The existing Lake package of MODFLOW2005 ((MerrittAndKonikow2000)) has been implemented in iMOD. With this package it is possible to compute lake stages in relation to the groundwater head. Given a bathymetry of the lake, iMOD will assign the lake to the appropriate model layers and assign the correct conductances to the lake. The SFR can be connected to locations where a lake is defined to route water in- and from a lake.
The implementation of the LAK package in iMOD is straightforward as several IDF files (and or constant values) need to be specified. iMOD computes the Lake Identifications and Lake conductances underneath and along the sides of the Lakes. In that same process, iMOD can adjust some of the geohydrologic parameters, such as top- and bottom elevation of model layers as well as permeability values. It is assumed that the position and spatial extent of the lake volume is defined by the specification of a volume of inactive cells within a three dimensional model grid. Because the model grid is used to define the lake volume, the lateral and vertical grid dimensions must be appropriately chosen so that the spatial extent and bathymetry of the lake are defined with the necessary accuracy. In some cases this may require a finer horizontal discretization in the vicinity of the lake and a finer vertical discretization than would be necessary to simulate heads in the aquifer. iMOD will modify the vertical discretization internally, this is explained the following figure.
Suppose a Lake is considered that intersects two model layers, the user enters the bathymetry of the lake (\(L_B\)). Whenever the lake bathymetry is lower than the top of a model layer (\(Z_T\)) and higher than the bottom of that model layer (\(Z_B\)) the bottom of the lake is supposed to be in that particular model layer. The bottom of a model layer contains an existing interbed with thickness \(D_C\) as well. For the Lake package it is essential that the elevation of the model layers describe the bathymetry of the Lake as these are used to compute the table with depth, area, and volume relations. iMOD will adjust the bottom of a model layer to reflect the bathymetry and corrects for the removed aquifer and/or increased thickness of the interbed. In case there is an interbed underneath the Lake, iMOD will increase the permeability of that interbed such that the vertical resistance of that interbed remains identical though its thickness has been increased (\(\underline {D}_C>D_C\)). In case the lake bathymetry intersects the interbed itself, nothing is changed.
In case there is no interbed, the permeability that existed underneath the Lake bathymetry and in the same model layer, will be added to the layer below such that the transmissivity for (\(\underline {D}_Z\))remains identical to the sum of the original two model layers. The permeability of the model layer underneath will be increased or decreased which depends on the permeability fraction between the two model layers. Furthermore, the vertical resistance of the removed aquifer (\(\underline {C}_L\)), is added to the Lake resistance.
The side conductances (\(L_C\)) are the sum of resistances of a) the lake itself and b) the resistance through the subsoil.
There are some build-in limitations and assumptions:
• The RCH and EVT packages need to be assigned to model layer 0, which means they will be assigned to the upper active model layer. This is necessary in case a lake or part of lake dries up and blocks any recharge to the underlying aquifer;
• iMOD does not support the usage of sub lakes;
• the numbering of the lakes needs to be unique but it is not necessary to number them continuously. The lake number can have the format of a real number (e.g. 1.2 or 1.43) instead of an integer. Usage of integers is preferred as any connection to the SFR needs to be specified in the SFR package by an integer. iMOD will reassign a unique lake number internally, but the original lake number will be displayed in the LAK-package (*.lak);
• theta is the time weighting factor for computing lake stages during transient time steps. A theta of 0.5 represents the average lake stage during a time step. In iMOD the lake package is configured with a theta of -1.0 that represents the lake stage at the end of the time step; Moreover, a negative THETA applies for a SURFDEPTH that decreases the lakebed conductance for vertical flow across a horizontal lakebed caused both by a groundwater head that is between the lakebed and the lakebed plus SURFDEPTH and a lake stage that is also between the lakebed and the lakebed plus SURFDEPTH. This method provides a smooth transition from a condition of no groundwater discharge to a lake, when groundwater head is below the lakebed, to a condition of increasing groundwater discharge to a lake as groundwater head becomes greater than the elevation of the dry lakebed. The method also allows for the transition of seepage from a lake to groundwater when the lake stage decreases to the lakebed elevation. Values of SURFDEPTH ranging from 0.01 to 0.5 have been used successfully in test simulations. SURFDEP is configured by default to a value of 0.25.
• the interaction between the lake and groundwater is saved in the BDGLAK and is a per cell lumped volume.
• inspect the *.LST-file for more detailed information on total water balances per lake and in- and/or outflow to streams that are connected;
• the LAK package is very sensitive to non-convergence, a quasi steady-state approach and/or a transient implementation with small time steps is recommended.
• no solute transport is supported.