Single Reach¶
In this notebook the effect of different parameter settings of \(x\) and \(k\) is shown.
Note
This is written in old code and will be replaced later using the network model class. The other parts already use the network model class.
Initialising model¶
[1]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
[2]:
from context import fit_muskingum
from fit_muskingum import getParams
from fit_muskingum import calc_Out
from fit_muskingum import calc_C
---------------------------------------------------------------------------
ModuleNotFoundError Traceback (most recent call last)
<ipython-input-2-f10bf430f4fd> in <module>
----> 1 from context import fit_muskingum
2 from fit_muskingum import getParams
3 from fit_muskingum import calc_Out
4 from fit_muskingum import calc_C
~/checkouts/readthedocs.org/user_builds/rna/checkouts/stable/docs/context.py in <module>
5 sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), '..')))
6
----> 7 import RiverNetwork
8 import fit_muskingum
ModuleNotFoundError: No module named 'RiverNetwork'
[3]:
df = pd.read_excel('../data/example-inflow-karahan-adjusted.xlsx')
df = df.set_index('Time')
---------------------------------------------------------------------------
FileNotFoundError Traceback (most recent call last)
<ipython-input-3-eec210afa4a4> in <module>
----> 1 df = pd.read_excel('../data/example-inflow-karahan-adjusted.xlsx')
2 df = df.set_index('Time')
~/checkouts/readthedocs.org/user_builds/rna/envs/stable/lib/python3.7/site-packages/pandas/util/_decorators.py in wrapper(*args, **kwargs)
206 else:
207 kwargs[new_arg_name] = new_arg_value
--> 208 return func(*args, **kwargs)
209
210 return wrapper
~/checkouts/readthedocs.org/user_builds/rna/envs/stable/lib/python3.7/site-packages/pandas/io/excel/_base.py in read_excel(io, sheet_name, header, names, index_col, usecols, squeeze, dtype, engine, converters, true_values, false_values, skiprows, nrows, na_values, keep_default_na, verbose, parse_dates, date_parser, thousands, comment, skip_footer, skipfooter, convert_float, mangle_dupe_cols, **kwds)
308
309 if not isinstance(io, ExcelFile):
--> 310 io = ExcelFile(io, engine=engine)
311 elif engine and engine != io.engine:
312 raise ValueError(
~/checkouts/readthedocs.org/user_builds/rna/envs/stable/lib/python3.7/site-packages/pandas/io/excel/_base.py in __init__(self, io, engine)
817 self._io = _stringify_path(io)
818
--> 819 self._reader = self._engines[engine](self._io)
820
821 def __fspath__(self):
~/checkouts/readthedocs.org/user_builds/rna/envs/stable/lib/python3.7/site-packages/pandas/io/excel/_xlrd.py in __init__(self, filepath_or_buffer)
19 err_msg = "Install xlrd >= 1.0.0 for Excel support"
20 import_optional_dependency("xlrd", extra=err_msg)
---> 21 super().__init__(filepath_or_buffer)
22
23 @property
~/checkouts/readthedocs.org/user_builds/rna/envs/stable/lib/python3.7/site-packages/pandas/io/excel/_base.py in __init__(self, filepath_or_buffer)
357 self.book = self.load_workbook(filepath_or_buffer)
358 elif isinstance(filepath_or_buffer, str):
--> 359 self.book = self.load_workbook(filepath_or_buffer)
360 else:
361 raise ValueError(
~/checkouts/readthedocs.org/user_builds/rna/envs/stable/lib/python3.7/site-packages/pandas/io/excel/_xlrd.py in load_workbook(self, filepath_or_buffer)
34 return open_workbook(file_contents=data)
35 else:
---> 36 return open_workbook(filepath_or_buffer)
37
38 @property
~/checkouts/readthedocs.org/user_builds/rna/envs/stable/lib/python3.7/site-packages/xlrd/__init__.py in open_workbook(filename, logfile, verbosity, use_mmap, file_contents, encoding_override, formatting_info, on_demand, ragged_rows)
109 else:
110 filename = os.path.expanduser(filename)
--> 111 with open(filename, "rb") as f:
112 peek = f.read(peeksz)
113 if peek == b"PK\x03\x04": # a ZIP file
FileNotFoundError: [Errno 2] No such file or directory: '../data/example-inflow-karahan-adjusted.xlsx'
[4]:
t = df.index.values
I = np.array(df['Inflow'])
fig = plt.figure(figsize=(7,2.5),dpi=150)
fig.patch.set_alpha(0)
ax = fig.add_subplot(111)
for axis in ['top','bottom','left','right']:
ax.spines[axis].set_linewidth(0.5)
plt.plot(t,I,linewidth = 1 , label = 'inflow')
plt.rcParams.update({'font.size': 8, 'pgf.rcfonts' : False})
x = 0.2
k = 2
dt = 1
C0 = calc_C(k,x,dt) # k,x,dt
O0 = calc_Out(I,C0)
plt.plot(t, O0 ,'g',linewidth = 1, label = 'outflow')
plt.ylabel('Flow, $Q$ [m$^3$/s]')
plt.xlabel('Time [h]')
plt.legend();
# save to file
#plt.savefig('../thesis/report/figs/1reach.pdf', bbox_inches = 'tight')
#plt.savefig('../thesis/report/figs/1reach.pgf', bbox_inches = 'tight')
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-4-6e8c9438bf21> in <module>
----> 1 t = df.index.values
2 I = np.array(df['Inflow'])
3 fig = plt.figure(figsize=(7,2.5),dpi=150)
4 fig.patch.set_alpha(0)
5
NameError: name 'df' is not defined
The blue line is the inflow to the reach. The reach has parameters \(x = 0.2\), \(k = 2\) and \(\Delta t = 1\) The resulting outflow is shown in green.
Understanding \(k\)¶
To understand what happens the effect is of \(k\), it is varied while keeping \(x\) constant. \(x\) is fixed to 0.01 while \(k\) takes the values: 1, 3, 5, 10, 25, 50. Again \(\Delta t\) is set to 1.
[5]:
t = df.index.values
I = np.array(df['Inflow'])
length = 50
t = range(0,length,1)
I = np.append(I,np.full((1,length - len(I)),22))
fig = plt.figure(figsize=(7,2.5),dpi=150)
fig.patch.set_alpha(0)
ax = fig.add_subplot(111)
for axis in ['top','bottom','left','right']:
ax.spines[axis].set_linewidth(0.5)
plt.rcParams.update({'font.size': 8, 'pgf.rcfonts' : False})
plt.plot(t,I,linewidth = 1 , label = 'inflow')
klist = [1,3,5,10,25,50]
for k in klist:
x = 0.01
dt = 1
out = calc_Out(I,calc_C(k,x,dt))
plt.plot(t, out,linewidth = 1, label = 'outflow $k$ = ' + '{:02d}'.format(k))
plt.ylabel('Flow, $Q$ [m$^3$/s]')
plt.xlabel('Time [h]')
plt.legend();
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-5-842f2a25259a> in <module>
----> 1 t = df.index.values
2 I = np.array(df['Inflow'])
3
4 length = 50
5 t = range(0,length,1)
NameError: name 'df' is not defined
It is clear that k is related to the delay or lag of the peak. The peaks shift to the right with increasing \(k\). While the peaks shift, also the attenuation increases. Meanwhile, flow the total volume passed by, the area under the graph, remains the same.
Understanding \(x\)¶
In the following section we do the same for \(x\). It will take the values: 0, 0.25, 0.5. Both \(k\) and \(\Delta t\) are kept constant at 1
[6]:
t = df.index.values
I = np.array(df['Inflow'])
fig = plt.figure(figsize=(7,2.5),dpi=150)
fig.patch.set_alpha(0)
ax = fig.add_subplot(111)
for axis in ['top','bottom','left','right']:
ax.spines[axis].set_linewidth(0.5)
plt.rcParams.update({'font.size': 8, 'pgf.rcfonts' : False})
plt.plot(t,I,linewidth = 1 , label = 'inflow')
for x in [0,0.25,0.5]:
k = 1
dt = 1
out = calc_Out(I,calc_C(k,x,dt))
plt.plot(t, out,linewidth = 1, label = 'outflow $x$ = ' + '{:01.1f}'.format(x))
plt.ylabel('Flow, $Q$ [m$^3$/s]')
plt.xlabel('Time [h]')
plt.legend()
plt.xlim(2,20);
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-6-3b2d5c3a149c> in <module>
----> 1 t = df.index.values
2 I = np.array(df['Inflow'])
3
4 fig = plt.figure(figsize=(7,2.5),dpi=150)
5 fig.patch.set_alpha(0)
NameError: name 'df' is not defined
As a result we can see that the \(x\) behaves as the attenuation parameter. For all graphs have the peak at the same timestep, so no shift in time has occured. What differs is the height of each peak. For \(x = 0.5\) no attenuation occurs, while for \(x = 0\) maximum attenuation occurs.