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run_extreme_value_analysis.py
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# -*- coding: utf-8 -*-
"""
Created on Mon Mar 20 09:37:19 2023
@author: admin
"""
import pyextremes
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
def run_eva(df, tag, block_size=pd.Timedelta(pd.to_timedelta("365.2425D")),
csize=15, minima=False):
"""
run the extreme value analysis and create
1) a plot of the extremes in a timeseries
2) a summary plot of model fitting and return values
inputs
df - dataframe with datetime as index
tag - name of dataframe column to do EVA on
block_size - time length to chop data up into
csize - fontsize for plotting
minima - bool, whether to look for minima (if True, looking for negative peaks)
returns
gevd_fit_params - df containing shape_, location, scale, and distribution_name
extremes_df - df containing datetime and value of the detected extremes
fig_extremes - fig object showing timeseries of tag, with extremes highlighted
ax_extremes - ax object for fig_extremes
fig_model - fig object assessing model fit
ax_model - ax object for fig_model
summary - df of return values and their probabilities
"""
extremes_type='low' if minima==True else 'high'
# Initialise model
eva_model=pyextremes.EVA(df[tag])
eva_model.get_extremes("BM", block_size=block_size,extremes_type=extremes_type)
eva_model.fit_model(model="Emcee")
# Extract fit parameters
gevd_fit_params=pd.DataFrame(eva_model.model.fit_parameters, index=[0])
gevd_fit_params.rename(columns={'c':'shape_', 'loc':'location'}, inplace=True)
if eva_model.distribution.name == 'gumbel_r':
gevd_fit_params['shape_']=0.0
location_quantiles=np.quantile(eva_model.model.trace[:,:,0].flatten(), [0.025, 0.975])
scale_quantiles=np.quantile(eva_model.model.trace[:,:,1].flatten(), [0.025, 0.975])
gevd_fit_params['shape_lower_ci_width']=np.nan
gevd_fit_params['shape_upper_ci_width']=np.nan
gevd_fit_params['location_lower_ci_width']=gevd_fit_params.location-location_quantiles[0]
gevd_fit_params['location_upper_ci_width']=location_quantiles[1]-gevd_fit_params.location
gevd_fit_params['scale_lower_ci_width']=gevd_fit_params.scale-scale_quantiles[0]
gevd_fit_params['scale_upper_ci_width']=scale_quantiles[1]-gevd_fit_params.scale
else:
# Calculate the 95% confidence intervals on fit params
shape_quantiles=np.quantile(eva_model.model.trace[:,:,0].flatten(), [0.025, 0.975])
location_quantiles=np.quantile(eva_model.model.trace[:,:,1].flatten(), [0.025, 0.975])
scale_quantiles=np.quantile(eva_model.model.trace[:,:,2].flatten(), [0.025, 0.975])
gevd_fit_params['shape_lower_ci_width']=gevd_fit_params.shape_-shape_quantiles[0]
gevd_fit_params['shape_upper_ci_width']=shape_quantiles[1]-gevd_fit_params.shape_
gevd_fit_params['location_lower_ci_width']=gevd_fit_params.location-location_quantiles[0]
gevd_fit_params['location_upper_ci_width']=location_quantiles[1]-gevd_fit_params.location
gevd_fit_params['scale_lower_ci_width']=gevd_fit_params.scale-scale_quantiles[0]
gevd_fit_params['scale_upper_ci_width']=scale_quantiles[1]-gevd_fit_params.scale
gevd_fit_params['distribution_name']= eva_model.distribution.name
# Extract extremes
extremes_df=pd.DataFrame({'datetime':eva_model.extremes.index, tag:eva_model.extremes.values})
# Plot extremes
fig_extremes,ax_extremes=plt.subplots(figsize=(15,10))
ax_extremes.plot(df[tag], color='grey', linewidth=1.0, label=str(tag))
ax_extremes.plot(extremes_df.datetime, extremes_df[tag], color='mediumorchid', linewidth=0.0, label='extremes', marker='*', markersize=15)
ax_extremes.set_xlabel('Year', fontsize=csize)
ax_extremes.set_ylabel(str(tag), fontsize=csize)
for label in (ax_extremes.get_xticklabels() + ax_extremes.get_yticklabels()):
label.set_fontsize(csize)
ax_extremes.legend(fontsize=csize)
# Overall plot for assessing the model
fig_model, ax_model=plt.subplots(nrows=2, ncols=2, figsize=(12,12))
observed_return_values=pyextremes.get_return_periods(ts=eva_model.data, extremes=eva_model.extremes,
extremes_method=eva_model.extremes_method, extremes_type=eva_model.extremes_type,
block_size=eva_model.extremes_kwargs.get("block_size", None), return_period_size='365.2425D' )
return_period=np.linspace(observed_return_values.loc[:, "return period"].min(),
observed_return_values.loc[:, "return period"].max(),100,)
modeled_return_values = eva_model.get_summary(return_period=return_period, return_period_size='365.2425D',alpha=0.95)
ax_model[0,0].plot(observed_return_values['return period'], observed_return_values[tag], linewidth=0.0, marker='^', fillstyle='none', color='black', label='Observations')
ax_model[0,0].plot(modeled_return_values.index, modeled_return_values['return value'], linewidth=2.0, color='coral', label='Model')
ax_model[0,0].fill_between(modeled_return_values.index, modeled_return_values['lower ci'], modeled_return_values['upper ci'], color='grey', alpha=0.5, label='95% CI')
ax_model[0,0].set_xlabel('Return Period (years)', fontsize=csize)
ax_model[0,0].set_ylabel(str(tag)+' observed at least once\nper return period (nT)', fontsize=csize)
ax_model[0,0].set_xscale('log')
ax_model[0,0].legend(fontsize=csize, loc='lower right')
for label in (ax_model[0,0].get_xticklabels() + ax_model[0,0].get_yticklabels()):
label.set_fontsize(csize)
t=ax_model[0,0].text(0.06,0.94,'(a)', transform=ax_model[0,0].transAxes, fontsize=csize, va='top', ha='left')
t.set_bbox(dict(facecolor='white', alpha=0.5, edgecolor='grey'))
# Compare the distributions
ax_model[0,1].hist(eva_model.extremes.values, density=True, rwidth=0.8, color='grey', label='Observations')
pdf_support = np.linspace(eva_model.extremes.min(), eva_model.extremes.max(), 100)
pdf = eva_model.model.pdf(eva_model.extremes_transformer.transform(pdf_support))
ax_model[0,1].plot(pdf_support, pdf, color='coral', label='Model')
ax_model[0,1].set_xlabel('Extremes - '+str(tag), fontsize=csize)
ax_model[0,1].set_ylabel('Normalised Occurrence', fontsize=csize)
ax_model[0,1].legend(fontsize=csize)
for label in (ax_model[0,1].get_xticklabels() + ax_model[0,1].get_yticklabels()):
label.set_fontsize(csize)
t=ax_model[0,1].text(0.06,0.94,'(b)', transform=ax_model[0,1].transAxes, fontsize=csize, va='top', ha='left')
t.set_bbox(dict(facecolor='white', alpha=0.5, edgecolor='grey'))
#params_text=r'$\mu$ = '+str(float('%.4g' % gevd_fit_params.location))+'\n$\sigma$ = '+str(float('%.4g' % gevd_fit_params.scale))+'\n'+r'$\xi$ = '+str(float('%.4g' % gevd_fit_params.shape_))
params_text=r'$\mu$ = '+str(float('%.4g' % gevd_fit_params.location)) + ' (-' +str(float('%.4g' % gevd_fit_params.location_lower_ci_width)) +', +'+ str(float('%.4g' % gevd_fit_params.location_upper_ci_width)) +')'+'\n$\sigma$ = '+str(float('%.4g' % gevd_fit_params.scale)) + ' (-' +str(float('%.4g' % gevd_fit_params.scale_lower_ci_width)) +', +'+ str(float('%.4g' % gevd_fit_params.scale_upper_ci_width)) +')'+'\n'+r'$\xi$ = '+str(float('%.4g' % gevd_fit_params.shape_)) + ' (-' +str(float('%.4g' % gevd_fit_params.shape_lower_ci_width)) +', +'+ str(float('%.4g' % gevd_fit_params.shape_upper_ci_width)) +')'
t_m=ax_model[0,1].text(0.94,0.75,params_text,transform=ax_model[0,1].transAxes, fontsize=csize, va='top', ha='right' )
# # Plot a q-q plot
observed = observed_return_values.loc[:, eva_model.extremes.name].values
theoretical = eva_model.extremes_transformer.transform(eva_model.model.isf(observed_return_values.loc[:, "exceedance probability"].values))
# Observed is just the observed extreme B values
# Theoretical takes the probability for the observed B, and then extracts the predicted B from the model
#fig,ax=plt.subplots()
ax_model[1,0].plot(theoretical, observed, linewidth=0.0, marker='o', fillstyle='none', color='mediumslateblue')
min_value = min([min(ax_model[1,0].get_xlim()), min(ax_model[1,0].get_ylim())])
max_value = max([max(ax_model[1,0].get_xlim()), max(ax_model[1,0].get_ylim())])
ax_model[1,0].plot( [min_value, max_value], [min_value, max_value], linewidth=1.0, linestyle='--', color='black')
ax_model[1,0].set_xlabel('Model '+str(tag), fontsize=csize)
ax_model[1,0].set_ylabel('Observed '+str(tag), fontsize=csize)
ax_model[1,0].set_title('QQ plot', fontsize=csize)
for label in (ax_model[1,0].get_xticklabels() + ax_model[1,0].get_yticklabels()):
label.set_fontsize(csize)
t=ax_model[1,0].text(0.06,0.94,'(c)', transform=ax_model[1,0].transAxes, fontsize=csize, va='top', ha='left')
t.set_bbox(dict(facecolor='white', alpha=0.5, edgecolor='grey'))
fig_model.tight_layout()
# Plot a table of return values
summary = eva_model.get_summary(
return_period=[2, 5, 10,15,20, 25, 50, 100],
alpha=0.95 )
summary=summary.reset_index()
# Format the DF for the table
summary=summary.round()
summary=summary.rename(columns={"return period": "period",
"return value": "value",
"lower ci": "-95% CI",
"upper ci": "+95% CI"})
summary_new=pd.DataFrame({"period":summary['period'],
"value":summary['value'],
"-95% CI":summary['value'] - summary['-95% CI'],
"+95% CI":summary['+95% CI'] - summary['value']
})
table=ax_model[1,1].table(cellText=summary_new.values, colLabels=summary_new.columns, loc='center')#, fontsize=csize+2)
table.auto_set_font_size(False) # stop auto font size
table.set_fontsize(csize) # increase font size
table.scale(1,3) # don't increase cell width (1) but increase height x3
ax_model[1,1].axis('off')
t=ax_model[1,1].text(0.06,0.94,'(d)', transform=ax_model[1,1].transAxes, fontsize=csize, va='top', ha='left')
t.set_bbox(dict(facecolor='white', alpha=0.5, edgecolor='grey'))
plt.show()
return gevd_fit_params, extremes_df, fig_extremes, ax_extremes, fig_model, ax_model, summary