Estimating Penman–Monteith Reference Evapotranspiration Using Artificial Neural Networks and Genetic Algorithm: A Case Study

Modern Techniques to Modeling Reference Evapotranspiration in a Semiarid Area Based on ANN and GEP Models

Evapotranspiration (ET) is a significant aspect of the hydrologic cycle, notably in irrigated agriculture. Direct approaches for estimating reference evapotranspiration (ET0) are either difficult or need a large number of inputs that are not always available from meteorological stations. Over a 6-year period (2006–2011), this study compares Feed Forward Neural Network (FFNN), Radial Basis Function Neural Network (RBFNN), and Gene Expression Programming (GEP) machine learning approaches for estimating daily ET0 in a meteorological station in the Lower Cheliff Plain, northwest Algeria. ET0 was estimated using the FAO-56 Penman–Monteith (FAO56PM) equation and observed meteorological data. The estimated ET0 using FAO56PM was then used as the target output for the machine learning models, while the observed meteorological data were used as the model inputs. Based on the coefficient of determination (R2), root mean square error (RMSE), and Nash–Sutcliffe efficiency (EF), the RBFNN and GEP models showed promising performance. However, the FFNN model performed the best during training (R2 = 0.9903, RMSE = 0.2332, and EF = 0.9902) and testing (R2 = 0.9921, RMSE = 0.2342, and EF = 0.9902) phases in forecasting the Penman–Monteith evapotranspiration.

Development of Boosted Machine Learning Models for Estimating Daily Reference Evapotranspiration and Comparison with Empirical Approaches

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.

Differential evolution based radial basis function neural network model for reference evapotranspiration estimation

The present study is an effort to examine the capability of a differential evolution based radial basis function neural network (RBFDE) to model weekly reference evapotranspiration (ET0) as a function of climatic parameters in different agro-climatic zones (ACZs) of a moist sub-humid region in East-Central India. The ET0 computed using the empirical equation of Penman–Monteith suggested by the Food and Agricultural Organization (FAO56-PM) is considered as a target variable for investigation. The performance of the proposed RBFDE model is compared with particle swarm optimization based radial basis function (RBFPSO), radial basis function neural network (RBFNN), multilayer artificial neural network (MLANN) models and conventional empirical equations of Hargreaves, Turc, Open-Pan, and Blaney-Criddle. Weekly ET0 estimates that are obtained using RBFDE, RBFPSO, and RBFNN and MLANN are observed to be more consistent than equivalent empirical methods. For a critical analysis of simulation results, mean absolute percentage error (MAPE), root means square error (RMSE), determination coefficient (R2) and Nash–Sutcliffe efficiency factor (NSE) is computed. Low MAPE and RMSE values along with higher R2 and NSE close to 1, obtained with soft computing models exhibit that, soft computing models produce better estimates of ET0 than empirical methods. Among the soft computing models, RBFDE provides improved results as compared to RBFPSO, RBFNN, and MLANN models. This method can be extended for ET0 estimation in other ACZs.

Modeling of Heat Transfer Coefficient in Solar Greenhouse Type Drying Systems

As a sustainable energy source, solar energy is used in many applications. A greenhouse type dryer, which is a food drying system, directly benefits from solar energy. Convective heat transfer coefficient (hc) is an important parameter in food drying systems, in terms of system design and performance. Many parameters and equations are used to determine hc. However, as it is difficult to manually process and analyze large amounts of data and different formulations, machine learning algorithms are preferred. In this study, natural and forced convective solar greenhouse type dryers were designed. In a solar greenhouse type dryer, grape is dried in natural (GDNC) and forced convection (GDFC). For convective heat transfer coefficient (hc), predictive models were created using a multilayer perceptron (MLP)—which has many uses in drying applications, as mentioned in the literature—and decision tree (DT), which has not been used before in food drying applications. The machine learning algorithms and results of the estimated models are compared in this study. Error analyses were performed to determine the accuracy rates of the obtained models. As a result, the hc value of the dried grape product in a natural convective solar greenhouse type dryer was 11.3% higher than that of the forced type. The DT algorithm was found to be a more successful model than the MLP algorithm in estimating hc values in HDFC according to Root Mean Square Error. (RMSE = 0.0903). On the contrary, the MLP algorithm was more successful than the DT algorithm in estimating hc values in GDNC (RMSE = 0.0815).

A Hybrid Data-Driven Machine Learning Technique for Evapotranspiration Modeling in Various Climates

In the current research, gene expression programming (GEP) was applied to model reference evapotranspiration (ETo) in 18 regions of Iran with limited meteorological data. Initially, a genetic algorithm (GA) was employed to detect the most important variables for estimating ETo among mean temperature (Tmean), maximum temperature (Tmax), minimum temperature (Tmin), relative humidity (RH), sunshine (n), and wind speed (WS). The results indicated that a coupled model containing the Tmean and WS can predict ETo accurately (RMSE = 0.3263 mm day−1) for arid, semiarid, and Mediterranean climates. Therefore, this model was adjusted using the GEP for all 18 synoptic stations. Under very humid climates, it is recommended to use a temperature-based GEP model versus wind speed-based GEP model. The optimal and lowest performance of the GEP belonged to Shahrekord (SK), RMSE = 0.0650 mm day−1, and Kerman (KE), RMSE = 0.4177 mm day−1, respectively. This research shows that the GEP is a robust tool to model ETo in semiarid and Mediterranean climates (R2 > 0.80). However, GEP is recommended to be used cautiously under very humid climates and some of arid regions (R2 < 0.50) due to its poor performance under such extreme conditions.