STATISTICAL METHODS FOR CLIMATE CHANGE ANALYSIS

The course deals with analysing the statistics of weather and climate by taking uncertainties and random fluctuations into account and provide objective assessment of various statistical hypotheses. The course also deals with analysing weather/climate fields to construct main patterns or modes of variability that control weather/climate variation. The course discusses basic concepts of probability and statistics, stationary time series, statistical significance and hypotheses testing, spectral analysis, regression analysis, empirical orthogonal functions and their
extension. Finally an overview is given on the analysis of extreme values.

The techniques covered in this course address important problems in identifying statistical relations between climate variables, assessing the quality of weather and climate predictions,
estimating high dimensional fields from sparse observations, distinguishing observed climate changes from natural variability, and attributing observed climate changes to human influences. Emphasis will
be placed on practical issues that arise in climate science, especially the problem of estimating more unknown parameters than samples.
After taking this course, the student should be able to address related problems with appropriate statistical methods while recognizing the major limitations and pitfalls of the methods.
The course provides students with practical experience through problem sets based on climate-related data.

Basic knowledge of calculus, linear algebra, probability and statistics at the level of an introductory bachelor course.
Prerequisite contents

Introduction to Probability and Counting
Interpreting Probabilities
Sample Spaces and Events
Permutations and Combinations

Some Probability Laws
Axioms of Probability
Conditional Probability
Independence and the Multiplication Rule

Discrete Distributions
Random Variables
Discrete Probablility Densities
Expectation and Distribution Parameters
Binomial Distribution

Continuous Distributions
Continuous Densities
Expectation and Distribution Parameters
Normal Distribution
Normal Approximation to the Binomial Distribution

Joint Distributions
Joint Densities and Independence
Expectation and Covariance
Correlation

Descriptive Statistics
Random Sampling
Picturing the Distribution
Sample Statistics
Boxplots
Estimation
Point Estimation
The Method of Moments and Maximum Likelihood
Interval Estimation and the Central Limit Theorem

Inferences on the Mean and Variance of a Distribution
Interval Estimation of Variability
Estimating the Mean and the Student-t Distribution
Hypothesis and Significance Tests on the Mean

Inferences on Proportions
Estimating Proportions
Testing Hypothesis on a Proportion
Comparing Two Proportions: Estimation
Comparing Two Proportions: Hypothesis Testing

Comparing Two Means and Two Variances
Point Estimation
Comparing Variances: The F Distribution
Comparing Means: Variances Equal (Pooled Test)

Sample Linear Regression and Correlation
Model and Parameter Estimation (Properties of Least-Squares Estimators)
(Confidence Interval Estimation and Hypothesis Testing)
Residual Analysis
Correlation

1. Data summary and smoothing
2. Predictive modelling
3. Time series regression analysis
4. Spectral analysis
5. Multivariate Data Analysis (Principal Component Analysis
6. Extreme value analysis

There is no official text book for this course. Lecture notes will be made available electronically a few days after each lecture. The following text may prove useful:

Statistical Analysis in Climate Research by von Storch and Zwiers, Cambridge Univ Press.

1) Class participation and homeworks 30% 
Students are expected to play an active role during the course and the labs.

2) Project 40% 
Each student will be assigned a data set about a climate-change problem. The student will be asked to analyse the data and write a brief summary report.

3) Final exam 30% 
The final exam consists of an oral discussion of the project.

Theoretical lectures complemented by lab classes. Teaching material prepared by the lecturer will be distributed during the course. The statistical software used in the course is R (www.r-project.org). 

oral

This subject deals with topics related to the macro-area "Climate change and energy" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development