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

The mixed linear model approach was introduced and applied in studying the effects of spatial variation of the saturated hydraulic conductivity (Ks) 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 Ks 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 (LxLy) of Ks 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.

[1]  Gedeon Dagan,et al.  Solute Dispersion in Unsaturated Heterogeneous Soil at Field Scale: I. Theory , 1979 .

[2]  R. Govindaraju,et al.  Areal Infiltration Modeling over Soils with Spatially Correlated Hydraulic Conductivities , 2001 .

[3]  Shu Tung Chu,et al.  Infiltration during an unsteady rain , 1978 .

[4]  Ashok K. Keshari,et al.  Relative sensitivity of ESP profile to spatial and temporal variability in cation exchange capacity and pore water velocity under simulated field conditions , 2006 .

[5]  C. R. Henderson.  Applications of linear models in animal breeding , 1984 .

[6]  R. Bonhomme,et al.  Seasonal changes in tree-grass complementarity and competition for water in a subhumid tropical silvopastoral system , 2004 .

[7]  M. Sharma,et al.  Spatial variability of infiltration in a watershed , 1980 .

[8]  Rao S. Govindaraju,et al.  Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields 2. Numerical simulations , 1994 .

[9]  P. Kitanidis,et al.  Maximum likelihood parameter estimation of hydrologic spatial processes by the Gauss-Newton method , 1985 .

[10]  Gedeon Dagan,et al.  Solute Dispersion in Unsaturated Heterogeneous Soil at Field Scale: II. Applications1 , 1979 .

[11]  David A. Woolhiser,et al.  EFFECT OF STORM RAINFALL INTENSITY PATTERNS ON SURFACE RUNOFF , 1988 .

[12]  M. Bruen,et al.  Incremental distributed modelling investigation in a small agricultural catchment: 2. Erosion and phosphorus transport , 2007 .

[13]  D. Lindenmayer,et al.  Use of farm dams as frog habitat in an Australian agricultural landscape: factors affecting species richness and distribution , 2001 .

[14]  Peter C. Young,et al.  Parallel Processes in Hydrology and Water Quality: A Unified Time‐Series Approach , 1992 .

[15]  Russ Wolfinger,et al.  Computing Gaussian Likelihoods and Their Derivatives for General Linear Mixed Models , 1994, SIAM J. Sci. Comput..

[16]  M. Sharma,et al.  Areal distribution of infiltration parameters and some soil physical properties in lateritic catchments , 1987 .

[17]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[18]  Taesung Park,et al.  Covariance models for nested repeated measures data: analysis of ovarian steroid secretion data. , 2002, Statistics in medicine.

[19]  K. Loague.  An assessment of rainfall-runoff modeling methodology , 1986 .

[20]  Antti Taskinen,et al.  Statistical analysis of the effects on overland flow of spatial variability in soil hydraulic conductivity / Analyse statistique des effets de la variabilité spatiale de la conductivité hydraulique du sol sur l'écoulement de surface , 2008 .

[21]  Brent Clothier,et al.  Measuring unsaturated sorptivity and hydraulic conductivity using multiple disc permeameters , 1989 .

[22]  T. Penttilä,et al.  Stand structural dynamics on drained peatlands dominated by Scots pine , 2005 .

[23]  Janice L. Stolzy,et al.  Effects of spatial variability of soil hydraulic properties in water budget modeling , 1977 .

[24]  D. Buschiazzo,et al.  Mechanical control of shrubs in a semiarid region of Argentina and its effect on soil water content and grassland productivity , 2004 .

[25]  S. R. Searle.  Linear Models , 1971 .

[26]  J. D. Cooper,et al.  Variability of unsaturated zone water transport parameters: implications for hydrological modelling. 1. In situ measurements , 1993 .

[27]  F. Melone,et al.  On the interaction between infiltration and Hortonian runoff , 1998 .

[28]  K. Smettem.  CHARACTERIZATION OF WATER ENTRY INTO A SOIL WITH A CONTRASTING TEXTURAL CLASS: SPATIAL VARIABILITY OF INFILTRATION PARAMETERS AND INFLUENCE OF MACROPOROSITY , 1987 .

[29]  R. Littell.  SAS System for Mixed Models , 1996 .

[30]  D. Russo,et al.  A univariate versus a multivariate parameter distribution in a stochastic‐conceptual analysis of unsaturated flow , 1982 .

[31]  Vijay P. Singh,et al.  Hydrologic Systems: Rainfall-Runoff Modeling , 1988 .

[32]  Geert Molenberghs,et al.  Linear Mixed Models in Practice: A SAS-Oriented Approach , 1997 .

[33]  C. A. Constantindes.  Numerical techniques for a two-dimensional kinematic overland flow model , 1981 .

[34]  Gedeon Dagan,et al.  Unsaturated flow in spatially variable fields: 1. Derivation of models of infiltration and redistribution , 1983 .

[35]  D. Huett,et al.  Nitrogen and phosphorus removal from plant nursery runoff in vegetated and unvegetated subsurface flow wetlands. , 2005, Water research.

[36]  D. L. Brakensiek,et al.  Estimation of Soil Water Properties , 1982 .

[37]  D. Goodrich,et al.  Model For Rainfall Excess Patterns on Randomly Heterogeneous Areas , 2000 .

[38]  C. Aelion,et al.  Assessing in situ mineralization of recalcitrant organic compounds in vadose zone sediments using delta13C and 14C measurements. , 2005, Journal of contaminant hydrology.

[39]  B. Sturtevant,et al.  Comparing estimates of forest site quality in old second-growth oak forests , 2004 .

[40]  D. R. Nielsen,et al.  Spatial variability of field-measured soil-water properties , 1973 .

[41]  Geert Molenberghs,et al.  Linear Mixed Models in Practice , 1997 .

[42]  M. Bruen,et al.  Incremental distributed modelling investigation in a small agricultural catchment: 1. Overland flow with comparison with the unit hydrograph model , 2007 .

[43]  J. Susan Milton,et al.  Probability and statistics in the engineering and computing sciences , 1986 .

[44]  J. Burkholder,et al.  Seasonal physical–chemical structure and acoustic Doppler current profiler flow patterns over multiple years in a shallow, stratified estuary, with implications for lateral variability , 2004 .

[45]  A. Jones,et al.  In situ estimation of hydraulic conductivity using simplified methods , 1984 .

[46]  Michael Bruen,et al.  Generation of two-dimensionally variable saturated hydraulic conductivity fields: Model theory, verification and computer program , 2008, Comput. Geosci..

[47]  Charles L. Mulchi,et al.  Fluorescence sensing systems: In vivo detection of biophysical variations in field corn due to nitrogen supply , 2003 .