Developing a Mass Transfer-Based Reference Evapotranspiration Estimation Model Using Nonlinear Regression Method

Abstract

Reference evapotranspiration (ETo) is defined as the total mass of water vapour transferred to the atmosphere by evaporation from the soil surface and transpiration from the reference grass plant. ETo occurs through mass transfer based on atmospheric vapour pressure deficit and is used as primary data in many studies within the scope of hydrology science. ETo can be measured directly with lysimeter systems. However, measurement processes performed with these systems are difficult and time-consuming. For this reason, the approach of estimating the ETo using mass transfer-based empirical models is more preferred in practice. This study aims to create a mass transfer-based ETo estimation model compatible with Van province microclimate area climatic and environmental conditions. The estimation model was created via the Microsoft Excel program solver add-on using the 11-year daily average climate data measured between 2012 and 2022, and was tested with the same data. The mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE) and determination coefficient (R2) calculated as an indicator of the deviation between the daily ETo values estimated using this model and the daily ETo values estimated using the standard FAO-56 Penman & Monteith (PM) equation, were determined as 0.27 mm/day, 7.02%, 0.32 mm/day and 0.98, respectively. It is concluded that the mass transfer-based model can be used as an alternative to the standard FAO-56 PM equation in Van conditions. Additionally, it is believed that this model will be beneficial for preparing irrigation schedules and drought action plans under local conditions.

Keywords

• Nonlinear regression
• Mass transfer
• Penman-Monteith
• Reference evapotranspiration
• Estimation model

Doğrusal Olmayan Regresyon Yöntemi Kullanılarak Kütle Transferine Dayalı bir Referans Evapotranspirasyon Tahmin Modeli Geliştirilmesi

Abstract

Referans evapotrasnpirasyon (ETo), toprak yüzeyinden buharlaşma ve referans çim bitkisinden terleme yolu ile atmosfere transfer edilen toplam su buharı kütlesi olarak tanımlanmaktadır. Hidroloji bilimi kapsamındaki birçok çalışmada temel veri olarak kullanılan ETo, atmosferik buhar basıncı açığına dayalı kütle transferi yolu ile gerçekleşmektedir. ETo, lizimetre sistemleri ile doğrudan ölçülebilmektedir. Ancak, bu sistemler ile gerçekleştirilen ölçme işlemleri zor ve zaman alıcıdır. Bu nedenle, kütle transferine dayalı ampirik modeller kullanılarak ETo miktarının tahmin edilmesi yaklaşımı pratikte daha fazla tercih edilmektedir. Bu çalışmada, Van ili mikroklima alanı iklim ve çevre koşulları ile uyumlu kütle transferine dayalı bir ampirik ETo tahmin modelinin oluşturulması amaçlanmıştır. Tahmin modeli, 2012 ile 2022 yılları arasında ölçülen 11 yıllık günlük ortalama iklim verileri kullanılarak, Microsoft Excel programı çözücü eklentisi aracılığıyla oluşturulmuş ve aynı verilerle test edilmiştir. Bu model kullanılarak tahmin edilen günlük ETo değerleri ile standart FAO-56 Penman & Monteith (PM) eşitliği kullanılarak tahmin edilen günlük ETo değerleri arasındaki sapmanın bir göstergesi olarak hesaplanan ortalama mutlak hata (MAE), ortalama mutlak yüzde hata (MAPE), karekök ortalama karesel hata (RMSE) ve regresyon katsayısı (R2) katsayısı sırasıyla 0.27 mm/gün, %7.02, 0.32 mm/gün ve 0.98 olarak belirlenmiştir. Kütle transferine dayalı modelin Van ili koşullarında standart FAO-56 PM eşitliğinin alternatifi olarak kullanılabileği sonucuna ulaşılmıştır. Ayrıca, bu modelin yöre koşullarında hazırlanacak sulama programı ve kuraklık eylem planı çalışmalarında faydalı olacağı düşünülmektedir.

Keywords

• Doğrusal olmayan regresyon
• Kütle transferi
• Penman-Monteith
• Referans evapotranspirasyon
• Tahmin modeli

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