SOES 3042/6025 – Assignment 1

This assignment accounts for 40% of your total module grade. The deadline to submit your answer is Monday 2 pm 10^th November 2025.  Submit your answer as one PDF file via Turnitin on the module’s site and name the file: “SOES3042-A1_StudentID_LastName.pdf”. Replace “StudentID” with your 8-digit student ID and “LastName” with your last name. If you are taking SOES6025, replace “3042” with “6025”.

Complete this assignment by following the instructions below:

(1) Write your answer in the form. of an individual written, well-structured short report accompanied by suitable figures, using the Word answer template provided. Once you complete your answers, save your final answers as a PDF file and submit it via Turnitin. Please:

· Ensure that each task is clearly addressed and that you also describe your approach to the task (do this without referring to programming details).

· Go beyond simply producing figures and answers to direct questions. Ask yourself and try to provide answers to questions such as: What approximations or assumptions have I made in answering this point? Can I justify these? How might they affect my results? Is there a way to verify this expectation (the answer may be no)? High marks will be awarded only to answers demonstrating this thought process.

(2) While using the answer template, you may adjust the size of the answer boxes for the “short report” and “figures” for each problem (i.e., Problem 1, Problem 2, etc.).  Yet, please ensure that the answer for each problem (with “short report” and “figures” combined) does not exceed one side of an A4 page. Start the answer for a new problem (i.e., problem 2, problem 3, etc.) on a new page.  Use single line spacing and a font size no smaller than 12 pt.

(3) You must also submit your Jupyter Notebook file used to perform. the calculations and to produce the results shown in your report.  Please name the code file “SOES3042-A1_StudentID_Last Name.ipynb” and submit it via Turnitin.  The code will not be marked, but it will enable the marker to the source of your result, so it is in your interest to organize your code well. Do not include any technical programming details in the main body of your report.

ARC Policy for SOES 3042/6025 Assignment 1

Collaboration Policy

You may discuss ideas with your classmates; however, you must complete all coding and write the report independently. You MUST disclose the names of all collaborators. For this assignment, a collaborator is any individual (including classmates, tutors, or external persons) with whom you have discussed the assignment in sufficient detail that it may have influenced your work, regardless of whether any material was directly shared or copied.

Failure to do so will flag substantial risk of a breach of external authorship and will be treated as academic misconduct under the Academic Responsibility and Conduct (ARC) framework, potentially triggering a formal investigation.

GenAI usage Policy (Tier 1)

In this assignment, you are stickly prohibited from using any GenAI tools, such as ChatGPT, Copilot, or Grammarly Premium for any part of this assignment.  This includes entering any part of the assignment or your assessed work to GenAI, whether by pasting/typing, uploading files, or describing content directly or through plugins.

This policy applies to both report writing and coding. Using any GenAI tools to produce or paraphrase content, suggest sentence phrasing, counting down word count, summarise information, generate code, or provide new ideas is strictly prohibited.  Rewriting your own text using GenAI also counts as content generation and is not permitted.

Note that code blocks for answering each of the problems have been provided in individual practical sessions.

Declaration

You MUST complete, sign, and submit an ARC declaration as the last page of SOES3042-A1_StudentID_LastName.pdf to confirm your understanding and agreement with these policies. The form. can be found at the end of the Word answer template. Failure to submit this declaration will result in your assignment not being graded.

Be advised: any detected breach of these policies, including undisclosed collaboration or the use of Generative AI, will be treated as academic misconduct under the ARC framework. Such breaches will result in severe penalties, including but not limited to receiving a grade of zero for this assignment and potential further disciplinary action.

The assignment

Throughout the statistics part of this course, we've explored various statistical methods and their applications in understanding climate phenomena. In our final lecture, we used the Empirical Orthogonal Function (EOF) technique to uncover significant patterns of sea-level pressure variability in the Tropical Pacific—a key atmospheric variable. Given the dynamic coupling between the atmosphere and the ocean, it stands to reason that corresponding signals would manifest in oceanic variables as well.

This homework assignment delves into the oceanic component of climate variability by analysing sea-surface temperature (SST) datasets. Through this exercise, you will replicate the methodologies employed by climate scientists to identify and analyse El Niño and La Niña events. These phenomena, along with their atmospheric counterparts, constitute the El Niño-Southern Oscillation (ENSO), one of the most significant modes of global climate variability, influencing weather and climate patterns worldwide.

You will apply the skills and knowledge acquired throughout the course to perform. a comprehensive analysis of ENSO and complete this assignment. This includes:

(1) K-S Test (Lecture 5)

(2) Correlation Analysis (Lecture 6)

(3) Linear Regression (Lecture 7)

(4) Model Selection (Lecture 8)

(5) PCA/EOF Analysis (Lecture 9)

Let's embark on this analytical journey to uncover the secrets of ENSO through the lens of a climate scientist.

The dataset you will need to use are listed in below:

Problem 1. Calculating and Analysing the Nino3 Index

(20pts for SOES3042, 15pts for SOES6025)

The term "El Niño" (Spanish for "the boy" or "the Christ child") was first used by Peruvian fishermen in the late 19th century to describe the appearance of unusually warm water in the eastern Pacific Ocean around Christmas time.   The Nino3 index, calculated by averaging SST anomalies over the region bounded by 5°N-5°S and 210°-270°E, is a widely used measure of the oceanic component of ENSO.

(a) Remove seasonal cycles from the loaded monthly SST and calculate the Nino3 index for each month. Create a time series plot of the Nino3 index.

(b) Plot a histogram of the monthly Nino3 index values. Would you expect the index to be normally distributed?  Why?  Visually, does the distribution appear to be normal?

(c) Find a quantitative approach to test whether the monthly Nino3 index follows a normal distribution. What is the null hypothesis? What are the test statistics? What is the p-value of the test, and what does it mean regarding the normality of the distribution?

Problem 2. Correlation between Atmosphere and Ocean

(25pts for SOES3042, 20pts for SOES6025)

The atmosphere and the ocean are closely coupled.  In this problem, we are going to quantify this coupling.  Now please:

(a) Calculate the Southern Oscillation (SO) index by subtracting the sea-level pressure (SLP) anomalies at Tahiti from the SLP at Darwin.  Plot it alongside the Nino3 index calculated from Problem 1.

(b) Plot the two indices as a scatter plot.  Calculate the correlation coefficient between the SO index and the Nino3 index (calculated in Task 1).  Based on the data distribution, which type of correlation is appropriate?  What is the strength and direction of the correlation?

(c) Determine the statistical significance of the correlation. Is the correlation statistically significant?  Consider which approach to use. What assumptions are involved? How might they affect the significance of the correlation?

Problem 3. EOF Analysis of Tropical SST anomalies

(25pts for SOES3042, 25pts for SOES6025)

Building on our understanding of Empirical Orthogonal Functions (EOF) from Lecture 6, this problem focuses on analysing detrended sea-surface temperature (SST) anomalies in the tropics (0-360°E, 20°S-20°N). EOF analysis will enable us to identify dominant patterns of variability within the dataset and understand their temporal evolution. Please:

(a) Remove the seasonal cycle and long-term warming trends of SST at each location and then perform. an EOF analysis on the SST anomalies.  Should each grid point have equal weight in an EOF analysis? Why? If not, what should we do to ensure the EOF is performed properly?

(b) Plot the spatial patterns (U) and the corresponding time series (DV^T) of the first two EOF modes.   Compare the principal components (PCs) with the Nino3 index calculated in Problem 1, then find and describe the spatial pattern of El Niño events.

(c) Assess how much of the total SST variance is explained by each of the first two modes individually, as well as their combined contribution.

Problem 4. Exploring the Relationship between EOF1 and EOF2 of SST

(30pts for SOES3042, 40pts for SOES6025)

In this problem, we will investigate the dynamics between the first two principal components (EOF1 and EOF2) derived from the SST dataset.  Please:

(a) Do you expect any significant linear relationship to emerge between the two PCs?  Why?  What does this result remind you of when interpreting Pearson’s correlation coefficient?

(b) Create a scatter plot of PC2 (y-axis) versus PC1 (x-axis) during the October to March timeframe.  Then perform. linear and quadratic regression of PC2 against PC1 using ordinary least squares (OLS).  Plot your fitted lines and associated uncertainties (95% confidence interval).  Are the fitted models statistically significant?

(c) List at least three assumptions behind OLS and evaluate whether each holds for the quadratic model.

(d) Explore polynomial regression models to describe the relationship between PC1 and PC2, selecting the best model using quantitative approaches. (optional bonus points for SOES3042; required for SOES 6025)