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Modelling effects of spatial variability of saturated hydraulic conductivity on autocorrelated overland flow data: linear mixed model approach

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Abstract

The mixed linear model approach was introduced and applied in studying the effects of spatial variation of the saturated hydraulic conductivity (K s ) on the variation of the overland flow. Analysis was carried out with 2,000 rainfall-runoff events, all generated through transformation of real, observed rainfall events and different spatially variable K s fields in a small (12 ha) agricultural catchment. The parameters accounting for the variation in the generation method were the coefficient of variation (cv) and correlation length (L x L y ) of K s both having two levels of values obtained from field measurements of other studies. The analysis showed that the combinations with both parameters having the smaller or bigger value during flow peaks only caused different response in the overland flow. However, the parameters were statistically significant only at the 10% level. Most of the flow variation was explained by the event dynamics. The mixed models were able to model the structure of the data efficiently with less restrictive assumptions than for example the analysis of variance, hence producing more reliable results. The method was able to take into account autocorrelation of the test series, correlation between the factors and unequal variances. The usefulness of the method was supported by the fact that the conclusions drawn by it were confirmed by simple, conventional methods of a previous study, added with statistical criteria and confidence levels for each calculation moment. The findings of the study can be utilized in practise for example when designing the field sampling experiments.

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References

  • Adema EO, Buschiazzo DE, Babinec FJ, Rucci TE, Gomez Hermida VF (2004) Mechanical control of shrubs in a semiarid region of Argentina and its effect on soil water content and grassland productivity. Agric Water Manage 68:185–194

    Article  Google Scholar 

  • Bresler E, Dagan G (1979) Solute dispersion in unsaturated heterogeneous soil at field scale: II. applications. Soil Sci Soc Am J 43:467–472

    Article  Google Scholar 

  • Burden DS, Selim HM (1989) Correlation of spatially variable soil water retention for a surface soil. Soil Sci Soc Am J 148:436–447

    Google Scholar 

  • Chen Z, Govindaraju RS, Kavvas ML (1994) Spatial averaging of unsaturated flow equation under infiltration conditions over areally heterogeneous fields. 2. Numerical simulations. Water Resour Res 30:535–548

    Article  Google Scholar 

  • Chu ST (1978) Infiltration during an unsteady rain. Water Resour Res 14:461–466

    Article  Google Scholar 

  • Constantinides CA (1981) Numerical techniques for a two-dimensional kinematic overland flow model. Water SA 7:234–248

    Google Scholar 

  • Corp LA, McMurtrey JE, Middleton EM, Mulchi CL, Chappelle EW, Daughtry CST (2003) Fluorescence sensing systems: in vivo detection of biophysical variations in field corn due to nitrogen supply. Remote Sens Environ 86:470–479

    Article  Google Scholar 

  • Corradini C, Morbidelli R, Melone F (1998) On the interaction between infiltration and Hortonian runoff. J Hydrol 204:52–67

    Article  Google Scholar 

  • Dagan G, Bresler E (1983) Unsaturated flow in spatially variable fields. 1. derivation of models of infiltration and redistribution. Water Resour Res 19:413–420

    Article  Google Scholar 

  • Dulormne M, Sierra J, Bonhomme R, Cabidoche YM (2004) Seasonal changes in tree–grass complementarity and competition for water in a subhumid tropical silvopastoral system. Eur J Agron 21:311–322

    Article  Google Scholar 

  • Govindaraju RS, Morbidelli R, Corradini C (2001) Areal infiltration modeling over soils with spatially correlated hydraulic conductivities. J Hydrol Eng ASCE 6:150–158

    Article  Google Scholar 

  • Grah OJ, Hawkins RH, Cundy TW (1983) Distribution of infiltration on a small watershed. In: Borrelli J, Hasfurther VR, Burman RD (eds) Proceedings of the speciality conference on advances in irrigation and drainage: surviving external pressures (Jackson, Wyoming, July 20–22, 1983). ASCE, New York, pp 44–54

    Google Scholar 

  • Hazell D, Cunningham R, Lindenmayer D, Mackey B, Osborne W (2001) Use of farm dams as frog habitat in an Australian agricultural landscape: factors affecting species richness and distribution. Biol Conserv 102:155–169

    Article  Google Scholar 

  • Henderson CR (1984) Applications of linear models in animal breeding. University of Guelph, Guelph

    Google Scholar 

  • Huett DO, Morris SG, Smith G, Hunt N (2005) Nitrogen and phosphorus removal from plant nursery runoff in vegetated and unvegetated subsurface flow wetlands. Water Res 39:3259–3272

    Article  CAS  Google Scholar 

  • Jones AJ, Wagent RJ (1984) In situ estimation of hydraulic conductivity using simplified methods. Water Resour Res 20:1620–1626

    Article  Google Scholar 

  • Kaledhonkar MJ, Keshari AK, Van Der Zee, SEATM (2006) Relative sensitivity of ESP profile to spatial and temporal variability in cation exchange capacity and pore water velocity under simulated field conditions. Agric Water Manage 83:58–68

  • Kirtland BC, Aelion CM, Stone PA (2005) Assessing in situ mineralization of recalcitrant organic compounds in vadose zone sediments using δ13C and 14C measurements. J Contam Hydrol 76:1–18

    Article  CAS  Google Scholar 

  • Kitanidis PK, Lane RW (1985) Maximum likelihood parameter estimation of hydrologic spatial processes by the Gauss–Newton method. J Hydrol 79:53–71

    Article  Google Scholar 

  • Littell RC, Milliken GA, Stroup WW, Wolfinger RD (1996) SAS system for mixed models. SAS Institute, Cary

    Google Scholar 

  • Loague KM (1986) An assessment of rainfall-runoff modeling methodology. PhD Thesis, University of British Columbia, Vancouver, Canada

  • McLean RA, Sanders WL (1988) Approximating degrees of freedom for standard errors in mixed linear models. In: Proceedings of the statistical computing section. American Statistical Association, New Orleans, pp 50–59

    Google Scholar 

  • Milton JS, Arnold JC (1987) Probability and statistics in the engineering and computing sciences. McGraw-Hill, Singapore

    Google Scholar 

  • Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models, part I—discussion of principles. J Hydrol 10:282–290

    Article  Google Scholar 

  • Nielsen DR, Biggar JW, Erh KT (1973) Spatial variability of field measured soil-water properties. Hilgardia 42:215–259

    Google Scholar 

  • Orlob GT (1972) Mathematical modelling of estuarial systems. In: Biswas AK (ed) Proceedings, international symposium on mathematical modelling techniques in water resources systems, Canada Department of the Environment, vol 1

  • Park T, Lee YJ (2002) Tutorial in biostatistics. Covariance models for nested repeated measures data: analysis of ovarian steroid secretion data. Stat Med 21:143–164

    Article  Google Scholar 

  • Peck AJ, Luxmoore RJ, Stolzy JL (1977) Effects of spatial variability of soil hydraulic properties in water budget modeling. Water Resour Res 13:348–354

    Article  Google Scholar 

  • Ragab R, Cooper JD (1993) Variability of unsaturated zone water transport parameters: implications for hydrological modelling, 1. In situ measurements. J Hydrol 148:109–131

    Article  Google Scholar 

  • Rawls WJ, Brakensiek DL, Saxton KE (1982) Estimation of soil water properties. T ASAE 25 SW:1316–1320, 1328

  • Reed RE, Glasgow HB, Burkholder JM, Brownie C (2004) Seasonal physical–chemical structure and acoustic Doppler current profiler flow patterns over multiple years in a shallow, stratified estuary, with implications for lateral variability. Estuar Coast Shelf S 60:549–566

    Article  CAS  Google Scholar 

  • Russo D, Bresler E (1982) A univariate versus a multivariate parameter distribution in a stochastic-conceptual analysis of unsaturated flow. Water Resour Res 18:483–488

    Article  CAS  Google Scholar 

  • Sarkkola S, Hokka H, Laiho R, Päivänen J, Penttilä T (2005) Stand structural dynamics on drained peatlands dominated by Scots pine. For Ecol Manag 206:135–152

    Article  Google Scholar 

  • SAS system for Windows (1999–2000) OnlineDoc®. Release 8.01. Sas Institute, Cary, NC, USA

  • Searle SR (1971) Linear models. Wiley, New York

    Google Scholar 

  • Sharma ML, Gander GA, Hunt CG (1980) Spatial variability of infiltration in a watershed. J Hydrol 45:101–122

    Article  Google Scholar 

  • Sharma ML, Barron RJW, Fernie MS (1987) Areal distribution of infiltration parameters and some soil physical properties in lateritic catchments. J Hydrol 94:109–127

    Article  Google Scholar 

  • Singh VP (1988) Hydrologic systems. Rainfall-runoff modeling, vol I. Prentice Hall, Englewood Cliffs

  • Smettem KRJ (1987) Characterization of water entry into a soil with a contrasting textural class: spatial variability of infiltration parameters and influence of macroporosity. Soil Sci 144:167–174

    Article  Google Scholar 

  • Smettem KRJ, Clothier BE (1989) Measuring unsaturated sorptivity and hydraulic conductivity using multiple disc permeameters. Soil Sci Soc Am J 40:563–568

    Google Scholar 

  • Smith RE, Goodrich DC (2000) Model for rainfall excess patterns on randomly heterogeneous areas. J Hydrol Eng ASCE 5:355–362

    Article  Google Scholar 

  • Soil Conservation Service (SCS) (1982) Procedures for collecting soil samples and methods of analysis for soil survey. Soil survey investigations report 1, Washington, DC

  • Sturtevant BR, Seagle SW (2004) Comparing estimates of forest site quality in old second-growth oak forests. For Ecol Manag 191:311–328

    Article  Google Scholar 

  • Taskinen A (2002) Mathematical modelling of overland flow, erosion and transport of phosphorus. PhD Thesis, University College Dublin, Dublin

  • Taskinen A, Bruen M (2007a) Incremental distributed modelling investigation in small agricultural catchment: (1) Overland flow with comparison with Unit Hydrograph model. Hydrol Process 21:80–91

    Article  Google Scholar 

  • Taskinen A, Bruen M (2007b) Incremental distributed modelling investigation in small agricultural catchment: (2) Erosion and phosphorus transport. Hydrol Process 21:92–102

    Article  CAS  Google Scholar 

  • Taskinen A, Sirviö H, Bruen M (2006a) Generation of two-dimensionally variable saturated hydraulic conductivity fields: model theory, verification and computer program. Comput Geosci (submitted)

  • Taskinen A, Sirviö H, Bruen M (2006b) Statistical analysis of the effects on overland flow of spatial variability in soil hydraulic conductivity. Hydrolog Sci J (submitted)

  • Verbeke G, Molenberghs G (1997) Linear mixed models in practice: a SAS-oriented approach. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Wolfinger RD, Tobias RD, Sall J (1994) Computing Gaussian likelihoods and their derivatives for general linear mixed models. SIAM J Sci Comput 15:1294–1310

    Article  Google Scholar 

  • Woolhiser DA, Goodrich DC (1988) Effect of storm rainfall intensity patterns on surface runoff. J Hydrol 102:335–354

    Article  Google Scholar 

  • Young PC (1992) Parallel processes in hydrology and water quality: a unified time-series approach. J Inst Water Environ Manage 6:598–612

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The first author gratefully acknowledges the financial support of the Centre for Water Resources Research at UCD, the EU Copernicus programme, UCD, Academy of Finland, Center for International Mobility (CIMO), Sven Hallinin tutkimussäätiö, Antti ja Jenny Wihurin rahasto, Maa- ja Vesitekniikan tuki ry., Maj ja Tor Nesslingin säätiö, Ella ja Georg Ehrnroothin säätiö, Oskar Öflunds Stiftelse, Teknillisen korkakoulun tukisäätiö and Suomalainen Tiedeakatemia (Vilho, Yrjö ja Kalle Väisälän rahasto). The authors are also thankful to Dr Seppo Rekolainen (Finnish Environment Institute) for providing the data of the Hovi catchment.

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Authors and Affiliations

  1. Department for Expert Services, Hydrological Services Division, Finnish Environment Institute, Mechelininkatu 34 a, P.O Box 140, 00251, Helsinki, Finland

    Antti Taskinen & Hannu Sirviö

  2. Centre for Water Resources Research, School of Architecture, Landscape and Civil Engineering, UCD Dublin, Earlsfort Terrace, Dublin 2, Ireland

    Michael Bruen

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  1. Antti Taskinen
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  2. Hannu Sirviö
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Correspondence to Antti Taskinen.

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Taskinen, A., Sirviö, H. & Bruen, M. Modelling effects of spatial variability of saturated hydraulic conductivity on autocorrelated overland flow data: linear mixed model approach. Stoch Environ Res Risk Assess 22, 67–82 (2008). https://doi.org/10.1007/s00477-006-0099-5

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