<p>Drought intensity and recurrence are progressively increasing across Pakistan, posing serious threats to socio-ecological resilience, agricultural sustainability, and long-term water security. We develop a scenario-driven spatiotemporal framework for modeling nonlinear drought dynamics and systemic risks using coupled Ordinary Differential Equations (ODEs). The framework formulates a non-autonomous dynamical system driven by four normalized drought-related state variables: Climate Stressor (CS), Resilience Capacity (RC), Tipping Point Probability (TPP), and Bifurcation Transition Index (BTI), which define the Ecological-Climatic Strain Index (ECSI). The model captures abrupt shifts, threshold behavior, and transitions between drought states, normal, onset, crisis, recovery, and prolonged severe drought through nonlinear interactions and conditional feedback. This study focused on meteorological drought, which was measured using Standardized Precipitation Evapotranspiration Index (SPEI) projection data. The calculations are based on monthly precipitation projections from CMIP6 global climate models, namely the CNRM-CM6-1-HR model, under low, moderate, and high emission scenarios. Using long-term projections from CMIP6 and AO-GCM outputs under SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios (2015–2100), we demonstrate the model’s ability to represent evolving drought risks. The analysis shows that changes in climate conditions started as early in dry lowland areas and are expected to continue through the middle and end of the century. Our model results reveal that the drought vulnerability of Pakistan has strong scenario dependency and is regionally heterogeneous. The results under scenario SSP1-2.6 indicate that Sindh and Balochistan are the most drought-affected regions, while Punjab, Khyber Pakhtunkhwa (KPK) and the northern mountainous regions are more likely to be wet, reducing drought impacts and increasing adaptive capacity. SSP2-4.5, on the other hand, intensifies the frequency and intensity of droughts over southern Punjab, Sindh and western Balochistan, whereas SSP5 8.5 results in the occurrence of widespread drought conditions for long periods of time in the country with limited recovery potential. Model evaluation shows that ECSI has greater uncertainty than TPP and RC indices. At certain times between 2020 and 2055, there will be noticeable increases in the intensity of these phenomena, implying that at these times, the system is more vulnerable. For spatial distribution we used Ordinary kriging (OK) to investigate spatial distribution of all indices for the three emission scenarios (SSP1-2.6, SSP2-4.5 and SSP5-8.5). For each index and time slice, several semi variogram models were tested: K-Bessel, Rational Quadratic, Spherical, Circular, and Gaussian. The performance of the models was evaluated using cross-validation statistics, and the model with the least Root Mean Square Error (RMSE) was considered the best model. Semi variogram model that gave the lowest RMSE was chosen as optimum and was used for final interpolation because of its better predictive accuracy and lower interpolation uncertainty. Spatial analysis indicates that the Punjab and KPK show lower stress and stronger resilience, whereas Sindh and Balochistan remain chronic hotspots of ecological instability and drought risk. Future projections (2085) show an increase in stress corridors under high emission scenarios, with reduced adaptive capacity in the southern and western parts of the region. These findings highlight the urgent need for coordinated adaptation, including water conservation, climate-resilient agriculture, and integrated risk management to mitigate escalating drought risks and enhance socio-ecological resilience.</p>

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Exploring nonlinear drought dynamics through stress, resilience, and tipping transitions using a non-autonomous dynamical systems framework with CMIP6 projections

  • Habib Ullah,
  • Rizwan Niaz,
  • Ijaz Hussain,
  • Mohammed M. A. Almazah,
  • Laila A. AL-Essa,
  • Mhassen. E. E. Dalam

摘要

Drought intensity and recurrence are progressively increasing across Pakistan, posing serious threats to socio-ecological resilience, agricultural sustainability, and long-term water security. We develop a scenario-driven spatiotemporal framework for modeling nonlinear drought dynamics and systemic risks using coupled Ordinary Differential Equations (ODEs). The framework formulates a non-autonomous dynamical system driven by four normalized drought-related state variables: Climate Stressor (CS), Resilience Capacity (RC), Tipping Point Probability (TPP), and Bifurcation Transition Index (BTI), which define the Ecological-Climatic Strain Index (ECSI). The model captures abrupt shifts, threshold behavior, and transitions between drought states, normal, onset, crisis, recovery, and prolonged severe drought through nonlinear interactions and conditional feedback. This study focused on meteorological drought, which was measured using Standardized Precipitation Evapotranspiration Index (SPEI) projection data. The calculations are based on monthly precipitation projections from CMIP6 global climate models, namely the CNRM-CM6-1-HR model, under low, moderate, and high emission scenarios. Using long-term projections from CMIP6 and AO-GCM outputs under SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios (2015–2100), we demonstrate the model’s ability to represent evolving drought risks. The analysis shows that changes in climate conditions started as early in dry lowland areas and are expected to continue through the middle and end of the century. Our model results reveal that the drought vulnerability of Pakistan has strong scenario dependency and is regionally heterogeneous. The results under scenario SSP1-2.6 indicate that Sindh and Balochistan are the most drought-affected regions, while Punjab, Khyber Pakhtunkhwa (KPK) and the northern mountainous regions are more likely to be wet, reducing drought impacts and increasing adaptive capacity. SSP2-4.5, on the other hand, intensifies the frequency and intensity of droughts over southern Punjab, Sindh and western Balochistan, whereas SSP5 8.5 results in the occurrence of widespread drought conditions for long periods of time in the country with limited recovery potential. Model evaluation shows that ECSI has greater uncertainty than TPP and RC indices. At certain times between 2020 and 2055, there will be noticeable increases in the intensity of these phenomena, implying that at these times, the system is more vulnerable. For spatial distribution we used Ordinary kriging (OK) to investigate spatial distribution of all indices for the three emission scenarios (SSP1-2.6, SSP2-4.5 and SSP5-8.5). For each index and time slice, several semi variogram models were tested: K-Bessel, Rational Quadratic, Spherical, Circular, and Gaussian. The performance of the models was evaluated using cross-validation statistics, and the model with the least Root Mean Square Error (RMSE) was considered the best model. Semi variogram model that gave the lowest RMSE was chosen as optimum and was used for final interpolation because of its better predictive accuracy and lower interpolation uncertainty. Spatial analysis indicates that the Punjab and KPK show lower stress and stronger resilience, whereas Sindh and Balochistan remain chronic hotspots of ecological instability and drought risk. Future projections (2085) show an increase in stress corridors under high emission scenarios, with reduced adaptive capacity in the southern and western parts of the region. These findings highlight the urgent need for coordinated adaptation, including water conservation, climate-resilient agriculture, and integrated risk management to mitigate escalating drought risks and enhance socio-ecological resilience.