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Soil erosion modeling of watershed using cubic, quadratic and quintic splines

Author

Listed:
  • Sarita Gajbhiye Meshram

    (Ton Duc Thang University)

  • Vijay P. Singh

    (Texas A & M University
    Texas A & M University)

  • Ozgur Kisi

    (Ilia State University)

  • Chandrashekhar Meshram

    (College of Chhindwara University)

Abstract

Soil erosion is widespread with spatio-temporal variability and is central to the determination of sediment yield, which is vital to proper management of watersheds. We propose a relation between the Curve Number (SCS 1956) and the Sediment Yield Index (SYI) using cubic, quadratic and quintic splines in this research. Using Mohgaon watershed (part of Narmada Basin) data, the relation between observed and computed SYI is found to have a coefficient of determination (R2) value of 0.87, 0.40 and 0.10 corresponding cubic, quadratic and quintic splines suggesting that such a relation can be used to determine SYI from the available CN value. The cubic spline was found to be the best method with respect to Absolute Prediction Error (APE), Integral Square Error (ISE), Coefficient of Efficiency (CE), Coefficient of Correlation (CC) and degree of agreement (d) (i.e., APE = 1.35, ISE = 3.09, CE = 62.08, CC = 79.60 and d = 0.99). The quintic spline (with an average value of APE = 19.59, ISE = 7.84, CE = − 165.73, CC = 19.30 and d = 0.26) and the quadratic spline (with an average value of APE = 20.99, ISE = 8.92, CE = − 199.90, CC = 8.95 and d = 0.15) ranked as the 2nd and the 3rd best methods, respectively.

Suggested Citation

  • Sarita Gajbhiye Meshram & Vijay P. Singh & Ozgur Kisi & Chandrashekhar Meshram, 2021. "Soil erosion modeling of watershed using cubic, quadratic and quintic splines," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(3), pages 2701-2719, September.
    • Handle: RePEc:spr:nathaz:v:108:y:2021:i:3:d:10.1007_s11069-021-04796-5
    DOI: 10.1007/s11069-021-04796-5
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    References listed on IDEAS

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    1. Moghaddam, B.P. & Machado, J.A.T. & Behforooz, H., 2017. "An integro quadratic spline approach for a class of variable-order fractional initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 354-360.
    2. Wen-chuan Wang & Dong-mei Xu & Kwok-wing Chau & Guan-jun Lei, 2014. "Assessment of River Water Quality Based on Theory of Variable Fuzzy Sets and Fuzzy Binary Comparison Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(12), pages 4183-4200, September.
    3. Sarita Gajbhiye Meshram & Vijay P. Singh & Ercan Kahya & Ehsan Alvandi & Chandrashekhar Meshram & Shailesh Kumar Sharma, 2020. "The Feasibility of Multi-Criteria Decision Making Approach for Prioritization of Sensitive Area at Risk of Water Erosion," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(15), pages 4665-4685, December.
    4. Luo, Wei-Hua & Huang, Ting-Zhu & Wu, Guo-Cheng & Gu, Xian-Ming, 2016. "Quadratic spline collocation method for the time fractional subdiffusion equation," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 252-265.
    5. Khalid, Nauman & Abbas, Muhammad & Iqbal, Muhammad Kashif, 2019. "Non-polynomial quintic spline for solving fourth-order fractional boundary value problems involving product terms," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 393-407.
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