the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Aug 2023
Fractal-based numerical simulation of multivariate typhoon wind speeds utilizing Weierstrass Mandelbrot function
Abstract. This paper proposes a fractal-based technique for simulating multivariate nonstationary wind speed fields by the stochastic Weierstrass Mandelbrot function. Upon conducting a systematic fractal analysis, it was found that the structure function method is more suitable and reliable than the box counting method, variation method, and R/S analysis method for estimating the fractal dimension of the stochastic wind speed series. Wind field measurement at the meteorological gradient tower with a height of 356 m in Shenzhen was conducted during Typhoon Mangkhut (2018). Significant non-stationary properties and fractal dimensions of typhoon wind speed data at various heights were analyzed and used to demonstrate the effectiveness of the proposed multivariate typhoon wind speed simulation method. The multivariate wind speed components simulated by the proposed fractal-based method are in good agreement with the measured records in terms of the fractal dimension, standard deviation, probability density function, wind spectrum and cross-correlation coefficient.
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CC1: 'Comment on wes-2023-91', Luigi Fortuna, 20 Aug 2023
The paper sounds very interesting and timely.
THe proposed appoach based on non integer order time series, and in particular the used strategyis appealing and represents a newÂ
appealing approach for studying time series.
The authors focused thei attention to the wind timw sweies moreover the same approach could be very useful to vollcano eruption time series.
The authors could remark this idea and to cite the following contribution:
Lava flow simulations using discharge rates from thermal infrared satellite imagery during the 2006 Etna eruptionAuthorsAnnamaria Vicari, Alessia Ciraudo, Ciro Del Negro, Alexis Herault, Luigi FortunaPublication date2009/9JournalNatural HazardsVolume50Pages539-550PublisherSpringer NetherlandsDisclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2023-91-CC1 -
AC3: 'Reply on CC1', Ming Feng Huang, 07 Oct 2023
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2023-91/wes-2023-91-AC3-supplement.pdf
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AC3: 'Reply on CC1', Ming Feng Huang, 07 Oct 2023
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RC1: 'Comment on wes-2023-91', Anonymous Referee #1, 02 Sep 2023
The authors of this manuscript develop a fractal-based technique for simulating multivariate nonstationary wind speed fields by the stochastic Weierstrass Mandelbrot function. Based on the comparative analysis of the four methods, it was found that the structure function is more suitable and reliable. For case study, the authors also analysed the significant non-stationary properties and fractal dimensions of Typhoon wind speed data at various heights and demonstrate the effectiveness of the proposed multivariate typhoon wind speed simulation method.
The paper is well-structure and detailed, with a lot of pages that are mathematical and technical but it still easy to follow. I truly congratulate the authors on this manuscript, which I believe should be considered for publication after major changes.
The manuscripts, in my opinion, deserve revision on the following issues.
- Line 113, a reference of the box counting method should be added.
- Line 169-179, The explanation of the results in Figures 1-4 is too concise, especially lacking the comparison of some quantitative results. For example, in Figure 4, quantitative value is needed to show the accuracy improvement of the structure function method compared to other methods.
- Line 242, multivariate synchronous simulation of wind speeds, such as?
- Line 303, whether 526 is a sufficient sample?
- Line 307, why the author chose Typhoon Mangkhut as an example? It is better to give brief reason to show its representativeness.
- Line 433. The discussion section can be enriched, highlighting the main contributions of this research, as well as possible future applications. As such a highly technical paper, this will make it clearer to the general reader what problem the article is trying to solve.
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Citation: https://doi.org/10.5194/wes-2023-91-RC1 - AC2: 'Reply on RC1', Ming Feng Huang, 07 Oct 2023
-
RC2: 'Comment on wes-2023-91', Anonymous Referee #2, 05 Sep 2023
- AC1: 'Reply on RC2', Ming Feng Huang, 07 Oct 2023
Status: closed
-
CC1: 'Comment on wes-2023-91', Luigi Fortuna, 20 Aug 2023
The paper sounds very interesting and timely.
THe proposed appoach based on non integer order time series, and in particular the used strategyis appealing and represents a newÂ
appealing approach for studying time series.
The authors focused thei attention to the wind timw sweies moreover the same approach could be very useful to vollcano eruption time series.
The authors could remark this idea and to cite the following contribution:
Lava flow simulations using discharge rates from thermal infrared satellite imagery during the 2006 Etna eruptionAuthorsAnnamaria Vicari, Alessia Ciraudo, Ciro Del Negro, Alexis Herault, Luigi FortunaPublication date2009/9JournalNatural HazardsVolume50Pages539-550PublisherSpringer NetherlandsDisclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2023-91-CC1 -
AC3: 'Reply on CC1', Ming Feng Huang, 07 Oct 2023
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2023-91/wes-2023-91-AC3-supplement.pdf
-
AC3: 'Reply on CC1', Ming Feng Huang, 07 Oct 2023
-
RC1: 'Comment on wes-2023-91', Anonymous Referee #1, 02 Sep 2023
The authors of this manuscript develop a fractal-based technique for simulating multivariate nonstationary wind speed fields by the stochastic Weierstrass Mandelbrot function. Based on the comparative analysis of the four methods, it was found that the structure function is more suitable and reliable. For case study, the authors also analysed the significant non-stationary properties and fractal dimensions of Typhoon wind speed data at various heights and demonstrate the effectiveness of the proposed multivariate typhoon wind speed simulation method.
The paper is well-structure and detailed, with a lot of pages that are mathematical and technical but it still easy to follow. I truly congratulate the authors on this manuscript, which I believe should be considered for publication after major changes.
The manuscripts, in my opinion, deserve revision on the following issues.
- Line 113, a reference of the box counting method should be added.
- Line 169-179, The explanation of the results in Figures 1-4 is too concise, especially lacking the comparison of some quantitative results. For example, in Figure 4, quantitative value is needed to show the accuracy improvement of the structure function method compared to other methods.
- Line 242, multivariate synchronous simulation of wind speeds, such as?
- Line 303, whether 526 is a sufficient sample?
- Line 307, why the author chose Typhoon Mangkhut as an example? It is better to give brief reason to show its representativeness.
- Line 433. The discussion section can be enriched, highlighting the main contributions of this research, as well as possible future applications. As such a highly technical paper, this will make it clearer to the general reader what problem the article is trying to solve.
Â
Â
Citation: https://doi.org/10.5194/wes-2023-91-RC1 - AC2: 'Reply on RC1', Ming Feng Huang, 07 Oct 2023
-
RC2: 'Comment on wes-2023-91', Anonymous Referee #2, 05 Sep 2023
- AC1: 'Reply on RC2', Ming Feng Huang, 07 Oct 2023
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