ABSTRACT

Evaporation estimate is an important topic in water resource management, especially in arid and semi-arid regions. In this paper, a hybrid model was developed to predict daily evaporation in a semi-arid region using two machine-learning algorithms, namely, the cascade correlation neural network (CCNN) algorithm and the generalized linear model (GLM) algorithm. Two types of inputs were used, the first was the daily evaporation time series data with different input patterns, and the second was daily climate data, which included maximum and minimum temperatures, maximum and minimum relative humidity, and wind speed. The results demonstrated the accuracy of the proposed hybrid model in estimating daily pan evaporation, with the coefficient of determination values reaching 0.95 and 0.93 for the training and validation periods, respectively.

1 INTRODUCTION

The process of estimating evaporation is one of the important issues in hydrology because it plays a major role in influencing the water balance, especially in arid and semi-arid regions. Evaporation affects the volume of water available for irrigation, human, and industrial uses, especially in the case of water scarcity.

Data mining models are one of the important topics widely applied in hydrology, especially at the beginning of the twenty-first century (Shaofu et al. 2021). Various methods have been applied to model evaporation for data mining, including genetic programming methods, gene expression programming, neural network methods such as artificial neural networks and support vector machine, in addition to decision tree models. Artificial neural network and multivariate non-linear regression were used to estimate evaporation in the semi-arid region of Iran, and the results showed the efficiency of the artificial neural network model compared with the multivariate non-linear regression model (Tabari et al. 2010). The results of four models for estimating daily evaporation, namely linear regression, artificial neural networks, and traditional estimation models such as Penman, Priestley-Taylor, and Stephens and Stewart, using six climate variables as inputs, were compared. The results showed the accuracy of the artificial neural network model compared to other models (Shirsath and Singh 2010). Daily pan evaporation was modeled using three kinds of the neural networks in the Republic of Korea and Iran. The results indicated that support vector machine models are better than multilayer perceptron neural networks models and generalized regression neural networks models (Kim et al. 2012). The results of the M5 tree model were compared with the results of the Penman Monteith method for estimating evaporation in the Khuzestan plain (southwest Iran), and the results showed the efficiency of the M5 model compared with the results of Penman Monteith model (Rahimikhoob et al. 2013). The daily evaporation model of two meteorological stations in South Korea was built using three different neural network models with inputs based on temperature, radiation, and sunshine duration combined under time delay patterns (Kim et al. 2013). The results demonstrated the efficiency of the neural models in estimating daily evaporation for the study area Three different machine learning algorithms were used to model daily evaporation for the Mersin and Antalya stations located in the Mediterranean region of Türkiye (Kisi et al. 2015). The results showed the efficiency of the three models in modeling evaporation for the study area. Artificial neural network, radial basis function network, and support vector regression algorithms were used to estimate monthly evaporation by Tezel and Buyukyildiz (2016). The study demonstrated the efficiency of these algorithms in modeling monthly evaporation. The results of six different soft computing methods were compared with the results of multiple linear regression models for predicting monthly evaporation (Wang et al. 2017). The results showed the superiority of soft computing techniques over the results of linear regression models. Artificial neural network, wavelet-based artificial neural network, radial function-based SVM, linear function-based SVM and multilinear regression models were used with inputs from different meteorological variables to model pan evaporation and the results showed that the radial function-based SVM model was more accurate compared with the other three models (Kumar et al. 2021). To study the modeling of evaporation in arid regions, where evaporation is the most influential hydrological process in water scarcity in these regions, the results of three machine learning techniques (regression trees, Gaussian processes, and vector autoregression) were compared to the evaporation model in Kuwait using a number of different atmospheric variables. The results showed the efficiency of the models used under different input formulas over the traditional evaporation models based on physics and statistics (Alsumaiei 2024).

At the beginning of the twenty-first century, hybrid models began to be widely used in hydrological modeling. Hybrid models are developed by linking more than one data mining model to obtain a highly efficient hydrological forecasting model. A hybrid wavelet-support vector machines model was developed to estimate daily pan evaporation in climatically contrasting zones, and the results proved the efficiency of proposed hybrid model to estimate daily pan evaporation (Pammar and Deka 2017). A hybrid multilayer perceptron-firefly algorithm (MLP-FFA) model was applied to estimate pan evaporation in North Iran (Ghorbani et al. 2018). The results showed the importance of the Firefly algorithm in improving the performance of the proposed hybrid model. A hybrid model was developed using Response Surface Method (RSM) and Support Vector Regression (SVR) methods to predict monthly pan evaporation (Keshtegar et al. 2019). Wu et al. 2020 developed a hybrid model using an extreme machine learning model with a whale optimization algorithm and a flower pollination algorithm for monthly evapotranspiration. A deep neural network model with long short-term memory (Deep-LSTM) cell was proposed by Majhi et al. (2020) to predict daily evaporation with minimal inputs for three agricultural regions of India and the results demonstrate the efficiency of the proposed model. Multiple hybrid models were developed to increase the accuracy of monthly evaporation prediction using the output of artificial intelligence models by Ghorbani et al. (2021). The impact of global warming on the increase in global evaporation and its effect on the volume of available water was studied using a hybrid model by combining the Penpan (PM) model and the Random Forest model (Du et al. 2023). A Wild Horse Optimizer (WHO) algorithm using two AI algorithms, Long Short-Term Memory (LSTM) and Support Vector Regression (SVR), to improve daily evaporation forecasting using maximum and minimum temperature, relative humidity, wind speed, and sunshine hours data from two meteorological stations in Iran. The results showed the efficiency of the hybrid LSTM-WHO model for both stations (Shabani et al. 2024).

In this research, a hybrid model using two machine learning algorithms was developed to predict daily evaporation. The cascade neural network algorithm was used to predict daily evaporation for two sets of inputs, the first set included the time series of daily evaporation while the second set included hydrological variables, including maximum and minimum temperature, maximum and minimum relative humidity, and wind speed. The evaporation results from both models were used as inputs to the second model, which used the generalized linear model algorithm to improve the daily evaporation prediction for the study area. The main objective of the study was to develop a hybrid model to model daily evaporation in arid and semi-arid regions due to the significant impact of evaporation on water resources management in arid regions of the world.

2 MATERIALS AND METHODS

2.1 Study region and data

The study area is in Nineveh Governorate, northern Iraq, and the climatic data were obtained from the meteorological station at the Mosul Dam site (Figure 1). Daily climatic data for the period from 1/9/2015 to 31/8/2020 were used to test the proposed hybrid model. The study area is located within the semi-arid region of the world with an annual evaporation rate of 8 mm. The maximum, minimum, and average daily evaporation are 24, 0.1, and 8 mm, respectively. The maximum temperature is 46°C, and the minimum temperature is -4°C. The maximum and minimum relative humidity are 100% and 4%, respectively. The maximum, minimum and average wind speeds are 36, 0.2 and 8.2 km/h. There was no missing data during the study period.

Figure 1 Study area.

2.2 Cascade-correlation neural networks (CCNN)

The CCNN algorithm was developed by Fahlman and Christian (1990) as self-organizing neural network. The network consists of inputs and outputs only. A set of candidates is used to select neurons. Neurons are added to the hidden layer during the training process. Since the algorithm is self-organizing, the number of layers and neurons to be used in the network does not have to be determined in advance. This method is suitable for large training datasets because it is 100 times faster than traditional neural networks (ANN). The neural network is built in two main steps, in the first step the hidden neural network is added one-by-one and remains unchanged during the training process. In the second step, the learning algorithm is used with the aim of maximizing the correlation between the outputs of the new unit. The network starts with inputs with one or more output units without hidden units. Each input unit is connected to each output unit with an adjustable connection weight. A constant called bias is added to both the output and input neurons. Bias is multiplied by weight and added to the sum of neurons. There are many activation functions in the CCNN algorithm including linear and non-linear functions. Figure 2 shows the structure of CCNN algorithm.

Figure 2 Structure of the CCNN algorithm.

2.3 Generalized linear model (GLM)

The GLM algorithm was developed by Nelder and Wedderburn (1972) as a development of the traditional linear model to improve the accuracy of linear models to solve complex problems. The algorithm uses different correlation functions to link the variables in the model. The dependent variable is subject to a number of statistical distributions, and the distribution that gives the highest correlation to the outputs is adopted.

In the GLM algorithm, the appropriate statistical distribution for the dependent variable is chosen, and then an appropriate linear function is chosen for the dependent variable. In the last stage, a correlation function is chosen to obtain the best linear relationship between the dependent variable and the average value of the distribution function. The GLM algorithm has different models of correlation functions that are tested during the training phase to choose the best function according to the accuracy of the output. The model in the GLM algorithm is based on eight assumptions.

1. The data is distributed independently.
2. The normal distribution of the dependent variable data is not required.
3. The relationship between the dependent variable and the independent variables is not linear.
4. The relationship between the transformed dependent variable and the independent variables is linear.
5. Non-linear transformation of the independent variable is used in some cases.
6. Homogeneity of the data is not required.
7. The error must be independent and not normally distributed; and
8. It uses the maximum probability method to estimate the parameters.

2.4 Hybrid model

A CCNN-GLM hybrid model was developed to predict daily evaporation using climatic data affecting evaporation and evaporation time-series data. The hybrid model is divided into two parts. The first part of the hybrid model is divided into two sections and the CCNN algorithm is used to predict daily evaporation in each section. In the first section, the time series data of daily evaporation for 1, 2 ...n lag days (E_(t-1), E_(t-2), E_(t-3)) are used to predict the daily evaporation. In the second section, the daily climatic data affecting the evaporation process is used, which is the maximum and minimum temperature (T_max, T_min), maximum and minimum relative humidity (Rh_max, Rh_min) and wind speed (Ws). Both sections are calibrated using daily evaporation data for day t. After reaching the best setting for the CCNN algorithm for both sections through performance evaluation criteria, the optimal results are obtained for each section. The outputs of both sections from the first part of the hybrid model include daily evaporation data at time t. The outputs of the first part of the hybrid model are the inputs into the second part of the model. The GLM algorithm is used to manage the second part of the hybrid model. The second part of the hybrid model is calibrated using daily evaporation data at time t, and the output is the final predicted daily evaporation. Figure 3 shows the structure of the CCNN-GLM hybrid model.

Figure 3 Structure of CCNN-GLM hybrid model.

3 RESULTS AND DISCUSSION

The selection of input variables is one of the essential elements of modeling using data mining methods. In this study, a CCNN model was used to develop a predictive model of daily evaporation using daily evaporation time series data. The data was divided into two parts. Seventy percent of the data was used to train the models, while the rest of the data was used to test the models. The coefficient of determination (R²), and root mean square error (RMSE) were used to evaluate the models. The CCNN algorithm was used with several different combinations of inputs to test the proposed time series model. The results proved the accuracy of the model composed of inputs E_t-1, E_t-2, and E_t-3. The results are summarized in Table 1. As shown in Table 1, the R² is 0.88 in the training phase, and 0.85 in the validation phase for the model composed of inputs E_t-1, E_t-2, and E_t-3. It can be clearly seen in Figure 4 that there is a good match between the observed and predicted values using the CCNN algorithm with the input data E_t-1, E_t-2, and E_t-3.

Table 1 Statistical indices results.

Where:

Figure 4 Line and scatter plots between observed and predicted daily pan evaporation values by using a CCNN model and daily evaporation time series data.

The predictive model was tested using climate data as inputs to the CCNN model for different input sets. The results showed the accuracy of the model composed of the inputs (daily maximum temperature, daily minimum temperature, daily maximum relative humidity, daily minimum relative humidity, and wind speed). As shown in Table 1, the R² is 0.86 in the training phase, and 0.83 in the validation phase using climate data as inputs. It can be seen in Figure 5 that there is a good match between the observed and predicted values using the CCNN algorithm with climate data as input.

Figure 5 Line and scatter plots between observed and predicted daily pan evaporation values using a CCNN model and climate data.

The second part of the hybrid model was developed using the outputs of the CCNN algorithm for the time series model and a predictive model based on the climate data mentioned above. The second part of the model was developed using the GLM algorithm. The results in Table 1 showed the accuracy of the proposed hybrid model. The R² values were 0.95 and 0.93 in the training and validation periods, respectively. Figure 6 shows a comparison between the observed and predicted values of daily pan evaporation for the training and validation periods. It is observed that most of the values are close to the 1:1 line. By analyzing Figure 6, it is clear that there is a good match between the observed values and the values predicted by the hybrid model in the validation period. Comparing the results in Table 1 shows that the accuracy of the proposed hybrid model is better than the CCNN models developed using the CCNN algorithm alone. The RMSE values in the training period were 2.11 mm/day for the time series model, 2.02 mm/day for the predictive model, and 1.75 mm/day for the hybrid model. The RMSE values in the validation period were 2.27 mm/day for the time series model, 2.13 mm/day for the predictive model, and 1.82 mm/day for the hybrid model. It was found that the proposed hybrid model improved the results by 10% compared to the CCNN models used in this research. The performance of the proposed hybrid model was tested by comparing the daily evaporation statistics including mean, maximum, minimum, and standard deviation in the training and validation periods. Table 2 summarizes the statistical analysis of the results. As shown in Table 2, the R² is 0.88 in the training phase and 0.85 in the validation phase. The results in Figure 6 demonstrate the accuracy of the proposed hybrid model.

Figure 6 Line and scatter plots between observed and predicted daily pan evaporation values using a hybrid model.

Table 2 Statistical analysis of the results.

To compare the efficiency of the proposed hybrid model, the results of the hybrid model were compared with the results of modeling daily evaporation in Kuwait, whose climatic characteristics are similar to those of Iraq, as both countries are located in the arid and semi-arid regions of the world. Daily evaporation in Kuwait was modeled using three machine learning algorithms, namely regression trees, Gaussian processes, and automated support vector regression (Alsumaiei 2024). The coefficient of determination values ranged from 0.73 to 0.85, while the coefficient of determination value in the validation period for the hybrid model applied in the current research was 0.93, which proves the efficiency of the proposed hybrid model in modeling daily evaporation in arid and semi-arid regions.

4 CONCLUSION

Estimating daily evaporation is one of the most important challenges facing experts in water resource management in arid and semi-arid regions of the world. The results demonstrated the accuracy of the proposed hybrid model by reducing the differences between the predicted data and the observed data, as the R² values of the hybrid model reached 0.95 and 0.93 for the training and validation period, respectively. The results also showed that the proposed hybrid model improved the prediction of daily evaporation by 10% compared to the CCNN models in the study. The researcher suggests examining the proposed hybrid model in the current study using climate data generated using climate change scenario models, as well as examining the model for climate and evaporation data for stations located in the humid region of the world.

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