Advertisement

Application of cubic spline in soil erosion modeling from Narmada Watersheds, India

  • Sarita Gajbhiye Meshram
  • Pournima Laxman Powar
  • Vijay P. Singh
  • Chandrashekhar Meshram
Original Paper

Abstract

Soil erosion by water is ubiquitous, exhibits spatio-temporal variability, and is fundamental to determining sediment yield which is key to proper watershed management. In this study, we propose a relationship between the curve number and sediment yield index (SYI) using cubic splines. Using field data from four watersheds, the relation between observed and computed SYI is found to have a coefficient of determination (R2) value from 0.63 to 0.88 suggesting that such a relation can be used to determine SYI from the available CN value. It is found that cubic splines perform satisfactorily with Nash-Sutcliff efficiency ranging from 60.18 to 64.01%, absolute prediction error from 1.35 to 5.56%, integral square error from 1.21 to 5.82%, coefficient of correlation from 79.32 to 93.78%, and degree of agreement from 0.87 to 0.99%.

Keywords

Cubic spline interpolation Watershed Runoff curve number (CN) Sediment yield index (SYI) 

Notes

Acknowledgements

The authors are thankful to the anonymous reviewers for their valuable suggestions and critical comments to improve the quality of this paper. The first author is thankful to UGC-New Delhi for providing financial support under the scheme of Dr. D.S. Kothari Postdoctoral Fellowship (DSKPDF).

References

  1. Adinarayana J, Rama Krishna N (1995) An approach to land use planning in a hilly watershed using GIS. Land Degrad Rehabil 6(3):171–178CrossRefGoogle Scholar
  2. Adinarayana J (1996) Prioritization of basins based on silt yield index an integrated approach, erosion and sediment yield: global and regional perspectives (Proceedings of the Exeter Symposium July 1996). IAHS Publ no 236, pp 549–554Google Scholar
  3. Adinarayana J, Gopal Rao K, Rama Krishna N, Venkatachalam P, Suri JK (1998) A site-specific systems-approach model for soil erosion and silt yield studies for hilly watershed management, Modelling Soil Erosion, Sediment Transport and Closely Related Hydrological Processes (Proceedings of a symposium held at Vienna, July 1998J. IAHS Publ. no. 249, pp 143–148Google Scholar
  4. AISLUS (1991) Methodology of Priority Delineation Survey, All India Soil & Land Use Survey Technical Bulletin 9, Department of Agriculture and Cooperation, IndiaGoogle Scholar
  5. Amani M, Safaviyan A (2015) Sub-basins prioritization using morphometric analysis-remote sensing technique and GIS-Golestan-Iran. Int Let Nat Sci 38:56–65Google Scholar
  6. Anthony VJ, Garrett JM (2005) Understanding Interobserver Agreement: The Kappa Statistic. Fam Med 37:360–363Google Scholar
  7. Bali YP, Karale KL (1977) A sediment yield index as a criterion for choosing priority basins. Proceding of Erosion and solid matter transport in inland waters, Paris, pp 180–188Google Scholar
  8. Barth J, Kraft A, Kraft J (1976) Estimation of the liquidity trap using spline functions. Rev Econ Stat 58:218–222CrossRefGoogle Scholar
  9. Bhuyan SJ, Marjen LJ, Koelliker JK, Harrington JA, Barnes PL (2002) Assessment of runoff and sediment yield using remote sensing, GIS and AGNPS. J Soil Water Conserv Soil Water Conserv Soc USA 57(6):351–363Google Scholar
  10. Das RK (2012) Sediment yield estimation for watershed prioritization: a remote sensing study. Indian J Sci Technol 5(3):2374–2378Google Scholar
  11. De Boor C (1978) A Practical guide to splines. Springer-Verlag, New YorkCrossRefGoogle Scholar
  12. Eubank RL (1984) Approximate regression models and splines. Communications in Statistics - Theo and Meth 13:433–484CrossRefGoogle Scholar
  13. Fuller WA (1969) Grafted polynomials as approximating functions. Aust J Agic Econ 13:35–46Google Scholar
  14. Gajbhiye S, Sharma SK (2012) Land use and land cover change detection through remote sensing using multi-temporal satellite data. Int J Geo Geosci 3(1):89–96Google Scholar
  15. Gajbhiye S, Mishra SK, Pandey A (2013) Effect of seasonal/monthly variation on runoff curve number for selected watersheds of Narmada Basin. Int J Env Sci 3(6):2019–2030Google Scholar
  16. Gajbhiye S, Mishra SK, Pandey A (2014a) Prioritizing erosion-prone area through morphometric analysis: an RS and GIS perspective. Appl Water Sci 4(1):51–61CrossRefGoogle Scholar
  17. Gajbhiye S, Mishra SK, Pandey A (2014b) Hypsometric analysis of Shakkar River catchment through geographical information system. J Geol Soc India, (SCI-IF 0.596) 84(2):192–196CrossRefGoogle Scholar
  18. Gajbhiye S, Mishra SK, Pandey A (2014c) Relationship between SCS-CN and sediment yield. Appl Water Sci 4(4):363–370CrossRefGoogle Scholar
  19. Gajbhiye S, Sharma SK, Meshram C (2014d) Prioritization of watershed through sediment yield index using RS and GIS approach. Int J u e-Ser, Sci Tech 7(6):47–60CrossRefGoogle Scholar
  20. Gajbhiye S, Mishra SK, Pandey A (2015) Simplified sediment yield index model incorporating parameter CN. Arab J Geosci 8(4):1993–2004CrossRefGoogle Scholar
  21. GSI (2000) Jabalpur earth quack -22nd May 1997-A Geoscientific Study. GSI special publication No. 51. July 2000Google Scholar
  22. Hawkins RH (1973) Improved prediction of storm runoff from mountain watersheds. J Irrig Drain Div 99(4):519–523Google Scholar
  23. Hawkins RH (1978) Runoff curve numbers with varying site moisture. J Irrig Drain Div 104(4):389–398Google Scholar
  24. Holt JN, Jupp DLB (1978) Free-knot spline inversion of a Fredholm integral equation from astrophysics. J Inst Math Applics 21:429–443CrossRefGoogle Scholar
  25. Javed A, Tanzeel K, Aleem M (2016) Estimation of sediment yield of Govindsagar Catchment, Lalitpur District, (U.P.), India, using remote sensing and GIS techniques. J Geogr Inf Syst 8:595–607Google Scholar
  26. Jupp DLB, Vozoff K (1975) Stable iterative methods for the inversion of geophysical data. Geophys J R Astron Soc 42:957–976CrossRefGoogle Scholar
  27. Kothyari UC, Jain SK (1997) Sediment yield estimation using GIS. Hydrol Sci 42(6):833–843CrossRefGoogle Scholar
  28. Landis J, Koch G (1977) The measurement of observer agreement for categorical data. Biometrics 33:159–174CrossRefGoogle Scholar
  29. Lechner JA, Reeve CP, Spiegelman CH (1982) An implementation of the Scheff; approach to calibration using spline functions, illustrated by a pressure- volume calibration. Technometrics 24:229–234CrossRefGoogle Scholar
  30. Meshram SG, Powar PL (2017) Piecewise regression using cubic spline-a case study. Int J Hyb Infor Tech 10(1):75–84Google Scholar
  31. Meshram SG, Sharma SK, Tignath S (2017a) Application of remote sensing and geographical information system for generation of runoff curve number. Appl Water Sci 7:1773–1779CrossRefGoogle Scholar
  32. Meshram SG, Powar PL, Singh VP (2017b) Modelling soil erosion from a watershed using cubic splines. Arab J Geosci 10:155–168.  https://doi.org/10.1007/s12517-017-2908-1 CrossRefGoogle Scholar
  33. Mishra SK, Singh VP (2003) Derivation of SCS-CN parameter S from linear Fokker Planck equation. Act Geophy Polo 51(2):180–202Google Scholar
  34. Mishra SK, Singh VP (2004) Long-term hydrologic simulation based on the soil conservation service curve number. Hydrol Process 18(7):1291–1313CrossRefGoogle Scholar
  35. Mishra SK, Gajbhiye S, Pandey A (2013) Estimation of design runoff curve numbers for Narmada watersheds (India). J Appl Water Engg Resea 1(1):69–79CrossRefGoogle Scholar
  36. Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms. Exhibit A of Appendix B, Interim Survey Rep. Grand (Neosho) River Watershed, USDA, Washington, D.C.Google Scholar
  37. Natural Resources Conservation Service (NRCS) (2001) “Section 4: Hydrology” National Engineering Handbook, Natural Resources Conservation Service. U.S. Department of Agriculture, Washington, DCGoogle Scholar
  38. Pal DK (1998) Remote Sensing and GIS in study of land use and soil in some watersheds. Unpublished Ph.D. Thesis, Dep. Agri. Food. Engg, IIT, Kharagpur (India)Google Scholar
  39. Pandey A, Chowdary VM, Mal BC (2007) Identification of critical erosion prone areas in the small agricultural watershed using USLE, GIS and Remote Sensing. Water Resour Manag (Springer) 21(4):729–746CrossRefGoogle Scholar
  40. Poirier DJ (1975) On the use of Cobb-Douglas splines. Int Econ Rev 16:733–744CrossRefGoogle Scholar
  41. Pyasi S, Singh JK (2004) Sediment prediction by modelling runoff sediment process. In J Soil Con 32(2):100–107Google Scholar
  42. Rallison RE (1980) Origin and evolution of the SCS runoff equation. Proceedings of ASCE irrigation and drainage division symposium on watershed management, ASCE, New York, NY, 2:912–924Google Scholar
  43. Ratnam N, Srivastava YK, Venkateswara Rao V, Amminedu E, KSR M (2005) Check dam positioning by prioritization of micro-watershed using SYI model and morphometric analysis-Remote sensing and GIS perspective. J Indian Soc Remote Sens 33(1):25–38CrossRefGoogle Scholar
  44. Rice JR (1968) Characterization of Chebyshev approximations by splines. SIAM J Numer Anal 4:557–565CrossRefGoogle Scholar
  45. SCS (1956, 1964, 1969, 1971, 1972, 1985, 1993) Hydrology, National Engineering Handbook, Supplement A, Section 4, Chapter 10, Soil Conservation Service, USDA, Washington, DCGoogle Scholar
  46. Sharma SK, Gajbhiye S, Tignath S (2013a) Application of principal component analysis in grouping geomorphic parameters of Uttela watershed for hydrological modelling. Int J Remote Sen Geosci 2(6):63–70Google Scholar
  47. Sharma SK, Tignath S, Gajbhiye S, Patil R (2013b) Use of geographical information system in hypsometric analysis of Kanhiya Nala watershed. Int J Remote Sen Geosci 2(3):30–35Google Scholar
  48. Sharma SK, Gajbhiye S, Tignath S (2014a) Application of principal component analysis in grouping geomorphic parameters of a watershed for hydrological modelling. Appl Water Sci 5(1):89–96CrossRefGoogle Scholar
  49. Sharma SK, Gajbhiye S, Nema RK, Tignath S (2014b) Assessing vulnerability to soil erosion of a watershed of tons river basin in Madhya Pradesh using remote sensing and GIS. Int J Env Res Dev 4(2):153–164Google Scholar
  50. Shit PK, Nandi AS, Bhunia GS (2015) Soil erosion risk mapping using RUSLE model on Jhargram sub-division at West Bengal in India. Model Earth Syst Environ 1:28CrossRefGoogle Scholar
  51. Singh VP, Yadava RN (2003) Watershed management. Allied publisher private limited. ISBN 81-7764-545-5Google Scholar
  52. Soulis KX, Valiantzas JD (2012) SCS-CN parameter determination using rainfall-runoff data in heterogeneous watersheds—the two-CN system approach. Hydrol Earth Syst Sci 16:1001–1015CrossRefGoogle Scholar
  53. Srivastava RK, Imtiyaz M (2016) Testing of coupled SCS curve number model for estimating runoff and sediment yield for eleven watersheds. J Geol Soc India 88(5):627–636CrossRefGoogle Scholar
  54. Vinod VH, Singh VK, Jeyaseelan AT (2010) Sediment Yield Index and Morphometric Index based Prioritization of Upper Subarnarekha Watershed. Int J Earth Sci Eng 3(4):497–511Google Scholar
  55. Wahba G, Wendelberger J (1980) Some new mathematical methods for variational objective analvsis using splines and cross validation. Mon Weather Rev 108(1122–1):143Google Scholar
  56. Williams JD, LaSeur WV (1976) Water yield model using SCS curve numbers. J Hydraul Div 102(9):1241–1253Google Scholar
  57. Wischmeier WH, Smith DD (1978) Predicting rainfall erosion losses. A guide to conservation planning. U. S. Dep. Agri., USDA handbook, No. 537, Washington D CGoogle Scholar
  58. Wold S (1971) Analysis of kinetic data by means of spline functions. Chem Scripta 1:97–102Google Scholar

Copyright information

© Saudi Society for Geosciences 2018

Authors and Affiliations

  • Sarita Gajbhiye Meshram
    • 1
  • Pournima Laxman Powar
    • 1
  • Vijay P. Singh
    • 2
  • Chandrashekhar Meshram
    • 1
  1. 1.Department of Mathematics and Computer ScienceR.D. UniversityJabalpurIndia
  2. 2.Department of Biological and Agricultural Engineering and Zachry Department of Civil EngineeringTexas A & M UniversityCollege StationUSA

Personalised recommendations