Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya

Morris Mbithi Wambua; Joseph Kyalo Mung’atu; Jane Akinyi Aduda

doi:doi:10.11648/j.ijdsa.20200605.12

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Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya

Morris Mbithi Wambua, Joseph Kyalo Mung’atu, Jane Akinyi Aduda

Published in International Journal of Data Science and Analysis (Volume 6, Issue 5)

Received: 28 September 2020 Accepted: 9 October 2020 Published: 17 October 2020

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Abstract

The impacts of extremely high temperatures on plants, human beings and animals’ health have been studied in several parts of the world. However, extreme events are uncommon and have only attracted attention recently. In this study, extreme temperature behavior was modelled through the application of extreme value theory using maximum monthly temperatures over a 36 years period. Data on monthly maximum temperature from the Mandera, Wajir and Lodwar stations was modelled using generalized extreme value (GEV) and generalized Pareto distributions (GPD) models. The results revealed that the GEV model was better in modelling extreme temperature behavior because it had the least AIC and BIC values. Two comparative tests, namely, Anderson-Darling and Kolmogorov-Smirnov confirmed the GEV model to be adequate for the data. Diagnostic checks of the two models using probability-probability (PP) plot, quantile-quantile (QQ) plot, return level plot and mean residual life plot revealed that the GEV fitted the data well. Return periods of 5, 10, 20, 50 and 100 years also revealed an increasing trend for long return periods.

Published in	International Journal of Data Science and Analysis (Volume 6, Issue 5)
DOI	10.11648/j.ijdsa.20200605.12
Page(s)	130-136
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), 2020. Published by Science Publishing Group

Keywords

Extreme Temperature, Generalized Extreme Value, Return Level, Extreme Value Theory, Generalized Pareto Distribution, Peak over Threshold, Maximum Likelihood Estimation

References

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[2]	Hasan, H., Radi, N. A., & Kassim, S. (2012, July). Modeling of extreme temperature using generalized extreme value (GEV) distribution: A case study of Penang. In World Congress on Engineering (Vol. 1, No. 2012, pp. 181-186).
[3]	Siliverstovs, B., Ötsch, R., Kemfert, C., Jaeger, C. C., Haas, A., & Kremers, H. (2010). Climate change and modelling of extreme temperatures in Switzerland. Stochastic environmental research and risk assessment, 24 (2), 311-326.
[4]	Ayuketang, N., & Joseph, E. (2014). Modelling extreme temperature in Cameroon using generalized extreme value distribution. University of Buea and AIMS-Cameroon.
[5]	Tramblay, Y., & Hertig, E. (2018). Modelling extreme dry spells in the Mediterranean region in connection with atmospheric circulation. Atmospheric research, 202, 40-48.
[6]	Feng, S., Nadarajah, S., & Hu, Q. (2007). Modeling annual extreme precipitation in China using the generalized extreme value distribution. Journal of the Meteorological Society of Japan. Ser. II, 85 (5), 599-613.
[7]	Omondi, P. A. O., Awange, J. L., Forootan, E., Ogallo, L. A., Barakiza, R., Girmaw, G. B.,... & Kilavi, M. (2014). Changes in temperature and precipitation extremes over the Greater Horn of Africa region from 1961 to 2010. International Journal of Climatology, 34 (4), 1262-1277.
[8]	Matimolane, S. W. (2018). Impacts of Climate Variability and Change on Maize (Zea may) production in Makhuduthamaga Local Municipality, Limpopo Province, South Africa (Doctoral dissertation).
[9]	De Haan, L., & Ferreira, A. (2007). Extreme value theory: an introduction. Springer Science & Business Media.
[10]	Bali, T. G. (2003). The generalized extreme value distribution. Economics letters, 79 (3), 423-427.
[11]	Castillo, E., & Hadi, A. S. (1997). Fitting the generalized Pareto distribution to data. Journal of the American Statistical Association, 92 (440), 1609-1620.
[12]	Segers, J. (2005). Generalized Pickands estimators for the extreme value index. Journal of Statistical Planning and Inference, 128 (2), 381-396.
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[14]	Davison, A. C., & Smith, R. L. (1990). Models for exceedances over high thresholds. Journal of the Royal Statistical Society: Series B (Methodological), 52 (3), 393-425.
[15]	Bommier, E. (2014). Peaks-over-threshold modelling of environmental data.
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[17]	Massey Jr, F. J. (1951). The Kolmogorov-Smirnov test for goodness of fit. Journal of the American statistical Association, 46 (253), 68-78.

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APA Style

Morris Mbithi Wambua, Joseph Kyalo Mung’atu, Jane Akinyi Aduda. (2020). Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya. International Journal of Data Science and Analysis, 6(5), 130-136. https://doi.org/10.11648/j.ijdsa.20200605.12

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ACS Style

Morris Mbithi Wambua; Joseph Kyalo Mung’atu; Jane Akinyi Aduda. Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya. Int. J. Data Sci. Anal. 2020, 6(5), 130-136. doi: 10.11648/j.ijdsa.20200605.12

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AMA Style

Morris Mbithi Wambua, Joseph Kyalo Mung’atu, Jane Akinyi Aduda. Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya. Int J Data Sci Anal. 2020;6(5):130-136. doi: 10.11648/j.ijdsa.20200605.12

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@article{10.11648/j.ijdsa.20200605.12,
  author = {Morris Mbithi Wambua and Joseph Kyalo Mung’atu and Jane Akinyi Aduda},
  title = {Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya},
  journal = {International Journal of Data Science and Analysis},
  volume = {6},
  number = {5},
  pages = {130-136},
  doi = {10.11648/j.ijdsa.20200605.12},
  url = {https://doi.org/10.11648/j.ijdsa.20200605.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20200605.12},
  abstract = {The impacts of extremely high temperatures on plants, human beings and animals’ health have been studied in several parts of the world. However, extreme events are uncommon and have only attracted attention recently. In this study, extreme temperature behavior was modelled through the application of extreme value theory using maximum monthly temperatures over a 36 years period. Data on monthly maximum temperature from the Mandera, Wajir and Lodwar stations was modelled using generalized extreme value (GEV) and generalized Pareto distributions (GPD) models. The results revealed that the GEV model was better in modelling extreme temperature behavior because it had the least AIC and BIC values. Two comparative tests, namely, Anderson-Darling and Kolmogorov-Smirnov confirmed the GEV model to be adequate for the data. Diagnostic checks of the two models using probability-probability (PP) plot, quantile-quantile (QQ) plot, return level plot and mean residual life plot revealed that the GEV fitted the data well. Return periods of 5, 10, 20, 50 and 100 years also revealed an increasing trend for long return periods.},
 year = {2020}
}

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TY  - JOUR
T1  - Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya
AU  - Morris Mbithi Wambua
AU  - Joseph Kyalo Mung’atu
AU  - Jane Akinyi Aduda
Y1  - 2020/10/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ijdsa.20200605.12
DO  - 10.11648/j.ijdsa.20200605.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 130
EP  - 136
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20200605.12
AB  - The impacts of extremely high temperatures on plants, human beings and animals’ health have been studied in several parts of the world. However, extreme events are uncommon and have only attracted attention recently. In this study, extreme temperature behavior was modelled through the application of extreme value theory using maximum monthly temperatures over a 36 years period. Data on monthly maximum temperature from the Mandera, Wajir and Lodwar stations was modelled using generalized extreme value (GEV) and generalized Pareto distributions (GPD) models. The results revealed that the GEV model was better in modelling extreme temperature behavior because it had the least AIC and BIC values. Two comparative tests, namely, Anderson-Darling and Kolmogorov-Smirnov confirmed the GEV model to be adequate for the data. Diagnostic checks of the two models using probability-probability (PP) plot, quantile-quantile (QQ) plot, return level plot and mean residual life plot revealed that the GEV fitted the data well. Return periods of 5, 10, 20, 50 and 100 years also revealed an increasing trend for long return periods.
VL  - 6
IS  - 5
ER  -

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Author Information

Morris Mbithi Wambua

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Joseph Kyalo Mung’atu

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Jane Akinyi Aduda

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Morris Mbithi Wambua, Joseph Kyalo Mung’atu, Jane Akinyi Aduda. (2020). Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya. International Journal of Data Science and Analysis, 6(5), 130-136. https://doi.org/10.11648/j.ijdsa.20200605.12

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ACS Style

Morris Mbithi Wambua; Joseph Kyalo Mung’atu; Jane Akinyi Aduda. Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya. Int. J. Data Sci. Anal. 2020, 6(5), 130-136. doi: 10.11648/j.ijdsa.20200605.12

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AMA Style

Morris Mbithi Wambua, Joseph Kyalo Mung’atu, Jane Akinyi Aduda. Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya. Int J Data Sci Anal. 2020;6(5):130-136. doi: 10.11648/j.ijdsa.20200605.12

Copy | Download

@article{10.11648/j.ijdsa.20200605.12,
  author = {Morris Mbithi Wambua and Joseph Kyalo Mung’atu and Jane Akinyi Aduda},
  title = {Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya},
  journal = {International Journal of Data Science and Analysis},
  volume = {6},
  number = {5},
  pages = {130-136},
  doi = {10.11648/j.ijdsa.20200605.12},
  url = {https://doi.org/10.11648/j.ijdsa.20200605.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20200605.12},
  abstract = {The impacts of extremely high temperatures on plants, human beings and animals’ health have been studied in several parts of the world. However, extreme events are uncommon and have only attracted attention recently. In this study, extreme temperature behavior was modelled through the application of extreme value theory using maximum monthly temperatures over a 36 years period. Data on monthly maximum temperature from the Mandera, Wajir and Lodwar stations was modelled using generalized extreme value (GEV) and generalized Pareto distributions (GPD) models. The results revealed that the GEV model was better in modelling extreme temperature behavior because it had the least AIC and BIC values. Two comparative tests, namely, Anderson-Darling and Kolmogorov-Smirnov confirmed the GEV model to be adequate for the data. Diagnostic checks of the two models using probability-probability (PP) plot, quantile-quantile (QQ) plot, return level plot and mean residual life plot revealed that the GEV fitted the data well. Return periods of 5, 10, 20, 50 and 100 years also revealed an increasing trend for long return periods.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Modelling Extreme Temperature Using Extreme Value Theory: A Case Study Northern Kenya
AU  - Morris Mbithi Wambua
AU  - Joseph Kyalo Mung’atu
AU  - Jane Akinyi Aduda
Y1  - 2020/10/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ijdsa.20200605.12
DO  - 10.11648/j.ijdsa.20200605.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 130
EP  - 136
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20200605.12
AB  - The impacts of extremely high temperatures on plants, human beings and animals’ health have been studied in several parts of the world. However, extreme events are uncommon and have only attracted attention recently. In this study, extreme temperature behavior was modelled through the application of extreme value theory using maximum monthly temperatures over a 36 years period. Data on monthly maximum temperature from the Mandera, Wajir and Lodwar stations was modelled using generalized extreme value (GEV) and generalized Pareto distributions (GPD) models. The results revealed that the GEV model was better in modelling extreme temperature behavior because it had the least AIC and BIC values. Two comparative tests, namely, Anderson-Darling and Kolmogorov-Smirnov confirmed the GEV model to be adequate for the data. Diagnostic checks of the two models using probability-probability (PP) plot, quantile-quantile (QQ) plot, return level plot and mean residual life plot revealed that the GEV fitted the data well. Return periods of 5, 10, 20, 50 and 100 years also revealed an increasing trend for long return periods.
VL  - 6
IS  - 5
ER  -

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