Estimation of Evaporation Rate Using Advanced Methods

Abstract

One of the hydrological components of the cycle is evaporation, which has actual quantities that are challenging to quantify in the field. As a result, estimations of the evaporation rate's value are made using empirical relationships derived from data on climate components. Several applications of water resources, including hydrological, hydraulic, and an optimal agricultural irrigation system, depend heavily on accurate estimation of evaporation losses. Accurately estimating and forecasting hydrological phenomena is thought to be one of the most critical aspects of managing and developing water resources, as well as creating future water plans that consider various climate change scenarios. The Artificial Neural Network (ANN) and Support Vector Regression (SVR) methods are cutting-edge models that have been employed in several recent research to estimate various hydrological parameters. In the current study, the evaporation rate of Haditha Dam Lake on the Euphrates River in the Al-Anbar Governorate, Iraq, was predicted using ANN and SVR methods. It was designed to receive daily meteorological data, such as temperature, sunshine duration, wind speed, and humidity levels. Evaporation was chosen as the network's output. The present study presented several input scenarios with different input variables to examine the performance of the proposed models. Several statistical indicators have been used to evaluate the prediction results which are root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE), mean absolute error (MAE), and correlation (R 2) the prediction accuracy. The outcomes demonstrated that ANN could predict evaporation value with a high degree of accuracy better than the SVR method. The best prediction model achieved high correlation and mean error between actual and predicted data.

Full text

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An-Najah University Journal for Research – A
Natural Sciences
Estimation of Evaporation Rate Using Advanced Methods
Mohammed Falah Allawi
1
,*, Uday Hatem Abdulhameed1, Mohammed Freeh Sahab1 &
Sadeq Oleiwi Sulaiman1
Received: 23rd Dec. 2024, Accepted: 8th Mar. 2025, Published: ××××, DOI: https://doi.org/10.xxxx
Accepted Manuscript, In Press
Abstract: One of the hydrological components of the cycle is evaporation, which has actual
quantities that are challenging to quantify in the field. As a result, estimations of the evaporation
rate's value are made using empirical relationships derived from data on climate components.
Several applications of water resources, including hydrological, hydraulic, and an optimal
agricultural irrigation system, depend heavily on accurate estimation of evaporation losses.
Accurately estimating and forecasting hydrological phenomena is thought to be one of the most
critical aspects of managing and developing water resources, as well as creating future water
plans that consider various climate change scenarios. The Artificial Neural Network (ANN) and
Support Vector Regression (SVR) methods are cutting-edge models that have been employed
in several recent research to estimate various hydrological parameters. In the current study, the
evaporation rate of Haditha Dam Lake on the Euphrates River in the Al-Anbar Governorate,
Iraq, was predicted using ANN and SVR methods. It was designed to receive daily
meteorological data, such as temperature, sunshine duration, wind speed, and humidity levels.
Evaporation was chosen as the network's output. The present study presented several input
scenarios with different input variables to examine the performance of the proposed models. Several statistical indicators have been used to evaluate
the prediction results which are root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE), mean absolute error (MAE), and correlation (R2)
the prediction accuracy. The outcomes demonstrated that ANN could predict evaporation value with a high degree of accuracy better than the SVR
method. The best prediction model achieved high correlation and mean error between actual and predicted data.
Keywords: Evaporation, Data-driven model, hydrology.
Introduction
Iraq and most other countries in arid or semi-arid regions
struggle with a lack of water resources for diverse uses (1,2).
These nations' growing populations and the effects of climate
change have increased the frequency of their droughts, which
has reduced the amount of water available for use (3–6). As a
result, these nations must manage and utilize their water
resources as best they can (7,8). For sensible water resource
management, the amount of water revenues has to be calculated
and compared to the entire amount of water demand, together
with the amount of losses, which include transpiration and
evaporation (9–13). The practical of evaporation is one of the
essential elements of the natural hydrological cycle
phenomenon. One of the key components that the decision-
maker needs in order to estimate the agricultural, industrial, and
environmental plans as well as the water budget is the depth of
evaporation (14–18). Evaporation from bodies of water, such as
lakes, can be determined using several direct or indirect
methods. One of the direct methods is the pan evaporation of
several kinds. Numerous equations, including the Penman
equation and Blaney-Criddle equations, have been produced by
researchers from various parts of the world.
In fact, the Penman method is unsuitable for arid regions due
to its reliance on intermittent large water usage, which poses a
challenge in these areas. Additionally, The Blaney-Criddle
method may not be suitable for large bodies of water, such as
1
Dams and Water Resources Engineering Department, College of Engineering, University of Anbar, Ramadi, Iraq
* Corresponding author email: mohmmd.falah@gmail.com
Haditha Lake which is a case study. This is because the Blaney-
Criddle equation relies primarily on temperature and does not
consider the impact of wind, humidity, or local weather
conditions, all of which significantly affect evaporation rates.
Researchers have employed various alternative techniques
to gauge the amount of evaporation from water bodies due to the
advancement and speed of computers. In (19), an evaporation
simulation was created and assessed, and the effectiveness of
a hybrid model was utilized to estimate the mean daily
evaporation in northern Iran at the Talesh meteorological station.
Two plants in Iraq had their monthly evaporation loss estimated
using sophisticated machine learning algorithms (20), where the
monthly climate data were utilized as inputs to replicate the
monthly depth of evaporation.
1.1 Objectives
The present study introduced a robust prediction method
based on data-driven models. The proposal model is applied to
predict daily evaporation rate parameters. The research tried to
discover the effect of the two different meteorological parameters
on the prediction results. Therefore, daily temperature and
relative humidity were utilized to investigate reliable prediction
results. A comprehensive comparison has been made between
two different models.
Case Study
With a storage capacity of 8.28 billion m3, Haditha Lake and
Dam is situated 7 kilometers ahead of Haditha City on the

Euphrates River in the Anbar Governorate (1). The dam
measures 57 meters in height, 8933 meters in length at its peak,
386 meters in breadth at its base, 20 meters at its top, and 154
meters above sea level (21,22). The dam lake spans 503 square
kilometers and has an operational level of 147 meters.
With a reservoir size of 575 square kilometers and a storage
volume of 10.0 billion m3, the emergency level of the flood is
150.2 m (23–25). The Haditha Dam meteorological station has a
Class A evaporation pan to record daily data on temperature
minimums and maximums, relative humidity, wind speed, solar
radiation, and evaporation depth.
Figure 1: Haditha Lake which is located on Euphrates River in Iraq.
Methodology
3.1 Artificial Neural Network (ANN)
An artificial neural network (ANN) is made up of several
simple parts that function together (26,27). Connections and
communication channels between these components frequently
convey numerical data or weight. The units only utilize internal
data and inputs obtained through connections in order to
function. The field of artificial neural networks (ANN) is primarily
motivated by the goal of developing artificial systems that are
able to do sophisticated computations, much like the human
brain (28,29).
A structured learning rule that adjusts the connection weights
according to input/output data should be a part of an ANN
(30,31). Or, to put it another way, an ANN exhibits strong
representational capability outside of the training set and learns
given instances (of well-known input/output sequences). ANN
usually has great potential for parallelism because the
component calculations are essentially independent of each
other (32). Because they can tolerate certain errors and have
access to a wealth of training data, artificial neural networks
(ANN) are especially useful in real-world applications for
problems involving categorization and function interpolation
methods (33,34). The artificial neural network method's
architecture is displayed in Figure 2.
Figure 2: The structure of artificial neural network method.
2.2 Support vector regression:
Support vector regression (SVR), which was introduced by
(35) based on the theory of statistical learning, is a set of
supervised learning methods used for classification and
regression tasks. SVR is a popular technique for prediction,
pattern recognition, classification, regression, and function
approximation (36,37). (38) introduced SVMs for dividing a set
of vectors into two classes. SVMs are based on a hyperplane in
the form of w. X+b=0 that optimally separates a set of n-
dimensional vectors (Xi  Rn) into two categories. This optimal
hyperplane has the farthest distance from support vectors and
the nearest data points from each class. Finding w is equivalent
to solving a quadratic programming problem. To solve this
problem, a trade-off parameter (c > 0) needs to be determined.
To categorize vectors that are not linearly separable, a kernel
function such as degreed polynomial, radial basis, or hyperbolic
tangent is used to map the observed multidimensional vectors to
a space with higher dimensions (39). The following radial basis
function was used:
󰇛i 󰇜   󰇛 󰇜 (1)
Where γ>0 is the parameter of the kernel and Xi, Xj represents
feature vectors in some input space. The nonlinear regression
version of SVMs is written as follows:
  󰇛
󰇜󰇛 󰇜  

󰇝󰇞 (2)
Where m indicates the total number of input data;  and 
 are
the Lagrange multipliers for upper and lower constraints,
respectively, and k denotes the kernel function employed to map
the n-dimensional input vectors. There are some fundamental
kernel functions provided by support vector machines such as
linear, polynomial, sigmoid, and radial basis functions. Among
these functions, the radial basis function (RBF) was used by
some researchers (39), and the RBF kernel was selected for this
study. Figure 3 shows the structure of the SVR model.
Input layer
Hidden layer
Output layer

3
Figure 3: The structure of the support vector regression method.
Results and Discussion
Predicting the evaporation rate has been done using the
Artificial Neural Network (ANN) approach. Four distinct
architecture models were created to investigate the predictive
model's effectiveness with various input variables. The
architecture of the evaporation prediction models with ANN and
SVR methods are expressed as the following:
  󰇛 󰇛  󰇜󰇜
(3)
    
(4)
    
(5)
     
(6)
Where Ef = the predicted evaporation value, Ea = actual
evaporation, Ha = actual humidity, and Ta = actual temperature.
The accuracy of the evaporation prediction is displayed in
the table. The (M4) model was the least accurate model,
obtaining the highest values of RMSE (0.86) and MAE (0.69),
also the lowest value of NASH = 0.81. Nonetheless, the ANN
approach produced very good prediction results when the
second model's structure was considered.
Table 1 lists the ANN model's evaluation performance metrics.
Model No.
RMSE
MAE
NASH
M 1
0.44
0.34
0.86
M 2
0.41
0.29
0.94
M 3
0.86
0.62
0.83
M4
0.86
0.69
0.81
Figure 4 presents a comparison of model performance
based on the correlation coefficient indication. The outcomes
showed adequate prediction accuracy offered by models 1 and
4. In contrast, model 2 was able to attain a high degree of
correlation between the actual and anticipated evaporation data.
Compared to the other models, the Artificial Neural Network
(ANN) approach using the (M2) model is a more trustworthy
forecasting procedure.

Figure 4: The correlation coefficient indicator for each proposed model based on the ANN method.
Support Vector Regression has also been employed to
predict the monthly evaporation rate. The performance of the
proposed model was examined with different input variables. The
prediction results based on several indicators are presented in
Table 2. The evaluation indicators showed that Model-2
achieved a minimum RMSE value between actual and predicted
data. The higher RMSE value was obtained by Model-4 as
shown in the Table. The prediction results indicated that Model-
4 can provide high level accuracy compared to other models.
Table 2 lists the SVR model's evaluation performance metrics.
Model No.
RMSE
MAE
NASH
M 1
0.62
0.44
0.82
M 2
0.57
0.35
0.90
M 3
0.92
0.66
0.78
M4
0.93
0.72
0.77
Correlation between actual and predicted data during the
testing period using SVR method is presented in Figure 5. The
correlation magnitude was calculated for each proposed model
(i.e, Model-1 to Model-2). The lowest correlation has been
attained using Model-4. It can be seen that the results of Model-
1 and Model-3 are relatively close. The prediction results
indicated that high prediction accuracy can be obtained with
Model-2.
Figure 5: The correlation coefficient indicator for each proposed model based on the SVR method.

5
Conclusion
Based on data inputs from meteorological stations, this study
discovered that the ( ANN ) model created had good accuracy
and prediction of the daily evaporation from Haditha Lake's
values. In order to create an efficient model that can be used to
estimate the daily evaporation rate in the Governorate of Anbar
with a high degree of accuracy, the study suggests testing the
(ANN) model developed using climatic data gathered from all Al-
Anbar governorate meteorological stations. The research
suggests that decision-makers and water resource managers
should utilize artificial neural network models to predict
evaporation and manage water scarcity. Moreover, the proposed
model can enhance irrigation scheduling, oversee water
resources, and assess water quality.
Disclosure Statements
 Ethical Approval: The manuscript is conducted within the
ethical manner advised by the targeted journal.
 Consent for publication: Not applicable.
 Availability of data and materials: The raw data required to
reproduce these findings are available in the body and
illustrations of this manuscript.
 Author's contribution: First author: Write the original
manuscript, Second and third author: Formal analysis and
investigation and Fourth author: Review and editing.
 Funding: Not applicable.
 Conflicts of interest: The authors declare that there is no
conflict of interest regarding the publication of this article.
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