PS1: Nonstationary Rainfall Frequency Analysis (Due Oct 3)

Houston Daily Rainfall Extremes and Climate Change

Comprehensive analysis of nonstationary rainfall extremes using EVT, Bayesian methods, and hierarchical modeling
Author

CEVE 543 Fall 2025

Published

Wed., Aug. 27

This problem set spans approximately 5-6 weeks of class time and corresponds to the full scope of Module 1. The difficulty level reflects this substantial time commitment.

1 Provided

  • Daily precipitation data for Houston-area stations
  • Boilerplate Quarto template with data loading and basic plotting functions
  • util.jl file from the labs is available for use
  • Code from previous labs for analysis

1.1 Julia Package Installation

You will need to install Julia packages for this assignment. To do this:

  1. Open the Julia REPL
  2. Type ] to enter package mode
  3. Install packages with add PackageName (e.g., add GeoMakie CSV DataFrames Turing)

Note: The packages listed above are examples. Check the lab files to see which specific packages you need for your analysis. If you try to run code that uses a package you haven’t installed, you’ll get an error like ArgumentError: Package PackageName not found in current path.

2 Tasks

  1. Stationary GEV Analysis (ready after Lab 3)
    • Select one Houston-area station for primary analysis throughout tasks 1, 3, 4
    • Extract annual maximum daily precipitation from station data (provided)
    • Implement MLE using maximum_likelihood from Turing.jl (see Lab 3); benchmark results against Extremes.jl for validation
    • Implement Bayesian GEV inference using MCMC with Turing.jl; specify and justify physically-informed priors for location, scale, and shape parameters based on Houston climate knowledge (see Lab 4 for multiple approaches - pick and justify one)
    • Compare posterior distributions to MLE results and ensure convergence (see Lab 4)
    • Calculate and plot 50-year and 100-year return period estimates with posterior uncertainty bounds (see Lab 4)
  2. Multi-station Regional Analysis (ready after Lab 4)
    • Repeat Task 1 for 4 additional Houston-area stations using identical methods (pick one method from Task 1 - you don’t need to do all three models)
    • Create summary table comparing 50-year return level estimates across stations
    • Plot time series of all 5 stations on same axes to visualize synchronous behavior
  3. Nonstationarity Analysis (ready after Lab 5)
    • Conduct Mann-Kendall trend test on annual maxima; report test statistic, p-value, and interpretation
    • Repeat nonstationarity analysis for all 5 stations and create summary table comparing trend test p-values
    • Fit at least two nonstationary GEV models for your selected station
    • Justify your choice of covariate(s) and which parameters vary with the covariate(s)
    • Generate return level plots showing how extreme events change over time under your models
  4. Regional Parameter Estimation (ready after Lab 5)
    • Choose and justify your regional model specification: which nonstationary GEV parameters should vary by station vs shared regionally
    • Define and justify your choice of regional boundaries/stations to include based on geographic proximity, climate similarity, or other criteria
    • Implement your chosen regional model where some parameters are shared across stations while others remain station-specific
    • Compare posterior uncertainty in 50-year return levels: single-station vs regional estimates for stations with different data lengths
  5. Communication (can be drafted throughout)
    • Write exactly 2 paragraphs (150-200 words each) responding to this scenario: “A senior infrastructure engineer argues that 50 years of local data provides sufficient information for design and that climate models add unnecessary complexity and uncertainty.”
    • Paragraph 1: Address uncertainty quantification - explain how Bayesian methods and regional parameter sharing actually reduce parameter uncertainty compared to single-station MLE
    • Paragraph 2: Address model selection and risk - discuss evidence for nonstationarity and practical implications of underestimating future extreme events for infrastructure design
    • Reference specific results from your model comparison, prior specification, and uncertainty analysis to make concrete technical arguments