A comparison of the SCS-CN-based models for hydrological simulation of the Aghanashini River, Karnataka, India

Water is essential for human survival, and rivers have been crucial in shaping human civilization throughout history (Sofi et al. 2021). They serve as a vital source of freshwater, providing a crucial resource for various purposes such as water supply, irrigation, and the generation of hydropower (Rautela et al. 2022a, 2022b). The climatic and streamflow extremes caused by human and natural factors profoundly impact spring and rain-fed river basins, leading to the drying up of streams and springs and a significant alteration of land use (Sharma et al. 2019; Galavi & Mirzaei 2020; Singh et al. 2023). These alterations will have a profound impact on the surface and sub-surface water flow dynamics of the basins, significantly affecting their hydrological response (Galavi et al. 2019; Sofi et al. 2021). The consequences of these changes are significant and highlight the need for an increased understanding and management of our freshwater resources. Hydrologic simulation of surface runoff is a computational approach to predicting the movement of water in catchments, from precipitation to surface water bodies, including rivers. It is particularly useful in ungauged catchments where limited data are available, as it allows for the estimation of flow based on the complex physical and meteorological processes that govern water movement (Kumar & Bhattacharjya 2021).

The simulation process involves mathematical modelling of the physical processes involved in water movement, including precipitation, evaporation, infiltration, and storage (Amini-Zad et al. 2018; Rautela et al. 2023). These models are based on hydrology, meteorology, and soil science principles and incorporate data on precipitation, temperature, and land use (Kumar & Bhattacharjya 2021). The simulation results provide valuable information on the hydrologic response of a catchment to changes in land use and management practices. With the rapid increase in population, there is a growing need for water conservation and identifying new water resources. Accurate estimates of water flow in a region are crucial for making informed decisions about water management and flood control (Kumar & Bhattacharjya 2021). The results of the hydrologic simulation of surface runoff can be used to estimate the impacts of land use changes on water resources, to identify the best strategies for conserving water, and to reduce the risk of flash flooding, which can cause severe damage to properties near riverbanks.

Empirical models are mathematical formulas that use a limited number of easily measurable variables, such as precipitation and temperature, to estimate runoff. These models are simple and quick to implement and can provide useful estimates for areas where data are limited (Rawat et al. 2021). However, empirical models have limitations as they often cannot account for complex processes in a watershed, such as the effect of soil type and land use on runoff (Sen & Altunkaynak 2006). Hydrological models, conversely, are more complex and detailed models that simulate the complete water cycle within a watershed, including precipitation, infiltration, evapotranspiration, and runoff. These models can provide more accurate runoff estimates as they consider a wider range of variables and processes (Bunganaen et al. 2021). Examples of hydrological models used for runoff estimation include the Hydrological Modelling System (HEC-HMS) and the Soil and Water Assessment Tool (SWAT) (Murmu & Murmu 2021). However, these models require more data and computational resources and may require more time and expertise. The choice between the two methods depends on the desired accuracy, data availability, and computational resources (Young et al. 2009).

In the Soil Conservation Service Curve Number (SCS-CN) method, the curve number is the only parameter that is used for the computation of runoff, which depends on the Land Use Land Cover (LULC), hydrological soil group, and Antecedent Moisture Condition (AMC) (SCS 1956). The RS and GIS techniques are used for LULC and soil classification of the catchment area. The soils are classified into four Groups A, B, C, and D, depending on their runoff generation potential of soils. The curve number is assigned to the hydrologic units formed on intersecting LULC and soil map, which compute the runoff. The curve number depends on the soil's AMC condition, which depends on the previous 5-day precipitation. Very few studies (Mishra et.al. 2004; Verma et al. 2020; Rawat et al. 2021) are available in the literature that presents the comparative application of several SCS-CN-based models for runoff estimation. The present study performs the hydrologic simulation using six mathematical models based on the SCS-CN method. The SCS-CN with slope correction, λ optimization are simple models, while Mishra and Singh (MS) (Mishra & Singh 2004), Michel-Vazken-Perrin (MVP) (Michel et al. 2005), and Activation Soil Moisture Accounting SCS-CN (ASMA-SCS-CN) (Verma et al. 2020) consider the long-term effect are used for simulation. The model parameters are optimized for the catchment area, and simulation is performed for the period of 18 years (2001–2018) at a daily time scale. The performance of the models is compared with the help of goodness-of-fit statistics. The selected model can be utilized to predict runoff in physioclimatically similar ungauged catchments. This will provide crucial baseline information to local authorities for developing effective water conservation strategies and flood management plans.

The daily district-level precipitation data of Uttara Kannada district and daily streamflow data at Santeguli Station are obtained from the India-WRIS web portal from 1 January 2001 to 31 December 2018. The 30 m resolution Digital Elevation Model (DEM) is obtained from the CARTOSAT-1 satellite of the Indian Space Research Organization (ISRO). For the LULC classification, the Web Map Service layer from ISRO with a resolution of 50 K prepared during 2015–16 is used. The soil map used in this study is obtained from the National Bureau of Soil Survey and Land Use Planning (NBSS and LUP), Nagpur, in cooperation with the Department of Agriculture, Karnataka, on a scale of 1:500000.

The Web-based Hydrograph Assessment Tool (WHAT) is used to carry out the baseflow separation from observed streamflow to compute the surface runoff (Lim et al. 2005). In the WHAT programme, the recursive digital filter algorithm is used considering the values of the filter parameter and maximum baseflow index as 0.98 and 0.80, respectively.

The soil map is geo-referenced and digitized using the QGIS tool. The hydrological soil classification is done depending on the texture of the soil and the soil is divided into Groups B, C, and D, hydrological soil groups (Figure 2(b)). Group B soil covers 27.22 km², Group C soil covers 681.53 km², and Group D soil covers 289.26 km² of the catchment area. The largest area is covered by Group C hydrological soil type with moderately high runoff-producing potential.

The slope of the land is also a significant factor affecting the runoff. The catchment is divided into six zones from slope 0 to 144% based on the slope class having an equal slope interval (Figure 2(c)). From the slope map, it is observed that about 705.10 km² area has a slope ranging between 0 and 24%. The steep slopes of the order of 120–144% occupy a very small area (i.e. 0.3 km²).

The six mathematical models based on the SCS-CN method are used for hydrologic simulation. The SCS-CN is a simple method that uses LULC, soil type, and AMC conditions to compute the curve number (Chow et al. 2010). In the SCS-CN with slope correction, a slope factor is applied on the curve number, which takes the effect of the slope of the catchment into account (Shi & Wang 2020). It is observed from the studies that the value of the coefficient for the initial abstraction of 0.3 is substantial (Woodward et al. 2003). In the SCS-CN with λ (initial abstraction coefficient) optimization method, the value of the initial abstraction coefficient is optimized for the catchment. The MS model modifies the existing SCS-CN model by including the cumulative static infiltration component in the formulation and simulates runoff for the long-term (Mishra & Singh 2004). The soil moisture accounting procedure is incorporated into the MVP method by using the initial soil moisture (Michel et al. 2005). In the ASMA-SCS-CN method, the concept of activation soil moisture is used by combining the soil moisture accounting with static infiltration for long-term runoff simulation (Verma et al. 2020).

In the above mathematical models (Table 1), Q is the daily surface runoff, P is the daily precipitation, I_a is the initial abstraction, S is the amount of potential maximum retention in soil, λ is initial abstraction coefficient, F_c is cumulative static infiltration, S_a is the threshold soil moisture, V_o is the initial soil moisture, and V_et is the revised threshold soil moisture.

Table 1

Mathematical models used in the study with method of formulation

S. No. .	Method name .	Case .	Method formulation .
1.	SCS-CN
2.	SCS-CN with slope correction
3.	SCS-CN with λ optimization
4.	Mishra and Singh
5.	MVP
6.	Activation Soil Moisture ASMA-SCS-CN		Q = 0

S. No. .	Method name .	Case .	Method formulation .
1.	SCS-CN
2.	SCS-CN with slope correction
3.	SCS-CN with λ optimization
4.	Mishra and Singh
5.	MVP
6.	Activation Soil Moisture ASMA-SCS-CN		Q = 0

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In the mathematical models, the parameters need to be optimized for the given catchment area and give the maximum efficiency in terms of goodness-of-fit statistics. The SOLVER tool is used for optimization, which uses the Generalized Reduced Gradient (GRG) non-linear method of optimization (Hirpurkar & Ghare 2015). The initial values and optimized values of all parameters are shown in Table 2.

Flood frequency analysis is a statistical method used to estimate the probability of flood events of various magnitudes occurring at a particular location. The annual maximum discharge series was derived from the daily observed discharge to conduct flood frequency analysis using the Gumbel's method (Subramanya 2017). The distribution fitting tool in the ‘Statistics and Machine Learning Toolbox’ of MATLAB has been adopted for assessing the goodness-of-fit of different probability distributions for the annual maximum discharge series. After fitting the distribution, the goodness-of-fit is evaluated using a quantile–quantile plot. Sensitivity analysis is performed to assess the impact of different distribution functions and parameter estimation methods on the results. Based on the criteria suggested by Kale & Hire (2004), the flood events can be classified based on the return period (T) as: small floods (T ≤ 2.33 years), moderate floods (2.33 < T < 6.33 years), and large floods (T ≥ 6.33 years).

The simulation of the surface runoff is performed for six different mathematical models in Microsoft Excel. In the present study, the calibration is performed for the years 2001–2009, while the validation is carried out for the years 2010–2018.

The SCS-CN with slope correction method considers the catchment's mild slope and shows slightly good results compared to the SCS-CN method. The simulated curve lies below the observed curve showing a difference of −15.86 m³/s in the average value and a deviation of −415.76 m³/s in the maximum value (Figure 4(b)). A slight rise in the simulated values is observed compared to the SCS-CN method due to the consideration of the effect of the mild slope. The scatter plot shows a trend similar to the SCS-CN method, which shows an R² of 0.61 (Figure 5(b)).

A good fit between observed and simulated values is noticed for the SCS-CN with λ the optimization method as compared to previous methods (Figure 4(c)). The optimized value of 0.017 of the initial abstraction ratio increases the simulated runoff and decreases the deviation as compared to previous methods. In calibration, a difference of −6.23 m³/s is observed in the average value and a deviation of −445.78 m³/s is observed for the maximum value of the runoff. While in validation, a difference of −3.97 m³/s (−240.25 m³/s) is observed for the average (peak) runoff value (Figure 4(c)). From Figure 4(c), the runoff values show good agreement for the calibration period, while some deviations are noticed for the validation period due to the lower peak flows. The scatter plot shows the R² of 0.72 and 0.61 for the calibration and validation period, respectively (Figure 5(c) and 5(d)).

In the Mishra and Singh method, the observed and simulated values exhibit better conformity compared to previous methods (Figure 4(d)). In calibration, the simulated average and peak values exhibited deviations of −6.95 and −369.51 m³/s, respectively, with respect to the corresponding observed values. A similar result was derived for the validation phase also. This method yielded an improvement in RMSE, NSE, PBIAS, and MAE compared to the SCS-CN and SCS-CN with slope correction; however, it could not outperform the SCS-CN with λ-optimization method. The scatter plot shows the R² of 0.69 and 0.58 for the calibration and validation periods, respectively (Figures 5(e) and (f)).

The MVP method shows better statistical performance in terms of NSE, RMSE, PBIAS, MAE, and RSR than all previous methods. The MVP method significantly improves the PBIAS than the previous methods, indicating superior model performance (Table 3). The best fit is observed in the MVP method compared to other methods between observed and simulated values (Figure 4(e)). The MVP method improves the accuracy in estimating average runoff as the deviations from the observed values during the calibration (−0.7 m³/s) and validation (1.67 m³/s) periods were minimal. On the other hand, the estimation of peak runoff exhibited marginally higher deviations as compared to the other methods. The scatter plot shows better agreement of observed and simulated runoff with higher R² of 0.73 and 0.63 for the calibration and validation periods, respectively (Figures 5(g) and (h)).

In the ASMA-SCS-CN method, the result shows slightly higher deviations from peak values than the MVP method. (Figure 4(f)). During calibration, the mean simulated value exceeded the mean observed value by −1.37 m³/s, and a deviation of −487.72 m³/s was observed between the maximum values of runoff. In the validation period, a difference of 0.93 m³/s was observed between average values, and a deviation of −331.05 m³/s was observed between the maximum values of runoff. The scatter plot shows similar results to the MVP method, as R² of 0.73 and 0.62 for the calibration and validation period, respectively (Figures 5(i) and (j)). In general, all the methods used in the study produced satisfactory to good R², NSE, RMSE, nRMSE, PBIAS, SE, and RSR values, which means that the simulated discharge was able to closely follow the observed discharge. In certain cases, the models are not able to accurately capture the peak discharge because of the significant contribution of baseflow to the river discharge.

The performance of these models is evaluated through goodness-of-fit statistics such as NSE, RMSE, nRMSE, PBIAS, MAE, SE, and RSR, as shown in Table 3. As per Moriasi et al. (2007), all six models perform satisfactorily as their NSE values lie between 0.5 and 0.65. The MVP method shows superior performance compared to other methods with the least RMSE and nRMSE values. According to criteria suggested by Moriasi et al. (2007) and Durbude et al. (2011), the MVP and ASMA-SCS-CN models give better performance with a PBIAS value of less than 10%, while the MS method and SCS-CN with λ optimization reflected fair performance having a PBIAS less than 25%. All the other methods show unsatisfactory performance having PBIAS greater than 25%. Table 3 shows the lowest values of MAE and SE for the MVP method. All the models' performances are satisfactory, with an RSR value between 0.6 and 0.7 (Moriasi et al. 2007; Durbude et al. 2011).

The distribution fitting tool in MATLAB 2018a was adopted for modelling the annual maximum discharge series. In this study, the Gumbel's Extreme Value, Generalized Extreme Value (GEV), Log Normal 2 Parameter (LN2P) and Weibull distribution are used to fit the annual maximum series. The results indicated that GEV and LN2P are the best-performing distributions for the annual maximum series; however, we adopted LN2P for the flood frequency analysis due to parsimony considerations. The location (μ) and scale (σ) parameters for the LN2P distribution are 6.1 and 0.89, respectively. From the analysis, the computed magnitude of mean annual flood was 613.8 m³/s corresponding to a return period (T) of 2.78 years. Table 4 shows that three large flood events have been observed in the Aghanashini catchment in the years 2005, 2013, and 2014. The results of this study provide valuable information for designing flood protection measures. This information can be used to set design standards for flood walls or determine the height of riverbanks, depending on the specific location and the level of protection required.

The study assesses the magnitude and the temporal variations in the stream discharge using six mathematical models based on the SCS-CN method for the Aghanashini River catchment for the period of 18 years. The baseflow contribution in the Aghanashini River is considerable due to the predominance of dense forests, pasture land, and the presence of soils with moderately low runoff potential, thus allowing considerable infiltration. The simulation results reflect that the MVP model, exhibiting the highest predictive efficiency and lowest errors, is superior for long-term hydrologic simulations in the Aghanashini River catchment compared to other models. The flood frequency analysis reflects the frequent occurrence of moderate and high floods in the catchment, which stresses the importance of serving flood mitigation and protection measures. The Aghanashini River catchment, unaffected by human interventions, presents a valuable opportunity for developing small- and medium-scale water resources. This study is helpful for the concerned policymakers and stakeholders to adopt a suitable method to simulate the runoff for water resources and flood management in the catchment.

The authors express their heartfelt gratitude and appreciation to the Director of Punjab Engineering College (Deemed to be University) and the PG coordinator of the Water Resources Engineering Department for providing the necessary facilities to conduct the present study. Without their support, this research would not have been possible. Additionally, the authors would like to express their sincere appreciation to the Indian Institute of Technology, Indore for their valuable support and assistance throughout the course of the study. Their contributions have been indispensable in the success of this research. The authors also extend their thanks to the Central Water Commission (CWC) India for providing the discharge data through the India-WRIS portal. The authors are truly grateful for the support and encouragement received from all these institutions.

Harmandeep Singh and Kuldeep Singh Rautela developed and designed the manuscript and wrote it under the supervision of Mohammad Afaq Alam and Priyank J. Sharma. All authors read and approved the final manuscript.

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

The authors declare there is no conflict.