Final Project: Independent Method Exploration

Contributing to Course Knowledge Base

Student-driven exploration of hydroclimate methods with teaching component

The field of hydroclimate risk assessment draws from a vast array of statistical and machine learning techniques. While this course covers foundational methods, many specialized approaches remain unexplored. This project provides an opportunity to independently investigate a method not covered in class while contributing to the collective learning experience through teaching and knowledge sharing.

1 Topic Selection

Choose a specific statistical or machine learning method that you want to learn about and that is relevant to hydroclimate applications. Your focus must be on understanding and teaching the method itself—how it works, when to use it, its assumptions, and its limitations.

Important: Your presentation and lecture notes should teach the method, not just present an application. While you should illustrate the method with concrete examples, the core content must explain the methodological approach itself. This is not a literature review or case study presentation—it is a methods tutorial that enables your classmates to understand and potentially use the technique.

1.1 Suggested Topics

Consider these examples:

• Bootstrap methods
• Kernel density estimation
• Copulas
• Spectral analysis
• Discrete wavelet decomposition
• Weather typing
• Spatial interpolation methods (kriging, thin plate splines)
• 1D and 2D Gaussian processes
• Diffusion models

1.2 Scope Considerations

Note that topics vary significantly in breadth. Some methods like diffusion models represent entire research domains, while others like weather typing are more narrowly defined techniques. Regardless of your chosen topic’s inherent scope, focus your exploration on specific implementations and applications rather than attempting comprehensive coverage.

Base your work on two primary sources (research papers or textbooks) that provide both theoretical foundation and practical guidance. When multiple implementation approaches exist, acknowledge this diversity but concentrate your detailed analysis on a single, well-documented example.

2 Deliverables

2.1 Topic Proposal (October 17)

Submit a one-page PDF file to Canvas that includes:

• Your chosen method with brief justification for why it interests you
• Two primary sources (research papers or textbook chapters) that provide both theoretical foundation and practical implementation guidance
• Brief statement of how this method connects to course concepts

2.2 Draft Lecture Notes (November 14) — 10 points

Submit a complete draft of your lecture notes as a Quarto document in a GitHub repository, following the structure of past assignments. Create a repository, clone it to your computer, create a Quarto document, and push your work to GitHub. Render to PDF using Typst (or another backend of your choice) and submit the PDF to Canvas along with a link to your repository.

Your draft should include:

• Mathematical framework with proper notation and stated assumptions
• At least one worked example demonstrating the method’s application
• Discussion of strengths, limitations, and appropriate use cases
• Connections to course themes (uncertainty quantification, model evaluation, risk assessment)
• Proper citations and bibliography

This draft should be substantively complete to receive full credit and allow meaningful formative feedback before your teaching session.

2.3 Final Lecture Notes (December 5) — 40 points

Revise your lecture notes based on feedback received on your draft. Submit the final version following the same format: render to PDF and submit to Canvas with a link to your updated GitHub repository.

Your final contribution should be suitable for inclusion in the course textbook and follow the existing structure and style of current chapters.

2.4 Teaching Presentation (December 1, 3, or 5) — 50 points

Deliver a 20-minute instructional presentation during the Student Teaching Sessions. Use traditional teaching tools like chalkboard or whiteboard rather than prepared slides.

Your presentation should work through a concrete example that illustrates the method’s practical application. Clearly explain when, why, and how to use this approach, making explicit connections to techniques and concepts we’ve previously covered in class. Most importantly, facilitate meaningful discussion with your classmates about the method’s applications, limitations, and potential extensions.

3 Assessment and Grading Rubric

This assignment constitutes 20% of your final course grade and is assessed out of 100 total points.

3.1 Lecture Notes (50 points total)

Draft lecture notes (10 points) are graded on completeness and effort to enable meaningful feedback. Final lecture notes (40 points) are assessed using the rubric below:

Criterion	Excellent (36-40 pts)	Proficient (31-35 pts)	Developing (26-30 pts)	Inadequate (<26 pts)
Mathematical Framework (15 pts)	Clear, rigorous presentation with proper notation; assumptions explicitly stated and justified	Generally clear mathematical exposition with minor notation issues; most assumptions identified	Mathematical framework present but with some unclear elements or missing assumptions	Mathematical content incomplete, unclear, or contains significant errors
Application Examples (15 pts)	Clear, practical examples demonstrating method application; well-chosen illustrations	Good examples with adequate explanation; examples generally appropriate	Examples present but could be clearer or more relevant	Examples missing, unclear, or inappropriate
Critical Analysis & Course Integration (10 pts)	Thoughtful discussion of strengths/limitations; excellent connections to course concepts	Good analysis with clear connections to course material	Basic discussion of strengths/limitations; some course connections	Superficial analysis; weak or missing course connections

3.2 Teaching Presentation (50 points)

Criterion	Excellent (45-50 pts)	Proficient (39-44 pts)	Developing (33-38 pts)	Inadequate (<33 pts)
Clarity and Engagement (25 pts)	Exceptionally clear explanation; highly engaging presentation that maintains class attention	Clear explanation with good engagement; students follow the material well	Generally clear but some confusing moments; moderate engagement	Unclear explanation; poor engagement or class appears confused
Course Integration (17 pts)	Explicit, meaningful connections to multiple course concepts; demonstrates deep understanding	Clear connections to course material with good understanding evident	Some connections made but could be stronger or more explicit	Weak or missing connections to course concepts
Interactive Discussion (8 pts)	Skillfully facilitates meaningful discussion; encourages participation and handles questions well	Facilitates good discussion with appropriate participation	Basic discussion facilitation; some participation encouraged	Poor discussion facilitation; minimal or forced participation