Optimal data series length for calibration using SIMHYD model: Insights from Bhima basin

Introduction

A rainfall runoff model is a mathematical representation used to simulate the process of rainfall turning into surface runoff. This process is vital in hydrology and is essential for understanding water resource management, flood forecasting and environmental impact assessment as every component is interconnected (Kokkonen et al., 2001; Sitterson et al., 2017) [13,17] . Rainfall runoff models typically depends on various factors such as rainfall intensity, duration, antecedent soil moisture conditions, topography, land use, soil properties and soil type to predict how much rainfall will become surface runoff and how it will flow through the drainage network (Yang et al., 2015) [20] . Rainfall-runoff models are essential tools in hydrology for predicting the transformation of rainfall into runoff within a watershed. They are employed in various applications such as flood forecasting and mitigation, water resources management, infrastructure design, erosion control and environmental impact assessments. These models can be categorized into two main types, namely, empirical models and process-based models. Empirical models are based on observed data and statistical relationships between rainfall and runoff. They are relatively simple and require less computational effort. Examples include the rational method, which estimates peak runoff rates based on rainfall intensity and the SCS (Soil Conservation Service) Curve Number method, which considers soil moisture and land use to estimate runoff (Dawson &Wilby, 2001) [12] . Process-based models simulate the physical processes involved in rainfall-runoff generation, such as infiltration, surface runoff and channel routing. They are more complex and require detailed input data but provide a more comprehensive understanding of the hydrological system. Examples include the Soil and Water Assessment Tool (SWAT) (USDA, 1986; Di Luzio et al. 2002) [10,11] , Hydrologic Engineering Center-Hydrologic Modeling System (HEC-HMS) (Scharffenberg et al. 2000) [8] and the Variable Infiltration Capacity (VIC) model (Lohmann et al. 1998) [9] . Rainfall runoff models can be further classified based on spatial scale (e.g., lumped or distributed) and temporal scale (e.g., event-based or continuous). Lumped models represent the entire watershed as a single unit and are suitable for small watersheds or quick assessments, while distributed models divide the watershed into smaller spatial units and simulate runoff processes at each unit, providing more detailed results but requiring more data and computational resources. Overall, rainfall runoff models are essential tools for hydrologists, engineers and policymakers to understand and manage water resources effectively, especially in regions prone to flooding or water scarcity. They play a crucial role in flood forecasting, water supply management and ecosystem conservation (Liu et al., 2015) [19] . Simple hydrology (SIMHYD) is one of the conceptual lumped daily rainfall-runoff models are widely used for surface runoff predictions in poorly gauged or ungauged catchments. Model was developed in the 1970s (Porter and McMahon 1975) [27] which is simple, easy to calibrate and relatively accurate in runoff predictions with inputs precipitation and potential evapotranspiration (Siriwardena, 2005) [7] . The SIMHYD model, ignores the spatial diversity of watershed attributes, may require less extensive input data compared to other models like SWAT, which can be advantageous in situations where data availability is limited or uncertain on the other hand potentially reducing the time and effort required to obtain satisfactory model performance provided the output data depends on the quality of observed data. Present study focused on the importance of calibration data length required to estimate the performance of model. This can help improve application of conceptual rainfall-runoff model in poorly gauged and ungauged catchments. The impact of length of data series in generation the runoff for which we have selected different lengths of data series depending on the availability of the observed data over the catchment of two basins viz, Bhima upper and Bhima lower basin. Four schemes were selected for the Pulgaon catchment of Bhima upper basin and 4 schemes were selected for the Jeewangi catchment of the Bhima lower basin. Li et al., 2010 studied on different lengths of data series ranging from one to ten years and found that eight years of data are sufficient to obtain steady estimates. Studies were conducted by other researches with five, seven (Buzacott, et al., 2019 Rao, et al., 2024) [23,24] , eight and ten years of data period showed reliable results depending on the selection of parameter range, wet period of data than the dry period (Peel et al. 2000) [25] and humid catchments compared to arid catchment.

Materials and Methods

Model description

The SimHYD (Simulation model for Hydrology and Development) is a lumped rainfall-runoff model is a widely used hydrological model designed for simulating runoff processes in watershed systems and is developed by Donohue et al. (2001). It has been tested and used extensively across Australia (Chiew et al. 2002) [7] . The lumped model considers the catchment as a single unit disregarding the spatial variability in the catchment parameters. Model used in this study has 9 parameters as shown in the Table1 with minimum and maximum parameter range and Fig. 1 showing the Structure of lumped rainfall runoff model SIMHYD. Moisture infiltration is channeled through various pathways including interflow, groundwater recharge and retention within the soil moisture store. Interflow is determined by a linear relationship with soil wetness, representing the ratio of soil moisture level to capacity and reflecting areas of potential saturation excess runoff within the catchment. Groundwater recharge follows a similar linear function with soil wetness. Any remaining moisture is stored in the soil moisture store, with evapotranspiration from this store modeled linearly constrained by the maximum rate of potential evapotranspiration. The soil moisture store's finite capacity leads to overflow into the groundwater store, from which base flow is simulated as a linear recession (Podger, 2004) [22] . This model delineates runoff generation from three main sources: infiltration excess runoff, interflow (including saturation excess runoff) and base flow. Study uses a version of the SIMHYD model with nine parameters whose ranges are taken from Podger (2004) [22] . 2004) [22] [1,2,3,4,14] . Each section has distinct characteristics regarding runoff patterns, contributing factors and water management challenges. Few researches suggests flooding in some watersheds of Bhima lower basin (DDMA, 2019; Swarnakar and Channabasappa, 2022) [6] requires proper planning of watershed management techniques. Two catchments selected for the study are part of Krishna basin viz. Pulgaon of Bhima upper basin and Jeewangi of Bhima lower basin. The catchment area of Pulgaon is 2205 km 2 and Jeewangi is1920 km 2 .

The fundamental equations of the model are

The source of the data used in the study are daily rainfall data at grid interval of 0.25 o X 0.25 o and maximum and minimum temperatures at grid interval of 1 o X 1 o are obtained from Indian meteorological department website for the study period. Stream flow data on daily time steps was downloaded from Indian water resource information system website for the study period which is used for calibration and validation of the model output. This paper aims to assess the effect of data series length on the runoff calibration of catchments. The maximum length of study period for the two catchments is based on the available stream flow data which is used for calibration and validation. Calibration and validation runs for Pulgaon catchment were conducted for three, four, five, six and seven years. Based on model performance of the Pulgaon basin, indicators such as stability of calibrated parameters and consistency between calibration and validation results, four representative data series lengths were chosen for Jeewangi catchment. These selected lengths provided a balance between data availability and reliable model performance and were therefore considered suitable for further analysis. Thus for Jeewangi catchment calibration and validation runs were conducted for three, six, ten and sixteen years data length (Table 2). The total length of selected time series data was divided into three parts: model warm up period, calibration and validation (Swain and Patra, 2017) [18] which are detailed in table 2. This method is more suitable for catchments where hydrological data are limited and fragmentary because it is based on a conceptual lumped rainfall-runoff modelling framework that requires relatively few input variables while maintaining reliable predictive capability. Lumped conceptual models such as SIMHYD utilize basin-averaged rainfall and potential evapotranspiration, thereby reducing dependence on detailed spatial datasets that are often unavailable in poorly gauged or ungauged catchments (Siriwardena, 2005) [7] . Several studies have shown that acceptable model performance and stable parameter estimation can be achieved using relatively short calibration data lengths, typically ranging from five to eight years (Li et al., 2010; Peel et al., 2000) [21,25] .

Parameter optimization

The objective function measures the over goodness-of-fit between the simulated flow and observed flow; thus, it produces the calibration accuracy value of rainfall-runoff models. It also interprets the observed and modelled outputs into a single number (Vaze et al., 2011) [16] For this study, from the available objective functions Nash Sutcliffe Efficiency (NSE), Coefficient of Determination (R 2 ) used during the calibration process. The performance of the model was analyzed during calibration and validation with statistical indices such as Nash Sutcliffe Efficiency (NSE) and Coefficient of Determination (R 2 ). The details of the model performance indices are given below.

Nash Sutcliffe Efficiency (NSE)

Nash Sutcliffe Efficiency (NSE) is a statistical measure used to evaluate the performance of hydrological or environmental models. It is the normalized statistic and ranges from one to infinity. It is used to estimate the magnitude of variance in comparison to observed data variance (Nash and Sutcliffe, 1970) [15] . This parameter depicts better idea of how the observed and simulated values perfectly fit linearly. The NSE ranges from negative infinity to 1, where 1 indicates perfect model performance, 0 indicates the model performance is as good as the mean of the observed data and negative values indicate the model performs worse than simply using the mean of the observed data. The NSE was calculated with following equation. Where = observed discharge at time i, m 3 s -1 = Simulated discharge at time i, m 3 s -1 = Mean observed discharge at time i, m 3 s -1 n = Is the total number of data points

Coefficient of Determination (R 2 )

Is a parameter used to check the goodness of fit between observed and simulated data. The coefficient of determination is commonly called r-squared (or r 2 ) for the statistical value it represents. This measure is represented as a value between 0.0 and 1.0, where a value of 1.0 indicates a perfect correlation. R 2 is calculated using the following formula Where, Mean simulated discharge at time i, m 3 s -1 , observed and simulated discharges respectively are in m 3 s -1 mean observed and mean simulated discharges respectively are in m 3 s -1

The performance of each calibration was evaluated for the different selected period, using Nash-Sutcliffe efficiency and then validated for the varied time series from the available observed data for the selected catchments one from each of the two basins.

Results and Discussion

Application of SIMHYD model for evaluation of minimal data length required for optimal estimation of discharges were taken up with nine schemes. Five on Pulgaon catchments of Bhima upper basin and four for Jeewangi of Bhima lower basin. NSE was chosen as the primary objective function as it is sensitive to high flows (Smith et al., 2019) [26] and then by applying a genetic algorithm in defining the objective function NSE. Parameters are further evaluated within the limits. Calibration runs were conducted using data lengths shown in table2, and was applied for five different calibration schemes to Pulgaon catchments of Bhima upper basin and two distinct catchments, utilizing the available observation data. For the Pulgaon catchment in the Bhima Upper Basin, performed 100 random samples with data series lengths of three, four, five, six and seven years. Similarly, for the Jeewangi catchment in the Bhima Lower Basin, data series lengths of three, six, ten and sixteen years were used. For the three-year data series, data from each year were sampled independently across the entire observation dataset. We did not impose any constraints on the random sampling process, allowing calibration years to be selected freely from any part of the record, whether they were dry, normal, or wet years. This method ensured that the calibration data included a wide range of hydrological conditions, thus providing more variability and independent hydrological characteristics compared to using continuous year periods. This approach is particularly advantageous for catchments with limited data availability. In each case, the data from the first year were used to warm up the hydrological model, which helps to minimize initialization errors and improve the reliability of the calibration. The performance of each calibration was evaluated over the entire period using the Nash-Sutcliffe efficiency metric, a standard measure for assessing the predictive power of hydrological models. 2) of calibration and validation periods with warmup period (Fig. 3). The NSE value is achieved at 0 for the base flow coefficient, 3.588 for impervious threshold, 343.529 for infiltration coefficient, 0.274 for infiltration shape, 0 for interflow coefficient's, 0.956 for previous fraction, 4.980 for rainfall interception store capacity, 0.737 for recharge coefficient and 462.819 for soil moisture store capacity (Fig. 4). Calibration values of the 9 parameters (Fig. 4) scatter plots for daily and monthly stream flows (Fig. 4). The coefficient of determination (R 2 ) shown in Fig. 4, indicate that there is a good agreement between observed and simulated daily flows. 5) of calibration and validation periods with warmup period, calibration values of the 9 parameters (Fig. 6) scatter plots for daily and monthly stream flows provided by the model (Fig. 6&7). The NSE value is achieved at 0.066 for the base flow coefficient, 4.745 for impervious threshold, 186.66 for infiltration coefficient, 0.039 for infiltration shape, 0 for interflow coefficient's, 1 for previous fraction, 4.862 for rainfall interception store capacity, 0.623 for recharge coefficient and 478.474 for soil moisture store capacity (Fig. 5). Finally, the Fig. 7 shows that the coefficient of determination (R 2 ) for daily and monthly stream flow are in good agreement with R 2 0.821 and 0.899 for daily and monthly flows respectively.

Acknowledgement

Acknowledgements Research was supported by the Indian Council of Agricultural Research, Department of Agricultural Research and Education, Government of India. The authors thank ICAR -Central Research Institute for Dryland Agriculture for supporting this research work and providing facilities for undertaking the research.

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