{ "cells": [ { "cell_type": "markdown", "id": "7fa5cb12", "metadata": {}, "source": [ "# Extreme Value Analysis" ] }, { "cell_type": "markdown", "id": "eaa08a9d", "metadata": {}, "source": [ "
\n", " \n", "Solution\n", " \n", "Only the solution and the explanations (in italics) are included here; see the assignment document for the complete questions. All code blocks are retained so that you can still run the notebook locally.\n", "\n", "Also, remember that the workshop will be based on this assignment and use some of the Python code you were asked to write!\n", "
\n", "\n", " \n", "Task 1:\n", "Calculate the design return period using: (1) the Binomial approximation, and (2) the Poisson approximation. \n", "Comment the results (differences, reasons for them if any...) and choose the design return period.\n", "
\n", "\n", " | date_&_time | \n", "significant_wave_height_(m) | \n", "mean_wave_period_(s) | \n", "Peak_wave_Period_(s) | \n", "mean_wave_direction_(deg_N) | \n", "10_meter_wind_speed_(m/s) | \n", "Wind_direction_(deg_N) | \n", "
---|---|---|---|---|---|---|---|
0 | \n", "1950-01-01 00:00:00.000000000 | \n", "1.274487 | \n", "4.493986 | \n", "5.177955 | \n", "199.731575 | \n", "8.582743 | \n", "211.166241 | \n", "
1 | \n", "1950-01-01 04:00:00.000026880 | \n", "1.338850 | \n", "4.609748 | \n", "5.255064 | \n", "214.679306 | \n", "8.867638 | \n", "226.280409 | \n", "
2 | \n", "1950-01-01 07:59:59.999973120 | \n", "1.407454 | \n", "4.775651 | \n", "5.390620 | \n", "225.182820 | \n", "9.423382 | \n", "230.283209 | \n", "
3 | \n", "1950-01-01 12:00:00.000000000 | \n", "1.387721 | \n", "4.800286 | \n", "5.451532 | \n", "227.100041 | \n", "9.037646 | \n", "238.879880 | \n", "
4 | \n", "1950-01-01 16:00:00.000026880 | \n", "1.660848 | \n", "5.112471 | \n", "5.772289 | \n", "244.821975 | \n", "10.187995 | \n", "242.554054 | \n", "
\n", " \n", "Task 2:\n", "Plot the wave height time series. \n", "
\n", "\n", " \n", "Task 3:\n", "Calculate the basic descriptive statistics. What can you conclude from them?\n", "
\n", "\n", " | significant_wave_height_(m) | \n", "mean_wave_period_(s) | \n", "Peak_wave_Period_(s) | \n", "mean_wave_direction_(deg_N) | \n", "10_meter_wind_speed_(m/s) | \n", "Wind_direction_(deg_N) | \n", "
---|---|---|---|---|---|---|
count | \n", "155598.000000 | \n", "155598.000000 | \n", "155598.000000 | \n", "155598.000000 | \n", "155598.000000 | \n", "155598.000000 | \n", "
mean | \n", "1.590250 | \n", "5.634407 | \n", "6.636580 | \n", "232.701281 | \n", "8.319785 | \n", "204.579953 | \n", "
std | \n", "1.025524 | \n", "1.292642 | \n", "2.034652 | \n", "88.523561 | \n", "3.449235 | \n", "93.936119 | \n", "
min | \n", "0.085527 | \n", "2.331908 | \n", "1.826027 | \n", "0.000001 | \n", "0.337945 | \n", "0.013887 | \n", "
25% | \n", "0.845189 | \n", "4.691991 | \n", "5.280570 | \n", "195.018128 | \n", "5.749446 | \n", "125.038362 | \n", "
50% | \n", "1.343157 | \n", "5.493290 | \n", "6.347569 | \n", "257.075066 | \n", "8.063807 | \n", "221.875462 | \n", "
75% | \n", "2.072028 | \n", "6.442927 | \n", "7.606390 | \n", "303.985158 | \n", "10.585083 | \n", "286.772466 | \n", "
max | \n", "9.537492 | \n", "13.610824 | \n", "21.223437 | \n", "359.985729 | \n", "28.536715 | \n", "359.997194 | \n", "
\n", " \n", "Task 4:\n", "Based on the results of the two previous analysis, which data should we consider for our EVA? Why?\n", "
\n", "\n", " \n", "Task 5:\n", "Apply Yearly Maxima to sample the extreme observations. Plot the results.\n", "
\n", "\n", " \n", "Task 6:\n", "Fit the sampled extremes to fit a Generalized Extreme Value distribution.\n", "
\n", "\n", " \n", "Task 7:\n", "Assess the goodness of fit of the distribution using a QQplot. Comment about the results of the fitting.\n", "
\n", "\n", " \n", "Task 8:\n", "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. \n", " \n", "*Hint: check the definition of return period, it is very easy!*\n", "
\n", "\n", " \n", "Task 9:\n", "**Select two** out of the four techniques listed below and prepare a function for them: (1) Peak Over Threshold (POT), (2) Dispersion Index plot (DI), (3) Parameter stability plots, and (4) Mean residual life plot (MRL).\n", "
\n", "