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An Approximately Semi-Analytical Model for Describing Surface Runoff of Rainwater Over Sloped Land

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Abstract

Accurate prediction of surface runoff is critical to watershed management. In this research a semi-analytical model was adopted to solve the kinematic wave equation based on the assumption that the rate of overland-flow depth change is proportional to the rainfall excess. Simulations were compared with the results from laboratory experiments at various rain intensities. Parameters of infiltration rate and Manning’s roughness coefficient were determined. The accuracy of the semi-analytical model was evaluated by numerical simulations. The predicted outflow rates from the numerical simulations agreed well with the observed data. Further, our study indicated that the ratio (c) of the overland-flow depth change to the rainfall excess was a power function of the rain intensity. The depth and velocity of water flow at any time and distance could be calculated with the semi-analytical model. Hydraulic parameters including Reynolds number, Froude number, hydraulic shear stress, stream power and Darcy-Weisbach friction factor characterizing the dynamic features of overland flow of rainwater were calculated based on calculated overland-flow depth and velocity. The proposed analytical method can provide a new way to predict infiltration and runoff over sloped land.

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References

  • Abrahams AD, Parsons AJ, Luk SH (1986) Resistance to overland flow on desert hillslopes. J Hydrol 88:343–363

    Article  Google Scholar 

  • Abrahams AD, Li G, Parsons AJ (1996) Rill hydraulics on a semiarid hill slope, southern Arizona. Earth Surf Process Landf 21:35–47

    Article  Google Scholar 

  • Akratos CS, Papaspyros JNE, Tsihrintzis VA (2008) An artificial neural network model and design equations for BOD and COD removal prediction in horizontal subsurface flow constructed wetlands. Chem Eng J 143(1–3):96–110

    Article  Google Scholar 

  • Bennie ATP, Hofmann JE, Coetzee MJ, Vrey HS (1994) Storage and use of rainwater in soil for stabilising plant production in semi-arid areas. Water Res Commission report No.227/1/94, Pretoria, South Africa

  • Bothma CB, Van Bensburg LD, Le Roux PAL (2012) rain intensity and soil physical properties influence on infiltration and runoff under in-field rain-water harvesting conditions. Irrig Drain 61(2):41–49

    Article  Google Scholar 

  • Chen CN, Tsai CH, Tsai CT (2011) Simulation of runoff and suspended sediment transport rate in a basin with multiple watersheds. Water Resour Manag 25(3):793–816

    Article  Google Scholar 

  • Cundy TW, Tento SW (1985) Solution to the kinematic wave approach to overland flow routing with rainfall excess given by Philip’s equation. Water Resour Res 21(8):1132–1140

    Article  Google Scholar 

  • De Lima JLMP, Van der Molen WH (1988) An analytical kinematic model for the rising limb of overland flow on infiltrating parabolic shaped surfaces. J Hydrol 104:363–370

    Article  Google Scholar 

  • Deckers DLEH, Booij MJ, Rientjes THM, Krol MS (2010) Catchment variability and parameter estimation in multi-objective regionalisation of a rainfall-runoff model. Water Resour Manag 24(14):3961–3985

    Article  Google Scholar 

  • Eagleson PS (1970) Dynamic hydrology. McGraw Hill, New York

    Google Scholar 

  • Emmett WW (1970) The hydraulics of overland flow on hillslopes. Geological Survey Professional Paper U.S. 662-A, p. 68.

  • Foster GR, Huggins LF, Meyer LD (1992) A laboratory study of rill hydraulics I: velocity relationships. Soil Technol 5:289–301

    Google Scholar 

  • Govers G (1992) Relationships between discharge, velocity, and flow area for rills eroding loose, non-layered materials. Earth Surf Process Landf 17:515–528

    Article  Google Scholar 

  • Gwenzi W, Nyamadzawo G (2014) Hydrological impacts of urbanization and urban roof water harvesting in water-limited catchments: a review. Environ Process 1(4):573–593

    Article  Google Scholar 

  • Haverkamp R, Kutilek M, Parlange JY, Rendon L, Krejca M (1988) Infiltrationunder ponded conditions: Infiltration equations tested for parameter time dependence and predictive use. Soil Sci 145:317–329

    Article  Google Scholar 

  • Hillel AJ, Rossiter PL (1981) Resistivity mechanisms during clustering in alloys. Philos Mag B 44(3):383–388

    Article  Google Scholar 

  • Horton RE, Leach HR, Vliet VR (1934) Laminar sheet flow. Trans Am Geophys Union 15:393–404

    Article  Google Scholar 

  • Kibler DF, Woolhiser DA (1972) Mathematical properties of the kinematic cascade. J Hydrol 15:131–145

    Article  Google Scholar 

  • Lei TW, Nearing MA (2000) Flume experiments of determining rill hydraulic characteristic erosion and rill patterns. J Hydraul Eng (China) 11:49–54

    Google Scholar 

  • Lei TW, Xia WS, Zhao J, Liu Z, Zhang QW (2005) Method for measuring velocity of shallow water flow for soil erosion with an electrolyte tracer. J Hydrol 301:139–145

    Article  Google Scholar 

  • Li P (2015) Helps to deal with water issues in the context of climate change and human activity. Environ Process 2(2):441–444

    Article  Google Scholar 

  • Liu H, Lei TW, Zhao J, Yuan CP, Fan YT, Qu LQ (2011) Effects of rain intensity and antecedent soil water content on soil infiltrability under rainfall conditions using the run off-on-out method. J Hydrol 396(1–2):24–32

    Article  Google Scholar 

  • Mao LL, Lei TW, Braltsc VF (2011) An analytical approximation method for the linear source soil infiltrability measurement and its application. J Hydrol 411:169–177

    Article  Google Scholar 

  • Munoz-Carpena R, Parsons JE, Gilliam JW (1993) Numerical approach to the overland flow process in vegetative filter strips. T ASAE 36(3):761–770

    Article  Google Scholar 

  • Parida B, Moalafhi D, Kenabatho P (2006) Forecasting runoff coefficients using ANN for water resources management: the case of notwane catchment in eastern Botswana. Phys Chem Earth A/B/C 31(15–16):928–934

    Article  Google Scholar 

  • Philip JR (1957) The theory of infiltration: the infiltration equation and its solution. Soil Sci 83(5):345–357

    Article  Google Scholar 

  • Singh VP, Woolhiser DA (1996) A nonlinear kinematic wave model for watershed surface runoff. J Hydrol 31:221–243

    Article  Google Scholar 

  • Smith RE, Hebbert RHB (1979) A Monte Carlo analysis of the hydrologic effects of spatial variability of infiltration. Water Resour Res 15(2):419–429

    Article  Google Scholar 

  • Smith RE, Woolhiser DA (1971) Overland flow on an infiltrating surface. Water Resour Res 7:899–913

    Article  Google Scholar 

  • Stephenson D (1981) Stormwater hydrology and drainage. Elsevier, New York

    Google Scholar 

  • Stone JJ, Lane LJ, Shirley ED (1992) Infiltration and runoff simulation on a plane. T ASAE 35(1):161–170

    Article  Google Scholar 

  • Tabach EL, Lancelot L, Shahrour I, Najjar Y (2007) Use of artificial neural network simulation metamodelling to assess groundwater contamination in road project. Math Comput Model 45:766–776

    Article  Google Scholar 

  • Wallach R, Grigorin G, Byk JR (1997) The errors in surface runoff prediction by neglecting the relationship between infiltration rate and overland flow depth. J Hydrol 200(1):243–259

    Article  Google Scholar 

  • Wooding RAA (1965) Hydraulic model for the catchment-stream problem: I. Kinematic-wave theory. J Hydrol 3(3):254–267

    Article  Google Scholar 

  • Woolhiser DA, Smith RE, Giraldez JV (1996) Effects of spatial variability of saturated hydraulic conductivity on Hortonian overland flow. Water Resour Res 32(3):671–678

    Article  Google Scholar 

  • Yang T, Wang QJ, Xu D, Lv JB (2015) A method for estimating the interaction depth of surface soil with simulated rain. Catena 124:109–118

    Article  Google Scholar 

  • Yang T, Wang QJ, Liu YL, Zhang PY (2016) A comparison of mathematical models for chemical transfer from soil to surface runoff with the impact of rain. Catena 137:191–202

    Article  Google Scholar 

  • Zerihun YT (2015) Numerical simulation of flow in open channels with bottom intake racks. Water Util J 11:49–61

    Google Scholar 

Download references

Acknowledgment

This research was supported by the National Natural Science Foundation of China (51239009).

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Authors and Affiliations

  1. State Key Laboratory Base of Eco-hydraulic engineering in Arid Area, Xi’an University of Technology, Xi’an, 710048, China

    Ting Yang, Quanjiu Wang, Lijun Su, Guangxu Zhao, Yanli Liu & Pengyu Zhang

  2. Department of Environmental Sciences, University of California, Riverside, CA, 92521, USA

    Ting Yang & Laosheng Wu

  3. State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Northwest Agriculture&Forestry University, 712100, Yangling, China

    Quanjiu Wang

Authors
  1. Ting Yang
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  2. Quanjiu Wang
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  3. Lijun Su
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  4. Laosheng Wu
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  5. Guangxu Zhao
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  6. Yanli Liu
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  7. Pengyu Zhang
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Correspondence to Quanjiu Wang.

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Yang, T., Wang, Q., Su, L. et al. An Approximately Semi-Analytical Model for Describing Surface Runoff of Rainwater Over Sloped Land. Water Resour Manage 30, 3935–3948 (2016). https://doi.org/10.1007/s11269-016-1400-0

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  • DOI: https://doi.org/10.1007/s11269-016-1400-0

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