A comparative analysis of innovative MADM technique BHARAT and Hall's statistical approach to design rain gauge network for runoff prediction

An accurate runoff prediction is the most important aspect of water resources management under an extremely changing climate. Data availability and reliable meteorological conditions are important aspects for accurate runoff prediction. The primary requirement for runoff prediction is precipitation (Mehta et al. 2023b). Due to unforeseen reasons, it may not always be possible to get the measured rainfall data from all the rain gauges installed in the basin (Lohani et al. 2014). Reliable rainfall data are important for various applications such as water budget studies, flood prediction and control, reservoir operation and water resources management (Obled et al. 1994; Ajami et al. (2008); Shaghaghian & Abedini 2013; Sit et al. 2020). Thus, an optimal rain gauge network that efficiently helps to predict the runoff is necessary. In the Middle Tapi Basin (MTB) of India, the rain gauges are installed haphazardly and no spatial distribution has been observed. Due to this, the areas represented by rain gauges to be considered for hydrological applications overlap while other parts of basins are found to be ungauged. In these circumstances, an efficient rain gauge network is required. Thus, in the present study, the optimal rain gauge network for the MTB has been designed for reliable application of the measured rainfall for hydrological applications. Various techniques have been used for the rain gauge network design globally based on the catchment characteristics and recommendations by the standard codes or methods Basalirwa et al. (1993); Moore et al. 2000; Tsintikidis et al. 2002; Adhikary et al. 2015). The traditional statistical approach developed by Hall (1972) has been utilized for a selection of key rain gauges based on ranking. Kar et al. (2015) have applied Hall's approach to selecting key rain gauges for the lower Mahanadi Basin, India. Hall's method considers the rainfall measured by each rain gauge to rank the key rain gauges accordingly. Mehta et al. (2023a) used hierarchical clustering and the Thiessen polygons for designing the rain gauge network for the Narmada River Basin and suggested that the Thiessen polygon-based method is proven to be effective for reliable runoff prediction. Other multi-criteria decision-making (MCDM) techniques such as the analytical hierarchy process (AHP) and TOPSIS can also be used for the selection of key rain gauges considering the factors affecting the selection of the rain gauges. Within the literature, numerous multiple attribute decision-making (MADM) methods have gained significant attention for the selection or ranking of attributes (Tella & Balogun 2020; Shadmehri Toosi et al. (2020); Chowdhury et al. (2021); Ouali et al. (2022); Lyu & Yin (2023); Mehri et al. 2024). Shaikh et al. (2024) linked AHP and fuzzy logic for flood hazard mapping in urban areas. Fuzzy logic has been incorporated for various applications such as rainfall–runoff modelling, runoff prediction, flood frequency analysis, groundwater modelling etc (Chau et al. 2005; Jothiprakash & Magar 2009; Kar et al. (2012); Kisi et al. (2013); Kumar et al. (2015); Hussain et al. (2019); Ramkar & Yadav (2021); Asaad et al. (2022)). However, each approach carries its own set of strengths and weaknesses (Rao & Lakshmi 2021). For instance, the TOPSIS method demands extensive computations, becoming more complex as the number of alternatives and attributes increases. The ranking of alternatives in TOPSIS can differ based on the normalization technique employed for the data. Razavi Toosi & Samani (2014) proposed an integrated method consisting of MADM with ANP (analytical network process), fuzzy TOPSIS along fuzzy max–min set techniques for the evaluation of water transfer projects. In the case of the VIKOR method, greater computational complexity exists (Opricovic & Tzeng 2007). Furthermore, varying ranking lists might yield different outcomes even with the same attribute weights, and the ‘majority of attributes’ technique might hold weights ranging from 0 to 1 Rao (2024a). An innovative approach named BHARAT has been explored in the present study which was recently developed by Rao (2024b) and has been designed to solve industrial problems. The novelty of the present work lies in the exploration of the BHARAT algorithm for the hydrologic problem of selection of key rain gauges of the MTB for reliable runoff prediction. The designed rain gauge network has been evaluated based on the runoff response at the outlet, for which the lumped conceptual hydrologic model has been developed. Yadav & Yadav (2024) utilized the BHARAT MADM technique to rank the best available EPS (ensemble prediction system) and showed that BHARAT can be effectively used for decision-making. Various hydrological models are used worldwide for developing the rainfall–runoff relation globally. The open-source hydrological models using HEC-HMS can be an effective model for developing the relation between rainfall and runoff (Bhattacharya et al. 2019; Thameemul Hajaj et al. 2019; Hussain et al. 2021; Patel & Yadav 2022). Kantharia et al. (2024) have used a neuro-fuzzy model for rainfall-runoff simulation and focused on the consideration of soil moisture. Panchal & Yadav (2023b) utilized artificial neural network and multiple linear regression methods for runoff prediction, but these methods utilize longer periods of data length. The lumped conceptual hydrologic model using the MIKE 11 NAM model has been used successfully around the globe (Singh et al. (2014); Loliyana & Patel (2015); Kumar et al. 2020; Mohite et al. 2020; Sneha et al. 2020; Teshome et al. (2020); Parvaze et al. 2021; Panchal & Yadav 2023a). The present study pursues two primary objectives: the development of a rain gauge network and an assessment of the applicability of the MADM technique. BHARAT, a recently innovated technique for industrial problem-solving and decision-making, is utilized to select key rain gauges, ensuring reliability in hydrologic applications. In this investigation, the MADM technique BHARAT and the statistical approach of Hall's method have been employed to optimize the design of a rain gauge network tailored for the MTB. The effectiveness of the networks generated by each approach is evaluated using a hydrologic model, and the resulting runoff is compared against observed data.

In the present study, rain gauges installed in the MTB have been ranked based on their attributes such as measured rainfall, the elevation of the rain gauge station, the correlation between observed rainfall with areal average storm rainfall and the distance of the rain gauge station from the catchment outlet. The recently innovated MADM technique named BHARAT by Rao (2024b) has been explored to rank the rain gauge stations that can be used effectively for runoff prediction. Another statistical approach by Hall (1972) has been used for the ranking and selection of key rain gauges. The rain gauge network designed by each approach has been evaluated based on the runoff response using the MIKE NAM conceptual model. The study utilizes ten years of continuous daily data on rainfall, discharge, and evaporation to design the rain gauge network. The lumped conceptual hydrologic model has been simulated for a period of seven years (year 2007–2013) and validated for three years (years 2014–2016). The detailed methodology flowchart is shown in Figure 3.

In 1972, Hall introduced an effective method to identify the key station network, a vital step in establishing the best rain gauge network. The process involves computing correlation coefficients between average storm rainfall and individual station recordings. These coefficients are then ranked in descending order, with the station showing the highest correlation becoming the first key station. After excluding this station's data, the process repeats to find the second key station, using the next set of correlation coefficients. This iterative method gradually expands the key station network. At each stage, the overall variance is analyzed to assess the network's performance. Incorporating more rain gauges increases the multiple correlation coefficient while decreasing the sum of squared deviations. Eventually, a saturation point is reached where further improvements in either coefficient or deviation sum become negligible. In this study, the number of rain gauges in the representative network is considered optimal for estimating areal rainfall, following Hall's approach (Kar et al. 2015).

A fully lumped model simplifies the representation of a catchment by using a single, spatially averaged value for each input variable and model parameter across the entire area. However, there are a few limitations of the lumped model. While inputs like precipitation may naturally vary across the catchment, the lumped model assumes a uniform value – such as an areal average – at each time-step. Likewise, despite the catchment having varied land-cover types (such as forests, croplands, and urban areas) with distinct hydrological properties like infiltration and runoff, the model consolidates these differences into one average value for each property. In the present study, the hydrologic model has been employed exclusively to validate the designed rain gauge network. In this study, it is used specifically to assess the effectiveness of the designed network. For more accurate and appropriate results, especially given the basin's characteristics, key rain gauges could be modelled using a semi-distributed or distributed hydrologic model. However, the focus is on recommending rain gauge network optimization techniques, and to evaluate the rain gauge network, the use of the lumped conceptual model is deemed appropriate. The MIKE 11-NAM rainfall–runoff model has gained significant usage across various Asian countries due to its advantages, such as low data-requirements, satisfactory performance, and a straightforward structure. Nevertheless, the process of calibrating the model parameters for this hydrological model can prove to be time-consuming and challenging when employing manual calibration methods. The MIKE 11-NAM model operates through a lumped conceptual approach, treating each sub-catchment area as a uniform unit. These elements represent average values for the entire sub-catchment and encompass water storage in four interconnected forms: snow, overland flow, interflow, and baseflow. The model utilizes a linear reservoir framework to depict these storage forms. In evaluating the rain gauge network's efficacy as designed by each method, the MIKE NAM conceptual model has been developed. This model leverages time-series data of rainfall, evaporation, and observed discharge to gauge the rain gauge network's performance. The hydrologic model has been developed for the period from 1 January 2007 to 31 December 2013 having daily rainfall, in which flood was observed on 23 September 2013 at Ukai. Utilizing data from the results of BHARAT and Hall's method, Thiessens have been created, and weighted factors have been derived. These weighted factors have been employed to generate the weighted time-series of rainfall, subsequently used as input for the MIKE NAM model. The calibrated model parameters of MIKE NAM are shown in Table 9. The developed hydrologic model is helpful in evaluating the performance of both the rain gauge networks.

The rainfall measured by the rain gauge stations selected by BHARAT and Hall's method, as listed in Table 6 and Table 8, have been modelled in the MIKE NAM for seven years of continuous daily data from 2007 to 2013. Here, two independent hydrologic models are simulated using rainfall data from rain gauges selected using BHARAT (Table 6) and Hall's approach (Table 8). The developed hydrologic model has been validated for the data for three years, from 2014 to 2016. The runoff generated by the designed rain gauge networks has been compared with the observed runoff data to evaluate the model performance. Figure 8 shows the observed and simulated runoff for BHARAT's and Hall's network. The scatter plot as shown in Figure 9 has been generated to check the correlation between the observed and simulated discharge for the calibration period. The statistical performance measures have been computed to check the accuracy of both the rain gauge networks. It is observed that the models simulated for Hall's network as well as BHARAT's network have performed fairly well and can be said to be reliable.

Table 10 presents the computed performance measures, with comparisons revealing that BHARAT's network outperforms Hall's. Correlation coefficients, Nash–Sutcliffe efficiency (NSE), and index of agreement (d) show higher values for BHARAT's network. BHARAT's method demonstrates reasonably good results for the hydrologic model, validating its efficiency in evaluating the rain gauge network. The validation period's outcomes also demonstrate strong performance, showing good alignment between observed and simulated runoff for both rain gauge networks designed by BHARAT and Hall's method.

Efficient rain gauge network design is the most important aspect for river basins which have randomly installed rain gauges in the basin or when basins are ungauged or partially gauged. Tekleyohannes et al. (2021) have used MCDA (multi-criteria decision analysis) combined with kriging and entropy for designing an optimized rain gauge network for the Tekeze River of Ethiopia and revealed that leveraging a combination of MCDA, kriging, and entropy methods proves beneficial in optimizing both the spatial distribution and the appropriate count of rain gauge stations within a given basin. Kar et al. (2015) utilized the HC clustering method to identify crucial rain gauge stations, forming two clusters, each with seven rain gauges. Notably, the unequal distribution of rain gauges within clusters underscores the flexibility of this approach, acknowledging the influence of basin characteristics and rainfall patterns. It is crucial to recognize that the applicability of clustering methods may not be universal across basins due to inherent variations. The AHP was used for designing the optimal rain gauge network by Kar et al. (2015). However, AHP demands extensive surveys and expert opinions, making it time-consuming. Traditional methods like Hall's approach rank rain gauges based solely on measured rainfall, overlooking other factors that can influence the importance of different gauges. Our proposed MADM approach, named BHARAT, addresses these limitations by considering multiple attributes in the ranking process. However, it is crucial to apply domain knowledge and expertise when selecting and weighing these attributes and alternatives in the BHARAT method. The ranking of attributes should be informed by the expertise of the subject matter to ensure accurate and relevant results. The resulting runoff from BHARAT demonstrates a commendable correlation with observed runoff, showcasing its reliability. The innovative application of BHARAT in this study not only addresses the limitations of traditional methods but also offers a more efficient and adaptable solution for rain gauge network optimization. This advancement is of global significance for hydrologists and researchers, providing a robust methodology that minimizes the drawbacks of traditional approaches. The proposed framework recommends designing a key rain gauge network for the basin to streamline runoff and flood prediction during emergencies. This approach is particularly useful when it is not feasible to collect data from all installed rain gauges, or when time constraints make it impractical to use data from every station. By focusing on these strategically selected key rain gauges, the framework allows for reliable runoff estimates without taking excessive time for modelling that involves all available rain gauge data. This framework will help timely forecasting of floods which eventually help local authorities to take mitigation measures. The study's findings contribute to the global hydrological community by presenting a novel framework that can be tailored to diverse basin characteristics, enhancing the precision of runoff predictions and advancing the field of hydrological modelling on a broader scale.

In the MTB, India, the existing network of 26 rain gauges is distributed randomly, which often leads to overlapping measurements and inefficiencies in streamflow forecasting. Identifying key rain gauges is critical to optimize this network, improve data utility and enhance runoff predictions. The present study applies Hall's method and the BHARAT MADM technique to address this challenge. Hall's method focused solely on rainfall data, identifying key gauges based on statistical importance. However, it lacked the flexibility to consider other hydrological factors influencing runoff, limiting its applicability in comprehensive flood forecasting scenarios. In contrast, the BHARAT MADM technique, originally developed for industrial applications, was applied as a novel approach to hydrological problem-solving. By incorporating multiple parameters such as upstream runoff, rainfall variability, and spatial distribution, BHARAT enabled a more informed selection of rain gauges. Optimization using BHARAT resulted in a streamlined rain gauge network that significantly enhanced the accuracy of hydrologic models. Performance evaluation showed a 29.4% reduction in NRMSE during calibration and a 24.5% reduction during validation, demonstrating the superiority of the BHARAT-based network over Hall's method. These results emphasize BHARAT's ability to provide a more comprehensive framework for rain gauge selection, contributing to more efficient and reliable flood forecasting. The applicability of the BHARAT MADM approach is an important and valuable tool for decision-makers and hydrologists. Prioritizing strategically selected rain gauges avoids overloading hydrologic models with redundant data while maintaining accuracy.

Future work may focus on the real-time operational flood forecasting system with the integration of the BHARAT MADM technique. This can be tested for other hydrologic basins having varying climatic conditions, LULC patterns and changing rainfall patterns to validate the broader applicability of both approaches. The incorporation of real-time remote-sensing and satellite data sets could further enhance the reliability and precision of the designed rain gauge network and hydrologic model. This could ensure that the flood control and streamflow forecasting strategies remain robust and reliable.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

A.P. contributed to data curation, writing – original draft preparation, software, validation, editing. S.M.Y. contributed to visualization, conceptualization, supervision, and review.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.