Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation

Ezenugu Isaac Amazuilo; Nseobong. I. Okpura; Enyenihi Henry Johnson

doi:doi:10.11648/j.ijssam.20160104.19

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Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation

Ezenugu Isaac Amazuilo, Nseobong. I. Okpura, Enyenihi Henry Johnson

Published in International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 4)

Received: 16 October 2016 Accepted: 28 December 2016 Published: 21 January 2017

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Abstract

When computing rain attenuation with the International Telecommunication Union (ITU) model the rain rate is normally needed. However, only limited rain rate data are published by ITU for the various regions all over the globe. In order to obtain the missing rain rate data for ITU rain attenuation model, two empirical models used to generate the rain rate data for the fifteen ITU rain zones are presented in this paper. The performance of the two empirical models (referred to as Model 1 and Model 2) is also presented. Specifically, two ITU rain zones (N and P) are considered and Model 1 is used for estimating the rain rate in rain zone P, whereas, Model 2 is used for estimating the rain rate in rain zone N. The rain attenuation computed based on the ITU rain rate generated from the empirical models and the rain attenuation computed from the actual ITU rain rata data are compared in terms of Root Mean Square Error (RMSE), coefficient of determination (r²) and prediction accuracy. According to the results, in respect of rain rate prediction for rain zone N, Model 2 has RMSE (3.491375), Coefficients of Determination (r²= 0.99816) and Prediction Accuracy (92.49319835%). Also, for rain zone N, with respect to the rain attenuation, Model 2 had RMSE of 0.792219, the Coefficients of Determination (r²) of 0.99855 and the Prediction Accuracy of 90.51054739%. Similarly, in respect of rain rate prediction for rain zone P, Model 1 has RMSE (4.924732), Coefficients of Determination (r²= 0.99798) and Prediction Accuracy (92.29421163%). In addition, with respect to the rain attenuation for rain zone P, Model 1 has RMSE is 1.276727, the Coefficients of Determination (r²) is 0.99812 and the Prediction Accuracy 90.31393492%. In all, the two prediction accuracies of the two empirical models are adjudged very good in predicting the rain rates. As such, the rain rates predicted by those models are suitable for computing the rain attenuations for the ITU rain zones.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 4)
DOI	10.11648/j.ijssam.20160104.19
Page(s)	86-90
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), 2017. Published by Science Publishing Group

Keywords

Rain Rate, Rain Attenuation, Empirical Models, ITU Rain Zone, RMSE, Coefficients of Determination, Prediction Accuracy

References

[1]	Sujimol, M. R., Acharya, R., Singh, G., & Gupta, R. K. (2015). Rain attenuation using Ka and Ku band frequency beacons at Delhi Earth Station. Indian Journal of Radio & Space Physics, 44, 45-50.
[2]	Mandeep, J. S., Hassan, S. I. S., Ain, M. F., & Tanaka, K. (2008). Rainfall propagation impairments for medium elevation angle satellite-to-earth 12 GHz in the tropics. International Journal of Satellite Communications and Networking, 26 (4), 317-327.
[3]	Dissanayake, A., Allnutt, J., & Haidara, F. (1997). A prediction model that combines rain attenuation and other propagation impairments along earth-satellite paths. Antennas and Propagation, IEEE Transactions on, 45 (10), 1546-1558.
[4]	Mandeep, J. S., Hassan, S. I. S., Ain, M. F., & Tanaka, K. (2008). Rainfall propagation impairments for medium elevation angle satellite-to-earth 12 GHz in the tropics. International Journal of Satellite Communications and Networking, 26 (4), 317-327.
[5]	Ojo, J. S., & Joseph-Ojo, C. I. (2008). An estimate of interference effect on horizontally polarized signal transmission in the tropical locations: a comparison of rain-cell models. Progress In Electromagnetics Research C, 3, 67-79.
[6]	Yussuff, AbayomiIsiaka, and NorHishamKhamis. "Rain Attenuation Modelling and Mitigation in The Tropics: Brief Review." International Journal of Electrical and Computer Engineering (IJECE) 2.6 (2012): 748-757.
[7]	Yussuff, Abayomi IO, and NorHisham Haji Khamis. "Modified ITU-R Rain Attenuation Prediction Model for a Tropical Station." Journal of Industrial and Intelligent Information Vol 1.3 (2013).
[8]	T. V. Omotosho and C. O. Oluwafemi, “Impairment of radio wave signal by rainfall on fixed satellite service on earth-space path at 37 stations in Nigeria,” Journal of Atmospheric and Solar-Terrestrial Physics, vol. 71, no. 8, pp. 830-840, June, 2009.
[9]	P. S. Ray, “Broad Complex Refractive Indices of Ice and Water,” Applied Optics, Vol. 11, August 1972, pp. 1836-1844.
[10]	Ishii, S. (2010). Rain attenuation at Terahertz. Wireless Engineering and Technology, 1 (02), 92.
[11]	S. Ishii, S. Sayama and T. Kamei, "Measurement of Rain Attenuation in Terahertz Wave Range," Wireless Engineering and Technology, Vol. 2 No. 3, 2011, pp. 119-124. doi: 10.4236/wet.2011.23017.
[12]	Ononiwu, G., Ozuomba, S., & Kalu, C. (2015). DETERMINATION OF THE DOMINANT FADING AND THE EFFECTIVE FADING FOR THE RAIN ZONES IN THE ITU-R P. 838-3 RECOMMENDATION. European Journal of Mathematics and Computer Science Vol, 2 (2).
[13]	Recommendation, ITU-R, International Telecommunication Union, “Specific Attenuation Model for Rain for Use in Prediction Methods,” 2005, pp. 838-833.
[14]	Fenech, H., Tomatis, A., Amos, S., Serrano Merino, J., &Soumpholphakdy, V. (2014, April). An operator's perspective on propagation. In Antennas and Propagation (EuCAP), 2014 8th European Conference on (pp. 3349-3352). IEEE.
[15]	Specific attenuation model for rain for use in prediction methods, ITU-R P. 838-3, 2003.
[16]	Recommendation ITU-R PN.837-1 Characteristics Of Precipitation For Propagation Modelling.
[17]	Kalu, C., Ozuomba, S., & Jonathan, O. A. (2015). Rain Rate Trend-Line Estimation Models and Web Application For The Global Itu Rain Zones. European Journal of Engineering and Technology Vol, 3 (9).

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APA Style

Ezenugu Isaac Amazuilo, Nseobong. I. Okpura, Enyenihi Henry Johnson. (2017). Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation. International Journal of Systems Science and Applied Mathematics, 1(4), 86-90. https://doi.org/10.11648/j.ijssam.20160104.19

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ACS Style

Ezenugu Isaac Amazuilo; Nseobong. I. Okpura; Enyenihi Henry Johnson. Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation. Int. J. Syst. Sci. Appl. Math. 2017, 1(4), 86-90. doi: 10.11648/j.ijssam.20160104.19

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AMA Style

Ezenugu Isaac Amazuilo, Nseobong. I. Okpura, Enyenihi Henry Johnson. Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation. Int J Syst Sci Appl Math. 2017;1(4):86-90. doi: 10.11648/j.ijssam.20160104.19

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@article{10.11648/j.ijssam.20160104.19,
  author = {Ezenugu Isaac Amazuilo and Nseobong. I. Okpura and Enyenihi Henry Johnson},
  title = {Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {1},
  number = {4},
  pages = {86-90},
  doi = {10.11648/j.ijssam.20160104.19},
  url = {https://doi.org/10.11648/j.ijssam.20160104.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20160104.19},
  abstract = {When computing rain attenuation with the International Telecommunication Union (ITU) model the rain rate is normally needed. However, only limited rain rate data are published by ITU for the various regions all over the globe. In order to obtain the missing rain rate data for ITU rain attenuation model, two empirical models used to generate the rain rate data for the fifteen ITU rain zones are presented in this paper. The performance of the two empirical models (referred to as Model 1 and Model 2) is also presented. Specifically, two ITU rain zones (N and P) are considered and Model 1 is used for estimating the rain rate in rain zone P, whereas, Model 2 is used for estimating the rain rate in rain zone N. The rain attenuation computed based on the ITU rain rate generated from the empirical models and the rain attenuation computed from the actual ITU rain rata data are compared in terms of Root Mean Square Error (RMSE), coefficient of determination (r2) and prediction accuracy. According to the results, in respect of rain rate prediction for rain zone N, Model 2 has RMSE (3.491375), Coefficients of Determination (r2= 0.99816) and Prediction Accuracy (92.49319835%). Also, for rain zone N, with respect to the rain attenuation, Model 2 had RMSE of 0.792219, the Coefficients of Determination (r2) of 0.99855 and the Prediction Accuracy of 90.51054739%. Similarly, in respect of rain rate prediction for rain zone P, Model 1 has RMSE (4.924732), Coefficients of Determination (r2= 0.99798) and Prediction Accuracy (92.29421163%). In addition, with respect to the rain attenuation for rain zone P, Model 1 has RMSE is 1.276727, the Coefficients of Determination (r2) is 0.99812 and the Prediction Accuracy 90.31393492%. In all, the two prediction accuracies of the two empirical models are adjudged very good in predicting the rain rates. As such, the rain rates predicted by those models are suitable for computing the rain attenuations for the ITU rain zones.},
 year = {2017}
}

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TY - JOUR
T1 - Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation
AU - Ezenugu Isaac Amazuilo
AU - Nseobong. I. Okpura
AU - Enyenihi Henry Johnson
Y1 - 2017/01/21
PY - 2017
N1 - https://doi.org/10.11648/j.ijssam.20160104.19
DO - 10.11648/j.ijssam.20160104.19
T2 - International Journal of Systems Science and Applied Mathematics
JF - International Journal of Systems Science and Applied Mathematics
JO - International Journal of Systems Science and Applied Mathematics
SP - 86
EP - 90
PB - Science Publishing Group
SN - 2575-5803
UR - https://doi.org/10.11648/j.ijssam.20160104.19
AB - When computing rain attenuation with the International Telecommunication Union (ITU) model the rain rate is normally needed. However, only limited rain rate data are published by ITU for the various regions all over the globe. In order to obtain the missing rain rate data for ITU rain attenuation model, two empirical models used to generate the rain rate data for the fifteen ITU rain zones are presented in this paper. The performance of the two empirical models (referred to as Model 1 and Model 2) is also presented. Specifically, two ITU rain zones (N and P) are considered and Model 1 is used for estimating the rain rate in rain zone P, whereas, Model 2 is used for estimating the rain rate in rain zone N. The rain attenuation computed based on the ITU rain rate generated from the empirical models and the rain attenuation computed from the actual ITU rain rata data are compared in terms of Root Mean Square Error (RMSE), coefficient of determination (r2) and prediction accuracy. According to the results, in respect of rain rate prediction for rain zone N, Model 2 has RMSE (3.491375), Coefficients of Determination (r2= 0.99816) and Prediction Accuracy (92.49319835%). Also, for rain zone N, with respect to the rain attenuation, Model 2 had RMSE of 0.792219, the Coefficients of Determination (r2) of 0.99855 and the Prediction Accuracy of 90.51054739%. Similarly, in respect of rain rate prediction for rain zone P, Model 1 has RMSE (4.924732), Coefficients of Determination (r2= 0.99798) and Prediction Accuracy (92.29421163%). In addition, with respect to the rain attenuation for rain zone P, Model 1 has RMSE is 1.276727, the Coefficients of Determination (r2) is 0.99812 and the Prediction Accuracy 90.31393492%. In all, the two prediction accuracies of the two empirical models are adjudged very good in predicting the rain rates. As such, the rain rates predicted by those models are suitable for computing the rain attenuations for the ITU rain zones.
VL - 1
IS - 4
ER -

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Author Information

Ezenugu Isaac Amazuilo

Department of Electrical Engineering, Imo State University (IMSU), Owerri, Nigeria
Nseobong. I. Okpura

Department of Electrical/Electronic and Computer Engineering, University of Uyo, Akwa Ibom, Nigeria
Enyenihi Henry Johnson

Department of Electrical/Electronic Engineering, Akwa Ibom State University, Mkpat Enin, Nigeria

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Plain Text BibTeX RIS

APA Style

Ezenugu Isaac Amazuilo, Nseobong. I. Okpura, Enyenihi Henry Johnson. (2017). Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation. International Journal of Systems Science and Applied Mathematics, 1(4), 86-90. https://doi.org/10.11648/j.ijssam.20160104.19

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ACS Style

Ezenugu Isaac Amazuilo; Nseobong. I. Okpura; Enyenihi Henry Johnson. Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation. Int. J. Syst. Sci. Appl. Math. 2017, 1(4), 86-90. doi: 10.11648/j.ijssam.20160104.19

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AMA Style

Ezenugu Isaac Amazuilo, Nseobong. I. Okpura, Enyenihi Henry Johnson. Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation. Int J Syst Sci Appl Math. 2017;1(4):86-90. doi: 10.11648/j.ijssam.20160104.19

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@article{10.11648/j.ijssam.20160104.19,
  author = {Ezenugu Isaac Amazuilo and Nseobong. I. Okpura and Enyenihi Henry Johnson},
  title = {Performance Evaluation of Empirical Rain Rate Models for Computing Rain Attenuation},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {1},
  number = {4},
  pages = {86-90},
  doi = {10.11648/j.ijssam.20160104.19},
  url = {https://doi.org/10.11648/j.ijssam.20160104.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20160104.19},
  abstract = {When computing rain attenuation with the International Telecommunication Union (ITU) model the rain rate is normally needed. However, only limited rain rate data are published by ITU for the various regions all over the globe. In order to obtain the missing rain rate data for ITU rain attenuation model, two empirical models used to generate the rain rate data for the fifteen ITU rain zones are presented in this paper. The performance of the two empirical models (referred to as Model 1 and Model 2) is also presented. Specifically, two ITU rain zones (N and P) are considered and Model 1 is used for estimating the rain rate in rain zone P, whereas, Model 2 is used for estimating the rain rate in rain zone N. The rain attenuation computed based on the ITU rain rate generated from the empirical models and the rain attenuation computed from the actual ITU rain rata data are compared in terms of Root Mean Square Error (RMSE), coefficient of determination (r2) and prediction accuracy. According to the results, in respect of rain rate prediction for rain zone N, Model 2 has RMSE (3.491375), Coefficients of Determination (r2= 0.99816) and Prediction Accuracy (92.49319835%). Also, for rain zone N, with respect to the rain attenuation, Model 2 had RMSE of 0.792219, the Coefficients of Determination (r2) of 0.99855 and the Prediction Accuracy of 90.51054739%. Similarly, in respect of rain rate prediction for rain zone P, Model 1 has RMSE (4.924732), Coefficients of Determination (r2= 0.99798) and Prediction Accuracy (92.29421163%). In addition, with respect to the rain attenuation for rain zone P, Model 1 has RMSE is 1.276727, the Coefficients of Determination (r2) is 0.99812 and the Prediction Accuracy 90.31393492%. In all, the two prediction accuracies of the two empirical models are adjudged very good in predicting the rain rates. As such, the rain rates predicted by those models are suitable for computing the rain attenuations for the ITU rain zones.},
 year = {2017}
}

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