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Modelling soil erosion from a watershed using cubic splines

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Abstract

Erosion in a watershed exhibits spatial and temporal variability, and its determination is fundamental to determining sediment yield which is a key to proper watershed management. In this study, we propose a relationship between the curve number (SCS 1956) and Sediment Yield Index (SYI) using cubic splines. The method is illustrated with a case study of one watershed of Narmada Basin located in Mandla district of Madhya Pradesh, India. Cubic splines are found to perform satisfactorily with Nash efficiency of 63.64%, absolute prediction error of 2.64%, integral square error of 1.22%, coefficient of correlation of 93.78% and degree of agreement of 0.99%. The relation between observed and computed SYI values is correlated with a coefficient of determination (R 2) of 0.87. Such a relationship can be used to determine SYI from the available CN value, which may be quite useful in field applications.

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References

  • AISLUS (1977) Priority Delineation, Matatilla RVP, U.P Report No.Agri.484

  • AISLUS (1991) Methodology of priority delineation survey, all India Soil & Land Use Survey Technical Bulletin 9. Department of Agriculture and Cooperation, New Delhi

    Google Scholar 

  • Arnold JG, Williams JR, Nicks AD, Sammons NB (1990) SWRRB: A basin scale simulation model for soil and water resources management. Texas A&M University Press, College Station. 142 pp, 10 appendices

  • Barth J, Kraft A, Kraft J (1976) Estimation of the liquidity trap using spline functions. Rev Econ Statist 58:218–222

    Article  Google Scholar 

  • Boomer KB, Weller DE, Jordan TE (2008) Empirical model based on the universal soil loss equation fail to predict sediment discharge from Chesapeake Bay catchment. Journal of Environment Quality 37:79–89

    Article  Google Scholar 

  • Choudhry RS, Sharma PD (1998) Erosion hazard assessment and treatment prioritization of Giri river catchment, north western Himalayas. Indian Journal of Soil Conservation 26(1):6–11

    Google Scholar 

  • De Boor C (1978) A Practical guide to splines. Springer-Verlag, New York

    Book  Google Scholar 

  • Delmas M, Olivier C, Mouchel JM, Manuel G (2009) A method for developing a large-scale sediment yield index for European river basins. Journal of Soils Sediments 9:613–626

    Article  Google Scholar 

  • Eubank RL (1984) Approximate regression models and splines. Communications in Statistics - Theory and Methods 13:433–484

    Article  Google Scholar 

  • Fan F, Deng Y, Hu X, Weng Q (2013) Estimating composite curve number using an improved SCS-CN method with remotely sensed variables in Guangzhou, China. Remote Sens 5:1425–1438

    Article  Google Scholar 

  • Fuller WA (1969) Grafted polynomials as approximating functions. Australian J of Ag Econ 13:35–46

    Google Scholar 

  • Gajbhiye S (2015) Estimation of Surface Runoff Using Remote Sensing and Geographical Information System. Int. J. U-and E-Service, Sci. and Tech. 8(4):118–122

    Article  Google Scholar 

  • Garde RJ, Kothari UC (1987) Sediment yield estimation. Journal of Irrigation Power (India) 44(3):97–123

    Google Scholar 

  • Gbur EE, Thomas GL, Miller FR (1979) The use of segmented regression models in the determination of the base temperature in heat accumulation models. Agronomy J 71:949–953

    Article  Google Scholar 

  • Hawkins RH (1973) Improved prediction of storm runoff from mountain watersheds. Journal of Irrigation and Drainage Division, ASCE 99(4):519–523

    Google Scholar 

  • Hawkins RH (1978) Runoff curve numbers with varying site moisture. Journal of Irrigation and Drainage Division 104(4):389–398

    Google Scholar 

  • Holt JN, Jupp DLB (1978) Free-knot spline inversion of a Fredholm integral equation from astrophysics. J Inst Math Applics 21:429–443

    Article  Google Scholar 

  • Jupp DLB, Vozoff K (1975) Stable iterative methods for the inversion of geophysical data. Geophys J Roy Astronom Soc 42:957–976

    Article  Google Scholar 

  • Kumar A, Sharma HC, Singh R, Prasad S (2011) Modelling of spring discharge in mid hills of North West Himalaya. Indian Journal of soil conservation 39(2):95–99

    Google Scholar 

  • Lal M, Mishra SK (2015) Characterization of Surface Runoff, Soil Erosion, Nutrient Loss and their Relationship for Agricultural Plots in India. Current World Environment 10(2):593–601

    Article  Google Scholar 

  • Lal M, Mishra SK, Pandey A, Pandey RP, Meena PK, Chaudhary A, Jha RK, Shreevastava AK, Kumar Y (2016) Evaluation of the Soil Conservation Service curve number methodology using data from agricultural plots. Hydrogeol J. doi:10.1007/s10040-016-1460-5

    Google Scholar 

  • 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 24:229–234

    Article  Google Scholar 

  • Lin K, Lv F, Chen L, Singh VP, Zhang Q, Chen X (2014) Xinanjiang model combined with Curve Number to simulate the effect of land use change on environmental flow. J. Hydrol. 519:3142–3152

    Article  Google Scholar 

  • Meshram SG, Sharma SK, Tignath S (2015) Application of remote sensing and geographical information system for generation of runoff curve number. Applied Water Science. doi:10.1007/s13201-015-0350-7

    Google Scholar 

  • Mishra SK, Singh VP (1999a) Another look at SCS-CN method. J Hydrol Eng ASCE 4(3):257–264

    Article  Google Scholar 

  • Mishra SK, Singh VP (1999b) Behaviour of SCS-CN method in C-Ia-λ spectrum. International Conference Water, Environment, Ecology, Socio-economics, and Health Engineering, Oct. 18–21, Korea

  • Mishra SK, Singh VP (2003c) Derivation of SCS-CN parameter S from linear Fokker Planck equation. Acta Geophysica Polonica 51(2):180–202

    Google Scholar 

  • Mishra SK, Singh VP (2004a) Long-term hydrologic simulation based on the soil conservation service curve number. Hydrol Process 18(7):1291–1313

    Article  Google Scholar 

  • 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, DC

  • Mondal A, Guha S, Mishra PK, Kundu S (2011) Land use/Land cover changes in Hugli Estuary using Fuzzy C-Mean algorithm. Int. J Geomatics and Geosciences 2(2):613–626

    Google Scholar 

  • Natural Resources Conservation Service (NRCS) (2001) “Section 4: Hydrology.” National Engineering Handbook, Natural Resources Conservation Service, U.S. Department of Agriculture, Washington, DC

  • Nazzareno D, Sergio G (2009) An improved correlation model for sediment delivery ratio assessment. Environment Earth Science 59(1):223–231

    Article  Google Scholar 

  • NRSA (1995) Integrated Mission for Sustainable Development Technical Guidelines, National Remote Sensing Agency. Dept. of Space, Hyderabad

    Google Scholar 

  • Pandey A, Dabral PP (2004) Estimation of runoff for hilly catchment using satellite data and GIS. Journal of Indian Society of Remote Sensing 32(2):235–240

    Article  Google Scholar 

  • Pandey A, Sahu AK (2002) Generation of curve number using remote sensing and geographic information system. Map Asia 2002

  • Pandey A, Sahu AK (2004) Estimation of runoff using IRS-1 B LISS-II data. Indian Journal of Soil Conservation 32(1):58–60

    Google Scholar 

  • Pandey A, Mishra SK, Gautam AK, Kumar D (2015) Soil erosion assessment of a Himalayan river basin using TRMM data. Proceedings of the 11th Kovacs Colloquium, Paris, France, IAHS Publ. 366

  • Patel DP, Srivastava PK, Gajjar CA (2012) Prioritization of Malesari mini-watersheds through morphometric analysis: a remote sensing and GIS perspective. Environmental Earth Science 69(8):2643–2656

    Article  Google Scholar 

  • Poirier DJ (1975) On the use of-cobb-Douglas splines. Internat Econom Rev 16:733–744

    Article  Google Scholar 

  • Ponce VM, Hawkins RH (1996) Runoff curve number: has it reached maturity? J Hydrol Eng ASCE 1(1):11–18

    Article  Google Scholar 

  • Pyasi S, Singh JK (2004) Sediment prediction by modelling runoff sediment process. Indian Journal of Soil conservation 32(2):100–107

    Google Scholar 

  • Rallison RE (1980) Origin and evolution of the SCS runoff equation. Procedings of ASCE Irrigation and Drainage Division Symposium on Watershed Management, ASCE, New York, N.Y., 2, 912–924

  • Ramakrishnan D, Bandopadhay A, Kusuma KN (2009) SCS-CN and GIS-based approach for identifying potential runoff harvesting sites in the Kali watershed, Mahi River basin, India. Journal of Earth System Science 118(4):355–368

    Article  Google Scholar 

  • Renard KG, Foster GR, Weesies GA, McCool DK, Yoder DC (1997) Predicting soil erosion by water: a guide to conservation planning with the revised universal soil loss equation (RUSLE). U.S. Department of Agriculture-Agriculture Handbook No. 703

  • Rodrigues JO, Andrade EM, Queiroz Palácio HA, Ribeiro Mendonça LA, dos Santos JCN (2013) Sediment loss in semiarid small watershed due to the land use. Revista Ciência Agronômica 44(3):488–498

    Article  Google Scholar 

  • Sarma S, Saikia T (2012) Prioritization of subwatersheds in Khanapara-Bornihat area of Assam Meghalaya (India) based on land use and slope analaysis using remote sensing and GIS. Journal of Indian Society Remote Sensing 40(3):435–446

    Article  Google Scholar 

  • SCS (1956, 1964, 1969, 1971, 1972, 1985, 1993) Hydrology, National Engineering Handbook, Supplement A, Section 4, Chapter 10, Soil Conservation Service, USDA, Washington, DC

  • Sebestain M, Jayaraman V, Chandrashekher MG (1995) Space technology application for development of watershed. Technical report. ISRO-HQ-TR-104-95. ISRO, Banglore, pp 1–41

    Google Scholar 

  • 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. International Journal of Environmental Research and Development 4(2):153–164 ISSN 2249-313

    Google Scholar 

  • Singh VP, Yadava RN (2003) Watershed Management. Allied publisher private limited. ISBN 81–7764–545-5

  • Singh PK, Mishra SK, Berndtsson R, Jain MK, Pandey RP (2015) Development of a modified SMA based MSCS-CN model for runoff estimation. Water Resour Manag 29(11):4111–4127

    Article  Google Scholar 

  • Suresh M, Sudhakar S, Tiwari KN, Chowdary VM (2004) Prioritization of watersheds using morphometric parameters and assessment of surface water potential using remote sensing. Journal of Indian Society Remote Sensing 32(3):249–259

    Article  Google Scholar 

  • Wahba G, Wendelberger J (1980) Some new mathematical methods for variational objective analysis using splines and cross validation. Mon Weather Rev 108(1122–1):143

    Google Scholar 

  • Williams JD, LaSeur WV (1976) Water yield model using SCS curve numbers. J Hydraul Div 102(9):1241–1253

    Google Scholar 

  • Wold S (1971) Analysis of kinetic data by means of spline functions. Chem Scripta 97-102

  • Woodward D, Plummer A (2001) Antecedent moisture conditions: NRCS view point. Watershed Management and Operations Management 2000:1–5

    Google Scholar 

Download references

Acknowledgements

The authors are thankful to two 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).

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Authors and Affiliations

  1. Department of Water Resources Development & Management, Indian Institute of Technology, Roorkee, Uttrakhand, India

    Sarita Gajbhiye Meshram

  2. Department of Mathematics and Computer Science, R. D. University, Jabalpur, Madhya Pradesh, India

    Sarita Gajbhiye Meshram & P. L. Powar

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

    Vijay P. Singh

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

    Vijay P. Singh

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  1. Sarita Gajbhiye Meshram
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Correspondence to Sarita Gajbhiye Meshram.

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Meshram, S.G., Powar, P.L. & Singh, V.P. Modelling soil erosion from a watershed using cubic splines. Arab J Geosci 10, 155 (2017). https://doi.org/10.1007/s12517-017-2908-1

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