Add 'distributions.py'

inputs/distributions.py

@@ -0,0 +1,128 @@
+"""Calculate probability distributions for IPCC sea level rise forecasts.
+
+This will calculate the values required to generate triangular distributions,
+i.e. 'min', 'mode', and 'max' in the `numpy.random.triang()` function.
+
+The values are written to 'triang-values.csv'
+
+D. Howe
+d.howe@wrl.unsw.edu.au
+2022-05-05
+"""
+import os
+import re
+import numpy as np
+import pandas as pd
+from scipy import stats, optimize
+import matplotlib.pyplot as plt
+
+PLOT = False
+
+
+def norm_cdf(x, loc, scale):
+    """Calculate cumulative density function, using normal distribution."""
+    return stats.norm(loc=loc, scale=scale).cdf(x)
+
+
+def triang_cdf(x, loc, scale, c):
+    """Calculate cumulative density function, using triangular distribution."""
+    return stats.triang(loc=loc, scale=scale, c=c).cdf(x)
+
+
+# Read data
+xlsx_path = '20220502_Probabilistic_Erosion_Parameters_1st_DRAFT_FOR_DISCUSSION.xlsx'
+
+df = pd.read_excel(xlsx_path, sheet_name='IPCC AR6', index_col=[0, 1, 2, 3, 4])
+df = df.sort_index()
+dff = df.loc[838, 'total', 'medium', 'ssp585'].T
+dff.index.name = 'year'
+percentiles = dff.columns.to_numpy() / 100
+
+# Make SLR relative to 2020 level (at the 50th percentile)
+dff -= dff.loc[2020, 50]
+
+for i, row in dff.iterrows():
+    values = row.to_numpy()
+
+    # Fit normal distribution
+    loc, scale = optimize.curve_fit(norm_cdf, values, percentiles)[0]
+    p_norm = {'loc': loc, 'scale': scale}
+
+    # Fit triangular distribution
+    loc, scale, c = optimize.curve_fit(triang_cdf,
+                                       values,
+                                       percentiles,
+                                       p0=[values[0] - 0.1, 0.5, 0.5])[0]
+    p_triang = {'loc': loc, 'scale': scale, 'c': c}
+
+    # Get triangular distribution parameters
+    left = p_triang['loc']
+    centre = p_triang['loc'] + p_triang['scale'] * p_triang['c']
+    right = p_triang['loc'] + p_triang['scale']
+
+    dff.loc[i, 'min'] = left
+    dff.loc[i, 'mode'] = centre
+    dff.loc[i, 'max'] = right
+
+    if PLOT:
+        fig, ax = plt.subplots(1, 2, figsize=(10, 3))
+
+        x_min = stats.triang.ppf(0.01, **p_triang) - 0.2
+        x_max = stats.triang.ppf(0.99, **p_triang) + 0.2
+        x = np.linspace(x_min, x_max, num=1000)
+
+        ax[0].plot(x, 100 * stats.norm.cdf(x, **p_norm))
+        ax[0].plot(x, 100 * stats.triang.cdf(x, **p_triang))
+        ax[0].plot(values, 100 * percentiles, '.', c='#444444')
+
+        ax[1].plot(x, stats.norm.pdf(x, **p_norm), label='Normal')
+        ax[1].plot(x, stats.triang.pdf(x, **p_triang), label='Triangular')
+        ax[1].plot([], [], '.', c='#444444', label='IPCC data')
+        ax[1].legend()
+
+        ax[1].axvline(x=left, c='C3')
+        ax[1].axvline(x=centre, c='C3')
+        ax[1].axvline(x=right, c='C3')
+
+        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[['min', 'mode', 'max']].to_csv('triang-values.csv', float_format='%0.3f')
+
+if PLOT:
+    # Plot all triangular 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
+        ax.plot(row[['min', 'mode', 'max']], [0, 1, 0], c=c[j])
+        if j % 2 == 0:
+            ax.annotate(f' {i}', (row['mode'], 1),
+                        ha='center',
+                        va='bottom',
+                        rotation=90)
+
+    ax.set_xlabel('SLR (m)', labelpad=10)
+    ax.set_ylabel('Probability density (-)', labelpad=10)
+
+    ax.spines['top'].set_visible(False)
+    ax.spines['right'].set_visible(False)
+    plt.show()