Entropy Based Regional Precipitation Prediction in the Case of Gediz River Basin

Öz

The Shannon’s entropy concept is defined to measure the information content of hydrological processes in hydrology and water resources. Entropy concept has also provided an opportunity to solve several related topics in water resources engineering. The presented study aims to define the regional distribution of the expected long-term annual total precipitation, by using the entropy concept. For this purpose, the frequency analysis of the observed long-term total monthly precipitation data for each station is analyzed, and entropy values are calculated using the frequency histogram called " Intensity Entropy – IE". By using the IE values, it is possible to define the regional information of long-term expected precipitation even if the gauging stations have different observation periods without missing any information of available data. In addition, there is no need to complete the data of the missing observation years (months) to define the precipitation-elevation relations for producing an isometric map. In regional analysis, it is possible to create isoentropy map, by using the determined IE values for each gauging station. The IE method is performed and isoentropy map is created for Gediz Basin as a case study, and the a priori conditions of using IE method results for regional information are discussed in the paper.

Anahtar Kelimeler

• Water resources management
• Entropy
• Uncertainty
• Hydrological processes
• Intensity entropy
• Gediz River Basin

Kaynakça

1. Harmancioglu N. B., Singh V. P., An Information-Based Approach to Monitoring and Evaluation of Water Quality Data. Athens, ECOWARM, European Conference on Advances in Water Resources Technology, A.A. Balkema Publishers, pp. 377-386, 1991.
2. Cherry C., On Human Communication: A Review. A Survey and a criticism. Massachusetts, the Technology Press of Massachusetts Institute of Technology, 333 p, 1957.
3. Shannon C.E., Mathematical Theory of Information. In The Mathematical Theory of Information, the University of Illinois Press: Urbana, IL, USA, 27: 170–180, 1948.
4. Singh V. P., The Use of Entropy in Hydrology and Water Resources. Hydrological Processes, Hydrol. Process., 11: 587-626, DOI: 10.1002/(SICI)1099-1085(199705)11:6<587::AID-HYP479>3.0.CO;2-P, 1997.
5. Singh V.P., The Entropy Theory as a Tool for Modelling and Decisionmaking in Environmental and Water Resources. Water S.A. 26(1):1-10., 2000.
6. Kawachi T., Maruyama T., Singh V. P., Rainfall Entropy for Delineation of Water Resources Zones in Japan, Journal of Hydrology, 246: 36-44, DOI: 10.1016/S0022-1694(01)00355-9, 2001.
7. Mishra A.K., Ozger M., Singh V.P., An Entropy Based Investigation into the Variability of Precipitation, Journal of Hydrology, 370:139–54, DOI: 10.1016/j.jhydrol.2009.03.006, 2009.
8. Zhang L., Li H., Liu D., Fu Q., Li M., Faiz M., A., Khan M., I., Li T., Identification and application of the most suitable entropy model for precipitation complexity measurement. Atmospheric Research 221, 88-97, ISSN 0169-8095, DOI: 10.1016/j.atmosres.2019.02.002, 2019.

9. Dey P., Mujumdar P.P., On the uniformity of rainfall distribution over India, Journal of Hydrology, 578, 124017, ISSN 0022-1694, DOI: 10.1016/j.jhydrol.2019.124017, 2019.
10. Wang W., Wang D., Singh V.P., Wang Y., Wu J., Zhang J., Liu J., Zou Y., He R., Information theory-based multi-objective design of rainfall network for streamflow simulation. Advances in Water Resources. 135-103476, ISSN 0309-1708, DOI: 10.1016/j.advwatres.2019.103476, 2020.
11. Maruyama T., Kawachi T., Singh V.P., Entropy-based Assessment and Clustering of Potential Water Resources Availability. Journal of Hydrology, 309, 104-113, DOI: 10.1016/j.jhydrol.2004.11.020, 2005.
12. Baran T., Hidrolojik süreçlerin bilgi içeriğindeki değişim miktarı olarak entropi tanımı. Dokuz Eylül Üniversitesi, Fen Bilimleri Enstitüsü, İnşaat Mühendisliği Bölümü, Hidrolik-Hidroloji ve Su Kaynakları Doktora Tezi No: 10, 1993.
13. Singh V.P., Systems of Frequency Distributions for Water and Environmental Engineering. Physica A: Statistical Mechanics and its Applications, 506: 50-74, ISSN 0378-4371, DOI: 10.1016/j.physa.2018.03.038, 2018.
14. Hines W.H., Montgomery D.C., Goldsman D.M., Borror C.M., Probability and Statistics in Engineering. John Wiley & Sons, 655 pp., ISBN 0-471-24087-7, 2003.
15. Temiz Ö., Baran T., Determination of Expected Value for Monthly Total Precipitation by Entropy Based Method Case Study: Gediz Basin. 10th International Congress on Advances in Civil Engineering, Paper No: 769, 10 p, 2012.
16. Baran T., Harmancioglu N.B., Cetinkaya C.P., Barbaros F., An Extension to the Revised Approach in the Assessment of Informational Entropy, Entropy, 19(12): 634, DOI: 10.3390/e19120634, 2017.
17. SHW, Environmental Master Plan of Gediz Basin, II. Directorate of State Hydraulic Works, Izmir, 2005.
18. Baran T., Temiz Ö., Gediz Havzası Yağışlarının Eğilim Analizi. IV. Ulusal Su Mühendisliği Sempozyumu, Bildiriler, s. 241 – 251, 2009.