Chapter 2
In the introduction of Chapter 2, an example of a cross-sectional model of thin rainwater lenses (recall Figure 2.1) was given. It was shown that when the con- ductance for the drains and ditches in the model with a low grid resolution was based on the classical method of McDonald and Harbaugh (1988), the resistance to groundwater-surface water interaction was tremendously underestimated. Con- sequently, the upward flow of saline groundwater was overestimated, which had important implications for the quantification of water fluxes and salt loads to the surface water system.
However, little attention was given to the implications of the overestimation of the upward flux of saline groundwater regarding the estimation of the thickness of the thin rainwater lenses. For the estimation of the thickness of the thin rain- water lenses, the upward flux from the low grid resolution model can be used as a boundary condition for a more detailed model (downscaling), which can be used to determine the thickness of the thin rainwater lenses. Eeman et al. (2011) and De Louw et al. (2011) also used such detailed models in their investigations of thin rainwater lenses.
Here, for illustration purpose, the upward flux from the low-resolution model of the example in the introduction of Chapter 2 is used in combination with a downscaled model to estimate the thickness of the thin rainwater lens. The an- alytical solution of Maas (2007) is used as a downscaled model. This analytical solution is based on the interface approach (Chapter 4). The analytical solution of Maas (2007) requires the hydraulic conductivity (K), groundwater recharge (N ), drain distance (Ldr), the densities of the fresh and saline groundwater (ρf and
ρs) and the upward (saline) groundwater flow rate (S) as input parameters for
estimating the thickness of the rainwater lens. These parameters can all be taken from the model of Figure 2.1, i.e., K = 0.01 m d−1, N = 0.0003 m d−1, L
dr= 10
m, ρf = 1000 kg m−3and ρs= 1025 kg m−3. S is taken as the specific discharge
towards the drain in the model with a low grid resolution, and therefore depends on which kind of conductance method is used. The two conductance methods that were used in the example (the conductance methods of McDonald and Harbaugh (1988) and De Lange (1999); see Figure 2.9) are used here, and S is taken from from these two models with a low grid resolution.
resembles the thickness of the rainwater lens (approximated as 50% of the max- imum standardized concentration in the model) in the reference example, when S is taken from the low grid resolution model using the conductance expression of De Lange (1999). Eeman et al. (2011) also showed nice comparisons between their numerical models and the analytical solution of Maas (2007), which indicates that S was appropriate. In contrast, in case the conductance method of McDonald and Harbaugh (1988) is used, there is no flux towards the drains, as all water is discharged by the ditches. In case the upward flow towards the ditches is taken as representative flux for S, the thickness of the lens is greatly underestimated.
Figure 6.1: Scaled concentrations (shown in color, from 0 (minimum concentration) - 1 (maximum concentration)) of the model with a high resolution at x = 480 - 485 m of the example of the introduction of Chapter 2. The black and white dashed lines indicate the estimated thickness of the freshwater lens using the analytical solutions of Maas (2007) when S is taken from the upscaled model using the conductance expressions of (De Lange, 1999) and McDonald and Harbaugh (1988), respectively. The drain tile is located at x = 5 m.
This example shows that, in theory, a regional scale investigation of the thick- ness of shallow rainwater lenses can be made by combining a regional scale ground- water model using the conductance expression of De Lange (1999) in conjunction with the downscaled of Maas (2007). In practice, however, many complexities introduce uncertainty in this approach. For example, the thickness of the thin rainwater lens shows seasonal variation (De Louw et al., 2013a), and mixing pro- cesses in the unsaturated zone likely influence the salinity of the groundwater recharge (De Louw, 2013), which both pose questions to the appropriateness of the analytical solution of Maas (2007). Nevertheless, it is evident that the conduc- tance expression of De Lange (1999) leads to a much better estimate of the flux of upward flowing saline groundwater compared to classical expressions for the
conductance, and therefore a better boundary condition for downscaled models. Chapter 5
This example considers a groundwater flow model of a freshwater lens in an un- confined coastal aquifer, with the key parameters as shown in Figure 6.2. The freshwater lens is bordered at the land-ocean boundary by an intertidal area, and the groundwater flow is influenced by tides. In Chapter 5, it was described that under these conditions, tides influence the time-averaged hydraulic heads near the shore and that under certain conditions this effect can also have an important influence further inland.
thickness of the freshwater lens (H): 45 m tidal amplitude (A): 1.5 m, slope intertidal area (α): 0.04 time-averaged hydraulic head: 1.05 m groundwater divide hydraulic head (h): 1.08 m controlled water level
groundwater recharge (N): 0.001 m d-1
width of the freshwater lens (L): 1000 m isotropic hydraulic
conductivity (K): 10 m d-1
dimensionless density difference (δ): 0.025
Figure 6.2: Concept of a freshwater lens subjected to tides in a homogeneous aquifer.
In case the tidal effect is neglected in the model, the groundwater divide will be exactly halfway the freshwater lens (0.5L). The hydraulic head at this location can be calculated using Equation 5.111using N = 0.001 m d−1, K = 10.0 m d−1,
L= 1000 m and δ = 0.025, which results in 0.78 m. Equation 5.17 using A = 1.5 m and α = 0.04 indicates that the tides have a significant effect on the time- averaged hydraulic head at the high tide mark (1.05 m). Furthermore, Equation 5.11 shows that at the location 0.5 L, the hydraulic head (1.08 m) caused by these tidal conditions is also significantly higher (0.3 m) compared to a a situation with a static mean sea level. Moreover, the freshwater lens is 12 m thicker.
Now, suppose that field data is available to calibrate the model, then ignoring the effect of tides in the model calibration results in erroneous estimation of other parameters. For example, K should be decreased with a factor of 2 or N should be increased by a factor of 2 to yield an hydraulic head of 1.08 m at the location 0.5L. Such erroneous model parameters may then influence other model outcomes, such as quantifying saltwater intrusion rates (Watson et al., 2010; Webb and Howard,
2011) or free convection of seawater as a result of marine inundations (Gingerich and Voss, 2014).
Although this example is simple and idealized, it does indicate the importance of quantitative support when doing assumptions in models, even when data is available for calibration.