Integrating IHACRES with a data-driven model to investigate the possibility of improving monthly flow estimates

Accurately measured data and reliable estimates of basin yield are one of the most critical tools in water resources management. However, many basins in Iran lack suitable long-term data on runoff due to various limitations (Salehpoor Laghani et al. 2018). Rainfall-runoff models have always attracted the interest of hydrologists because they are a tool that can be used to simulate basin behavior in response to precipitation to obtain reliable estimates of basin output. In recent decades, various models with different perspectives in simulating the rainfall-runoff process have been developed.

IHACRES (identification of unit hydrograph and component flows from rainfall, evapotranspiration, and streamflow) is one of the rainfall-runoff conceptual models developed to minimize the need for input data. It comprises two in series modules: the non-linear loss module and the linear unit hydrograph module. The model inputs (precipitation and temperature) are first converted into effective precipitation by the nonlinear module, and then the linear module produces the runoff flowing out of the basin. Many studies have been carried out worldwide using this model and have reported its acceptable performance. Goodarzi et al. (2013) studied the performance of the soil and water assessment tool (SWAT), simple hydrology (SYMHID) and IHACRES models in simulating a basin in Western Iran. They reported that although SWAT performed better than IHACRES according to the statistical criteria, IHACRES was a suitable model for the studied basin because it required a smaller amount of input data while exhibiting acceptable accuracy. Khairfam et al. (2013) conducted a research on seven basins in Northeastern Iran and stated that the model underestimated the peak discharges. In a study on a basin in northern Iran, Dodangeh et al. (2017) noticed that IHACRES had weaknesses in simulating the peak discharges but it performed well in general. Vaze et al. (2016) used four hydrological models including IHACRES to study the impact of climate change on the hydrology of 61 catchments in Southeast Australia. They concluded that the results of the IHACRES model were more acceptable than those of the other three. The results presented by Sadeghi et al. (2016) and Lotfirad et al. (2019a, 2019b) suggested that IHACRES exhibited acceptable efficiency in estimating the runoff in the Navarood Basin in Northern Iran and the Hablehroud Basin in Central Iran. Niromandfard et al. (2018) used the IHACRES model to investigate the effect of climate change on the characteristics of flow in a basin in Northeastern Iran. They reported that the Nash-Sutcliffe coefficient (NS) of the model is 0.5 in the calibration phase and 0.49 in the validation phase. Ahmadi et al. (2019) compared IHACRES, SWAT, and artificial neural networks (ANNs) and reported that IHACRES has acceptable performance in modeling daily, monthly, and annual flows; however, their results showed that ANNs outperform IHACRES and SWAT. Choubin et al. (2019) calibrated and validated the IHACRES model in four gauged basins in Iran and reported that the NS of the models range between 0.57 to 0.71 in the calibration phase and 0.53 to 0.62 in the validation phase, suggesting that the performance of the model is good or satisfactory. However, based on the NS values in four pseudo ungauged basins (−0.54 to 0.39), they concluded that the IHACRES is not an appropriate choice for flow regionalization. Esmaeili-Gisavandani et al. (2021) calibrated four hydrological models including IHACRES in a basin in Central Iran and concluded that the IHACRES model has acceptable performance in the calibration phase. However, they reported that in the validation phase the SWAT model outperformed the other three models.

The above-mentioned studies suggest that the IHACRES model could be considered as an appropriate choice for modeling the process of rainfall-runoff, and the model can generate acceptable estimates of basins yield in different time steps with minimum input data. Accordingly, IHACRES was used to estimate the outflow of the basins located in our study area, i.e. the Talesh-Anzali Basin, Northern Iran. However, due to the factors such as the climate of the basins under study, the basins' physical characteristics and, most importantly, the quality of the data, the model's performance was worse than expected. So, the possibility of improving the IHACRES model's performance by integrating it with a data-based model and developing a hybrid conceptual data-based model was examined in the present study. Hybrid models attracted less interest in previous research, but the few studies that were conducted using them suggested that hybrid models could perform better than each one. The research by Ashrafzadeh & Rizi (2009) (a hybrid model of time series and artificial neural networks for streamflow simulation), the work by Noori & Kalin (2016) (a combined use of SWAT and an artificial neural network for estimating daily flow in a basin in Atlanta), and the study by Fathian et al. (2019) (a combination of time series models and artificial neural networks to estimate monthly discharge in two basins in Canada) are examples of using hybrid models. To the best of our knowledge, integrating the IHACRES and data-based models has not been reported in previous studies. The developed hybrid models in the present study could be used in flow regionalization studies to estimate the outflow of the ungauged basins in the study area (the Talesh-Anzali Basin, Northern Iran).

Data-based models, especially models based on artificial intelligence, attracted great interest in the past two decades in modeling the rainfall-runoff process (Salehpoor Laghani et al. 2020). These models can find the nonlinear relationships between the recorded data on precipitation and runoff, and their different forms have been studied and evaluated in various research projects. The data-based model used in the present study is group method of data handling (GMDH). This intelligent-based model was introduced by Ivakhnenko (1971) for solving multidimensional interpolation problems. It has the capability of finding complicated relationships between the inputs and outputs of nonlinear systems. Walton et al. (2019) assessed GMDH performance in estimating maximum two-year return period discharges using the measured data in 365 hydrometric stations in Iowa. They recommended GMDH as an acceptable model for basins without statistical data. Dodangeh et al. (2020) used this model to prepare maps of areas prone to floods in a basin in Northeastern Iran and stated that GMDH yielded completely acceptable results with the minimum input data. Li et al. (2020) also reported that the performance of this model in predicting water levels in two rivers in China was ‘acceptable.’ Intelligence-based models are non-parsimonious models and use many parameters for simulating complex processes such as the rainfall-runoff process. However, the level of complexity of a process can justify choosing an intelligence-based model. Among intelligence-based models, GMDH has the advantage that its best structure is selected automatically and less parameters are needed to be optimized. So, in the present study, GMDH was chosen to transfer the output of the IHACRES model to the outflow of the basins under study.

Guilan is one of the northern provinces in Iran with an area of 14,711 km². The Talesh-Anzali Basin, which is the smallest Class II basin in Iran, is located entirely in Guilan Province except for a very small part situated in Ardabil Province. This basin, which lies between the Aras and Sefidroud Basins, is divided into two parts by the Sefidroud Basin. The northern part includes several small coastal rivers originating from the Talesh Mountains. The other part also includes rivers pouring into the Anzali Lagoon. Figure 1 shows the location of the Talesh-Anzali Basin in Iran. In the present study, 19 sub-basins were selected in the Talesh-Anzali Basin (named s1 to s19) for modeling. The altitude of the outlet points in the selected sub-basins (the locations of the gauging stations) varies from −23 to 250 m. The area, the average annual precipitation, the average annual temperature, and the average annual flow of each sub-basin are listed in Table 1.

The data set used in the present study consisted of ground-based precipitation, temperature and flow data, and satellite-based precipitation data. The precipitation and temperature data from 17 weather stations were considered for the present study. Monthly precipitation and temperature data over 15 years (2003–2017) were retrieved from the database of Iran Meteorological Organization (IMO) and Iran Water Resources Management Company (IWRMC) and were considered as input to the IHACRES model. Also, monthly flow data recorded in 19 gauging stations located at the end of the sub-basins under study were extracted from the database of IWRMC and were considered for the calibration and validation of the IHACRES model. The dataset was divided into calibration and validation parts, and IHACRES was calibrated over the period of 2003–2015 and validated over the period of 2015–2017. Satellite-based precipitation data including Tropical Rainfall Measuring Mission (TRMM), Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN), and Climate Hazards group InfraRed Precipitation with Station data (CHIRPS) datasets were also considered for the present study. Precipitation data from the three satellite-based datasets were averaged and considered as the substitute for the ground-based precipitation data and were used to calibrate the IHACRES model.

In the present study, the IHACRES output (the estimated monthly flow for each sub-basin), as well as the observed flows in two previous months, was considered as the input for the GMDH model, and the observed flow for each sub-basin was estimated. The calibration and validation periods for the GMDH model were similar to those used for the IHACRES model, and the model performance was evaluated for both periods. The flowchart describing the steps of developing the hybrid models of IHACRES and GMDH is presented in Figure 2.

This section presents separately the calibration and validation results for the IHACRES and GMDH models. Since the GMDH model received the flows estimated by the IHACRES model as its input, its output was considered as the flows estimated by the hybrid model. The performance measures for the calibration and validation phases of the IHACRES model in each sub-basin are listed in Tables 2 and 3. As is shown in these tables, the NS for the IHACRES model ranges from 0.14 to 0.68 in the calibration phase and from 0.09 to 0.73 in the validation phase. NS values of 0.45 to 0.85 (Vaze et al. 2016), 0.57 to 0.71 (Choubin et al. 2019), and 0.61 (Ahmadi et al. 2019) have been reported in previous studies in the calibration phase. So, the performance of the IHACRES model in the present study was worse than expected. This might be because of the quality of the input data (rainfall and temperature) and, more importantly, the poor quality of the flow data recorded at gauging stations in the sub-basins under study. It is also worth noting that the length of the data series used for model calibration was not identical for all 19 sub-basins under study, and it was observed that the model shows better performance in the sub-basins with longer calibration data series. The NS is usually considered a basis for performance evaluation of rainfall-runoff models. If the value of this coefficient is <0.30, 0.30–0.50, 0.50–0.75, or >0.75, the performance of the model is considered, respectively, ‘unacceptable,’ ‘acceptable,’ ‘good,’ and ‘very good.’ Based on this, and considering Table 2, the performance of the model for the calibration phase in eight out of 19 sub-basins was ‘unacceptable,’ and the model's performance in six sub-basins was ‘good.’ Table 3, which presents the validation results, indicates that the values of the NS in 10 sub-basins were less than 0.30 and hence the model performance in these sub-basins was ‘unacceptable.’ It is noteworthy that the values of NS for the validation period increased in some sub-basins (for example, from 0.28 to 0.40 in the s1 sub-basin and from 0.58 to 0.83 in the s2 sub-basin) so that the model performance for the validation period in these two sub-basins was ‘acceptable’ and ‘very good’, respectively.

As stated before, the focus of the present study was to investigate the possibility of improving the performance of the IHACRES model. To achieve this, we first assessed the replacement of the ground-based rainfall data in the sub-basins under study (the input to the model) by satellite-based precipitation data. The results of using the satellite-based data for precipitation in calibrating the IHACRES model are presented in Tables 4 and 5. As shown in these tables, the values of the NS for the sub-basins under study decreased by 10–75% compared to modeling in which the ground-based precipitation data were used. In all, the use of remote sensing data decreased the accuracy of modeling. Consequently, the models calibrated using the ground-based data were used in the next stage.

After calibrating and validating the IHACRES models, hybrid models were developed to improve the performance of IHACRES. The hybrid models were developed by integrating the IHACRES and GMDH models. The outputs of the IHACRES model in the studied sub-basins, as well as the observed monthly flow in two previous months, were considered as the inputs for the GMDH model. So, the hybrid models, which consist of the IHACRES and GMDH models, receive rainfall and temperature as input and generate estimates of the outflow of the sub-basins under study. Tables 6 and 7 list the results of evaluating the performance of the hybrid model in the calibration and validation phases for each sub-basin. To better compare the results, the increases in the values of the NS in the hybrid model compared to the IHACRES model for the studied sub-basins are also presented in Tables 6 and 7.

As shown in Tables 6 and 7, the combination of the IHACRES and GMDH models considerably increased the values of the NS and improved the results for the calibration and validation phases. In other words, it was shown that the hybrid model outperforms the IHACRES model. Based on the values of the NS in the validation phase, the hybrid model had ‘acceptable’ performance in six of the sub-basins in which the IHACRES model had ‘unacceptable’ performance. Moreover, the performance of the hybrid model was ‘very good’ in two sub-basin. In all, the hybrid model improved the results in 10 out of the 19 sub-basins under study. Although the performance of the hybrid model was still ‘unacceptable’ in four sub-basins in the validation phase, the increase in the values of the NS compared to the IHACRES model suggests that integrating the IHACRES and GMDH models could improve the results.

The results of the present study showed that an integration of a conceptual hydrological model (IHACRES) and a data-based model (GMDH) could improve the performance of the hydrological model. The output of the hydrological model was used as the input of GMDH, and in other words, the data-based model was used as an optimization tool for improving the estimates generated by the IHACRES model. An advantage of the methodology used in the present study was avoiding examining different combinations of meteorological variables that are normally used as the input of data-based models. Usually, finding the optimum combination of input variables is a challenging task in developing data-based models such as GMDH. However, in the present study, this was avoided by considering the output of IHACRES as the input of GMDH, and hybrid models were developed to estimate the outflow of the basins under study. All the basins under study had identical climates and conditions; however, according to the NS, the qualitative performance of the IHACRES model varied from ‘unacceptable’ to ‘very good.’ Integrating the IHACRES and GMDH models either increased modeling accuracy in all the studied basins or, if it did not improve modeling accuracy, the qualitative performance of the model did not change as shown by the values of the NS.

The authors wish to thank Iran Meteorological Organization and Guilan Regional Water Authority for providing part of the data used in this study. We should also like to thank the reviewers and the editors who have given up valuable time to review the manuscript and offer valuable comments.

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The authors prefer all the potential reviewers from the authors' country are excluded from reviewing the manuscript.

All authors contributed to the study's conception and design. Material preparation and data collection were performed by Parisa Fattahi. Data analysis and interpreting the results were performed by Parisa Fattahi, Afshin Ashrafzadeh, Nader Pirmoradian, and Majid Vazifehdoust. The first draft of the manuscript was written by Parisa Fattahi and Afshin Ashrafzadeh, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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All relevant data are available from an online repository or repositories. https://data.irimo.ir/http://wrs.wrm.ir/amar/login.asp