Development of an adaptive neuro-fuzzy inference system (ANFIS) model to predict sea surface temperature (SST)

Sea surface temperature (SST) is one of the most important parameters in Earth observation aimed at monitoring the global climate (Mahongo & Deo 2013). SST plays an important role in the process of interactions between the atmosphere and the Earth’s surface (Zhang et al. 2017). It is a critical parameter for understanding and forecasting rainfall and hurricanes (Nobre & Shukla 1996).

Assessment and reconstruction of the ocean dynamics are key challenges (Ouala et al. 2018). Estimation and reconstruction of geophysical properties of the sea surface rely on model-based techniques that make significant use of a dynamic model to perform simulations based on specific ocean conditions (Gordon et al. 2000). On the other hand, the selection and parameterization of a dynamic model are still a complex issue for understanding the relationships between spatial and temporal changes in the ocean surface. Data-driven approaches have emerged as an attractive strategy to describe certain dynamic models with an increased amount of observational and simulation data. Neural networks are a state-of-the-art approach to many different issues related to machine learning (Ouala et al. 2018). They are an efficient and remarkable data-driven approach to estimating and reconstructing sea surface dynamics. An artificial neural network (ANN) has an important advantage in the system modelling, which does not require a well-defined physical relationship to systematically transform input data into output data (Farokhnia et al. 2011).

Predicting water temperature of seas, lakes, and streams is important in planning and management of water resources (Heddam et al. 2020). Several machine learning approaches have been extensively used to model water temperature. Their performance varies depending on the input variables and models used. Piccolroaz et al. (2013) proposed a simple lumped model (air2water) to forecast lake water surface temperature by using air temperature as an input predictor. The proposed model has been broadly used by several researchers for forecasting lake water surface temperature due to its higher accuracy and simplicity (Toffolon et al. 2014; Piccolroaz 2016; Piccolroaz et al. 2016; Zhu et al. 2020). As documented by Graf et al. (2019) and Zhu et al. (2020), the use of hybrid models offers some advantages in forecasting water temperature. Heddam et al. (2020) proposed machine learning approaches, including extremely randomized trees (ERT), multivariate adaptive regression splines (MARS), the M5 Model Tree (M5Tree), the random forest (RF), and the multilayer perceptron neural network (MLPNN) to model daily lake surface water temperature by using air temperature. The authors compared the results of the proposed approaches with the air2stream model and reported that none of the proposed approaches provided better results in predicting water temperature than the air2stream model. Graf et al. (2019) forecasted water temperature in the Warta River in Poland using the wavelet-neural network hybrid modelling approach. The authors proposed a hybrid model that combines discrete wavelet transforms and the ANN for forecasting water temperature. They used daily air temperatures from seven meteorological stations to predict daily water temperature. Zhu et al. (2020) developed and applied the multi-layer perceptron neural network (MLPNN) model and an integrated model of the wavelet transform and the MLPNN (WT-MLPNN) to forecast daily lake surface water temperature of eight lowland lakes in Poland. The authors used long-term daily lake surface water temperature and daily air temperatures as input variables. It was found that the hybrid WT-MLPNN model performed slightly better than the traditional MLPNN model in forecasting the lake surface water temperature. Zhu et al. (2019a) applied four different machine learning models, including multilayer perceptron neural network models (MLPNN), ANFIS with the subtractive clustering method (ANFIS-SC), ANFIS with the grid partition method (ANFIS-GP) and ANFIS with the fuzzy c-mean clustering algorithm (ANFIS-FC), to predict daily river water temperature. The authors used air temperature, river flow discharge, and the components of the Gregorian calendar as input variables. Piotrowski et al. (2020) employed shallow neural networks to model stream water temperature in six catchments. The authors used air temperature, river discharge, and the declination of the Sun as input parameters.

Zadeh (1965) first introduced the theory of fuzzy sets and fuzzy logic to describe basic properties and implications of a concept that plays an important role in human thinking. The principal idea underlying the fuzzy logic control was proposed and described in detail by Zadeh (1968) and Zadeh (1973). Jang (1993) developed a neuro-fuzzy approach that is a combined method to improve the efficacy of a model compared to the ANN and fuzzy logic. The neuro-fuzzy system combines neural networks and fuzzy logic and implements learning techniques developed in the ANN into the fuzzy inference system (FIS; Brown and Harris 1994). The adaptive neuro-fuzzy inference system (ANFIS) is a specific approach in neuro-fuzzy systems and Jang et al. (1997) indicated that the ANFIS produced noteworthy results in modelling of nonlinear functions. The ANFIS uses an adaptive network for learning and is a popular approach for predicting parameters related to water resources (Nayak et al. 2004; Aqil et al. 2007; Sönmez et al. 2018).

In recent years, artificial intelligence (AI) techniques have become increasingly important in water and climate applications due to their capability of learning concealed patterns from historical data and estimating non-linear systems (Awan and Bae 2016). Several researchers applied some artificial intelligence (AI) techniques to forecast water temperature in rivers and streams (Piccolroaz et al. 2013, 2016; Graf et al. 2019; Zhu & Heddam 2019; Zhu et al. 2019a,b,c; 2020; Heddam et al. 2020; Piotrowski et al. 2020) and sea surface temperature (Garcia-Gorriz and Garcia-Sanchez 2007; Mahongo & Deo 2013; Piotrowski et al. 2015; Patil et al. 2016; Samadianfard et al. 2016; Zhang et al. 2017; Ouala et al. 2018). However, there is no study on the SST prediction for the Çanakkale Strait. Therefore, the main objective of the present study was to develop an adaptive neuro-fuzzy inference system (ANFIS) model to predict SST by using climate data for the Çanakkale Strait.

Four categories of input data (air temperature, evaporation, precipitation, and month) were considered when developing the prediction models for SST. Descriptive statistics of observed parameters are given in Table 1. The table shows that the air temperature was the most correlated parameter with SST.

Both the grid partition method and the subtractive clustering method have four different versions in terms of the number of inputs. In both methods, version 1 (GP1 and SC1) includes only air temperature, version 2 (GP2 and SC2) includes air temperature and evaporation, version 3 (GP3 and SC3) includes air temperature, evaporation and precipitation, while version 4 (GP4 and SC4) includes all parameters (month, air temperature, evaporation, and precipitation) as input parameters.

The accuracy of the prediction relative to the observation was checked during the training and testing stages. Six performance evaluation parameters were used to evaluate the developed models for the prediction of SST: mean square error (MSE), root mean squared error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE), Nash-Sutcliffe efficiency (NSE) and coefficient of determination (R²). The application of multiple error criteria allowed for a better understanding of the differences between the observed and predicted SST values. The comparison between the four versions of the ANFIS-SC and ANFIS-GP models revealed that ANFIS-SC4 (the model with four inputs as predictors: month, air temperature, evaporation and precipitation) yielded the best accuracy among all the developed models. The ANFIS-SC4 model performs better than all the other versions of SC and GP with regard to lower MAE and RMSE and higher NSE and R-squared values. Moreover, since R-squared and NSE values closer to 1 indicate a better model, the ANFIS-SC4 was considered the best model. The performance measures of the hybrid ANFIS models are presented in Table 2. A clear increase in model performance from version 1 to version 4 can be observed for both ANFIS-SC and ANFIS-GP models. Predicted SST values usually correlate with observed SST values for most models during the training stage. The R-squared values gradually increased during the training stage for all models. On the other hand, the R-squared values have decreased from version 1 to version 2 for both ANFIS-SC and ANFIS-GP models during the validation stage. Versions 3 of both models have similar values with versions 2. Then, versions 4 showed increased R-squared values in both models. Although ANFIS-GP4 had the highest R-squared value for the training stage in all models, this case was reversed in the validation stage and ANFIS-GP2, ANFIS-GP3 and ANFIS-GP4 had lower performance during the validation stage compared to ANFIS-GP1. The fact remains that the overall performance of ANFIS-GP4 was better than other versions of ANFIS-GP models in terms of higher NSE and R-squared values, lower MAE, MSE, RMSE, and MAPE values.

The results of ANFIS-SC2 and ANFIS-SC3 indicate that the inclusion of the precipitation in the models provides almost similar outcomes. In this case, it can be concluded that the use of precipitation is not compulsory for predicting SST in the Çanakkale Strait. Similar conclusions were also reached for ANFIS-GP2 and ANFIS-GP3 models. In the models with two inputs, on the other hand, the use of evaporation provided more improvement than the consideration of precipitation for both ANFIS-SC and ANFIS-GP. These results confirm that the role of air temperature and evaporation in SST modelling is much more important than precipitation.

First, the ANFIS creates suitable membership functions for each input variable at the training stage. Then, the membership functions are modified according to the error correction training method by using the back-propagation algorithm. In addition, the constant parameter of the linear output functions is adapted for the period of the learning stage based on the least mean square algorithm. The ANFIS model operates 1000 training data items during training periods. The training data constituted 75% of the dataset, while 25% of the dataset was allocated for testing in the ANFIS. The hybrid algorithm was selected as a training algorithm for the ANFIS. Figure 3 presents the diagram of the observed values for the monthly SST and the predicted values obtained using the ANFIS models. It illustrates the comparison between the observed and predicted SST values.

Figure 3

The highest correlation coefficient (0.96) was found between the observed and predicted SST values in the ANFIS-SC4 model for the overall prediction of SST time series. Moreover, the ANFIS-GP4 model outperformed during the training stage in terms of the R-squared value (0.97). Figure 4 presents the scatter plots of the observed and predicted SST values for all models. The respective correlation coefficient indicates an acceptable estimation of the model.

Figure 4

The output surface maps for the developed ANFIS-SC4 and ANFIS-GP4 models were presented in Figure 5 and Figure 6. In addition, the input-output surfaces produced by the ANFIS-SC3 and ANFIS-GP3 models are presented in Figure 7. These figures show the relationships between the predicted SST values and the other two inputs, respectively. The 3D surface visualization of the relationships between the inputs and the output for the ANFIS-SC2 and ANFIS-GP2 models was plotted in Figure 8.

Figure 5

Figure 6

Figure 7

Figure 8

This study presents the ANFIS models developed to predict SST in the Çanakkale Strait in Turkey. Six performance evaluation criteria were used to evaluate the ANFIS models developed for SST prediction. The Takagi–Sugeno fuzzy inference system was implemented and the training data accounted for 75% of the dataset, while 25% of the dataset was allocated for testing in the ANFIS. The hybrid algorithm was selected as a training algorithm for the ANFIS. The average testing error was 0.91. The rules of the models were determined according to the relationships between the inputs and the output by the adaptive neuro-fuzzy inference system. The observed and predicted SST values were compared and Figure 4 presents the scatter plots of the observed and predicted SST values in the Çanakkale Strait. The respective correlation coefficient of 0.96 was found between the observed and predicted SST values in the ANFIS-SC4 model. The output surface maps for the developed ANFIS models were plotted and presented in Figures 5–8.

The SST is an important parameter in oceanographic research and planning of miscellaneous offshore activities (scientific, traditional, commercial and recreational events such as research, fishing, and marine transportation). It is one of the most important parameters in Earth observation aimed at monitoring the global climate (Mahongo & Deo 2013). Therefore, an accurate estimation of SST is very important. Data-driven approaches and physical observations are used to predict SST. Data-driven approaches range between traditional stochastic techniques, such as regression analysis (Kug et al. 2004), empirical canonical correlation analysis (Collins et al. 2004), trend analysis (Kale et al. 2016a,b, 2018; Ejder et al. 2016a,b; Kale & Sönmez 2018a,b; 2019a,b,c; Sönmez & Kale 2020, Arslan et al. 2020), Markov model (Xue & Leetmaa 2000), genetic algorithms (Neetu et al. 2011), and modern artificial intelligence approaches, such as neural networks (Patil et al. 2016), adaptive neuro-fuzzy inference systems (Sönmez et al. 2018).

Many researchers applied artificial intelligence techniques in research on water resources and climate with respect to environmental monitoring, assessment and forecasting (Altunkaynak et al. 2005; Kisi 2005; Ocampo-Duque et al. 2006; Sengorur et al. 2006; Terzi et al. 2006; Icaga 2007; Elhatip & Kömür 2008; Ay & Kisi 2011; Areerachakul 2012; Hisar et al. 2012; Qasaimeh et al. 2012; Ranković et al. 2012; Sönmez et al. 2012; Sönmez et al. 2013a,b; Ay & Kisi 2014; Emamgholizadeh et al. 2014; Heddam 2014; Alte & Sadgir 2015; Piotrowski et al. 2015; Khadr & Elshemy 2016; Bayatzadeh Fard et al. 2017; Csábrági et al. 2017; Sönmez et al. 2018). On the other hand, several attempts have been made to predict SST globally (Garcia-Gorriz & Garcia-Sanchez 2007; Mahongo & Deo 2013; Patil et al. 2016; Samadianfard et al. 2016; Zhang et al. 2017; Ouala et al. 2018). Unfortunately, there is no research on the assessment of the adaptive neuro-fuzzy inference system for predicting SST. However, some researchers developed adaptive neuro-fuzzy models to estimate SST and compare the accuracy of the performance with other techniques. Garcia-Gorriz and Garcia-Sanchez (2007) used the ANN to predict sea surface temperatures in the western Mediterranean Sea. The authors trained the ANN with meteorological variables and documented that the ANN successfully predicted the mean monthly SST consistent with in situ observations. Similarly, Patil et al. (2016) combined numerical and neural networks to predict SST of the Indian Ocean at daily, weekly and monthly time scales. The authors reported that by combining the two techniques it was possible to make precise forecasts for selected locations. Zhang et al. (2017) developed a neural network and implemented a long short-term memory to predict SST in the coastal seas of China. The authors confirmed the efficacy of the suggested method. Ouala et al. (2018) proposed neural networks for the forecasting of SST off the coast of South Africa. Researchers indicated that the suggested patch-level neural network-based representations surpassed other data-driven models in terms of forecasting and missing data interpolation performance. Xu et al. (2020) predicted a spatio-temporal distribution of SST time series in the offshore waters of China. To achieve this objective, the authors developed a regional convolution long short-term memory (RC-LSTM) model. The prediction accuracy of the model was enhanced by merging spatial and temporal information. The authors reported that the developed model was more accurate than traditional estimation models. Therefore, they suggested that the developed model should be applied in future research. Wei et al. (2019) predicted SST in the South China Sea by the ANN and the authors recommended discrete time series of SST data in two datasets to construct two neural network models. The researchers stated that the suggested training method provides adequate forecasting accuracy. In the present study, a commonly used method that separates the dataset into training and testing stages was used to train and test the time series of SST. The method proposed by Wei et al. (2019) reduced the standard deviation of the prediction outputs and thus improved the accuracy of the prediction. Therefore, it may be considered for further research.

Artificial neural networks and adaptive neuro-fuzzy inference system models have also been developed and proposed by several scientists to predict surface water temperature of lakes, rivers, and streams. Zhu et al. (2019a) applied four different machine learning models, including multilayer perceptron neural network models (MLPNN), ANFIS with the subtractive clustering method (ANFIS-SC), ANFIS with the grid partition method (ANFIS-GP), and ANFIS with the fuzzy c-mean clustering algorithm (ANFIS-FC) to predict daily river water temperature. The authors used air temperature, river flow discharge and the components of the Gregorian calendar as input variables. They reported that the MLPNN model generally provided the highest performance, even though ANFIS-FC and ANFIS-GP were slightly more accurate at some river stations. In the present study, although the developed ANFIS models include similar methods (ANFIS-SC and ANFIS-GP), ANFIS-SC4 was found to be more accurate to predict SST in the Çanakkale Strait. On the other hand, Zhu et al. (2019a) documented that the highest correlation value between the observed and predicted water temperature was 0.9764, while in the present study it was 0.956. The values were relatively close to each other. Therefore, the prediction capacity of the developed models is relatively applicable to predict SST for other locations. Zhu et al. (2020) developed and applied the multi-layer perceptron neural network (MLPNN) model and integrated the model of the wavelet transform and MLPNN (WT-MLPNN) to forecast daily lake surface water temperature of eight lowland Polish lakes. The authors used long-term daily lake surface water temperature and daily air temperatures as input variables. It was found that the hybrid WT-MLPNN model performed slightly better than the traditional MLPNN model for forecasting lake surface water temperature. The use of hybrid models has some advantages in forecasting water temperature, as documented by both Zhu et al. (2020) and Graf et al. (2019). Graf et al. (2019) forecasted river water temperature of the Warta River in Poland using the wavelet-neural network hybrid modelling approach. The authors proposed a hybrid model that combines discrete wavelet transforms and artificial neural networks (ANN) for forecasting water temperature. They used daily air temperatures from seven meteorological stations to predict daily water temperature. The authors reported that the WT-ANN models performed well in modelling and forecasting water temperature of the river. In addition, it was also documented that the superior performance of the WT-ANN models is principally observed for extreme weather conditions, such as heat waves and drought. Similarly, the ANFIS models developed in this study outperformed during such conditions, with the highest temperature and evaporation recorded.

Samadianfard et al. (2016) predicted hourly water temperatures at a buoy station in Yuan-Yang Lake, Taiwan, at different depths. They used different soft computing techniques, including the ANN, ANFIS, and gene expression programming (GEP). The authors noted that the GEP provided rationally realistic trends for predicting an hourly water temperature at different depths. However, the correlation coefficient of GEP (0.73) was relatively lower for all depths to accurately predict the water temperature. The developed ANFIS model has a much higher correlation according to the findings of Samandianfard et al. (2016). In addition, the researchers noted that the ANFIS model considerably underestimated high values (> 13°C). Conversely, the ANFIS model developed in the present study predicted sea surface temperature with high accuracy. The difference in the estimation performance of ANFIS models between the two studies could be related to input variables and water characteristics. The sea surface is more saline than lake waters. Lower salinity can lead to higher fluctuations in the surface temperature. Therefore, the comparison of all techniques should be conducted by using a more comprehensive dataset.

A relatively higher correlation (0.96) was found between the observed and predicted SST values. The forecasting capability of the ANFIS model is closely equal to the findings reported by Soyupak et al. (2003) and Zhao et al. (2007). Soyupak et al. (2003) documented that the coefficient of determination was 0.95, whereas Zhao et al. (2007) noted that it was 0.94 between the observed and predicted dissolved oxygen (DO) values. Moreover, the correlation in this study was relatively higher compared to Sönmez et al. (2018), Singh et al. (2009) and Akpomie et al. (2016). Sönmez et al. (2018) developed an ANFIS model to predict Cd ion concentration in the Filyos River. The authors investigated the hybrid learning algorithm and used the Gaussian membership function to design a Takagi–Sugeno type fuzzy inference system. They documented that the correlation was 0.91 between the observed and predicted Cd ion concentrations. Singh et al. (2009) indicated that the coefficient of correlation was 0.85 for the observed and predicted DO values, while Akpomie et al. (2016) reported a similar finding, i.e. 0.86 for Cd ion concentration. On the other hand, Daneshmand et al. (2015) used the ANFIS to model the minimum temperature based on spectral analysis of climate indices. The authors used a hybrid training algorithm to train the system, and they found a high correlation coefficient of 0.987 between the predicted and observed values. Mahongo and Deo (2013) used the ANN to estimate seasonal and monthly SST anomalies in the western Indian Ocean and informed that the neural network model had provided the best overall performance. The authors noted that RMSE between predictions and observations was about 0.06°C and 0.13°C for seasonal and monthly SST anomalies, whereas the mean coefficient of correlation was about 0.98 and 0.88, respectively. The difference between those studies and this study may be related to dissimilarities in the data period. In the present study, mean annual SST data (obtained from the monthly average) were analyzed, while Mahongo and Deo (2013) analyzed both monthly and seasonal SST data and Daneshmand et al. (2015) experimented with the daily minimum temperature to estimate the monthly minimum temperature. In addition, correlations show similarities for both studies in terms of the monthly SST time series. Sönmez et al. (2013a) implemented a fuzzy logic assessment method to evaluate the quality of water in the Karasu Stream and the authors endorsed the fuzzy logic assessment method as a tool for water quality assessment. Sönmez et al. (2018) reported that the ANFIS presented high reliability and robustness. Similarly, the present study revealed that the ANFIS achieved high accuracy in predicting the SST values in the Çanakkale Strait by using a limited set of climatic data.

The analyses provided evidence that SST responds to changes (both increase and decrease) in air temperature. They support the argument that SST will be susceptible and strongly affected by climate change. Similarly, Kale (2017a) reported that the increase in temperature trends causes climatic changes. The author stated that the city of Çanakkale would be affected by global warming and climate change, and also would have a warmer climate in the future. Similarly, Kale (2017b) also reported that the annual evaporation would increase in the future, similarly to temperature. Therefore, accurate estimation of SST is important for aquatic ecosystems.

Piotrowski et al. (2015) compared different ANN types (multi-layer perceptron ANN, product-unit ANN, adaptive-network-based fuzzy inference systems, and wavelet ANN) for the prediction of water temperature in rivers. The authors reported that the multi-layer perceptron ANN performed better than the product-unit ANN. The performance of adaptive-network-based fuzzy inference systems and the wavelet ANN was found to be poor. Similarly, Ay and Kisi (2014) indicated the advantage of the multi-layer perceptron ANN over the ANFIS in modelling the chemical oxygen demand in rivers. On the other hand, Kisi et al. (2012) noted that the ANFIS outperformed the multi-layer perceptron ANN in modelling the suspended sediment, whereas Wang et al. (2009) documented that the ANFIS performed better than the multi-layer perceptron ANN in estimating monthly rive discharges. In addition, He et al. (2014) reported that the performance of the ANFIS and the multi-layer perceptron ANN was similar and the superiority of one model over another could depend on the number of input variables. The present paper revealed that the developed ANFIS model is highly efficient in predicting SST.

One of the limitations of the present study could be the limited input dataset. Shaltout (2019) indicated that SST of the Red Sea was correlated with the mean sea level pressure, air temperature at 2 m above sea level, cross-coast wind stress and sensible heat flux. Similarly, the air temperature at 2 m above sea level was used as an input variable to train the neuro-fuzzy model in the present study. In addition, evaporation and rainfall are key parameters in the hydrological cycle. Therefore, this limitation could be overcome by using these parameters in the training phase of the ANFIS model. On the other hand, there is no information about the most effective parameters on the SST in the Çanakkale Strait. Consequently, more research should be carried out to understand the most effective parameters on the SST in the Çanakkale Strait in the forthcoming periods. Nevertheless, as documented by Nayak et al. (2004), one of the advantages of the ANFIS is that it does not require an a priori model structure, unlike most of the time series modelling methods. Thus, the developed ANFIS model stands out among other SST prediction techniques.

One of the problems sometimes encountered when training a fuzzy system is the over-fitting of data where the model cannot be generalized and instead begins to learn certain patterns. This may be due to the use of a large number of hidden nodes or training examples. In this study, several experiments have been conducted on the ANFIS architecture and the rate of training and test data to ensure that this is not the case. The epoch number was set as 1000 to resolve this issue. The ANFIS implements a multiple iterative learning procedure and rapidly converges due to the hybrid learning algorithm used. The high level of accuracy that occurs during the testing stage can show that there is no excessive fit.

Finally, the size of training data is one of the most critical factors increasing the accuracy of the developed model to predict SST. The ANFIS uses the excellent learning algorithms of the ANN and the excellent estimate functions of the FIS. It can provide computations without mathematical modelling and offer an agreeable solution to the non-linear prediction problem. The ANFIS has an adaptable background and uses training data to produce a fuzzy inference system. Therefore, the ANFIS was preferred in this study. The results of the study showed that the developed ANFIS model is capable of predicting SST values.

In the present study, an adaptive neuro-fuzzy inference system has been developed and suggested for predicting sea surface temperature in the Çanakkale Strait. A relatively higher correlation (0.96) was achieved between the observed and predicted SST values. The analyses provided evidence that SST responds to changes in air temperature. Thus, the SST will be susceptible and extremely affected by climatic changes. Therefore, an accurate estimation of SST is crucial for aquatic ecosystems. It can be concluded that the developed ANFIS model is able to predict SST values in the Çanakkale Strait by using a limited set of climatic data. The proposed model can be effectively used to predict sea surface temperature.