get_transmissivities_example.py

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#     section: flopy
#     authors:
#       - name: Andrew Leaf
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# # Computing transmissivity-weighted averages
#
# Demonstration of `flopy.utils.get_transmissivities` method
# for computing open interval transmissivities (for weighted averages of heads or fluxes)
# In practice this method might be used to:
#
# * compute vertically-averaged head target values representative of observation wells of varying open intervals (including variability in saturated thickness due to the position of the water table)
# * apportion boundary fluxes (e.g. from an analytic element model) among model layers based on transmissivity.
# * any other analysis where a distribution of transmissivity by layer is needed for a specified vertical interval of the model.

# +
import sys
from tempfile import TemporaryDirectory

import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np

import flopy

print(sys.version)
print(f"numpy version: {np.__version__}")
print(f"matplotlib version: {mpl.__version__}")
print(f"flopy version: {flopy.__version__}")
# -

# ### Make up some open interval tops and bottoms and some heads
# * (these could be lists of observation well screen tops and bottoms)
# * the heads array contains the simulated head in each model layer,
#   at the location of each observation well (for example, what you would get back from HYDMOD if you had an entry for each layer at the location of each head target).
# * make up a model grid with uniform horizontal k of 2.

sctop = [-0.25, 0.5, 1.7, 1.5, 3.0, 2.5]  # screen tops
scbot = [-1.0, -0.5, 1.2, 0.5, 1.5, -0.2]  # screen bottoms
# head in each layer, for 6 head target locations
heads = np.array(
    [
        [1.0, 2.0, 2.05, 3.0, 4.0, 2.5],
        [1.1, 2.1, 2.2, 2.0, 3.5, 3.0],
        [1.2, 2.3, 2.4, 0.6, 3.4, 3.2],
    ]
)
nl, nr = heads.shape
nc = nr
botm = np.ones((nl, nr, nc), dtype=float)
top = np.ones((nr, nc), dtype=float) * 2.1
hk = np.ones((nl, nr, nc), dtype=float) * 2.0
for i in range(nl):
    botm[nl - i - 1, :, :] = i
botm

# ### Make a flopy modflow model

# +
# temporary directory
temp_dir = TemporaryDirectory()
model_ws = temp_dir.name

m = flopy.modflow.Modflow("junk", version="mfnwt", model_ws=model_ws)
dis = flopy.modflow.ModflowDis(
    m, nlay=nl, nrow=nr, ncol=nc, botm=botm, top=top
)
upw = flopy.modflow.ModflowUpw(m, hk=hk)
# -

# ### Get transmissivities along the diagonal cells
# * alternatively, if a model's coordinate information has been set up, the real-world x and y coordinates could be supplied with the `x` and `y` arguments
# * if `sctop` and `scbot` arguments are given, the transmissivites are computed for the open intervals only
#   (cells that are partially within the open interval have reduced thickness, cells outside of the open interval have transmissivities of 0). If no `sctop` or `scbot` arguments are supplied, trasmissivites reflect the full saturated thickness in each column of cells (see plot below, which shows different open intervals relative to the model layering)

r, c = np.arange(nr), np.arange(nc)
T = flopy.utils.get_transmissivities(
    heads, m, r=r, c=c, sctop=sctop, scbot=scbot
)
np.round(T, 2)

m.dis.botm.array[:, r, c]

# ### Plot the model top and layer bottoms (colors)
# open intervals are shown as boxes
# * well 0 has zero transmissivities for each layer, as it is below the model bottom
# * well 1 has T values of 0 for layers 1 and 2, and 1 for layer 3 (K=2 x 0.5 thickness)

fig, ax = plt.subplots()
plt.plot(m.dis.top.array[r, c], label="model top")
for i, l in enumerate(m.dis.botm.array[:, r, c]):
    label = f"layer {i + 1} bot"
    if i == m.nlay - 1:
        label = "model bot"
    plt.plot(l, label=label)
plt.plot(heads[0], label="piezometric surface", color="b", linestyle=":")
for iw in range(len(sctop)):
    ax.fill_between(
        [iw - 0.25, iw + 0.25],
        scbot[iw],
        sctop[iw],
        facecolor="None",
        edgecolor="k",
    )
ax.legend(loc=2)

# ### example of transmissivites without `sctop` and `scbot`
# * well zero has T=0 in layer 1 because it is dry; T=0.2 in layer 2 because the sat. thickness there is only 0.1

T = flopy.utils.get_transmissivities(heads, m, r=r, c=c)
np.round(T, 2)

try:
    # ignore PermissionError on Windows
    temp_dir.cleanup()
except:
    pass