HW#1: Extreme Rainfall Deficit in Singapore

HW#1: Extreme Rainfall Deficit in Singapore#

Objectives

This homework will help you gain a better understanding in terms of the ways how to:

  • Fit Generalized Extreme Value (GEV) distribution

  • Estimate the return level of extreme rainfall deficit

Happy coding!

Submission Guide

Deadline: Sunday 11:59 pm, 3rd November 2024 (Note: Late submissions will not be accepted).

Please upload your solutions to Canvas in a Jupyter Notebook format with the name “Homework1_StudentID.ipynb”. Make sure to write down your student ID and full name in the cell below.

For any questions, feel free to contact Prof. Xiaogang HE (hexg@nus.edu.sg), Haoling CHEN (h.chen@u.nus.edu) or Meilian LI (limeilian@u.nus.edu).

## Fill your student ID and full name below.

# Student ID:
# Full name:

Data: You will need to use the historical (1981-2020) daily total rainfall at Singapore’s Changi station for this homework. You can create a DataFrame using Pandas by reading file “../../assets/data/Changi_daily_rainfall.csv”.

Q1: Calculate daily rainfall statistics (10 marks)#

Calculate the following statistics for daily rainfall during DJF (December-January-February): (i) mean, (ii) variance, (iii) skewness, and (iv) kurtosis.

Hint:

  • You can filter the daily rainfall time series for DJF using Pandas’ boolean filtering method. Details on filtering values can be found in the Pandas tutorial.

  • DJF spans across two calendar years. Make sure you only include complete DJF seasons. For the period 1891 to 2020, this results in 39 complete DJF seasons, from DJF 1981-1982 to DJF 2019-2020.

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Q2: Fit the GEV distribution (40 marks)#

Find the seasonal maximum rainfall deficit for DJF, based on the 30-day centered moving average rainfall deficit. This will result in a data set of 39 values, one value for each year. Fit a GEV distribution to the time series of seasonal maximum rainfall deficits. To do this, estimate the GEV parameters using (i) Maximum Likelihood and (ii) L-Moments, respectively. (Details on fitting a GEV distribution can be found in the Scipy tutorial)

Hint: The rainfall deficit is calculated by subtracting the 30-day moving average rainfall from the mean rainfall calculated in Q1.

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Q3: Estimate the return level of the extreme events (20 marks)#

Using the GEV parameters estimated with L-Moments in Q2, estimate the rainfall deficit for events with return periods of 50 years, 100 years, and 1000 years.

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Q4: Test the goodness-of-fit (30 marks)#

In this task, you will compare how different distributions fit the same dataset and interpret the results using statistical analyses.

  • Repeat the distribution fitting as in Q2, but this time using a normal distribution and the Maximum Likelihood method. (5 marks)

  • Use the Kolmogorov-Smirnov (KS) test to evaluate the goodness-of-fit for both the normal distribution and the GEV distribution you obtained in Q2. (Details on the KS test can be found in the Scipy tutorial) (10 marks)

  • Based on the KS test results, discuss how well each distribution (Normal and GEV) fits the data. (15 marks)

Bonus (10 marks):

  • Plot the CDF (Cumulative Distribution Function) to visually compare the fitted normal distribution, the GEV distribution from Q2, and the empirical distribution derived from the data. Compare the behavior of the two distributions at different return periods. Are the KS statistic results consistent with your observations from the CDF plot?

Hint: You can recycle the empirical distribution estimation and CDF plotting code from the Scipy tutorial.

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