Fractional Poisson and Gamma Models for Rainfall: Implications Climate Change and Marine Ecosystems

Abstract

This research explores the benefits of using fractional Poisson and fractional Gamma models in rainfall modeling, highlighting their advantages in handling zero-inflated data, reducing overdispersion, and providing greater flexibility and accuracy. The second part of this study delves into the dynamic interplay between oceanic ecosystems and global climate change. It focuses on the role of phytoplankton in oxygen production and the impact of warming waters on this delicate balance. By employing mathematical models integrating differential equations and Brownian motion, the study offers a comprehensive framework for understanding how varying rates of oxygen production influence the sustainability of oceanic ecosystems. Finally, the research incorporates fractional Brownian motion into modeling plankton-oxygen dynamics, addressing the limitations of traditional Brownian motion. This approach captures the long-range dependencies and persistent effects critical for predicting the response of marine ecosystems to climate change. The findings underscore the need for nuanced mitigation strategies to address the imminent risks posed by global warming on marine life and atmospheric oxygen levels.