GROUND WATER/SURFACE WATER INTERACTIONS JULY 1-3 AWRA!!3IJMMER SPECIALTY CONFERENCE 2002

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1 GROUND WATER/SURFACE WATER INTERACTIONS JULY 1-3 AWRA!!3IJMMER SPECIALTY CONFERENCE 2002 RELATIONSHE S BETWEEN SURFACE, SUBSURFACE AND GROUNDWATER COMPONENTS IN A STREAM-SANDBAR INTERACTION SYSTEM Abu Musa Md. Motaher Ahmed, Tetsuya Sum, and Tetsuro Tsujimotol ABSTRACT: The interaction between surface water and subsurface water under sandbar in a river and its relationship with groundwater flow, being treated as three-dimensional problem, has been studied by separating the subsurface water and groundwater components for various bed shapes and hydraulic conditions. Also the relationships among the subsurface water exchange ratio, bed shape and hydraulic parameters are presented on the basis of non-dimensionalized vertical 2-D numerical simulations. The exchange between surface water and subsurface water under sandbar is characterized mainly by inflow from the surface water to sandbar, which is discussed in this paper with regard to subsurface water property and vertical distribution of components at the edge of sandbar. In this study, we considered vertical water movement near the surface water edge with sandbar and conducted vertical 2-D (V2-D) numerical simulation after verification with the laboratory tracer experiments. The experiment as well as V2D simulation shows that the subsurface water components are predominant. Two separate equations showing the relationships among the subsurface water exchange ratio, bed shape and hydraulic parameters have been proposed. KEY TERMS: surface-subsurface water interaction; sandbar; V2-D model: component separation. INTRODUCTION Ahmed et nl. (2002) found that subsurface flow structures at the upstream and downstream parts of the sandbar are diverging and converging types, respectively. The characteristics of the diverging type are surface flow infiltrates to the sandbar through its upstream face and exfiltrates immediately to the pool after exchanged with subsurface water. The characteristics of the converging flow are surface flow infiltrates from pool and exchanged with subsurface water and then exfiltrates to surface water through downstream face. Here, infiltration (section A-A, Figure I) is termed as inflow condition and exfiltration (section B-B, Fig.1) is outflow condition. In this investigation, component separation is done for inflow condition only taking a representative cross-section along the subsurface flow lines observed in the previous studies. When we evaluate surface water interaction with subsurface water under sandbar, we should consider the groundwater flow, which is directly linked with the subsurface water. For many natural purposes, for example, evaluation of habitat for benthos and hypohreo and purification of surface water by the sandbar, we should know the flow rate and thickness of subsurface water exchanged only by surface water. In order to know the distribution of these two parameters, we should separate the groundwater component from the subsurface water component treating as a vertical 2-D problem. For initial understanding, we separate the components along the surface water edge with sandbar. The investigation on the separation of components is done by V2-D numerical simulation with support of the tracer experiment. Many researchers extensively used this approach in the field. Castro and Hornberger (1991) used tracer approach to study surface-subsurface water interactions in an alluviated mountain stream channel. Harvey er nl. (1996) evaluated the reliability of stream tracer approach to describe stream-subsurface water exchange. whereas Benner et nl. (1995) studied the effect of groundwater and surface water mixing on transport of solutes. In this study, tracer experiment is conducted in an experimental flume under the sinuous bed shape that represents the sandbar in a river. IRespectively, Doctoral Student, Assistant Professor. Professor, Nagoya University, Dept. of Geo- and Environmental Engineering, Furo-cho, Chikusa-ku. Nagoya , Japan, Phone: Fax: , ahmed@genv.nagoya-u.ac.jp. 359

2 A typical cross-section representing the inflow condition (Section A-A', Figure I) is schematically shown in Figure 2. which is used in the tracer experiments and V2-D numerical simulations on dimensional scale. In this figure, L is the length of surface water column;& is the length of subsurface water column; zl, is the bed elevation; H is the surface water depth with respect to the impermeable layer; /is is the surface water depth, dh is the difference between surface and subsurface water levels; hss is the subsurface water depth; /ig is the groundwater depth; qss is the subsurface water flux and 4G is the groundwater flux, x and z are x- and z-coordinates respectively. In this study. the bed surface model in Figure 2 is given according to the following sine curve z, = H + h,y m 2L sin - The objective of this investigation is mainly to discuss the variations of rhs and rn.. with different bed shapes and hydraulic conditions. Here, rh,, is the ratio of subsurface water depth to total water depth and rns. is the ratio of subsurface water flux, q.,, to total flux, 4. These two ratios are explained in this paper as the subsurface water exchange ratio and may be expressed as Figure 1. Interaction between surface and subsurface water in a river with alternate sandbar; a) Plane view, b) Section A-A' (inflow condition) and c) Section B-B' (outflow condition) surf*ce water bvcl H Subrurfdce water H~dh Groundwater impermeable layer Figure 2. Schematic diagram of a typical cross-section showing the inflow problem Figure 3. Non-dimensionalized description of the inflow problem 360

3 VERTICAL 2-D SIX1LZ.ATION In order to simulate the problems of separating the subsurface and ground\\ater components and to establish generalized relationships among subsurface \Later exchange ratio. bed shape and hydraulic parameters. a non-dimensionalized ~ertic31 2DW2-D) model is used. The governing non-dimensionalized equation of the model based on 2-D Darcy theory can be written as follow: (3 I in = : + p/pg ; o is the hydraulic potential..y* =.Y/ L is the non-dimensionalized.v-distance. = z / L is the non-dimensionalized :-distance. p is the pressure. pis the specific gravity of nater and g is the acceleration Z' due to gravity. The non-dimensionalized J and?' components of Darcy flux is defined as in which q, and q, are the x- and x- components of Darcy flux. respectively and * indicates the non-dimensionalized values, k is the hydraulic conductivity. In numerical simulation, it is assumed that flow is steady state. bottom impervious layer is horizontal and the distribution of sand is homogeneous and isotropic. The boundary conditions followed in the numerical simulation are: A-B: B-C: C-D D-E E-A a@*/az*= 0 (impermeable = H*-d/i* p = z *@ = 0, subsurface water = H *(subsurface water at the surface water edge with = H *(groundwater) Under these boundary conditions, governing equation (eq.3) is solved using Finite Difference Method on the staggered grid. The superscripts * and ** are used to define the non-dimensionalized parameters. All scale parameters and axises are non-dimensionalized by dividing them with L, however, only /I, is non-dimensionalized by dividing it with H and L. The non-dimensionalized parameters are as follows: The non-dimensionalized description of the inflow problem with parameters is shown in Figure 3. which is similar to Figure 2 but the parameters are non-dimensionalized and used as the numerical set-up of this investigation. In this set-up. a and non-dimensional length both are considered to be unity. Here /I,* is the aspect ratio of the stream and /I.*" is the ratio of surface water depth to total water depth at the surface water edge. dh* is the average gradient of the subsurface water table. It can be assumed that h,* and H* represents the non-dimensioanlized bed shape. whereas /I,** and d/i* represents the nondimensionalized hydraulic conditions. In order to separate the subsurface water and groundwater components. numerical tracer is introduced in the V2D simulation and the tracer's path line indicates the 'separation line'. Putting the numerical tracer at the point E as shown in Figure 2 or in Figure 3, we obtain the separation lines by adjoining the tracer's relative positions in the computational grid cells (Sumi et al. 2002). The approximate movement of the tracer can be depicted in Figure 2 or in Figure 3. The tracer's movement is detected by the distribution of pore water velocity vector. The.v- and x- components of pore water velocity may be expressed as: 361

4 ~ 0.6 in which ne is the effective porosity of the porous medium. RESULTS AND DISCUSSION The V2-D model is verified by comparison between the calculation with dimension and the tracer experiment, which is described in details in Sumi er nl. (2002). The results are compared with respect to the distribution of subsurface water potentials and components separation line and the comparisons for a case is shown in Figure 4. The agreement between experiment and V2-D simulation is found reasonably satisfactory. Figure 4a or 4h shows that the contour lines of the subsurface water potentials are inclined under surface water, which shows 2-D flow patterns. But under the subsurface water table (x>40cm), contour lines are almost parallel which indicates one-dimensional flow trend and this property agrees well with the Dupuit's assumption for 50<x<80cm. At inflow region, due to sinuous bed shape, surface water generates most of the inflow fluxes those flows through the subsurface layer and the bed shape governs the direction of flow. It is also envisaged that the geometric conditions as a function of h,, H and L determines the distribution of rh, and rqss values. sa N 20 Suhurfacr wafer table N x) W x (cm) x (cm) a) Experiment b) Numerical Figure 4. Distribution of subsurface water potentials (Sumi et nl. 2002) Relationships of rhrr and rqss with Bed Shape and Hydraulic Parameters As h,*, h,**, H* and dh* represents the bed shape and hydraulic parameters, attempts have been made to correlate these parameters with rh,, and rqss.the plots of rh, values against h,* with different H* for a fixed value of dh* are shown in Figure 5a. This figure shows that rhss is greater with smaller H* and vice-versa and increases with h,*. This happens because increase of H* makes shorter the bed curvature under surface water for which the groundwater depth becomes higher. On the other hand, increase of h,* makes longer the bed curvature under surface water and as a result subsurface water depth becomes higher. The similar plots of r,fs,shows the same trend as of rhur which is evident from Figure 5h. The plots of r,,, against dh* with different h,* show that rh, is less sensitive to the average gradient of subsurface water table, dh* (Figure 6a). The relationships show that rhs increases with increasing dh* and for higher h,*, rh, is nearly the same. Another plots of rf,.cs against dh* with different H* also confirmed that for larger H*, rh,, increases with dh* and for smaller H*, r,,>, is nearly the same. The similar plots of rqss also shows its less sensitivity to dh* (Figure 6b) and revealed that rqas decreases with increasing of dh* and magnitude is larger for higher /I,* and lower H*. However, the decreasing trend is greater for lower h,* and larger H*. _c I u th'=l.' /I,* h, * 362

5 Figure 5a. Plot of r,,,$ against h,* (dh*=0.25) Figure 5b. Plot of r9rs against H* (dh*=0.25) I, I dh* Figure 6a. Plots of r,,,, against dh* (H*=1.5) dh* Figure 6b. Plots of rqas against dh* (H*=1.5) Based on the trend and the sensitivity of the ratios to the parameters, the functional relationships among them can be written as: But we can ignore the second term, because its effect is smaller than the effects by H* and h,* and hence eq.6 may be rewritten as: A base value of dh* (dh,* =0.25) has been selected to show the plausible relationships among rks, h,**. H* and rqss, h,**, H* and two empirical equations are derived for rks and rn.. separately. The relationships seemed to be expressed by in which exponents a,, a*, a3 and a4 are the functions of H* and can be assumed as Figure 7 shows the plots of l-rhss against I-h,** and Figure 8 shows the plots of l-r,,,t against I-h,** and good currt-lations are found to exist in both cases. The eq.7 and eq.8 satisfy the following conditions: H'+-: r,,, + h; = h, - (narrow width stream) (12) H h; +l: rhss + 1 (no groundwater) (13) It may be mentioned that the eq.10 (Figure 7) and eq.1 I (Figure 8) has less non-linear effect 363

6 .. H*=I.O 0.3 H* d H*=O I I-hs** Figure 7. Plots of l-rhs,, against I-h,** I-hs** Figure 8. Plots of against I-h,** CONCLUSIONS Separation between subsurface water and groundwater components at the surface water edge with sandbar is studied for various bed shapes under given hydraulic conditions. The non-dimensional V2-D simulation results show that rhs and r9ss are the functions of H*, k,** and dh*, however, the effect of dh* is smaller in comparison with the other parameters. Based on the simulated data, relationships of rhs and r9,s with H* and h,** are established and two equations for the inflow problems are proposed ignoring the effect of dh*. Using these two equations one can estimate the subsurface water thickness and flow rate at the surface water's edge with sandbar. The similar analysis for outflow condition may be needed for the extensive use in the horizontal 2-D analysis. REFERENCES Ahmed, A. M. M. M., Sumi, T. and Tsujimoto, T., A study on subsurface flow under an alternate sandbar in a river by numerical model and its application to the Kim River. Journal of Hydroscience and Hydraulic Engineering, JSCE, Japan (Accepted). Benner, S.G. Smart, E.W. and Moore, J.N., Metal behavior during surface-groundwater interaction. Environ. Sci. Technol., Vo1.29, pp , Silver Bow Creek, Montona. Castro, N.M. and Hornberger, G.M., Surface-subsurface water interactions in an alluviated mountain stream channel, Water Resour. Res., Vo1.27, pp Harvey, 1. W., Wagner, B.J. and Bencala, K. E., Evaluating the reliability of the stream tracer approach to characterize stream-subsurface water exchange, Water Resour. Res., Vo1.32(8), pp Sumi, T., Ahmed, A. M. M. M., and Tsujimoto, T., Separation of subsurfact: and groundwater components in a river with sandbar. Annual Journal of Hydraulic Engineering, JSCE, Vol. 46, pp , Japan. 364