دانشگاه محقق اردبیلی مدل سازی و مدیریت آب و خاک 2783-2546 6 1 2026 03 21 Estimation of Groundwater Levels in Arid Climates Using Machine Learning and Fuzzy Intelligent Systems برآورد سطح آب زیرزمینی در اقلیم خشک با رویکرد یادگیری ماشین و سامانه‌های هوشمند فازی 332 349 3998 10.22098/mmws.2025.17978.1637 FA سپیده زراعتی نیشابوری دانشجوی دکتری، گروه علوم و مهندسی آب، دانشکده کشاورزی، دانشگاه بیرجند، بیرجند، ایران عباس خاشعی سیوکی استاد، گروه علوم و مهندسی آب، دانشکده کشاورزی، دانشگاه بیرجند، بیرجند، ایران محمد قاسم اکبری دانشیار، گروه آمار، دانشکده علوم ریاضی و آمار، دانشگاه بیرجند، بیرجند، ایران Journal Article 2025 08 03 Abstract<br /><br />Introduction<br /><br />The escalating global demand for water, driven by population growth, urbanization, climate change, and excessive use of fertilizers and pesticides, has significantly impacted groundwater levels, leading to soil salinization and desertification. Continuous groundwater extraction exacerbates aquifer depletion, increasing pumping costs and limiting production capacity. Accurate groundwater level estimation is critical for effective water resource management, especially in arid and semi-arid regions like South Khorasan, Iran, where water scarcity is pronounced. This study aims to address the challenge of predicting monthly groundwater level fluctuations in the Birjand plain using advanced modeling techniques. Traditional physical and numerical models, while reliable, face limitations such as high computational demands, data dependency, and inability to handle nonlinear conditions effectively. In contrast, data-driven and artificial intelligence-based models offer simplicity, speed, and reasonable accuracy, particularly when historical data is available (Norouzi Khatiri et al., 2023). Fuzzy logic-based models, especially nonlinear fuzzy regression, excel in handling uncertainty and complex relationships in hydrological systems (Asadollahi, 2023). This research evaluates three fuzzy-based models—nonlinear fuzzy support vector regression (NLF-SVR), fuzzy nonlinear autoregressive regression (FNAR), and fuzzy linear least squares regression (FLSR)—using climatic variables (temperature, precipitation, humidity, and evapotranspiration) to enhance prediction accuracy and support sustainable groundwater.<br /><br />Materials and Methods<br /><br />The study was conducted in the Birjand plain, South Khorasan, Iran, a region characterized by an arid climate with an average annual rainfall of 169 mm in the plain and 216 mm in the highlands. The Birjand aquifer, spanning 3155 km², is heavily exploited, making it a critical case study for groundwater management. A comprehensive dataset covering daily climatic variables—mean air temperature (Tave), precipitation (Prc), relative humidity (RH), and evapotranspiration (ETo)—from April 1998 to March 2017 was compiled from regional meteorological and water authority stations. After quality control and preprocessing, daily data were aggregated into monthly values. The dataset was split into 70% for model training and 30% for validation. Three fuzzy-based models were developed: (1) Fuzzy Linear Least Squares Regression (FLSR), which extends classical regression to handle fuzzy data; (2) Nonlinear Fuzzy Support Vector Regression (NLF-SVR), combining fuzzy logic with support vector machines for nonlinear relationships; and (3) Fuzzy Nonlinear Autoregressive Regression (FNAR), designed for multi-variable fuzzy predictions. Model performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Nash-Sutcliffe Efficiency (NSE). Fuzzy numbers, particularly triangular fuzzy numbers, were used to model uncertainty, with Gaussian kernels applied for FNAR and NLF-SVR. Parameter optimization was achieved using grid search and generalized cross-validation (GCV).<br /><br />Results and Discussion<br /><br />The analysis revealed that the NLF-SVR model outperformed both FNAR and FLSR in predicting monthly groundwater levels in the Birjand plain, achieving an average RMSE of 0.15 m, MAE of 0.37 m, and NSE of 0.99. The model effectively captured complex, nonlinear relationships between climatic variables (Tave, Prc, RH, ETo) and groundwater levels, particularly during warmer months (July–September), where regular water consumption and evapotranspiration patterns enhanced predictability. In contrast, performance dipped in colder months (November–February) due to irregular precipitation and delayed groundwater recharge, aligning with findings by Zhang et al. (2022). The FNAR model showed acceptable performance, with higher sensitivity to seasonal climatic shifts, while FLSR struggled to model nonlinear dynamics, exhibiting higher errors and lower NSE. Nonlinear fuzzy models demonstrated robustness against outliers and noisy data, maintaining approximately 85% of their initial accuracy even with 30% noise, compared to a 60% accuracy drop in classical models. These findings align with studies by Sahoo et al. (2017) and Kumar et al. (2023), confirming the superiority of fuzzy-based approaches in handling hydrological uncertainties. Limitations include the study’s focus on a single region and reliance on climatic inputs alone, suggesting future inclusion of factors like land use and geological characteristics. The NLF-SVR model’s high accuracy supports its application in early.<br /><br />Conclusion<br /><br />This study demonstrates that nonlinear fuzzy models, particularly NLF-SVR, provide superior accuracy for predicting monthly groundwater levels in the Birjand plain, with RMSE of 0.15 m and NSE of 0.99, outperforming FNAR and FLSR. The ability of NLF-SVR to model complex, nonlinear relationships and handle data uncertainties makes it a robust tool for hydrological forecasting in arid climates. Key findings include the models’ enhanced performance during warmer months and reduced accuracy in colder seasons due to variable precipitation patterns. The robustness of fuzzy models against outliers and noisy data eliminates extensive preprocessing, preserving valuable information. Practically, NLF-SVR supports sustainable groundwater management through applications like drought warning systems and optimized irrigation scheduling. However, limitations such as region-specific data and the exclusion of non-climatic factors (e.g., land use, geology) suggest caution in generalizing results. Future research should test these models across diverse hydrogeological settings, integrate deep learning techniques, and incorporate additional variables like climate indices and satellite data. Developing multi-scale models to capture both short- and long-term fluctuations and creating decision-support systems for real-time water management are recommended. This study underscores the potential of fuzzy intelligent systems to enhance groundwater management in water-scarce regions, paving the way for advanced hydrological modeling. پایش دقیق تراز آب زیرزمینی، به‌ویژه در شرایط بهره‌برداری بی‌رویه در کشورهای در حال توسعه، برای مدیریت پایدار منابع و پیشگیری از پیامدهایی چون کاهش توان پمپاژ، نشست زمین و تراکم آبخوان‌ها ضرورتی انکارناپذیر است. با توجه به پیچیدگی فرآیندهای هیدرولوژیکی و عدم قطعیت‌های موجود در داده‌های اقلیمی، این مطالعه با هدف ارزیابی و مقایسه عملکرد مدل‌های فازی برای پیش‌بینی ماهانة تراز آب زیرزمینی دشت بیرجند انجام شد. سه مدل شامل رگرسیون بردار پشتیبان غیرخطی فازی (NLF-SVR)، رگرسیون تجمعی غیرخطی فازی (FNAR) و رگرسیون کم‌ترین مربعات خطی فازی (FLSR) با استفاده از داده‌های اقلیمی دما، رطوبت نسبی، بارش و تبخیر و تعرق طراحی و پیاده‌سازی شدند. نتایج نشان داد که مدل NLF-SVR با متوسط RMSE 0/15 متر، MAE 0/37 متر و NSE نزدیک به 99/0 عملکرد برتری نسبت به سایر مدل‌ها دارد. بر اساس معیارهای ارزیابی، مدل FNAR در جایگاه دوم قرار گرفت و حساسیت بیش‌تری نسبت به تغییرات فصلی نشان داد؛ در حالی که مدل FLSR به‌دلیل ماهیت خطی خود کم‌ترین دقت را داشت و قادر به بازنمایی پیچیدگی‌های فرآیند هیدرولوژیکی نبود. بیش‌ترین دقت مدل‌ها در ماه‌های گرم و ضعیف‌ترین عملکرد در ماه‌های سرد مشاهده گردید. این الگو ناشی از پایداری نسبی روابط بین متغیرهای اقلیمی و سطح آب زیرزمینی در فصول گرم و پیچیدگی‌های غیرخطی ناشی از تغییرات ناگهانی دما، یخبندان و نوسانات شدید بارش در فصول سرد است. در مجموع، مدل NLF-SVR به‌عنوان ابزاری کارآمد برای توسعه سامانه‌های هشدار زودهنگام، بهینه‌سازی برنامه‌ریزی کشاورزی و مدیریت پایدار منابع آب در مناطق خشک پیشنهاد می‌شود. https://mmws.uma.ac.ir/article_3998_bf22b01fd6f50fb0a3b3f6557350e59d.pdf