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, 5th November 2023 (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), or Zhixiao NIU (niu.zhixiao@u.nus.edu).

## Fill your student ID and full name below.

# Student ID:
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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 extreme rainfall statisitics#

First, divide the data into the following seasons: DJF (Dec-Jan-Feb), MAM (Mar-Apr-May), JJA (Jun-Jul-Aug), and SON (Sep-Oct-Nov) using Pandas’ filtering methods. Calculate the following statistics of daily rainfall for each season: (i) mean; (ii) variance; (iii) skewness; and (iv) kurtosis. Based on the results, identify the driest season. (Details on the filtering method can be found in the Pandas tutorial). (Hint: The driest season can refer to the season with the lowest mean of daily rainfall) (10 marks)

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Q2: Fit the GEV distribution#

For the driest season you identified in Q1, find the seasonal maximum rainfall deficit based on the 30-day moving average rainfall deficit (please use centered moving average). This will result in a data set of 40 values, one value for each year. Fit two GEV distributions of seasonal maximum rainfall deficit using data from the first 20 years (1981-2000) and the last 20 years (2001-2020) separately. 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 can be obtained by subtracting the 30-day moving average rainfall from the mean rainfall calculated in Q1) (40 marks)

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Q3: Compare differences in GEV distributions#

Based on the estimated GEV parameters using L-Moments in Q2, discuss, for the driest season, whether there are statistical differences between the two distributions estimated from the first and last 20 years. (Hint: You can use the KS test to compare the underlying distributions of the two samples) (30 marks)

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Q4: Estimate the return level of the extreme events#

Based on the estimated GEV parameters using L-Moments in Q2, estimate the rainfall deficit for events with return periods of 50 years, 100 years, and 200 years. (Hint: You can use the GEV distribution fitted from the data of the last 20 years.) (20 marks)

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