Araştırma Makalesi
BibTex RIS Kaynak Göster

Evaluation of precipitation variability in the Western Black Sea Basin with an entropy-based approach

Yıl 2022, Cilt: 12 Sayı: 1, 344 - 356, 15.01.2022

Filiz Barbaros

https://doi.org/10.17714/gumusfenbil.995514

Öz

The most obvious effect of global climate change on meteorological conditions is on temperature and precipitation. The negative effects of both flood and drought events are increasing day by day. While all natural disasters reveal the importance of climate change, they also bring the evaluation of meteorological events to a more important point. For this purpose, by examining the precipitation observation data in the Western Black Sea Basin, precipitation variability and possible risk areas related to this variability were defined, and risk maps were obtained as a result of regional analysis. Long term precipitation data of 13 meteorological stations in the Basin were taken into account and the variability in the observed precipitation was defined with the Intensity Variability Index (IVI) based on Intensity Entropy (IE). After the irregularities in precipitation were defined with indices, regions with high probability of precipitation were determined with index-based maps, created based on these indices. The produced entropy-based maps will be an effective tool for the planning of decision makers when faced with climate change and flood risk.

Anahtar Kelimeler

West Black Sea Basin Variability Entropy Intensity variability index Precipitation Türkiye

Kaynakça

  • Alfonso, L., Ridolfi, E., Gaytan-Aguilar, S., Napolitano, F., & Russo, F. (2014). Ensemble entropy for monitoring network design. Entropy, 16(3), 1365–1375. https://doi.org/10.3390/e16031365
  • Bacanlı, U. G., Baran, T., & Dikbaş, F. (2017). Paylaştırılmış entropi kavramının kuraklık ölçütü olarak kullanılabilirliği. Pamukkale Üniviversitesi. Mühendislik Bilimleri Dergisi, 23(3), 232-237. https://doi.org/10.5505/pajes.2016.80664
  • Baran, T., Harmancioglu, N. B., Cetinkaya, C. P., & Barbaros, F. (2017). An Extension to the Revised Approach in the Assessment of Informational Entropy. Entropy, 19(12), 634. https://doi.org/10.3390/e19120634
  • Bozoglu, O., Baran, T., & Barbaros, F. (2022). Entropy Based Regional Precipitation Prediction in the Case of Gediz River Basin. Teknik Dergi. https://doi.org/10.18400/tekderg.724164
  • Büyükkaracığan, N. (2019). Hidrolojik Verilerin Değişkenlik Analizi ve Uygulamaları, İKSAD yayınevi, ISBN: 978-625-7029-03-2, 118 s.
  • Çeribaşı, G. (2018). Batı Karadeniz Havzasının Yağış Verilerinin Yenilikçi Şen Yöntemi ile Analizi, Academic Platform - Journal of Engineering and Science, 6(3),168-173. https://doi.org/10.21541/apjes.431965
  • Cheng, L., Niu, J., & Liao, D. (2017). Entropy-Based Investigation on the Precipitation Variability over the Hexi Corridor in China. Entropy, 19(12), 660. https://doi.org/10.3390/e19120660
  • Ciriello, V., Lee, J., & Tartakovsky, D. M. (2021). Advances in uncertainty quantification for water resources applications. Stochastic Environmental Research and Risk Assessment, 35, 955–957. https://doi.org/10.1007/s00477-021-01998-y
  • Clark, P. U., Alley, R. B., & Pollard, D. (1999). Northern hemisphere ice-sheet influences on global climate change. Science, 286(5442), 1104–1111. https://doi.org/10.1126/science.286.5442.1104
  • Cleridou, N., Benas, N., Matsoukas, C., Croke, B., & Vardavas, I. (2014). Water resources of Cyprus under changing climatic conditions: modelling approach, validation and limitations. Environ. Model. Softw. 60, 202–218. https://doi.org/10.1016/j.envsoft.2014.06.008
  • Cui, H., & Singh, V. P. (2012). On the cumulative distribution function for entropy-based hydrologic modeling. Transactions of the ASABE. 55(2), 429-438. https://doi.org/10.13031/2013.41384
  • Cui, H., Sivakumar, B., & Singh, V. P. (2018). Entropy Applications in Environmental and Water Engineering, Entropy, 20, 598, https://doi.org/10.3390/e20080598
  • Gu, H., Yu, Z., Li, G., Luo, J., Ju, Q., Huang, Y., & Fu, X. (2020). Entropy-Based Research on Precipitation Variability in the Source Region of China’s Yellow River. Water, 12, 2486. https://doi.org/10.3390/w12092486
  • Harmancioglu, N. B. (1981). Measuring the information content of hydrological processes by the entropy concept. Journal of Civil Engineering, 13-38, Faculty of Engineering, Special Issue for the Centennial of Ataturk’s Birth, Ege University, Izmir, Turkey.
  • Harmancioglu, N. B., & Alpaslan, N. (1992). Water quality monitoring network design: A problem of multiobjective decision making. Water Resources Bulletin, 28(1), 179–192.
  • Harmancioglu, N. B., Alpaslan, N., & Singh, V. P. (1992a). Application of the entropy concept in design of water quality monitoring networks. Singh, V. P. and Fiorentino, M. (Ed.), Entropy and Energy Dissipation in Water Resources. (s. 283-302.). Kluwer Academic Publishers, Dordrecht.
  • Harmancioglu, N. B., Singh, V. P., & Alpaslan, N. (1992b). Versatile uses of the entropy concept in water resources. Singh, V. P. and Fiorentino. M. (Ed.), Entropy and Energy Dissipation inWater Resources. (s. 91-117.). Kluwer Academic Publishers, Dordrecht.
  • Huh, S., Dickey, D. A., Meador, M. R., & Ruhl, K. E. (2005). Temporal analysis of the frequency and duration of low and high streamflow: years of record needed to characterize streamflow variability. Journal of Hydrology, 310(1-4), 78–94.
  • Kayhan, M., & Alan, İ. (2012). Türkiye Alansal Yağış Analizi 1971-2010, Coğrafi Bilgi Sistemleri ile Havza Bazında Alansal Yağış Analizi. Meteoroloji Genel Müdürlüğü. Erişim adresi https://www.mgm.gov.tr/FILES/genel/kitaplar/alansalyagisanalizi.pdf
  • Koutsoyiannis D. (2005). Uncertainty, entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling. Hydrological Sciences Journal,50(3), 381–404. https://doi.org/10.1623/hysj.50.3.381.65031
  • Li, C., Singh, V. P., & Mishra, A. K. (2012). Entropy theory-based criterion for hydrometric network evaluation and design: maximum information minimum redundancy. Water Resources Research, 48, W05521. https://doi.org/10.1029/2011WR011251
  • Maruyama, T., Kawachi, T., & Singh, V. P. (2005). Entropy-based assessment and clustering of potential water resources availability. Journal of Hydrology, 309(1–4), 104–113, https://doi.org/10.1016/j.jhydrol.2004.11.020
  • Mishra, A. K., Özger, M., & Singh, V. P. (2009). An entropy-based investigation into the variability of precipitation. Journal of Hydrology, 370(1–4), 139-154, ISSN 0022-1694. https://doi.org/10.1016/j.jhydrol.2009.03.006
  • Okkan, U., & Altun, H. (2019). Susurluk Havzası Akımlarının Hidrolojik Kuraklık Analizinde Standardize Akım İndeksi ve Paylaştırılmış Entropi Yöntemlerinin Kıyaslanması. 4th International Symposium on Innovative Approaches in Engineering and Natural Sciences, SETSCI Conference Proceedings, 4 (6), 329-335. https://doi.org/10.36287/setsci.4.6.084
  • Rehana, S., Rajulapati, C. R., Ghosh, S., Karmakar, S., & Mujumdar, P. (2020). Uncertainty Quantification in Water Resource Systems Modeling: Case Studies from India. Water, 12, 1793; https://doi.org/10.3390/w12061793
  • Renard, P., Delay, F., Tartakovsky, D. M., & Vesselinov, V. V. (2020). Parameter Estimation and Uncertainty Quantification in Water Resources Modeling. Lausanne: Frontiers Media SA. https://doi.org/10.3389/978-2-88963-674-7
  • Roushangar, K., Alizadeh, F., Adamowski, J., & Saghebian, S. M. (2019). Exploring the multiscale changeability of precipitation using the entropy concept and self-organizing maps. Journal of Water and Climate Change, 11(3), 655–676. https://doi.org/10.2166/wcc.2019.097
  • Shannon C.E. (1948). Mathematical Theory of Information. The Mathematical Theory of Information, 27, 170–180, the University of Illinois Press: Urbana, IL, USA.
  • Shannon, C. E., & Weaver, W. (1949). The mathematical theory of communication. Urbana, Illinois: University of Illinois Press.
  • Singh, V. P. (1989). Hydrologic modelling using entropy. Journal of the Institution of Civil Engineers,70, 55-60.
  • Singh, V. P. (1997). The use of entropy in hydrology and water resources. Hydrol. Process. https://doi.org/10.1002/(SICI)1099-1085(199705)11:6<587::AID-HYP479>3.0.CO;2-P
  • Singh, V. P. (2000). The Entropy theory as tool for modeling and decision-making in environmental and water resources. Water SA, 26,1, ISSN: 0378-4738
  • Singh, V. P. (2013). Entropy theory and its application in environmental and water engineering. Wiley – Blackwell, USA. https://doi.org/10.1002/9781118428306
  • Singh, V. P. (2014). Entropy theory in hydrologic science and engineering, McGraw-Hill Education, ISBN: 9780071835466
  • Singh V. P. (2018). Systems of frequency distributions for water and environmental engineering. Physica A: Statistical Mechanics and its Applications, 506, 50-74, ISSN 0378-4371. https://doi.org/10.1016/j.physa.2018.03.038, 2018.
  • SYGM (2016) İklim Değişikliğinin Su Kaynaklarına Etkisi Projesi. Tarım Orman Bakanlığı, Su Yönetimi Genel Müdürlüğü. Erişim adresi https://www.tarimorman.gov.tr/SYGM/Belgeler/iklim%20de%C4%9Fi%C5%9Fikli%C4%9Finin%20su%20kaynaklar%C4%B1na%20etkisi/Iklim_Nihai_Rapor_Bat%C4%B1_Karadeniz_Ek_15_REV_nihai.pdf
  • SYGM (2019). Batı Karadeniz Havzası Taşkın Yönetim Planı. Tarım Orman Bakanlığı, Su Yönetimi Genel Müdürlüğü. Erişim adresi http://taskinyonetimi.tarimorman.gov.tr/_engine//_engine/file.axd?file=/Dokumanlar/Havzalar/bati_karadeniz/bati_karadeniz_typ.pdf
  • TÜBİTAK MAM (2013) Havza Koruma Eylem Planlarının Hazırlanması Projesi Batı Karadeniz Havzası. TÜBİTAK Marmara Araştırma Merkezi. Çevre ve Temiz Üretim Enstitüsü, Proje Kodu: 5118601, Proje Nihai Raporu. Erişim adresihttps://www.tarimorman.gov.tr/SYGM/Belgeler/havza%20koruma%20eylem%20planlar%C4%B1/Bat%C4%B1%20Karadeniz_web_rev3.pdf
  • Wehri, A. (1978). General properties of entropy, Reviews of Modern Physics, 50(2), 221-260. https://doi.org/10.1103/RevModPhys.50.221
  • Xiong, F., Guo, S., Chen, L., Chang, F., Zhong, Y., & Liu, P. (2018). Identification of flood seasonality using an entropy-based method. Stochastic Environmental Research and Risk Assessment, 32(1-4). https://doi.org/10.1007/s00477-018-1614-1
  • Zhang, Q., Singh, V. P., Sun, P., Chen, X., Zhang, Z., & Li, J. (2011). Precipitation and streamflow changes in China: changing patterns, causes and implications. Journal of Hydrology, 410(3-4), 204–216. https://doi.org/10.1016/j.jhydrol.2011.09.017
  • Zhang, Q., Zheng, Y., Singh, V. P., Xiao, M., & Liu, L. (2016). Entropy-based spatiotemporal patterns of precipitation regimes in the Huai River basin, China, International Journal of Climatology, 36, 2335–2344. https://doi.org/10.1002/joc.4498

Batı Karadeniz Havzası yağış değişkenliklerinin entropi tabanlı bir yaklaşımla değerlendirilmesi

Yıl 2022, Cilt: 12 Sayı: 1, 344 - 356, 15.01.2022

Filiz Barbaros

https://doi.org/10.17714/gumusfenbil.995514

Öz

Küresel iklim değişikliğinin meteorolojik koşullar üzerindeki en belirgin etkisi sıcaklık ve yağışlar üzerinedir. Son yıllarda görülme sıklıkları artan gerek taşkın gerekse kuraklık olaylarının canlı hayat üzerindeki olumsuz etkileri, gün geçtikçe belirgin bir şekilde karşımıza çıkmaktadır. Yaşanan tüm doğal afetler iklim değişikliğinin önemini daha çok ortaya koyarken, meteorolojik olayların değerlendirilmesini de daha önemli bir noktaya taşımaktadır. Bu amaçla, Batı Karadeniz Havzasındaki yağış gözlem verileri incelenerek, yağış değişkenliği ve bu değişkenliğe bağlı olası risk bölgeleri tanımlanmış, bölgesel analiz sonucu risk haritaları elde edilmiştir. Bu amaçla, Batı Karadeniz Havzasında bulunan 13 adet meteoroloji istasyonuna ait uzun dönem yağış verileri ele alınarak, gözlenen yağışlardaki değişkenlik Şiddet Entropisine (ŞE) dayalı Şiddet Değişkenliği İndisi (ŞDİ) ile tanımlanmıştır. Yağışlardaki değişkenlikler indisler ile tanımlandıktan sonra, bu indislere bağlı oluşturulan indis temelli haritalar ile olasılığa bağlı yüksek yağış alabilecek bölgeler belirlenmiştir. Elde edilen entropi tabanlı haritalar, iklim değişikliği ve taşkın riski ile mücadelede karar vericilerin oluşturacakları planlamalar çerçevesinde etkili bir araç olacaktır.

Anahtar Kelimeler

Batı Karadeniz Havzası Değişkenlik Entropi Şiddet değişkenlik indisi Yağış Türkiye

Kaynakça

  • Alfonso, L., Ridolfi, E., Gaytan-Aguilar, S., Napolitano, F., & Russo, F. (2014). Ensemble entropy for monitoring network design. Entropy, 16(3), 1365–1375. https://doi.org/10.3390/e16031365
  • Bacanlı, U. G., Baran, T., & Dikbaş, F. (2017). Paylaştırılmış entropi kavramının kuraklık ölçütü olarak kullanılabilirliği. Pamukkale Üniviversitesi. Mühendislik Bilimleri Dergisi, 23(3), 232-237. https://doi.org/10.5505/pajes.2016.80664
  • Baran, T., Harmancioglu, N. B., Cetinkaya, C. P., & Barbaros, F. (2017). An Extension to the Revised Approach in the Assessment of Informational Entropy. Entropy, 19(12), 634. https://doi.org/10.3390/e19120634
  • Bozoglu, O., Baran, T., & Barbaros, F. (2022). Entropy Based Regional Precipitation Prediction in the Case of Gediz River Basin. Teknik Dergi. https://doi.org/10.18400/tekderg.724164
  • Büyükkaracığan, N. (2019). Hidrolojik Verilerin Değişkenlik Analizi ve Uygulamaları, İKSAD yayınevi, ISBN: 978-625-7029-03-2, 118 s.
  • Çeribaşı, G. (2018). Batı Karadeniz Havzasının Yağış Verilerinin Yenilikçi Şen Yöntemi ile Analizi, Academic Platform - Journal of Engineering and Science, 6(3),168-173. https://doi.org/10.21541/apjes.431965
  • Cheng, L., Niu, J., & Liao, D. (2017). Entropy-Based Investigation on the Precipitation Variability over the Hexi Corridor in China. Entropy, 19(12), 660. https://doi.org/10.3390/e19120660
  • Ciriello, V., Lee, J., & Tartakovsky, D. M. (2021). Advances in uncertainty quantification for water resources applications. Stochastic Environmental Research and Risk Assessment, 35, 955–957. https://doi.org/10.1007/s00477-021-01998-y
  • Clark, P. U., Alley, R. B., & Pollard, D. (1999). Northern hemisphere ice-sheet influences on global climate change. Science, 286(5442), 1104–1111. https://doi.org/10.1126/science.286.5442.1104
  • Cleridou, N., Benas, N., Matsoukas, C., Croke, B., & Vardavas, I. (2014). Water resources of Cyprus under changing climatic conditions: modelling approach, validation and limitations. Environ. Model. Softw. 60, 202–218. https://doi.org/10.1016/j.envsoft.2014.06.008
  • Cui, H., & Singh, V. P. (2012). On the cumulative distribution function for entropy-based hydrologic modeling. Transactions of the ASABE. 55(2), 429-438. https://doi.org/10.13031/2013.41384
  • Cui, H., Sivakumar, B., & Singh, V. P. (2018). Entropy Applications in Environmental and Water Engineering, Entropy, 20, 598, https://doi.org/10.3390/e20080598
  • Gu, H., Yu, Z., Li, G., Luo, J., Ju, Q., Huang, Y., & Fu, X. (2020). Entropy-Based Research on Precipitation Variability in the Source Region of China’s Yellow River. Water, 12, 2486. https://doi.org/10.3390/w12092486
  • Harmancioglu, N. B. (1981). Measuring the information content of hydrological processes by the entropy concept. Journal of Civil Engineering, 13-38, Faculty of Engineering, Special Issue for the Centennial of Ataturk’s Birth, Ege University, Izmir, Turkey.
  • Harmancioglu, N. B., & Alpaslan, N. (1992). Water quality monitoring network design: A problem of multiobjective decision making. Water Resources Bulletin, 28(1), 179–192.
  • Harmancioglu, N. B., Alpaslan, N., & Singh, V. P. (1992a). Application of the entropy concept in design of water quality monitoring networks. Singh, V. P. and Fiorentino, M. (Ed.), Entropy and Energy Dissipation in Water Resources. (s. 283-302.). Kluwer Academic Publishers, Dordrecht.
  • Harmancioglu, N. B., Singh, V. P., & Alpaslan, N. (1992b). Versatile uses of the entropy concept in water resources. Singh, V. P. and Fiorentino. M. (Ed.), Entropy and Energy Dissipation inWater Resources. (s. 91-117.). Kluwer Academic Publishers, Dordrecht.
  • Huh, S., Dickey, D. A., Meador, M. R., & Ruhl, K. E. (2005). Temporal analysis of the frequency and duration of low and high streamflow: years of record needed to characterize streamflow variability. Journal of Hydrology, 310(1-4), 78–94.
  • Kayhan, M., & Alan, İ. (2012). Türkiye Alansal Yağış Analizi 1971-2010, Coğrafi Bilgi Sistemleri ile Havza Bazında Alansal Yağış Analizi. Meteoroloji Genel Müdürlüğü. Erişim adresi https://www.mgm.gov.tr/FILES/genel/kitaplar/alansalyagisanalizi.pdf
  • Koutsoyiannis D. (2005). Uncertainty, entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling. Hydrological Sciences Journal,50(3), 381–404. https://doi.org/10.1623/hysj.50.3.381.65031
  • Li, C., Singh, V. P., & Mishra, A. K. (2012). Entropy theory-based criterion for hydrometric network evaluation and design: maximum information minimum redundancy. Water Resources Research, 48, W05521. https://doi.org/10.1029/2011WR011251
  • Maruyama, T., Kawachi, T., & Singh, V. P. (2005). Entropy-based assessment and clustering of potential water resources availability. Journal of Hydrology, 309(1–4), 104–113, https://doi.org/10.1016/j.jhydrol.2004.11.020
  • Mishra, A. K., Özger, M., & Singh, V. P. (2009). An entropy-based investigation into the variability of precipitation. Journal of Hydrology, 370(1–4), 139-154, ISSN 0022-1694. https://doi.org/10.1016/j.jhydrol.2009.03.006
  • Okkan, U., & Altun, H. (2019). Susurluk Havzası Akımlarının Hidrolojik Kuraklık Analizinde Standardize Akım İndeksi ve Paylaştırılmış Entropi Yöntemlerinin Kıyaslanması. 4th International Symposium on Innovative Approaches in Engineering and Natural Sciences, SETSCI Conference Proceedings, 4 (6), 329-335. https://doi.org/10.36287/setsci.4.6.084
  • Rehana, S., Rajulapati, C. R., Ghosh, S., Karmakar, S., & Mujumdar, P. (2020). Uncertainty Quantification in Water Resource Systems Modeling: Case Studies from India. Water, 12, 1793; https://doi.org/10.3390/w12061793
  • Renard, P., Delay, F., Tartakovsky, D. M., & Vesselinov, V. V. (2020). Parameter Estimation and Uncertainty Quantification in Water Resources Modeling. Lausanne: Frontiers Media SA. https://doi.org/10.3389/978-2-88963-674-7
  • Roushangar, K., Alizadeh, F., Adamowski, J., & Saghebian, S. M. (2019). Exploring the multiscale changeability of precipitation using the entropy concept and self-organizing maps. Journal of Water and Climate Change, 11(3), 655–676. https://doi.org/10.2166/wcc.2019.097
  • Shannon C.E. (1948). Mathematical Theory of Information. The Mathematical Theory of Information, 27, 170–180, the University of Illinois Press: Urbana, IL, USA.
  • Shannon, C. E., & Weaver, W. (1949). The mathematical theory of communication. Urbana, Illinois: University of Illinois Press.
  • Singh, V. P. (1989). Hydrologic modelling using entropy. Journal of the Institution of Civil Engineers,70, 55-60.
  • Singh, V. P. (1997). The use of entropy in hydrology and water resources. Hydrol. Process. https://doi.org/10.1002/(SICI)1099-1085(199705)11:6<587::AID-HYP479>3.0.CO;2-P
  • Singh, V. P. (2000). The Entropy theory as tool for modeling and decision-making in environmental and water resources. Water SA, 26,1, ISSN: 0378-4738
  • Singh, V. P. (2013). Entropy theory and its application in environmental and water engineering. Wiley – Blackwell, USA. https://doi.org/10.1002/9781118428306
  • Singh, V. P. (2014). Entropy theory in hydrologic science and engineering, McGraw-Hill Education, ISBN: 9780071835466
  • Singh V. P. (2018). Systems of frequency distributions for water and environmental engineering. Physica A: Statistical Mechanics and its Applications, 506, 50-74, ISSN 0378-4371. https://doi.org/10.1016/j.physa.2018.03.038, 2018.
  • SYGM (2016) İklim Değişikliğinin Su Kaynaklarına Etkisi Projesi. Tarım Orman Bakanlığı, Su Yönetimi Genel Müdürlüğü. Erişim adresi https://www.tarimorman.gov.tr/SYGM/Belgeler/iklim%20de%C4%9Fi%C5%9Fikli%C4%9Finin%20su%20kaynaklar%C4%B1na%20etkisi/Iklim_Nihai_Rapor_Bat%C4%B1_Karadeniz_Ek_15_REV_nihai.pdf
  • SYGM (2019). Batı Karadeniz Havzası Taşkın Yönetim Planı. Tarım Orman Bakanlığı, Su Yönetimi Genel Müdürlüğü. Erişim adresi http://taskinyonetimi.tarimorman.gov.tr/_engine//_engine/file.axd?file=/Dokumanlar/Havzalar/bati_karadeniz/bati_karadeniz_typ.pdf
  • TÜBİTAK MAM (2013) Havza Koruma Eylem Planlarının Hazırlanması Projesi Batı Karadeniz Havzası. TÜBİTAK Marmara Araştırma Merkezi. Çevre ve Temiz Üretim Enstitüsü, Proje Kodu: 5118601, Proje Nihai Raporu. Erişim adresihttps://www.tarimorman.gov.tr/SYGM/Belgeler/havza%20koruma%20eylem%20planlar%C4%B1/Bat%C4%B1%20Karadeniz_web_rev3.pdf
  • Wehri, A. (1978). General properties of entropy, Reviews of Modern Physics, 50(2), 221-260. https://doi.org/10.1103/RevModPhys.50.221
  • Xiong, F., Guo, S., Chen, L., Chang, F., Zhong, Y., & Liu, P. (2018). Identification of flood seasonality using an entropy-based method. Stochastic Environmental Research and Risk Assessment, 32(1-4). https://doi.org/10.1007/s00477-018-1614-1
  • Zhang, Q., Singh, V. P., Sun, P., Chen, X., Zhang, Z., & Li, J. (2011). Precipitation and streamflow changes in China: changing patterns, causes and implications. Journal of Hydrology, 410(3-4), 204–216. https://doi.org/10.1016/j.jhydrol.2011.09.017
  • Zhang, Q., Zheng, Y., Singh, V. P., Xiao, M., & Liu, L. (2016). Entropy-based spatiotemporal patterns of precipitation regimes in the Huai River basin, China, International Journal of Climatology, 36, 2335–2344. https://doi.org/10.1002/joc.4498
Toplam 42 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Filiz Barbaros 0000-0002-2697-911X

Yayımlanma Tarihi 15 Ocak 2022
Gönderilme Tarihi 14 Eylül 2021
Kabul Tarihi 1 Ocak 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 12 Sayı: 1

Kaynak Göster

APA Barbaros, F. (2022). Batı Karadeniz Havzası yağış değişkenliklerinin entropi tabanlı bir yaklaşımla değerlendirilmesi. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 12(1), 344-356. https://doi.org/10.17714/gumusfenbil.995514
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