Controlling the rain fall statistics using Mean-Reverting Jump Diffusion model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915927458578432 |
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| author | GhoshDastider, Joya Pal, D. Mishra, Pankaj Kumar |
| author_facet | GhoshDastider, Joya Pal, D. Mishra, Pankaj Kumar |
| contents | We present a stochastic mean-reverting jump-diffusion model to simulate rainfall time series and validate it using long-term half-hourly rain fall data from the North-East region of India. The model captures the intermittent and extreme-event dynamics of rainfall, reproducing superdiffusive behavior with an exponent $\sim 1.8$, along with the observed probability distributions and multifractal features. By systematically varying key parameters, we demonstrate a transition between Log-Normal and Gamma distributions, and show how the occurrence of extreme events and dry-patch durations can be controlled. Spectral and wavelet analyses further confirm that the simulated series reproduces the dominant temporal scales observed in real rainfall data. Our proposed framework provides a robust tool for generating realistic synthetic rainfall series and serves as an effective approach for understanding the influence of underlying stochastic processes that governs the rainfall statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08338 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Controlling the rain fall statistics using Mean-Reverting Jump Diffusion model GhoshDastider, Joya Pal, D. Mishra, Pankaj Kumar Statistical Mechanics Chaotic Dynamics We present a stochastic mean-reverting jump-diffusion model to simulate rainfall time series and validate it using long-term half-hourly rain fall data from the North-East region of India. The model captures the intermittent and extreme-event dynamics of rainfall, reproducing superdiffusive behavior with an exponent $\sim 1.8$, along with the observed probability distributions and multifractal features. By systematically varying key parameters, we demonstrate a transition between Log-Normal and Gamma distributions, and show how the occurrence of extreme events and dry-patch durations can be controlled. Spectral and wavelet analyses further confirm that the simulated series reproduces the dominant temporal scales observed in real rainfall data. Our proposed framework provides a robust tool for generating realistic synthetic rainfall series and serves as an effective approach for understanding the influence of underlying stochastic processes that governs the rainfall statistics. |
| title | Controlling the rain fall statistics using Mean-Reverting Jump Diffusion model |
| topic | Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2604.08338 |