Note

Go to the end to download the full example code

Model time discretization#

iMOD Python provides nice functionality to discretize your models into stress periods, depending on the timesteps you assigned your boundary conditions. This functionality is activated with the create_time_discretization() method.

Basics#

To demonstrate the create_time_discretization() method, we first have to create a Model object. In this case we’ll use a Modflow 6 simulation, but the imod.wq.SeawatModel and imod.flow.ImodflowModel also support this.

Note

The simulation created in this example misses some mandatory packes, so is not able to write a functional simulation. It is purely intended to describe the workings of the time_discretization method. For a fully functional Modflow 6 model, see the examples in MODFLOW6.

Wel’ll start off with the usual imports:

import numpy as np
import pandas as pd
import xarray as xr

import imod

We can discretize a simulation as follows, this creates a TimeDiscretization object under the key "time_discretization".

simulation = imod.mf6.Modflow6Simulation("example")
simulation.create_time_discretization(
    additional_times=["2000-01-01", "2000-01-02", "2000-01-04"]
)

simulation["time_discretization"]
TimeDiscretization
<xarray.Dataset>
Dimensions:              (time: 2)
Coordinates:
  * time                 (time) datetime64[ns] 2000-01-01 2000-01-02
Data variables:
    timestep_duration    (time) float64 1.0 2.0
    n_timesteps          int64 1
    timestep_multiplier  float64 1.0


To view the data inside TimeDiscretization object:

simulation["time_discretization"].dataset

<xarray.Dataset>
Dimensions:              (time: 2)
Coordinates:
  * time                 (time) datetime64[ns] 2000-01-01 2000-01-02
Data variables:
    timestep_duration    (time) float64 1.0 2.0
    n_timesteps          int64 1
    timestep_multiplier  float64 1.0


Notice that even though we specified three points in time, only two timesteps are included in the time coordinate, this is because Modflow requires a start time and a duration of each stress period. iMOD Python therefore uses three points in time to compute two stress periods with a duration.

simulation["time_discretization"].dataset["timestep_duration"]

<xarray.DataArray 'timestep_duration' (time: 2)>
array([1., 2.])
Coordinates:
  * time     (time) datetime64[ns] 2000-01-01 2000-01-02


These two stress periods use their respective start time in their time coordinate.

Boundary Conditions#

The create_time_discretization method becomes especially useful if we add boundary conditions to our groundwater model. We’ll first still have to initialize a groundwater flow model though:

gwf_model = imod.mf6.GroundwaterFlowModel()

We’ll create a dummy grid, which is used to provide an appropriate grid to the boundary condition packages.

template_data = np.ones((2, 1, 2, 2))

layer = [1]
y = [1.5, 0.5]
x = [0.5, 1.5]

dims = ("time", "layer", "y", "x")

Next, we can assign a Constant Head boundary with two timesteps:

chd_times = pd.to_datetime(["2000-01-01", "2000-01-04"])
chd_data = xr.DataArray(
    data=template_data,
    dims=dims,
    coords={"time": chd_times, "layer": layer, "y": y, "x": x},
)

gwf_model["chd"] = imod.mf6.ConstantHead(head=chd_data)

gwf_model["chd"].dataset

<xarray.Dataset>
Dimensions:        (time: 2, layer: 1, y: 2, x: 2)
Coordinates:
  * time           (time) datetime64[ns] 2000-01-01 2000-01-04
  * layer          (layer) int64 1
  * y              (y) float64 1.5 0.5
  * x              (x) float64 0.5 1.5
Data variables:
    head           (time, layer, y, x) float64 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
    print_input    bool False
    print_flows    bool False
    save_flows     bool False
    observations   object None
    repeat_stress  object None


We’ll also assign a Recharge boundary with two timesteps, which differ from the ConstantHead boundary:

rch_times = pd.to_datetime(["2000-01-01", "2000-01-02"])
rch_data = xr.DataArray(
    data=template_data,
    dims=dims,
    coords={"time": rch_times, "layer": layer, "y": y, "x": x},
)

gwf_model["rch"] = imod.mf6.Recharge(rate=rch_data)

gwf_model["rch"].dataset

<xarray.Dataset>
Dimensions:        (time: 2, layer: 1, y: 2, x: 2)
Coordinates:
  * time           (time) datetime64[ns] 2000-01-01 2000-01-02
  * layer          (layer) int64 1
  * y              (y) float64 1.5 0.5
  * x              (x) float64 0.5 1.5
Data variables:
    rate           (time, layer, y, x) float64 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
    print_input    bool False
    print_flows    bool False
    save_flows     bool False
    observations   object None
    repeat_stress  object None


We can now let iMOD Python figure out how the simulation’s time should be discretized. It is important that we provide an endtime, otherwise the duration of the last stress period cannot be determined:

endtime = pd.to_datetime(["2000-01-06"])

simulation_bc = imod.mf6.Modflow6Simulation("example_bc")
simulation_bc["gwf_1"] = gwf_model

simulation_bc.create_time_discretization(additional_times=endtime)

simulation_bc["time_discretization"].dataset

<xarray.Dataset>
Dimensions:              (time: 3)
Coordinates:
  * time                 (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-04
Data variables:
    timestep_duration    (time) float64 1.0 2.0 2.0
    n_timesteps          int64 1
    timestep_multiplier  float64 1.0


Notice that iMOD Python figured out that the two boundary conditions, both with two timesteps, should lead to three stress periods!

Specifying extra settings#

The TimeDiscretization package also supports other settings, like the amount of timesteps which Modflow should use within a stress period, as well as a timestep multiplier, to gradually increase the timesteps modflow uses within a stress period. This can be useful when boundary conditions change very abruptly between stress periods. These settings are set by accessing their respective variables in the dataset.

times = simulation_bc["time_discretization"].dataset.coords["time"]

simulation_bc["time_discretization"].dataset["timestep_multiplier"] = 1.5
simulation_bc["time_discretization"].dataset["n_timesteps"] = xr.DataArray(
    data=[2, 4, 4], dims=("time",), coords={"time": times}
)

simulation_bc["time_discretization"].dataset

<xarray.Dataset>
Dimensions:              (time: 3)
Coordinates:
  * time                 (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-04
Data variables:
    timestep_duration    (time) float64 1.0 2.0 2.0
    n_timesteps          (time) int64 2 4 4
    timestep_multiplier  float64 1.5


Total running time of the script: (0 minutes 0.093 seconds)

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