Experimental and Modeling Investigation of Shallow Water Table Fluctuations in Relation to Reverse Wieringermeer Effect ()
1. Introduction
Shallow groundwater systems (SGS) are important as a source of water, for sustenance of stream base flow and of wetland and riparian ecosystems [1]. They have been recognized to have effects on a broad variety of earth system processes [2,3]. Accordingly, the proper management of these valuable groundwater resources requires an accurate quantification of their recharge rates. Such quantification is not easy to handle due to the dynamic nature of these systems having a very fast response time to hydrologic change owing to their closeness to soil surface [1]. In fact, many researchers reported rapid and disproportionate water table rise in response to rainfall events observed in shallow groundwater systems [4-6]. They showed that shallow water tables can often rise disproportionately compared to the volume of infiltrated water. This rise has been attributed by numerous researchers to one of two major phenomena. The first, known as the Lisse effect, occurs when infiltration caused by intense rain seals the surface soil layer to airflow, trapping and compressing air under pressure in the unsaturated zone [7,8]. For a comprehensive outline of the Lisse effect, the reader is referred to [8]. The second is the reverse Wieringermeer effect (RWE) dealing with the case where the capillary fringe extends from the water table almost to the ground surface leading to a limited or no storage capacity in the zone between water table and soil surface as well as a specific yield approaching zero value. In these conditions the pores within the capillary fringe are saturated and the addition of a very small amount of water relieves the tensions in the capillaries resulting in a rapid and high water table rise to the land surface [9,10]. The specific yield was defined as the volume of water that an aquifer releases from storage per unit surface area of aquifer per unit decline in the water table [11].
It was demonstrated through numerical studies and laboratory as well as field investigations that, under RWE conditions, the estimation of water table responses to recharge events based on the maximum or ultimate specific yield, which can be estimated from an equilibrium soil water profile, is erroneous and always underestimates the rate and total amount of water table rise [12, 13]. Gillham [9] pointed out that the shallow water table response to added water could be explained by considering the specific yield above a shallow water table to be variable, with values decreasing as the water table approaches ground surface.
In view of the facts mentioned above, the aim of this work is threefold: 1) to investigate experimentally shallow groundwater responses to surface and sub-surface recharge events using two soil types (sandy and clayey), 2) to verify the applicability of RWE concept under these experimental conditions, 3) to develop a quantitative analysis based on hysteresis model in order to simulate the experimental results.
2. Theoretical Background
Figure 1 depicts the hypothetical moisture profiles above a rising deep water table (WT1) and shallow water table (WT2). These profiles are represented by the moisture retention curve of the soil with the assumption that static equilibrium conditions prevailed. After a change of water level, the water table WT1, which was initially at depth d, will rise by dh to a new level d′. It is assumed that the static equilibrium profile is re-attained instantaneously. Further, the flow is assumed to be one-dimensional and no water flux at the bottom boundary. In these conditions, the dotted area A representing the volume of water per unit area that is added to storage due to the water-level rise from d to d′ is equal to Sydh, where Sy is the specific yield of the soil.
Consider now the case of a shallow water table WT2 being initially at the level d″. This depth is not great enough to allow moisture content at land surface to reach the value of residual moisture content. In this case, the dotted area A representing the water yield is less than Sydh (Figure 1). The discrepancy between actual yield and that calculated on knowledge of Sy and dh has been observed to increase as depth to water table decreases [9, 11,12]. This phenomenon, referred to as the reverse Wieringermeer effect, is reflected by a nearly instantaneous rise in water level in response to only a small amount of infiltration.
The dotted area A can be mathematically expressed as:
(1)
where θs is saturated water content and θ(h) is the water content-pressure head relationship. The minus sign is used to account for the negative pressure head.
The van Genuchten model (hereafter VG) of water retention relationship [14] was used in the present study to describe the boundary drying and wetting curves. This model assumes that the main drying and wetting retention curves can be described accurately by the expression:
(2)
where θr is residual water content, α, m, n are fitting parameters, with m = 1 – 1/n. Replacing Equation (2) in Equation (1) yields:
(3)
In order to account for hysteresis effect, we assume that between the initial water table level d and the final depth d’, the groundwater will follow a scanning wetting curve starting from a preceding drying curve (reversal point). Scanning curves can be determined experimentally by a series of wetting and drying experiments. Such measurements are extremely time-consuming and delicate to carry out. Therefore, a theory is needed to estimate the water-retention function for any drying and wetting loop based on the envelope of main drying and wetting curves. Numerous models have been developed in order to describe the hysteretic behavior of a particular soil [15-18]. In the present study we used the modified Kool and Parker model [17] developed by Huang et al. [18]. This model of simple formulation uses α, n, θsd = θsw and θrd = θrw as variables (d and w denote for drying and wetting, respectively). Additionally, αw, nw and αd, nd are assigned the same values in describing various wetting and drying scanning curves. In this model, the relationship of θ (h) for the ith-order scanning curve with no pumping effect can be obtained using θsw(i) and θrw(i) or θsd(i) and θrd (i). Hence, once θs(i) and θr(i) are defined, Equation (3) is integrated numerically using the trapezoidal rule of integration in order to estimate the water supply amount AH (H for hysteresis) between water table depths d and d′. Equation (3) becomes:
(4)
where θs(i) and θr(i) are saturated and residual water contents, respectively, corresponding to the ith-order scanning curve, αw, nw, mw are fitting parameters and h pressure head.
3. Material and Methods
3.1. Soil Column and Measurement System Set up
Soils of two textures were used for this research: i) Toy-
Figure 1. Conceptualized moisture profiles above a deep water table (WT1) and a shallow water table (WT2). CF: capillary fringe; A: water recharge; θr: residual water content; θs: saturated water content (adapted from Healy and Cook [11]).
oura sand from Toyoura, Yamaguchi, Japan, having a grain size ranges between 0.02 mm to 0.30 mm with a mean value of 0.125 mm, and ii) Chiba light clay (Chiba LiC) collected at a depth of 80 cm in an experimental farm at Chiba Prefectural, Agricultural and Forestry Research Center. Particle-size analyses for the Chiba LiC soil showed percentage distributions of 52.8/20.7/26.5 for sand/silt/clay, respectively.
In the present study, laboratory measurements of θ(h) in the drying and wetting processes for Toyoura sand and Chiba LiC were carried out using the hanging method [19]. The measurements of drying and wetting curves were done separately on different soil samples. In relevance to our experimental conditions, described above, we restricted our analysis in the range of pressure 0 - 100 cm H2O. The experimental data were then fitted using the VG model. Figure 2 shows both measured and simulated data of the main water retention curves of Toyoura sand and Chiba LiC. It can be seen clearly that the two pathways (i.e. drying and wetting) produce curves that are not identical. The water content in the drying curve is higher for a given matric potential than that in the wetting branch depicting the hysteretic nature of both soils. The VG model fitted fairly well (R2 = 0.99) the observed main wetting and drying curves in the case of Toyoura sand and Chiba LiC soils. The θ(h) curves are useful to estimate the height of the capillary fringe defined as the region between h = 0 and h = ha where ha is the pressure
Figure 2. Water retention curves of Toyoura sand and Chiba light clay.
head at which the first pore drains. Hence, Figure 2 shows that for Chiba LiC soil, the capillary fringe extends, in the drying process, to approximately 15 cm while in the case of Toyoura sand this zone extends to almost 40 cm above the water table level.
Toyoura sand and Chiba LiC soils were packed homogenously into two acrylic columns with 50 cm length and 7.5 cm inner diameter. The Toyoura sand column was equipped with 17 acrylic resin porous cups along the profile (Figure 3). The Chiba soil column was equipped with 11 ceramic porous cups made of very thin, small and sensitive ceramics in order to insure a reasonably rapid response time. In both columns, the porous cups were connected to a series of pressure transducers with a 0 to 100 kPa range, for continuous measurement of pressure head at each of the monitoring locations. The water table level was monitored by means of a water manometer. Two Mariotte tubes with 5 cm and 0.7 cm inner diameters have been used for soil saturation process and for water recharge from the bottom side of the column, respectively.
3.2. Experimental Procedure
Two experiments (Exp 1 and Exp 2) have been conducted using Toyoura sand and Chiba light clay, respect-
Figure 3. Schematic diagram of the laboratory experimental apparatus.
tively. The Exp 1 consisted of performing the total of four experimental runs numbered 1 through 4. During the runs 1 and 2, water table was positioned initially at 20 cm and 40 cm, respectively, by using a drip point. Then, various amounts of water have been added from the top side of the soil column, as simulated rainfall events (surface recharge). The hydrostatic condition in the entire soil column after each rainfall event formed the initial condition for the subsequent water supply. During the runs 3 and 4, water was supplied from the bottom (subsurface recharge). In the Exp 2, the total of six experimental runs numbered 5 through 10, have been carried out. Almost, the same procedure used in Exp 1 was reproduced in Exp 2 during which water table was set initially at 15 cm, 30 cm and 70 cm depths.
4. Results and Discussion
4.1. Water Table Fluctuations in Response to Recharge Events
In all experimental runs during the experiments 1 and 2, the water table rise after each water supply event was isolated and plotted against water applied amount (Figure 4). Linear trend lines have been fitted to each of the experimental runs and regression equations have been developed.
In all experimental runs, recharge events and their water table responses exhibited a linear relationship of the form: WTL = a·R, where WTL (cm) is the water table level, a (dimensionless) is a regression coefficient and R (cm) is the recharge amount. In the case of Toyoura sand, the regression equation developed from the water table response during the experimental run 1, shows that the addition of 1 mm water as a rainfall event brought about
Figure 4. Correlations between cumulative added water events as surface and sub-surface recharge and the corresponding change in water table level in the case of Toyoura sand (WT at 20 cm) and Chiba LiC (WT at 15 cm) soils. TS: Toyoura sand; CH: Chiba LiC.
120 mm water table rise for initial water table position at 20 cm depth, reflecting a reverse Wieringermeer response type. Considering the specific yield of Toyoura sand used in this experiment of 0.3 [20], multiplied by the water table rise of 120 mm would result in 36 mm of recharge water compared with the 1 mm of simulated rain that actually has been added during the run 1. This shows that the specific yield method gives erroneous estimates of recharge if used under RWE conditions.
Similar to the case of Toyoura sand, the water table increase during Chiba LiC experiment was also highly correlated to rainfall in all experimental runs (R2 ³ 0.97). Compared to Toyoura sand, the water table rise in Chiba LiC experiment was less pronounced suggesting the soil type effect on groundwater response. With respect to water table responses to sub-surface recharge events, it can be seen, as shown in Figure 4, that in the case of Toyoura sand, sub-surface recharge caused a disproportionate water table rise. In the case of Chiba LiC, the water table increased linearly in response to sub-surface water input, with remarkably a lower magnitude than that observed for Toyoura sand.
4.2. Pressure Head Responses to Recharge Events
Figure 5 illustrates the pressure head profiles at several times across Toyoura sand and Chiba LiC columns, for