2025

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Modeling the impacts of chemical substances and time delay to mitigate regional atmospheric pollutants and enhance rainfall
(Elsevier B.V., 2025) Gauri Agrawal; Alok Kumar Agrawal; Arvind Kumar Misra
Rainfall, a crucial process of the hydrological cycle, involves the condensation of atmospheric cloud droplets into raindrops that fall on the Earth's surface, providing essentials for human well-being and ecosystem. Research studies show that the condensation–nucleation process for forming raindrops is reduced due to atmospheric pollutants. In this scenario, introducing chemical substances may effectively mitigate regional atmospheric pollution, and reduced atmospheric pollution may lead to adequate rainfall. In the present research work, we analyze rainfall dynamics using a modeling approach with the incorporation of a time lag involved between measuring the data for atmospheric pollution and introducing chemical substances in the regional atmosphere. Here, we assume the formation rate of cloud droplets as a decreasing function of atmospheric pollutants. It is also assumed that introducing chemical substances reduces regional atmospheric pollution. Involving time delay as a bifurcation parameter, we analyze the stability, direction, and period of the bifurcating periodic solutions arising through Hopf bifurcation. Along with this, the presented numerical simulations corroborate the analytical results of our mathematical model. The modeling study reveals that the use of chemical substances in proportion to the concentration of atmospheric pollutants measured at time (t−τ) becomes crucial to mitigate the atmospheric pollutants because as time delay exceeds a threshold value, the system loses its stability and undergoes Hopf bifurcation. © 2025 Elsevier B.V.
A COMPREHENSIVE INVESTIGATION INTO DETERMINISTIC AND STOCHASTIC MODELS CONCERNING THE EFFECTS OF SEEDING ON RAINFALL AND ATMOSPHERIC POLLUTION
(World Scientific, 2025) Amita Tripathi; Sayan Mandal; Pankaj Kumar Tiwari; Arvind Kumar Misra; Maia Martcheva
This study introduces a mathematical model aimed at evaluating the potential influence of aerosol introduction into the atmosphere for inducing rainfall and managing atmospheric pollution. By expanding on the proposed model, we incorporate stochastic elements to encompass environmental white noises that impact the system’s dynamics. Both mathematical and numerical methods are employed to analyze the system’s behavior. In the context of the deterministic model, we examine the solutions’ positivity and boundedness, identify feasible equilibria, and scrutinize the stability characteristics both locally and globally. The analysis of the stochastic system encompasses discussions regarding the existence of a unique solution, its ultimate boundedness, and the conditions that prompt the establishment of a unique stationary distribution characterized by ergodic properties. Our simulations illustrate that augmenting cloud formation rates and externally introduced aerosols can amplify rainfall while mitigating atmospheric pollution levels. Minor intensities of white noise do not alter the system’s behavior, whereas significant intensities result in high-amplitude oscillations of the system’s variables. We explore the effects of white noise intensities using histograms and stationary distributions, highlighting long-term rainfall trends in a noisy environment. © 2025 World Scientific Publishing Company.
When to perform cloud seeding for maximum agricultural crop yields? A modeling study
(Emerald Publishing, 2025) Arvind Kumar Misra; Gauri Agrawal; Akash Yadav
Purpose – Agricultural crops play a crucial role in food security and require commensurating environmental conditions, including adequate rainfall to ensure optimum growth. However, in the recent past, a reduction in the agriculture crop yield has been observed due to the deteriorating rainfall pattern. This paper aims to present a novel mathematical model to analyze the impact of rainfall on the growth of agriculture crops, as well as the impact of cloud seeding for promoting the rainfall, in case of less rainfall to ensure the optimum growth of agriculture crops. Design/methodology/approach – The authors formulate a mathematical model assuming that the growth of agriculture crops wholly depends on rainfall. Also, agricultural crops can sustain and give optimal yields at a threshold of rainfall, after which rainfall negatively affects the growth rate of agriculture crops. Further, if the agriculture crops get insufficient rain to grow, the authors assume that cloud seeding agents are introduced in the regional atmosphere in proportion to the density of cloud droplets to increase rainfall. Findings – This research shows that while cloud seeding agents boost crop yield, excessive rainfall poses significant risks on the yield. For any given value of (conversion of cloud droplets into raindrops because of introduced cloud seeding agents), we have identified the threshold value of (introduction rate of cloud seeding agents into clouds) where crop yield can be maximized. Research limitations/implications – This model highlights the delicate balance between rainfall and cloud seeding, offering policymakers valuable insights for maximizing agricultural crop yields. Originality/value – This research provides strategies to mitigate crop loss due to unpredictable rainfall patterns. © 2024 Emerald Publishing Limited

2025

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