# Model creation

## Model parameters

The model definition must be started by setting scalar parameters values in the parametres table (Figure 103).

Figure 15 parametres table to fulfill.

These parameters are typical values of the site and can be modified later in a specific study. They are defined as :

- WC, cinematic porosity

- VGA, Alpha van Genuchten (\(m^{-1}\))

- VGN, n van Genuchten

- VGR, residual saturation

- VGS, maximal saturation

- VGE, inlet pression (\(m\))

- WT, total porosity

- VM, volumic mass (kg/m³)

- DK, partition coefficient (m³/kg)

- SL, solubility limit (kg/m³)

- DLZNS, ZNS longitudinal dispersivity (m)

- DLZS, ZS longitudinal dispersivity (m)

- WM, matrix porosity

Then, the permeability field must be defined by clicking on the Model button which offers 3 choices :

- Create model with a constant permeability field value : this creates an hydrogeologic model based on an uniform permeability field, whose value must be filled in the dialog,

- Create model from a permeability field : this creates an hydrogeologic model based on a permeability field given by an external tif file, which must be selected in the dialog,

- Create model with inversion : this enables an inversion process based on measured piezometric values and pilot points, see img_inversion.

## Inversion

### Pilot points

Pilot points must first be defined in the points_pilote layer, and the zone where they belong and the measured piezometric value (altitude_piezo_mesuree) must be set. Zones must be numbered from 1 without empty number. Several pilot points can belong to the same zone.

The points_pilote layer provides the following fields :

- OGC_FID : unique ID

- nom : name of the pilot point

- groupe : group of pilot points used for correlation display

- zone : zone, used to associate pilot points with same permeability value

- altitude_piezo_mesuree : measured altitude of the water table (m)

- altitude_piezo_calculee : calculated altitude of the water table (m)

- difference_calcul_mesure : difference between calculated and measured water table altitude (m)

- permeabilite : permeability (m/s)

Note

The four attributes nom, groupe, zone and altitude_piezo_mesuree must be filled, the others will be calculated during inversion process.

It is possible to import delimited text files in QGIS (QGIS menu Layer>Add a layer>Add a delimited text layer) and do copy/paste actions between the imported layer and the points_pilote layer. To ease the copy/paste action, it is recommended to name the columns in the imported layer according to the points_pilote table columns (nom, zone, altitude_piezo_mesuree).

We provide a point_pilote.csv file which can be opened by using Layer>Add Layer>Add Delimited Text Layer (Figure 104).

Figure 16 Loading the point_pilote.csv file with Add Delimited Text Layer

The QGIS dialog must be answered by selecting the right X and Y coordinates columns (Figure 105).

Figure 17 Selecting X and Y coordinates columns in the Text Delimited dialog

The points_pilote layer can be completed by copy/paste from the loaded csv layer. Only column names with the same name as the points_pilote layer can be pasted.

At the end, the attribute table of the points_pilote layer should look like Figure 106.

Figure 18 Attributes table of the points_pilote layer

### Inversion parameters

The inversion process depends on the parameters of the hynverse_parametres table :

- infiltration : yearly mean infiltration in m/s. For heterogeneous infiltration, please enter 0 value and provide a [u_infiltration.node.sat or u_infiltration.elem.sat] file.

- icalc : calcul type (default value : 3),

- niter : maximum iteration number (default value : 20, but higher values are useful to obtain a good convergence),

- errlim : error limit : process stops when the error is less than this value (default value : 0.1 m),

- alfmin : minimal value for \(\alpha\) : process stops when \(\alpha\) is less than this value (default value : \(10^{-5}\)),

- alfa : initial \(\alpha\) value (default value : 0.5),

- terr : initial value of the maximum permissible growth rate of error (default value : 1.2) : if the growth rate of error is larger, the last iteration is not taken into account and a new one is done by dividing \(\alpha\) by 2. This can be done nbessaismax times (see below),

- nessaismax : number of possible iterations by dividing \(\alpha\) by 2 (default value : 10),

- permini : initial permeability value (default value : \(2.10^{-5}\)),

- permin : minimal permeability value (default value : \(2.10^{-7}\)),

- permax : maximal permeability value (default value : \(2.10^{-4}\)),

- nv_npp : number of closest nodes from the pilot points, used for pilot points potential estimation (default value : 4),

- nv_ppm : number of closest pilot points from mesh centers, used for meshes permeability estimation (default value : 10),

- dv_pp : radius (m) around pilot points to smooth permeability field by moving average (default value : 300 m),

- d_mesh : min length from mesh center to node with imposed potential or to existing pilot point, used to add the mesh center as pilot point (in case of an external reference potential) (default value : 100 m).

To change these parameters, select the hynverse_parametres layer, click on the edit button and open the attribute table (Figure 107).

Figure 19 Opening attribute table of the hynverse_parametres layer

Here the infiltration value must be set to \(4.75 10^{-9}\) (enter 4.75e-09 in the attribute table).

### Computation

Inversion process is launched by cliking on the Model button (Figure 108).

Figure 20 Model button

then by selecting Create model with inversion in the Model button dialog (Figure 109).

Figure 21 Model button dialog

Several layers are created :

- potentiel_reference : reference piezometric level (m), if an external reference potentiel layer has been specified,

- potentiel : calculated piezometric level (m),

- epaisseur_zs : groundwater thickness (saturated zone) (m),

- epaisseur_zns : unsaturated zone thickness (m),

- permeabilite_x : permeability on x axis (m/s),

- v_norme : Darcy velocity norm (m/s),

During the inversion process, the permeabilite_x layer is updated at each iteration. Graphics showing the convergence are also updated (Figure 110).

Figure 22 QGIS canvas with inversion graphics

The upper graphic shows the mean error between measured and estimated water table altitude. The lower graphic shows the correlation between measured and estimated water table altitude.

Finally save your mesh project by clicking to Project>Save or doing Ctrl + S