Climate Extreme Events Modelling

Statistical modelling of extreme precipitation events in Southern France using climate projections, Generalized Linear Models (GLM) and Extreme Value Theory (EVT).

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Project Overview

This project was developed as part of an actuarial research project on climate risk.

The objective is to analyse historical and projected climate data in order to:

• explore the spatial distribution of extreme precipitation;
• identify geographic areas exposed to higher frequencies of heavy rainfall;
• model precipitation intensity using Gamma Generalized Linear Models;
• estimate the behaviour of extreme rainfall through Peaks-Over-Threshold (POT) and Generalized Pareto Distribution (GPD) models.

The project combines exploratory data analysis, spatial visualisation and statistical modelling to study the occurrence and severity of extreme precipitation events.

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Data

The analysis uses climate data for Southern France composed of:

• historical observations;
• climate projections;
• daily precipitation;
• wind speed;
• temperature;
• geographic coordinates (latitude and longitude).

Historical precipitation is converted from kg/m²/s to mm/day before the analysis.

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Methodology

The project follows the workflow below.

1. Data preparation

• data cleaning;
• date conversion;
• precipitation unit conversion;
• creation of calendar variables;
• merging historical and projected datasets.

2. Exploratory Data Analysis

• precipitation time series;
• precipitation distribution;
• annual and monthly summaries;
• threshold exceedance analysis.

3. Spatial Analysis

Interactive Leaflet maps are used to visualise the spatial distribution of extreme precipitation.

Geographic locations are segmented according to the average annual number of threshold exceedances.

4. Gamma Generalized Linear Models

Positive precipitation amounts are modelled using Gamma GLMs.

Candidate models are compared through:

• 10-fold cross-validation;
• RMSE;
• AIC;
• BIC.

5. Extreme Value Theory

Extreme precipitation is analysed using a Peaks-Over-Threshold approach.

The project includes:

• Mean Residual Life plots;
• Threshold Choice plots;
• Stationary Generalized Pareto models;
• Non-stationary GPD models with time-varying scale parameters.

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Main Results

The analysis highlights:

• strong spatial heterogeneity in extreme precipitation;
• locations exhibiting higher frequencies of threshold exceedances;
• the usefulness of Gamma GLMs for modelling strictly positive precipitation;
• the relevance of EVT for characterising the tail behaviour of extreme rainfall.

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Repository Structure

.
├── climate_extreme_events.Rmd
├── README.md
├── data/
│   ├── historical_precipitation.txt
│   └── projected_precipitation.txt
├── outputs/
│   ├── figures/
│   └── tables/
└── renv.lock

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Technologies

• R
• dplyr
• data.table
• ggplot2
• leaflet
• extRemes
• POT
• lubridate

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Statistical Methods

• Exploratory Data Analysis
• Spatial Data Analysis
• Gamma Generalized Linear Models
• Cross-Validation
• Model Selection (RMSE, AIC, BIC)
• Extreme Value Theory
• Peaks Over Threshold (POT)
• Generalized Pareto Distribution (GPD)

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Reproducibility

Clone the repository and open the R Markdown notebook.

install.packages("renv")
renv::restore()

Render the notebook with

rmarkdown::render("climate_extreme_events.Rmd")

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Actuary | Climate Risk | Statistical Modelling | Machine Learning