Articles | Volume 30, issue 1
Research article
08 Mar 2023
Research article |  | 08 Mar 2023

Rain process models and convergence to point processes

Scott Hottovy and Samuel N. Stechmann

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Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Cited articles

Abbott, T. H., Stechmann, S. N., and Neelin, J. D.: Long temporal autocorrelations in tropical precipitation data and spike train prototypes, Geophys. Res. Lett., 43, 11–472, 2016. a, b, c, d
Ahmed, F. and Neelin, J. D.: Explaining scales and statistics of tropical precipitation clusters with a stochastic model, J. Atmos. Sci., 76, 3063–3087, 2019. a
Albano, G., Giorno, V., Nobile, A. G., and Ricciardi, L. M.: Modeling refractoriness for stochastically driven single neurons, Scientiae Mathematicae Japonicae, 67, 173–190, 2008. a
Bender, C. M. and Orszag, S. A.: Advanced mathematical methods for scientists and engineers I: Asymptotic methods and perturbation theory, Springer Science & Business Media, ISBN 0387989315, 2013. a, b
Bhat, V. N.: Renewal approximations of the switched Poisson processes and their applications to queueing systems, J. Oper. Res. Soc., 45, 345–353, 1994. a
Short summary
Rainfall is erratic and difficult to predict. Thus, random models are often used to describe rainfall events. Since many of these random models are based more on statistics than physical laws, it is desirable to develop connections between the random statistical models and the underlying physics of rain. Here, a physics-based model is shown to converge to a statistics-based model, which helps to provide a physical basis for the statistics-based model.