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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 <img src="AW&H2015.tiff" style="float
Step1:  Setup a New Directory and Change Paths
For this tutorial, we will work in a new subdirectory underneath the directory where the notebook is located. We can use some fancy Python tools to help us manage the directory creation. Note that if you encounter path problems with this workbook, you can stop and then restart the kernel and the paths will be reset.
Step2:  Define the Model Extent, Grid Resolution, and Characteristics
It is normally good practice to group things that you might want to change into a single code block.  This makes it easier to make changes and rerun the code.
Step3:  Create the MODFLOW Model Object
Create a flopy MODFLOW object
Step4:  Discretization Package
Create a flopy discretization package object
Step5:  Basic Package
Create a flopy basic package object
Step6:  Upstream Weighting Package (like Layer Property Flow Package)
Create a flopy layer property flow package object
Step7:  Well Package
Create a flopy output control object
Step8:  Output Control
Create a flopy output control object
Step9:  Newton-Raphson Solver
Create a flopy pcg package object
Step10:  Recharge Package
Create a flopy pcg package object
Step11:  Writing the MODFLOW Input Files
Before we create the model input datasets, we can do some directory cleanup to make sure that we don't accidently use old files.
Step12:  Yup.  It's that simple, the model datasets are written using a single command (mf.write_input).
Check in the model working directory and verify that the input files have been created.  Or if you might just add another cell, right after this one, that prints a list of all the files in our model directory.  The path we are working in is returned from this next block.
Step13:  Running the Model
Flopy has several methods attached to the model object that can be used to run the model.  They are run_model, run_model2, and run_model3.  Here we use run_model3, which will write output to the notebook.
Step14:  Post Processing the Results
To read heads from the MODFLOW binary output file, we can use the flopy.utils.binaryfile module. Specifically, we can use the HeadFile object from that module to extract head data arrays.
Step15:  Look at the bottom of the MODFLOW output file (ending with a *.list) and note the water balance reported.
Step16:  Now Change Starting Heads to 2000 m
Step17:  How do the two versions of starting head compare?  What does this conceptualization need to keep this problem from being a relative result?
Part b.
Take one of the models you designed in part (a) and replace one constant flux node on either the river or swamp boundary with a specified head node equal to 1000 m. Run the model to steady state. Compare the results with those in
part (a) and with P4.3a. Explain the differences.
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Python Code:
%matplotlib inline
import sys
import os
import shutil
import numpy as np
from subprocess import check_output
# Import flopy
import flopy
Explanation: <img src="AW&H2015.tiff" style="float: left">
<img src="flopylogo.png" style="float: center">
Problem P4.5 Hubbertville Areal Model Perimeter Boundary Conditions
In Problem P4.3 in Anderson, Woessner and Hunt (2015), we are asked to construct an areal 2D model to assess impacts of pumping.  The town of Hubbertville is planning to expand its water supply by constructing a pumping well in an unconfined gravel aquifer (Fig. P4.3). The well is designed to pump constantly at a rate of 20,000 m3/day. Well construction was halted by the State Fish and Game Service who manage the Green Swamp Conservation area. The agency claimed that pumping would “significantly reduce” groundwater discharge to the swamp and damage waterfowl habitat. The town claimed the fully penetrating river boundary to the north and the groundwater divide located near the center of the valley would prevent any change in flow to the swamp.
Building on P4.3, in Problem P4.5 on page 175 we are asked to replace the constant head boundaries at both the river and swamp in Problem P4.3a with specified flow boundaries. Use the water balance results from Problem P4.3a to calculate the boundary fluxes at the river and swamp. Note that all the boundaries of the model are now specified flow boundaries, including the zero flow lateral boundary conditions.
Part a.
Run the model with specified flow boundaries using starting heads of 1000 m and then a second time with starting heads of 2000 m. (Note: Some GUIs will warn that using all specified flow boundaries can create errors, or will not
permit the model to execute under these conditions). Compare the results with those in P4.3a and explain the differences.
In this notebook, we will again work through the problem using MODFLOW and the Python tool set Flopy. Notice how much code is reused from P4.1 because the variable names remained the same.
<img src="P4.3_figure.tiff" style="float: center">
Below is an iPython Notebook that builds upon the Python Notebook created in Problem P4.3. See the Github wiki associated with this Chapter for information on one suggested installation and setup configuration for Python and iPython Notebook.
[Acknowledgements: This tutorial was created by Randy Hunt and all failings are mine.  The exercise here has benefited greatly from the online Flopy tutorial and example notebooks developed by Chris Langevin and Joe Hughes for the USGS Spring 2015 Python Training course GW1774]
Creating the Model
Using the same steps as in P4.3, we will create a simple groundwater flow model by following the tutorial included on the Flopy website.  We will make a few small changes  so that the tutorial works with our file structure.
Visit the tutorial website here.
Setup the Notebook Environment and Import Flopy
Load a few standard libraries, and then load flopy.
End of explanation
# Set the name of the path to the model working directory
dirname = "P4-5_Hubbertville"
datapath = os.getcwd()
modelpath = os.path.join(datapath, dirname)
print 'Name of model path: ', modelpath
# Now let's check if this directory exists.  If not, then we will create it.
if os.path.exists(modelpath):
    print 'Model working directory already exists.'
else:
    print 'Creating model working directory.'
    os.mkdir(modelpath)
Explanation: Setup a New Directory and Change Paths
For this tutorial, we will work in a new subdirectory underneath the directory where the notebook is located. We can use some fancy Python tools to help us manage the directory creation. Note that if you encounter path problems with this workbook, you can stop and then restart the kernel and the paths will be reset.
End of explanation
# model domain and grid definition
# for clarity, user entered variables are all caps; python syntax are lower case or mixed case
# In a contrast to P4.1 and P4.2, this is an areal 2D model
LX = 4500.
LY = 11000.   # note that there is an added 500m on the top and bottom to represent the boundary conditions,that leaves an aqufier lenght of 10000 m  
ZTOP = 1030.  # the system is unconfined so set the top above land surface so that the water table never > layer top
ZBOT = 980.
NLAY = 1
NROW = 22
NCOL = 9
DELR = LX / NCOL  # recall that MODFLOW convention is DELR is along a row, thus has items = NCOL; see page XXX in AW&H (2015)
DELC = LY / NROW  # recall that MODFLOW convention is DELC is along a column, thus has items = NROW; see page XXX in AW&H (2015)
DELV = (ZTOP - ZBOT) / NLAY
BOTM = np.linspace(ZTOP, ZBOT, NLAY + 1)
HK = 50.
VKA = 1.
RCH = 0.001
WELLQ = 0.   #recall MODFLOW convention, negative means pumped out of the model domain (=aquifer)
print "DELR =", DELR, "  DELC =", DELC, '  DELV =', DELV
print "BOTM =", BOTM
print "Recharge =", RCH 
print "Pumping well rate =", WELLQ
Explanation: Define the Model Extent, Grid Resolution, and Characteristics
It is normally good practice to group things that you might want to change into a single code block.  This makes it easier to make changes and rerun the code.
End of explanation
# Assign name and create modflow model object
modelname = 'P4-5'
#exe_name = os.path.join(datapath, 'mfnwt.exe') # for Windows OS
exe_name = os.path.join(datapath, 'mfnwt')     # for Mac OS
print 'Model executable: ', exe_name
MF = flopy.modflow.Modflow(modelname, exe_name=exe_name, model_ws=modelpath)
Explanation: Create the MODFLOW Model Object
Create a flopy MODFLOW object: flopy.modflow.Modflow.
End of explanation
# Create the discretization object
TOP = ZTOP * np.ones((NROW, NCOL),dtype=np.float)
DIS_PACKAGE = flopy.modflow.ModflowDis(MF, NLAY, NROW, NCOL, delr=DELR, delc=DELC,
                               top=TOP, botm=BOTM[1:], laycbd=0)
# print DIS_PACKAGE  #uncomment this on far left to see information about the flopy object
Explanation: Discretization Package
Create a flopy discretization package object: flopy.modflow.ModflowDis.
End of explanation
# Variables for the BAS package
IBOUND = np.ones((NLAY, NROW, NCOL), dtype=np.int32)  # all nodes are active (IBOUND = 1)
# In this problem we have no specified heads 
print IBOUND
STRT = 1000 * np.ones((NLAY, NROW, NCOL), dtype=np.float32)  # P4.5a starting head =1000 m throughout model domain
print STRT
BAS_PACKAGE = flopy.modflow.ModflowBas(MF, ibound=IBOUND, strt=STRT)
# print BAS_PACKAGE  # uncomment this at far left to see the information about the flopy BAS object
Explanation: Basic Package
Create a flopy basic package object: flopy.modflow.ModflowBas.
End of explanation
LPF_PACKAGE = flopy.modflow.ModflowUpw(MF, laytyp=1, hk=HK, vka=VKA)  # we defined the K and anisotropy at top of file
# print LPF_PACKAGE  # uncomment this at far left to see the information about the flopy LPF object
Explanation: Upstream Weighting Package (like Layer Property Flow Package)
Create a flopy layer property flow package object: flopy.modflow.ModflowUpw.
End of explanation
STRESS_PERIOD_DATA = [
                      [0, 0, 0, -2500],   #layer, row, column, Specified flux Q from P4.3 northern BC
                      [0, 0, 1, -2500],   #remember Python indexing is zero based
                      [0, 0, 2, -2500],
                      [0, 0, 3, -2500],
                      [0, 0, 4, -2500],
                      [0, 0, 5, -2500],
                      [0, 0, 6, -2500],
                      [0, 0, 7, -2500],
                      [0, 0, 8, -2500],
                      [0, 21, 0, -2500],   #layer, row, column, Specified flux Q from P4.3 southern BC
                      [0, 21, 1, -2500],   #remember Python indexing is zero based
                      [0, 21, 2, -2500],
                      [0, 21, 3, -2500],
                      [0, 21, 4, -2500],
                      [0, 21, 5, -2500],
                      [0, 21, 6, -2500],
                      [0, 21, 7, -2500],
                      [0, 21, 8, -2500]]    
WEL_PACKAGE = flopy.modflow.ModflowWel(MF, stress_period_data=STRESS_PERIOD_DATA)  # remember python 0 index, layer 0 = layer 1 in MF
#print WEL_PACKAGE  # uncomment this at far left to see the information about the flopy WEL object
Explanation: Well Package
Create a flopy output control object: flopy.modflow.ModflowWel.
End of explanation
OC_PACKAGE = flopy.modflow.ModflowOc(MF)   # we'll use the defaults for the model output
# print OC_PACKAGE  # uncomment this at far left to see the information about the flopy OC object
Explanation: Output Control
Create a flopy output control object: flopy.modflow.ModflowOc.
End of explanation
NWT_PACKAGE = flopy.modflow.ModflowNwt(MF, headtol=0.001, fluxtol=5000, maxiterout=900) 
# print NWT_PACKAGE  # uncomment this at far left to see the information about the flopy PCG object
Explanation: Newton-Raphson Solver
Create a flopy pcg package object: flopy.modflow.ModflowNwt.
End of explanation
#In Problem P4.3 the River and Swamp were specified head BCs. MODFLOW does not include recharge added to a 
#a specified head node in its water budget.  Now that we've changed them to active nodes (IBOUND=1) these would receive 
#recharge, and our model would be out of balance if we simply plugged in the BC fluxes. Try it, you should see that
#perimeter boundary fluxes calculated from P4.3 < recharge specified in P4.5).  Therefore, we'll adjust the recharge
#array so that the perimeter BC nodes are given a recharge rate = 0.
RCH_ARRAY = RCH * np.ones((NROW, NCOL), dtype=np.float32)  # set the variable RCH specifed above for model domain
RCH_ARRAY[0, :] = 0  #don't forget arrays are zero-based!
RCH_ARRAY[-1, :] = 0  #-1 is Python for last in array
print RCH_ARRAY
RCH_PACKAGE = flopy.modflow.ModflowRch(MF, rech=RCH_ARRAY)
# print RCH_PACKAGE  # uncomment this at far left to see the information about the flopy RCH object
Explanation: Recharge Package
Create a flopy pcg package object: flopy.modflow.ModflowRch.
End of explanation
#Before writing input, destroy all files in folder to prevent reusing old files
#Here's the working directory
print modelpath
#Here's what's currently in the working directory
modelfiles = os.listdir(modelpath)
print modelfiles
#delete these files to prevent us from reading old results
modelfiles = os.listdir(modelpath)
for filename in modelfiles:
    f = os.path.join(modelpath, filename)
    if modelname in f:
        try:
            os.remove(f)
            print 'Deleted: ', filename
        except:
            print 'Unable to delete: ', filename
#Now write the model input files
MF.write_input()
Explanation: Writing the MODFLOW Input Files
Before we create the model input datasets, we can do some directory cleanup to make sure that we don't accidently use old files.
End of explanation
# return current working directory
print "You can check the newly created files in", modelpath
Explanation: Yup.  It's that simple, the model datasets are written using a single command (mf.write_input).
Check in the model working directory and verify that the input files have been created.  Or if you might just add another cell, right after this one, that prints a list of all the files in our model directory.  The path we are working in is returned from this next block.
End of explanation
silent = False  #Print model output to screen?
pause = False   #Require user to hit enter? Doesn't mean much in Ipython notebook
report = True   #Store the output from the model in buff
success, buff = MF.run_model(silent=silent, pause=pause, report=report)
Explanation: Running the Model
Flopy has several methods attached to the model object that can be used to run the model.  They are run_model, run_model2, and run_model3.  Here we use run_model3, which will write output to the notebook.
End of explanation
#imports for plotting and reading the MODFLOW binary output file
import matplotlib.pyplot as plt
import flopy.utils.binaryfile as bf
#Create the headfile object and grab the results for last time.
headfile = os.path.join(modelpath, modelname + '.hds')
headfileobj = bf.HeadFile(headfile)
#Get a list of times that are contained in the model
times = headfileobj.get_times()
print 'Headfile (' + modelname + '.hds' + ') contains the following list of times: ', times
#Get a numpy array of heads for totim = 1.0
#The get_data method will extract head data from the binary file.
HEAD = headfileobj.get_data(totim=1.0)
#Print statistics on the head
print 'Head statistics'
print '  min: ', HEAD.min()
print '  max: ', HEAD.max()
print '  std: ', HEAD.std()
#Create a contour plot of heads
FIG = plt.figure(figsize=(15,13))
#setup contour levels and plot extent
LEVELS = np.arange(989., 1005., 0.5)
EXTENT = (DELR/2., LX - DELR/2., DELC/2., LY - DELC/2.)
print 'Contour Levels: ', LEVELS
print 'Extent of domain: ', EXTENT
#Make a contour plot on the first axis
AX1 = FIG.add_subplot(1, 2, 1, aspect='equal')
AX1.set_xlabel("x")
AX1.set_ylabel("y")
YTICKS = np.arange(0, 11000, 500)
AX1.set_yticks(YTICKS)
AX1.set_title("Hubbertville contour map")
AX1.text(2000, 10500, r"River", fontsize=10, color="blue")
AX1.text(1800, 340, r"Green Swamp", fontsize=10, color="green")
AX1.contour(np.flipud(HEAD[0, :, :]), levels=LEVELS, extent=EXTENT)
#Make a color flood on the second axis
AX2 = FIG.add_subplot(1, 2, 2, aspect='equal')
AX2.set_xlabel("x")
AX2.set_ylabel("y")
AX2.set_yticks(YTICKS)
AX2.set_title("Hubbertville color flood")
AX2.text(2000, 10500, r"River", fontsize=10, color="black")
AX2.text(1800, 340, r"Green Swamp", fontsize=10, color="black")
cax = AX2.imshow(HEAD[0, :, :], extent=EXTENT, interpolation='nearest')
cbar = FIG.colorbar(cax, orientation='vertical', shrink=0.45)
Explanation: Post Processing the Results
To read heads from the MODFLOW binary output file, we can use the flopy.utils.binaryfile module. Specifically, we can use the HeadFile object from that module to extract head data arrays.
End of explanation
#look at the head in column = 4 from headobj, and then plot it
#print HEAD along a column; COL is a variable that allows us to change this easily
COL = 4
print HEAD[0,:,COL]
# we see this is what we want, but is flipped because MODFLOW's array does not = Python, so we reverse the order (flip them) and call it 
Y = np.flipud(HEAD[0,:,COL])
print Y
#for our cross section create X-coordinates to match with heads
XCOORD = np.arange(0, 11000, 500) + 250
print XCOORD
fig = plt.figure(figsize=(10, 5))
ax = fig.add_subplot(1, 1, 1)
TITLE =  'cross section of head along Column = ({0})'.format(COL)
ax.set_title(TITLE)
ax.set_xlabel('y')
ax.set_ylabel('head')
ax.set_xlim(0, 11000.)
ax.set_ylim(980.,1020.)
ax.text(10480, 998, r"River", fontsize=10, color="blue",rotation='vertical')
ax.text(300, 998, r"Green Swamp", fontsize=10, color="green",rotation='vertical')
ax.text(5300,1009., r"Groundwater Divide", fontsize=10, color="black",rotation='vertical')
ax.plot(XCOORD, Y)
Explanation: Look at the bottom of the MODFLOW output file (ending with a *.list) and note the water balance reported.
End of explanation
#in order to keep the problem unconfined we'll have to raise the top above what was set in P4.3 (=1030 m)
ZTOP = 2030.
STRT = 2000 * np.ones((NLAY, NROW, NCOL), dtype=np.float32)  # P4.5a starting head=2000 m throughout model domain
print STRT
#we have to update the MODFLOW's BAS Package with the new IBOUND array 
BAS_PACKAGE = flopy.modflow.ModflowBas(MF, ibound=IBOUND, strt=STRT)
#in order to keep the problem unconfined we'll have to raise the top above what was set in P4.3 (=1030 m)
TOP = 2030.
#in order to keep the same transmissivity we need to raise the base so the resulting saturated thickness is the same
BOT = 1980.
DIS_PACKAGE = flopy.modflow.ModflowDis(MF, NLAY, NROW, NCOL, delr=DELR, delc=DELC,
                               top=TOP, botm=BOT, laycbd=0)
# print DIS_PACKAGE  #uncomment this on far left to see information about the flopy object
#delete these files to prevent us from reading old results
modelfiles = os.listdir(modelpath)
for filename in modelfiles:
    f = os.path.join(modelpath, filename)
    if modelname in f:
        try:
            os.remove(f)
            print 'Deleted: ', filename
        except:
            print 'Unable to delete: ', filename
#Now write the model input files
MF.write_input()
print "New MODFLOW input files = ", modelfiles
print "You can check the newly created files in", modelpath
#rerun MODFLOW-NWT
silent = False  #Print model output to screen?
pause = False   #Require user to hit enter? Doesn't mean much in Ipython notebook
report = True   #Store the output from the model in buff
success, buff = MF.run_model(silent=silent, pause=pause, report=report)
#As before, let's look at the results and compare to P4-3 Part a.
#imports for plotting and reading the MODFLOW binary output file
import matplotlib.pyplot as plt
import flopy.utils.binaryfile as bf
#Create the headfile object and grab the results for last time.
headfile = os.path.join(modelpath, modelname + '.hds')
headfileobj = bf.HeadFile(headfile)
#Get a list of times that are contained in the model
times = headfileobj.get_times()
print 'Headfile (' + modelname + '.hds' + ') contains the following list of times: ', times
#Get a numpy array of heads for totim = 1.0
#The get_data method will extract head data from the binary file.
HEAD = headfileobj.get_data(totim=1.0)
#Print statistics on the head
print 'Head statistics'
print '  min: ', HEAD.min()
print '  max: ', HEAD.max()
print '  std: ', HEAD.std()
#-999.99 is the Inactive node flag so we'll use our previous contour settings
#Create a contour plot of heads
FIG = plt.figure(figsize=(15,13))
#setup contour levels and plot extent
LEVELS = np.arange(1989., 2005., 0.5)
EXTENT = (DELR/2., LX - DELR/2., DELC/2., LY - DELC/2.)
print 'Contour Levels: ', LEVELS
print 'Extent of domain: ', EXTENT
#Make a contour plot on the first axis
AX1 = FIG.add_subplot(1, 2, 1, aspect='equal')
AX1.set_xlabel("x")
AX1.set_ylabel("y")
YTICKS = np.arange(0, 11000, 500)
AX1.set_yticks(YTICKS)
AX1.set_title("Hubbertville contour map")
AX1.text(2000, 10500, r"River", fontsize=10, color="blue")
AX1.text(1800, 340, r"Green Swamp", fontsize=10, color="green")
AX1.contour(np.flipud(HEAD[0, :, :]), levels=LEVELS, extent=EXTENT)
#Make a color flood on the second axis
AX2 = FIG.add_subplot(1, 2, 2, aspect='equal')
AX2.set_xlabel("x")
AX2.set_ylabel("y")
AX2.set_yticks(YTICKS)
AX2.set_title("Hubbertville color flood")
AX2.text(2000, 10500, r"River", fontsize=10, color="black")
AX2.text(1800, 340, r"Green Swamp", fontsize=10, color="black")
cax = AX2.imshow(HEAD[0, :, :], extent=EXTENT, interpolation='nearest', vmin=1989)
cbar = FIG.colorbar(cax, orientation='vertical', shrink=0.45)
COL = 4
# recall we need to flip because MODFLOW's array does not = Python, so we reverse the order (flip them) and call it 
Y = np.flipud(HEAD[0,:,COL])
print Y
#for our cross section create X-coordinates to match with heads
XCOORD = np.arange(0, 11000, 500) + 250
print XCOORD
fig = plt.figure(figsize=(10, 5))
ax = fig.add_subplot(1, 1, 1)
TITLE =  'cross section of head along Column = ({0})'.format(COL)
ax.set_title(TITLE)
ax.set_xlabel('y')
ax.set_ylabel('head')
ax.set_xlim(0, 11000.)
ax.set_ylim(1980.,2020.)
ax.text(10480, 1998, r"River", fontsize=10, color="blue",rotation='vertical')
ax.text(300, 1998, r"Green Swamp", fontsize=10, color="green",rotation='vertical')
ax.text(5400,2006., r"Groundwater Divide", fontsize=10, color="black",rotation='vertical')
ax.plot(XCOORD, Y)
Explanation: Now Change Starting Heads to 2000 m
End of explanation
# let's use the first model of Part a so that the starting head of 1000 m is not below the bottom of the aquifer 
TOP = 1030.
BOT = 980.
#we'll set the cell in the first row and first column to a specified head (changing it's IBOUND value to -1)
IBOUND[:, 0, 0] = -1 
print IBOUND
#change the starting head to equal 1000 m
STRT = 1000 * np.ones((NLAY, NROW, NCOL), dtype=np.float32)
print STRT
#we have to update MODFLOW's BAS Package with the new IBOUND and STRT heads 
BAS_PACKAGE = flopy.modflow.ModflowBas(MF, ibound=IBOUND, strt=STRT)
print 'aquifer top =', TOP
print 'aquifer bottom =', BOT
#we have to update MODFLOW's DIS Package for the new tops and bottoms 
DIS_PACKAGE = flopy.modflow.ModflowDis(MF, NLAY, NROW, NCOL, delr=DELR, delc=DELC,
                               top=TOP, botm=BOT, laycbd=0)
#delete old files to prevent us from reading old results
modelfiles = os.listdir(modelpath)
for filename in modelfiles:
    f = os.path.join(modelpath, filename)
    if modelname in f:
        try:
            os.remove(f)
            print 'Deleted: ', filename
        except:
            print 'Unable to delete: ', filename
#Now write the model input files
MF.write_input()
print "New MODFLOW input files = ", modelfiles
print "You can check the newly created files in", modelpath
#rerun MODFLOW-2005
silent = False  #Print model output to screen?
pause = False   #Require user to hit enter? Doesn't mean much in Ipython notebook
report = True   #Store the output from the model in buff
success, buff = MF.run_model(silent=silent, pause=pause, report=report)
#As before, let's look at the results and compare to P4-3 Part a.
#imports for plotting and reading the MODFLOW binary output file
import matplotlib.pyplot as plt
import flopy.utils.binaryfile as bf
#Create the headfile object and grab the results for last time.
headfile = os.path.join(modelpath, modelname + '.hds')
headfileobj = bf.HeadFile(headfile)
#Get a list of times that are contained in the model
times = headfileobj.get_times()
print 'Headfile (' + modelname + '.hds' + ') contains the following list of times: ', times
#Get a numpy array of heads for totim = 1.0
#The get_data method will extract head data from the binary file.
HEAD = headfileobj.get_data(totim=1.0)
#Print statistics on the head
print 'Head statistics'
print '  min: ', HEAD.min()
print '  max: ', HEAD.max()
print '  std: ', HEAD.std()
#Create a contour plot of heads
FIG = plt.figure(figsize=(15,13))
#setup contour levels and plot extent
LEVELS = np.arange(1000., 1011., 0.5)
EXTENT = (DELR/2., LX - DELR/2., DELC/2., LY - DELC/2.)
#Make a contour plot on the first axis
AX1 = FIG.add_subplot(1, 2, 1, aspect='equal')
AX1.set_xlabel("x")
AX1.set_ylabel("y")
YTICKS = np.arange(0, 11000, 500)
AX1.set_yticks(YTICKS)
AX1.set_title("Hubbertville contour map")
AX1.text(2000, 10500, r"River", fontsize=10, color="blue")
AX1.text(1800, 340, r"Green Swamp", fontsize=10, color="green")
AX1.contour(np.flipud(HEAD[0, :, :]), levels=LEVELS, extent=EXTENT)
#Make a color flood on the second axis
AX2 = FIG.add_subplot(1, 2, 2, aspect='equal')
AX2.set_xlabel("x")
AX2.set_ylabel("y")
AX2.set_yticks(YTICKS)
AX2.set_title("Hubbertville color flood")
AX2.text(2000, 10500, r"River", fontsize=10, color="black")
AX2.text(1800, 340, r"Green Swamp", fontsize=10, color="black")
cax = AX2.imshow(HEAD[0, :, :], extent=EXTENT, interpolation='nearest', vmin=998.2)
cbar = FIG.colorbar(cax, orientation='vertical', shrink=0.45)
#as before let's plot a north-south cross section
COL = 4
# recall we need to flip because MODFLOW's array does not = Python, so we reverse the order (flip them) and call it 
Y = np.flipud(HEAD[0,:,COL])
#for our cross section create X-coordinates to match with heads
XCOORD = np.arange(0, 11000, 500) + 250
fig = plt.figure(figsize=(10, 5))
ax = fig.add_subplot(1, 1, 1)
TITLE =  'cross section of head along Column = ({0})'.format(COL)
ax.set_title(TITLE)
ax.set_xlabel('y')
ax.set_ylabel('head')
ax.set_xlim(0, 11000.)
ax.set_ylim(980.,1020.)
ax.text(10480, 998, r"River", fontsize=10, color="blue",rotation='vertical')
ax.text(300, 998, r"Green Swamp", fontsize=10, color="green",rotation='vertical')
ax.text(5400,1007., r"Groundwater Divide", fontsize=10, color="black",rotation='vertical')
ax.plot(XCOORD, Y)
Explanation: How do the two versions of starting head compare?  What does this conceptualization need to keep this problem from being a relative result?
Part b.
Take one of the models you designed in part (a) and replace one constant flux node on either the river or swamp boundary with a specified head node equal to 1000 m. Run the model to steady state. Compare the results with those in
part (a) and with P4.3a. Explain the differences.
End of explanation
<END_TASK>