Evaluation of the success of the hybrid wavelet-based ANFIS approach in the estimation of monthly stream flows of the Bitlis River, Turkey

Streamflow is one of the most critical components of the hydrological cycle. The successful prediction of monthly streamflow is vital for the safe design of water structures and the effective management of water resources. It also dramatically impacts many water-related sectors, such as construction, energy, agriculture, industry, and tourism. Therefore, having comprehensive knowledge about the behavior of water resources is of great significance for the design of water structures, water management, managing meteorological disaster risks such as drought and flood, determining the amount of drinking and utility water for the future, revealing the hydroelectric potential of the region, and increasing the economic and social welfare of the country.

There are generally two possible approaches to streamflow prediction. The first is the rainfall–runoff model, which depends on weather conditions, land use, the structure of the drainage basin, vegetation, ground humidity, infiltration, and evapotranspiration parameters (Kuchment et al. 1996; Mehr et al. 2013). The second is the pattern recognition methodology based on previous streamflows. However, this approach does not require a thorough understanding of the physical laws, and the data requirement is not as comprehensive as the rainfall–runoff model (Nourani et al. 2011).

Wavelet transform (WT) has recently become a popular tool with its ability to explain both spectral and temporal information in the signal. Wavelets are mathematical functions that divide the considered data into different frequency components and work on features with a resolution matched to their scales. Wavelet analysis is a helpful method for analyzing nonstationary variance to varying frequencies in a time series. The discrete wavelet transform (DWT) method divides a time series into various sub-signals and provides useful information. Thus, the artificial intelligence (AI) model's predictive power can be improved (Kim & Valdés 2003; Nourani et al. 2011).

Researchers' interest in hybrid models created by WT and AI techniques has constantly increased. Some of the highlights of these studies; Partal (2007) divided the precipitation data into sub-series by WT and used it as input to the adaptive network-based fuzzy inference system (ANFIS) model to estimate the daily precipitation data. It was determined that the wavelet-ANFIS (W-ANFIS) model used with the WT is much superior to the ANFIS model. Adamowski & Sun (2010) used discrete WT and artificial neural network (ANN) models for streamflow prediction. The performance of wavelet-neural network (WNN) models is compared with ANN models for streamflow predictions in Cyprus 1 and 3 days later. It was demonstrated that the WNN model provides more successful streamflow predictions than the ANN models. Yarar (2014) used ANFIS and W-ANFIS methods to model the monthly flow values of five different flow observation stations in the Sakarya Basin. It was determined that the results of the W-ANFIS model were more successful than the ANFIS model within five stations. Seo et al. (2015) applied ANN and ANFIS models and wavelet-based W-ANN and W-ANFIS models for daily water level estimation. As a result, it was seen that the results of the W-ANN and W-ANFIS models were better than single models. Seo & Kim (2016) used ANN, ANFIS, wavelet packet-based ANN (WP-ANN), and wavelet packet-based ANFIS (WP-ANFIS) methods to predict daily river stages in the Gam Stream Watershed, South Korea. As a result, the WP-ANN and WP-ANFIS models are superior to the ANN and ANFIS models. Taylan (2018) integrated the DWT technique and ANFIS techniques to predict the streamflows in the Dalaman river. The results of the study were compared with AR-ANFIS, an integrated auto-regressive (AR) process. In conclusion, it is noteworthy that the W-ANFIS model is superior to AR-ANFIS. Choubin et al. (2019) found that streamflow estimates generated from pseudo-unmetered basins, the procedure applied, and the semi-distributed precipitation-runoff model is useful techniques for estimating streamflow in unmetered basins. Kisi et al. (2019) applied various machine learning models to predict streamflow in the Mediterranean region of Turkey. According to the analysis results, by including the climate signal information in the streamflow prediction, LSSVM gave superior results than other models. Khazaee Poul et al. (2019) employed ANN and ANFIS and K-nearest neighbors (KNN) and multi-linear regression (MLR) methods and their wavelet-based combination to estimate the monthly streamflows in the St. Clair River. It was proven that the prediction performance of machine learning models increases with WT. Mosavi et al. (2021) propose a regionalization method for flow estimation of the Gharehsoo Hydrometry Station in Ardabil Province in northern Iran. For this purpose, it was applied the fuzzy c-means clustering method. As a result of the study, reasonable flow estimates were obtained. Abda et al. (2021) used W-ANFIS to predict daily flow rates in the Tizi Ouzou region. As a result, it was proposed to establish the W-ANFIS model using the db7 mother wavelet to estimate the daily flow rate. Katipoğlu (2022b) applied the ANN technique to predict the Karasu river's monthly flow in the Euphrates basin. According to the results, it was revealed that potential evapotranspiration values improved the performance of the flow estimation model. Katipoğlu (2022a) estimated monthly streamflow in the Amasya, Turkey, with a hybrid model that combines ANN and DWT. The performance of various mother wavelets was compared, and it identified that the Coiflet 5 mother wavelet gave the best results. The ANFIS model combines the learning capability of the neural network and the decision-making capability of fuzzy logic (FL), thus performing both learning and decision-making using the information extracted from the dataset. In this study, the ANFIS model was preferred because it is a powerful model that combines these two approaches. In addition, Guimarães Santos & Silva (2014); Seo et al. (2015); Kim et al. (2016); Nourani et al. (2019) studies, suggested to use the db10 wavelet in hydrological and meteorological forecasts due to being one of the best wavelets and improving the performance of the machine learning model. When the studies were examined, it was revealed that the studies on the W-ANFIS method with db10 wavelet in flow estimation have limited information. For this reason, the presented research is divided into various subcomponents by db10 WT for assessing the flow data in the Bitlis River. The components with high correlation are collected and presented to the ANFIS model.

This study aimed to increase the success of the ANFIS model by preprocessing the data with DWT in estimating the monthly stream flows of the Bitlis River, Turkey. For this purpose, inputs were decomposed to sub-signals by the db10 wavelet. Obtained sub-signals are presented as input to AI models for flow prediction. The main purpose of flow estimation is to prepare for natural disasters such as floods and droughts in the planning and operation of water resources. Furthermore, the streamflow estimation model was applied in the Bitlis River, which has a semi-arid climate, and the flow values depend on snowmelt. Therefore, evaluating the performance of the W-ANFIS model for regions with similar flow and climate regimes is crucial.

The Tigris Basin is the second-largest basin in Western Asia and borders Turkey, Iraq, Iran, and Syria (Muratoglu & Yuce 2016). Although the Tigris Basin does not have a very mountainous structure, the high mountains in the north significantly affect the basin's climate. The region is hot during the summer months because the mountains prevent the air mass from the north from descending to the south. The high-pressure area, effective in the winter, causes the winter months to be cold in the basin. The summer months are very hot because the basin is under the desert climate in the south, and the influence of the high mountains in the north prevents the air mass from entering the basin. The drainage area of the basin is 51,500 km², and the average temperature is 16–18 °C. In addition, the annual precipitation average reaches 450–700 mm in plains and 800–1,500 mm in mountainous lands (Alashan 2010).

The following steps are followed for the establishment of this model:

• Input and output data are separated as training and test sets.

• Each input data are decomposed into detailed (D) and approximate (A) components via DWT.

• For each input, the effective one of each sub-series is selected with the help of correlation analysis.

• The new input of ANFIS will be the most effective sub-time series component for each input variable, and the original output time series is the output of ANFIS.

• The accuracy of the W-ANFIS model is evaluated with various statistical criteria obtained using the test set (Abdourahmane 2019).

In the study, ANFIS and W-ANFIS methods were used to estimate the monthly streamflow data of the Bitlis River.

The ANFIS model was established by testing various model parameters such as iteration number, sub-sets number, and membership function type. The comparison of the statistical criteria of the based model is indicated in Table 1. When the R² and error values of the training and test data were compared, the model 4 combination was chosen as the most appropriate model. Accordingly, the lowest estimation error was obtained using the streamflow values with a delay of 1–4 months as input to predict the streamflow data. In addition, when the effect of lagged streamflow values on the estimation performance of a single ANFIS model is evaluated, lagged values from 1 to 4 increase the estimation power. However, it was seen that the success of estimating from 5 to 11 decreases in general (Table 1).

The selection of input variables is one of the most critical processes in optimizing ANFIS models. To develop the ANFIS models used in this study, four input combinations consisting of streamflow values with a lag time of up to 11 months were evaluated. These inputs used are divided into sub-signals with db10 DWT. The correlation coefficients between these inputs and outputs are presented in Table 2.

Table 2 shows the correlation coefficients of the approximate and detail components of the lagged streamflow values used in the setup of the W-ANFIS model with the output variable. As a result of the correlation analysis, the sum of the inputs with a correlation greater than 0.1 was used as an input to the W-ANFIS model. In WT, the approximation and detail components represent two different parts of the transformed signal. The approximation component, the low-frequency component, describes the general bias or soft part of the original signal. It shows the important properties of the signal to interpret the basic structure of the signal. The detail component, also known as the high-frequency component, represents the fine-scale or oscillating nature of the original signal. It can reveal signal features that the proximity component cannot detect. It is thought that the variability of the results obtained is due to the differences in the frequencies and delay values of the details and approximate components used.

The comparison of the statistical criteria of the most suitable W-ANFIS models is presented in Table 3. When W-ANFIS models are compared, it is noteworthy that model 6 is the most successful. Accordingly, it is seen that the best estimation model can be established by separating the 400 iterations, the Gbellmf membership function, and the inputs into two sub-series.

When the effect of the lagged streamflow values on the prediction performance of the W-ANFIS model was evaluated, the model's prediction accuracy increased when the lagged values from 1 to 6 were used as inputs. However, when the monthly lag values from 7 to 11 were used, it was seen that the estimation success generally decreased. As a result, the most successful streamflow estimation was obtained with the W-ANFIS model (model 6), which was preprocessed by separating the most successful model inputs into sub-signals (Table 3). When the statistical parameters of the ANFIS and W-ANFIS models were compared, it was determined that the W-ANFIS model was more successful than the ANFIS model, except for models 2, 3, 10, and 11.

In this study, ANFIS and W-ANFIS methods were used to estimate the monthly flows of the Bitlis River. It was revealed that the W-ANFIS model, which was decomposed into subcomponents with db10 wavelet and three decomposition levels, is more successful than the ANFIS model. Terzi & Barak (2015) used ANN and W-ANN methods to predict Söğütlühan flows. It is noteworthy that the W-ANN models obtained by applying the WT are more successful than the ANN models obtained with the original series. Yarar (2014) used ANFIS and W-ANFIS methods to estimate monthly flow values. The data were divided into sub-bands at different frequencies by the WT method, and all bands were collected by evaluating within themselves. The W-ANFIS method made more successful predictions than single ANFIS. Badrzadeh et al. (2018) applied ANFIS and wavelet neuro-fuzzy methods to estimate daily, weekly, and monthly flows at the Australian Railway Parade station. It was determined that the success of the ANFIS model increases when the Haar, Coiflet, and Daubechies main wavelets are used in estimation by separating the inputs into subcomponents. Yabar & Aydin (2020) estimated the daily flow series with W-ANN in the Bitlis River. Although W-ANN and ANN models gave successful results, the ANN model was insufficient to predict extreme peak flow rates. As a result, it was determined that W-ANN models are very successful in estimating flow series in Rivers and can be used in modeling hydrological processes. Dalkiliç & Hashimi (2020) applied the ANN, ANFIS, and WNN to predict the daily streamflow. As a result, it was concluded that the WNN model obtained the most successful predictions. Based on the literature, it was revealed that the use of WT significantly increases the prediction success of the models, even if the time-scale (monthly or daily) or input variables of the data used are different. This indicates that the presented study largely overlaps with the literature. It was deduced that the historical current data, which is decomposed into sub-signals by WT in different regions and time periods, when used with machine learning models, significantly improves the performance of the model. Khazaee Poul et al. (2019) combined WT of multiple linear regression (MLR), KNN, ANN, and ANFIS techniques for the estimation of river flows in the St. Clair River of the US and Canada. As a result of the study, it was revealed that the WT significantly increased the performance of the single models, and the W-ANFIS hybrid model showed successful results for some data scenarios. Khazaee Poul et al. (2019) supports the current study in terms of its satisfactory performance in streamflow prediction. Yilmaz et al. (2022) combined ANN and DWT techniques to predict streamflow data in four stations on the Çoruh Basin. It has been determined that the hybrid model built by ANN and DWT shows more successful results than single ANN with RMSE: 14.29 and R² 0.817 values. When the obtained outputs are compared, it has been revealed that the DWT-ANN hybrid model is slightly successful in the DWT-ANFIS model. In addition, Saraiva et al. (2021); Güneş et al. (2021); Momeneh & Nourani (2022); Wang et al. (2022) studies suggested using the hybrid model by separating the model into sub-signals with the WT to increase the performance of the AI technique. The mentioned studies align with the work done in improving the performance of streamflow estimation models in monthly and daily time periods with WT. Reliable streamflow estimates can help water managers assess the availability of sufficient water to meet the needs of agriculture, industry, and communities during dry periods. In addition, accurate streamflow estimates are essential for evaluating the need for water to sustain aquatic ecosystems and their dependent plants and animals.

This study estimated Bitlis River's monthly average streamflow values by ANFIS and W-ANFIS methods. Models were established using 476 monthly flow rates. While the models were being built, about 75% of the data were used for training and 25% for testing. In addition, for the W-ANFIS model, which requires a preprocessing process, the data are divided into four bands by WT. The prominent results of the study can be listed as follows:

• The ANFIS model obtained using input values with a delay of up to 4 months is superior to the single ANFIS models.

• The most effective model was the W-ANFIS model obtained using input values lagged up to 6 months. It was observed that the success of the model and effectiveness of the W-ANFIS model increased with the number of inputs.

• The W-ANFIS model was established by combining the WT and the ANFIS model, which can be used effectively in improving the prediction performance of the ANFIS models.

• The most appropriate W-ANFIS model, created by collecting the sub-signals related to the output values, increased the R² values while reducing the training and testing errors in the streamflow estimation.

• Trimf and Gbellmf were the most effective membership functions in obtaining the best estimates in the ANFIS and W-ANFIS models, respectively.

• Db10 WT can be used effectively to predict monthly average streamflow.

This study was carried out at the Baykan station 2610, in streams fed by snowmelt and the semi-arid climate zone. The study results contribute to using the W-ANFIS model in regions with similar climate structures. In addition, the study's results can help water resource managers, engineers, and planners make informed decisions about water management and control and can also help mitigate the effects of floods and droughts.

For future studies, it is thought that the prediction success may be increased a little more by using climatic factors such as precipitation, evaporation, and transpiration, which have a high relationship with output values as inputs to the model.

The author thanks the General Directorate for State Hydraulic Works of Turkey for the streamflow data provided; the Editor and the anonymous reviewers for their contributions to the content and development of this paper.

All relevant data are available from an online repository or repositories. The data is available at the link below (https://www.dsi.gov.tr/Sayfa/Detay/744).

The authors declare there is no conflict.