تحلیل الگوهای مکانی و زمانی تبخیر- تعرق پتانسیل با تلفیق روش‎های هارمونیک، استوکستیک و مونت کارلو (مطالعه موردی: حوضه آبریز زاینده رود)

نوع مقاله : مقاله کامل علمی پژوهشی

نویسندگان

1 دانشجوی دکتری منابع آب، گروه مهندسی آب، دانشکده کشاورزی، دانشگاه شهرکرد، شهرکرد، ایران

2 نویسنده مسئول، دانشیار گروه مهندسی آب، دانشکده کشاورزی، دانشگاه شهرکرد، شهرکرد، ایران

3 دانشیار گروه مهندسی آب، دانشکده کشاورزی، دانشگاه شهرکرد، شهرکرد، ایران

4 استاد گروه مهندسی آب، دانشکده کشاورزی، دانشگاه شهرکرد، شهرکرد، ایران

چکیده

سابقه و هدف: این تحقیق به ارائه روشی برای بررسی و تحلیل الگوهای مکانی و زمانی تبخیر- تعرق پتانسیل (ETp) در حوضه آبریز زاینده‎رود می‌پردازد. با توجه به اهمیت مدیریت منابع آب استفاده از روش‌های کارآمد برای پیش‌بینی تبخیر- تعرق (ET) ضروری است. تاکنون بررسی الگو‎های یاد‎شده به روش‎های متفاوت انجام شده است، با این‎حال روشی که بتواند ETp را در چارچوب دوره‎های خشک، نرمال و تر برای کل حوضه‎های آبریز با گام زمانی روزانه به‎مدت یک‎صد سال تحلیل کند، ارایه نشده است. در این مطالعه، یک روش تلفیقی برای این موضوع در سطح حوضه زاینده‎رود به عنوان محدوده تحقیق توسعه داده شد. این روش گام زمانی روزانه و شبکه‎ای نسبتا متراکم از نقاط را در سطح حوضه با هدف کاربرد در برنامه‎ریزی منابع و مصارف آب در‎نظر می‎گیرد.
مواد و روش‌ها: روش پیشنهادی از ترکیب سه روش تحلیل هارمونیک، استوکستیک و مونت کارلو برای مدل‌سازی و پیش‌بینی ETp استفاده می‎کند. روش هارمونیک به تحلیل الگوهای دوره‌ای، فصلی و سالیانه داده‌ها کمک می‌کند، روش استوکستیک به شبیه‌سازی نوسانات طبیعی در داده‌ها می‌پردازد و از روش مونت کارلو برای تحلیل سناریوهای مختلف آب و هوا استفاده می‎شود. در روش تلفیقی ابتدا تابع هارمونیک به داده‎های دمای هوای بیشینه و کمینه کل ایستگاه‎های حوضه زاینده‎رود و پیرامون آن در یک دوره آماری بلندمدت 26 ساله از 1994 تا 2019 برازش داده شد. سپس توزیع آماری باقیمانده‎ها مشخص شد، همبستگی بین پارامترهای دمای هوا تعیین و مراحل تولید اعداد تصادفی انجام گردید. با استفاده از روش‎های استوکستیک و مونت‎کارلو، یک‎صد سال آمار برای متغیرهای دمای هوای بیشینه و کمینه به صورت روز‎به‎روز تولید شد تا در گام بعدی به روش هارگریوز- سامانی بتوان ETp را محاسبه کرد. برآورد ETp در شبکه متراکمی از نقاط در کل حوضه به روش عکس مجذور فاصله برای دستیابی به الگوهای مکانی انجام شد. با استفاده از شاخص صدک‎ها که در آن صدک 20 درصد برای خشکسالی ملایم، 50 درصد برای نرمال و 80 درصد برای ترسالی ملایم پیشنهاد شد، شرایط رطوبتی مختلف قابلیت بررسی یافتند. اعتبارسنجی برای دوره نرمال مدل صورت پذیرفت. بدین منظور، داده‎های مدل با مقادیر مشاهداتی در گستره نواحی کشاورزی حوضه و برای دوره کشت گندم با آزمون‎های همبستگی و همچنین ANOVA یک طرفه، معنی‎دار بودن اختلاف میانگین‎ها را رد کرد و دقت نتایج مدل را تایید نمود.
یافته‌ها: روند افزایشی ETp در همه نواحی کشاورزی سرتاسر حوضه مشاهده شد، به نحوی که شیب روند به روش سن (Sen) از 28/1 میلی‎متر در دوره کشت گندم در اراضی پایین‎دست سد خمیران تا 73/3 میلی‎متر در دوره کشت گندم در اراضی مهیار و جرقویه تغییر می‎کند. با توجه به این که کمترین دوره کشت گندم مربوط به رودشت 211 روز و بیشترین دوره در فریدون‎شهر 288 روز می‎باشد، انتظار می‎رود مقدار ETp در شرایط نرمال به ترتیب 598 و 795 میلی‎متر در دوره کشت گندم باشد. بررسی‎ها در سطح حوضه آبریز نیز نشان می‎دهد مقدار ETp در نواحی کوهستانی حوضه و در شرایط نرمال بین 1299 تا 1515 میلی‎متر در سال تغییر می‎کند. این در حالی است که در مناطق مسطح شرقی، تغییرات ETp از 1524 تا 1609 میلی‎متر است. در شرایط خشک ملایم تغییرات ETp در نواحی مرتفع از 1320 تا 1540 و در نواحی مسطح از 1547 تا 1644 میلی‎متر در سال است. همین تغییرات برای شرایط ترسالی ملایم در نواحی کوهستانی از 1276 تا 1460 و در دشت‎ها از 1491 تا 1583 میلی‎متر در‎سال تخمین زده شده است.
نتیجه‎گیری: نتایج این مطالعه نشان می‌دهد که استفاده از روش تلفیقی می‌تواند به شناخت بهتری از الگوهای زمانی و مکانی ETp در حوضه‎های آبریز منجر شود، دقت پیش‌بینی‌ها را افزایش دهد و وضعیت حوضه را تحت شرایط آب و هوایی مختلف تحلیل نماید.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Analysis of spatial and temporal patterns of potential evapotranspiration by combining harmonic, stochastic and Monte Carlo methods (Case study: Zayandehrud basin)

نویسندگان [English]

  • Esmaeil Adib Majd 1
  • Rasoul Mirabbsi 2
  • Mehdi Asadi 3
  • Sayyed-Hassan Tabatabaei 4
1 Ph.D. Student of Water Resources, Dept. of Water Engineering, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran.
2 Corresponding Author, Associate Prof., Dept. of Water Engineering, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran
3 Associate Prof., Dept. of Water Engineering, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran.
4 Professor, Dept. of Water Engineering, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran
چکیده [English]

Background and objectives: This research presents a method to investigate and analyze the spatial and temporal patterns of potential evapotranspiration (ETp) in Zayandehroud basin. Due to the water resources management importance, it is necessary to use efficient methods to predict evapotranspiration (ET). So far, these patterns have been studied in different ways. However, a method that can estimate ETp for dry, normal and wet periods with a daily time step during a hundred years has not yet been presented. In this study, a hybrid method for temporal and spatial analysis of ETp was developed for the Zayandehroud basin as a research area. This method considers the daily time step and a relatively dense network of points at the basin level.
Materials and methods: The proposed method involves a combination of three approaches, namely harmonic, stochastic and Monte Carlo methods, to model and predict ETp. Harmonic method helps to analyze periodic, seasonal and annual patterns of data, stochastic method simulates natural fluctuations in data and Monte Carlo method is used to analyze different weather scenarios. In the hybrid method, the harmonic function was first fitted to the maximum and minimum air temperature data of all stations in the zayandehroud basin and its surroundings over a 26-years period, from 1994 to 2019. Then, the statistical distribution of the residuals and the correlation between the air temperature parameters were determined, and the steps of random number generation were performed. Using stochastic and Monte Carlo methods, 100-years of statistics for extremum air temperature variables were produced daily, so that ETp can be calculated in the next step using the Hargreaves-Samani method. Estimation of ETp was done in a dense network of points over the basin by the inverse squared distance method to obtain spatial patterns. By using the percentile index, in which 20% was suggested for mild drought, 50% for normal and 80% for mild drought, different humidity conditions could be investigated. The validation was performed for the normal period of the hybrid model. Thereby, the model data were compared with the observed values in the agricultural areas of the basin and for the period of wheat cultivation (PWC) using correlation tests and also one-way ANOVA, rejecting the significance of the mean difference and confirming the accuracy of the model results.
Results: The increasing trend of ETp was observed in all the agricultural areas throughout the basin, so that the slope of the trend according to the Sen method was from 1.28 mm/PWC in the lands downstream of Khamiran Dam to 3.73 mm/PWC is changing in Mahyar and Jarguyeh lands. The shortest growing period for wheat is observed in Roudasht with 211 days, while Fereidunshahr has the longest growing period of 288 days. Consequently, the expected ETp values under normal conditions are about 598 millimeters for Roudasht and 795 millimeters for Fereidunshahr in PWC. Investigations at the watershed level show that the ETp value in the mountainous regions of the basin typically varies between 1299 and 1515 mm/y under normal conditions. In contrast, the flat eastern areas have ETp values between 1524 and 1609 mm/y. Under moderately dry conditions, ETp values in the higher regions vary between 1320 and 1540 mm/y, while in the flat areas, they range between 1547 and 1644 mm/y. The same changes are estimated from 1276 to 1460 mm/y in the mountainous regions and from 1491 to 1583 mm/y in the plains.
Conclusion: The results show that using a hybrid approach improves the understanding of evapotranspiration patterns in a basin, increases prediction accuracy, and facilitates the analysis of events in the basin under different climatic conditions.

کلیدواژه‌ها [English]

  • Temporal and spatial
  • Climate changes
  • Modeling
  • Hargreaves Samani
  • Random generators

مراجع

1.Senay, G. B., Leake, S., Nagler, P. L., Artan, G., Dickinson, J., Cordova, J. T., & Glenn, E. P. (2011). Estimating basin scale evapotranspiration (ET) by water balance and remote sensing methods. Hydrological Processes, 25 (26), 4037-4049. https://doi.org/10.1002/hyp.8379.
2.Smith, M. (2000). The application of climatic data for planning and management of sustainable rainfed and irrigated crop production. Agricultural and Forest Meteorology, 103 (1), 99-108. https://doi.org/10.1016/S0168-1923(00) 00121-0.
3.Liu, X., & Yang, D. (2021). Irrigation schedule analysis and optimization under the different combination of P and ETp using a spatially distributed crop
model. Agricultural Water Management, 256, 10-89. https://doi.org/10.1016/j. agwat.2021.107084.
4.Snyder, R. L., Moratiel, R., Zhenwei Song, Swelam, A., Jomaa, I., & Shapland, T. (2011). Evapotranspiration Response to Climate Change. International Society for Horticultural Science. 922, 91-98. https://doi.org/10.17660/ActaHortic.2011.922.11.
5.Nikolaou, G., Neocleous, D., Manes, A., & Kitta, E. (2024). Calibration and validation of solar radiation-based equations to estimate crop evapotranspiration in a semi-arid climate. International Journal of Biometeorology, 68 (1), 1-15. https://doi.org/10. 1007/ s00484-023-02566-5.
6.Dinpashoh, Y., Jahanbakhsh-Asl, S., & Mosavi-Jahani, L. (2023). Evaluation of the three empirical models in estimation of potential evapotranspiration (Case study: Urmia Lake basin), Water and Soil Science, 33 (3), 21-32. doi: 10.22034/ ws.2021.46416.2419.
7.Dinpashoh, Y., & Babamiri, O. (2020). Trends in reference crop evapotranspiration in Urmia Lake basin. Arabian Journal of Geosciences, 13, 1-16.
8.Dinpashoh, Y., Jhajharia, D., Fakheri-Fard, A., Singh, V. P., & Kahya, E. (2011). Trends in reference crop evapotranspiration over Iran. Journal of Hydrology, 399 (3-4), 422-433.
9.Hargreaves, G. H., & Samani, Z. A. (1985). Reference crop evapotranspiration from temperature. Applied Engineering in Agriculture, 1 (2), 96-99. doi: 10. 13031/2013.26773) @1985.
10.Blaney, H. F., & Criddle, W. D. (1962). Determining consumptive use and irrigation water requirements No. 1275. U.S. Department of Agriculture, Beltsville.
11.Yang, Y., Shang, S., & Jiang, L. (2012). Remote sensing temporal and spatial patterns of evapotranspiration and the responses to water management in a large irrigation district of North China. Agricultural and Forest Meteorology, 164, 112-122. https://doi.org/ 10.1016/ j.agrformet.2012.05.011.
12.Chen, X., Yu, S., Zhang, H., Li, F., Liang, C., & Wang, Z. (2023). Estimating the Actual Evapotranspiration Using Remote Sensing and SEBAL Model in an Arid Environment of Northwest China. Water, 15 (8), 1555-1573. https://doi.org/10.3390/w15081555.
13.Mekonnen, Y. G., Alamirew, T., Malede, D. A., Pareeth, S., Bantider, A., & Chukalla, A. D. (2024). Tailoring the surface energy balance algorithm for land-improved (SEBALI) model using high-resolution land/use land cover for monitoring actual evapotranspiration. Agricultural Water Management, 303, 109058-109071. https://doi.org/ 10.1016/j.agwat.2024.109058.
14.Xu, T., Liu, S., Xu, L., Chen, Y., Jia, Z., Xu, Z., & Nielson, J. (2015). Temporal upscaling and reconstruction of thermal remotely sensed instantaneous evapotranspiration. Remote Sensing, 7 (3), 3400-3425. https://doi.org/10. 3390/rs70303400.
15.Fakhar, M. S., & Kaviani, A. (2024). Estimation of water consumption volume and water efficiency in irrigated and rainfed agriculture based on the WaPOR database in Iran. Journal of Water and Climate Change, 15 (6), 2731-2752. https://doi.org/10. 2166/wcc.2024.655.
16.Gundekar, H. G., Khodke, U. M., Sarkar, S., & Rai, R. K. (2008). Evaluation of pan coefficient for reference crop evapotranspiration for semi-arid region. Irrigation Science, 26, 169-175. https://doi.org/10.1007/ s00271-007-0083-y.
17.Bruton, J. M., McClendon, R. W., & Hoogenboom, G. (2000). Estimating daily pan evaporation with artificial neural networks. Transactions of the ASAE, 43 (2), 491-496. doi: 10.13031/ 2013.2730) @2000.
18.Zhao, H., Di, L., Guo, L., Zhang, C., & Lin, L. (2023). An Automated Data-Driven Irrigation Scheduling Approach Using Model Simulated Soil Moisture and Evapotranspiration. Sustainability, 15 (17), 12908-12922. https://doi.org/ 10.3390/su151712908.
19.Christensen, L., Tague, C. L., & Baron, J. S. (2008). Spatial patterns of simulated transpiration response to climate variability in a snow dominated mountain ecosystem. Hydrological Processes, 22 (18), 3576-3588. https:// doi.org/10.1002/hyp.6961.
20.Song, L., Liu, S., Kustas, W. P., Nieto, H., Sun, L., Xu, Z., ... & Li, Q. (2018). Monitoring and validating spatially and temporally continuous daily evaporation and transpiration at river basin scale. Remote sensing of Environment,
219, 72-88. https://doi.org/10.1016/ j.rse.2018.10.002.
21.Sun, Z., Lotz, T., & Huang, Q. (2021). An ET-based two-phase method for the calibration and application of distributed hydrological models. Water Resources Management, 35, 1065-1077. https:// doi.org/10.1007/s11269-021-02774-x.
22.Cui, L., Meng, J., Li, Y., An, J., Zou, Z., Zhong, L., ... & Wu, G. (2024). Spatiotemporal Evolution Characteristics of 2022 Pakistan Severe Flood Event Based on Multi-Source Satellite Gravity Observations. Remote Sensing, 16 (9), 1601-1619. https://doi.org/10. 3390/rs16091601.
23.Okkan, U., Fistikoglu, O., Ersoy, Z. B., & Noori, A. T. (2024). Analyzing the uncertainty of potential evapotranspiration models in drought projections derived for a semi-arid watershed. Theoretical and Applied Climatology, 155 (3), 2329-2346. https:// doi.org/ 10.1007/ s00704-023-04817-2.
24.Wilhite, D. A., & Glantz, M. H. (1985). Understanding: the Drought Phenomenon: The Role of Definitions. Water International, 10 (3), 111-120. https://doi.org/10.1080/02508068508686328.
25.Mishra, A. K., & Singh, V. P. (2010). A review of drought concepts. Journal of Hydrology, 391 (1-2), 202-216. https://doi.org/10.1016/j.jhydrol.2010.07.012.
26.Gibbs, W. J., & Maher, J. V. (1967). Rainfall deciles drought indicators. Bureau of Meteorology. Commonwealth of Australia, Melbourne, Australia, 48-84.
27.Carpintero, E., Anderson, M. C., Andreu, A., Hain, C., Gao, F., Kustas, W. P., & González-Dugo, M. P. (2021). Estimating evapotranspiration of mediterranean oak savanna at multiple temporal and spatial resolutions. Implications for water resources management. Remote Sensing, 13 (18), 3701-3722. https://doi.org/10. 3390/rs13183701.
28.Zhang, P., Cai, Y., Yang, W., Yi, Y., Yang, Z., & Fu, Q. (2019). Multiple spatio-temporal patterns of vegetation coverage and its relationship with climatic factors in a large dam-reservoir-river system. Ecological Engineering, 138, 188-199. https://doi.org/10.1016/ j.ecoleng.2019.07.016.
29.Saxena, D., Choudhary, M., & Sharma, G. (2024). Land use and land cover change impact on characteristics of surface evapotranspiration in semi-arid environment of Western Rajasthan, India. Water Practice & Technology, 19 (1), 154-169. https://doi.org/10. 2166/wpt.2023.222.
30.Song, Y., Khalid, Z., & Genton, M. G. (2024). Efficient stochastic generators with spherical harmonic transformation for high-resolution global climate simulations from CESM2-LENS2. Journal of the American Statistical Association, (just-accepted), 1-23. https://doi.org/10.1080/01621459.2024.2360666.
31.Fetene, Z. A., Weldegerima, T. M., Zeleke, T. T., & Nigussie, M. (2018). Harmonic analysis of precipitation time series in Lake Tana Basin, Ethiopia. Advances in Meteorology, 2018 (1), 1598195-1598217. https:// doi.org/10.1155/2018/1598195.
32.Raczyński, K., & Dyer, J. (2023). Harmonic oscillator seasonal trend (HOST) model for hydrological drought pattern identification and analysis. Journal of Hydrology, 620, 129514-129522. https://doi.org/10.1016/j.jhydrol.2023.129514.
33.Javadi, A., Ghahremanzadeh, M., Sassi, M., Javanbakht, O., & Hayati, B. (2024). Impact of climate variables change on the yield of wheat and rice crops in Iran (application of stochastic model based on Monte Carlo simulation). Computational Economics, 63 (3), 983-1000. https://doi.org/10. 1007/s10614-023-10389-0.
34.Mundform, D. J., Schaffer, J., Kim, M. J., Shaw, D., & Thongteeraparp, A. (2011). Number of replications required in Monte Carlo simulation studies: a synthesis of four studies. Journal of Modern Applied Statistical Methods,
10, 19-28. https://doi.org/10.56801/ 10.56801/v10.i.520.
35.Cassettari, L., Mosca, R., & Revetria, R. (2012). Monte Carlo simulation models evolving in replicated runs: a methodology to choose the optimal experimental sample size. Mathematical Problems in Engineering, 2012 (1), 463873-463884. https://doi.org/10.1155/2012/463873.
36.Schmidt, S. (2009). Shall we really do it again? The powerful concept of replication is neglected in the social sciences. Review of General Psychology, 13 (2), 90-100. https://doi.org/10.1037/ a0015108.
37.Cova, F., Strickland, B., Abatista, A., Allard, A., Andow, J., Attie, M., ... & Zhou, X. (2021). Estimating the reproducibility of experimental philosophy. Review of Philosophy and Psychology, 12, 9-44. https://doi.org/ 10.1007/s13164-018-0400-9.
38.Khalili, A., Bazrafshan, J., & Cheraghalizadeh, M. (2022). A Comparative study on climate maps of Iran in extended de Martonne classification and application of the method for world climate zoning, Journal of Agricultural Meteorology,
10 (1), 3-16. doi: 10.22125/agmj.2022. 156309. [In Persian]
39.Sabbaghi, M. A., Nazari, M., Araghinejad, S., & Soufizadeh, S. (2020). Economic impacts of climate change on water resources and agriculture in Zayandehroud river basin in Iran. Agricultural Water Management, 241, 106323-106345. https://doi.org/ 10.1016/j.agwat.2020.106323.
40.Naderianfar, E., Delbari, M., Afrasiab, P., & Kahkhamoghaddam, P. (2020). Comparing Different Processes for Mapping Reference Evapotranspiration in Iran. Irrigation Sciences and Engineering, 43 (3), 17-31. https:// doi.org/10.22055/jise.2017.20116.1439.
41.Steele, T. D. (1978). A simple-harmonic model for depicting the annual cycle of seasonal temperatures of streams. US Geological Survey, 78-155. https:// doi.org/10.3133/ofr78155.
42.Phillips, W. F. (1984). Harmonic analysis of climatic data. Solar Energy, 32 (3), 319-328. https://doi.org/10. 1016/0038-092X(84)90274-3.
43.Tarawneh, Q. (2016). Harmonic analysis of precipitation climatology in Saudi Arabia. Theoretical and Applied Climatology, 124, 205-217. https://doi. org/10.1007/s00704-015-1408-z.
44.Wang, K., Li, Y., Luo, Z., Yin, S., & Chan, P. W. (2018). Harmonic analysis of 130-year hourly air temperature in Hong Kong: detecting urban warming from the perspective of annual and daily cycles. Climate Dynamics, 51, 613-625. https://doi.org/ 10.1007/ s00382-017-3944-y.
45.Yang, Z. C. (2024). Data-driven discrete cosine transform (DCT)-based modeling and simulation for hourly air humidity prediction. Soft Computing, 28 (1), 541-563. https://doi.org/10. 1007/s00500-023-08297-4.
46.L’Ecuyer, P. (2012). Random Number Generation. In: Gentle, J., Härdle, W., Mori, Y. (eds) Handbook of Computational Statistics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https:// doi.org/10.1007/978-3-642-21551-3_3.
47.Babamiri, O., & Dinpajooh, Y. (2014). Comparison and Calibration of Nine Mass Transfer-Based Reference Crop Evapotranspiration Methods at Urmia Lake Basin, Journal of Water and Soil Conservation, 5 (21), 135-153. [In Persian]
48.Thomas, J., & Β Fiering, M. (1962). Mathematical Synthesis of Streamflow Sequences for the Analysis of River Basins by Simulation. Design of Water-Resource Systems: New Techniques for Relating Economic Objectives, Engineering Analysis and Governmental Planning, 459-493. https://doi.org/10. 4159/harvard.9780674421042.c15.
49.Talaee, P. H., Some’e, B. S., & Ardakani, S. S. (2014). Time trend and change point of reference evapotranspiration over Iran. Theoretical and Applied Climatology, 116 (3-4), 639-647. https://doi.org/10. 1007/s00704-013-0978-x.
50.Sun, J., Wang, G., Sun, X., Lin, S., Hu, Z., & Huang, K. (2020). Elevation‐dependent changes in reference evapotranspiration due to climate change. Hydrological Processes, 34 (26), 5580-5594. https://doi.org/ 10.1002/hyp.13978.
51.Collins, B., Ramezani Etedali, H., Tavakol, A., & Kaviani, A. (2021). Spatiotemporal variations of evapotranspiration and reference crop water requirement over 1957–2016 in Iran based on CRU TS gridded dataset. Journal of Arid Land, 13, 858-878. https://doi.org/ 10.1007/ s40333-021-0103-4.
52.He, H., Wu, Z., Li, D., Zhang, T., Pan, F., Yuan, H., ... & Wang, F. (2022). Characteristics of winter wheat evapotranspiration in Eastern China and comparative evaluation of applicability of different reference evapotranspiration models. Journal of Soil Science and Plant Nutrition, 22 (2), 2078-2091. https://doi.org/ 10.1007/ s42729-022-00795-y.
53.Singandhupe, R. B., & Sethi, R. R. (2005). Estimation of reference evapotranspiration and crop coefficient in wheat under semi-arid environment in India. Archives of Agronomy and Soil Science, 51 (6), 619-631. https:// doi.org/10.1080/03650340500273831.
54.Poudyal, S., & Chaudhary, A. (2023). Evapotranspiration and Precipitation Data for Calculating Irrigation Requirements in Utah. Utah Climate Center, 435, 1-16. https://extension. usu.edu/irrigation/research/evapotranspiration-and-precipitation-data.
مجله پژوهش‌های حفاظت آب و خاک
دوره 31، شماره 4
دی 1403
صفحه 63-88

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