Analysis of sources of variability of runoff volume in a 40 plot experiment using a numerical model

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Abstract

Runoff volumes from field plots can be quite variable, but the reasons for this variability are not completely understood. Such variations can be important for understanding the hydrologic system, and for evaluating the effectiveness of infiltration, runoff and sediment models. In this study, we investigated the sources of variability among 40 replications in a previously reported experiment on fallow plots located on a claypan soil in Missouri, USA. A numerical model was calibrated using data from the experiment and from other published data on the variability of soil properties. The results describe qualitatively the trend in the observed relationship between the coefficient of variation (CV) and mean runoff volume per event, as well as the lack of stability in time of the relative differences in runoff volume among plots. Quantitatively, approximately 50% of the observed coefficients of variation among the replicated plots were explained by the spatial variability of Ks, surface storage, and the depth to claypan. The remaining 50% may be due to the variability in rainfall among plots, measurement error in runoff, the fact that some published rather than site specific information was used in the analyses, and simplifications introduced in the modeling process. Our results suggested that changes in the relative differences in runoff volumes between plots during the season might be explained by the modification of the spatial distribution of Ks and surface storage which occurs during tillage. The introduction of these sources of variability in the model formulation produced a realistic description of the variance of the observed values of runoff volume, as well as a relatively clear delineation between the explained and unexplained variability. The results may also serve as an index of model performance in predicting observed data.

Introduction

Data from runoff plots show a large variability. Rüttimann et al. (1995) reported a coefficient of variation (CV) for seasonal runoff volume ranging from 30 to 50% using three replications of runoff plots per treatment. This CV was in the same general range of magnitude as that reported by Wendt et al. (1986) using 40 replicated plots, wherein the observed CV for seasonal runoff volume was approximately 30%. It has been suggested that the magnitude of the observed CV should decrease as a function of increasing plot size (Bryan, 1979, Luk and Morgan, 1981). However, Rüttimann et al. (1995) analyzed published CV values for plots of areas ranging from 0.0929 to 87.68 m2 and did not find such a relationship apparent in those data. Attempts to relate the observed differences in runoff between the replications to differences in soil properties were unsuccessful in the studies of Hjemfelt and Burwell, 1984, Wendt et al., 1986, even though an extensive soil-testing program was undertaken. Also in the study of Hjemfelt and Burwell (1984), the relative differences between replications did not persist in time. This result was corroborated by Rüttimann et al. (1995). If one plot yielded more runoff than another in one particular event, the differences could be reversed in another event. Wendt et al. (1986), analyzing the correlation of plot runoff among events, attributed this erratic behavior, in part at least, to the modification of soil surface properties by tillage.

The main consequence of the relatively high level of unexplained CV is the requirement of a large number of replications in the experimental design in order to have statistical significance of the results (Hudson, 1997). As a corollary, small differences in experimental work are difficult to detect. The large variation of replicates also hinders evaluation of simulation models. Unless one has some knowledge of the variability in observed data, it is difficult to delineate that portion of the observed error coming from the model prediction from that coming from the unexplained variability in the data (Nearing et al., 1999).

Freeze (1980) estimated the spatial variability of 20 soil properties or profile characteristics to implement a hydrologic model using the Monte Carlo method to analyze its impact in the variation of runoff at the hillslope scale. In a similar way, Binley et al. (1989) explained with a physically based model the runoff production on heterogeneous hillslopes. Smith and Herbert (1979) also performed a Monte Carlo analysis of the hydrologic effects of spatial variability of infiltration. The objective of these modelling studies was to get insight of the role of spatial variability in the hydrological response of the hillslopes. Apparently, they fulfilled their goals, despite the fact that without knowledge of the spatial dependence scale ‘a rigorous treatment of watershed hydrology with spatially distributed properties is not possible’ (Smith and Herbert, 1979). The results of the previously cited works showed how this spatial variation might lead to significant differences among hillslopes that are similar in terms of their average properties. Significant efforts have been made in the characterization of the spatial variation of either infiltration rate (De Roo et al., 1992) or hydraulic conductivity (Woolhiser et al., 1996, Gupta et al., 1998), affecting the variability of runoff. There are many reports on the large CV values under field conditions for both infiltration rate (Starr, 1990, Vieira et al., 1981) and hydraulic conductivity (Bosch and West, 1998, Gupta et al., 1993, Logsdon and Jaynes, 1996).

The objective of this study is to improve our understanding of the variability in runoff volume in field plot experiments. For this, we used a physically based model of runoff generation, and the results from 40 replicated plots presented previously (Hjemfelt and Burwell, 1984, Wendt et al., 1986). The spatial variation of soil properties was inferred from published values to estimate the impact on runoff variability from three main sources of variability: hydraulic conductivity, surface storage associated with random roughness, and depth to the claypan. We also improved the extrapolation and prediction capabilities of the numerical model by taking into account the spatial variability of these sources of variability. The inferences from modeling and field studies can be different due, among other reasons, to the degree of simplification of the models used or assumptions made in the calibration process. In the author's opinion, the possibility of compare the results of our simulation analysis with the observed results first reported and analyzed by Hjemfelt and Burwell (1984) could help to improve further field or modeling studies on this subject.

Section snippets

Observed data

Wendt et al. (1986) recorded the runoff generated in a 40-plot experiment located near Kingdom City, MO. The data was collected in 1981 (Table 1). Each plot was 3.2-m wide and 27.4-m long, oriented parallel to the steepest line of a slope of 0.03–0.035 m m−1, and separated by a 2.13-m wide border strip. The 40 plots were arranged in two lines occupying an area of approximately 140×100 m2. The soil was a Mexico silt loam, with a slowly permeable layer of illuvial clay (claypan) beginning at depths

Observed data

Fig. 2 shows the observed CV in plot event runoff for the study of Wendt et al. (1986). The magnitude of CV was greater for the smaller runoff events, but still significant, at approximately 20%, for the larger runoff events. Fig. 3 shows the time stability parameter, λ, and its 90% confidence interval bars. This parameter is defined according to Starr (1990) asλij=XijX̄j−1andX̄j=(1/n)i=1i=nXijwhere Xij denote the values of runoff at different plot locations (i) and different times (j), over n

Discussion

The observed plot runoff showed coefficients of variation quite large for small events and still important for the larger runoff events (Fig. 2). Similar results have been reported by Smith and Herbert, 1979, De Roo et al., 1992 simulating with the Monte Carlo method spatially variable infiltration in both a virtual and an actual catchment. We are not aware of previous works trying to explain the observed CV in plot experiments using numerical models. Our results indicate that the numerical

Conclusions

The analysis of the CV in runoff volume between replicated plots from a field experiment using a numerical model showed that the spatial variability of Ks within individual plots, surface storage, and depth to claypan explain qualitatively the observed trend and approximately 50% of the observed CV. Experimental error and assumptions made during the calibration and modeling steps could explain this quantitative difference. The experimental plots exhibited time instability in terms of the

Acknowledgements

This work was made when the senior author was a visiting scientist at the USDA-ARS-National Soil Erosion Research Laboratory, on a grant from the Spanish Ministry of Education. This support is gratefully acknowledged. We also appreciate the comments made by A. de Roo and one anonymous reviewer during the revision process that helped improving the quality of the manuscript.

References (56)

  • A.P.J. De Roo et al.

    Estimating the effects of spatial variability of infiltration on the output of a distributed runoff and soil erosion model using Monte Carlo methods

    Hydrol. Process.

    (1992)
  • J.Y. Diiwu et al.

    Effect of tillage on the spatial variability of soil water properties

    Can. Agric. Engng

    (1998)
  • T.E. Engman

    Roughness coefficient for routing surface runoff

    J. Irrig. Drain. Engng

    (1986)
  • F.R. Fiedler et al.

    A numerical method of simulating discontinuous shallow flow over an infiltrating surface

    Int. J. Numer. Methods Fluids

    (2000)
  • Flanagan, D.C., Nearing, M.A., 1995. USDA-Water Erosion Prediction Project. Hillslope profile and watershed model...
  • R.A. Freeze

    A stochastic-conceptual analysis of rainfall–runoff processes on a hillslope

    Water Resour. Res.

    (1980)
  • Gómez, J.A., 1998. Modelización de los procesos de interceptación de lluvia en un olivar. PhD Thesis, Department of...
  • J.A. Gómez et al.

    Analysis of infiltration in an olive orchard under to tillage

    Soil Sci. Soc. Am. J.

    (2001)
  • R.K. Gupta et al.

    Comparison of saturated hydraulic conductivity measured by various field methods

    Trans. ASAE

    (1993)
  • R. Gupta et al.

    Modeling infiltration with varying hydraulic conductivity under simulated rainfall conditions

    J. Am. Water Resour. Assoc.

    (1998)
  • R.H. Hawkins

    Interpretation of source-area variability in rainfall–runoff relationships

  • A.T. Hjemfelt et al.

    Spatial variability of runoff

    J. Irrig. Drain. Div., ASCE

    (1984)
  • Hudson, N.W., 1997. Medición sobre el terreno de la erosion del suelo y de la escorrentı́a. Boletı́n de suelos de la...
  • V.C. Jamison et al.

    Soil and water research on a claypan soil

    (1968)
  • A. Journel

    Fundamentals of geostatistics in five lessons

    (1989)
  • A.G. Journel et al.

    Mining geostatistics

    (1978)
  • A. Klute

    Tillage effects on the hydraulic properties of soil: a review

  • M. Kutı́lek et al.

    Soil Hydrology

    (1994)
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