Modeling of the evaporation process using the hybrid algorithm of the COOT bird and artificial neural network

Introduction
Due to global warming, accurately estimating evaporation has become a key challenge in water resource management, and due to the important role it plays in the withdrawal of water from human reach, it has always attracted the attention of researchers. Therefore, modeling and awareness of the value of evaporation as one of the hydrological variables is of great importance in agricultural research and soil and water conservation. Gorgan was chosen for the study due to its proximity to the Caspian Sea with a humid climate and a higher rate of evaporation than other cities. On the other hand, Shiraz has a hot and dry climate, is located in central Iran far from water resources such as the sea, and has a lower evaporation rate. Kish also has a warm and humid climate due to its proximity to the sea, with a lower evaporation rate than Shiraz but higher than Gorgan. Several meteorological variables affect the process of evaporation and transpiration, and due to the complexity of the evaporation parameter, a method with high accuracy should be used to determine them. Recently, artificial neural network methods have become very popular among researchers due to their common use and the ease with which they can solve complex problems. Therefore, many intelligent algorithms have been suggested to find the best solution for complex engineering problems, as they can find optimal answers faster and more accurately.
 
Materials and Methods
Artificial neural networks are designed based on inspiration from the memory and learning mechanisms in the human brain. To train artificial neural networks, a set of valid input and output data is used based on the type of problem. The accuracy of the network output depends on the amount of training data and how the inputs and their features are processed. To design different scenarios for adjusting input data, the correlation values of the data with evaporation were used. In this study, three synoptic stations with different climates, including Gorgan, Shiraz, and Kish, were chosen. Three stations with different climates were used to better evaluate and repeat the steps of the method so that the efficiency of the method could be more accurately assessed. Considering the importance of the value of evaporation in nature, evaporation modeling with the ANN and its combination with the COOT algorithm, which mimics the natural life of a COOT bird, was performed using five meteorological parameters, including the minimum air temperature, maximum air temperature, wind speed, average relative humidity, and sunshine hours on a monthly between 2000 and 2022. The dataset was divided into two phases: training (70 % of the dataset) and testing (30% of the dataset). To evaluate the performance of developed models, statistical indices of these models such as correlation coefficient (R), root-mean-square error (RMSE), Nash-Sutcliffe coefficient (NS), and their graphical representations were compared with each other.
 
Results and Discussion
As mentioned, four models of ANN-COOT with varying input parameters were developed and compared to four conventional ANN models. Statistical performances were calculated, and comparison plots were made in the training and testing phases to find the most adequate model for the prediction of evaporation. Comparing of obtained results from statistical indices for the testing phase revealed that the COOT-ANN4 model had the best performance for Gorgan with the R, RMSE, and NS equal to 0.99, 8.19, and 0.99 respectively. Shiraz also obtained values of the R, RMSE, and NS equal to 0.99, 18.43, and 0.98 respectively. Similarly, for Kish, the values of the R, RMSE, and NS equal to 0.97, 19.36, and 0.93 respectively, have better performance than the other models. Compared with the results of different input combinations, the hybrid ANN-COOT model (ANN-COOT4) at three stations was found superior with input combinations of Tmin, Tmax, SSH, RH, and WS. Additionally, to evaluate the accuracy of developed models, Scatter plots, Violin plots, Relative error percent plots (RE %), Taylor diagrams, and Histograms were drawn. By comparing the graphical representations, it can be determined that the hybrid COOT with ANN4, namely the COOT-ANN4 model, has improved the artificial neural network at Gorgan, Shiraz, and Kish stations.
 
Conclusion
The algorithm of COOT is an optimization algorithm that is generally used to solve optimization problems. As observed from the overall performance of the results of the hybrid model in predicting evaporation, the objective function was minimized. The results indicated that scenario four of the COOT-ANN4 hybrid model with input parameters of minimum temperature, maximum temperature, sunshine hours, relative humidity, and wind speed has better accuracy and performance at all three stations. In general, the findings of this study revealed that the COOT algorithm can improve the artificial neural network (ANN) structure in any climate and provide a hybrid model with higher accuracy and less error for modeling the evaporation parameter. Considering that the COOT algorithm is powerful and efficient, it is better to use it in various fields to improve the performance and accuracy of models. The testing results revealed that the lowest Root Mean Square Error RMSE (18.43, 19.36 and 8.19) and highest coefficient of correlation R (0.99, 0.97, and 0.99), and the highest Nash–Sutcliffe Efficiency Coefficient (N-S) (0.98, 0.93 and 0.99) attained by the ANN-COOT4 hybrid model (relative to other ANN and ANN-COOT models) tested for three selected stations in Shiraz, Kish and Gorgan sites. Concerning the predictive efficiency, the developed ANN-COOT hybrid model, improved the modeling performance at extreme points, which outperforms the ANN model, indicating its capability in the prediction of monthly evaporation.