Modelling Hillslope Soil Water Status during Drainage

A model is used to simulate soil water conditions during drainage on a range of hillslopes having differing soil parameters and topographies. It is demonstrated that only in the specific cases of high hydraulic conductivities (> 10-4 cm sec-') and high slopes (> 25') do soil water flow paths always converge into hillslope hollows. For all other conditions simulated, more complex patterns of cross hollow-spur movements were shown to occur, with the possibilities of higher soil water potentials existing on the downstream spur location than in the centre of the adjacent upslope hollow. It is concluded that improvements in the identification of particular requirements for differing soil water flow configurations will only be effected when greater information is available on stochastic effects, such as local variations in soil parameter values. INTRODUCTION Empirical evidence has been presented elsewhere to show two contrasting soil water conditions on hillslopes. First, where the soils are permeable (1 x 10-3 cm sec-1) and the topography is steep (30') soil water convergence is shown to always occur into hillslope hollows irrespective of antecedent conditions (Anderson and Burt, 1977). Secondly, for a shallow topography (6') with less permeable soils (1 x 10-5 cm sec-1) it has been shown that the focus of soil water convergence may oscillate across hollow-spur topography, inducing, in extreme cases, higher soil water potentials on downstream spur locations than in the hillslope hollow centre (Anderson and Kneale, 1982). Available evidence from these two sources indicate that while, during the storm event itself, there is near uniformity of response in terms of hollow convergence, it is the drainage characteristics that differ significantly. This paper, by the application of a drainage simulation model, seeks to determine the nature of the thresholds for the initiation of the higher soil water potential zones. It is evident that the two principal factors that interact in this context in hollow and spur topographies are hydraulic conductivity and hillslope angle, based on the empirical evidence referred to above. However, it is of particular interest to be able to isolate: (a) those conditions of hydraulic conductivity and slope angle that, following storm cessation, maintain down-hollow soil water convergence, and those conditions that maintain cross hollow-spur movement, and (b) those conditions of hydraulic conductivity and slope angle that, on drainage, occasion high soil water potentials in the hollow centre, and those that give rise to higher values on the downstream spur. While instrumented hillslope sites can provide an important base from which this work can begin, the combination of parameter requirements necessary to identify threshold values of hydraulic conductivity and hillslope angle are too large to be examined empirically. Trans. Inst. Br. Geogr. N.S. 7: 337-53 (1982) Printed in Great Britain This content downloaded from 207.46.13.78 on Thu, 21 Jul 2016 04:27:05 UTC All use subject to http://about.jstor.org/terms 338 MALCOLM G. ANDERSON Accordingly, this investigation is based upon a drainage simulation model, calibrated and tested from data obtained in the study reported by Anderson and Kneale (1982). Previous work in this field has been more concerned with estimating peak hillslope discharge by means of simulation (Beven, 1977; Freeze, 1972) than with an examination of control thresholds on hillslope soil water status during drainage. The contention here is that if it can be shown that a wide range of specified circumstances can induce soil water flow paths to migrate across slope with attendant changes in the soil water potentials, then it may be possible to be more specific concerning the true location and controls of variable source areas during recession. SIMULATION PROCEDURE AND EXPERIMENTAL DESIGN The equation determining the flux from one point to another in the soil is F = K grad (1) where F is the flux of moisture per unit area, K is the hydraulic conductivity, and 0 is the total potential. If K was known throughout the entire hillside and for all moisture states, then the flux could be predicted at all points. However, hydraulic conductivity is not constant but varies with soil moisture content (0). Campbell (1974) illustrated a method of determining unsaturated hydraulic conductivity directly from the moisture retention function and a single measurement of hydraulic conductivity at some water content. If the moisture retention function can be represented by v = ~e (0/0,)-1b (2) where qie is the air entry water potential, 8, is the saturated water content, and q1 is the soil water potential, then the hydraulic conductivity is given by K = K (8/8)2b+3 (3) where K, is saturated hydraulic conductivity. The moisture retention function is well known to contain hysteresis dependent upon the antecedent wetting and drying states (Poulovassilis, 1962). However, certain writers have ignored such hysteresis in the establishment of initial modelling thresholds as distinct from specific accurate numerical simulations (e.g. Hillel, 1977). In any case, the argument for not incorporating hysteresis is that the concern here is with simulating drainage only. Having established the moisture retention function on the drying cycle, together with K,, then it is possible to predict 0 and K for given values of 0 and hence predict the flux F. The initial conditions requiring specification are the initial V, K,, depth of each cell, distance from cell midpoint to cell midpoint, the moisture retention function, and the utilization of the Campbell method for obtaining K. Clapp and Hornberger (1978) and Brakensiek (1979) have commented on the applicability of the Campbell procedure, which, among other requirements, necessitates that since equation (2) describes the moisture retention function for the soil, the data points plotted on a log-log scale should produce a straight line with slope equal to b. If this condition is not met equation (3) will not produce valid estimates of K. This content downloaded from 207.46.13.78 on Thu, 21 Jul 2016 04:27:05 UTC All use subject to http://about.jstor.org/terms Modelling hillslope soil water 339 i Te nsiomet er grid (see C) / Catchment divide / / Stream S A with weir o-Height / 0 in metres / D.. ?. s Stream .c , source WINFORD NR. BRISTOL / ... . : 0 250 m ? *21 6m20 5m7 -*19 *018 *17 5m 4m SHollow *12 / 013 -@ Spur Spur