Rainfall–runoff modeling using an Adaptive Neuro-Fuzzy Inference System considering soil moisture for the Damanganga basin

The prediction of availability of water plays an effective role in the planning and management of water resource projects (Vakili & Mousavi 2022). The calculation of runoff resulting from rainfall on river catchments is the first step in the estimation of water availability (Vakili & Mousavi 2022). In order to manage water resources, river flow forecasting helps to control reservoir outflows during low river flows and warns of impending stages during floods (Anusree & Varghese 2016). Hydrologic systems have seen several changes as a result of rapid urbanization, industrialization, deforestation, transformation of the land's cover, and irrigation. In addition to the climate change, soil heterogeneity directly affects different river flows all over the world (Devia et al. 2015). Rainfall–runoff transformation is impacted by soil moisture (Casper et al. 2007). As it regulates the amount of rainfall entering the ground, runoff or evaporation from the soil, it is considered the main factor in the hydrologic system (Brocca et al. 2009). The hydric condition of the soil is greatly influenced by hydrological models. Therefore, the efficiency of the rainfall–runoff process should increase with more precise depiction of the variable in the basin.

Various techniques have been developed by hydrologists to see the effects of rainfall on runoff where numerous models have attempted to demonstrate the physical processes that occur within it (Tayfur & Singh 2011). The rainfall–runoff models are distinguished as empirical or data-driven models, conceptual models, and physically-based models (Meshram et al. 2022). Data-driven models use nonlinear relationships between inputs and outputs. They are observation-oriented and depend heavily on input accuracy (Masih et al. 2010). Conceptual models interpret runoff processes by connecting simplified components in the overall hydrological process. They are based on reservoir storages and simplified equations of the physical hydrological process, which provide a conceptual idea of the behaviors in a catchment (Devia et al. 2015). Physical models, also called process-based or mechanistic models, are based on the understanding of the physics related to the hydrological processes (Jehanzaib et al. 2022). Physically-based equations govern the model to represent multiple parts of real hydrologic responses in the catchment.

An Adaptive Neuro-Fuzzy Inference System (ANFIS) model was applied for event-based rainfall–runoff modeling and its performance was compared with that of a well-established physical-based model (Talei et al. 2010). The results indicated that ANFIS yielded comparable results to the physical model and provided superior peak flow estimation. Similarly, Dorum et al. (2010) investigated rainfall–runoff data utilizing artificial neural network (ANN) and ANFIS models, juxtaposed against a multi-regression (MR) model. Their findings suggested that both ANN and ANFIS models were effective in discerning the rainfall–runoff relationship, offering viable alternatives to traditional MR methods (Panigrahi & Mujumdar 2000).

The ANFIS is developed to simulate daily discharge for the Damanganga basin. ANFIS is a data-driven model that has no parametric transfer function for the correlation of input and output variables. The model used rainfall and soil moisture at three distinct depths (5 cm, 100 cm and bedrock) as the input parameters for the simulation of the daily discharge and to see the accuracy of the model at a certain depth. The length of the data is 39 years (1983–2022).

The objective of the present study is to develop a rainfall–runoff model considering soil moisture at three different depths (5 cm, 100 cm and bedrock) in the Damanganga basin.

Fuzzy logic, despite its uncertainty in hydrological processes, has emerged as a valuable tool for modeling rainfall–runoff phenomena. Rather than exact numerical values, it approaches variables parametrically with a focus on uncertainty. In a neuro-fuzzy system, neural networks utilize training data to establish membership functions and fuzzy rules for the fuzzy system. (Heydari et al. 2018). Numerous neuro-fuzzy systems support the utilization of gradient descent learning, particularly when employing differentiable membership functions (Morales et al. 2021). These systems are built upon the fuzzy architecture pioneered by Takagi, Sugeno, and Kang (Takagi & Sugeno 1985). ANFIS, one of the earliest and widely recognized neuro-fuzzy systems, was initially endorsed by Jang in 1991 and has since found extensive application in rainfall–runoff modeling (Anusree & Varghese 2016).

The ANFIS model, proposed by Takagi & Sugeno (1985), combines the strengths of ANNs and fuzzy logic systems. By leveraging learning capabilities of ANNs, ANFIS can derive fuzzy IF-THEN rules with appropriate membership functions, allowing it to effectively model nonlinear functions and identify nonlinear components online in a control system (Tayfur & Brocca 2015). This unique integration enables ANFIS to learn from imprecise input data and provide inference capabilities, making it adept at predicting chaotic time series. Additionally, ANFIS benefits from a more stable training process by effectively utilizing the self-learning and memory abilities inherent in neural networks (Gohil et al. 2024). This combination of features contributes to ANFIS's remarkable results in various applications requiring nonlinear modeling and prediction tasks.

In the present study, ANFIS is used to simulate the daily discharge considering the soil moisture by using the Fuzzy Logic Toolbox in the MATLAB software. Fuzzy logic was developed as a valuable method to model the rainfall–runoff phenomenon. However, it is not quite certain how hydrological processes work (Erdik 2009; Vakili & Mousavi 2022). An ANFIS is similar to ANNs which mainly depends on the Takagi-Sugeno method which was developed in first initial year of the 1990s (Sajindra et al. 2023). By combining ANN and fuzzy logic models, it is possible to capture the benefits of both the techniques in a single model. The neural network uses training data to determine the membership functions and fuzzy rules of a fuzzy logic system in the frame of a neuro-fuzzy system (Kapadia et al. 2023). It has the ability to learn and approximate nonlinear functions, and resembles a set of IF-THEN fuzzy rule (Mehta et al. 2023). The ANFIS network's initial layer explains how it differs from a standard neural network. In order to operate, neural networks often preprocess the data, converting the characteristics into normalized values between 0 and 1. A sigmoid function is not required by an ANFIS neural network, but it performs the preprocessing phase by turning numerical inputs into fuzzy values (Tahmasebi 2012). For the analysis, 70% of the data are used for training purpose and 30% are used for testing purposes (Brocca et al. 2011, 2012).

Tables 1 and 2 show the basic statistics of the rainfall, soil moisture at 5 cm, soil moisture at 100 cm, soil moisture at bedrock and discharge data of the Pingalwada, Ozerkheda and Nanipalsan Stations.

The ANFIS model is developed for the simulation of daily discharge on the basis of rainfall and observed soil moisture for the time period of 1983–2022 for the Damanganga basin. The model employed two variables and investigated three cases. Rainfall data are used for all cases with soil moisture data at 5 cm (case 1), 100 cm (case 2) and bedrock (case 3). Soil moisture data at 5 cm, 100 cm and bedrock with rainfall can form four input variables and nine fuzzy membership functions are selected for each subset. The model uses nine fuzzy membership functions for each variable. The membership functions are very very low (VVL), very low (VL), low (L), medium low (ML), medium (M), medium high (MH), high (H), very high (VH), very very high (VVH). Soil moisture at 5 cm had a range of 0–9% vol/vol, soil moisture at 100 cm had a range of 0–41% vol/vol, soil moisture at bedrock had a range of 0–0.88% vol/vol, rainfall had a range of 0–227.45 mm/day and discharge had a range of 0–762.218 m³s⁻¹ and nine subsets are formed using the commonly employed triangular membership functions. FIS properties, membership functions and rules were manually adjusted by using the ANFIS GUI editor tool.

In this study, the ANFIS model is developed to simulate daily discharge as a function of soil moisture (5 cm, 100 cm and bedrock) and rainfall for the Damanganga basin. Nine fuzzy membership functions for each variable of soil moisture, rainfall and discharge are constructed. The analysis for the model is carried out for the time period of 1983–2022. As per the regression analysis, the soil moisture at bedrock gives more precise values of coefficient of determination R² and NSE as compared to the values obtained from soil moisture at 5 and 100 cm. The better results obtained for the soil moisture (surface to bedrock) agree well with the anticipated hydrological behavior, which depends more on measurements made in the sub-surface soil than in the surface soil for determining runoff, as the soil found in the bedrock is saturated. The drawback of the models is the handling of the imprecise data and the firing strength of the rules is weak. The future research for this study includes the simulation of daily discharge by MISDc (Modello Idrologico Semi-Distribuito in continuo), ANNs and Genetic Algorithm (GA) models. This study can be helpful for future research scholars and to hydrological scientists in selecting appropriate rainfall–runoff models.

All authors have read, understood, and have complied as applicable with the statement on ‘Ethical responsibilities of Authors’ as found in the Instructions for Authors.

This research received no external funding.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.