Prediction of Precipitation Rate Based on Stationary Extreme Value Theory

Justin Han

doi:doi:10.11648/j.ajam.20210905.13

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Prediction of Precipitation Rate Based on Stationary Extreme Value Theory

Justin Han

Published in American Journal of Applied Mathematics (Volume 9, Issue 5)

Received: 23 September 2021 Accepted: 25 October 2021 Published: 30 October 2021

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Abstract

For the determination of the effectiveness of weather forecasts such as temperature or flooding forecast, the single variable linear regression or simple exponential smoothing will not be an effective way. To accurately predict the effectiveness of such a trend, iterative and statistical methods that can determine the status of temperature or flooding in the United States were chosen in this paper. The task of modeling the pattern in a focused period and performing data analysis was performed. For the analysis, the extreme value theory was used to assess extreme events within probability distributions by quantifying tail behavior. The python tools are utilized for the analysis of big data. By analyzing the maximum values of samples, it was possible to determine probabilities for extreme events. A comparison was made with events previously observed and analyzed for authenticity. As evident in our observations, lower values of data have much shorter return periods. In other words, they are more likely to reoccur; however, as the values increase for higher precipitation values, the length of the return periods increase exponentially. Therefore, there is a tendency for precipitation values to remain in lower ranges. In this paper, the USGS geographical information and Gumbel distribution were used to find the return period corresponding to the exceedance probability. The Gumbel distribution is applied to Allegheny River, New York and Whetstone River, San Diego.

Published in	American Journal of Applied Mathematics (Volume 9, Issue 5)
DOI	10.11648/j.ajam.20210905.13
Page(s)	186-191
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

The Extreme Value Theory, Flooding Forecast, Precipitation

References

[1]	Chang, Li-Chiu; Shen, Hung-Yu; Chang, Fi-John (2014). "Regional flood inundation nowcast using hybrid SOM and dynamic neural networks". Journal of Hydrology. 519 (Part A): 476–489. doi: 10.1016/j.jhydrol.2014.07.036.
[2]	F. D. Mwale (2014), Application of self-organising maps and multi-layer perceptron-artificial neural networks for streamflow and water level forecasting in data-poor catchments: the case of the Lower Shire floodplain, Malawi.
[3]	J. Schaake (2016), Hydrologic Ensemble Prediction Experiment an informal yet highly active group of researchers in the field of predictive hydrologic uncertainty.
[4]	"AMS Glossary". allenpress.com (2015) Archived from the original on 16 July 2012. Retrieved 9 July 2015.
[5]	Surface Water for USA: Peak Streamflow. (2021). U.S. Department of the Interio.https://nwis.waterdata.usgs.gov/nwis/peak?site_no=03011020&agency_cd=USGS&format=html
[6]	P. G. Guest, Philip George Guest (2013) Numerical Methods of Curve Fitting. Page 349.
[7]	Marrten K. Van Aalst, “The impacts of climate change on the risk of natural disasters”, Disasters, (2006) Wiley Online Library.
[8]	P. Hoeppe, “Trends in weather related disasters-Consequences for insurers and society”, Weather and climate extremes (2016) Elsevier.
[9]	D. Alexander, “The study of natural disasters, 1977-97: Some reflections on a changing field of knowledge”, Disasters, (1997), Wiley Online Library.
[10]	M. Masozera, M. Bailey, C. Kerchner, “Distribution of impacts of natural disasters across income groups: A case study of New Orleans”, Ecological Economics (2007), Elsevier.

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Justin Han. (2021). Prediction of Precipitation Rate Based on Stationary Extreme Value Theory. American Journal of Applied Mathematics, 9(5), 186-191. https://doi.org/10.11648/j.ajam.20210905.13

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Justin Han. Prediction of Precipitation Rate Based on Stationary Extreme Value Theory. Am. J. Appl. Math. 2021, 9(5), 186-191. doi: 10.11648/j.ajam.20210905.13

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Justin Han. Prediction of Precipitation Rate Based on Stationary Extreme Value Theory. Am J Appl Math. 2021;9(5):186-191. doi: 10.11648/j.ajam.20210905.13

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@article{10.11648/j.ajam.20210905.13,
  author = {Justin Han},
  title = {Prediction of Precipitation Rate Based on Stationary Extreme Value Theory},
  journal = {American Journal of Applied Mathematics},
  volume = {9},
  number = {5},
  pages = {186-191},
  doi = {10.11648/j.ajam.20210905.13},
  url = {https://doi.org/10.11648/j.ajam.20210905.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210905.13},
  abstract = {For the determination of the effectiveness of weather forecasts such as temperature or flooding forecast, the single variable linear regression or simple exponential smoothing will not be an effective way. To accurately predict the effectiveness of such a trend, iterative and statistical methods that can determine the status of temperature or flooding in the United States were chosen in this paper. The task of modeling the pattern in a focused period and performing data analysis was performed. For the analysis, the extreme value theory was used to assess extreme events within probability distributions by quantifying tail behavior. The python tools are utilized for the analysis of big data. By analyzing the maximum values of samples, it was possible to determine probabilities for extreme events. A comparison was made with events previously observed and analyzed for authenticity. As evident in our observations, lower values of data have much shorter return periods. In other words, they are more likely to reoccur; however, as the values increase for higher precipitation values, the length of the return periods increase exponentially. Therefore, there is a tendency for precipitation values to remain in lower ranges. In this paper, the USGS geographical information and Gumbel distribution were used to find the return period corresponding to the exceedance probability. The Gumbel distribution is applied to Allegheny River, New York and Whetstone River, San Diego.},
 year = {2021}
}

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TY  - JOUR
T1  - Prediction of Precipitation Rate Based on Stationary Extreme Value Theory
AU  - Justin Han
Y1  - 2021/10/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ajam.20210905.13
DO  - 10.11648/j.ajam.20210905.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 186
EP  - 191
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20210905.13
AB  - For the determination of the effectiveness of weather forecasts such as temperature or flooding forecast, the single variable linear regression or simple exponential smoothing will not be an effective way. To accurately predict the effectiveness of such a trend, iterative and statistical methods that can determine the status of temperature or flooding in the United States were chosen in this paper. The task of modeling the pattern in a focused period and performing data analysis was performed. For the analysis, the extreme value theory was used to assess extreme events within probability distributions by quantifying tail behavior. The python tools are utilized for the analysis of big data. By analyzing the maximum values of samples, it was possible to determine probabilities for extreme events. A comparison was made with events previously observed and analyzed for authenticity. As evident in our observations, lower values of data have much shorter return periods. In other words, they are more likely to reoccur; however, as the values increase for higher precipitation values, the length of the return periods increase exponentially. Therefore, there is a tendency for precipitation values to remain in lower ranges. In this paper, the USGS geographical information and Gumbel distribution were used to find the return period corresponding to the exceedance probability. The Gumbel distribution is applied to Allegheny River, New York and Whetstone River, San Diego.
VL  - 9
IS  - 5
ER  -

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Author Information

Justin Han

The International School of Kuala Lumpur, Kuala Lumpur, Malaysia

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APA Style

Justin Han. (2021). Prediction of Precipitation Rate Based on Stationary Extreme Value Theory. American Journal of Applied Mathematics, 9(5), 186-191. https://doi.org/10.11648/j.ajam.20210905.13

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ACS Style

Justin Han. Prediction of Precipitation Rate Based on Stationary Extreme Value Theory. Am. J. Appl. Math. 2021, 9(5), 186-191. doi: 10.11648/j.ajam.20210905.13

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AMA Style

Justin Han. Prediction of Precipitation Rate Based on Stationary Extreme Value Theory. Am J Appl Math. 2021;9(5):186-191. doi: 10.11648/j.ajam.20210905.13

Copy | Download

@article{10.11648/j.ajam.20210905.13,
  author = {Justin Han},
  title = {Prediction of Precipitation Rate Based on Stationary Extreme Value Theory},
  journal = {American Journal of Applied Mathematics},
  volume = {9},
  number = {5},
  pages = {186-191},
  doi = {10.11648/j.ajam.20210905.13},
  url = {https://doi.org/10.11648/j.ajam.20210905.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210905.13},
  abstract = {For the determination of the effectiveness of weather forecasts such as temperature or flooding forecast, the single variable linear regression or simple exponential smoothing will not be an effective way. To accurately predict the effectiveness of such a trend, iterative and statistical methods that can determine the status of temperature or flooding in the United States were chosen in this paper. The task of modeling the pattern in a focused period and performing data analysis was performed. For the analysis, the extreme value theory was used to assess extreme events within probability distributions by quantifying tail behavior. The python tools are utilized for the analysis of big data. By analyzing the maximum values of samples, it was possible to determine probabilities for extreme events. A comparison was made with events previously observed and analyzed for authenticity. As evident in our observations, lower values of data have much shorter return periods. In other words, they are more likely to reoccur; however, as the values increase for higher precipitation values, the length of the return periods increase exponentially. Therefore, there is a tendency for precipitation values to remain in lower ranges. In this paper, the USGS geographical information and Gumbel distribution were used to find the return period corresponding to the exceedance probability. The Gumbel distribution is applied to Allegheny River, New York and Whetstone River, San Diego.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Prediction of Precipitation Rate Based on Stationary Extreme Value Theory
AU  - Justin Han
Y1  - 2021/10/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ajam.20210905.13
DO  - 10.11648/j.ajam.20210905.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 186
EP  - 191
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20210905.13
AB  - For the determination of the effectiveness of weather forecasts such as temperature or flooding forecast, the single variable linear regression or simple exponential smoothing will not be an effective way. To accurately predict the effectiveness of such a trend, iterative and statistical methods that can determine the status of temperature or flooding in the United States were chosen in this paper. The task of modeling the pattern in a focused period and performing data analysis was performed. For the analysis, the extreme value theory was used to assess extreme events within probability distributions by quantifying tail behavior. The python tools are utilized for the analysis of big data. By analyzing the maximum values of samples, it was possible to determine probabilities for extreme events. A comparison was made with events previously observed and analyzed for authenticity. As evident in our observations, lower values of data have much shorter return periods. In other words, they are more likely to reoccur; however, as the values increase for higher precipitation values, the length of the return periods increase exponentially. Therefore, there is a tendency for precipitation values to remain in lower ranges. In this paper, the USGS geographical information and Gumbel distribution were used to find the return period corresponding to the exceedance probability. The Gumbel distribution is applied to Allegheny River, New York and Whetstone River, San Diego.
VL  - 9
IS  - 5
ER  -

Copy | Download