Hydrological Sciences-Journal-des Sciences Hydrologiques, 44(3) June 1999
447
Modelling solute leaching during fingered flow by integrating and expanding various theoretical and empirical concepts
GERRIT H. DE ROOIJ Department of Environmental Sciences, Sub-department Water Resources, Wageningen Agricultural University, Nieuwe Kanaal 11, 6709 PA Wageningen, The Netherlands e-mail:
[email protected]
HIROYUKI CHO Department of Agricultural Sciences, Saga University, Honjou 1, Saga-shi 840-8502, Japan Abstract Wetting front instability (fingered flow) accelerates solute transport through the unsaturated zone to the groundwater table. Whether fingers widen or dissipate close to the groundwater is unclear. Water flow in a two-dimensional artificial capillary fringe below a dry layer exhibiting fingered flow was investigated. The flow diverged strongly in the wet soil, suggesting that fingers dissipate. Expressions for the finger radius in dry and wet soil were combined and adapted to a soil hydraulic property parameterization popular in numerical modelling. The modified equation provided finger radii for soils in humid and arid climates. The fingers in the arid soil were excessively wide. The finger radii were used to model solute transport, assuming fingers dissipated in the subsoil. Modelling was cumbersome for the arid climate. One shower may often be insufficient to trigger fingering in arid regions with short, heavy showers. In soils with shallow groundwater, the diverging subsoil flow determines solute leaching.
Modélisation de la lixiviation de la matière dissoute le long de chemins préférentiels combinant et étendant quelques concepts théorétiques et empiriques Résumé L'instabilité du front d'humectation (désigné ci-dessous comme un drainage selon des chemins préférentiels) accélère le transport des matières dissoutes vers la nappe phréatique. Au voisinage de la nappe, il est difficile de dire si les chemins préférentiels s'élargissent ou disparaissent. La recherche a été menée sur l'écoulement de l'eau à travers un système capillaire artificiel à deux dimensions (représentant une couche de sol humide), situé au dessous d'une couche de sol sec où apparaissent des chemins préférentiels. La forte divergence des chemins préférentiels dans la couche humide suggère leur disparition. Quelques expressions du rayon des chemins préférentiels en sol sec ou humide ont été combinées et adaptées à une paramétrisation des propriétés hydrauliques du sol fréquemment utilisée dans les modèles numériques. L'expression qui en résulte a permis de fournir une estimation du rayon des chemins préférentiels des sols pour des climats humides ou arides. Les rayons des chemins préférentiels des sols arides étaient particulièrement grands. Le transport des matières dissoutes est modélisé en utilisant ces rayons et en supposant que les chemins préférentiels disparaissent dans le sol humide sousjacent. La modélisation du sol en climat aride s'est révélée difficile. Dans ces climats, où les pluies sont de courte durée et de forte intensité, la quantité d'eau peut être insuffisante pour provoquer la formation de chemins préférentiels. Dans les sols où la nappe phréatique est peu profonde, la divergence des chemins préférentiels dans le sol humide sous-jacent est décisive pour le transport des matières dissoutes.
Open for discussion until 1 December 1999
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NOTATION aa shape factor of Gardner's (1958) K(h) function ( c m 1 ) h pressure head (cm) hae air-entry value (cm) hcc pressure head corresponding to 0CC (cm) hF pressure head behind (above) the wetting front (cm) hi initial pressure head (cm) hin pressure head at the inflection point of the soil water retention curve (cm) hwe water-entry value (cm) K unsaturated soil hydraulic conductivity (cm day" 1 ) Kf soil hydraulic conductivity within the finger (cm day" 1 ) KF soil hydraulic conductivity behind (above) the wetting front (cm day" 1 ) Ks saturated soil hydraulic conductivity (cm day"1) / shape factor of van Genuchten's (1980) K(h) function L distance solutes travelled below the distribution zone (cm) Ld thickness of the distribution zone (cm) Lf finger length (cm) Lw thickness of the prewetted subsoil (cm) m shape factor of the soil hydraulic property curves n shape factor of the soil hydraulic property curves P rainfall rate (cm day" 1 ) Pc cumulative rainfall (cm) r radial coordinate (cm) R radius of the distribution zone (cm) Rf finger radius (cm) td time required to fill the distribution zone (days) tr duration of a rain shower (days) a shape factor of the soil hydraulic property curves ( c m 1 ) Ow value of a for the wetting curve starting at Qr (cm" 1 ) 9 volumetric soil water content Qcc volumetric soil water content defined by (9 c e - Qr)/(QS - 9/-) = 0-5 Qd volumetric water content of the distribution zone Qe volumetric water content of a finger after 24-48 h of drainage 9/ volumetric water content of a finger QF volumetric water content behind (above) the wetting front 0,- initial volumetric water content 9,„ volumetric water content at the inflection point of the soil water retention curve Qr residual volumetric water content 9., saturated volumetric water content INTRODUCTION Preferential flow caused by wetting front instability enhances solute leaching to the groundwater and reduces crop water availability. Various works, both theoretical
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(Raats, 1973; Philip, 1975; see also the overview of Glass & Nicholl, 1996) and experimental (e.g. Hill & Parlange, 1972; Glass et al, 1989a; Baker & Hillel, 1990; Selker et al, 1992b; Glass & Nicholl, 1996), have revealed many of the physical processes governing wetting front instability. Field experiments have demonstrated the effect of preferential flow on solute leaching (e.g. Starr et al, 1978, 1986; Ritsema et al, 1993; Dekker & Ritsema, 1994; Ritsema & Dekker, 1994, 1995). The capillary fringe above a groundwater table markedly affects fingered flow, but few experimental results are available. Starr et al (1986) observed a finger that widened dramatically after reaching a prewetted layer. Liu et al. (1991, 1994a,b) reported much less finger widening and argued that finger size depends on the initial water content. Fingers in their study became increasingly wetter with depth in the dry topsoil, but drier with depth in the wet subsoil. De Rooij (1995) interpreted this reversal of the moisture profile as an indication that the flow regimes in the dry and wet soil differed. He postulated that flow in the wet subsoil was Darcian and the fingers dissipated. Research is now shifting from investigations of the physical processes governing preferential flow to developing application-oriented models of preferential flow under natural circumstances (e.g. Steenhuis et al, 1996). Steenhuis et al. (1994) presented a simple model to describe vertical solute movement in a finger and the thin layer between the soil surface and the finger (distribution zone). They hypothesized that different rainfall rates resulted in different finger sizes, with the water flux density in the finger (nearly) equal to the saturated hydraulic conductivity. Consequently, solutes travelled downward at a relatively high velocity irrespective of the rainfall rate. De Rooij (1995, 1996) developed an analytical steady-state model for solute transport in soils with a water-repellent top layer over a wettable subsoil with a shallow groundwater table. The distribution zone and the finger were in the water-repellent topsoil. The model accounted for the presumed finger dissipation caused by matric forces in the wettable subsoil. Although geared towards water-repellent soils, the model can also be used in wettable soils when conditions are such that fingers form in the topsoil. The models of Steenhuis et al. (1994) and de Rooij (1995, 1996) require the finger size on input. Theoretical expressions for the finger width during the early stage of wetting front instability were obtained by Saffman & Taylor (1958), Chuoke et al (1959), Philip (1975—modified by White et al, 1976), Parlange & Hill (1976), and Liu et al (1994a). Except for the one by Liu et al. (1994a), these expressions are valid only for initially very dry soils. Liu et al. (1994a) adapted the expression of Parlange & Hill (1976) for initially moist soils. Nevertheless, they retained the assumption of a nearly sharp wetting front, and therefore, the soil should still be relatively dry. While these expressions all serve to provide the initial finger size, the experiments of Glass et al (1989b) provided support for the expression of Parlange & Hill (1976) and thus, indirectly, for the expression of Liu et al (1994a). The goals of this study are to investigate experimentally the flow in a moist subsoil (finger widening or dissipation), and to combine models for solute transport in the distribution zone, the finger, and the wettable subsoil with theoretical predictions of the finger size to provide an integrated approach to assess solute leaching as a result of wetting front instability. The approach will be demonstrated on soils in two strongly
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different climatic regions. One climatic region (in The Netherlands) is humid, with 75 cm of yearly rainfall. While potential évapotranspiration slightly exceeds the rainfall during summer, approximately 30 cm infiltrates below the root zone on a yearly basis. The other climatic region (in Niger) is semiarid. Rainfall averages 60 cm a year, but is very variable and concentrated in the period May-September. The average annual potential évapotranspiration is approximately 250 cm (Sivakumar, 1989). Showers are generally short with very high intensities. MATERIALS AND METHODS Experiments The experimental set-up consisted of a transparent chamber (inner dimensions: 80 cm wide, 69 cm high, 1 cm deep) with 75 openings (4.5 mm diameter) in one of the walls (10 mm thick) through which tensiometers could be installed. The bottom contained 52 drainage outlets (4.0 mm diameter) that were filled with self-priming glass fibre material (Boll et ai, 1992) to prevent air bubbles from blocking the drainage flow. The chamber was packed with air-dry glass beads of 0.120-0.150 mm diameter by filling the chamber in layers of about 5 cm. Each layer was packed by tamping, and the top 2 cm disturbed before the next layer was added. The top 2 cm of the final layer was removed and the remaining material packed to give a level surface 64 cm above the chamber bottom. A 3 cm thick top layer of fine glass beads (< 0.038 mm diameter) was added. The surface of the top layer was covered with wire gauze to prevent disturbance during ponding. The chamber was then placed in a water-filled reservoir with the water level at 1 cm above the chamber bottom. Water infiltrated through the drainage openings and created a capillary fringe. After 24 h the chamber was taken from the reservoir and prepared for the experiment. Microtensiometers were installed and connected to pressure transducers. Each tensiometer consisted of a hypodermic needle (cut to 20 mm length, 0.70 mm outer diameter) that penetrated a conical silicon plug (15 mm long, diameter decreasing from 7 to 5 mm). A 10 mm long ceramic tube (air-entry value approximately -150 cm) of 0.8 mm inner diameter and 1.2 mm outer diameter was fitted over the needle and epoxy glued to it at the bottom end. The open tip of the ceramic tube was also closed with epoxy glue. The tensiometers were stored in deaerated water prior to installation. All but one of the tensiometer ports that were not occupied by a tensiometer were closed with silicon plugs. The one remaining open port served as an air outlet. In the course of the experiment, tensiometers could be moved to other ports as the fingers developed. One tensiometer was installed in a finger just above the interface between the dry and the prewetted material, and another tensiometer 5 cm below the interface, in the prewetted soil. A datalogger recorded pressure heads at 0.5 min intervals. At the start of the experiment, the soil surface was rapidly ponded with a dye solution (2% by volume of red fountain pen ink) in distilled water. A Mariotte-device kept the ponding depth constant at 1 cm. The infiltration rate was monitored automatically by an electronic balance that weighed the Mariotte-bottle at 0.5 min
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intervals. Drainage was collected in 17 flasks placed under the drainage outlets. Finger development was recorded on video and by photographs. The wetting front at regular time intervals was traced from the photographs.
Soils and rainfall rates Two sandy soils were selected for the modelling part of this study (Table 1). Their hydraulic properties are described by van Genuchten's (1980) parametric functions (see Appendix). The analytical model of de Rooij (1995, 1996) requires Gardner's (1958) K(h) relationship: K = Kse""h
(1)
The values of the van Genuchten parameters in Table 1 were fitted to soil water retention and unsaturated soil hydraulic conductivity data using the RETC code (Yates et ai, 1992). The shape parameter aa in equation (1) was fitted by linear regression of a series of points of ln(AT) vs h generated from the wetting K{h) curve described by the van Genuchten parameters. The points were obtained at h = 0 cm and at 0.1 increments of log(-/z) (0.1 < log(~h) < 4.2). During the fit, Ks was fixed at the measured value in Table 1. The data of the Dutch soil (Barchem) were supplied by Dr J. H. M. Wôsten of the Winand Staring Centre (Wageningen, The Netherlands). The data of the soil from Niger (Sadoré) were taken from the UNSODA database (Leij et al, 1996; see also West et al, 1984). Since only drying curves were measured, the wetting scanning curve starting at the residual water content Br was approximated by doubling the value for the main drying curve of the shape parameter a to give a„, and using the drying values for the remaining parameters (Kool & Parker, 1987). Three rainfall rates were applied to each soil. For the Barchem soil, these were assumed to be those of 60 min showers with recurrence times of 0.2, 1.0, and 25 years (Buishand & Velds, 1980). For the soil from Niger, rates were assumed to be those of
Table 1 Properties of the soils used in this study. The subsoil is bounded below by the groundwater level. Sadoré has a very deep groundwater table. Parameter Thickness (cm)
e, e,
a (cm"1) a», (cm"1) n Ks (cm day"1)
/ td
(4b)
The steady-state model of de Rooij (1995) for a single finger accounts for the groundwater-affected subsoil below the finger (Fig. 2; Ritsema et al, 1993). In that region the fingers are assumed to dissipate due to matric forces. The distribution zone is assumed to be of uniform thickness with a uniform water content. As in the model of Steenhuis et al (1994), unit gradient flow is assumed in the finger. From Rj, P, and K/, the radius of the distribution zone is calculated by requiring equal fluxes at the soil surface and through the finger: t = td
wet-
dry
t > td
; . " . • •
distribution'' zone finger
"_wet
5. In general, only the main drying curve is measured. In that case, hwe can best be set to 0J6hae (Brakensiek, 1977) and « can be given a high value. The value of a for the main wetting curve can then be found from equation (A13) or (A14). Received 10 April 1998; accepted IS December 1998
