Introduction

Prediction of average daily evaporation is valuable in various fields such as water resource management, agri-culture, etc. Evaporation is also one of the input components for evaluation models, ecological and hydrological models. On the other hand, many scientific centers try to investigate atmospheric problems, because weather has a major impact on the social and individual life of humans. Weather forecasting is about how the weather changes from day to day. Temperature, evaporation and precipitation are the most important climatic elements that play a major role in determining the role and distribution of other climatic elements. Since temperature plays an essential role in climate classification, its fluctuations and changes are important. It is well known that temperature affects evapotranspiration, surface water, disease, forest fires, and drought. Daily evaporation is the most important climate parameter that is calculated by accurate and approximate methods in weather stations. Studies have shown that this method has low accuracy and usually the difference is 3 degrees Celsius. Today, intelligent methods are used to predict nonlinear phenomena, of which Wavelet Neural Network (WNN) and Artificial Neural Network (ANN) methods are two examples of them.

Methodology

Dehno weather station (Kakareza) is one of the most important synoptic stations in the north of Lorestan prov-ince, and this area is the main agricultural center dependent on evaporation and temperature. Therefore, accurate modeling of daily evaporation at this station is necessary to increase the efficiency of agricultural practices and water management. The present study aims to estimate daily evaporation using wavelet neural network and artificial neural network. The wavelet neural network is able to divide the signal into high and low frequencies, and the low-pass and high-pass signals decomposed from the wavelet have suitable sinusoidal equations, so that the accuracy increases with the increase in resolution. Low-pass frequencies are more noisy, but the signal becomes smoother as the level of decomposition increases.

Artificial neural network is widely used in hydrology studies and water resources management. The structure of neural network consists of input layer, hidden layer and output layer. The input layer is a tool for data prepara-tion. The output layer contains the values predicted by the network and the hidden layer or middle layer consists of processing nodes for data processing. The first application of artificial neural network was implemented using multilayer perceptron. Learning algorithms, back-propagation (BP) and feed-forward neural network with three-layer architecture are mostly used to solve complex engineering problems and predict hydrological time series. The criteria of coefficient of determination, root mean square error and Nash Sutcliffe coefficient were used to evaluate the accuracy and compare the performance of the models.

Results and Discussion

In order to estimate the rate of evaporation of Kakarza station, wavelet neural network model with different number of neurons was used. In the wavelet neural model, the appropriate wavelet (simlet) was first selected. Then by applying the transformation on the data, the approximation coefficients and their details were extracted and the data are transformed by the Mexican hat wavelet function as the activation function which is the second derivative of the Gaussian function. To train the network, the gradient descent algorithm was used, which is used in learning neural networks and minimizing the amount of error and adjusting the network parameter.

Also, artificial neural network model of multi-layer perceptron network with hidden layers with different num-ber of neurons has been used. Hyperbolic tangent function is the most common form of stimulus function, which was used in this research to construct the output layer of artificial neural networks. Training of multi-layer perceptron networks using back propagation training algorithm called Lunberg-Marquardt algorithm was used due to faster convergence in network training.

The results showed that both models can simulate the daily evaporation rate for the studied area, so that both models perform well according to the observed values. Also, the results showed that both models perform better in the combined structure consisting of all input data. Overall, the results showed that the wavelet neural net-work model showed high accuracy and less error in estimating the daily evaporation rate.

Conclusions

In this research, it was tried to evaluate the effectiveness of artificial neural network and wavelet neural network models to simulate the daily evaporation rate of Kakarza synoptic station located in the north of Lorestan province using daily data during the years 2013 to 2023. The results showed that the increase of the parameter It causes better efficiency in estimating daily evaporation rate. It was observed that the wavelet neural network model provided better results through signal decomposition and discontinuous performance compared to the artificial neural network. As a result, the wavelet neural network model well estimated the air temperature during 10 statistical years in this study and its results can help to improve water resources and agriculture.