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ex-gwf-twri.py.
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TWRI
This problem is described in McDonald and Harbaugh (1988) and duplicated in Harbaugh and McDonald (1996). This problem is also is distributed with MODFLOW-2005 (Harbaugh, 2005) and MODFLOW 6 (Langevin and others, 2017).
Initial setup
Import dependencies, define the example name and workspace, and read settings from environment variables.
[1]:
import os
import pathlib as pl
import flopy
import git
import matplotlib.pyplot as plt
import numpy as np
from flopy.plot.styles import styles
from modflow_devtools.misc import get_env, timed
# Example name and workspace paths. If this example is running
# in the git repository, use the folder structure described in
# the README. Otherwise just use the current working directory.
sim_name = "ex-gwf-twri01"
try:
root = pl.Path(git.Repo(".", search_parent_directories=True).working_dir)
except:
root = None
workspace = root / "examples" if root else pl.Path.cwd()
figs_path = root / "figures" if root else pl.Path.cwd()
# Settings from environment variables
write = get_env("WRITE", True)
run = get_env("RUN", True)
plot = get_env("PLOT", True)
plot_show = get_env("PLOT_SHOW", True)
plot_save = get_env("PLOT_SAVE", True)
Define parameters
Define model units, parameters and other settings.
[2]:
# Scenario parameter units - make sure there is at least one blank line before next item
# add parameter_units to add units to the scenario parameter table
parameter_units = {"recharge": "$ft/s$"}
# Model units
length_units = "feet"
time_units = "seconds"
# Model parameters
nper = 1 # Number of periods
nlay = 5 # Number of layers
ncol = 15 # Number of columns
nrow = 15 # Number of rows
delr = 5000.0 # Column width ($ft$)
delc = 5000.0 # Row width ($ft$)
top = 200.0 # Top of the model ($ft$)
botm_str = "-150.0, -200.0, -300.0, -350.0, -450.0" # Layer bottom elevations ($ft$)
strt = 0.0 # Starting head ($ft$)
icelltype_str = "1, 0, 0, 0, 0" # Cell conversion type
k11_str = "1.0e-3, 1.0e-8, 1.0e-4, 5.0e-7, 2.0e-4" # Horizontal hydraulic conductivity ($ft/s$)
k33_str = (
"1.0e-3, 1.0e-8, 1.0e-4, 5.0e-7, 2.0e-4" # Vertical hydraulic conductivity ($ft/s$)
)
recharge = 3e-8 # Recharge rate ($ft/s$)
# Static temporal data used by TDIS file
perlen = 8.640e04
nstp = 1
tsmult = 1.0
tdis_ds = ((perlen, nstp, tsmult),)
# parse parameter strings into tuples
botm = [float(value) for value in botm_str.split(",")]
k11 = [float(value) for value in k11_str.split(",")]
k33 = [float(value) for value in k33_str.split(",")]
icelltype = [int(value) for value in icelltype_str.split(",")]
# Create TWRI Model Boundary Conditions
# Constant head cells are specified on the west edge of the model
# in model layers 1 and 2 `(k, i, j)` = $(1 \rightarrow 2, 1 \rightarrow 15, 1)$
chd_spd = []
for k in (0, 2):
chd_spd += [[k, i, 0, 0.0] for i in range(nrow)]
chd_spd = {0: chd_spd}
# Constant head cells for MODFLOW-2005 model
chd_spd0 = []
for k in (0, 1):
chd_spd0 += [[k, i, 0, 0.0, 0.0] for i in range(nrow)]
chd_spd0 = {0: chd_spd0}
# Well boundary conditions
wel_spd = {
0: [
[4, 4, 10, -5.0],
[2, 3, 5, -5.0],
[2, 5, 11, -5.0],
[0, 8, 7, -5.0],
[0, 8, 9, -5.0],
[0, 8, 11, -5.0],
[0, 8, 13, -5.0],
[0, 10, 7, -5.0],
[0, 10, 9, -5.0],
[0, 10, 11, -5.0],
[0, 10, 13, -5.0],
[0, 12, 7, -5.0],
[0, 12, 9, -5.0],
[0, 12, 11, -5.0],
[0, 12, 13, -5.0],
]
}
# Well boundary conditions for MODFLOW-2005 model
wel_spd0 = []
layer_map = {0: 0, 2: 1, 4: 2}
for k, i, j, q in wel_spd[0]:
kk = layer_map[k]
wel_spd0.append([kk, i, j, q])
wel_spd0 = {0: wel_spd0}
# Drain boundary conditions
drn_spd = {
0: [
[0, 7, 1, 0.0, 1.0e0],
[0, 7, 2, 0.0, 1.0e0],
[0, 7, 3, 10.0, 1.0e0],
[0, 7, 4, 20.0, 1.0e0],
[0, 7, 5, 30.0, 1.0e0],
[0, 7, 6, 50.0, 1.0e0],
[0, 7, 7, 70.0, 1.0e0],
[0, 7, 8, 90.0, 1.0e0],
[0, 7, 9, 100.0, 1.0e0],
]
}
# Solver parameters
nouter = 50
ninner = 100
hclose = 1e-9
rclose = 1e-6
Model setup
Define functions to build models, write input files, and run the simulation.
[3]:
def build_models():
sim_ws = os.path.join(workspace, sim_name)
sim = flopy.mf6.MFSimulation(sim_name=sim_name, sim_ws=sim_ws, exe_name="mf6")
flopy.mf6.ModflowTdis(sim, nper=nper, perioddata=tdis_ds, time_units=time_units)
flopy.mf6.ModflowIms(
sim,
outer_maximum=nouter,
outer_dvclose=hclose,
inner_maximum=ninner,
inner_dvclose=hclose,
rcloserecord=f"{rclose} strict",
)
gwf = flopy.mf6.ModflowGwf(sim, modelname=sim_name, save_flows=True)
flopy.mf6.ModflowGwfdis(
gwf,
length_units=length_units,
nlay=nlay,
nrow=nrow,
ncol=ncol,
delr=delr,
delc=delc,
top=top,
botm=botm,
)
flopy.mf6.ModflowGwfnpf(
gwf,
cvoptions="perched",
perched=True,
icelltype=icelltype,
k=k11,
k33=k33,
save_specific_discharge=True,
)
flopy.mf6.ModflowGwfic(gwf, strt=strt)
flopy.mf6.ModflowGwfchd(gwf, stress_period_data=chd_spd)
flopy.mf6.ModflowGwfdrn(gwf, stress_period_data=drn_spd)
flopy.mf6.ModflowGwfwel(gwf, stress_period_data=wel_spd)
flopy.mf6.ModflowGwfrcha(gwf, recharge=recharge)
head_filerecord = f"{sim_name}.hds"
budget_filerecord = f"{sim_name}.cbc"
flopy.mf6.ModflowGwfoc(
gwf,
head_filerecord=head_filerecord,
budget_filerecord=budget_filerecord,
saverecord=[("HEAD", "ALL"), ("BUDGET", "ALL")],
)
return sim
def build_mf5model():
sim_ws = os.path.join(workspace, sim_name, "mf2005")
mf = flopy.modflow.Modflow(
modelname=sim_name, model_ws=sim_ws, exe_name="mf2005dbl"
)
flopy.modflow.ModflowDis(
mf,
nlay=3,
nrow=nrow,
ncol=ncol,
delr=delr,
delc=delc,
laycbd=[1, 1, 0],
top=top,
botm=botm,
nper=1,
perlen=perlen,
nstp=nstp,
tsmult=tsmult,
)
flopy.modflow.ModflowBas(mf, strt=strt)
flopy.modflow.ModflowLpf(
mf,
laytyp=[1, 0, 0],
hk=[k11[0], k11[2], k11[4]],
vka=[k11[0], k11[2], k11[4]],
vkcb=[k11[1], k11[3], 0],
ss=0,
sy=0.0,
)
flopy.modflow.ModflowChd(mf, stress_period_data=chd_spd0)
flopy.modflow.ModflowDrn(mf, stress_period_data=drn_spd)
flopy.modflow.ModflowWel(mf, stress_period_data=wel_spd0)
flopy.modflow.ModflowRch(mf, rech=recharge)
flopy.modflow.ModflowPcg(
mf, mxiter=nouter, iter1=ninner, hclose=hclose, rclose=rclose
)
oc = flopy.modflow.ModflowOc(
mf, stress_period_data={(0, 0): ["save head", "save budget"]}
)
oc.reset_budgetunit()
return mf
def write_models(sim, mf, silent=True):
sim.write_simulation(silent=silent)
mf.write_input()
@timed
def run_models(sim, mf, silent=True):
success, buff = sim.run_simulation(silent=silent)
if not success:
print(buff)
else:
success, buff = mf.run_model(silent=silent)
assert success, buff
Plotting results
Define functions to plot model results.
[4]:
# Figure properties
figure_size = (6, 6)
def plot_results(sim, mf, silent=True):
with styles.USGSMap():
sim_ws = os.path.join(workspace, sim_name)
gwf = sim.get_model(sim_name)
# create MODFLOW 6 head object
hobj = gwf.output.head()
# create MODFLOW-2005 head object
file_name = gwf.oc.head_filerecord.get_data()[0][0]
fpth = os.path.join(sim_ws, "mf2005", file_name)
hobj0 = flopy.utils.HeadFile(fpth)
# create MODFLOW 6 cell-by-cell budget object
cobj = gwf.output.budget()
# create MODFLOW-2005 cell-by-cell budget object
file_name = gwf.oc.budget_filerecord.get_data()[0][0]
fpth = os.path.join(sim_ws, "mf2005", file_name)
cobj0 = flopy.utils.CellBudgetFile(fpth, precision="double")
# extract heads
head = hobj.get_data()
head0 = hobj0.get_data()
print(head0.shape)
vmin, vmax = -25, 100
# check that the results are comparable
for idx, k in enumerate(
(
0,
2,
4,
)
):
diff = np.abs(head[k] - head0[idx])
msg = (
"aquifer {}: ".format(idx + 1)
+ f"maximum absolute head difference is {diff.max()}"
)
assert diff.max() < 0.05, msg
if not silent:
print(msg)
# extract specific discharge
qx, qy, qz = flopy.utils.postprocessing.get_specific_discharge(
cobj.get_data(text="DATA-SPDIS", kstpkper=(0, 0))[0],
gwf,
)
frf = cobj0.get_data(text="FLOW RIGHT FACE", kstpkper=(0, 0))[0]
fff = cobj0.get_data(text="FLOW FRONT FACE", kstpkper=(0, 0))[0]
flf = cobj0.get_data(text="FLOW LOWER FACE", kstpkper=(0, 0))[0]
sqx, sqy, sqz = flopy.utils.postprocessing.get_specific_discharge(
(frf, fff, flf), mf, head0
)
# modflow 6 layers to extract
layers_mf6 = [0, 2, 4]
titles = ["Unconfined aquifer", "Middle aquifer", "Lower aquifer"]
# Create figure for simulation
extents = (0, ncol * delc, 0, nrow * delr)
fig, axes = plt.subplots(
2,
3,
figsize=figure_size,
dpi=300,
# constrained_layout=True,
sharey=True,
)
for ax in axes.flatten():
ax.set_aspect("equal")
ax.set_xlim(extents[:2])
ax.set_ylim(extents[2:])
for idx, ax in enumerate(axes.flatten()[:3]):
k = layers_mf6[idx]
fmp = flopy.plot.PlotMapView(model=gwf, ax=ax, layer=k, extent=extents)
ax.get_xaxis().set_ticks([])
fmp.plot_grid(lw=0.5)
plot_obj = fmp.plot_array(head, vmin=vmin, vmax=vmax)
fmp.plot_bc("DRN", color="green")
fmp.plot_bc("WEL", color="0.5")
cv = fmp.contour_array(
head,
levels=[-25, 0, 25, 75, 100],
linewidths=0.5,
colors="black",
)
plt.clabel(cv, fmt="%1.0f")
fmp.plot_vector(qx, qy, normalize=True, color="0.75")
title = titles[idx]
letter = chr(ord("@") + idx + 1)
styles.heading(letter=letter, heading=title, ax=ax)
for idx, ax in enumerate(axes.flatten()[3:6]):
fmp = flopy.plot.PlotMapView(model=mf, ax=ax, layer=idx, extent=extents)
fmp.plot_grid(lw=0.5)
plot_obj = fmp.plot_array(head0, vmin=vmin, vmax=vmax)
fmp.plot_bc("DRN", color="green")
fmp.plot_bc("WEL", color="0.5")
cv = fmp.contour_array(
head0,
levels=[-25, 0, 25, 75, 100],
linewidths=0.5,
colors="black",
)
plt.clabel(cv, fmt="%1.0f")
# fmp.plot_discharge(
# frf, fff, flf, head=head0, normalize=True, color="0.75",
# )
fmp.plot_vector(sqx, sqy, normalize=True, color="0.75")
title = titles[idx]
letter = chr(ord("@") + idx + 4)
styles.heading(letter=letter, heading=title, ax=ax)
# create legend
ax = fig.add_subplot()
ax.set_xlim(extents[:2])
ax.set_ylim(extents[2:])
ax.set_xticks([])
ax.set_yticks([])
ax.spines["top"].set_color("none")
ax.spines["bottom"].set_color("none")
ax.spines["left"].set_color("none")
ax.spines["right"].set_color("none")
ax.patch.set_alpha(0.0)
# ax = axes.flatten()[-2]
# ax.axis("off")
ax.plot(
-10000,
-10000,
marker="s",
ms=10,
mfc="green",
mec="green",
label="Drain",
)
ax.plot(
-10000,
-10000,
marker="s",
ms=10,
mfc="0.5",
mec="0.5",
label="Well",
)
ax.plot(
-10000,
-10000,
marker="$\u2192$",
ms=10,
mfc="0.75",
mec="0.75",
label="Normalized specific discharge",
)
ax.plot(-10000, -10000, lw=0.5, color="black", label=r"Head contour, $ft$")
styles.graph_legend(ax, ncol=1, frameon=False, loc="center left")
# plt.tight_layout(h_pad=-15)
plt.subplots_adjust(top=0.9, hspace=0.5)
# plot colorbar
cax = plt.axes([0.525, 0.55, 0.35, 0.025])
cbar = plt.colorbar(plot_obj, shrink=0.8, orientation="horizontal", cax=cax)
cbar.ax.tick_params(size=0)
cbar.ax.set_xlabel(r"Head, $ft$", fontsize=9)
if plot_show:
plt.show()
if plot_save:
fpth = figs_path / f"{sim_name}.png"
fig.savefig(fpth)
Running the example
Define and invoke a function to run the example scenario, then plot results.
[5]:
def scenario(silent=True):
sim = build_models()
mf = build_mf5model()
if write:
write_models(sim, mf, silent=silent)
if run:
run_models(sim, mf, silent=silent)
if plot:
plot_results(sim, mf, silent=silent)
# Simulated heads in model the unconfined, middle, and lower aquifers (model layers
# 1, 3, and 5) are shown in the figure below. MODFLOW-2005 results for a quasi-3D
# model are also shown. The location of drain (green) and well (gray) boundary
# conditions, normalized specific discharge, and head contours (25 ft contour
# intervals) are also shown.
scenario()
<flopy.mf6.data.mfstructure.MFDataItemStructure object at 0x7f7c2d20dc10>
run_models took 56.69 ms
(3, 15, 15)
