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Investigating an empirical approach to predict sediment yield for a design storm: a multi-site multi-variable study

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Abstract

It is of common experience that the sizeable portion of sediment yield generated over a period in a catchment occurs largely due to only a few extreme storm events rather than the numerous small rain events, suggesting the vital role of rain duration besides its magnitude. This paper presents a novel empirical approach based on the Soil Conservation Service Curve Number equation and Universal Soil Loss Equation coupled with a sediment yield model to predict sediment yield resulting from a storm of a certain duration (t) and return period (T). To this end, an empirical relation relating potential erosion (A) with ‘T’ and ‘t’ is proposed and calibrated/validated using historical rainfall-runoff-sediment series data from ten Indian and 12 United States (US) watersheds, respectively. It is calibrated with a low nRMSE, high NSE, and very less PBIAS values in all the sub-watersheds (mean nRMSE ≤ 0.285, NSE ≥ 0.84 and PBIAS <  ± 10%). In validation, the proposed approach shows an excellent performance in 9 of the 10 sub-watersheds of India (0.77 ≤ NSE ≤ 0.98, 0.85 ≤ R2 ≤ 0.99 and PBIAS ≤  ± 20%) a good performance in 8 out of 12 sub-watersheds of the USA (0.50 ≤ NSE ≤ 0.97, R2 > 0.91 and PBIAS ≤  ± 30%). Finally, a correlation between the calibrated empirical parameters of the proposed relation and the catchment characteristics was ascertained, which showed that the size and stream length influence these parameters more in large sub-watersheds, while slope and stream length influence more in small sub-watersheds.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors wish to thank Indian Institute of Technology Roorkee for providing the requisite space and resources during the study.

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Authors and Affiliations

  1. Department of Water Resources Development and Management, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Ishan Sharma, Surendra Kumar Mishra & Ashish Pandey

  2. Western Himalayan Regional Centre, National Institute of Hydrology, Jammu, India

    Ishan Sharma

  3. Department of Water Resources and Irrigation Engineering, College of Engineering and Technology, Dilla University, Dilla, Ethiopia

    Henok Mekonnen Aragaw

  4. Department of Biological and Agricultural Engineering, Zachry Department of Civil Engineering, Texas A&M University, College Station, TX, 77843-2117, USA

    Vijay P. Singh

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Appendix

Appendix

1.1 Description of SWAT model

SWAT is a process-based, semi-distributed, continuous-time scale river basin model for simulating runoff, sediment and nutrient transport form agricultural watersheds (Arnold et al., 2012). It divides the basin into small groups termed as hydrological response units (HRUs) based on similar land use, soil-type and terrain slope which will provide similar hydrological responses in the basin (Neitsch et al., 2011). The model simulates different physical processes (e.g. evapotranspiration, surface runoff, ground water flow and sediment yield, etc.) involved in the hydrological cycle at the HRU level first and thereafter the runoff is routed to the catchment outlet. The SWAT model follows the basic water balance equation to simulate the hydrological processes (Arnold et al., 1998):

$${\text{SW}}_{{\text{t}}} = {\text{ SW}}_{{\text{o}}} + \mathop \sum \limits_{{{\text{i}} = 1}}^{{\text{t}}} \left( {{\text{R}}_{{\text{d}}} - {\text{Q}}_{{{\text{sr}}}} - {\text{E}}_{{\text{a}}} - {\text{W}}_{{{\text{seep}}}} - {\text{Q}}_{{{\text{gw}}}} } \right)$$
(10)

where SWt is the final soil water content in mm, SW0 is the initial soil water content on day i in mm, t is the time in days, Rd is the amount of precipitation on day i (mm), Qsr is the amount of surface runoff on day i (mm), Ea is the amount of evapotranspiration on day i (mm), Wseep is the water percolated into a vadose zone on a day i (mm) and Qgw is the amount of return flow on day i (mm). Details of each process involved in the SWAT model and model equations are provided in a document available online (http://swatmodel.tamu.edu/).

1.2 SWAT model setup, calibration and validation

The SWAT model was established using the ArcSWAT extension (version 2012.10_7.24), a graphical user interface for the SWAT model in the ArcMAP software (version 10.7.1). The following major steps are followed to set-up the model: (1) Watershed delineation, (2) HRU definition and HRU analysis, (3) Weather data input, (4) Run SWAT simulation, (5) Parameter sensitivity analysis, and (6) Calibration and validation.

The DEM raster was used to delineate the study area, stream network and basin outlet points. A threshold value of 10,000 Ha of drainage area was chosen which divided the basin in to 35 sub-basins (See Fig. 3). The LULC, soil and slope map were imported, overlaid and linked to the prepared soil and LULC database in the SWAT for the HRU definition. A threshold value of 10%, 10%, and 10% was considered for land use, soil class and slope, respectively to discretize the 35 sub-catchments into 232 HRU’s representing homogeneous land-use, slope and soil. After that, IMD gridded data for rainfall and minimum–maximum temperature was supplied through input database files. The missing weather parameters such as wind speed, solar radiation, details of dry days, wet days, etc. were supplied to the weather generator in the form of a ‘.xls’ file prepared by the IMD for Indian region, which is available on the SWAT website (https://swat.tamu.edu/data/india-dataset/). The details of all the aforementioned input data have been provided in Table 11. At last, the SCS-CN method (USDA, 1972), Penman–Monteith method (Monteith, 1965), and Kinematic storage routing method was selected for simulating surface runoff, evapotranspiration, and lateral flow, respectively.

Table 11 SWAT input data resolution and source information
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After the model is setup, SWAT is run and the output files are used as an input for SWAT CUP (Calibration and Uncertainty Program) (Abbaspour et al., 2018) for calibration and validation. Before calibration, global sensitivity analysis is performed in SWAT CUP to identify the most sensitive parameters because taking into account only the sensitive parameters for calibration can greatly shorten the model’s runtime in obtaining desirable results (Himanshu et al., 2016). A total of 16 parameters were considered for runoff, and their ranks were determined based of the t-static and p-value as shown in Fig. 8. It can be deduced from Fig. 8 that CH_N2, CH_K2, ALPHA_BNK, CN2 and SOL_AWC were the five most sensitive parameters (p < 0.05).

Fig. 8
figure 8

Sensitivity analysis of SWAT parameters showing most to least sensitive parameter

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NSE was chosen as the objective function for calibration, and 500 simulations were run several times, by adjusting the value of the five sensitive parameters till the optimum value of NSE was achieved. The calibrated values of 16 parameters are presented in Table 12.

Table 12 SWAT parameters calibrated
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The calibration and validation of the SWAT model was done using the Sequential Uncertainty Fitting (SUFI-2) algorithm. Calibration period was from 1997–2009 with 2 years (from 1997 to 1998) used for warming up, and validation was done from 2010 to 2015. The performance of the SWAT model during calibration and validation was evaluated using the various statistical indicators whose values are shown in Table 13. The runoff hydrograph (observed vs simulated) for the calibration and validation period are also presented in Figs. 9 and 10, respectively for further evaluation of the model’s performance.

Table 13 Statistical evaluation of model performance
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Fig. 9
figure 9

Daily observed versus simulated flow during calibration period (1997–2009)

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Fig. 10
figure 10

Daily observed versus simulated flow during validation period (2010–2015)

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From Table 13, it can be observed that the performance of the SWAT model was very good in terms of NSE ( 0.75 during calibration and 0.78 during validation) and PBIAS (− 10.6% and 5.7% during calibration and validation, respectively) (Moriasi et al., 2007a, 2007b). In terms of R2, the performance of the model was good during calibration (R2 > 0.7) and very good during validation (R2 > 0.8) (Moriasi et al., 2012). The performance in terms of KGE was also good (KGE > 0.6) during both calibration and validation with KGE value slightly higher during calibration. Figures 9 and 10 shows a good correlation between the observed and simulated runoff hydrograph, both during calibration and validation. However, the SWAT model was not able to simulate the peak flows accurately which may be due to the limitation of using the SCS-CN method for runoff estimation during extreme rainfall events (Qiu et al., 2012). Overall, the model was well setup and was able to simulate the runoff reasonably good in the Ashti catchment during calibration and validation.

1.3 Conclusion

The SWAT model was applied to generate simulated sediment data for the Ashti catchment of India. For this, the model was calibrated and validated using the observed stream flow from the year 1997 to 2015. The performance of the model was very good in terms of predicting the streamflow, as shown by various statistical indicators. The results showed that the simulated runoff exhibited very good correlation with the observed runoff, both during calibration and validation (R2 = 0.76 and 0.84). The performance was also good in terms of NSE (> 0.75), PBIAS (< ± 10%) and KGE (> 0.65) during the validation period. Thus, it would be fair to assume that the sediment yield simulated using the same SWAT model would be in the acceptable range, if not very accurate. Therefore, the sediment data generated using the above model could be reasonably used to develop any new empirical model having a physical basis.

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Sharma, I., Mishra, S.K., Pandey, A. et al. Investigating an empirical approach to predict sediment yield for a design storm: a multi-site multi-variable study. Environ Dev Sustain (2024). https://doi.org/10.1007/s10668-024-04832-x

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