Preprints
https://doi.org/10.5194/npg-2023-28
https://doi.org/10.5194/npg-2023-28
15 Jan 2024
 | 15 Jan 2024
Status: this preprint is currently under review for the journal NPG.

Application of Advection-Diffusion Equation for Nonlinearly Evolving Precipitation Field

Ji-Hoon Ha

Abstract. Analytic solutions for the Advection-Diffusion equation have been explored in diverse scientific and engineering domains, aiming to understand transport phenomena, including heat and mass diffusion, along with the movement of water resources. Precipitation, a vital component of water resources, presents a modeling challenge due to the complex interplay between advection-diffusion effects and source terms. This study aims to improve the modeling of nonlinearly evolving precipitation fields by specifically addressing advection-diffusion equations with time-varying source terms. Utilizing analytic solutions derived through the integral transform technique, we modeled the time-varying source term and investigated the correlation between advection-diffusion and source term effects. While the growth of the field is mainly influenced by the amplitude, size, and timescale of the source term, it can be modulated by advection and diffusion effects. When the timescale of source injection is significantly shorter than the dynamic scale of the system, advection and diffusion effects become independent of the field growth. Conversely, when the timescale of source term injection is sufficiently long, the system evolution primarily depends on advection and diffusion effects. In turbulent regimes with strong diffusion and weak advection effects, a quasi-equilibrium state between growth and decay can be established by regulating the decay caused by advection. However, in regimes where advection effects are crucial, the decay process predominates over the growth process.

Ji-Hoon Ha

Status: open (until 23 Mar 2024)

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Ji-Hoon Ha
Ji-Hoon Ha

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Short summary
This study enhances precipitation modeling by addressing the interplay between advection-diffusion effects and source terms. Focused on nonlinearly evolving precipitation, we employed analytic solutions derived through the integral transform technique. Particularly, the field's growth is influenced by source term characteristics (i.e., amplitude, size, timescale) but modulated by advection and diffusion effects. These findings contribute to precipitation-associated water resource management.