Status: this preprint has been withdrawn by the authors.
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.
This preprint has been withdrawn.
Received: 23 Dec 2023 – Discussion started: 15 Jan 2024
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The paper presents a comprehensive study on the modeling of nonlinearly evolving precipitation fields using the Advection-Diffusion equation. By incorporating time-varying source terms into the Advection-Diffusion equation, the research aims to improve the understanding and prediction of precipitation. The paper is well written and clearly structured. However, the following comments should be addressed before its publication:
Major comments:
The paper does a goodjob of explaining the Advection-Diffusion equation and its relevance to modeling precipitation fields. However, it might be beneficial to include a more detailed discussion on the implications in real-world scenarios, such as how they might influence the real predictions.
All the results in the paper are based on numerical experiments. It is suggested to addcomparison of the experiment results with actual observational data.
Specific comments:
Line 30: For the precipitation models and precipitationpredictions, it is suggested to cite more recent publications, such as Yang et al., (2023) and Song et al., (2021).
Yang, L., Franzke, C., & Duan, W. (2023). Evaluation and Projections of Extreme Precipitation using a Spatial Extremes Framework. International Journal of Climatology, 130(1-2), 535-544.
Song, L., Chen, S., Chen, W. et al.(2021). Interdecadal change in the relationship between boreal winter North Pacific Oscillation and Eastern Australian rainfall in the following autumn. Clim Dyn 57, 3265–3283.
Line 96: The use of thegeneralized integral transform technique to derive analytic solutions for the Advection-Diffusion equation is a robust methodological approach. It is suggested to add more detailed explanations of the technique.
The figures are informative, but the paper could include more tables or summary statistics to provide a clearer picture of the model's performance across different experiments.
The paper presents a comprehensive study on the modeling of nonlinearly evolving precipitation fields using the Advection-Diffusion equation. By incorporating time-varying source terms into the Advection-Diffusion equation, the research aims to improve the understanding and prediction of precipitation. The paper is well written and clearly structured. However, the following comments should be addressed before its publication:
Major comments:
The paper does a goodjob of explaining the Advection-Diffusion equation and its relevance to modeling precipitation fields. However, it might be beneficial to include a more detailed discussion on the implications in real-world scenarios, such as how they might influence the real predictions.
All the results in the paper are based on numerical experiments. It is suggested to addcomparison of the experiment results with actual observational data.
Specific comments:
Line 30: For the precipitation models and precipitationpredictions, it is suggested to cite more recent publications, such as Yang et al., (2023) and Song et al., (2021).
Yang, L., Franzke, C., & Duan, W. (2023). Evaluation and Projections of Extreme Precipitation using a Spatial Extremes Framework. International Journal of Climatology, 130(1-2), 535-544.
Song, L., Chen, S., Chen, W. et al.(2021). Interdecadal change in the relationship between boreal winter North Pacific Oscillation and Eastern Australian rainfall in the following autumn. Clim Dyn 57, 3265–3283.
Line 96: The use of thegeneralized integral transform technique to derive analytic solutions for the Advection-Diffusion equation is a robust methodological approach. It is suggested to add more detailed explanations of the technique.
The figures are informative, but the paper could include more tables or summary statistics to provide a clearer picture of the model's performance across different experiments.
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.
This study enhances precipitation modeling by addressing the interplay between...
The paper presents a comprehensive study on the modeling of nonlinearly evolving precipitation fields using the Advection-Diffusion equation. By incorporating time-varying source terms into the Advection-Diffusion equation, the research aims to improve the understanding and prediction of precipitation. The paper is well written and clearly structured. However, the following comments should be addressed before its publication:
Major comments:
Specific comments: