مقایسه توانایی توابع درون‌یابی اسپیلاین و بزیر در مدل‌سازی تبخیر-تعرق مرجع با استفاده از داده‌های تصاویر ماهواره‌ای

تبخیر-تعرق مرجع (et0) یکی از مهم‌ترین پارامترها در مدیریت و برنامه‌ریزی دقیق‌تر منابع آب است که بررسی آن، امکان مدل‌سازی و پیش‌بینی مصرف آب گیاهان را فراهم می‌کند. تصاویر ماهواره‌ای منبع ارزشمند با فواصل چندین روزه برای جبران کمبود اطلاعات هواشناسی هستند. در این پژوهش، جهت ریز مقیاس‌سازی داده‌های تصاویر ماهواره لندست و سنجنده‌ مادیس شامل دمای سطح زمین (lst) و شاخص تفاضل نرمال‌شده گیاهی (ndvi)، دو روش درون‌یابی اسپیلاین (s) و بزیر (b) استفاده شدند. با این توابع، داده‌های چند روزه تصاویر ماهواره‌ای شامل دمای سطح زمین، شاخص سطح برگ و شاخص تفاضل نرمال شده‌ پوشش گیاهی، به داده‌های روزانه تبدیل شدند و با کاربرد الگوریتم جنگل تصادفی (rf)، et0 روزانه تخمین زده شد. نتایج حاصل نشان داد که صحت تخمین et0 در ایستگاه تبریز در مدل‌های s-rf-10، b-rf-14 و در اردبیل با تلفیق پارامترهای هواشناسی و ماهواره‌ای به مقادیر حاصل از روش پنمن-مانتیث-فائو نزدیک‌تر بود. علاوه بر این، تحلیل آماری پارامترهای خطای مدل s-rf-10 در تبریز (0.98=r2، 0.36=rmse، 0.98=ns) و مدل b-rf-14 (0.98=r2، 36 /0=rmse، 0.98=ns)، در اردبیل مدل s-rf-9 (0.93=r2، 0.43=rmse، 0.95=ns) و b-rf-12 (0.95=r2، 459 /0=rmse، 0.94=ns) نشان دادند که در صورت استفاده از تمام داده‌های هواشناسی و ماهواره‌ای هر دو روش نتایج نزدیک به هم دارند، ولی در صورت کاهش اطلاعات ورودی، روش درون‌یابی اسپیلاین نسبت به بزیر صحت بالاتری در ریز مقیاس‌سازی جهت برآورد et0 روزانه دارد. یافته‌های پژوهش نشان داد که با استفاده از روش درون‌یابی اسپیلاین، بزیر و کاربرد روش جنگل تصادفی می‌توان مقادیر تبخیر–تعرق روزانه را با صحت قابل قبولی تخمین زد.

evaluation of spline and bezier interpolation functions in reference evapotranspiration modeling using satellite image data

introduction reference evapotranspiration (et0) is a crucial component in water resource management, forming the backbone of planning and forecasting agricultural water requirements. accurate calculations of et0 are indispensable for modeling crop water needs effectively. however, while satellite imagery provides valuable data for estimating et0, the irregularity of data capture intervals can hinder the availability of detailed meteorological information necessary for precise calculations. this issue presents a significant challenge, which this study aims to address. the importance and necessity of this research stem from its potential to significantly improve agricultural water management practices. by effectively combining satellite data with meteorological inputs, our study seeks to develop a methodology that enhances the accuracy of daily et0 estimations. such advancements are vital for ensuring efficient water usage and better resource management, ultimately promoting sustainable agricultural practices. thus, the goal of this research is to harness the complementary strengths of satellite-derived data and meteorological insights to create a robust and high-accuracy tool for estimating daily et0.materials and methods the standard fao-penman-monteith method, which is based on the penman-monteith equation that integrates radiometric and aerodynamic parameters, was adopted as the base method for calculating et0 of a reference crop. however, this method demands a large amount of meteorological data such as solar radiation, relative humidity, wind speed, and maximum/minimum temperature, which can be challenging to obtain. to overcome this limitation, satellite images from google earth engine system for the years 2001 to 2021 were processed using landsat sensors to extract parameters such as land surface temperature (lst), enhanced vegetation index (evi), leaf area index (lai), and normalized difference vegetation index (ndvi). these parameters can be used to estimate effective evapotranspiration continuously in the short term by applying models and interpolations. one of the problems of planning and management based on satellite image data is the lack of daily images of the study area. interpolation is a mathematical process that estimates unknown data at other points using data available at specific points. this process is used to fill in gaps, increase resolution, or create continuous maps from satellite data. the lst (8 days) and vegetation cover data (16 days) were converted into daily data using spline and cubic spline interpolation functions. this work was done using spline and bezier interpolation functions and for days without data at equal intervals, coded in mathematica.results and discussion the analysis identified that saturation vapor pressure and land surface temperature, recorded both during the day and night, exhibited the highest correlation and coefficient of determination with et0. for the tabriz station, scenario 10 demonstrated the most accurate et0 estimation, achieving a root mean square error (rmse) of 0.364. in comparison, the ardabil station reached its highest accuracy in scenario 12, with an rmse of 0.430. these findings indicate that models integrating both meteorological and satellite parameters are superior for achieving accurate et0 estimations. when comparing interpolation methods, the spline method provided more precise modeling than the bezier method, demonstrating its effectiveness in addressing the complexities inherent in et0 estimation tasks. however, incorporating additional parameters into the machine learning model, particularly the lai, unexpectedly decreased the model’s accuracy, suggesting that a more refined parameter selection may enhance predictive capabilities. conclusion the study explored the use of spline and bezier interpolation functions in conjunction with the random forest algorithm to enhance the accuracy of daily et0 modeling using satellite image data. by leveraging satellite imagery data, such as land surface temperature, leaf area index, and normalized difference vegetation index, alongside meteorological data, this research aimed to address the challenge of limited data availability often encountered in traditional methods like the fao-penman-monteith. in analyzing results from the tabriz and ardabil stations, it was revealed that the combination of meteorological and satellite data significantly improved the accuracy of et0 predictions. the spline interpolation method, particularly when paired with the random forest algorithm, consistently provided more precise estimations compared to the bezier method, especially under scenarios with reduced input information. at the tabriz station, the best et0 estimations were recorded in the s-rf-10 model (rmse = 0.364), while in ardabil, the s-rf-9 model yielded high accuracy (rmse = 0.430). importantly, the saturation vapor pressure emerged as the most influential meteorological factor, whereas land surface temperature held the highest correlation among satellite parameters.