Deep learning approaches for predicting solar radiation and freshwater yield in modified pyramid solar still

Abstract

Water deficiency is a significant globally challenge that requires the advancement of sustainable and effective desalination methods. Solar stills provide a feasible solution for the production of fresh water in areas dealing with water limitations, particularly in remote locations. However, their efficacy is frequently limited by fluctuating climatic conditions. The intermittent and changing character of solar radiation imposes significant limitations on most applications. Accurate solar radiation forecasting is crucial for estimating the distillate yield of a solar still system. With computer technology developing so quickly, a growing many deep learning models are employed in solar radiation prediction. For this purpose, the article evaluates the freshwater yield of the modified pyramid solar still in Tehran and Zahedan, Iran. Utilizing monthly data from 1984 to 2023 and employing Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Convolutional Neural Network (CNN), and CNN-LSTM algorithms, predictions for solar irradiance and temperature are calculated for the next ten years. The results validated the better performance of the CNN and GRU models for Tehran, while the LSTM model succeeded for Zahedan in forecasting global solar irradiance (GHI) and temperature. The presented models are utilized for predict the monthly output of the studied solar stills. The predicted average annual freshwater yield for the ten years from 2024 to 2033 is calculated to be 2630 L in Tehran and 2710 L in Zahedan.

Introduction

Water is regarded as the fundamental basis of life and a crucial part that sustains world, permeating ecosystems, economics, and everyday activities by humans¹. It is concerning that fewer than 1% of the Earth water is drinkable and accessible. There is a legitimate concern about a future water scarcity. Up to 2030, the United Nations predicts that 40% of the global social would face water deficiency². Due to the rapid pace of industrialization and urbanization in the current era, energy and water consumption has risen to unprecedented levels, thereby exacerbating environmental degradation and contributing to increased greenhouse gas emissions³. Despite its essential nature, billions globally encounter the issue of obtaining safe and potable water for drinking. The emergence of novel technology in solar distillation is recognized as a promising advancement in water purification and desalination methods⁴. Solar stills have demonstrated efficacy in diverse environments, such as remote locations with restricted access to potable water, disaster-stricken regions, and communities that function autonomously from centralized power systems. They represent a prevalent and efficient solar desalination technology that uses solar energy without impacting the environment⁵. Solar stills are available in numerous configurations, such as traditional, tubular, pyramid, and stepped designs, each having distinct characteristics and operational features⁶. Beside these conventional systems some newer emerging technologies such as interfacial solar evaporation can be found⁷. Interfacial solar evaporation plays a crucial role in desalination because of its sustainable, eco-friendly characteristics. Solar-thermal-driven desalination has been recognized as a promising solution to the global freshwater scarcity challenge under the drive for energy conservation and carbon footprint reduction⁸. Recent advances in interfacial water evaporation technologies have shown significant potential to enhance the performance of solar-driven desalination systems by localizing heat at the air- water interface and minimizing thermal losses. Such approaches can greatly improve evaporation rates and freshwater yield compared to conventional bulk-heating mechanisms. Recent progress in the functionalization of solar-driven steam generation has been reported, indicating its emerging role in broader applications related to water and energy sustainability^9,10. Zhang et al.¹¹ proposed a photothermal textile with vertically confined water layers for scalable, high-flux, and long-term-reliable solar desalination. Also, an interfacial solar evaporation platform (ISEP) combined with a microplastics adsorbent has been proposed as a “one stone, two birds” strategy to produce clean water while enhancing microplastics removal¹². Furthermore, to improve the efficiency of photothermal evaporation-driven lithium extraction, the development of evaporator structures with high solar conversion and rational design has been emphasized¹³. Chen et al.¹⁴ designed the polymer sponge evaporator to regulate the solar thermal gradient by incorporating copper–carbon core–shell nanoparticles, which possess comparable solar absorptance. This design aimed to investigate the influence of the solar thermal gradient, or localized heating, on evaporation performance. Future integration of interfacial evaporation strategies may significantly improve efficiency and freshwater yield. Also, the integration of desalination units into hybrid drying systems has been highlighted as a means to strengthen their contribution within the water–energy–food nexus, particularly in arid and island regions. Barzigar et al.¹⁵ investigated the application of artificial intelligence technologies, which can further enhance system performance by optimizing heat distribution between drying and desalination processes, dynamically adjusting desalination rates in response to projected water demand, and effectively managing thermal energy flows across multiple operational functions. Critical factors to consider such as solar irradiance, ambient temperature, wind speed, desired feed water flow rate (highest possible water levels in the saline water storage tank), feed water temperature (temperature differential between water and glass), humidity, surface area of the basin, angle of inclination of the top cover, and transparency of glass for solar radiation¹⁶. Accurate forecasting and precise solar radiation analysis are useful in decreasing risk and facilitating asset utilization in the most economical approach. As they are meteorological characteristics, Intensity of solar irradiance, ambient temperature, and wind speed could not modified; however, by forecasting these values, future production can be assessed across several intervals¹⁷.

Artificial Neural Networks (ANN) have been extensively studied and employed in time series predicting because of their ability to learn from input features, infer the latent components of incomplete dataset, and manage non-linearity. Deep learning algorithms have received significant consideration in applications of their proficiency in time series analysis in extracting complicated patterns formed by raw data. Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), and Gated Recurrent Unit (GRU), are the main models employed for time series analysis for their capability in processing sequential information and modeling long-term horizons^18,19,20. According to studies, these algorithms have received special attention for weather forecasting. Three ANN models, mainly Recurrent Neural Network (RNN), LSTM, and GRU, were employed to forecast solar irradiation in some urban areas in Bangladesh. Regarding the three algorithms, the GRU-based algorithms exhibited the greatest efficiency for Mean Absolute Percentage Error (MAPE)²¹. Deep learning models, involving RNN, LSTM, and GRU, were utilized for solar energy forecasting, revealing that LSTM and RNN outperformed the GRU algorithm significantly because of their capacity to maintain long-term horizons²². Furthermore, it demonstrated that GRU and LSTM considerably enhance accuracy of predicting when utilizing multivariate data in comparison to univariate data²³. Convolutional Neural Networks (CNNs) are also effective in time series analysis²⁴. The hybrid technique may effectively increase forecasting performance as it is utilized for time series and provides the capability to extract spatial and temporal properties, making it suitable for numerous applications. In order to address the identified constraints and obstacles, researchers are employing hybrid deep learning models that combine the advantages of many architectures, especially CNN, LSTM, and GRU, among others. Each of these models provides specific benefits. CNN is capable in recognizing spatial patterns, make them valuable for detecting correlations in multivariate meteorological data. Park et al.²⁵ shown that hybrid models integrating domain-specific forecasting methodologies can adjust to sudden weather fluctuations, hence greatly enhancing predicting accuracy. Wang et al.²⁶ presented that the CNN-LSTM model exhibits enhanced accuracy in PV energy Prediction performance in comparison with that of the individual LSTM and CNN models. Kumari et al.²⁷ revealed that the CNN-LSTM hybrid enhances forecasting accuracy in comparison to individual methods like RNN, LSTM, CNN, and GRU. Uluocak et al.²⁸ presented hybrid models that integrate CNN with various neural networks, including GRU and LSTM. The models have demonstrated enhanced efficacy in one-day ahead air temperature forecasts, exceeding individual networks and machine learning algorithms. Finally, Table 1 provides a summary of the recent researches relevant to weather prediction with different forecast horizons and their best evaluation parameters. Advancements have been made in applying algorithms in desalination process, with numerous studies exploring how weather forecasts influence water production of solar still. For this propose, Elsheikh et al.²⁹ utilized an LSTM model to predict the output of a single slope and stepped solar stills. The stepped solar still yields freshwater was enhanced up to 128% in comparison to a conventional solar still. The coefficient of determination for the forecasted findings is 0.97 for the traditional solar still and 0.99 for the stepped solar distiller. Farouk et al.³⁰ concentrated on three essential meteorological variables: sun irradiance, wind speed, and ambient temperature, all of that significant impact the system of distilling of the pyramidal solar. Regression models are developed to predict the impacts of many performance factors by applying Response Surface Methodology (RSM) with a central composite design that includes four parameters and five levels. Alawee et al.⁶ examined the performance, production, and predicted production of two kinds of solar stills: the traditional tubular solar still and the convex tubular solar still. The results were evaluating the distillation output of solar stills and studying the utilization of an advanced gradient boosting machine learning (ML) model for predicting distillation productivity. Murugan et al.³¹ developed the optimal ML model designed for forecasting solar still output under particular weather conditions. Various ML models were evaluated, including linear regression, random forests, decision trees, multilayer perceptron, and support vector machines. Migaybil et al.³² introduced an ANN model to predict the water output of solar stills. The main aim referred to implement the transfer learning method in the RI ANN model for traditional solar stills. The water output was forecasted utilizing kernel-based ML approaches³³. The diurnal distillation output of a single slope solar still was modeled utilizing a conventional ANN model trained on meteorological data³⁴. The efficiency of the inclined stepped solar distillation still was analyzed via a cascaded forward neural network³⁵. A Harris Hawks optimizer and a multilayer perceptron neural network have been combined to create a hybrid an artificial intelligence approach for predicting water output in an active solar still system combined with an external condenser³⁶.

Table 1 Relevant recent researches in weather prediction.

To our knowledge, there are limited publications in the field of long-term forecasting, that encouraged researchers to investigate novel methodologies for forecasting long-term solar still output. This study employs various algorithms, that includes LSTM, CNN, GRU, and a hybrid algorithm named CNN-LSTM, to predict the output of the studied solar stills located in Tehran and Zahedan, Iran, for the next ten years. Solar irradiance and temperature are forecasted to assess the potential of suitable solar still placement in an allocated region. The results are compared using Root Mean Square Error (RMSE), Mean Square Error (MSE), coefficient of determination (${\text{R}}^{2}$), Mean Absolute Error (MAE), and Coefficient of Variance (COV), used as evaluation parameters, the evaluation metrics of the algorithms are compared.

Experimental methodology

Test-setup

Modified pyramidal solar still with rotational mechanism to enhance the condensation and evaporation processes was designed and constructed. The system utilizes a pyramidal configuration operating at a rotational speed of 1 rpm. The experimental setup is equipped with rotating wheels connected to a central shaft, which is driven by a 6 W DC motor. Figure 1and 2 illustrate the experimental configuration. The tests were performed at the University of Science and Technology in Tehran, located at a latitude of 35.44° N and longitude of 51.41° E. Productivity of freshwater was determined hourly and collected utilizing a measuring jar for distilled water to recording total Solar distillation system yield per day².

Fig. 1

Constructed testing apparatus of the pyramidal solar still².

Fig. 2

Illustration of the experimental configuration².

The factors influencing the performance of the distiller system were recorded and evaluated in the specified time period. The parameters include wind velocity, sun irradiance, ambient temperature, and rotational speed. The configuration of the pyramidal distillation system requires the consideration of parameters including the exposed surface area to solar irradiation. The design specifications feature an absorptive plate of 70 × 70 cm. The basin of water is constructed using 1.5 mm thick galvanized iron, and the cover of pyramid comprises four clear glass panels, each 4 mm in thickness. Feedwater system of the solar still technique consists of a small funnel connected to a floating water buoy in the tank. The data logger, feeding system, and distillated water jug for collection are attached to the exterior perimeter of the solar still. The examination setup connected to a rotating shaft driven. A solar panel was utilized to eliminate the need for fossil-based energy systems. The pyramid-shaped solar still follows the proportions of prior models, featuring a tilt angle of the glass cover that corresponds using the local latitude².

Measuring tools

Solar distiller performance is often evaluated on numerous critical features, involving solar irradiance, temperature, distillated volume, and air speed. The configuration is supplied with several measurement instruments essential for collecting data and analysis. This equipment is included into the monitoring system and document the important variables through the experiential tests. Appropriate instruments are employed to determine those features via experimentation³⁰. A solar meter is utilized to measure irradiation values at different daily interval. Determinations of temperatures were obtained using thermocouple wires. Furthermore, the anemometer is employed to measure air velocity. The solar distiller yield is assessed utilizing the accurate balance mechanism. Table 2 represents comprehensive details of the instruments employed in the experimental analysis².

Table 2 Comprehensive specifications of the instruments.

System efficiency

The performance of several solar distiller models has been evaluated using energy and exergy efficiency⁴⁵. The efficiency depends on the water output of the solar distiller and the heat transfer mechanism within it. The condensation rate indicates the distillate yield of freshwater generated by the solar still system, additionally referred to as the hourly or daily the system productivity. The overall thermal efficiency of a solar still unit in passive and active operation types, as presented by Kabeel et al.⁴⁶, allows for the hourly distilled yield of the solar still to be defined as follows in Eq. (1):

$${\dot{\text{m}}}_{{\text{W}}} = \frac{{{\upeta }_{{{\text{th}}}} \times A \times \sum {{\text{I}}\left( {\text{t}} \right) \times 3600} }}{{{\text{h}}_{{{\text{fg}}}} }}$$

(1)

where $\eta_{th}$ is presented as the thermal efficiency, ${\text{h}}_{{{\text{fg}}}}$ is the latent heat of vaporization, ${\text{I}}\left( {\text{t}} \right)$ and $A$ are the average daily solar radiation, the total area respectively. According to Eq. (2), the thermal efficiency over the day is then⁴⁷:

$${\upeta }_{{{\text{th}}}} = 0.727 - 2.88 \times 10^{2} \frac{{\text{T}}}{{{\text{I}}\left( {\text{t}} \right)}}$$

(2)

where ${\text{I}}\left( {\text{t}} \right)$ is the mean daily solar irradiance on the still from sunrise to sunset. T is the time period.

Besides, $h_{fg}$ is determined by the water temperature ($T_{W}$), by Emad et al.⁴⁸ as follows in Eq. (3):

$${\text{h}}_{{{\text{fg}}}} = 10^{3} \times \left[ {2501.09 - 2.40706 \times {\text{T}}_{{\text{W}}} + 1.192217 \times 10^{ - 3} \times {\text{T}}_{{\text{W}}}^{2} - 1.5863 \times 10^{ - 5} \times {\text{T}}_{{\text{W}}}^{3} } \right]$$

(3)

${\text{T}}_{{\text{W}}}$ is proportional to the ambient temperature in each season.

Deep neural networks

LSTM model

LSTM, a specialized type of recurrent neural network (RNN), is developed to address the vanishing gradient issue. Its sophisticated architecture allows LSTM networks Aimed at accurately capturing and processing long-term dependencies in sequential data. These networks are extensively utilized across different sectors, involving speech recognition, challenges including sequence modeling and natural language processing. The primary advancement of LSTM is the incorporation of memory cells and gating processes. In the LSTM architecture illustrated in Fig. 3, the forgetting gate eliminates input data while maintaining critical data⁴⁹. It generates a vector ranging from 0 to 1 to ascertain which data in the cell state Ct−1 should be preserved. Input control gate modifies x_t using the sigmoid function and ht−1 using the tanh function to collectively update the cell state. Output control gate comprises two components: The output at time t, o_t, along with the updated hidden state h_t, with o_t determined by x_t and oh_t-1. The detailed operational concept is articulated by Eqs. (4) to (9) ⁵⁰:

$${\text{f}}_{{\text{t}}} = {\upsigma }\left( {{\text{W}}_{{\text{f}}} .\left[ {{\text{h}}_{{{\text{t}} - 1}} ,{\text{x}}_{{\text{t}}} } \right] + {\text{b}}_{{\text{f}}} } \right)$$

(4)

$${\text{i}}_{{\text{t}}} = {\upsigma }\left( {{\text{W}}_{{\text{i}}} .\left[ {{\text{h}}_{{{\text{t}} - 1}} ,{\text{x}}_{{\text{t}}} } \right] + {\text{b}}_{{\text{i}}} } \right)$$

(5)

$${\text{g}}_{{\text{t}}} = {\text{tanh}}({\text{W}}_{{\text{g}}} .\left[ {{\text{h}}_{{{\text{t}} - 1}} ,{\text{x}}_{{\text{t}}} } \right] + {\text{b}}_{{\text{g}}}$$

(6)

$${\text{C}}_{{\text{t}}} = {\text{g}}_{{\text{t}}} \times {\text{i}}_{{\text{t}}} + {\text{C}}_{{{\text{t}} - 1}} \times {\text{f}}_{{\text{t}}}$$

(7)

$${\text{o}}_{{\text{t}}} = {\upsigma }\left( {{\text{W}}_{{\text{o}}} .\left[ {{\text{h}}_{{{\text{t}} - 1}} ,{\text{x}}_{{\text{t}}} } \right] + {\text{b}}_{{\text{o}}} } \right)$$

(8)

$${\text{h}}_{{\text{t}}} = {\text{o}}_{{\text{t}}} \times \tanh \left( {{\text{C}}_{{\text{t}}} } \right)$$

(9)

Fig. 3

The LSTM model structure.

W_f, W_i, W_g and W_o represent the matrix weights of the respective gates, while b_f, b_i, b_g and b_o denote the bias terms. The sigmoid activation function, represented by × , and the tanh function are both employed as activation functions in the model.

CNN model

CNNs are classified as a type of feedforward network models that utilize convolutional operations and consist of convolutional layers, pooling layers, and fully connected layers, as seen in Fig. 4. The convolutional layers execute localized operations on small segments of the input information using a convolutional kernel, as indicated in Eq. (10), therefore capturing spatial patterns and characteristics⁵¹.

$${\text{F}} \otimes {\text{w}} = \mathop \sum \limits_{{{\text{i}} = 1}}^{{{\text{H}}_{{\text{k}}} }} \mathop \sum \limits_{{{\text{j}} = 1}}^{{{\text{W}}_{{\text{k}}} }} \left( {{\text{F}}\left( {{\text{i}},{\text{j}}} \right).{\text{w}}\left( {{\text{i}},{\text{j}}} \right)} \right)$$

(10)

Fig. 4

The CNN model structure.

In the above context, ⨂ signifies convolutional computation, F represents a segment of the input information, while w, H_k, and W_k stand for the convolution kernel weight parameter, height, and width, respectively⁵².

CNN-LSTM model

A common design for analyzing time-series data is CNN-LSTM, which combines CNN and LSTM networks. This study uses a hybrid approach to feature extraction using the CNN layer and subsequently transmitting them to the LSTM layer. As seen in Fig. 5, the time-sequenced data are first fed toward the feature-extracting convolutional layer in the CNN of features, followed by the pooling layer, which extracts hidden data, and the flatten layer, which decreases the feature dimension. For more time-series modeling and prediction, the gathered feature sequences are then fed into the LSTM. The aggregated features are subsequently fed into the fully connected layer for forecasting. CNN extracts spatial features in time series data, whilst LSTM captures temporal dependencies; this combination leverages the potential of both models, enhancing the modelling and predictive capabilities of time series data⁵³.

Fig. 5

The CNN-LSTM model structure.

GRU model

The GRU neural network is a simplified variant of the LSTM, designed to reduce the number of gates while maintaining long-term memory capabilities, effectively addressing the vanishing gradient issue. GRU comprise two gates: the update gate and the reset gate. The former refers the information discarded related to a new input and the update data incorporated, while the next articulates the extent of long-term or prior data discarded by the forget gate. Equations (11) and (13) refer to the reset and forget gates²³.

$${\text{z}}_{{\text{t}}} = {\upsigma }\left( {{\upomega }_{{{\text{zh}}}} .{\text{h}}_{{{\text{t}} - 1}} + {\upomega }_{{{\text{zx}}}} .{\text{x}}_{{\text{t}}} + {\text{b}}_{{\text{z}}} } \right)$$

(11)

$${\text{r}}_{{\text{t}}} = {\upsigma }\left( {{\upomega }_{{{\text{rh}}}} .{\text{h}}_{{{\text{t}} - 1}} + {\upomega }_{{{\text{rx}}}} .{\text{x}}_{{\text{t}}} + {\text{b}}_{{\text{r}}} } \right)$$

(12)

$${\text{h}}_{{\text{t}}}{\prime} = \tanh ({\upomega }_{{{\text{xh}}}} .{\text{x}}_{{\text{t}}} + {\text{r}}_{{\text{t}}} {\upomega }_{{{\text{hh}}}} .{\text{h}}_{{{\text{t}} - 1}} )$$

(13)

In Eq. (13), the input data x_t and the prior time step data h_t-1 are linearly combined, with the various matrices ω being multiplied correspondingly on the right side. Subsequently, the reset gate r_t and ω_hh. h_t−1 are multiplied. Finally, the updated information regarding the present condition is computed using an activation function, often the tanh function⁵⁴.

$${\text{h}}_{{\text{t}}} = {\text{z}}_{{\text{t}}} .{\text{h}}_{{{\text{t}} - 1}} + \left( {1 - {\text{z}}_{{\text{t}}} } \right){\text{h}}_{{\text{t}}}{\prime}$$

(14)

As per equation (14), the multiplication of z_t and h_t−1 indicates the conclusive data information retained from the preceding time step. The output and the information retained from the present memory to the long-term memory. correspond to the output h_t generated by the final gate unit. Figure 6 illustrates the structure of the GRU.

Fig. 6

GRU structure.

Evaluation metrics analysis

Various error measuring techniques can assess the precision of models for forecasting. The study suggests utilizing five assessment measures to assess the model accuracy: mean absolute error (MAE), root mean square error (RMSE), square error (MSE), coefficient of determination (R²), mean and coefficient of variance (COV). Equations (15) to (19) are used to determine the five parameters^29,43,55,56:

$${\text{MAE}} = \frac{1}{{\text{N}}}\mathop \sum \limits_{{{\text{i}} = 1}}^{{\text{N}}} \left| {{\text{x}}_{{\text{i}}} - {\text{y}}_{{\text{i}}} } \right|$$

(15)

$${\text{MSE}} = \frac{1}{{\text{N}}}\mathop \sum \limits_{{{\text{i}} = 1}}^{{\text{N}}} \left( {{\text{x}}_{{\text{i}}} - {\text{y}}_{{\text{i}}} } \right)^{2}$$

(16)

$${\text{R}}^{2} = 1 - \frac{{\mathop \sum \nolimits_{{{\text{i}} = 1}}^{{\text{N}}} ({\text{x}}_{{\text{i}}} - {\text{y}}_{{\text{i}}} )^{2} }}{{\mathop \sum \nolimits_{{{\text{i}} = 1}}^{{\text{N}}} \left( {{\text{y}}_{{\text{i}}} } \right)^{2} }}$$

(17)

$${\text{RMSE}} = \sqrt {\frac{1}{{\text{N}}}\mathop \sum \limits_{{{\text{i}} = 1}}^{{\text{N}}} \left( {{\text{x}}_{{\text{i}}} - {\text{y}}_{{\text{i}}} } \right)^{2} }$$

(18)

$${\text{COV}} = \frac{{{\text{RMSE}}}}{{{\overline{\text{y}}}}} \times 100$$

(19)

Input data

Case study

Iran contains broad desert landscapes and clear sky, providing advantageous conditions for solar energy, which exhibits significant variability in potential across various regions⁵⁷. Calculations indicate that the annual solar radiation hours in Iran reach 2800 h. The sun irradiance in Iran is 2.5 times greater than that of European countries. The region contains significant solar energy potential, including approximately 300 days of sunlight annually and an mean solar radiation of 2200 kWh/m²⁵⁸. The Global Horizontal Irradiation (GHI) atlas for Iran (see Supplementary Fig. S1 online), indicating significant sun irradiation values in the southeastern region, so providing it a suitable option for the establishment of a solar distiller⁵⁹. Tehran, the capital of Iran, is situated in the northern part of the country, located at coordinates latitude of 35.44, longitude of 51.41. July exhibits the peak intensity of sun irradiation, often exceeding 7 kWh/m²/day and December has the lowest solar irradiation level, usually around 2.5 kWh/m²/day. Zahedan is a city situated in southeastern Iran (latitude 29.47, longitude 60.90) that possesses one of the greatest levels of solar radiation, with a low of 3.97 kWh/m²/day in December and a maximum of 8.5 kWh/m²/day in June. Meteorological data for Tehran and Zahedan from 1984 to 2023 (480 months) have been obtained every month from the NASA website⁶⁰.

Data pre-processing and feature selection

Solar irradiance, temperature, from Tehran and Zahedan were obtained from the NASA website⁶⁰ for the period between 1984 and 2023. Details of the characteristic can be presented in Table 3. The dataset contains no missing values; nevertheless, preprocessing is still necessary. This preparation phase involves feature engineering and data normalization.

Table 3 Description of features.

Feature selection is used to determine the most significant characteristics influencing the result in order to reduce computing costs and improve prediction accuracy. One approach of feature selection involves utilizing features that have the strongest association with the output variable⁶¹. Pearson correlation is employed in this investigation as the method for feature selection. This coefficient is appropriate for use with continuous input and target parameters in time series data, quantifying relationships on a scale from − 1 to 1. It is typically employed to compute the standard variations of input and target features, indicating the degree of correlation through the coefficient. When the value of the coefficient is between 0 and 1, the target feature rises as the input feature enhanced. On the other hand, When a coefficient ranges between 0 and − 1, it indicates that the target feature decreases as the input variable increases⁶². The heat map in Fig. 7 and 8 demonstrate the strong correlation between PS, QV2M, T2MDEW, and TS with GHI, T2M, and WS10M for Tehran and Zahedan. Thus, these characteristics have been regarded as input variables in neural network-based multivariate time series forecasting. According to these matrixes, characteristics exhibiting a correlation exceeding 0.7 with solar irradiance and T2M have been identified as a significant element for predicting. As can easily be understood from matrix for Tehran, T2MDEW, T2MWET, RH2M, TS, and PS are highly correlated with GHI and T2M. T2MWET, RH2M and TS exhibit the strongest interaction with sun radiation. and temperature in Zahedan.

Fig. 7

Heat map of Tehran based on Pearson coefficient.

Fig. 8

Heat map of Zahedan based on Pearson coefficient.

Data normalization

In addition, differences in the scale and range of data can reduce the accuracy and efficiency of deep learning approaches. Normalization addresses this issue by scaling all numerical features to a uniform range, thereby ensuring no single variable disproportionately influences the model due to its scale. Research employing solar and wind power prediction models frequently utilizes the min–max scaling technique for normalization purposes. By rescaling the data according to the highest and lowest values, this method normalizes the data by transforming it to have a standard scale. By standardizing the data ranges between 0 and 1, this makes it easier to compare and understand different kinds of data⁶³. The data normalization process is defined by Eq. (20) ⁶⁴:

$$x_{{{\text{scaled}}}} = \frac{{x - {\text{min}}\left( x \right)}}{{\max \left( x \right) - {\text{min}}\left( x \right)}}$$

(20)

The time series data must then be defined as a supervised learning problem. Multistep forecasting could forecast all times during one stage⁶⁵. Using previous time steps as input features and future time steps as target variables, this study employed the direct approach for multistep ahead data prediction. Figure 9 illustrates that each expected data can be predicted multiple times. To avoid overfitting and underfitting, the dataset is divided into test and train portions in a 30–70 ratio. The methods used in this work to predict temperature and solar radiation is shown in Fig. 10. This methodology comprises four primary processes: (a) data collecting, (b) data preprocessing, (c) training the model, and (d) model evaluation.

Fig. 9

A multistep forward prediction strategy schematic.

Fig. 10

The step-by-step process of the present research for forecasting.

Results

The input features are situated in two locations: a. Tehran, b. Zahedan. The results from the assessment of multivariate multi-step forecasts over the defined prediction horizon are presented in Supplementary Tables S1 and S2 online. As mentioned before, two separate situations were tested. The first case is located in Tehran, and the second case is located in Zahedan city. GHI is the primary target variable forecasted by the model, followed by T2M as the secondary output. It should be considered that changes in prediction priorities require hyperparameter reconfiguration. Moreover, increasing data volume and incorporating multivariate features tend to enhance the model forecasting accuracy.

Solar radiation prediction

The results of different models used to predict GHI in Tehran and Zahedan are shown. The CNN model in Tehran showed the best accuracy across all parameters, with the lowest testing RMSE (0.0526), MSE (0.0027), and MAE (0.0402). Additionally, a significant correlation between the predicted and actual values is indicated by its R² value of 0.9671. With an R² of 0.9664, the GRU model showed consistent performance across target features despite being significantly less accurate. Both LSTM and CNN-LSTM models demonstrated strong performance, with LSTM slightly surpassing CNN-LSTM in RMSE and MAE metrics. Their results were not as strong as those of the CNN models used alone, though, indicating that simpler models may be enough for predicting GHI in this region.

The LSTM model performed better for Zahedan than the other models, with an R² of 0.9595 and an RMSE of 0.0547 during testing. The CNN-LSTM and GRU models performed well, with CNN-LSTM yielding slightly better results than GRU, where CNN-LSTM achieved an COV of 10.39% compared to 10.46% for GRU. Interestingly, while these models displayed slightly higher error metrics, their R² values remained above 95%, indicating strong predictive capability. In contrast to Tehran, the CNN model performed the least effectives. Overall, Tehran yielded slightly better prediction accuracies across all models compared to Zahedan, possibly due to differing environmental conditions.

Temperature prediction

The performance metrics for temperature prediction across models and locations are summarized. Unlike solar radiation predictions, GRU showed the best performance in Tehran, obtaining an RMSE of 0.0458, an MSE of 0.0021, and an R² of 0.9721 during testing. The CNN model, though marginally less precise, exhibited consistent performance with an R² score of 0.9719 throughout the target feature. The LSTM and CNN-LSTM models demonstrated competitive results, with LSTM marginally surpassing CNN-LSTM in terms of RMSE (0.0474) and MAE (0.0371). The hybrid CNN-LSTM models offered competitive performance but did not consistently outperform standalone CNN and LSTM models. For instance, CNN-LSTM achieved an R² of 0.9690 in Tehran, indicating strong predictive capabilities but falling slightly short of LSTM.

In Zahedan, the LSTM model again exhibited strong performance, similar to its results in GHI prediction, with an RMSE of 0.0554 and an R² of 0.9589. Also, GRU and CNN-LSTM provided comparable performance, GRU had an MSE of 0.0031 and an R² of 0.9588, closely rivaling CNN-LSTM. However, its MSE was slightly higher than that of CNN-LSTM, which achieved a value of 0.0034. As with GHI prediction, Tehran exhibited slightly better predictive accuracy across all models for temperature, which could be attributed to the quality of input data or environmental factors.

According to Table 4, the CNN algorithm demonstrates the maximum performance for Tehran, while the LSTM model succeeds for Zahedan in GHI prediction, the GRU algorithm demonstrates the superior Tehran performance. The LSTM algorithm demonstrates the best performance for forecasting in Zahedan over a 10-year horizon in prediction in temperature prediction. Hybrid CNN-LSTM models demonstrated strong performance but did not always surpass standalone other models, indicating that hybridization may not necessarily improve prediction accuracy in all cases.

Table 4 GHI and Temperature evaluation parameters of models.

In multi-step direct forecasting, as illustrated in Fig. 9, each observation is predicted many times, and the forecasts for each observation are averaged to supply a visual comparison of method performance on the dataset. Figure 11 illustrates the CNN and GRU performance algorithms in predicting GHI and T2M in Tehran using training data to forecast the next ten years. Figure 12 illustrates forecasting performance of the LSTM model applied to GHI data and T2M in Zahedan employing training data to predict trends over the next ten years, which confirms a reasonable alignment of predicted values with actual data.

Fig. 11

Predicted data of (a) solar radiation for CNN and (b) Temperature for GRU.

Fig. 12

Predicted data of (a) solar radiation and (b) Temperature for LSTM.

Fitting a regression line between observed and predicted values offers an alternative method for evaluating model performance. A strong correlation between the expected and actual data is seen by the distribution of points close to the line y = x. There is a strong correlation between the actual and predicted values of T2M and GHI (see Supplementary Fig. S2 and S3 online).

Further validating the suggested CNN model ability to forecast GHI and the GRU model capacity to predict T2M in Tehran during the subsequent decade to satisfactory accuracy and effectiveness, that was the objective of this research is presented (see Supplementary Fig. S4 online). Also, the suggested LSTM model capacity to forecast GHI and T2M in Zahedan for the last ten years is illustrated (see Supplementary Fig. S5 online).

This kind of prediction is highly beneficial for anyone aiming to construct and evaluate the environmentally friendly and economic feasibility of solar distiller in a particular region. Equations (1) to (3) indicate that two factors, GHI and T2M, are required to forecast the solar still capacity to produce fresh water. Consequently, considering into account the GHI and T2M obtained from the CNN and GRU models for Tehran, along with the LSTM model for Zahedan, the freshwater output of this solar still is computed. Figure 13 and 14 illustrate the yearly freshwater output for the proposed solar still located in Tehran and Zahedan from 1984 to 2033. Also, a comparison of the water productivity in Tehran and Zahedan for the next 10 years is shown (see Supplementary Fig. S6 online). It is important to remember that certain elements, like freezing temperatures, particulate matter, and foggy climate, have been excluded from the numerical estimates of water productivity.

Fig. 13

Annual output of freshwater from the solar still in Tehran.

Fig. 14

Annual output of freshwater from the solar still in Zahedan.

Discussion

The findings of this study indicate that deep learning models, are effective in long-term forecasting of solar radiation and temperature for the selected regions of Tehran and Zahedan. The comparison of model performance across multiple evaluation metrics provides key insights into the suitability of these methods for renewable energy applications.

In Tehran, the CNN and GRU models consistently outperformed GRU, LSTM, and hybrid CNN-LSTM models across for solar radiation and temperature prediction, these models achieved the highest accuracy, as indicated because of its low RMSE, MSE, and MAE values, along with its high R². This performance advantage is a result of their capability to efficiently capture spatial features within the data, which are particularly important for modeling environmental parameters such as solar radiation and temperature. In Zahedan, LSTM demonstrated better performance than other models, albeit with slightly higher error metrics compared to other models in Tehran. The observed performance difference between the two locations may be attributed to variations in climatic conditions, geographical factors, or differences in the quality and distribution of the input data. This finding highlights the importance of regional calibration when applying forecasting models to diverse geographical settings.

While hybrid CNN-LSTM models provided competitive results, they did not consistently outperform the standalone models. For instance, CNN-LSTM achieved high accuracy in Tehran but was slightly inferior to CNN in terms of RMSE and R² values. Similarly, CNN-LSTM provided strong predictions in Zahedan but did not surpass the performance of LSTM. This suggests that the added complexity of combining convolutional and recurrent layers may not always yield significant improvements, particularly when the spatial features dominate the data, as in the case of solar radiation and temperature. The evaluation metrics used in this investigation, performed an extensive analysis of model performance. The consistently high R² values across all models in both locations, exceeding 97% in most cases, indicate that the models effectively captured the variability in solar radiation and temperature data.

The comparative analysis between regions, Tehran consistently exhibited better prediction accuracy than Zahedan across all models and metrics. This trend could be explained by several factors, including a more stable and homogeneous climate in Tehran, which may make it easier for models to learn underlying patterns. Conversely, more variable climatic conditions of Zahedan might introduce additional noise into the data, making predictions more challenging. Additionally, differences in solar irradiance and temperature profiles between the two regions might affect the ability of model to generalize.

The findings of this research provide practical insights for the placement and operation of solar stills in Tehran and Zahedan. The ability to accurately forecast solar radiation and temperature is crucial for improving design efficiency and placement of solar stills to maximize their efficiency. The superior performance of selected models suggests that they can be reliably used for long-term forecasting, aiding decision-making processes for renewable energy projects. Furthermore, the model ability to handle regional variations underscores their potential applicability to other locations with different environmental conditions.

Conclusion

The purpose of this research was to forecast the freshwater output of the pyramid solar still. This research evaluates four models (LSTM, CNN, CNN-LSTM, and GRU) to predict multistep GHI and T2M for two locations in Iran, Tehran and Zahedan, over the next ten years through numerical simulations utilizing real GHI and T2M histories. The direct technique was employed in this work to forecast multistep forward data due to its lack of error propagation problems found in the recursive method. Five evaluation metrics were used to compare the outcomes, RMSE, MSE, MAE, COV, and ${R}^{2}$. The results validated the better performance of the CNN and GRU models for GHI and T2M prediction in Tehran, while the LSTM model succeeded in Zahedan, compared with other models in properly aligning with the real test value using two specified inputs that highlights the importance of location-specific calibration. Hybrid CNN-LSTM models offered competitive results, though they did not consistently outperform standalone CNN models, suggesting that added model complexity may not always yield significant gains. Recurrent models, such as LSTM, performed adequately but were generally less accurate than CNN models, likely due to the spatially dominance of the input data. The aim of the GHI and T2M forecast was to perform a predictability analysis of freshwater yield for the next ten year to inform planning analysis. The difference between the actual and forecasted information proved the model optimal consistency in following the trend and forecasting values.

The study also highlighted regional differences, with Tehran exhibiting slightly better prediction accuracy than Zahedan. The importance of region-specific data analysis is highlighted by these findings and model fine-tuning to account for variations in environmental conditions. This study shows how deep learning models can be used, particularly CNNs, as reliable tools for long-term forecasting of solar still productivity. Accurate predictions of solar radiation and temperature can support the optimal placement and design of solar stills, ultimately enhancing the efficiency of renewable energy systems. Future studies should emphasis on growing the dataset to contain more variety of locations and exploring advanced hybrid or ensemble approaches to further improve predictive accuracy and generalizability. The major conclusions are presented as follows:

• The predicted monthly variation of GHI and T2M over the next years in Tehran is between 97.8 and 330.8 W/m², while the temperature is expected to range from 2 to 31.6 °C. The monthly variation range for GHI and T2M during the next ten years in Zahedan is 167.1–354.6 W/m², whereas the temperature range is between 6.4 and 43.6 ◦C.

• Between 2024 and 2033, the predicted freshwater yield of the solar still is estimated to reach 2630 L in Tehran and 2710 L in Zahedan.