end_index = 10000
shift = 0
#%matplotlib qt
import matplotlib.pyplot as plt
#plt.plot(recharge_time_series)
#plt.show()
recharge_time_series = recharge_time_series[begin_index:end_index]
head_time_series = head_time_series[begin_index+shift:end_index+shift]
####################################################################
"""
# calculate the power spectrum: Shh, output to FIT with analy solution only!
frequency_output, Shh = power_spectrum(
input=recharge_time_series,
output=head_time_series,
time_step_size=time_step_size,
method="scipyffthalf",
o_i="o",
)
frequency_input, Sww = power_spectrum(
input=recharge_time_series,
output=head_time_series,
time_step_size=time_step_size,
method="scipyffthalf",
o_i="i",
)
# cut higher frequencies than cut_freq_higher
cut_array_higher = np.less(frequency_input, cut_freq_higher)
Sww = Sww[cut_array_higher]
Shh = Shh[cut_array_higher]
"/Users/houben/phd/modelling/20190318_spectral_analysis_homogeneous/models_test/1001_24.1127_5.00e-01_8.00e-02/rfd_curve#1.txt"
)
from transect_plot import extract_timeseries, plot_head_timeseries_vs_recharge, extract_rfd
path_to_project = "/Users/houben/phd/modelling/20190318_spectral_analysis_homogeneous/models_test/1001_24.1127_5.00e-01_8.00e-02"
#time_time_series, recharge_time_series = extract_rfd(path=path_to_project, rfd=1)
recharge_time_series = recharge_time_series * L
L = 1000
x = 200
artificial_data = True
#################################################
#'''
frequency_Shh_Sww, Shh_Sww = power_spectrum(recharge,
gw_head,
time_step_size,
o_i="oi")
frequency_Sww, Sww = power_spectrum(recharge,
gw_head,
time_step_size,
o_i="i")
frequency_Shh, Shh = power_spectrum(recharge,
gw_head,
time_step_size,
o_i="o")
# cut the power spectrum
# cut_value of frequency
#cut_freq = 1e-4
def discharge_ftf_fit(input,
output,
time_step_size,
aquifer_length,
method='scipyffthalf',
initial_guess=1e-2):
"""
This functions computes the power spectrum of input and output with
power_spectrum from power_spectrum.py. The resulting spectrum is taken to
derive the aquifer parameters t_c (char time.) and D (T/S) with the
transfer function of the discharge from Linear Dupuit Aquifer with a
Dirichlet BC (discharge_ftf).
Parameters
----------
input : 1D array
Y-values of time series of input (i.e. recharge)
output: 1D array
Y-values of time series of output (i.e. discharge)
time_step_size : float
Time in seconds between two time steps / two measurements
aquifer_length : float
The length of the aquifer from the water divide to the stream.
method : string, Default: 'scipyffthalf'
--> see power_spectrum.py for explanation
Yields
------
power_spectrum : 1D array
The power spectrum.
frequency : 1D array
The coresponding frequencies.
# t_c : float
# The characteristic time of the aquifer after Russian et al. 2013
D : float
The aquifer diffusivity [m^2/s].
"""
import numpy as np
from power_spectrum import power_spectrum
import scipy.optimize as optimization
from functools import partial as prt
frequency_input, power_spectrum_result = power_spectrum(
input, output, time_step_size, method="scipyffthalf", o_i="oi")
partial = prt(discharge_ftf, aquifer_length=aquifer_length)
popt, pcov = optimization.curve_fit(partial,
frequency_input,
power_spectrum_result,
p0=initial_guess)
theta_q = discharge_ftf(frequency_input, popt[0], aquifer_length)
# check results
#import matplotlib.pyplot as plt
#plt.loglog(frequency_input, theta_q)
#plt.loglog(frequency_input, power_spectrum_result)
#plt.show()
return popt, pcov, frequency_input, power_spectrum_result
alpha = alpha_reg(discharge_time_series, area)
baseflow_time_series = filter_Eck(BFImax, discharge_time_series, alpha)
#plt.plot(discharge_time_series)
#plt.plot(baseflow_time_series)
popt, pcov, frequency_input, power_spectrum_result = discharge_ftf_fit(
recharge_time_series,
baseflow_time_series,
time_step_size,
1000,
method='scipyffthalf',
initial_guess=1e-2)
power_spectrum_input = power_spectrum(recharge_time_series,
power_spectrum_result,
time_step_size,
method="scipyffthalf",
o_i="i")[1]
plt.loglog(frequency_input, power_spectrum_result)
plt.loglog(frequency_input, power_spectrum_input)
#data = np.hstack((spectrum_input, power_spectrum_result))
#plot_spectrum(data, frequency_input, path=path, name="test")
'''
def plot_spectrum(
data,
frequency,
name=None,
labels=None,
path=None,
