کاربرد منطق فازی جهت برآورد تبخیر - تعرق پتانسیل شهرستان گناباد
محورهای موضوعی : انرژی های تجدید پذیرحسن رضائی 1 , غلامعباس فلاح قالهری 2
1 - دکتری اقلیم شناسی کشاورزی، مدرس دانشگاه افسری امام علی(ع).
2 - دانشیار دانشکده جغرافیا و علوم محیطی، دانشگاه حکیم سبزواری. * (مسول مکاتبات).
کلید واژه: تبخیر تعرق پتانسیل, گناباد, روش پنمن – فائو- مونتیث, سیستم استنتاج فازی,
چکیده مقاله :
زمینه و هدف: تبخیر- تعرق پتانسیل یکی از اجزای اصلی چرخه ی هیدرولوژیکی است که تعیین صحیح آن در مطالعات بیلان آبی، طراحی سیستم های آبیاری و برنامه ریزی و مدیریت منابع آب برای دست یابی به توسعه ی پایدار نقش به سزایی دارد. تبخیر و تعرق به علت نیاز به عوامل اقلیمی مختلف و اثر متقابل این عوامل بر یکدیگر یک پدیده ی غیرخطی و پیچیده است. یکی از مراحل پیچیده در مدل سازی سیستم های غیرخطی، پیش پردازش پارامتر های ورودی جهت انتخاب ترکیبی مناسب از آنهاست. پیش پردازش داده ها سبب کاهش مراحل سعی و خطا و شناخت مهم ترین پارامترهای مؤثر بر پدیده ی مورد نظر جهت مدل سازی با استفاده از روش های هوشمند می گردد. این پژوهش با هدف استفاده از توانمندیهای سیستم استنتاج فازی برای برآورد تبخیر و تعرق با استفاده از داده های هواشناسی طی دوره 20 ساله (1372-1392) در شهر گناباد صورت گرفت. روش بررسی: براین اساس پس از بررسی مدل موجود و بررسی ترکیب های مختلف داده های هواشناسی، مدل نهایی برای برآورد تبخیر و تعرق ارایه شد. در این تحقیق در مجموع با داشتن 20 متغیر برای ورودی مدل و یک متغیر برای خروجی مدل (تبخیر و تعرق)، 50 قانون در سیستم استنتاج ممدانی تعریف شد. مقادیر تبخیر و تعرق پتانسیل حاصل از مدل فازی با مدل پنمن فائو- مونتیث مورد مقایسه قرار گرفت. بحث و نتیجه گیری: کارایی مدل فازی ارایه شده با استفاده از آماره های ریشه میانگین مربعات خطا، خطای انحراف میانگین، ضریب تعیین و معیار جاکوویدز (t) و معیار صباغ و همکاران (R2 /t) مورد ارزیابی قرار گرفت. مقایسه نتایج مدل فازی با مدل پنمن فائو- مونتیث مقایسه گردید. بیشترین تبخیر و تعرق در ماه ژوئیه اتفاق افتاده است. نتایج حاکی از همبستگی بالا بین این دو مدل فازی ارایه شده و روش پنمن فائو- مونتیث است.
Background and Objectives: Evapotranspiration are the main component of hydrologic cycle and estimation of the amount of evapotranspiration is important to study the water balance, design the irrigation systems and ultimately plan and manage the water resources to achieve the stable development. Evapotranspiration are nonlinear and complicated phenomenon due to requirement for different factors and their interactions. One important step in non-linear system modeling is pre- investigation of inputs to achieve suitable combination of them. Pre-investigation of input data prevents several trial and error steps and helps to understand the most important parameters which affect the phenomenon to be able to modeling the system in an intelligent way. Thereby, this study, has aimed to implement the ability of Fuzzy logic system to estimate Evapotranspiration by using the data from Gonabad weather station in a 21-year period (1993-2014). Material and Methods: To reach this aim, after investigation of available models and different combination of weather information, the final model to estimate Evapotranspiration has been designed. In this model with 20 surface as input and one surface as output or evaporation and transpiration, 50 rules were determined in Mamdani Inference System and the estimated value of Evapotranspiration from the Fuzzy Inference were compared with the results from Fao Penman Monteith (F-P-M). Results and Discussion: Statistical parameters including Root Mean Square Error (RMSE), Main Bias Error (MBE) Coefficient of Determination, Jacovides factor (t) and Sabbagh et al. factor (R2/t) have been used to investigate the efficiency of this model. Comparison of the results from the Fuzzy Model and the results from F-P-M shows a high level of correlation between these two methods indicating the highest level of Evapotranspiration in July (RMSE: 0.08, R2: 0.98, MBE: 0.05, t:0.25 and R2/t: 3.92).
- Waziri. ZH, Entesari. M, Masihi. M, Heydari. N. Dehghani, S., 2008, Evaporation and transpiration (instructions for calculating the water required by plants), Publications of the National Committee for Irrigation and Drainage, Tehran, 362. (In Persian)
- Jahanbakhsh Asl. Q, Movahed Danesh. A. and Rumi, and, 2001, Analysis of Evaporation and Transpiration Estimation Models for Tabriz Meteorological Station, Journal of Agricultural Knowledge, 11, 66-51. (In Persian)
- Kouchekzadeh. M, Bahmani. A., 2005, Evaluation of the performance of artificial neural networks in reducing the required parameters for estimating reference evapotranspiration, Journal ofAgricultural Sciences, 11 (4), 97-87. (In Persian)
- Alizadeh. A, Kamali. Gh, 2007, Water needs of plants in Iran, first edition, Astan Quds Razavi Publishing Institute, 228. (In Persian)
- Mousavi Baygi. M, mystics. M, Sarmad. M, 2009, Using Minimum Meteorological Data to Estimate Evapotranspiration of Reference Plant and Presenting Correction Coefficient (Case Study: Khorasan Razavi Province), Journal of Water and Soil (Agricultural Sciences and Industries), 23 (1), 9-19. (In Persian)
- Wang. Y.M Traore. S, Kerh. T,2009, Computational performance of Reference evapotranspiration in semiarid zone of Africa, Sci, Research and Essay, 4, 6. 577-583.
- Grismer. M.E, Oran. M, Snyder. R., Matyac, R,2002, Pan Evaporation toreference evapotranspiration conversion methods, ASCE J. Irrig. and Drain. Eng, 128(30),180-184.
- Rahimi Koob. A, 2008, Comparative study of Hargrives's and artificial neural network's methodologies in estimating reference evapotranspiration in a semiarid environment, Irrig. Sci, 26(3),253-259.
- Kisi. O, 2007, Evapotranspiration modeling from climatic data using a neural computing technique. Hydro. Process, 21(6),1925-1934.
- Kisi. O,2007, Adaptive neurofuzzy computing technique for Evapotranspiration Estimation, Journal of Irrigation and Drainage Engineering, 133(4), 368-379.
- Kumar. M, Bandyopadhyay. A, Raghuwanshi. N.S, Singh. R, 2008, Comparative study of conventional and artificial neural network-based ET0 estimation models, Irrig. Sci. 26(6), 531-545.
- Aytek. A, Kisi. O, 2008, A genetic programming approach to suspended sediment modeling, J. Hydro, 351,288-298.
- Kim. S, Kim. H, 2008, Neural Networks and genetic algorithm approach for nonlinear evaporation and evapotranspiration modeling, J. Hydro, 351, 299-317.
- Tzimopoulos. C, Mpallas. L, Papaevangelou. G, 2008, Estimation of evapotranspiration using fuzzy systems and comparison with the blaney-criddle method. Environ, Sci. and Technol,4(1), 181-186.
- Moghaddamnia. A, Ghafari Gousheh. M, Piri. J, Amin. S, Han. D, 2009, Evaporation estimation using artificial neural networks and adaptive neuro fuzzyinference system techniques, Advances in Water Resources,32(1),89-97.
- Lin. C, Chao C, Chen. W.F, 2008, Estimation regional evapotranspiration by adaptive network-based fuzzy inference system for Dan-Shui basin in Taiwan. J. Chinese Inst. Eng, 30(6), 1091-1096.
- Korepaz dezfouli. A, 2006, Principles of fuzzy set theory and its applications in modeling water problems, Amir Kabir University of Technology Jihad Publications, Tehran. (In Persian)
- Sudheer. K.P, Gosain. A.K. Ramasastri. K.S, 2003, Estimating actual evapotranspiration from limited climatic data using neural computing technique, J. Irrg. Drain. Eng. ASCE, 129(3),214-218.
- Kisi. O, Ozturk. O, 2007, Adaptive neurofuzzy computing technique for evaptotranspiration estimation, J. Irrig. Drain. Eng. ASCE, 133(4), 368-379.
- Shayan Nejad. M, 2006, Calculation of groundwater drainage distance in unsustainable conditions using artificial neural networks, National Conference on Irrigation and Drainage Network Management, Shahid Chamran University of Ahvaz, Iran. (In Persian)
- Zare Abyaneh. H, Qasim. A., Bayat Warkshi. M, famous. P., 2009, Evaluation of the accuracy of artificial neural network in predicting evapotranspiration of garlic using lysimetric data in Hamadan region. Journal of Water and Soil (Agricultural Sciences and Industries), 23 (2), 185-176. (In Persian)
- Odhiambo. L.O, Yoder. R.E, Yoder. D.C, 2001a, estimating of reference crop evapotranspiration using fuzzy state models. Trans of the ASAE. No. 44(3), 543-550.
- Jia Bing. C, 2004, Prediction of daily reference evapotranspiration using adaptive neurofuzzy inference system. Trans of the Chinese society of Agricultural Engineering, 20(4),13-16.
- Dogan. E, 2009, Reference Evapotranspiration Estimation using adaptive nerofuzzy inference system. Journal of Irrigation and Drianage Engineering, 58,617-628.
- Kisi. O, 2010, Fuzzy Genetic Approach for modeling Reference Evapotranspiration, Journal of Irrigation and Drianage Engineering .136(3),175-183.
- Sayyadi. H, Olad Ghaffari. A, Ashrafsadrodini. A., 2009, Comparison of RBF and MLP neural network performance in estimating reference plant evapotranspiration. Journal of Soil and Water Knowledge 1 (19), 12-1. (In Persian)
- Meteorological profile of Khorasan Razavi, 2014, monthly meteorological data of Gonabad station. (In Persian)
- Allen. R.G, Raes. L.S, Smith. M, 1998, Crop Evapotranspiration Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper. No. 56. FAO. Rome, Italy.
- Monem. M, Khorami. J, Heydarian. A., 2007, Evaluating the performance of irrigation networks or using fuzzy logic: A case study of Maroon network. Tarbiat Modares Technical and Engineering Journal, 27, 42-31. (In Persian)
- afari Mianai. C, Agriculture. A., 2008, Comparison of fuzzy method and statistical regression to estimate sediment load of rivers. Fourth National Congress of Civil Engineering, Tehran. (In Persian)
- Jacquin. A, Shamseldin. A, 2006, Development of rainfall–runoff models using Takagi–Sugeno fuzzy inference systems. Journal of Hydrology, 329(1-2), 154-173.
- Coa. Z, Kandel. A, 1989, Application of some Fuzzy Implication Operators, FSS. 3, 42-52.
- Lee. C.C, 1990, Fuzzy Logic in Control Systems: Fuzzy Logic in Controller – part I & II. IEEE Transaction on systems, Man and Cybernetics, 20(2). P.419-435.
- Jacovides. C.P, 1997. Reply to comment on Statistical procedures for the evaluation of evapotranspiration models, Agricultural water management, 3, 95-97.
- Sabziparvar. A, Tafazoli. F. Zare Abyaneh. H, Banzhad. H. Mousavi Baygi. M, Ghafouri. M. Mohseni Movahed. A., Marianji, 2008, Comparison of several models for estimating the evapotranspiration of the reference plant in a cold and semi-arid climate for optimal use of radiation models. Journal of Water and Soil (Agricultural Sciences and Industries). 2 (22), 340-328
- Waziri. ZH, Entesari. M, Masihi. M, Heydari. N. Dehghani, S., 2008, Evaporation and transpiration (instructions for calculating the water required by plants), Publications of the National Committee for Irrigation and Drainage, Tehran, 362. (In Persian)
- Jahanbakhsh Asl. Q, Movahed Danesh. A. and Rumi, and, 2001, Analysis of Evaporation and Transpiration Estimation Models for Tabriz Meteorological Station, Journal of Agricultural Knowledge, 11, 66-51. (In Persian)
- Kouchekzadeh. M, Bahmani. A., 2005, Evaluation of the performance of artificial neural networks in reducing the required parameters for estimating reference evapotranspiration, Journal ofAgricultural Sciences, 11 (4), 97-87. (In Persian)
- Alizadeh. A, Kamali. Gh, 2007, Water needs of plants in Iran, first edition, Astan Quds Razavi Publishing Institute, 228. (In Persian)
- Mousavi Baygi. M, mystics. M, Sarmad. M, 2009, Using Minimum Meteorological Data to Estimate Evapotranspiration of Reference Plant and Presenting Correction Coefficient (Case Study: Khorasan Razavi Province), Journal of Water and Soil (Agricultural Sciences and Industries), 23 (1), 9-19. (In Persian)
- Wang. Y.M Traore. S, Kerh. T,2009, Computational performance of Reference evapotranspiration in semiarid zone of Africa, Sci, Research and Essay, 4, 6. 577-583.
- Grismer. M.E, Oran. M, Snyder. R., Matyac, R,2002, Pan Evaporation toreference evapotranspiration conversion methods, ASCE J. Irrig. and Drain. Eng, 128(30),180-184.
- Rahimi Koob. A, 2008, Comparative study of Hargrives's and artificial neural network's methodologies in estimating reference evapotranspiration in a semiarid environment, Irrig. Sci, 26(3),253-259.
- Kisi. O, 2007, Evapotranspiration modeling from climatic data using a neural computing technique. Hydro. Process, 21(6),1925-1934.
- Kisi. O,2007, Adaptive neurofuzzy computing technique for Evapotranspiration Estimation, Journal of Irrigation and Drainage Engineering, 133(4), 368-379.
- Kumar. M, Bandyopadhyay. A, Raghuwanshi. N.S, Singh. R, 2008, Comparative study of conventional and artificial neural network-based ET0 estimation models, Irrig. Sci. 26(6), 531-545.
- Aytek. A, Kisi. O, 2008, A genetic programming approach to suspended sediment modeling, J. Hydro, 351,288-298.
- Kim. S, Kim. H, 2008, Neural Networks and genetic algorithm approach for nonlinear evaporation and evapotranspiration modeling, J. Hydro, 351, 299-317.
- Tzimopoulos. C, Mpallas. L, Papaevangelou. G, 2008, Estimation of evapotranspiration using fuzzy systems and comparison with the blaney-criddle method. Environ, Sci. and Technol,4(1), 181-186.
- Moghaddamnia. A, Ghafari Gousheh. M, Piri. J, Amin. S, Han. D, 2009, Evaporation estimation using artificial neural networks and adaptive neuro fuzzyinference system techniques, Advances in Water Resources,32(1),89-97.
- Lin. C, Chao C, Chen. W.F, 2008, Estimation regional evapotranspiration by adaptive network-based fuzzy inference system for Dan-Shui basin in Taiwan. J. Chinese Inst. Eng, 30(6), 1091-1096.
- Korepaz dezfouli. A, 2006, Principles of fuzzy set theory and its applications in modeling water problems, Amir Kabir University of Technology Jihad Publications, Tehran. (In Persian)
- Sudheer. K.P, Gosain. A.K. Ramasastri. K.S, 2003, Estimating actual evapotranspiration from limited climatic data using neural computing technique, J. Irrg. Drain. Eng. ASCE, 129(3),214-218.
- Kisi. O, Ozturk. O, 2007, Adaptive neurofuzzy computing technique for evaptotranspiration estimation, J. Irrig. Drain. Eng. ASCE, 133(4), 368-379.
- Shayan Nejad. M, 2006, Calculation of groundwater drainage distance in unsustainable conditions using artificial neural networks, National Conference on Irrigation and Drainage Network Management, Shahid Chamran University of Ahvaz, Iran. (In Persian)
- Zare Abyaneh. H, Qasim. A., Bayat Warkshi. M, famous. P., 2009, Evaluation of the accuracy of artificial neural network in predicting evapotranspiration of garlic using lysimetric data in Hamadan region. Journal of Water and Soil (Agricultural Sciences and Industries), 23 (2), 185-176. (In Persian)
- Odhiambo. L.O, Yoder. R.E, Yoder. D.C, 2001a, estimating of reference crop evapotranspiration using fuzzy state models. Trans of the ASAE. No. 44(3), 543-550.
- Jia Bing. C, 2004, Prediction of daily reference evapotranspiration using adaptive neurofuzzy inference system. Trans of the Chinese society of Agricultural Engineering, 20(4),13-16.
- Dogan. E, 2009, Reference Evapotranspiration Estimation using adaptive nerofuzzy inference system. Journal of Irrigation and Drianage Engineering, 58,617-628.
- Kisi. O, 2010, Fuzzy Genetic Approach for modeling Reference Evapotranspiration, Journal of Irrigation and Drianage Engineering .136(3),175-183.
- Sayyadi. H, Olad Ghaffari. A, Ashrafsadrodini. A., 2009, Comparison of RBF and MLP neural network performance in estimating reference plant evapotranspiration. Journal of Soil and Water Knowledge 1 (19), 12-1. (In Persian)
- Meteorological profile of Khorasan Razavi, 2014, monthly meteorological data of Gonabad station. (In Persian)
- Allen. R.G, Raes. L.S, Smith. M, 1998, Crop Evapotranspiration Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper. No. 56. FAO. Rome, Italy.
- Monem. M, Khorami. J, Heydarian. A., 2007, Evaluating the performance of irrigation networks or using fuzzy logic: A case study of Maroon network. Tarbiat Modares Technical and Engineering Journal, 27, 42-31. (In Persian)
- afari Mianai. C, Agriculture. A., 2008, Comparison of fuzzy method and statistical regression to estimate sediment load of rivers. Fourth National Congress of Civil Engineering, Tehran. (In Persian)
- Jacquin. A, Shamseldin. A, 2006, Development of rainfall–runoff models using Takagi–Sugeno fuzzy inference systems. Journal of Hydrology, 329(1-2), 154-173.
- Coa. Z, Kandel. A, 1989, Application of some Fuzzy Implication Operators, FSS. 3, 42-52.
- Lee. C.C, 1990, Fuzzy Logic in Control Systems: Fuzzy Logic in Controller – part I & II. IEEE Transaction on systems, Man and Cybernetics, 20(2). P.419-435.
- Jacovides. C.P, 1997. Reply to comment on Statistical procedures for the evaluation of evapotranspiration models, Agricultural water management, 3, 95-97.
- Sabziparvar. A, Tafazoli. F. Zare Abyaneh. H, Banzhad. H. Mousavi Baygi. M, Ghafouri. M. Mohseni Movahed. A., Marianji, 2008, Comparison of several models for estimating the evapotranspiration of the reference plant in a cold and semi-arid climate for optimal use of radiation models. Journal of Water and Soil (Agricultural Sciences and Industries). 2 (22), 340-328
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- Waziri. ZH, Entesari. M, Masihi. M, Heydari. N. Dehghani, S., 2008, Evaporation and transpiration (instructions for calculating the water required by plants), Publications of the National Committee for Irrigation and Drainage, Tehran, 362. (In Persian)
- Jahanbakhsh Asl. Q, Movahed Danesh. A. and Rumi, and, 2001, Analysis of Evaporation and Transpiration Estimation Models for Tabriz Meteorological Station, Journal of Agricultural Knowledge, 11, 66-51. (In Persian)
- Kouchekzadeh. M, Bahmani. A., 2005, Evaluation of the performance of artificial neural networks in reducing the required parameters for estimating reference evapotranspiration, Journal ofAgricultural Sciences, 11 (4), 97-87. (In Persian)
- Alizadeh. A, Kamali. Gh, 2007, Water needs of plants in Iran, first edition, Astan Quds Razavi Publishing Institute, 228. (In Persian)
- Mousavi Baygi. M, mystics. M, Sarmad. M, 2009, Using Minimum Meteorological Data to Estimate Evapotranspiration of Reference Plant and Presenting Correction Coefficient (Case Study: Khorasan Razavi Province), Journal of Water and Soil (Agricultural Sciences and Industries), 23 (1), 9-19. (In Persian)
- Wang. Y.M Traore. S, Kerh. T,2009, Computational performance of Reference evapotranspiration in semiarid zone of Africa, Sci, Research and Essay, 4, 6. 577-583.
- Grismer. M.E, Oran. M, Snyder. R., Matyac, R,2002, Pan Evaporation toreference evapotranspiration conversion methods, ASCE J. Irrig. and Drain. Eng, 128(30),180-184.
- Rahimi Koob. A, 2008, Comparative study of Hargrives's and artificial neural network's methodologies in estimating reference evapotranspiration in a semiarid environment, Irrig. Sci, 26(3),253-259.
- Kisi. O, 2007, Evapotranspiration modeling from climatic data using a neural computing technique. Hydro. Process, 21(6),1925-1934.
- Kisi. O,2007, Adaptive neurofuzzy computing technique for Evapotranspiration Estimation, Journal of Irrigation and Drainage Engineering, 133(4), 368-379.
- Kumar. M, Bandyopadhyay. A, Raghuwanshi. N.S, Singh. R, 2008, Comparative study of conventional and artificial neural network-based ET0 estimation models, Irrig. Sci. 26(6), 531-545.
- Aytek. A, Kisi. O, 2008, A genetic programming approach to suspended sediment modeling, J. Hydro, 351,288-298.
- Kim. S, Kim. H, 2008, Neural Networks and genetic algorithm approach for nonlinear evaporation and evapotranspiration modeling, J. Hydro, 351, 299-317.
- Tzimopoulos. C, Mpallas. L, Papaevangelou. G, 2008, Estimation of evapotranspiration using fuzzy systems and comparison with the blaney-criddle method. Environ, Sci. and Technol,4(1), 181-186.
- Moghaddamnia. A, Ghafari Gousheh. M, Piri. J, Amin. S, Han. D, 2009, Evaporation estimation using artificial neural networks and adaptive neuro fuzzyinference system techniques, Advances in Water Resources,32(1),89-97.
- Lin. C, Chao C, Chen. W.F, 2008, Estimation regional evapotranspiration by adaptive network-based fuzzy inference system for Dan-Shui basin in Taiwan. J. Chinese Inst. Eng, 30(6), 1091-1096.
- Korepaz dezfouli. A, 2006, Principles of fuzzy set theory and its applications in modeling water problems, Amir Kabir University of Technology Jihad Publications, Tehran. (In Persian)
- Sudheer. K.P, Gosain. A.K. Ramasastri. K.S, 2003, Estimating actual evapotranspiration from limited climatic data using neural computing technique, J. Irrg. Drain. Eng. ASCE, 129(3),214-218.
- Kisi. O, Ozturk. O, 2007, Adaptive neurofuzzy computing technique for evaptotranspiration estimation, J. Irrig. Drain. Eng. ASCE, 133(4), 368-379.
- Shayan Nejad. M, 2006, Calculation of groundwater drainage distance in unsustainable conditions using artificial neural networks, National Conference on Irrigation and Drainage Network Management, Shahid Chamran University of Ahvaz, Iran. (In Persian)
- Zare Abyaneh. H, Qasim. A., Bayat Warkshi. M, famous. P., 2009, Evaluation of the accuracy of artificial neural network in predicting evapotranspiration of garlic using lysimetric data in Hamadan region. Journal of Water and Soil (Agricultural Sciences and Industries), 23 (2), 185-176. (In Persian)
- Odhiambo. L.O, Yoder. R.E, Yoder. D.C, 2001a, estimating of reference crop evapotranspiration using fuzzy state models. Trans of the ASAE. No. 44(3), 543-550.
- Jia Bing. C, 2004, Prediction of daily reference evapotranspiration using adaptive neurofuzzy inference system. Trans of the Chinese society of Agricultural Engineering, 20(4),13-16.
- Dogan. E, 2009, Reference Evapotranspiration Estimation using adaptive nerofuzzy inference system. Journal of Irrigation and Drianage Engineering, 58,617-628.
- Kisi. O, 2010, Fuzzy Genetic Approach for modeling Reference Evapotranspiration, Journal of Irrigation and Drianage Engineering .136(3),175-183.
- Sayyadi. H, Olad Ghaffari. A, Ashrafsadrodini. A., 2009, Comparison of RBF and MLP neural network performance in estimating reference plant evapotranspiration. Journal of Soil and Water Knowledge 1 (19), 12-1. (In Persian)
- Meteorological profile of Khorasan Razavi, 2014, monthly meteorological data of Gonabad station. (In Persian)
- Allen. R.G, Raes. L.S, Smith. M, 1998, Crop Evapotranspiration Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper. No. 56. FAO. Rome, Italy.
- Monem. M, Khorami. J, Heydarian. A., 2007, Evaluating the performance of irrigation networks or using fuzzy logic: A case study of Maroon network. Tarbiat Modares Technical and Engineering Journal, 27, 42-31. (In Persian)
- afari Mianai. C, Agriculture. A., 2008, Comparison of fuzzy method and statistical regression to estimate sediment load of rivers. Fourth National Congress of Civil Engineering, Tehran. (In Persian)
- Jacquin. A, Shamseldin. A, 2006, Development of rainfall–runoff models using Takagi–Sugeno fuzzy inference systems. Journal of Hydrology, 329(1-2), 154-173.
- Coa. Z, Kandel. A, 1989, Application of some Fuzzy Implication Operators, FSS. 3, 42-52.
- Lee. C.C, 1990, Fuzzy Logic in Control Systems: Fuzzy Logic in Controller – part I & II. IEEE Transaction on systems, Man and Cybernetics, 20(2). P.419-435.
- Jacovides. C.P, 1997. Reply to comment on Statistical procedures for the evaluation of evapotranspiration models, Agricultural water management, 3, 95-97.
- Sabziparvar. A, Tafazoli. F. Zare Abyaneh. H, Banzhad. H. Mousavi Baygi. M, Ghafouri. M. Mohseni Movahed. A., Marianji, 2008, Comparison of several models for estimating the evapotranspiration of the reference plant in a cold and semi-arid climate for optimal use of radiation models. Journal of Water and Soil (Agricultural Sciences and Industries). 2 (22), 340-328