onlinegwmodel.php:   Convergent explicit groundwater model

 The four types of groundwater modeling.

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The ONLINEGWMODEL.PHP is an explicit formulation of the two-dimensional (x-y) diffusion equation of flow in porous media, applicable to a homogeneous isotropic aquifer.

Four type of model are available, varying: a) initial condition (steady equilibrium or non-equilibrium depleted water table), (b) presence or absence of pumping, and (c) boundary type (permeable or impermeable), as described in Table 1.

 Table 1  Testing scenarios. Scenario Initial condition Pumping Boundary type A Depleted water table No Permeable B Steady-equilibrium Yes Permeable C Depleted water table No Impermeable D Steady-equilibrium Yes Impermeable

The model has 16 input values, which are described as follows:

1.  Type of model

In this section of the online calculator input data, one of the four scenarios described in Table 1 may be selected.

• Type A: Scenario A, permeable hot-start test.

• Type B: Scenario B, permeable cold-start test.

• Type C: Sscenario C, impermeable hot-start test.

• Type D; Scenario D, impermeable cold-start test.

2.   Space interval ds

The space interval represents the distance between two adjacent grid points, expressed in meters. The model considers the area of the aquifer to be a square; therefore, the space interval is specified only once. The default value is ds = 100 m.

3.   Number of grid intervals nz

The number of grid intervals multiplied by the space interval corresponds to the length of one of the sides of the square which represents the aquifer. This is a dimensionless parameter; its default value is nz = 100.

4.   Percolation from rainfall R

The rainfall percolation rate is assumed to be uniformly distributed across the entire spatial domain. This parameter is expressed in mm/yr; its default value is R = 0 mm/yr.

5.   Percolation from irrigation I

The irrigation percolation rate is assumed to be uniformly distributed across the area defined by the user (See sections 3.3.6 and 3.3.7). The percolation from irrigation is expressed in mm/yr; its default value is I = 0 mm/yr.

6.   Left location indicator for percolation from irrigation irrleft

The left location indicator marks the corner grid point (on the top left) of the partial aquifer area in which the irrigation percolation rate is to be distributed. This parameter is dimensionless; its default value is irrleft = 25.

7.   Right location indicator for percolation from irrigation irrright

The right location indicator marks the corner grid point (on the bottom right) of the partial aquifer area in which the irrigation percolation rate is to be distributed. This parameter is dimensionless; its default value is irrright = 75.

8.   Transmissivity T

The aquifer transmissivity input value is expressed in units of m2/s. The default value is T = 0.01 m2/s.

9.   Specific yield S

The specific yield is dimensionless. The default value is S = 0.1.

10.   Reference aquifer elevation href

The groundwater level before pumping starts is defined as the reference aquifer elevation href, expressed in m. The default value is href = 500 m.

11.   Reference depletion elevation hdref

The groundwater level when pumping stops is defined as the reference depletion elevation hdref, expressed in m. The default value is hdref = 400 m.

12.   Left indicator for reference depletion locleft

The left location indicator marks the grid point in which the depleted aquifer area starts. As the model considers the aquifer to have a squared area, this value needs to be inputed only once. This parameter is dimentionless, and its default value is locleft = 25.

13.   Right indicator for reference depletion locright

The right location indicator marks the grid point in which the depleted aquifer area ends. As the model considers the aquifer to have a squared area, this value needs to be inputed only once. This parameter is dimentionless, and its default value is locleft = 75.

14.   Simulation time dt

The simulation time corresponds to the time in years, during which the chosen scenario will be analyzed. The default value is dt = 20 years.

15.   Printing interval tpd

As the model calculations advance, the results are printed at selected intervals. This option allows access to not only the final result but also the progress of the calculation. The default value is tpd = 30.4375 days, which corresponds to the average duration of a month, i.e., 1/12 of 365.25 days.

16.   Pumping rate p

The groundwater discharge being pumped from the aquifer may be entered in this section, in units of L/s. The default value is p = 250 L/s for each pump in the cold-start configuration.

The input values No. 11, 12 and 13 are exclusively used for cases A or C. On the other hand, the input value No. 16 is required only for cases B and D.

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