Estimation of the Extent of the Vulnerability of Agriculture to Climate Change Using Analytical and Deep-Learning Methods: A Case Study in Jammu, Kashmir, and Ladakh

Abstract

Climate stress poses a threat to the agricultural sector, which is vital for both the economy and livelihoods in general. Quantifying its risk to food security, livelihoods, and sustainability is crucial. This study proposes a framework to estimate the impact climate stress on agriculture in terms of three objectives: assessing the regional vulnerability (exposure, sensitivity, and adaptive capacity), analysing the climate variability, and measuring agricultural performance under climatic stress. The vulnerability of twenty-two sub-regions in Jammu, Kashmir, and Ladakh is assessed using indicators to determine the collective susceptibility of the agricultural framework to climate change. An index-based approach with min–max normalization is employed, ranking the districts based on their relative performances across vulnerability indicators. This work assesses the impact of socio-economic and climatic indicators on the performance of agricultural growth using the benchmark Ricardian approach. The parameters of the agricultural growth function are estimated using a linear combination of socio-economic and exposure variables. Lastly, the forecasted trends of climatic variables are examined using a long short-term memory (LSTM)-based recurrent neural network, providing an annual estimate of climate variability. The results indicate a negative impact of annual minimum temperature and decreasing land holdings on agricultural GDP, while cropping intensity, rural literacy, and credit facilities have positive effects. Budgam, Ganderbal, and Bandipora districts exhibit higher vulnerability due to factors such as low literacy rates, high population density, and extensive rice cultivation. Conversely, Kargil, Rajouri, and Poonch districts show lower vulnerability due to the low population density and lower level of institutional development. We observe an increasing trend of minimum temperature across the region. The proposed LSTM synthesizes a predictive estimate across five essential climate variables with an average overall root mean squared error (RMSE) of 0.91, outperforming the benchmark ARIMA and exponential-smoothing models by 32–48%. These findings can guide policymakers and stakeholders in developing strategies to mitigate climate stress on agriculture and enhance resilience.

1. Introduction

An increasing footprint of climatic variability has the potential to impact billions of people in terms of how they secure their sustenance. However, the implications of climate variability can vary in magnitude and severity. A global climate change phenomenon, as specified by the Intergovernmental Panel on Climate Change (IPCC) [1], refers to

“a change in the state of the climate that can be identified by changes in the mean and/or the variability of its properties, and that persists for an extended period, typically decades or longer”.

Researchers have been studying the effects of such dynamics that alter the configuration of the atmosphere for decades [2]. The progressively receding ice caps [3], rising sea levels, and rising global temperatures [4] provide a nominal estimate of changing environmental conditions. A plethora of such manifestations is attributed to climate change, like the increase in the incidence and number of extreme events, record temperatures [5], intense rainfalls, hailstorms, floods, droughts [6], and the outbreak of pests and diseases [7]. Severe exposure to such conditions may have long- and short-term repercussions on the economy [8] and livelihood. Crop efficiency and production have been observed to be influenced antagonistically as a consequence of climatic variability [9,10], increasing food and livelihood security issues. The thrust towards industrial modernization has already taken a heavy toll on plant and animal diversity. Long-term climatic stress could influence agriculture and horticulture in various ways, incorporating changes in average temperatures, patterns of precipitation, carbon dioxide concentration in the atmosphere [5], the nutritional quality of certain foods, water availability, agricultural productivity, and the growth of essential crops with a significant deterioration of soil. On the other hand, agriculture is the principal way in which land is used worldwide. About 1.2–1.5 billion hectares of land is under harvest, with another 3.5 billion hectares [11] being grazed. People utilize approximately another 4 billion hectares [11] of forest territory to different degrees [12,13]. Ensuring food security to accommodate the anticipated needs of the increasing global population is, thus, ineluctable. Agriculture is a requisite economic activity supporting the heavy burden of the working populace in India ($65\%$), although its share in the country’s GDP is declining. Moderate developments in the agrarian segment, in addition to changes in the climate, must be subject of significant consideration as they are closely linked to the food security and poverty status of a dominant part of the populace [14,15,16]. The dependence of the mass on farming practices and the risk of instability in agricultural production due to accumulating climatic stress increases the vulnerability of farmers and threat to the economy, development, and sustainability.

There are three main ways to address the threat of climate stress on the agricultural paradigm, namely (i) proactively predicting the implications of climate change on agriculture; (ii) actively studying the existing observable or perceivable effects of climate change; and (iii) passively framing adaptation policies for its mitigation measures. Our work focuses on the first two schemes of analysing climate change in terms of the three following objectives, namely characterising the vulnerability of the region to climate change; observing the forecasted trends of climate variables; and analysing the performance of agriculture in the current climatic scenario. Vulnerability assessment estimates the extent of climate change hazard, and is defined as the susceptibility and degree of risk of the region towards the impacts of long-term climatic variability, which depends on various geographic, economic, cultural, social, demographic, governance, institutional, and environmental factors [17]. The determinant variables and methodologies of estimating the vulnerability vary across studies [18,19]. A comprehensive assessment of the vulnerability of a system/region to climate change is recognized [1] as a three-fold process, namely assessments of sensitivity, exposure, and adaptive capacity variables. Exposure indicates the rate of climate variation [20] to which a region/system is exposed. Sensitivity specifies the degree to which a region/system is affected (positively or negatively, directly or indirectly) [17] and is a function of climate-related stimuli [20]. The response of the region/system that defines its recovery tendency from the effects of climate change in terms of countermeasures, potential, resources, behaviour, and technology is measured as adaptive capacity.

Deep learning has emerged as a powerful tool that has revolutionized various fields, including healthcare [21,22,23,24], education [25], and agriculture [26,27,28,29]. Its ability to process vast amounts of data and extract meaningful patterns has paved the way for transformative advancements [30]. In agriculture, deep learning has played a pivotal role in optimizing crop yields [26,31], monitoring soil conditions [32], and detecting pests and diseases early on, leading to increased productivity and sustainable practices. Statistical methods and deep learning has played a crucial role in assessing the extent of the vulnerability of agriculture to climate change, offering valuable insights into the potential impacts on crop production and guiding adaptation strategies [33,34]. By leveraging its ability to analyse complex datasets, deep learning algorithms can process diverse sources of information such as climate data, satellite imagery, and historical agricultural records. These models can identify intricate patterns and relationships that traditional statistical approaches may overlook, enabling a more accurate estimation of climate variability. One area where deep learning has made significant contributions is in crop yield prediction under climate change scenarios [35]. By training models on historical climate and agricultural data, deep learning algorithms can learn patterns and correlations that help estimate future yields [36]. These models can take into account various climate variables such as temperature, rainfall, and humidity. By incorporating these multidimensional inputs, deep learning models can provide the more precise predictions of crop yields under different climate change scenarios, helping farmers and policymakers understand the potential risks and plan accordingly. Recurrent networks in deep-learning are a valuable tool in estimating the extent of climate variability due to their ability to model temporal sequences, and identify intricate patterns and relationships that traditional methods may miss. This enables more accurate predictions of climate distributions, and helps identify the regions and crops that are most at risk. Deep learning’s capability to detect non-linear relationships and analyse historical trends contributes to a comprehensive understanding of the impact of climate change on agriculture, assisting in the development of effective adaptation strategies.

The aim of this paper is to assess the dynamics of agriculture-driven regions to climate change and their corresponding resilience. The significant contributions of this work are listed below:

1.

In this work, a standard dataset comprising forty-two determinant indicators was curated from the records of Digest of Statistics (Jammu and Kashmir) [37] for the years 1983 to 2020, in addition to five exposure indicators from NASA LaRC POWER [38] for the years 1983–2022 across twenty-two sub-regions (districts) of Jammu, Kashmir, and Ladakh (illustrated in Table 1). The descriptions of the variables defined in the dataset are illustrated in Tables 2 and 3. Seven additional indicators were derived from the curated exposure indicators.

2.

This study formalizes an index-based algorithm to estimate the span/extent of vulnerability of each sub-region to climate change.

3.

In this work, we analyse agricultural growth as a function of socio-economic, demographic, geographic, and climatic variables leveraging the benchmark Ricardian methodology. Each of the indicators is assessed for its contribution to the performance of agriculture.

4.

We study and present the forecasted trends of the climatic variables using a recurrent neural network-based approach to analyse climate change exposure in the studied region.

2. Recent Works

Depending upon the type of action undertaken to assess the vulnerability of agricultural systems in the presence of climate variability, this section is divided into studies of the impacts of climate change on the environment, works that discuss its observable and apprehensive impacts on agriculture and economy, proactive studies of vulnerability assessment, and studies on passive support and mitigation measures.

2.1. Studies on Climate Change and Environment

With reference to climate variability, the evident causal factors in the environment and their effects are apparent. The global average temperature increased by 0.74 ${}^{°}$C over the last 100 years and is projected to increase from 1.8 to 4.0 ${}^{°}$C by 2100 [39]. The notable predicted effects are sea-level rise [40], variability in precipitation patterns [41], delay/decrease in precipitation [42], increased temperatures [1,20,39], increased storminess and heatwaves [43], extreme weather conditions [44], droughts and floods [45], negative impacts on vegetation [46], loss of biodiversity [47], and the decreased availability of freshwater [48]. In similar studies, it has been observed that climatic stress may appear differently across geographical areas. In developing countries like India, where agriculture is the main occupation, the expected impacts include seasonal variation in temperature such as warmer winters [14] with a projected 2 ${}^{°}$C temperature rise in north India [49]. The increasing global population is estimated to have a positive correlation with the increasing rate of global carbon footprint [50], increase in the global temperature (due to anthropogenic activities) [48,51,52], extensive exploitation of fossils [53], deforestation and rapid urbanization [54], which is expected to increase climatic variability. Various researchers weigh the positive impacts of climate change with its negatives. Some studies show that increased levels of carbon dioxide ($C{O}_2$) could benefit certain plants and regions but is widely accepted to be harmful to the natural habitat [55]. Various studies show a correlation with a number of causal factors of climate change, such as the correlation of temperature balance and $C{O}_2$ concentrations [56] that contributes to approximately 77% of the concentration of GHGs [57], leading to global warming and environmental instability.

2.2. Studies on Agriculture, Economy, Livelihood, and Climate Stress

Several studies have evaluated the effects of climate variability on agriculture. There is a necessity to evaluate its impact on agriculture to minimize its associated risk. The global mean GDP loss is projected to be 1–5% for a 4 ${}^{°}$C warming [58]. Although the theories suggest that positive effects could also be witnessed, depending on the landscape. A study carried out by [59] in northwestern India revealed that rice (28%) and wheat (15%) could perform better under elevated $C{O}_2$ concentrations. However, impacts cannot be generalized across geographical regions. All optimistic scenarios predict an 8% increase in overall agricultural productivity [43], increased rice yields of 3.5–33.8% [60] and irrigation being optimized by 16–28% ) [61]. In contradiction, studies also predict a devastating effect on agricultural resources (in zero-response scenarios) by temperature-rise and rainfall variability, leading to various effects, such as food insecurity [59], and detrimental impacts on livestock growth and forage crops [44], a drastic decrease in food availability [62], a 4.5–9% reduction in major food crops [63], decrease in nutritional quality [58], 18% reduction in global water availability for agriculture by 2050 [62], economic instability and increase in pests, diseases, and pathogens [7].

2.3. Studies on Vulnerability Assessment

Estimation techniques that portray vulnerability assessment in region-level case studies are essential in determining the impacts of climate variability in agricultural settings. As such, multiple studies have performed vulnerability assessments on various dependent factors. A study by [64] represented a methodology for examining the susceptibility of Indian agriculture towards climate change at the regional level within the premise of various global effectors. Another study [65] proposed a statistical framework of vulnerability analysis, linking it to various exposure indicators, sensitivity indicators, and generic/specific adaptive capacity indicators. Indexing-based vulnerability assessment is followed in some studies. However, more models of vulnerability assessment have been explored [19]. The contribution of diverse effectors can vary across regions since vulnerability is shown [17] to be specific to geography and can be performed at many levels of the institution.

2.4. Studies on Mitigation and Adaptation Measures

Mitigation strategies help limit climate variability effects. Studies show the tremendous potential for adaptive capacity variables against climate risk. Mitigation measures like pollution control, afforestation [48], water system planning [45], disease control measures [66], pest-control measures, advanced water management technologies, minimizing environmental degradation [57], carbon sequestration, crop-selection, proper irrigation, usage of stress-resistant crops, soil conservation [67], manure management, cross vegetation, agroforestry, crop diversity, awareness, youth empowerment [68], adoption of scientific knowledge [69], education, and proactive policies [70] are seen by researchers to bring about agricultural sustainability. The agricultural sector has enormous potential to mitigate and adapt to climate change. In contrast, the absence of adaptation strategies, ignorance, lack of knowledge [63], poverty, and lack of technology are generically seen as hurdles to mitigation. Various developing countries in this paradigm are hence susceptible, unstable, sensitive, and vulnerable to climate risk.

3. Materials and Methods

3.1. Study Area: Area Selection and Its Agro-Climatic Setting

The present study intends to investigate the characteristics of agricultural growth in relationship with various intrinsic/extrinsic variables and assess the vulnerability of agriculture to climatic change in the region of Jammu, Kashmir, and Ladakh. This study area is situated in the northwestern portion of the Himalayan mountain range, characterised by significant variations in terrain elevation, snow-covered peaks, river systems, intricate geological formations, and diverse temperate plant and animal life. The studied area is centrally proximal to three climatic systems of Asia. The region of Punjab, characterised by a weak monsoon zone, is located in its southern border. It is bordered by the vast arid plateau of Tibet in its northeast. In contrast, the northwest border areas face the eastern limits of the Mediterranean climate. Two-thirds (2.3 million ha) of the total mountainous area of India (3.5 million ha) is found in this region. This region lies in the extreme north of the Himalayas. It constitutes about 67.5% of the northwest Himalayan region. There is diversity in the region’s agro-climatic conditions, ranging from temperate in Kashmir, cold arid in Ladakh, and sub-tropical in Jammu. However, the shift in micro-climatic scenarios varies widely across the whole area. A geographical outline of the area under study spans on a net area of about 101,387 km${}^2$ segregated into 22 sub-regions/districts (as shown in Figure 1).

Table 1. Global coordinates of the districts in the studied region.

District	Lat., Long.	District	Lat., Long.
Anantnag	33${}^{°}$ 49${}^{\prime }$ N, 75${}^{°}$ 15${}^{\prime }$ E	Jammu	32${}^{°}$ 44${}^{\prime }$ N , 74${}^{°}$ 51${}^{\prime }$ E
Bandipora	34${}^{°}$ 25${}^{\prime }$ N, 74${}^{°}$ 38${}^{\prime }$ E	Kathua	32${}^{°}$ 35${}^{\prime }$ N , 75${}^{°}$ 37${}^{\prime }$ E
Baramulla	34${}^{°}$ 10${}^{\prime }$ N, 74${}^{°}$ 22${}^{\prime }$ E	Kishtwar	33${}^{°}$ 19${}^{\prime }$ N , 75${}^{°}$ 46${}^{\prime }$ E
Budgam	33${}^{°}$ 55${}^{\prime }$ N, 74${}^{°}$ 38${}^{\prime }$ E	Poonch	33${}^{°}$ 42${}^{\prime }$ N , 74${}^{°}$ 15${}^{\prime }$ E
Ganderbal	34${}^{°}$ 13${}^{\prime }$ N, 74${}^{°}$ 47${}^{\prime }$ E	Rajouri	33${}^{°}$ 16${}^{\prime }$ N , 74${}^{°}$ 21${}^{\prime }$ E
Kulgam	33${}^{°}$ 39${}^{\prime }$ N, 75${}^{°}$ 0${}^{\prime }$ E	Ramban	33${}^{°}$ 20${}^{\prime }$ N , 75${}^{°}$ 12${}^{\prime }$ E
Kupwara	34${}^{°}$ 31${}^{\prime }$ N, 74${}^{°}$ 11${}^{\prime }$ E	Reasi	33${}^{°}$ 4${}^{\prime }$ N , 74${}^{°}$ 50${}^{\prime }$ E
Pulwama	33${}^{°}$ 57${}^{\prime }$ N, 75${}^{°}$ 3${}^{\prime }$ E	Samba	32${}^{°}$ 35${}^{\prime }$ N , 75${}^{°}$ 7${}^{\prime }$ E
Shopian	33${}^{°}$ 49${}^{\prime }$ N, 74${}^{°}$ 50${}^{\prime }$ E	Udhampur	32${}^{°}$ 55${}^{\prime }$ N , 75${}^{°}$ 20${}^{\prime }$ E
Srinagar	34${}^{°}$ 5${}^{\prime }$ N, 74${}^{°}$ 48${}^{\prime }$ E	Kargil	33${}^{°}$ 48${}^{\prime }$ N , 76${}^{°}$ 28${}^{\prime }$ E
Doda	33${}^{°}$ 8${}^{\prime }$ N, 75${}^{°}$ 35${}^{\prime }$ E	Leh	33${}^{°}$ 21${}^{\prime }$ N , 78${}^{°}$ 15${}^{\prime }$ E

specifies the global location of the districts in the studied area.

3.2. Data: Collection, Preprocessing, and Reference Period

This study is based on benchmark secondary data procured from two sources: (1) published records of the Digest of Statistics (Government of Jammu and Kashmir); and (2) NASA LaRC POWER. The data in

Table 2. Various vulnerability indicators categorized into components of exposure, sensitivity, and adaptive capacity along with their positive (+) or negative (−) functional relationship with vulnerability.

Components	Indicators (unit)	Representation	Func. Rel.
EXPOSURE	Annual precipitation (mm) Change in annual precipitation (%)	$PPT$ $\widetilde{PPT}$	+
	Annual maximum temperature ( ${}^{°}$C) Change in annual maximum temperature (%)	$T_{max}$ ${\tilde{T}}_{max}$	+
	Annual minimum temperature ( ${}^{°}$C) Change in annual maximum temperature (%)	$T_{min}$ ${\tilde{T}}_{min}$	+
	Annual average temperature ( ${}^{°}$C) Change in annual average temperature (%)	$T_{avg}$ ${\tilde{T}}_{avg}$	+
	Annual relative humidity (%)	$RH$	+
SENSITIVITY	Average land holding size (hectares)	$Q_{AVL}$	+
	Culturable waste land (% reported area)	$A_{CWL}$	+
	Gross irrigated area (% total sown area)	$A_{GI}$	+
	Net irrigated area (% net sown area)	$A_{NI}$	+
	Area under apple (% total fruit area)	$A_{apple}$	+
	Area under major food crops (% Total sown area)	$A_{major}$	+
	Area under rice (% total sown area)	$A_{rice}$	+
	Agricultural workers (% total workers)	$W_{agricultural}$	+
	Agricultural labourers (% agricultural workers)	$W_{labourers}$	+
	Population density (number per $k{m}^2$)	$D_{population}$	+
	Illiteracy rate (%)	$R_{illiteracy}$	+
	BPL population (% total population)	$P_{BPL}$	+
ADAPTIVE CAPACITY	Net sown area (% reported area)	$A_{sown}$	−
	Forest area (% reported area)	$A_{forest}$	−
	Area under all food crops (% total sown area)	$A_{food}$	−
	Area under fruit crops (% geographical area)	$A_{fruit}$	−
	Area under walnut (% total fruit area)	$A_{wal}$	−
	Total fodder area (% total sown area)	$A_{fodder}$	−
	Cropping intensity (%)	$I_C$	−
	Irrigation intensity (%)	$I_I$	−
	Villages electrified (%)	$E_{villages}$	−
	Cultivators (% agricultural workers)	$W_{cultivators}$	−
	Total workers (% total population)	$W_{total}$	−
	Livestock density (number per $k{m}^2$)	$D_{livestock}$	−
	Fish caught (quintals)	$Q_{fish}$	−
	Rationed population (% total population)	$P_{rationed}$	−
	Literacy rate (%)	$R_{literacy}$	−
	Bank branches (number per lakh hectares of net sown area)	$Q_{BB}$	−
	Credit societies (number per thousand hectares of net sown area)	$Q_{CS}$	−
	Health institutions (number per lakh population)	$Q_{HI}$	−
	Welfare centres (number per lakh population)	$Q_{WC}$	−
	Liveable houses (% total houses)	$H_{livable}$	−

Indicators highlighted by ( $\tilde{}$ ) are derived.

illustrate the exposure, sensitivity, and adaptive capacity variables used in this study for the vulnerability assessment.

Table 3. Socio-economic and climatic variables considered for the assessment of agricultural growth.

Indicators (Unit)	Representation
Net irrigated land (% net sown area) *	$A_{NI}$
Cropping intensity (%) *	$I_C$
Tractors (number per thousand hectares of total sown area)	$Q_T$
Tubewells energized (number per thousand hectares of total sown area)	$Q_{TE}$
Rural literacy rate (%)	$R_{RL}$
Average land holding (hectares) *	$Q_{AVL}$
Public investment in agriculture (rupees per hectare)	$Q_{PBIA}$
Agricultural credit (direct credit per hectare)	$Q_{AC}$
Variance in maximum temperature (%) *	${\overline{T}}_{max}$
Variance in minimum temperature (%) *	${\overline{T}}_{min}$
Variance in precipitation (%) *	$\overline{PPT}$
Change in annual maximum temperature (%) *	${\tilde{T}}_{max}$
Change in annual minimum temperature (%) *	${\tilde{T}}_{min}$
Change in annual precipitation (%) *	$\widetilde{PPT}$

Indicators highlighted by ( $\tilde{}$ ) and (−) are derived. * Some indicators are common to Table 2.

describes the socio-economic indicators that are used in this study for estimating agricultural growth in the presence of these variables. The reference period of study for climatic variables (exposure) spans the years 1983–2022, while the data pertaining to sensitivity and adaptative capacity indicators span from 2007 to 2020. The procured climate data are sampled daily, which was processed to obtain the annual figures as follows:

$T_{max}$ and $T_{min}$ represent the overall annual maximum and the minimum temperatures in a certain year. The daily data for average temperature and relative humidity on a certain day were averaged to obtain the annual mean figure, $T_{avg}$ and $RH$, respectively. The daily precipitation data were summed up to form its annual figure. Equations (1)–(5) detail the process of obtaining the annual data of the mentioned variables.

$$T_{max}=maximum\underset{i=1}{\overset{n}{\{}}{T}_{ma{x}_i}\}$$

(1)

$$T_{min}=minimum\underset{i=1}{\overset{n}{\{}}{T}_{mi{n}_i}\}$$

(2)

$$T_{avg}=average\underset{i=1}{\overset{n}{\{}}{T}_{av{g}_i}\}$$

(3)

$$RH=average\underset{i=1}{\overset{n}{\{}}R{H}_i\}$$

(4)

$$PPT=\sum _{i=1}^{n}PP{T}_i$$

(5)

where $T_{ma{x}_i}$, $T_{mi{n}_i}$, $T_{av{g}_i}$, $R{H}_i$, and $PP{T}_i$ denote the maximum temperature, minimum temperature, average temperature, relative humidity, and precipitation, respectively, on the ith day of the year (with n days). The annual data for variables ${\tilde{T}}_{max}$, ${\tilde{T}}_{min}$, ${\tilde{T}}_{avg}$, and $\widetilde{PPT}$ (as defined in Table 2) is derived from $T_{max}$, $T_{min}$, $T_{avg}$, and $PPT$, respectively. The other derived variables, ${\overline{T}}_{max}$, ${\overline{T}}_{min}$, and $\overline{PPT}$ (as defined in Table 3), are derived from $T_{max}$, $T_{min}$, and $PPT$, respectively. For all other sensitive, socio-economic, and adaptive capacity variables (as defined in Table 2 and Table 3), the data source exists in annual representation, as it is.

3.3. Vulnerability Assessment: Categorisation of Districts and Indexing of Districts

In this study, a hypothesis for the functional relationship between the vulnerability components and indicators (from Table 2) was established. District-wise vulnerability assessment is performed as an indexing-based standardization approach to categorize various regions on the basis of their relative rank derived from the functional hypothesis. The influence of each variable was captured with an assumption that each variable has a weight equal to that of the overall vulnerability to climate change.

Algorithm 1 illustrates the methodology (pseudo-code) followed in pursuing this objective. Initially, all the annually sampled indicators (${\varphi }_i$), given in Table 2 and Table 3 (except the derived indicators) are treated for the removal of noise, that could be present because of inter-year fluctuations, using the moving-average method on previous k years across all districts. Similarly outliers and missing values are adjusted using standard Gaussian filtering [71]. Then, the current smoothened value of the ith indicator is taken as a reference value of the respective indicator which is again retained for each of the districts. This is followed by the min–max normalization for determining the scaled value of the reference indicator among d districts, denoted by as $\lambda =[0,1]$. Given that the overall performance of a district is quantified separately as indices of exposure ($\xi$), sensitivity (§), and adaptive capacity ($\alpha$), the relative rank of the dth district among each indicator category is observed as a ranking of averaged $\lambda$, given as ${\mathcal{R}}_{\xi ,d}$, ${\mathcal{R}}_{\S ,d}$, and ${\mathcal{R}}_{\alpha ,d}$ each $\in \{1,2,3,...,n\}$ where n is the number of identified districts (in Table 1). Hence, the vulnerability index ($\vartheta$) of a district is formulated as defined in Equation (6).

$$\vartheta =\S +\xi +(1-\alpha )$$

(6)

Algorithm 1: Methodology for ranking districts on the basis of vulnerability to climate change.

3.4. Estimation of the Impact of Climate Change on Agricultural Growth

This study employed the Ricardian method developed by [72] with few modifications to capture the impact of climate change on agricultural growth. This analysis is based on the assumption of a direct cause-and-effect relationship between climate events and agricultural growth. As a modification of the Ricardian method to assess the contribution of environmental conditions towards agricultural growth, the estimated parameter of agricultural growth is taken as a proxy of land rent value (as defined by the original Ricardian model). A modelling function is employed to analyse the impact of different variables on agricultural growth in the presence of climatic variables. Several variables were attempted while estimating the function; however, certain variables (mentioned in Table 3) were retained in their final form. The model of the structural form, as defined in Equation (7), is estimated to give the best fit for the trend of agricultural growth ($\mathcal{AG}$) as a linear combination of the aforementioned variables:

$$\begin{array}{cc}\hfill \mathcal{AG}& ={\beta }_0+{\beta }_1{R}_{RL}+{\beta }_2{I}_C+{\beta }_3{Q}_T+{\beta }_4{Q}_{TE}+{\beta }_5{A}_{NI}+{\beta }_6{Q}_{AVL}+{\beta }_7{Q}_{PBIA}\hfill \\ & +{\beta }_8{Q}_{AC}+{\beta }_9{\overline{T}}_{max}+{\beta }_{10}{\overline{T}}_{min}+{\beta }_{11}\overline{PPT}+{\beta }_{12}{\tilde{T}}_{max}+{\beta }_{13}{\tilde{T}}_{min}+{\beta }_{14}\widetilde{PPT}\hfill \end{array}$$

(7)

where ${\beta }_0$ is a random bias term and ${\beta }_i$ ($i\ge 1$) represents the respective coefficients of the variables. The parameters ${\beta }_i$ ($i\ge 0$) of the function are estimated using ordinary least squares (OLS)-based linear regression. Prior to performing an analysis of this function, necessary requirements of the linear regression were tested for the purpose of verifying the distributional characteristics in the data. The results of these tests are specified in Appendix A.

3.5. Estimation of Climate Variability and Forecasting

The climatic data variables have temporal characteristics, and it is imperative to model the distribution of such data using recurrent neural networks that have found applications in numerous use-cases. This study leverages a standard long short-term memory [73] (LSTM)-based neural network model to approximate a function on the distribution of climate variables. Although many climatic variables could be compositely taken under consideration, this study mainly focuses on the exposure of climate variability and its impact within agricultural framework, hence the climatic variables under consideration are $CV=\{T_{max}$, $T_{min}$, $T_{avg}$, $RH$, $PPT\}$. Understanding the distribution system of these climate variables could provide a detailed analysis of the stability of agricultural systems in the current scenario.

Now, the climate variables represent individual time-series signals with distinct temporal distribution. LSTM model is viable for capturing such temporal features having long-range dependencies. Initially, the dataset is treated with standard scaling to mitigate inter-year fluctuations, the removal of noise, and fasten the convergence of the applied model. Standard scaling is applied on each climate variable using the formulation in Equation (8).

$$C{V}_{k_{scaled}}=\frac{C{V}_k-{\mu }_{C{V}_k}}{{\sigma }_{C{V}_i}}$$

(8)

where $C{V}_k\in CV$, and ${\mu }_{C{V}_k},{\sigma }_{C{V}_i}$ represent the mean and standard deviation of $C{V}_k$, respectively. The motivation to utilize the neural network approach for the objective of forecasting climate variables has three reasons: firstly, the universal approximation theorem suggests that neural networks are an excellent choice for modelling continuous functions [74]. This is true, irrespective of the possible trends, oscillations, seasonality or other properties in the data. Secondly, LSTM [73] neural networks have the tendency to capture temporal characteristics in the data samples that have long-range dependencies, on previous values, across time. The climate data distribution is expected to follow a Markov chain [75], and may not be stationary (such as in the case of temperature or precipitation). Furthermore, some climate variables do not follow a linear trend of expectation, and some can experience change in variances with time (such as precipitation and relative humidity). Hence, most climate data cannot be generalized well by linear econometric models (unless some additional processing is performed, such as when the first-order differences of the time series are modelled using these models instead of actual data). Thirdly, non-linear parametric econometric models [76,77,78] tend to assume the parameters of the model according to the statistical properties of the data, prior to modelling, which could fail in predicting uneven/sudden changes in the data (such as predicting erratic precipitation). The parameters are tuned according to the statistical characteristics found in the data prior to achieving the generalization. In contrast, the parameters of the neural network-based predictors are tuned as a process during its training phase by some suitable learning algorithms (such as SGD [79]). In the latter case, there is no need to manually re-engineer the parameters of the model or assume the statistical properties in the data (such as stationarity, scedasticity, or type of probability distribution); hence, there is the potential to achieve better generalization.

Now, some climate variables in the dataset could be correlated and some are apparent to be completely uncorrelated. To remove any hazard that could occur due to inter-variable dependency towards model convergence, an individual LSTM-based neural network is trained for each climate variable. This helps understand the trend of each variable discretely. Secondly, the agricultural systems tend to be complicated across geography. For instance, crops across regions can have distinct dependence on a specific subset or, sometimes, all of climate variables. It is thus essential to consider approximating the distributions of the climate variables in separation from one another for the objectives of forecasting. The scaled transformation of the data of each climate indicator is modelled using the proposed model (as illustrated in Figure 2). The input to the LSTM layer is first resampled into $m+1$ features which specifies the network to use m previous annual values to predict one futuristic estimate of the input variable. Hence, the series of 39 annually sampled values for each district is featured in the form of $\left({\displaystyle \frac{39-m}{stride}}+1\right)$ samples (each of length of m units) in each variable of each district. The defined LSTM layer has four cells. Consider the sequence ${\mathbf{x}}_{\mathbf{t}}$ as input to the LSTM cell at any time t which is transformed across its different gates [80] using the formulation (as shown in Equations (9)–(14)).

$${\mathbf{i}}_{\mathbf{t}}=sigmoid\left({\mathbf{L}}_{\mathbf{2}}[{\mathbf{x}}_{\mathbf{t}},{\mathbf{h}}_{{\mathbf{o}}_{\mathbf{t}-\mathbf{1}}}]\right)$$

(9)

$${\mathbf{f}}_{\mathbf{t}}=sigmoid\left({\mathbf{L}}_{\mathbf{3}}[{\mathbf{x}}_{\mathbf{t}},{\mathbf{h}}_{{\mathbf{o}}_{\mathbf{t}-\mathbf{1}}}]\right)$$

(10)

$${\mathbf{c}}_{\mathbf{t}}={\mathbf{i}}_{\mathbf{t}}{\mathbf{c}}_{\mathbf{t}}^{\prime }+{\mathbf{f}}_{\mathbf{t}}{\mathbf{c}}_{\mathbf{t}-\mathbf{1}}$$

(11)

$${\mathbf{o}}_{\mathbf{t}}=sigmoid\left({\mathbf{L}}_{\mathbf{4}}[{\mathbf{x}}_{\mathbf{t}},{\mathbf{h}}_{{\mathbf{o}}_{\mathbf{t}-\mathbf{1}}}]\right)\mathrm{and}{\mathbf{h}}_{{\mathbf{o}}_{\mathbf{t}}}={\mathbf{o}}_{\mathbf{t}}tanh\left({\mathbf{c}}_{\mathbf{t}}\right)$$

(12)

$${\mathbf{c}}_{\mathbf{t}}={\mathbf{i}}_{\mathbf{t}}{\mathbf{c}}_{\mathbf{t}}^{\prime }+{\mathbf{f}}_{\mathbf{t}}{\mathbf{c}}_{\mathbf{t}-\mathbf{1}}$$

(13)

$${\mathbf{c}}_t^{\prime }=tanh\left({\mathbf{L}}_{\mathbf{1}}[{\mathbf{x}}_{\mathbf{t}},{\mathbf{h}}_{{\mathbf{o}}_{\mathbf{t}-\mathbf{1}}}]\right)$$

(14)

where ${\mathbf{L}}_{\mathbf{i}},i\in \mathbb{N},i\le 4$ represents the trainable parameters of the LSTM baseline. The output vector ${\mathbf{x}}_{{\mathbf{o}}_{\mathbf{t}}}$ from the LSTM cell is forwarded (after 60% dropout) as input to two dense layers ($F{C}_1$ and $F{C}_2$), each with ten nodes. The output is forwarded to a ReLU activation layer to yield a normalized prediction value (y) as shown in Equation (15). ${\mathbf{F}}_{\mathbf{1}}$ and ${\mathbf{F}}_{\mathbf{2}}$ represent the trainable parameters of the fully connected layers.

$$y=\mathrm{relu}\left({\mathbf{F}}_{\mathbf{2}}\left[{\mathbf{F}}_{\mathbf{1}}\left[{\mathbf{h}}_{{\mathbf{o}}_{\mathbf{t}}}\right]\right]\right)$$

(15)

Then, a procedural inverse standard scalar processes the overall output to yield a futuristic estimate of the sample. We repeat the training procedure for multiple epochs until an apparent convergence of the model is reached. It is essential to realize that, even though LSTMs are capable of approximating data that are frequently sampled (such as daily or monthly), it is appropriate to generate year-long average predictions rather than generating for more frequent periods because of the following reason: climate change is observable for sufficiently long periods of time. Frequently sampled data tend to be more stochastic than otherwise. In this context, capturing stochasticity, something LSTMs would be capable of, is not the purpose. The purpose is to visualize year-long or decade-long projections. In this case, neural networks trained for more frequently sampled data would yield more error when generating such longer projections because they would expect stochastic behaviour to exist in yearly sampled data as well. To prevent the model to overfit, we limit the LSTM cells to be only four in comparison to the number of training samples in each variable. In addition, we add significant dropout rate to prevent any uncontrolled overfitting.

4. Results and Discussion

This section details the results observed and the corresponding experimental analysis of the objectives.

4.1. Estimation of Climate Variability and Forecasting

The set of initial settings and hyper-parameter space assumed during the training phase of the proposed LSTM-based framework for forecasting climate variables are illustrated in

Table 4. Hyper-parameter space of proposed deep-learning-based architecture for the analysis and forecasting of climate data.

Hyper-Parameters	Space
Optimizer	Adam
Learning rate	[0.01, 0.1]
Baseline	1 LSTM layer, 4 LSTM cells
Fully connected layers	2
Regularization	60% Dropout on LSTM output
Input dimensions	10 × 1
Output dimensions	1 × 1
Generalization loss	Mean squared error (MSE)
Epochs	[50, 100, 200, 300, 500]
Batch size	[8, 16, 32]
Convergence	Early stopping

.

Initially, the data corresponding to each district comprise 39 years’ worth of annually sampled data for each of five climate variables. The size of training window is $m=10$ and the stride length is $s=1$, yielding $\left(\frac{39-\left(10\right)}{1}+1\right)$ feature vectors in each district in each variable, each of which is 10 units long. There are a total of 22 districts under study. Hence, the dimensions of feature vectors across all districts in each variable are 638 × 10. The ratio of splitting training data, validation data, and test data was kept as 0.8:0.1:0.1 with the dimensions of 528 × 10, 66 × 10, 66 × 10 samples, respectively. The model is trained for 500 epochs and the learning algorithm is set with Adam optimization for faster convergence. Each input sample is $m=10$ in the dimension specifying the previous 10 annual values used to predict one futuristic estimate with a unit sliding window stride. Five different neural networks are thus trained for the five specified climate variables. The overall loss and convergence patterns of each network are illustrated in Figure 3a–e. The overall mean squared error (on normalized validation data) figures achieved on the proposed network for $T_{max}$, $T_{min}$, $T_{avg}$, $RH$, and $PPT$ variables are 0.0211, 0.0483, 0.0057, 0.0695, and 0.1022, respectively. Since the generated predictions are conditional on the first 10 annual values of each variable, the predictions are generated by the neural network model from the year 1993 onward, until the year 2023. We proceed to provide a comparative analysis of the proposed LSTM-framework for forecasting the climate variables with respect to some benchmark econometric models (illustrated in

Table 5. Comparative tabulation of root mean squared error (RMSE) and mean absolute error (MAE) between predicted values and target values in each model.

Model (→) Name of Variable (↓)	LSTM	ARIMA (10,1,2)	SES	HES
	RMSE
$PPT$	0.293801	0.488456	0.552951	0.567089
$RH$	2.602121	3.55365	4.611147	4.955605
$T_{avg}$	0.413821	0.455526	0.399482	0.412566
$T_{max}$	0.293187	0.539785	0.307205	0.298067
$T_{min}$	0.974485	1.057636	0.948449	1.038631
	MAE
$PPT$	0.230967667	0.38846	0.441161	0.442889
$RH$	2.129080667	2.854096	3.588261	3.975286
$T_{avg}$	0.324114	0.357876	0.316091	0.347007
$T_{max}$	0.240407	0.432585	0.250983	0.249933
$T_{min}$	0.771305333	0.821572	0.844976	0.816885

) in terms of root mean squared error (RMSE) and mean absolute error (MAE). We perform forecasting against the actual unnormalized target values from 1993 to 2023 (including unnormalized train, test, and validation data) across all the compared models, viz., LSTM, ARIMA(10,1,2) [76], simple exponential smoothing [77] and Holt’s exponential smoothing [78] (smoothing parameters of 0.3 and 0.5). Figure 4a–e showcase the variability patters and corresponding predictions generated from the compared models in the region for each of the climate variables.

As can be seen from the results, the proposed LSTM-based architecture achieves a considerable convergence and acceptable error. As seen from Figure 3a–e, the training loss and validation loss almost coincide at convergence, suggesting that the LSTM-approximator has a better fit to the distribution of climate data with respect to the compared models (as shown in Table 5). We proceed to analyse the climate variability using the specified neural network model by generating estimations of futuristic annual figures for all climate variables averaged across districts.

4.2. Analysis of Exposure of the Studied Region to Climate Change

As reported from the results, an overall decrease in the annual maximum temperature ($T_{max}$) is observed during the period 1993–2023. It is worth noting that $T_{max}$ does not represent an averaged number but a distribution of annually observed maximal temperature values. Significant impacts are seen in $T_{min}$ and $T_{avg}$. $T_{min}$ is observed to have a normal distribution during the years 1993–2023 with a deviation of about 1.05–1.28 ${}^{°}$C, and is observed to have an increasing trend. A similar observation was seen in [81]. On the other hand, $T_{avg}$ representing the average temperature is showing an increasing trend from 1993 of about 0.8–1 ${}^{°}$C with a variance of $0.07$. It is seen that the trends of annual relative humidity ($RH$) and annual precipitation ($PPT$) are increasing rapidly [82]. The repercussions of a collective system of these interacting variables can have diverse effects on the cropping framework across the spectrum. The extent of exposure is seen to vary across districts in the studied region. A heatmap representation of the studied region is shown in Figure 5 which illustrates the exposure in the studied region.

4.3. Analysis of Sensitivity to Climate Change

Due to commercialisation and urbanisation, land holdings ($Q_{AVL}$) have shrunk across the region. On such terrain, basic agricultural activities are undesirable, and it renders stakeholders susceptible to climate change. The average landholding has been decreasing over the years, exhibiting a $-0.95$ ha difference since 1983. The magnitude of sensitivity of an area is directly proportional to its area under culturable waste lands ($A_{CWL}$), and it is reported to show a decreasing trend. The premise of increasing freshwater scarcity [83] poses a threat to the populace that depends on water-demanding food crops (such as rice [84]). The quantity of the area utilized for such an agricultural product along with the associated population are, thus, susceptible. In the extension to this context, any long-term change in climate would impress an impact on the hydrological regimes of an area with consequent effects on its irrigation system, making water-dependent crops even more sensitive. We witnessed an increase in the gross irrigated area ($A_{GI}$) and net irrigated area ($A_{NI}$) with district Leh having the largest area under its influence. We also observed that the principal food crops in Jammu and Kashmir followed a decreasing trend since 1983. Rice acreage is declining due to the large-scale conversion of the area into commercial, residential, and horticultural fields (particularly apple orchards). Although the irrigation system of apple is less complex, meeting the requirements of sufficient chilling hours is essential for its sustainability. A long-term increase in $T_{min}$ threatens apple production. We proceed to quantify the illiteracy rate ($R_{illiteracy}$) as a parameter of sensitivity because it poses a hurdle in establishing mitigation measures and promoting awareness. Since the districts of Jammu, Kashmir and Ladakh largely qualify as socially suburban, all of the districts have average illiteracy rates (with district Budgam reporting the highest illiteracy rate). Illiteracy is also an indirect indicator of unemployment and poverty scenario in the district. Owing to all these factors, climate stress affects the populace that entirely depends on its agricultural footprint. However, we report a declining percentage of agricultural workers ($W_{agricultural}$) but an increasing percentage of agricultural labourers ($W_{labourers}$), with the highest percentage increase in district Kargil. Lastly, we analyse the role of population characteristics with the objective of specifying the sensitivity of the area. In densely populated areas, the distribution and availability of natural resources such as water, food, and energy become more challenging. Dense populations are more susceptible to the spread of climate-related diseases. In addition, social vulnerability can be higher in densely populated areas, as these communities often face challenges in accessing resources, services, and timely emergency response during climatic catastrophes. A region’s sensitivity is also measured in terms of its BPL population ($P_{BPL}$), both are positively correlated because of lower access to strategic resources. It was observed that the Srinagar district, followed by Bandipora, has the highest population density ($D_{population}$) while district Leh has the least. In this framework, Figure 6 illustrates a heatmap representation of the studied area to quantify its district-wise sensitivity to climate variability.

4.4. Analysis of Adaptation to Climate Change

The adaptive capacity of a system relies on various socio-economic elements, including the progress of infrastructure, availability of essential resources, and span of literacy. Infrastructure development indicators, such as health and educational facilities, as well as road density, play a significant role in determining the adaptation backbone of a region. Access to technology, electrification, percentage of the female workforce, infrastructural/institutional development, and literacy rate are its other essential indicators. Here, we proceed to discuss the trends of significant adaptive capacity indicators. An analysis of data in our study revealed a rise in regional cropping intensity ($I_C$) [85] and irrigation intensity ($I_I$) across all districts. Similarly, we saw an increase in the net sown area ($A_{sown}$) in various districts. An increase in livestock productivity is another positive indication of the adaptive capacity. Since ancient times, livestock and their products have supplemented crop production, provided means of sustenance during lean seasons, and improved resilience to climatic extremes [86]. Livestock productivity increases with the increase in fodder crops ($A_{fodder}$) and it was observed that Kargil has the highest percentage of land under fodder crops, Udhampur the lowest, while many districts lag behind this benchmark. On the other hand, the districts in the Kashmir sub-region saw a slight decrease in forest cover, which is otherwise effective in managing the micro-climate settings. This behaviour is attributed to the rapid exploitation of the natural habitat. We have taken the area under walnut ($A_{wal}$) as an adaption measure as these are robust fruit crops that may survive adverse weather conditions and reduce financial stress in the failure of field crops. Its cultivation has expanded due to public understanding of its benefits (with Kishtwar leading the spectrum). In the next context, the noticeable increase in literacy rates could help bring about preparation for and awareness of the impacts of climate change and help in developing the corresponding mitigation strategies [87]. Similarly, with the reported increase in rural electrification ($E_{villages}$) numbers, farming mechanisation could help in stressed areas by maximising land utilisation. Various other indicators pertinent to housing, infrastructure, and welfare, which help stakeholders in terms of financial stability and risk-coverage, have grown overall in the region. While the trends of all aforementioned indicators have been reported for the overall region, some districts show relatively worse performances. A heatmap representation is shown in Figure 7 that illustrates the relative performance of the adaptive capacity among the districts in the studied region.

4.5. Categorisation of Districts on the Basis of Climate Vulnerability

The vulnerability to climate change reflects an aggregate effect of various exposure, sensitivity, and adaptation parameters [18]. The Leh, Kathua, and Bandipora districts demonstrated the highest variability in the climate variables, especially due to a higher rate of change in precipitation and temperatures. As far as sensitivity variables are concerned, the Budgam, Bandipora, and Ganderbal districts were found to be highly sensitive, mainly due to higher illiteracy rates, population density, area under rice, area under apple, number of agri-labourers, and net irrigated area. On the other hand, the Budgam, Ganderbal, and Pulwama districts were found to be highly adaptive. Based upon the aggregation of exposure, sensitivity, and adaptation variables as defined by Equation 1, the districts Budgam, Bandipora, and Ganderbal were found to be the most vulnerable areas to climate change, while as the Kargil, Rajouri, and Poonch districts were found to be the least vulnerable due to various socio-economic factors and institutional measures. Furthermore, the central part of Kashmir valley was found to be the most vulnerable sub-region, followed by northern Kashmir, and then followed by southern Kashmir. Figure 8 illustrates a heatmap representation of the overall vulnerability pattern in the studied region.

4.6. Impact of Climate Change and Agricultural Growth Model

An ordinary least squares-based estimation scheme was employed to determine the coefficients of indicator variables (discussed in Equation (7)).

Table 6. Estimates of the coefficients pertinent to the agricultural growth model defined in Equation (7).

Coefficient (Indicator)	Value	Standard Error	Coefficient (Indicator)	Value	Standard Error
${\beta }_0$	17.075	4.039	${\beta }_7$ ($Q_{PBIA}$)	0.037 *	0.012
${\beta }_1$ ($R_{RL}$)	0.225 *	0.058	${\beta }_8$ ($Q_{AC}$)	0.325 *	0.104
${\beta }_2$ ($I_C$)	0.052 *	0.014	${\beta }_9$ (${\overline{T}}_{max}$)	−0.499	0.458
${\beta }_3$ ($Q_T$)	0.008	0.026	${\beta }_{10}$ (${\overline{T}}_{min}$)	−0.189 *	0.066
${\beta }_4$$Q_{TE}$	0.026	0.104	${\beta }_{11}$ ($\overline{PPT}$)	−0.170 *	0.079
${\beta }_5$ ($A_{NI}$)	0.070 *	0.024	${\beta }_{12}$ (${\tilde{T}}_{max}$)	0.010	0.007
${\beta }_6$ ($Q_{AVL}$)	−2.268 *	0.030	${\beta }_{13}$ (${\tilde{T}}_{min}$)	−0.011 *	0.004
			${\beta }_{14}$ ($\widetilde{PPT}$)	0.001	0.001
R${}^2$	0.879

* denotes significance at 0.05 or a better probability level.

summarises the estimates of these coefficients used in modelling agricultural growth [88] as a linear regression function. The estimates of these coefficients help us realize the correlation of the indicators with respect to agricultural growth. The variability in climate variables was seen to have a serious negative influence on the agricultural growth modelled as a Ricardian function (Equation (7)). The decreasing land holdings also show a significant negative impact on the growth. The determinant factor of this result is attributed to the increase in annual minimum temperature ($T_{min}$). The number of inputs, technology, and institutional variables, including the public investment in agriculture, have significantly contributed towards positive agricultural growth. The rural literacy rate was also found to be one of the important variables, influencing agricultural growth, in a positive direction. These findings advocate a holistic approach to reducing the negative influence of climate change and impart resilience in the production system of the region.

5. Conclusions

This study conducted an empirical investigation in the region of Jammu, Kashmir, and Ladakh with the aim of assessing its agricultural growth, modelled as a linear regression function under the influence of the variables of climatic stress and socio-economic indicators. The estimated coefficients detail the underlying dependence of agricultural performance on various variables that could help in establishing proactive/mitigation strategies in the agricultural paradigm against climate variability. We propose a framework for quantifying the vulnerability of twenty-two sub-regions (districts) of the studied region utilizing min–max normalization-based ranking scheme that helps to identify the underlying hazardous indicators in a region and its subsequent resilience factors. The sub-regions were categorised according to the indexed values that provide an understanding of the causes and prospective adaptive policies towards the threat of climate variability. An analysis of trends in climate variability was performed with the comprehensive detailing of region-level effects, using an LSTM-backbone model. Our proposed approach yields significant accuracy in predicting the annual estimate of five climate variables that have a direct relationship with the agricultural footprint in the region. Our work provides a baseline for all prospective studies towards the quantification of the region’s susceptibility to climate change.