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The geometrical conceptualisation and the unsaturated and saturated zone models are described in more detail below.
Figure 1. Conceptual illustration of the GN1D model structure, showing one bank of the river reach only.
Geometrical Conceptualisation
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- The position of the left hand and right hand riverbanks. The groundwater model uses the positions of the left and right banks to determine when overbank flow events occur.
- Manning's N and the link slope. Manning's N and the slope parameters can be used, if desired, to generate a streamflow rating curve from the cross section. Alternatively, the user can calculate and input their own rating curve.
Figure 2. Cross-section conceptualisation.
Groundwater Model Geometry
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- The subsections start either side of the riverbanks, as the groundwater model does not extend underneath the river.
- The left and right extents of the subsections are implemented as no flow boundaries.
- The depth of the subsections (z-coordinate) is defined by the user and is implemented as a no-flow boundary.
- The initial groundwater table height is constant across the subsections and is set by the user.
Figure 3. Example illustrating the representation of a cross-section within the groundwater model using 4 subsections per bank (grey shading).
Subsection height calculation
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- Kvsat – vertical saturated hydraulic conductivity
- – the initial soil moisture content (volumetric fraction)
- – the saturated soil moisture content (volumetric fraction)
- Save – average capillary suction at the wetting front
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Diffuse infiltration takes as input a time series of rainfall (or other diffuse source) intensities. The Mein and Larson equations model diffuse infiltration in two stages as illustrated in Figure 4 (Mein and Larson, 1973). The first stage predicts the volume of water that will infiltrate before the soil surface becomes saturated. From this point, surface runoff begins and the infiltration capacity is predicted by the Green-Ampt equation.
Figure 4. Infiltration rate as a function of time for steady rainfall.
Additional assumptions:
- The depth of ponded water at the surface is negligible
- The rainfall is of constant intensity until run-off begins.
- The soil is a homogeneous medium.
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Equation 1 is derived from Darcy's law using conservation of mass and assuming that transmissivity is homogeneous (constant) and isotropic (equal in all directions).
Figure 5. Illustration of the finite difference scheme.
The GN1D model solves equation (1) for groundwater head using an explicit finite difference scheme (illustrated in Figure 5):
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The GN1D model settings and parameters are described in Table 1. Typical values of the parameters for the Mein-Larson infiltration equations are given in Table 2.
Table 1. GN1D model settings and parameters.
Component | Variable | Symbol | Typical Units | Description |
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Geometry | River to no-flow boundary | None | m | The distance from the left and right hand river banks to the groundwater no-flow boundary |
Geometry | Divisions per bank | None | The number of subdivisions per bank | |
Geometry | Aquifer floor | None | m | The Y-coordinate of the aquifer basement (no-flow boundary). Uses the coordinate system defined by the cross section. |
Saturated Zone Model | Transmissivity | m2/day | The rate at which groundwater flows horizontally through an aquifer. The transmissivity for horizontal flow of an aquifer with saturated thickness and saturated horizontal conductivity is: | |
Saturated Zone Model | Specific yield | fraction (0…1) | The volumetric fraction that an aquifer will yield when all water is allowed to drain out of it under the force of gravity: | |
Saturated Zone Model | Initial groundwater table height | m | The initial groundwater table height at time step 0. | |
Unsaturated Zone Model | Saturated soil moisture content | fraction (0…1) | The volumetric fraction of water that an aquifer will hold when it is saturated, equivalent to porosity. | |
Unsaturated Zone Model | Initial soil moisture content | fraction (0…1) | The initial (time step 0) soil moisture content of the unsaturated zone as volumetric fraction of the total volume. | |
Unsaturated Zone Model | Saturated vertical hydraulic conductivity | m/day | The rate at which water moves vertically through saturated media. | |
Unsaturated Zone Model | Average capillary suction at the wetting front | m | The average capillary suction (head) at the wetting front as defined by Mein and Larson (1973). | |
Unsaturated Zone Model | Extinction depth | None | m | The maximum depth below the ground surface at which evapotranspiration can occur. |
Table 2. Average values of Green-Ampt parameters by USDA soil texture class (adapted from Rawls et al., 1983).
USDA Soil-Texture Class | Hydraulic Conductivity (cm/day) | Wetting-Front Suction Head (cm) | Porosity (Volumetric fraction) | Water Retained at Field Capacity (Volumetric fraction) | Water Retained at Wilting Point (Volumetric fraction) |
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Sand | 144.48 | 4.9 | 0.437 | 0.062 | 0.024 |
Loamy Sand | 35.97 | 6.1 | 0.437 | 0.105 | 0.047 |
Sandy Loam | 13.11 | 11 | 0.453 | 0.19 | 0.085 |
Loam | 3.96 | 8.89 | 0.463 | 0.232 | 0.116 |
Silt Loam | 7.92 | 16.99 | 0.501 | 0.284 | 0.135 |
Sandy Clay Loam | 1.83 | 22 | 0.398 | 0.244 | 0.136 |
Clay Loam | 1.22 | 21.01 | 0.464 | 0.31 | 0.187 |
Silty Clay Loam | 1.22 | 27 | 0.471 | 0.342 | 0.21 |
Sandy Clay | 0.61 | 24 | 0.43 | 0.321 | 0.221 |
Silty Clay | 0.61 | 29.01 | 0.479 | 0.371 | 0.251 |
Clay | 0.3 | 32 | 0.475 | 0.378 | 0.265 |
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Each time step, the GN1D model requires the river stage, which is calculated by the link using a rating curve. Other inputs are configured by the user and are summarised in Table 3.
Table 3. GN1D model data requirements, including typical units.
Component | Data Requirements | Comments |
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Cross section | Cross section X-Y coordinates (m) | Required. |
Potential Evapotranspiration (PET) | Time series of values (mm/day) | Optional |
Extraction Bore | Time series of values (ML/day) | Optional |
Injection Bore | Time series of values (ML/day) | Optional |
Diffuse Recharge | Time series of values (mm/day) | Optional |
Direct Diffuse Recharge | Time series of values (mm/day) | Optional |
Observation Bore | X-coordinate (m) | Optional |
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Mein, R.G., C.L. Larson (1973) Modeling infiltration during a steady rain, Water Resources Research, 9(2), 384-394.
Rawls, W. J., Brakensiek, D. L., & Miller, N. (1983). Green-Ampt infiltration parameters from soils data. Journal of hydraulic engineering, 109(1), 62-70. doi:10.1061/(ASCE)0733-9429(1983)109:1(62).