PS1: Nonstationary Rainfall Frequency Analysis (Due Oct 6)

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

2 Tasks

  1. Stationary GEV Analysis (ready after Lab 3 - Fri 9/12)
    • Select one Houston-area station for primary analysis throughout tasks 1-2, 4
    • Extract annual maximum daily precipitation from station data (provided)
    • Implement MLE using Turing.jl with optimize(model, MAP()) workflow; 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
    • Compare posterior distributions to MLE results and ensure convergence
    • Calculate and plot 50-year and 100-year return period estimates with posterior uncertainty bounds
  2. Nonstationarity Detection (ready after Lab 4 - Fri 9/19)
    • Using a 20-year rolling window analysis, plot the estimated 100-year return level over time
    • Conduct Mann-Kendall trend test on annual maxima; report test statistic, p-value, and interpretation
  3. Multi-station Regional Analysis (ready after Lab 4 - Fri 9/19)
    • Repeat Tasks 1-2 for 4 additional Houston-area stations using identical methods
    • Create summary table comparing trend test p-values and 50-year return level changes
    • Plot time series of all 5 stations on same axes to visualize synchronous behavior
  4. Nonstationary GEV Modeling (ready after nonstationarity lecture - Mon 9/22)
    • Fit GEV model with time-varying location parameter: \mu(t) = \mu_0 + \beta \cdot t for your selected station
    • Compare covariate options: (a) year, (b) temperature index for location parameter only
    • Compare models using multiple criteria: AIC/BIC, posterior predictive performance, parameter interpretability, and robustness to outliers
    • Which model would you trust most for infrastructure design and why? Consider trade-offs between model complexity and trustworthiness
    • Generate return level plots showing how 50-year event changes over time under best model
    • Quantify change in 50-year return level from 1970 to 2023 with 90% credible intervals
  5. Hierarchical Bayesian Regional Pooling (ready after Lab 5 - Fri 9/26)
    • Implement partial pooling hierarchical model with station-level parameters drawn from regional hyperpriors
    • Compare posterior uncertainty in 50-year return levels: station-specific vs pooled estimates
    • Show shrinkage effects for one station with short record
  6. 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 pooling 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