Predicted evaporation in Basrah using artificial neural networks

Zuhal Abdul Hadi Hamza

doi:10.1515/eng-2022-0590

Article Open Access

Predicted evaporation in Basrah using artificial neural networks

Zuhal Abdul Hadi Hamza

Published/Copyright: April 6, 2024

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From the journal Open Engineering Volume 14 Issue 1

Abstract

Accurate evaporation estimation is crucial for managing hydrologic, hydraulic, and agricultural systems, among many other applications of water resources. Empirical formulae for estimating evaporation exist, but their performance is not always sufficient due to the intricacy of the process and its nonlinear connection with other elements of the hydrological cycle. For this reason, a model of artificial neural networks was developed to estimate the daily potential evaporation in the southern Iraqi city of Basrah. A feedforward backpropagation (BP) network with a single hidden layer has been used to construct the mode. Different networks with various neuron counts were assessed. The developed models have been trained, tested, and validated using daily observations of the average rainfall, wind speed, average temperature, average relative humidity, and evaporation. The final evaporation was predicted using an artificial neural network (ANN) model. The proposed model was found to be more suitable to describe evaporation in any region of the world based on the values of the error analysis and the coefficient of determination, according to the ANN model. The Levenberg–Marquardt algorithm (LMA) was determined to have the lowest mean-squared error (MSE) and highest value of the coefficient of correlation (R) of the six proposed BP algorithms. The LMA’s hidden layer’s ideal neuron count was 30 neurons, with an MSE of 0.00288 and R ² = 99. As a result, ANN displayed excellent performance in terms of evaporation prediction value. The study’s findings highlight the significance of predicting evaporation as the main metric for evaluating the effects of climate change on water resources.

Keywords: ANN model; backpropagation; evaporation; feedforward

1 Introduction

Evaporation is an important factor in the hydrological cycle and an essential element of the water budget of any region. Its accurate estimation is a basic requirement for engineers and researchers in many fields, such as planning and overseeing irrigation projects and planning water resources, especially in areas that suffer from a shortage of available water resources [1,2,3,4].

The main meteorological variables that affect evaporation rate are air temperature, wind speed, relative humidity, and vapor pressure [5]. There are two ways to measure evaporation: direct methods and indirect methods. One of the techniques for direct measurement is pan evaporation [6]. Pan evaporation is the most widely used direct method. But sometimes, daily evaporation data may be missing, causing failure of measurements or recording. This missing data can be estimated indirectly using available metrological empirical equations [7,8,9]. Therefore, many studies have been conducted to determine the reliable relationship between evaporation and meteorological factors, among which ANNs have gained great popularity over the past few years due to their ability to model complex processes with high accuracy [9–11].

This study aims to determine the significance of prediction evaporation as the main metric for evaluating the effects of climate change on water resources. Table 1 shows some of these studies.

Table 1

Some of the previous studies on evaporation

Researcher	year	Results	References
Chaudhari et al.	2012	They modeled evaporation in the Nasik region of India using an ANN. The data used maximum and minimum humidity, maximum and minimum temperature, wind speed, and hours of solar radiation. They showed that the ANN gave better results compared to experimental methods. The results of ANN were R = 0.89 and RMSE = 1.03 mm/day	[12]
Dalkilic et al.	2014	They compared the performance of four models for forecasting daily evaporation. These models are the empirical Penman equation, the ANN with the LMA training algorithm, the radial basis neural network, and the generalized regression neural network. The study found that ANN models give better results than the Penman equation. The LMA network also outperforms the best of the models in estimating daily evaporation, with the RMSE = 1.51 mm/day and R = 0.853	[13]
Benzaghta	2014	He conducted a study that involved applying both ANN and empirical equations (Penman, Priestley Taylor, and Stevens Stewart) to estimate evaporation from a reservoir in Libya. Meteorological variables measured included daily monitoring of air temperature, wind speed, and relative humidity. By comparing the results of previous models and measured evaporation values, it was found that ANN gives better performance than empirical equations in estimating evaporation	[14]
Pallavi and Rajeev	2016	They developed an ANN model to evaluate daily evaporation in India. An error backpropagation (BP) feedforward network was used to create the model. According to the study, ANN(4-9-1) is the most accurate model for estimating evaporation, with a R = 0.987 correlation coefficient and an RMSE of 1.276 mm/day	[15]
Banhatti and Dubey	2016	They used an ANN to estimate daily evaporation from Abaya Lake in Ethiopia. The data used as input to the networks were temperature, precipitation, hours of sunshine, and wind speed. The results showed that there is a strong agreement between the values predicted by ANN and the actual observed values. It is also better accurate than the Penman results in calculating evaporation from this lake	[16]
Hussain and Saad	2017	Used twenty-two climatological stations for the period 2004–2013 in Iraq for calculating the conversion constant needed to calculate the value of evaporation and comparing it to measured values from seismology and the Iraqi meteorological organization. They showed a high correlation coefficient using CROPWAT 8.0. They formulated and suggested using the computed evapotranspiration value to determine the amount of evaporation for missing data from climatological Iraqi stations. The distributions of evaporation, evapotranspiration, and pan evaporation coefficient in Iraq are depicted on geological information system maps	[17]
Goutam et al.	2020	Employed a framework for non-parametric analysis to examine seasonal hydro-climate regimes. Using future climate projections from the coupled model intercomparison project phase 5 model, they used to evaluate changes in water availability caused by concurrent changes in mean and seasonal precipitation and evaporation changes. They demonstrated that, of the nine regimes, four had higher variation in precipitation and five had decreased variation in evaporation combined with higher mean evaporation and precipitation. Increases in the predicted seasonal variation of precipitation regimes that are already quite variable	[18]
Pedro et al.	2021	They investigated technological alternatives to reduce evaporation in Mexico. Using information from the El Cazadero or 32006 weather station, they used Penman’s semi-empirical equation to calculate the water evaporation in the El Cazadero Dam, which is situated in the State of Zacatecas, Mexico. This study area was chosen because of its aridity and recurrent drought issues that have an impact on the availability of water. When the theoretical model’s evaporation results are compared to the weather station’s reports, a strong correlation is observed. Furthermore, the hydrological year between November 2010 and October 2011, during which a severe drought occurred, was estimated using the average daily evaporation results. This estimate’s magnitude and economic significance point to the need for additional research and suggested governmental measures to create and put into effect technological substitutes that lessen this occurrence	[19]
Kumar and Singh	2022	They employed weekly pan evaporation modeling, multiple linear regression, multivariate adaptive regression splines, support vector machines, and random forest techniques for the Ranichauri station, which is located in Uttarakhand, India’s Mid-Himalayan region. The effectiveness of weekly pan evaporation estimating models was evaluated using statistical indices such as coefficient of determination (R ²), Nash–Sutcliffe coefficient of efficiency (NSE), and RMSE. The weekly pan evaporation values show both under- and over-predicted results. The findings indicated that the support vector regression (SVR) model had the highest R ² value for the testing period, and the RMSE values ranged from 0.542 to 0.689, while the NSE values ranged from 0.953 to 0.974. Consequently, it was discovered that the SVR model was better and that it could be used to forecast weekly pan evaporation values for the Ranichauri site	[20]
Dibs et al.	2023	They were able to refine the method for estimating the accurate method of the land use and land cover patterns. They did this by (a) adopting a noise removal model; (b) resampling satellite images; (c) image fusion, which involves combining and integrating between the visible and thermal images using the Grim Schmidt spectral method; and (d) applying image classification using Mahalanobis distance classifier (MH), maximum likelihood (ML), and ANN classifiers on datasets captured from the Landsat-8 thermal infrared (TIRS) and operational land imager (OLI) satellite systems. These images were captured from OLI and TIRS sensors in 2015 and 2020 to generate approximately 12 LC maps. (e) A comparison between each of the 12 classifiers was made. Compared to the other applied image classification techniques, they showed that the ANN technique has the highest accuracy when applied to the integrated images of the combined TIRS and OLI datasets. For the years 2015 and 2020, the kappa coefficients were 0.94 and 0.97, respectively, and the obtained overall accuracy was 96.31% and 98.40%. Still, the ML classifier outperforms the MH in terms of results	[21]

ANNs are widely utilized in engineering and many other sectors due to their ease of use in modeling, simulation, and prediction. Most studies, as in the case of this study, relied on two criteria to judge the accuracy of the results: the root mean square error (RMSE), which is considered ideal when its value reaches zero. The second is the correlation coefficient R, which is considered good and can be relied upon when its value is limited between 0.75 and 1.

Previous researchers have demonstrated the versatility of effective ANN applications in hydrological studies. Nevertheless, a review of the literature reveals no prior attempts to model the evaporation process. This article suggests that process behavior estimates, like evaporation, can be made even in the absence of complete data. As far as the author is aware, no research has been published in this area of Basrah.

1.1 Research problems

The measurements of evaporation precisely and consistently are a difficult process, and there are big problems regarding the evaporation measurements because there are no trusted evaporation data many times. Despite the fact that there are many empirical equations to estimate evaporations, these equations represent significantly different local circumstances. So it leads to different results when applied in other places. While there is no single model that can be applied under climate conditions, it is difficult to choose the best evaporation model for a particular region. In the absence of a measured rate of evaporation for long periods, as in the study case, a question arises about the ability to find methods that have the ability to model complicated and non-linear relationships and give precise and trusted estimations for daily evaporation depending on a specific number of parameters available in the monitoring stations of the studied area.

1.2 Aims of research

With the increasing water need and the shortage of available water resources, as huge amounts of water are lost annually due to evaporation, the importance of accurately estimating evaporation losses is a fundamental factor in the management, investment, and development of water resources, which calls for searching for more accurate alternative methods to estimate these losses. Therefore, this study aims to find an ANN model to estimate evaporation in the city of Basrah based on the data available in the study area.

2 Methodology of the research

2.1 Climatic data

Climatic data were collected from the Basrah Airport Meteorological Station. The station is located in the city of Basrah in the southern part of Iraq, about 20 km from the city center. Figure 1 shows the location of the study area. The data included daily measurements of wind speed, precipitation, temperature, and relative humidity. For the period extended from 2015 to 2020, these data were used as inputs to the model. The data also included daily measurements of evaporation, which were used as outputs of the model.

Figure 1

Location of the study area.

The box-and-whisker plot of the climate parameters, which were obtained over 5 years from 2015 to 2020, is shown in Figure 2. The values displayed are minimum, first quartile, median, third quartile, and maximum.

Figure 2

Box-and-whisker graphic showing the research area’s climate parameters.

2.2 Statistical analysis

Rain, wind speed, temperature, relative humidity, and daily evaporation are all statistically analyzed in Table 2. In addition to the mean, median, skewness, kurtosis, minimum, maximum, and standard deviation are included in the statistical analysis. A significant negative impact on the model’s performance has resulted from the moderate to severely skewed nature of the provided data. The standard deviation of the dataset indicates that values further from zero are indicative of more variability in the data. Consequently, the variance in the data is larger than the mean. The statistical features indicate that the climatic parameters are platykurtic and leptokurtic when the kurtosis values are greater than or equal to 3.

Table 2

Climate parameters’ statistical restrictions in the research area from 2015 to 2020

Statistical Parameters	Min	Max	Mean	Median	Stan. Dev.	Skewness	Kurtosis
Rain (mm)	0	64.5	8.62	0.6	14.63	2.14	3.96
Wind (m/s)	1.7	7.7	3.97	3.9	1.12	0.734	0.968
Temp. ©	10.4	47.5	27.39	28.1	9.7	−0.68	−1.27
Humidity	17	80	40.87	35.5	17.55	0.501	−1.04
Evaporation (mm/day)	41.4	630.5	284.17	255.05	176.59	0.325	−1.3

2.3 ANN

In recent years, the ANN approach has emerged as a dependable mathematically structured data processing tool that emulates the neural architecture and biological functions of the human brain because of its numerous potential applications. Layered feedforward neural networks, also known as multi-layer perception with BP learning algorithms, are a common type of ANN that is frequently used for process modeling [22–25].

The basic features of ANN are network structure, computational function, and network training.

2.4 Network structure

It is the number and organization of neurons, the type of connections between neurons, and the direction of the information flow in the network. The number of neurons in the input layer is the number of independent variables, while the number of neurons in the output layer corresponds to the number of predictable variables. The simple neural network model features a network consisting of three layers of processing units: an input layer, a hidden layer, and an output layer, which are connected to each other, as shown in Figure 3.

Figure 3

General structure of an ANN.

2.5 Computational functions

It is another feature of a neural network that consists of the processes of individual neurons and the way they are connected. Information is transmitted through connections between neurons in layers with the help of connected weights, where the weight expresses the intensity of the connection between a neuron before it and a neuron after it.

2.6 Network training

It aims to determine the main control parameters of ANN, which are called weights. The process of estimating these parameters is known as training, where the optimal connection weights are determined by minimizing the value of the error function.

Figure 3 illustrates the common arrangement utilizing input variables. The evaporation was forecast using an ANN model using the mathematical program MATLAB. While 30% of the data were used for model validation, 70% were used for model training. The ANN model’s three-layered BP neural network was designed with a linear transfer function (purlin) at the output layer and a tangent sigmoid transfer function (tansing) at the hidden layer. All input data must be normalized (X _norma) in the range of 0.1 to 0.9 because the function used in the hidden layer was sigmoid, and the normalization makes the values of the ANN elements close to each other, which improves the efficiency and effectiveness of the calculations and the quality of the performance of the network, and reduces the value of the error [26]. The following equation was used for this purpose:

(1) X norma = 0.1 + 0.8 × ( X i − min ( X i ) ) max ( X i ) − min ⁡ ( X i ) ,

where X _norma is the normalized value, X _i is the real value that needs to be normalized min, (X _i) is the minimum value, and max (X _i) is the maximum value.

By identifying a collection of biases and connection weights that result in the ANN generating outputs that are equal to or nearly equal to the target values, the training process’s main objective is to minimize error.

As the error function, mean-squared error (MSE) is employed. The following equation describes how MSE gauges the network’s accuracy in terms of performance [27].

(2) MSE = 1 N ∑ i = 1 n ( Y pred − Y obs ) 2 ,

where N is the number of data points, Y _pred is the predicted value of evaporation using the ANN model, and Y _obs is the observed value of evaporation:

R = ∑ ( Y pred − Y ̅ pred ) ( Y obs − Y ̅ obs ) ∑ ( Y pred − Y ̅ pred ) 2 + ∑ ( Y obs − Y ̅ obs ) 2 ,

where Y ̅ pred is the mean predicted data, and Y ̅ obs is the mean observed data.

3 Results and discussion

In this research, ANN models were built to estimate daily evaporation using data from the meteorological station located in the study area. This data includes daily measurements of rainfall, wind speed, temperature, humidity, and evaporation. For the time period between 2015 and 2020, Table 2 displays a summary of the statistical analysis of the data, such as minimum, maximum, mean, median, standard deviation, skewness, and kurtosis.

After performing the data normalization process using equation (1), use the Matlab program to build ANN. Network inputs included rainfall values, wind speed, temperature, and relative humidity, while evaporation data were used as network outputs. The data were divided into three sets: a training set, a validation set, and a test, with ratios of 70, 15, and 15, respectively. The training set was used to train the network, while the validation set was used to monitor or select the performance of the network at regular stages during training, where training stops when errors in the validation set reach a minimum. Finally, the network performance is evaluated on a test dataset that was not involved in the training process.

ANN modeling: for all BP algorithms, ten neurons were employed in the hidden layer. Six BP algorithms were compared to choose the best one. Levenberg–Marquardt BP with a minimum MSE emerged as the top algorithm among six BP algorithms (Table 3). Consequently, LMA was employed as the training method for the investigation. The best choice was determined by minimizing the MSE of the training and prediction sets. Optimization was carried out using LMA as the training algorithm, and a range of neuron counts from 5 to 40. Figure 4 shows the link between the MSE and the number of neurons in the LMA. As seen in Figure 4, when the number of neurons increased from 5 to 40, the MSE significantly dropped from 0.017 to 0.00288. The MSE did not significantly change when the number of neurons reached more than 30; it was then discovered. As can be seen in Figure 4, neuron 30 was chosen to represent the most appropriate BP algorithms (minimum error).

Table 3

Comparison of six BP algorithms with 10 neurons in the hidden layer

BP algorithm	Function	MSE	Epoch	R	BLE
Batch gradient descent	Train gd	0.093601	211	0.8612	E = 0.74T − 0.03
Flecher–Reeves conjugate gradient BP	Train cgf	0.061912	9	0.89419	E = 0.8T − 0.047
Broyden-Flecher-Goldfarb-Shanno quasi-Newton BP	Train bfg	0.047039	23	0.91982	E = 0.97T − 0.033
Polak–Ribiere conjugate gradient BP	Train cgp	0.078679	5	0.90358	E = 0.79T − 0.021
Powell–Beale conjugate gradient BP	Train cgb	0.044414	54	0.90449	E = 0.9T − 0.065
Levenberg–Marquardt BP	Train lm	0.015785	50	0.95898	E = 0.92T − 0.008

Figure 4

Relationship between neuron count and MSE in the LMA.

Once the right method has been chosen, a network is built by adjusting the hidden layer’s neuron count, which is found through experimentation to produce the lowest error. Several experiments were conducted on ANN with different structures by altering the number of neurons within the hidden layer. Each of these networks was trained 1,000 times, and then, the values of R were observed each time. Table 4 shows the criteria for evaluating the best performance of the resulting models with different structures.

Table 4

Performance assessment standards for the top-performing models that are produced

No. of hidden layer	No. of epoch	MSE	R
No. of hidden layer	No. of epoch	MSE	Training	Validation	Testing	All
5	34	0.038415	0.935	0.938	0.946	0.937
10	31	0.026979	0.95	0.957	0.968	0.954
15	40	0.011151	0.965	0.983	0.984	0.97
20	18	0.016892	0.958	0.974	0.987	0.964
25	55	0.0173	0.969	0.974	0.985	0.972
30	47	0.00288	0.990	0.996	0.994	0.992
35	93	0.0033	0.995	0.995	0.999	0.996
40	22	0.012883	0.968	0.979	0.991	0.973

We find from Table 4 that the ANN with (4-30-1) structure, which contains one hidden layer with 30 neurons, gives the best results and is most appropriate to the values of the studied phenomenon, and it uses the LM training algorithm. The correlation coefficients reached 0.99, 0.996, and 0.994 for the training, validation, and testing phases, respectively.

The networks were found to have a good understanding of the events they had been trained to identify. In addition, ANN demonstrated efficacy in generalizing training by forecasting evaporation for sets of unknown cases. High correlation coefficients and low mean square errors, which reached 0.992 and 0.00288, respectively, provided support for these positive results.

For the total dataset, the network gave a value of MSE = 0.00288. Figure 5 shows the network’s performance during the three stages and the mechanism for choosing the best epoch.

Figure 5

Network performance (4-30-1) during the three-stage and the mechanisms for selecting the best epoch.

3.1 Evaluation of network performance

Performance metrics were calculated independently for the training and unseen test data network forecasts. These metrics are crucial for demonstrating how well the network absorbs the events. It was trained to recognize and, to the extent that it can draw conclusions from its training, forecast events that were not addressed in the training (validation phase).

The purpose of validation is to assess the trained ANN’s behavior on unseen data. Throughout training, multiple examples are given to an ANN. The ANN modifies its internal parameters based on these labeled examples in order to obtain the desired outputs as close as possible.

In order to demonstrate the models’ efficacy on data that was not seen during training, validation techniques are employed. This analysis helps us determine whether the model needs to be more intelligent by highlighting trends or whether it has somehow picked up duplicate information from the training set and is unable to forecast new samples. It also helps us understand how adaptable the model is to new situations. The ANN has been overly focused on training data and making sure it learns the fundamental correlations and patterns that can be applied to new, unknown data.

So, validation is an essential and crucial stage in the creation and assessment of any ANN model. Information regarding the dependability and efficacy of ANNs is obtained through validation techniques. ANN’s capabilities in performance evaluation, generalization estimation, hyperparameter tuning, model selection, and overfitting control will be validated by finding the effective control of fitness value. Training with validation allows for the development of reliable, accurate, and well-generalized models that can be relied upon to produce predictions on data that have not been seen yet.

The simplest method for comparing various networks is to assess the error function using data that is separate from the training set, as our objective is to identify the network that performs the best on fresh data. A suitable error function that is defined in relation to a training data set is minimized in order to train different networks. Next, the error function of each network is assessed using a separate validation set to compare their performance. The network with the lowest error in relation to the validation set is chosen. An example of this process in action is early stopping, in which the training stops when the error on the validation set increases, selecting the prior model (the one with the least error), and the candidate models are progressively iterative versions of the same network.

Figure 5 shows the MSE variation concerning epochs for training, validation, and testing. The best validation performance is 0.0028866 at 47 epochs. The validation error is at its minimum at the 47th epoch; hence, training was stopped at that point.

The training and validation results are encouraging and accurately demonstrated with the minimum value of mean square error. A comparison between the actual, known daily evaporation and the predicted amount was one of the evaluation measures. For both training and validation, the correlation coefficient (R) and MSE were employed as additional evaluation metrics. The MSE indicates the network’s accuracy, whereas the correlation coefficient assesses how well the network describes the relationship between actual and predicted outputs.

Figure 6 also shows the values of the correlation coefficients between the values calculated by the network and the evaporation values taken from the evaporation basin for the three stages and the total data set. These values are high, which indicates the ability of the chosen model to simulate the studied phenomenon.

Figure 6

Regression plot between evaporation values and values generated by ANN for different groups.

These validated results in Figure 6 demonstrate the ANN output’s stability across all climate data variables and the quick convergence of the output’s evaporation to the predicted values, thereby demonstrating the efficacy of the suggested ANN modules. Furthermore, a significant improvement was achieved in the validation stage. The network was capable of predicting evaporation for unseen cases with an accuracy of 0.0028.

3.2 Comparison with measuring evaporation

The predicted evaporation obtained from the suggested ANN model is compared with the measuring values of evaporations, as shown in Figure 7. In this figure, the coefficient of correlation R ² = 0.9875. This value indicates that the proposed ANN model can predict accurate results, which provides an efficient method for predicting evaporation.

Figure 7

Regression analysis between predicted and measured values.

4 Conclusions

The following are the most significant inferences that can be drawn from the current investigation:

The ANN with the structure (4-30-1) showed its ability to calculate the evaporation per day from the airport station in the city of Basrah depending on the rainfall rate, wind speed, temperature, and relative humidity, with an MSE equal to 0.00288 and a correlation coefficient of 99.6 for the validation set based on the results.
The predicted values were very close to the measured rates.
The study can use the ANN created to supplement missing evaporation data for long periods of time.
For both predicted and measured evaporation, the best representation model is a linear equation with a coefficient of determination (R ²) of 0.987.
Our findings have important environmental, social, and economic implications because global warming will cause global evaporation loss to increase and worsen over time.
It is recommended to expand the use of ANN and artificial intelligence methods to predict hydrological phenomena and processes related to water resources.

Conflict of interest: The authors state no conflict of interest.
Data availability statement: Most datasets generated and analyzed in this study are in this submitted manuscript. The other datasets are available on reasonable request from the corresponding author with the attached information.

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Received: 2023-11-28

Revised: 2024-01-18

Accepted: 2024-01-22

Published Online: 2024-04-06

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/eng-2022-0590

Keywords for this article

ANN model; backpropagation; evaporation; feedforward

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BY 4.0