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95 lines
2.9 KiB
Python
95 lines
2.9 KiB
Python
import os
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import re
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import numpy as np
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import pandas as pd
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from scipy import stats, optimize
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WORKBOOK = '../inputs/20220505_Probabilistic_Erosion_Parameters_5th_JTC_REVIEWED_IPCC_SLR_OFFSET.xlsx' # noqa
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SHEET = 'IPCC AR6 WRL FINAL'
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VERSION = 'WRL V5 corrected to 2020' # First row of data
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def get_cdf(x, loc, scale):
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"""Calculate cumulative density function, using Cauchy distribution."""
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return stats.cauchy(loc=loc, scale=scale).cdf(x)
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def cauchy(n_runs, start_year, end_year):
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"""
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Use Monte Carlo simulation to generate sea level rise trajectories by
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fitting IPCC data to a Cauchy distribution.
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Args:
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n_runs (int): number of runs
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start_year (int): first year of model
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end_year (int): last year of model
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Returns:
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the simulated sea level rise (m)
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"""
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# Load IPCC SLR data
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df = pd.read_excel(WORKBOOK, sheet_name=SHEET, index_col='psmsl_id')
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idx = df.index.get_loc(VERSION) # First row containing values we want
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df = df.iloc[idx:idx + 5].set_index('quantile')
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df = df.drop(columns=['process', 'confidence', 'scenario']).T
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df.index.name = 'year'
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percentiles = df.columns.values / 100
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for i, row in df.iterrows():
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values = row.values
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# Set valid range of probability distribution function
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x_min = row[5] + (row[5] - row[50])
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x_max = row[95] + (row[95] - row[50])
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x = np.linspace(x_min, x_max, num=1000)
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# Fit Cauchy distribution
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loc, scale = optimize.curve_fit(get_cdf, values, percentiles)[0]
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if x_min == x_max:
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# Harcode values for start year (when everything is zero)
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scale = 0.001
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x_min = -0.001
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x_max = 0.001
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df.loc[i, 'loc'] = loc
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df.loc[i, 'scale'] = scale
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df.loc[i, 'min'] = x_min
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df.loc[i, 'max'] = x_max
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# Interpolate intermediate values
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index = np.arange(df.index.min(), df.index.max() + 1)
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df = df.reindex(index).interpolate(method='linear')
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df = df.loc[start_year:end_year] # Trim dataframe to given range
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# Prepare array for SLR values
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slr = np.zeros([len(df), n_runs], dtype=float)
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for i, (year, row) in enumerate(df.iterrows()):
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# Get probability distribution for current year
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dist = stats.cauchy(loc=row['loc'], scale=row['scale'])
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# Generate random samples
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for factor in range(2, 1000):
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s_raw = dist.rvs(n_runs * factor)
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# Take first samples within valid range
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s = s_raw[(s_raw > row['min']) & (s_raw < row['max'])]
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if len(s) > n_runs:
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break # Success
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else:
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continue # We need more samples, so try larger factor
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# Add the requried number of samples
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slr[i] = s[:n_runs]
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# Sort each row to make SLR trajectories smooth
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slr = np.sort(slr, axis=1)
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# Randomise run order (column-wise)
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slr = np.random.permutation(slr.T).T
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return slr
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