HYDROLOGICAL PROCESSES Hydrol. Process. 24, 3065– 3073 (2010) Published online 29 May 2010 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/hyp.7722
Experimental study and mathematical modelling of soluble chemical transfer from unsaturated/saturated soil to surface runoff Ju-Xiu Tong,1,2 Jin-Zhong Yang,1 Bill X. Hu2 * and Ru-chao Bao1 1
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, PR China 2 Department of Geological Sciences, Florida State University, 108 Carraway Building, Tallahassee, FL 32306, USA
Abstract: A one-dimensional, two-layer solute transport model is developed to simulate chemical transport process in an initially unsaturated soil with ponding water on the soil surface before surface runoff starts. The developed mathematical model is tested against a laboratory experiment. The infiltration and diffusion processes are mathematically lumped together and described by incomplete mixing parameters. Based on mass conservation and water balance equations, the model is developed to describe solute transport in a two-zone layer, a ponding runoff zone and a soil mixing zone. The two-zone layer is treated as one system to avoid describing the complicated chemical transport processes near the soil surface in the mixing zone. The proposed model was analytically solved, and the solutions agreed well with the experimental data. The developed experimental method and mathematical model were used to study the effect of the soil initial moisture saturation on chemical concentration in surface runoff. The study results indicated that, when the soil was initially saturated, chemical concentration in surface runoff was significantly (two orders of magnitude) higher than that with initially unsaturated soil, while the initial chemical concentrations at the two cases were of the same magnitude. The soil mixing depth for the initially unsaturated soil was much larger than that for the initially saturated soil, and the incomplete runoff mixing parameter was larger for the initially unsaturated soil. The higher the infiltration rate of the soil, the greater the infiltration-related incomplete mixing parameter. According to the quantitative analysis, the soil mixing depth was found to be sensitive for both initially unsaturated and saturated soils, and the incomplete runoff mixing parameter was sensitive for initially saturated soil but not for the initially unsaturated soil; the incomplete infiltration mixing parameter behaved just the opposite. Some suggestions are made for reducing chemical loss from runoff. Copyright 2010 John Wiley & Sons, Ltd. KEY WORDS
ponding water; two-layer model; chemical concentration in surface runoff; unsaturated/saturated soil; incomplete mixing parameters; soil mixing depth
Received 14 August 2009; Accepted 24 March 2010
INTRODUCTION Chemical transfer from soil to surface runoff during rainfall and irrigation periods decreases the efficiency of the applied chemical and deteriorates the quality of the surface water environment. The problem has become a serious issue for concern (Baker et al., 1978, 1982; Baker and Laften, 1982; Russo, 1991; Zhang et al., 1997, 1999; Walton et al., 2000; Wallach et al., 1988a, 2001; Wallach, 1991; Wallach and Shabtai, 1993; Gao et al., 2004, 2005; Mulqueen et al., 2004; Hesterberg et al., 2006; Yoshinaga et al., 2007; Tong and Yang, 2008). It is required to predict chemical transfer from soil to surface runoff for developing the corresponding management plans for preventing or reducing surface runoff and subsequent pollution. The soluble chemical transfer from soil to surface runoff is composed of many complex processes, and the processes are hardly separable in practice. To reduce the complexity, many investigators have lumped various * Correspondence to: Bill X. Hu, Department of Geological Sciences, Florida State University, 108 Carraway Building, Tallahassee, FL 32306, USA. E-mail:
[email protected] Copyright 2010 John Wiley & Sons, Ltd.
transport mechanisms together. The mixing zone (also called mixing layer) theory (Ahuja et al., 1981a; Ahuja, 1982) is one popular and simple method. The conventional mixing zone theory assumes that there exists a region below the soil surface in which surface water, soil solution and infiltrating water are assumed to mix completely and instantaneously, no chemical is transferred into that region from the soil below and the mixing layer depth is constant (Steenhuis and Walter, 1980; Emmerich et al., 1989). Based on the observations that the degree of interaction between rain water and soil water decreases exponentially with soil depth, Ahuja et al. (1981a) proposed the concept of an effective depth of interaction (EDI), within which the degree of mixing is uniform and same as the soil surface condition. The studies by Ahuja and Lehman (1983) and Zhang et al. (1997) indicated that the observed mixing layer depth was much shallower than the depth obtained from curve-fitting of the mixing layer models, and so the modelling results significantly deviated from the experimental data. Snyder and Woolhiser (1985) also concluded that the complete mixing model might only be appropriate when the infiltration rates were high. So, Ahuja (1982), Ahuja and
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Lehman (1983) and Heathman et al. (1985, 1986) simulated the chemical transport from soil to runoff using an incomplete mixing model. Based on the mass conservation law in EDI, Wang et al. (1998, 1999) established the soil chemical and runoff interaction model and further extended the incomplete non-uniform mixing theory. The incomplete mixing theory solves the problem of soil interaction depth limitation well. In the application of the method to fields, however, much attention has been paid to the chemical transport in saturated soil. In most studies, ponding–runoff is assumed to be the initial condition (Ahuja, 1982, 1990; Ahuja and Lehman, 1983; Heathman et al., 1985, 1986; Wallach et al., 1988b, 2001; Wallach and Genuchten, 1990; Wallach, 1993; Zhang et al., 1997; Gao et al., 2004, 2005). In the field, runoff could occur only when the ponding water reaches a certain depth (Steenhuis and Walter, 1980; Zhang et al., 1999; Cao et al., 2005). Gao et al. (2004) conducted laboratory experiments to study the effect of ponding water on soil surface on the soluble chemical transfer from soil to the surface runoff. Their experimental soil was initially saturated with certain depth of ponding water on the soil surface. Therefore, the process of ponding water increase is ignored. Moreover, Gao et al. (2004) did not consider the infiltration water during a rainfall event. On the other hand, Walter et al. (2007) considered the infiltration of water during the soil solute release into runoff, but they did not consider the ponding water on the soil surface. Therefore, a more complete process of chemical transfer from soil to runoff was not considered in the above studies. The process includes soil saturation, infiltration and water ponding on the soil surface at a later time. In this article, the incomplete mixing theory was applied to develop a two-layer model for soluble chemical transfer from soil to surface runoff in an initially unsaturated soil, where soil saturation, infiltration and water ponding were all considered. A ponding mixing zone of pre-runoff process was considered with our simulated rainfall. The model was verified with our experimental runoff data in initially unsaturated soil. In order to investigate the rule of incomplete mixing parameters and find ways to reduce chemical loss of soil, the model was also applied to our initially saturated experimental soil after some simplification. Comparison of results for initially unsaturated and saturated soils was made, which could provide quantitative analysis for the control of soluble chemical loss of fertilizer in the field under the condition of irrigation and drainage. MATHEMATICAL MODEL DEVELOPMENT A simple two-layer model, shown in Figure 1, is considered in this study. The upper layer is called the whole mixing layer, which includes the soil mixing zone (Ahuja et al., 1981a) and the surface ponding–runoff zone. In an unsaturated soil, the ponding–runoff layer is not a fixed initial condition but a process that is dependent on rainfall and infiltration. Similar to the assumptions made by Ahuja et al. (1981b) and Govindaraju et al. (1996), Copyright 2010 John Wiley & Sons, Ltd.
Figure 1. Sketch of the simple two-layer model
chemicals in the soil mixing layer are the only sources of chemical constituents in infiltration and runoff water, and the chemicals are considered to transfer only vertically. The chemicals in the soil mixing zone could move into the underlying soil through the interface between them and the infiltrated water. At the same time, the chemicals in the underlying layer could also move into the soil mixing zone through the mass diffusion process because the chemical concentration in the underlying soil is higher than that in the mixing soil zone. The ‘net’ chemical flux from the soil mixing zone into the underlyiong soil layer is expressed as iCw , where i is the water infiltartion flux (cm min1 ) and Cw is the chemical concentration in the soil mixing zone (µg cm3 ). Here, we should point out that the Cw is a function of time. is the percentage of the ‘net’ chemical flux after abstracting the upward mass diffusion. At the interface between the ponding–runoff and the soil mixing zones, the ejection of soil water by rainfall impact (Hairsine and Rose, 1991; Chen et al., 1996; Zhang et al., 1997; Heilig et al., 2001; Gao et al., 2003, 2004, 2005; Lei et al., 2006; Walker et al., 2007) is considered in this study. An incomplete mixing parameter ˛ (0 < ˛ 1) was adopted to describe the incomplete solute mixing in the ponding–runoff zone. The solute concentration in this zone is ˛Cw . To simplify the complicated chemical transport processes near the soil surface, the chemical concentration in every zone is assumed to be uniform, but it is different from one zone to another. The two zones are considered as a whole mixing layer, so the study system was called a ‘simple two-layer model’. In the whole mixing layer, according to mass conservation, we obtain the following equation: Mw D Cw [˛hw hmix s C hmix s ]
1
where Mw is the soluble chemical mass per unit area in water phase (µg cm2 ), hw is the water depth in the whole mixing layer (cm), hmix is the water depth in the soil mixing layer (cm) and s is the saturated volumetric water content in the soil mixing zone (cm3 cm3 ). If we assume that the solute chemical concentration in the rainfall water is zero, we can also obtain the following equation according to mass conservation: d[Mw t] D iCw t ˛qCw t dt
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STUDY ON SOLUBLE CHEMICAL TRANSFER
where q is the specific discharge rate of the overland flow (cm min1 ) and t is the time (min). Equations (1) and (2) provide the mathematical modelling of mass conservations in the ‘static’ and kinetic conditions in the whole mixing layer. The developed mathematical relationships will be experimentally and numerically studied below.
EXPERIMENTAL STUDY We design a sandbox laboratory experiment to test the mathematical model developed above. The experimental soil was fine sand from the banks of the Yangtse River. The experimental soil was dried, ground and sieved. The subsoil was gravel sieved to 5–10 mm and was used as filter layer. The experimental design is shown in Figure 2. A sand box with internal dimensions, 100 cm x ð 30 cm y ð 40 cm (z) was made of steel with stainless paint. There was a rectangular hatch on one side of the end wall, and a V-shaped trench made of Plexiglas was attached to the hatch to catch the runoff at the height of 25 cm from the box bottom. The box was packed with 5 cm of gravel at the bottom and covered by a nylon screen of 120 holes in1 . The gravel layer was used to allow the drainage water to smoothly flow out the box and the nylon screen was used to prevent the experimental soil particles from flowing into the gravel during the infiltration process. The experimental soil with a certain thickness was filled on the nylon screen. There was still some void space from the soil top to the bottom of the rectangular hatch, which was used to simulate the ponding–runoff zone. Because the saturated infiltration rate of sand was high, two drainage holes were made at the box bottom, as shown in Figure 2. The drainage outlets at the two holes could be used to control the bottom water depth during the experiment. In this study, the average bulk density of the soil was 1Ð47 g cm3 , and saturated soil water content was 0Ð443 cm3 cm3 . The experiments were conducted under two conditions: the initially unsaturated condition and initially saturated condition.
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For the initially unsaturated experiment, the experimental soil was prepared in the following way. Based on the obtained soil’s original water content, an additional amount of water was uniformly mixed with the soil to achieve the initial volumetric water content for the experiment. Certain amount of the KCl was added to the water before the spray. For the initially saturated experiment, the fieldobtained and treated soil was filled into the sandbox. The soil saturation was achieved by a slow spray of the KCl solution into it until the soil became totally saturated. The height of drainage outlet was set at a height of 25 cm above the box bottom to prevent drainage before the soil was saturated. After the entire soil box was saturated, water in the soil box was drained through the drainage outlet until a uniform distribution of soil water and chemicals in the soil box was achieved and the concentration of KCl in soil water was very close to the concentration of the solution applied. Thus, the wetted saturated soil was in equilibrium condition. The rainfall intensities were set to be 0Ð097 and 0Ð098 cm min1 for initially unsaturated and saturated sand, respectively. Rainfall was generated by a cuboid type simulator, with inserted 8# hypodermic needles on the undersurface of the simulator and drops of 8# hypodermic needles in diameter falling through the simulator at a height of 120 cm above the soil surface. Distilled water was used for the rainfall, so the chemical content of the water was low. The distilled water was pumped into the simulator by an YZ1515X type fixedflux pump, as shown in Figure 2. The ponding water above the soil surface was gradually increased until the water level reached the rectangular hatch and the maximum depth of ponding water was obtained and the surface runoff would start to flow out through the hatch. For each rainstorm, surface runoff was sampled for analysis after the start of the runoff. The sampling interval was 2 min for an initial certain time period after the runoff started, which was then increased to 3 or 5 min depending on the runoff flow rate. Later, samples were typically collected at even
Figure 2. Schematic of experimental setup (not to scale) Copyright 2010 John Wiley & Sons, Ltd.
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longer intervals as the dynamic behaviour of the system waned. The sediment in the runoff samples was neglected in experiments because of the zero slope of soil surface. The KCl concentrations of the various collected runoff samples were systematically measured through the measurements of their electrical conductivity (EC) using a conductivity meter Model DDS-11A. Preliminary work indicated that the EC of the KCl solution is linearly related to its concentration. When a runoff sample’s EC is large, the relationship between EC and KCl concentration can be described as c D 0Ð5952 ð EC 8Ð4593; otherwise, as c D 0Ð5039 ð EC 1Ð0367 when EC
