## 1 Introduction  
The rainfall-runoff (R-R) modelling process is conducted by hydrologists for forecasting hydrological information (discharge data) which may be helpful in water resources engineering [1, 2], flood mitigation planning [3], production of hydroelectric power [4],reservoir operation planning [5]. Additionally, river discharge forecasting information supports the design of dams or water-related infrastructure [3] and the prediction of disasters related to water [6]. Therefore, it is necessary to develop new models along with improving the existing ones to understand the regional and local changes in streamflow for ungauged basins [7] and support the aforementioned issues [8; 9]. The R-R process is very complicated due to the complex interaction of several environmental spatio-temporal factors and their effects [10; 11; 12]. In the R-R process, precipitation is distributed over a catchment and transformed into channel flow or streamflow of river comprises many interacting processes upon the Earth's surface. These interactions occur in several spatial and temporal scales. This is happening because of diverse characteristics and non-uniformity in the medium of water flow. The hydrological cycle interacts with other disciplines such as ecology, atmospheric science, geology, and mainly with agronomy and land-use management shows diversity of these medium. Therefore, most of the catchment system is highly dynamic and non-linear in nature. It is difficult to provide an effective system which simulates these complex natures. It is also difficult to collect more predictor variables with large samples from a catchment system. The main challenges in R-R modeling comes from the integration of complexities within a catchment system and the difficulty of precise and quantitative representation of available information. In general, the hydrological models can be defined by two groups: (i) physically based and conceptual models, (ii) empirical or data-driven models. The former models require a large number of input parameters, a great amount of hydro-meteorological dataset and precise simulation of nature's law for hydrological modeling such as R-R modeling. These requirements for the first group of models often limit their usability to model hydrological processes [13]. The data-driven models forecast time series data of hydrological ones using only lag information of time series observations of predictors. These models are broadly used in R-R modeling and do not require large dataset with more predictors and physical laws of nature [14; 15]. In recent studies, it was observed that the classical models like auto-regressive integrated moving average (ARIMA) may not be able to simulate the R-R process effectively due to its complex and non-linear nature. A typical data-driven model called single hidden layer feed-forward neural networks (SLFNs) has been broadly used in hydrological time series modeling [16; 17; 18]. However, the gradient-based learning parameter calibration in SLFNs may suffer from a local convergence problem, long training time and overfitting problem. The use of metaheuristic-based optimization approaches may provide a more generalized network [19; 20]. In recent machine learning model development, for significant enhancement of SLFNs, a novel approach called extreme learning machine (ELM) was proposed [21]. With faster learning capability, ELM provides good generalization ability in SLFNs compared to gradient-based SLFNs. This promotes the applicability of ELM in hydro-environmental modeling like streamflow forecasting [22; 23], temperature prediction [24], drought index forecasting [25], water quality parameter modeling [26], etc. However, the daily R-R modeling depends on generated rainfall and runoff data which are highly non-linear in nature and time-dependent. In forecasting runoff value, ELM may fall into the local optimum for the stochastic/random selection of input weights and hidden biases [27].