**1. Introduction**

Hydrologists have been attempting to understand the translation of rainfall to runoff for many years to estimate streamflow for objectives including water supply, flood control, irrigation, drainage, water quality, power production, recreation, and fish and wildlife propagation [1]. Rainfall-runoff modeling is one of the most prominent hydrological models used to examine the relationship between rainfall and runoff generated by various watershed physical factors [2]. In the real world, all physical catchment features influence rainfall-runoff; hence, generalizing all physical catchment characteristics is a difficult process. It is difficult to depict such a large range of values in a lumped hydrological model since the parameter values must be averaged for each watershed [3].

In the past, academics and hydrologists have presented different ways for effectively forecasting runoff by building several models of rainfall-runoff (RR) [4]. The process of rainfall-runoff is highly nonlinear and incredibly complex and is still poorly understood [5]. Furthermore, several rainfall-runoff models require a substantial amount of data, which are used for calibration and validation time scale, making them computationally intensive and, thus, unpopular [6]. Machine learning techniques are becoming more prevalent due to their ease of use, simplicity, and efficiency [7]. Machine learning techniques are a good

**Citation:** Mohseni, U.; Muskula, S.B. Rainfall-Runoff Modeling Using Artificial Neural Network—A Case Study of Purna Sub-Catchment of Upper Tapi Basin, India. *Environ. Sci. Proc.* **2023**, *25*, 1. https://doi.org/ 10.3390/ECWS-7-14232

Academic Editor: Athanasios Loukas

Published: 16 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Department of Civil Engineering, IIT Roorkee, Roorkee 247667, India; muskula\_sbr@ce.iitr.ac.in **\***Correspondence:mohseni\_ua@ce.iitr.ac.in

option when there are minimal data and the process is complex [8]. In the context of estimating issues, artificial neural networks (ANNs) are a subclass of machine learning that have received significant attention [9]. ANNs are data-processing systems that mimic the capabilities of the human brain [10]. ANNs were first developed in the 1940s and come in a wide variety [11]. ANN models are also known as black-box models [12]. The application of ANNs in the creation of models results in trustworthy and versatile learning ability, which makes ANNs promising for forecasting [13]. ANN models have been extremely prevalent in the domains of hydrology, water resources, and watershed managemen<sup>t</sup> in recent decades [14]. The ANN contains three layers, an input layer, a hidden layer, and an output layer [15]. The weight of communication is the relationship between the neurons in the consecutive layers [16]. In the given study, the input layer consists of six types of data, namely (rainfall, minimum temperature, maximum temperature, surface pressure, specific humidity, and wind speed). The hidden layer consists of layers with two different sets of number of neurons 10 and 20, respectively. The output layer comprises predicted runoff.

The objectives of the present study are as follows: (i) to develop a rainfall-runoff model for Upper Tapi using an Artificial Neural Networks Technique, (ii) compare ANN rainfall-runoff models developed using NNTOOL with different neural network types, i.e., FFBPNN and CFBPNN, and (iii) to compare ANN rainfall-runoff models trained using LM, BR, and SCG algorithms.

### **2. Materials and Methods**

### *2.1. Study Area and Data Collection*

The current study area comprises a portion of the Upper Tapi Basin known as the Purna sub-catchment (Figure 1). The area lies between Maharashtra and Madhya Pradesh, between latitudes of 20◦09 N to 22◦03 N and longitudes of 75◦56 E to 78◦17 E. It has subtropical to temperate climatic conditions. The mean annual precipitation in the chosen area varies from 833 to 990 mm. Table 1 reveals the sources of data for this study.

**Figure 1.** Index Map of the study area.

