Enhancing water security through advanced modeling: integrating deep learning and a novel metaheuristic optimization algorithm for accurate pan evaporation prediction

Evaporation, the process by which water is converted from liquid to vapor, is a crucial component of the water cycle and plays a significant role in the availability of water resources. Accurate prediction of evaporation rates is essential for managing water resources, particularly in regions with limited water supplies, such as Northern African countries (Algeria, Tunisia, Libya, and Egypt) that suffer from climate change and water scarcity (Benzaghta et al. 2012; Alazard et al. 2015; Latif 2024). Inadequate water resources can lead to water scarcity and negatively impact agriculture, industry, and the overall socioeconomic well-being of the region (Kherbache 2020; Frih et al. 2021; Bouznit et al. 2022; Ogunbode et al. 2024). Accurate prediction of evaporation rates can help optimize irrigation and water allocation and aid in managing droughts (Mouatadid et al. 2018). Furthermore, evaporation prediction plays a key role in climate modeling, as it is a key component of the water and energy balance of the earth (Mouatadid et al. 2018). Predicting evaporation rates can improve our understanding of the earth's climate system, thus providing valuable information for mitigating the effects of climate change (El-Mahdy et al. 2021).

Predicting evaporation is challenging because it is affected by various factors, including temperature, humidity, wind speed, and solar radiation. Numerous methods have been developed over the years to predict evaporation rates, such as empirical, theoretical, and database models (Zheng et al. 2011; Song et al. 2022; Alam et al. 2024). However, these methods often have limitations and may not be suitable for all climates or regions. Therefore, developing a method that accurately predicts evaporation rates across different climates is essential. Evaporation can be estimated using direct or indirect approaches, such as the Moran method (Moran et al. 1996) and the Penman empirical equation. One direct method involves measuring evaporation from a Class pan that is 1.22 m in diameter and 0.25 m deep, placed 0.15 m above the ground. This technique is simple, cost-effective, and provides accurate results over time but is limited to specific climatic regions.

In contrast, indirect methods use meteorological variables like sunshine duration, wind speed, relative humidity, and temperature to estimate evaporation. These indirect approaches are often used in empirical and semi-empirical models but can be problematic due to the dynamic nature of the variables involved (Patel & Majmundar 2016). To overcome this, developing reliable and robust intelligent prediction models for evaporation has become an important focus in water resources management and engineering.

Recently, numerous studies have focused on implementing machine learning models for evaporation estimation (Wang et al. 2017; Mohamadi et al. 2020; Rajput et al. 2024). Several models have emerged, including evolutionary computing (Ehteram et al. 2022), deep learning (Lakmini Prarthana Jayasinghe et al. 2022), Fuzzy Logic (Adnan Ikram et al. 2022), Random Forest (Adnan Ikram et al. 2022), and eXtreme Gradient Boosting (XGBoost) (Malik et al. 2022; Karbasi et al. 2024). These models have demonstrated impressive predictive accuracy (El-kenawy et al. 2022). The application of machine learning extends beyond evaporation prediction to other environmental factors. Kumar et al. (2023) reviewed deep learning applications in flood forecasting, while Mampitiya et al. (2023) demonstrated the effectiveness of models like LightBGM in predicting urban air quality. These studies underscore the potential of advanced machine learning techniques in addressing various environmental challenges.

Machine learning models like Support Vector Machines (SVMs), Gene Expression Programming (GEP), and Cascade Correlation Neural Networks (CCNNs) have significantly advanced hydrologic modeling (Thakur & Manekar 2022; Hussein et al. 2024). Hybrid models, which combine multiple approaches, have gained popularity for their superior accuracy in predicting evaporation rates under various conditions. For instance, at Iranshahr station and Chahnimeh Zabol reservoirs in Iran, Keshtegar et al. (2016) utilized nonlinear mathematical models of daily pan evaporation. They found that a conjugate line search method outperformed ANFIS and decision tree models. Similarly, Arunkumar et al. (2017) compared artificial neural networks (ANNs), genetic programming, and decision tree models with different meteorological inputs, concluding that genetic programming was the most precise.

In another study, Wang et al. (2017) discovered that the least squares SVM and fuzzy genetics were better predictors than decision tree models. At the Talesh Meteorological station in Iran, Ali Ghorbani et al. (2018) developed an MLP–FFA model by combining the Firefly algorithm with ANNs. This model outperformed both the stand-alone MLP and support vector machine models. Further research by Sebbar et al. (2019) employed an Online Sequential Extreme Learning Machine (OSELM) and an Optimal Pruned Extreme Learning Machine (OPELM) to predict evaporation with high accuracy at various dam reservoirs in Algeria's Mediterranean regions. Their findings showed that OSELM outperformed OPELM in estimating daily evaporation.

Additionally, Keshtegar et al. (2019) combined the response surface method with SVM (RSM-SVM) and found it more effective than using SVM, ANN, or RSM models alone. Guan et al. (2020) improved evaporation prediction accuracy by combining the SVM model with the Krill algorithm. The new SVM–Krill model proved suitable not only for evaporation prediction but also for other hydrologic variables.

Overall, hybrid models have several advantages over conventional models, such as integrating data from multiple sources, considering complex physical and statistical processes simultaneously, and processing data more efficiently. They are also more reliable because they can handle outliers and extreme values better. The application of these methods has led to improved evaporation prediction. However, more research is needed to understand the complex processes involved in evaporation fully and to develop even more accurate prediction models. Managing Algeria's water resources is important as the country's water demand increases due to population growth and the expansion of its industrial activities. In addition, Algeria is a semi-arid desert country, so the country's water resources are limited. Accurate prediction of evaporation rates is essential for successfully managing available water resources. However, each of the country's different climatic zones has characteristics that affect evaporation rates. Therefore, developing a technique capable of estimating evaporation rates in each climate zone is paramount.

This research explores a novel hybrid deep learning approach to predicting pan evaporation across Algeria's various climatic zones. The approach integrates long short-term memory (LSTM) networks with the BER algorithm. A binary version of the BER algorithm will be employed for feature selection, refining the dataset by identifying the most relevant variables for prediction. The proposed approach will be tested using historical data, with results compared against those from other machine learning techniques used for evaporation prediction.

Algeria is a country of remarkable geographical diversity, stretching from the Mediterranean coast to the vast expanses of the Sahara Desert, which accounts for over 80% of its landmass (El-Mahdy et al. 2021). This desert environment subjects the region to extreme conditions, including scorching summers, harsh droughts, frigid winters, and strong winds. The cities of Adrar (ADR), Bechar (BCH), and Tamanrasset (TAM) lie within this hot desert climate, where intense heat and minimal rainfall dominate. In contrast, Tizi Ouzou (TIZ), located in the Sebaou River basin in northern Algeria, experiences a subhumid bioclimatic zone. This area typically endures two distinct seasons: a dry period from May to September and a wet season from October to May.

Water management is a critical concern in a country with such diverse climates. Saggai et al. (2016) observed that the Algerian government's strategy to boost water reserves involves several initiatives, including the construction of dams and reservoirs. However, this approach encounters significant challenges, particularly due to meteorological conditions that lead to substantial evaporation, especially in arid regions. These regions were severely affected by prolonged droughts during the 1980s and 1990s (Khezazna et al. 2017; Elbeltagi et al. 2022; Habibi et al. 2024; Mihi et al. 2024; Oubadi et al. 2024; Zerouali et al. 2024). A study by Remini & Hallouche (2005) on evaporation losses in 39 dam lakes in arid and semi-arid regions of Algeria found that the volume of water lost to evaporation significantly exceeds that lost to siltation. On average, these losses amount to 250 million cubic meters annually across the 350 square kilometers of the dams studied, representing 6.5% of their total capacity. To address this issue, Saggai et al. (2016) and Saggaï & Bachi (2018) proposed a strategy to reduce evaporation in dams by using long-chain substances that form at the air–water interface, thereby enhancing water storage in arid regions.

The statistical data from the TAM, TIZ, ADR, and BCH stations under study are summarized in Table A2 (Supplementary Material). These data are presented on two time scales: daily and monthly. The TAM and TIZ stations provide daily data, while the ADR and BCH stations offer monthly reports. This variation in reporting frequency enables both detailed and broader trend analysis across different climatic regions. For the monthly data, the ADR station records a mean temperature of 25.9 °C, while the BCH station has a mean of 20.7 °C. The maximum temperature (T_max) at ADR is 33.9 °C, compared to 26.6 °C at BCH. The minimum temperature (T_min) at ADR is 17.3 °C, whereas at BCH, it is 14.4 °C. Maximum pan evaporation at ADR is 22.1 mm, while at BCH, it is 23.9 mm. These figures highlight the generally warmer and more extreme climate of ADR compared to BCH, which aligns with their respective geographic locations and climate classifications, as shown in Table A1 (Supplementary Material).

The daily data reveal a different pattern. At the TAM station, the mean temperature is 23.6 °C, whereas at the TIZ station, it is 18.8 °C. TAM's maximum temperature (T_max) reaches 48.4 °C, while TIZ records a slightly higher T_max of 49 °C. The minimum temperature (T_min) at TAM is −1.6 °C, compared to 0.0 °C at TIZ. Maximum pan evaporation is 21.4 mm at TAM and 14.5 mm at TIZ. These daily data indicate more extreme temperature ranges compared to the monthly averages, particularly for TAM and TIZ, which is essential for understanding short-term climate variations and their potential impacts on water resources.

In contrast, the BCH station displays a different distribution pattern. The peak relative frequency is 22.5% at 4.45 mm, representing the most common low pan evaporation range for this location. As bin-center values increase, frequencies decline sharply, indicating fewer instances of higher pan evaporation amounts. Notably, there are two secondary peaks at 6.75 mm (14.1%) and 20.55 mm (12.7%). Similar to ADR, extremely small (0% at 2.15 mm) or large (2.8% at 22.85 mm) pan evaporation amounts are rarely recorded. This distribution corroborates the slightly higher maximum pan evaporation of 23.9 mm for BCH reported in Table A2 (Supplementary Material), revealing a more complex pan evaporation pattern than what the summary statistics alone suggest.

At the TAM station, the distribution peaks at 20.5% in the moderately low 4.45 mm bin, representing the most common pan evaporation range. Substantial frequencies, ranging from 18.4 to 25.1%, persist across bin centers up to 11.35 mm. However, as pan evaporation amounts increase toward higher bins, frequencies drop, with minimal occurrences above 15.95 mm (3.4% or lower). This pattern is consistent with the daily maximum pan evaporation of 21.4 mm reported for TAM in Table A2 (Supplementary Material), highlighting a focus on typically low to moderate pan evaporation levels, with values rarely exceeding 18 mm.

Conversely, the TIZ station exhibits a strong skew toward lower pan evaporation amounts, with a significant peak frequency of 28.5% at the 4.45 mm bin. Frequencies decrease sharply to 12.8 and 5.2% for the next few bins, up to 11.35 mm, and taper off to 0% from 13.65 mm onwards. This distribution aligns with the lower maximum pan evaporation of 14.5 mm reported for TIZ in Table A2 (Supplementary Material), reflecting its location in a more humid climate as indicated by its classification in Table A1 (Supplementary Material).

The LSTM model makes predictions by considering the outputs from its four gates – input gate, forget gate (⁠⁠), output gate (⁠⁠), and update gate (⁠⁠) – at each time step t. These gates process the previous time step's model output and the current time step's inputs to make decisions. The weights and biases for the gates (⁠⁠, ⁠, ⁠, and ⁠) and (⁠⁠, ⁠, ⁠, and ⁠) are continually adjusted during the learning phase. The memory cell and the activation function σ also plays a crucial role in the LSTM's computations.

The Al-Biruni Earth Radius (BER) technique draws inspiration from swarm intelligence, particularly how insects like ants and bees communicate and collaborate to achieve their goals. The first was proposed by El-Kenawy et al. (2023), this cooperative optimization algorithm divides the population into two sub-groups, each focused on either exploration or exploitation. This approach simulates how swarms naturally split into sub-groups to complete different activities efficiently (El-kenawy et al. 2023). BER addresses the problem of local optima stagnation by maintaining a diverse collection of search agents that constantly explore different areas of the search space. It also dynamically adjusts the number of individuals investigating the space if performance stagnates. This approach leads to a more thorough investigation of the search space and a higher probability of finding the optimal solution to the optimization problem.

The BER algorithm has proven its effectiveness in several domains. It has optimized a deep convolutional neural network for classifying Monkeypox Disease (Khafaga et al. 2022), enhanced predictions for a hybrid solar desalination system (Ibrahim et al. 2023), and improved renewable energy forecasting through a stacking ensemble model (Alghamdi et al. 2023). This innovative approach demonstrates significant potential across various applications.

To maintain a balance between exploitation and exploration, the BER algorithm adjusts the size of its two sub-groups dynamically (Alazard et al. 2015). Initially, 70% of the population is assigned to exploration, while the remaining 30% focuses on exploitation. As the algorithm advances, this ratio shifts, with 70% of individuals eventually dedicated to exploitation and only 30% to exploration. This transition enables a more concentrated effort to enhance global fitness.

To ensure convergence, the algorithm employs an elitism strategy by retaining the best solution if a better one is not found. If a solution's fitness does not improve significantly for three consecutive iterations, potentially indicating a local optimum, the algorithm generates a new exploration individual through mutation.

The goal of the exploitation group is to enhance existing solutions. BER assesses the fitness values of all individuals at each iteration and identifies the optimal solution. BER implements two techniques to accomplish exploitation, which are explained in the following sections.

The mutation operation is used in the exploitation team to generate new solutions. Mutation helps the optimization process escape from local optima, leading to more extensive search space exploration. The BER optimization algorithm uses a mutation operation in the following way:

The BER algorithm is designed to consistently select the best solution to guide the search process. While the elitism method is effective, it can sometimes lead to premature convergence when solving multimodal functions. To address this issue, BER combines a mutation operation with a search around individuals in the exploration group, maintaining population diversity. This feature makes BER less susceptible to early convergence and enables it to explore more promising solutions.

The BER pseudo-code (Algorithm 1) requires inputs for iteration number, population size, and mutation rate. The population is divided into exploration and exploitation groups, with the number of individuals in each group dynamically adjusted throughout the search process. To maintain diversity, solutions are randomly reordered after each iteration. The elitism method ensures that the best solution is preserved. Consequently, a solution from the exploration group in one iteration may become part of the exploitation group in the next, demonstrating the dynamic nature of the BER algorithm.

RMSE provides a measure of the average magnitude of prediction errors. By taking the square root of the average squared differences, RMSE gives a straightforward indication of how close predictions are to actual values. A lower RMSE suggests that the model's predictions are closer to the true measurements, thereby enhancing the reliability of the model.

indicates the proportion of variance in the dependent variable that is predictable from the independent variable. A higher value reflects a better fit of the model to the data, showing that the model accounts for a larger portion of the variability.

First, five fundamental machine learning models were employed – Multilayer Perceptron (MLP), Support Vector Regressor (SVR), Decision Tree Regressor (DTR), Random Forest Regressor (RFR), and Nearest Neighbor Estimation (NNE) – at each station. The dataset was divided into two sets, with 80% allocated for training and 20% for testing. Min–max scaling was applied to enhance model accuracy.

Table 1 highlights the performance of various machine learning models across four stations, evaluated using the R² coefficient of determination on both monthly and daily time scales. The MLP model outperforms others in monthly predictions, achieving R² values of 0.9167 at the ADR station and 0.9573 at the BCH station. Following closely, the SVR model shows R² values of 0.8992 at ADR and 0.9520 at BCH. For daily predictions, the R² values generally decline. The DTR model performs best at the TAM station, with an R² of 0.2320, while the NNE model achieves the highest R² value of 0.8224 at the TIZ station. Despite the R² metric providing a useful measure of model performance, relying on it alone may not yield the most accurate model selection. Other metrics like MBE, RMSE, and bias should also be considered.

Table 2 presents a comparative analysis of machine learning models across four stations. The data reveals intriguing performance variations. RMSE values span from 0.0628 to 0.1958, indicating diverse prediction accuracies. MBE ranges from −0.0558 to 0.0603. This suggests varying degrees of model bias. The R² values exhibit the widest range, spanning from 0.0857 to 0.9573. For the ADR and BCH stations, the models generally exhibit low MBE, low RMSE, and high R² scores, indicating a good fit to the data. The MLP model performs particularly well at ADR, with MBE, RMSE, and R² values of 0.0341, 0.0758, and 0.9167, respectively. In contrast, the models for the TAM and TIZ stations show higher MBE and RMSE values coupled with lower R² scores. For TAM, the DTR model achieves the best performance, with MBE, RMSE, and R² values of −0.0396, 0.1795, and 0.2320, respectively. For TIZ, the NNE model excels with values of 0.0252, 0.0628, and 0.8224.

The variation in model performance across stations can be partly attributed to differences in pan evaporation patterns observed in Figure 2. For example, the complex distribution of pan evaporation at the TAM station, with substantial frequencies across a wider range of bin centers, may contribute to the lower R² scores and higher RMSE values at this station. Conversely, the strong skew toward lower pan evaporation amounts at the TIZ station, as shown in Figure 2, might explain the better performance of the NNE model there.

MLP, SVR, and NNE are the top-performing models for daily time scales, while MLP and SVR show the best results for monthly time scales. Interestingly, the model with the lowest RMSE and MBE values does not always correspond to the highest R² value, suggesting that different criteria may be necessary to determine the best-performing models. Minimizing RMSE and MBE generally results in the MLP model performing best across all stations and time scales. However, maximizing R² occasionally leads to models like SVR and NNE outperforming MLP. All models show relatively low R² values for the TAM station, indicating that they may not be well-suited for capturing the temporal variability of the data at this location. This observation aligns with the more extreme temperature ranges and higher maximum pan evaporation reported for TAM in Table A2 (Supplementary Material), suggesting that the complex climatic conditions at this station pose a particular challenge for these models. Exploring more complex models, such as deep learning techniques like LSTM, may be worthwhile for this type of data.

To further enhance the accuracy of the LSTM model, particularly given its superior performance compared to simpler models, as shown in Figure 4, we plan to implement a new step involving improving BER. This approach could potentially enhance the model's ability to capture the temporal variability of the data, especially for challenging stations like TAM.

Next, the model was tested against PSO–LSTM, GWO–LSTM, GA–LSTM, and WOA–LSTM across multiple stations and time scales. Table 3 summarizes the parameters and values of these optimization algorithms, highlighting their roles in enhancing model accuracy. The GWO algorithm employs 20 wolves over 19 iterations, with the parameter ‘a’ decreasing from 2 to 0, facilitating both exploration and exploitation phases. PSO operates with inertia weights ranging from 0.9 to 0.6, acceleration constants fixed at 2, and 20 particles over the same number of iterations, ensuring a well-balanced optimization process. The WOA algorithm similarly uses 20 whales and 19 iterations, with ‘a’ also ranging from 2 to 0, and introduces randomness through a variable ‘r’ within the [0, 1] interval. Finally, the GA algorithm features a mutation ratio of 0.1 and a crossover rate of 0.9, and it employs a roulette wheel selection mechanism with a population of 20 and 19 generations. Finally, the BER algorithm uses a population size of 30 over 500 iterations, with a mutation probability of 0.5, an exploration percentage of 70%, a K value decreasing from 2 to 0, and is run 19 times.

Table 3

Summary of algorithm parameters and values for optimization methods

Algorithms .	Parameter(s) .	Value(s) .
GWO		2–0
	#Wolves	20
	#Iterations	19
PSO	Inertia ⁠,	[0.9, 0.6]
	Acceleration constants ⁠,	[2, 2]
	#Particles	20
	#Iterations	19
WOA		2 to 0
		Random [0, 1]
	#Whales	20
	#Iterations	19
GA	Mutation ratio	0.1
	Crossover	0.9
	Selection mechanism	Roulette wheel
	#Population	20
	#Generations	19
BER	Size of population	30
	Iterations count	500
	Mutation probability	0.5
	Exploration percentage	70
	K (decreases from 2 to 0)	1
	Number of runs	19

Algorithms .	Parameter(s) .	Value(s) .
GWO		2–0
	#Wolves	20
	#Iterations	19
PSO	Inertia ⁠,	[0.9, 0.6]
	Acceleration constants ⁠,	[2, 2]
	#Particles	20
	#Iterations	19
WOA		2 to 0
		Random [0, 1]
	#Whales	20
	#Iterations	19
GA	Mutation ratio	0.1
	Crossover	0.9
	Selection mechanism	Roulette wheel
	#Population	20
	#Generations	19
BER	Size of population	30
	Iterations count	500
	Mutation probability	0.5
	Exploration percentage	70
	K (decreases from 2 to 0)	1
	Number of runs	19

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Finally, the analysis of Table A3 (Supplementary Material) underscores the clear superiority of the BER–LSTM model introduced in this study for pan evaporation prediction. Particularly in daily predictions, the model achieves an RMSE of 0.02341, marking a significant improvement over other models. For instance, compared to the study by Ghorbani et al. (2017), who reported an RMSE of 1.007 using MLP–FFA in northern Iran, the BER–LSTM model demonstrates a remarkable 97.67% reduction in error. Even when compared to the SVM model by BENCHAIBA et al. (2022), which achieved an RMSE of 0.224 in New Delhi, the BER–LSTM still shows an impressive 89.55% improvement. For monthly predictions, the BER–LSTM model's RMSE of 3.9303 also stands out. It is 86.74% lower than the 29.64 reported by Elbeltagi et al. (2023) using the AR-M5P model in Mosul, Iraq, and 91.03% lower than the 43.84 RMSE reported for the ARIMA model by (Benchaiba et al. 2022) at Ain Zada Dam, Algeria.

Overall, these comparisons clearly highlight the BER–LSTM model's superiority, particularly in its ability to significantly reduce prediction errors, reinforcing its effectiveness for both daily and monthly pan evaporation predictions.

This study aimed to develop an innovative hybrid approach combining LSTM networks with the BER technique and comparing them with various machine learning models for predicting pan evaporation across different stations and time scales in Algeria.

The findings revealed that MLP achieved the highest R² values for monthly predictions, particularly at the ADR and BCH stations. On a daily scale, models generally displayed lower R² values, with DTR and NNE demonstrating superior performance at the TAM and TIZ stations, respectively. This variability is likely due to differing climatic conditions and pan evaporation patterns at each station. While R² values provided useful insights, incorporating additional metrics such as MBE and RMSE offered a more comprehensive assessment of model performance.

Advanced models like LSTM showed improved accuracy compared to simpler models such as MLP and SVR. The BER–LSTM model, in particular, demonstrated significant enhancements in prediction accuracy across various stations and time scales. This enhanced version consistently outperformed not only the standard LSTM but also other optimization methods like PSO and GWO across multiple independent runs. The BER–LSTM model exhibited remarkable reductions in RMSE, with improvements ranging from 71.86 to 97.54% compared to the standard LSTM across different stations and time scales. These substantial reductions in RMSE underscore its effectiveness in capturing the temporal variability of pan evaporation data.

The results highlight the potential of advanced techniques and optimization strategies in improving predictive performance. The BER–LSTM model, with its superior accuracy, offers a valuable tool for enhancing the understanding and forecasting of pan evaporation in diverse environments. Future research could explore the applicability of these models to other geographical regions and assess their performance in long-term climate projections.

Princess Nourah-bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R120), Princess Nourah-bint Abdulrahman University, Riyadh, Saudi Arabia.

B.Z., N.B., and E.-S.M.E.-k. conceptualized the study; B.Z., N.B., K.B., D.S.K., A.H.A., and E.-S.M.E.-k. performed the methodology and did software validation; B.Z., K.B., G.M., A.H.A., and E.-S.M.E.-k. did formal analysis and wrote the original draft; N.B., G.M., A.K., D.S.K. wrote, reviewed and edited the article. All authors have read and agreed to the published version of the manuscript.

This research was funded by Princess Nourah-bint Abdulrahman University Researchers Supporting – Project number – (PNURSP2024R120), Princess Nourah-bint Abdulrahman University, Riyadh, Saudi Arabia.

We confirm that this manuscript is original, has not been published before, and is not currently being considered for publication elsewhere.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.