections between the broader encompassing concepts [26,28,30,35]. The qualitatively aggregated SCM comprises 23 concepts.

#### *2.3. FCM-Based Simulations*

The adaptation strategies that are likely to reduce climate risks and increase resilience adequately may be classified as effective adaptations. What cannot be ruled out is the possibility of an adaptation deficit ('a failure to adapt adequately to existing climate risks' [36]). Having implemented all adaptations in the area, climate risk possibilities can arise, presenting limits to adaptation. Therefore, it is crucial to understand the effectiveness of adaptation strategies.

In order to evaluate the effectiveness of current adaptation interventions, we conducted FCM-based simulations with the help of the aggregated SCM. Simulating the FCM model gives a deeper understanding of the concepts' behaviour, their relations, and the extent to which one concept has an impact on the rest. The simulation process was conducted by 'clamping/activating' the initial values of the key concepts (in Equation (1)) until the system reached a stabilisation point (known as the system steady-state). We developed a baseline by 'clamping/activating' the initial values of concepts C1—'climate variability and change' and C2—'climatic extremes' at |1|. This was done by taking into consideration the climate change projections in the region.

In FCMs, each concept varies from 0 to |1| where 0 means 'non-activated' and |1| means 'activated'. When one or more concepts are 'clamped/activated,' the activation spreads through the matrix following the weighted relationships in the FCM matrix. An iteration produces a new state vector with 'activated' concepts and 'non-activated' concepts [31,37]. The resulting concept values are used to interpret the outcomes of a particular scenario [27,28,31,37]. We multiplied the input vector concepts (Table 1) with the adjacency matrix and applied a squashing function (Equation (2)) after every multiplication as a threshold function. We iterated the process until the system (output vector) reached a steady-state. The FCMWizard tool ran the simulations. The FCMWizard can also perform simulations for different possible scenarios, in various scientific domains, using a very intuitive graphical user interface [38].


**Table 1.** Various future scenarios using fuzzy cognitive maps (FCM)-based simulations.

The first established approach in scenario planning is the selection of key concepts. Filtering the key concepts helps in linking storylines to the quantitative model while focusing on significant concepts that often have strong direct or indirect e ffects on the goal. It can, at the same time, significantly change the balance of the whole system. While conducting the FCM-based scenario analysis, recognition of crucial concepts mainly relies upon communities' perceptions, although some characteristics were elicited from the model facilitates the procedure. We identified four key adaptation strategies in the study area for assessing their e ffectiveness (Table 1). These concepts were selected as they were among the concepts with the highest centrality (see Table S1(a)) and could well influence the dynamics of the system.

Scenario 1 is devoted to increasing the concept of 'dykes and embankments', by 'clamping' it to one. We adopted the same procedure for the following three key concepts: 'water resource management', 'sustainable agriculture and aquaculture practices', and 'strengthening local institutions' where Scenario 2, Scenario 3, and Scenario 4 referred to the increase in the above corresponding concepts ('clamped' to one). We developed the fifth scenario by combining all the four key concepts/adaptation strategies used in the previous scenarios. We also conducted a sensitivity analysis to ascertain the stability of the system.
