You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
120 lines
3.1 KiB
Python
120 lines
3.1 KiB
Python
"""Calculate probability distributions for IPCC sea level rise forecasts.
|
|
|
|
This will calculate the values required to Cauchy Distributions for
|
|
different SLR projections.
|
|
|
|
Reads:
|
|
'IPCC AR6.xlsx'
|
|
|
|
Writes:
|
|
'cauchy-values.csv'
|
|
|
|
D. Howe
|
|
d.howe@wrl.unsw.edu.au
|
|
2022-05-12
|
|
"""
|
|
import os
|
|
import re
|
|
import numpy as np
|
|
import pandas as pd
|
|
from scipy import stats, optimize
|
|
import matplotlib.pyplot as plt
|
|
|
|
PLOT = True
|
|
|
|
|
|
def cauchy_cdf(x, loc, scale):
|
|
"""Calculate cumulative density function, using Cauchy distribution."""
|
|
return stats.cauchy(loc=loc, scale=scale).cdf(x)
|
|
|
|
|
|
# Read data
|
|
df = pd.read_excel('IPCC AR6.xlsx', index_col=[0, 1, 2, 3, 4])
|
|
df = df.sort_index()
|
|
|
|
# Use all 'medium' confidence scenarios for intermediate quantiles
|
|
scenarios = ['ssp119', 'ssp126', 'ssp245', 'ssp370', 'ssp585']
|
|
dff = df.loc[838, 'total', 'medium', scenarios].groupby('quantile').mean()
|
|
|
|
# Use ssp119/ssp585 for 5th and 95th quantiles
|
|
dff.loc[5] = df.loc[838, 'total', 'medium', 'ssp119', 5]
|
|
dff.loc[95] = df.loc[838, 'total', 'medium', 'ssp585', 95]
|
|
dff = dff.T
|
|
|
|
dff.index.name = 'year'
|
|
percentiles = dff.columns.values / 100
|
|
|
|
for i, row in dff.iterrows():
|
|
values = row.values
|
|
|
|
x_min = row[5] + (row[5] - row[50])
|
|
x_max = row[95] + (row[95] - row[50])
|
|
x = np.linspace(x_min, x_max, num=1000)
|
|
|
|
# Fit distribution
|
|
loc, scale = optimize.curve_fit(cauchy_cdf, values, percentiles)[0]
|
|
p = {'loc': loc, 'scale': scale}
|
|
|
|
dff.loc[i, 'loc'] = loc
|
|
dff.loc[i, 'scale'] = scale
|
|
|
|
if not PLOT:
|
|
continue
|
|
|
|
fig, ax = plt.subplots(1, 2, figsize=(10, 3))
|
|
|
|
ax[0].plot(x, 100 * stats.cauchy.cdf(x, **p))
|
|
ax[0].plot(values, 100 * percentiles, '.', c='#444444')
|
|
|
|
ax[1].plot(x, stats.cauchy.pdf(x, **p), label='Cauchy')
|
|
ax[1].plot([], [], '.', c='#444444', label='IPCC data')
|
|
ax[1].legend()
|
|
|
|
ax[0].set_ylabel('Percentile', labelpad=10)
|
|
ax[0].set_title('Cumulative distribution')
|
|
ax[1].set_title('Probability density')
|
|
|
|
ax[0].annotate(i, (-0.3, 1),
|
|
xycoords='axes fraction',
|
|
clip_on=False,
|
|
size=14)
|
|
for a in ax:
|
|
|
|
a.set_xlabel('SLR (m)', labelpad=10)
|
|
a.spines['top'].set_visible(False)
|
|
a.spines['right'].set_visible(False)
|
|
|
|
plt.show()
|
|
|
|
# Save distribution parameters
|
|
dff[['loc', 'scale']].to_csv('cauchy-values.csv', float_format='%0.3f')
|
|
|
|
if PLOT:
|
|
# Plot all distributions
|
|
fig, ax = plt.subplots(1, 1, figsize=(8, 4))
|
|
|
|
cmap = plt.cm.get_cmap('RdBu_r', len(dff))
|
|
c = list(cmap(range(cmap.N)))
|
|
|
|
j = -1
|
|
for i, row in dff.iterrows():
|
|
j += 1
|
|
|
|
y = stats.cauchy(loc=row['loc'], scale=row['scale']).pdf(x)
|
|
ax.plot(x, y * row['scale'], c=c[j])
|
|
if j % 2 == 0:
|
|
ax.annotate(f' {i}', (x[y.argmax()], 0.32),
|
|
ha='center',
|
|
va='bottom',
|
|
clip_on=False,
|
|
rotation=90)
|
|
|
|
ax.set_ylim(top=0.35)
|
|
ax.set_yticks([])
|
|
ax.set_xlabel('SLR (m)', labelpad=10)
|
|
ax.set_ylabel('Normalised probability density (-)', labelpad=10)
|
|
|
|
ax.spines['top'].set_visible(False)
|
|
ax.spines['right'].set_visible(False)
|
|
plt.show()
|