**1. Introduction**

Currently, water deficiency is increasing and becoming a challenge for human society. It is increasingly becoming the most important environmental limitation, which is limiting plant growth. According to the statistics, over 30 arid and semi-arid countries are expected to experience water deficiency in 2025 [1]. This will limit agricultural development, threaten food supplies, and inflame rural poverty. Evaporation estimations are essential for controlling and modelling the integrated hydrological resources connected to hydrology, agricultural business, arboriculture, irrigation, flooding, and lake ecosystems. Evaporation is described as the reduction of deposited water due to the conversion of liquid phase to steam phase, which is influenced by the climate situation, such as weather, wind velocities, relative humidity, and sunshine. According to the World Meteorological Organization (WMO), more than half of the total inflow (rainfall or any other sources) to Lake Victoria in the U.S. is lost due to evaporation, which results in relatively humid conditions [1].

The evaluation of evaporation from reservoirs in arid and semi-arid areas is also important. For example, Libya has built one of the largest civil engineering groundwater pumping and transferring systems to overcome water limitations and climate hindrance (high temperature and low rainfall). This project is known as the Manmade River Project (MRP) [1]. The purpose of this project was to supply the water demand of Libya by pumping underground water underneath the Sahara Desert and transfer it using a network

**Citation:** Jasmine, M.;

Mohammadian, A.; Bonakdari, H. On the Prediction of Evaporation in Arid Climate Using Machine Learning Model. *Math. Comput. Appl.* **2022**, *27*, 32. https://doi.org/10.3390/ mca27020032

Academic Editor: Nicholas Fantuzzi

Received: 27 March 2022 Accepted: 31 March 2022 Published: 5 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of huge underground pipes, especially for irrigation. The high cost of water pumping and lack of appropriate planning are the main concerns. In Egypt's Lake Nasser (located in an arid area), where the Nile's water is stored, downstream water loss, due to evaporation, is estimated to be 3 m in depth, or double that of Lake Victoria [1]. In Australia, it is calculated that around 95% of the precipitation evaporates and has no contribution to runoff [1].

Artificial intelligence models are becoming increasingly popular for forecasting data, instead of traditional models [2]. ANFIS model is one of them, which is also called a data-driven model [3,4], and can be used for different measurements, such as rainfall, streamflow, evaporation, water quality, and many others. A comparison has been made by Moghaddamnia et al. [5] on evaporation evaluation using an artificial neural network (ANN) and adaptive neuro fuzzy inference system (ANFIS). The ANFIS model was compared with the regression-based method by Dogana et al. [2], and ANFIS was declared to be the finest. A group of researchers [6] has published their work on ANN, LS-SVR, fuzzy logic, and ANFIS on daily pan evaporation, with the conclusion of fuzzy logic as being the best performer.

More recent research on evaporation is also conducted by AI methods. A new artificial technique, support vector regression (SVR), and a few nature-inspired algorithms (whale optimization algorithm, particle swarm optimization, and salp swarm algorithm) were investigated by a bunch of researchers in 2021 [7]. A unique contribution to evaporation estimation, based on maximum air temperature, was published earlier this year by scientists [8]. They became successful in the application of deep learning-based model to predict evaporation. However, a group of scholars found effective results of the application of the multiple learning artificial intelligence model in 2020 [9]. They analyzed multiple model-artificial neural networks (MM-ANN), multivariate adaptive regression spline (MARS), support vector machine (SVM), multi-gene genetic programming (MGGP), and 'M5Tree' to simulate the evaporation on a monthly scale basis (EPm) at two stations in India. Artificial neural network (MM-ANN) and multi-gene genetic programming (MGGP) posed the best results.

Some analysis was performed based on four climate variables, whereas some depended only on maximum temperature. Additionally, different researchers worked on different models for different locations. This is the first time ANFIS model, and few optimizers were adopted for this data set of Arizona, United States, along with six weather variables inputs. In this study, adaptive neuro-fuzzy inference system (ANFIS), ANFIS with firefly algorithm [10,11], ANFIS with genetic algorithm [5], and PSO [12] were analyzed and compared, for the first time, in order to investigate the best modeling approach for evaporation. The main objectives of this study are:


#### **2. Methodology**

#### *2.1. Adaptive Neuro Fuzzy Inference System (ANFIS)*

The ANFIS model is a mixture of fuzzy inference system (FIS) and artificial neural network (ANN). The fuzzy inference system (FIS) is a very successful and popular model, based on fuzzy logic, which was first proposed by Chang in his study [13]. For the modeling of reservoir performance and problems regarding data uncertainty, fuzzy logic is a highly recommended system [13]. This model is adopted mainly due to its good capacity of extraction of data from input to fuzzy values, in a range of 0 to 1. The ANN model was combined to overcome the limitation of the FIS model. ANN is adopted due to its ability to arrange input and output in pairs and make the structure ready to calibrate. ANN also has the following characteristics:


**Figure 1.** Flow chart of the ANFIS model.
