cumulative netTOA radiative flux vs thermal OHC anomaly
In [9]:
import numpy
import statsmodels.api as sm
from statsmodels.tsa.stattools import acf
import matplotlib.pyplot as plt
In [2]:
y_data = numpy.array([ 8.98702316e+21, 9.08387519e+21, 1.05062075e+22,
9.75610111e+21, 9.49869894e+21, 7.40206565e+21,
2.79996042e+21, 2.35518558e+21, -9.28130821e+20,
-4.71798477e+21, -1.35215844e+21, -1.99075328e+21,
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In [3]:
x_data = numpy.array([ 7.18168242e+21, 7.04896364e+21, 7.46852721e+21,
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3.09949187e+22, 3.04139540e+22, 2.70705491e+22,
2.52342011e+22, 2.64129998e+22, 2.27644485e+22,
1.92831507e+22, 2.45514797e+22, 2.39694636e+22,
2.62992778e+22, 2.63732820e+22, 1.45691475e+22,
1.75678905e+22, 1.12542498e+22, 1.08628253e+22,
7.83921505e+21, 4.00005505e+21, 1.13637708e+21,
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1.49320254e+21, 1.20054136e+21, -1.63804337e+21,
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3.05058838e+21, 6.42623565e+21, -5.86128004e+21,
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-1.70556272e+21, -1.52745943e+21, 1.39223580e+21,
2.66243014e+21, -4.84740273e+21, -3.69618799e+21,
2.82127066e+21, -1.05747703e+21, -4.39539728e+21,
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-6.93859860e+21, -7.63161263e+21, -3.49545078e+21,
2.32357522e+21, 4.52454445e+21, 1.20535296e+21,
-1.69817686e+21, 1.27416311e+21, 2.47849658e+21,
2.30216930e+21, 5.12946873e+21, 9.38231988e+21,
2.58608679e+21, 1.76133868e+21, 3.08256925e+21,
2.30843117e+21, 5.80821737e+21, 7.66294526e+21,
2.28156877e+21, 3.95634692e+21, 3.66141135e+21,
3.46433435e+21, 6.62999466e+20, -2.59756515e+21,
-2.10523033e+21, 8.96306391e+20, 2.45841820e+21,
1.55499853e+21, -9.26205923e+20, -2.10503652e+21,
-8.49672743e+20, 5.04144951e+21, 2.27800599e+21,
4.51228490e+20, 5.25390729e+20, 3.77602785e+21,
-2.37300910e+21, 3.01354392e+21, -3.63043617e+20,
1.42856690e+21, -9.04543946e+20, 2.79773700e+21,
-2.45302141e+21, 5.83667387e+20, -1.30331048e+20,
-4.33256191e+21, -4.70443368e+21, 2.22042459e+20,
-1.08125463e+20, -6.35033696e+21, 4.53807136e+21,
7.79740382e+21, 5.96966669e+20, 2.76293679e+21,
3.61176607e+21, 1.32907583e+21, 5.72521105e+21,
2.26063303e+21, -3.89654426e+21, -2.70178956e+21,
1.72529840e+21, 5.91796174e+21, -3.99113134e+20,
-1.87333475e+21, -1.12964572e+21, 2.06649128e+20,
1.46593734e+21, 2.83241964e+21, 2.74518699e+20,
1.82661966e+21, 2.57097893e+21, 6.20676725e+21,
1.04812037e+22, 1.37889838e+22, 1.49470189e+22,
1.90708559e+22, 2.23263482e+22])
In [4]:
model = sm.OLS(y_data, x_data)
results = model.fit()
results.summary()
Out[4]:
In [5]:
x_data2 = sm.add_constant(x_data)
model2 = sm.OLS(y_data, x_data2)
results2 = model2.fit()
results2.summary()
Out[5]:
In [8]:
results2.bse[-1]
Out[8]:
In [21]:
Out[21]:
In [25]:
results.resid.max() - results.resid.min()
Out[25]:
In [14]:
# From https://content.sciendo.com/view/journals/mms/17/1/article-p3.xml
n = int(results2.nobs)
autocorr_func = acf(y_data, nlags=n - 2)
# Calculate effective sample size (formula from Zieba2010, eq 12)
k = numpy.arange(1, n - 1)
r_k_sum = ((n - k[:]) / float(n)) * autocorr_func[1:]
n_eff = float(n) / (1 + 2 * r_k_sum.sum())
In [15]:
n_eff
Out[15]:
In [22]:
numpy.sqrt(n_eff)
Out[22]:
standard error = standard deviation / sqrt(N)
In [26]:
(results2.bse[-1] * numpy.sqrt(n)) / numpy.sqrt(n_eff)
Out[26]:
In [11]:
numpy.ma.polyfit(x_data, y_data, 1)
Out[11]:
In [14]:
plt.scatter(x_data, y_data)
Out[14]:
In [17]:
results2.conf_int()[-1]
Out[17]:
In [19]:
results2.params[-1]
Out[19]:
In [27]:
test = numpy.array([1,2,3,4,5,6,7,8,9,10,11])
To create the decadal mean...
In [54]:
width = 4
nchunks = math.ceil(len(test) / width)
test_split = [x for x in numpy.array_split(test, nchunks) if x.size == width]
test_split
Out[54]:
In [55]:
numpy.array(list(map(numpy.mean, test_split)))
Out[55]:
In [ ]: