Abstract
Proper irrigation scheduling and agricultural water management require a precise estimation of crop water requirement. In practice, reference evapotranspiration (ETo) is firstly estimated, and used further to calculate the evapotranspiration of each crop. In this study, two new coupled models were developed for estimating daily ETo. Two optimization algorithms, the shuffled frog-leaping algorithm (SFLA) and invasive weed optimization (IWO), were coupled on an adaptive neuro-fuzzy inference system (ANFIS) to develop and implement the two novel hybrid models (ANFIS-SFLA and ANFIS-IWO). Additionally, four empirical models with varying complexities, including Hargreaves–Samani, Romanenko, Priestley–Taylor, and Valiantzas, were used and compared with the developed hybrid models. The performance of all investigated models was evaluated using the ETo estimates with the FAO-56 recommended method as a benchmark, as well as multiple statistical indicators including root-mean-square error (RMSE), relative RMSE (RRMSE), mean absolute error (MAE), coefficient of determination (R2), and Nash–Sutcliffe efficiency (NSE). All models were tested in Tabriz and Shiraz, Iran as the two studied sites. Evaluation results showed that the developed coupled models yielded better results than the classic ANFIS, with the ANFIS-SFLA outperforming the ANFIS-IWO. Among empirical models, generally the Valiantzas model in its original and calibrated versions presented the best performance. In terms of model complexity (the number of predictors), the model performance was obviously enhanced by an increasing number of predictors. The most accurate estimates of the daily ETo for the study sites were achieved via the hybrid ANFIS-SFLA models using full predictors, with RMSE within 0.15 mm day−1, RRMSE within 4%, MAE within 0.11 mm day−1, and both a high R2 and NSE of 0.99 in the test phase at the two studied sites.
Highlights
The root-mean-square error (RMSE), relative RMSE (RRMSE), mean absolute error (MAE), R2, and Nash–Sutcliffe efficiency (NSE) statistical parameters obtained by the classic adaptive neuro-fuzzy inference system (ANFIS) at Tabriz and Shiraz stations are respectively presented in the first sections of Tables 5 and 6 for both training and test periods
The accuracy of classic ANFIS was enhanced by increasing the number of input predictors; there was a negligible difference between the performances of the
The inclusion of the wind speed (U2) in the M2 model (i.e., M3 model) led to further improvement of the performance of the classic ANFIS. This outcome confirmed the results of previous works [55,56] in that, wind speed solely showed the lowest accuracy in ETo modeling, considering this parameter along with the other meteorological parameters improved the ETo modeling performance
Summary
An accurate estimation of ET is required for many applications, such as optimal water resources management, irrigation planning, determination of irrigation intervals, design of irrigation systems, agricultural water management, and studies related to water balance at each area [1,2,3,4,5,6]. Lysimeters are commonly applied to directly measure the ET; measuring it with this method is costly and requires considerable time, making it difficult to use in many areas. Eddy covariance and Bowen ratio energy balance are other direct techniques of determining the ET that are not usually applied in practice due to their complexities and costs [7,8,9]. Indirect techniques are often used to estimate
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