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Extreme Value Analysis

1. Extreme Value Analysis#

In this workshop, we will complete our Extreme Value Analysis (EVA) to characterize wave loading. Remeber that we were using wave data in the North sea extracted from ERA5 database .

Now, let’s go back to our analysis. In the following steps, make use of the code you and your peers prepared home. Remember that we also calculated the value of the return period that was required for our design, RT = 475 years.

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from scipy import stats
from scipy.signal import find_peaks
import datetime
%matplotlib inline
from dispersion_index import DI_plot

EVA using POT + GPD#

First, we import the data. Note that you will have to change the name of the file depending on the selected dataset.

This workshop uses the same file as in HW2: Time_Series_DEN_lon_8_lat_56.5_ERA5.txt

pandas = pd.read_csv('Time_Series_DEN_lon_8_lat_56.5_ERA5.txt', delimiter=r"\s+", 
                     names=['date_&_time', 
                            'significant_wave_height_(m)', 
                            'mean_wave_period_(s)', 
                            'Peak_wave_Period_(s)', 
                            'mean_wave_direction_(deg_N)', 
                            '10_meter_wind_speed_(m/s)', 
                            'Wind_direction_(deg_N)'],  # custom header names
                     skiprows=1)  # Skip the initial row (header)

We will change the format of the time stamp and start taking looking how our data looks. Ensure you know what it is in each column of the dataframe.

pandas['date_&_time'] = pd.to_datetime(pandas['date_&_time']-719529, unit='D')

# The value 719529 is the datenum value of the Unix epoch start (1970-01-01), 
# which is the default origin for pd.to_datetime().

pandas.head()

We already plotted and performed basic analysis to our data in the previous assignment. Also, we selected the dominant wave direction and filtered the data accordingly. Check the solution notebook for the previous workshop in case of doubt.

plt.figure(2, figsize = (15,10), facecolor='white')

plt.subplot(2,3,1)
plt.scatter(pandas['mean_wave_direction_(deg_N)'], pandas['significant_wave_height_(m)'], s = 2)
plt.ylabel('${H_s (m)}$')

print(pandas['significant_wave_height_(m)'].quantile(0.99))
pandas_99 = pandas[pandas['significant_wave_height_(m)']>=pandas['significant_wave_height_(m)'].quantile(0.99)]

plt.subplot(2,3,2)
plt.title('Dominant Wave Direction')
plt.scatter(pandas['mean_wave_direction_(deg_N)'], pandas['significant_wave_height_(m)'], s = 2)
plt.scatter(pandas_99['mean_wave_direction_(deg_N)'], pandas_99['significant_wave_height_(m)'], color='orange', s = 2)
plt.axvline(x = 200, color = 'r', linestyle = 'dashed')
plt.axvline(x = 320, color = 'r', linestyle = 'dashed')
plt.xlabel('$Mean Wave Direction (ºN)$')


pandas_angle = pandas[(pandas['mean_wave_direction_(deg_N)'].between(200, 320))]

plt.subplot(2,3,3)
plt.scatter(pandas_angle['mean_wave_direction_(deg_N)'], pandas_angle['significant_wave_height_(m)'], s = 2)
plt.axvline(x = 200, color = 'r', linestyle = 'dashed')
plt.axvline(x = 320, color = 'r', linestyle = 'dashed')
plt.xlim([0, 350])

Note that we stored the filtered data in the dataframe ‘pandas_angle’, so that’s the one you should use in the subsequent analysis.

Task 1: Apply POT to sample the extreme observations (you should have already done the function as homework!). Plot the results.

Use a threshold of 5 meters and a declustering time of 72h.

#You can add you code here

Task 2: Fit the sampled extremes to fit a Generalized Pareto distribution. Print the shape parameter. What type of GPD are you obtaining?

Hint: what kind of tail is implied by the parameter value?

#You can add you code here

Task 3: Assess the goodness of fit of the distribution using a QQplot. Comment about the results of the fitting and compare it to those obtained using BM and GEV. Which one would you choose?

#You can add you code here

Task 4: Plot the return level plot and determine the value of the significant wave height that you need for design according to your calculated return period. Remember that return level plot presents in the x-axis the values of the variable (wave height, here) and in the y-axis the corresponding values of the return period.

Compare it to the results obtained using BM + GEV.

#You can add you code here

We have performed the analysis with a given threshold = 5m and declustering time = 72h. But are they reasonable?

Task 5: Apply two methods to justify why a threshold=5m and a declustering time=72h are reasonable or not. Write your conclusions.

#Technique 1 here

#Interpretation to technique 1

#Technique 2 here

#Interpretation to technique 2

#Final recommendation and conclusions
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