http://www.gfi.uib.no/ nilsg/kurs/klimaanalyse.html

Dr. David B. Stephenson¹
Department of Meteorology
University of Reading
Earley Gate PO Box 243
Reading RG6 6BB, U.K.
E-mail: D.B.Stephenson@reading.ac.uk

Dr. Rasmus E. Benestad
Norwegian Meteorological Institute DNMI
P.O. Box 43, Blindern
N-0313 Oslo
E-mail: rasmus.benestad@dnmi.no

Course Aim: To introduce the basic statistical concepts relevant to environmental science and to provide experience in the correct use and interpretation of the various statistical methods currently used in the analysis of weather/climate observed and model simulated data.

Practical Exercises Each topic covered in the lectures will be followed by exercises using real data in practical classes.

Prerequisites Minimal statistical knowledge but some basic mathematics and computer skills will be assumed.

Day	Morning 10:00-12:00	Afternoon 14:00-16:00
Monday	1. Introduction (DBS)	2. Descriptive statistics (DBS)
Tuesday	3. Probability Distributions (REB)	4. Outliers and extremes (REB)
Wednesday	5. Statistical Inference (REB)	6. Linear modelling I (DBS)
Thursday	7. Linear modelling II (DBS)	8. Multivariate methods (REB)
Friday	9. Time series I (DBS)	10. Time series II (REB)

(***) denotes initials of the lecturer who will present the topic

List of Course Participants

4-8 September 2000

Participant	E-mail address
Jan Kristian Jensen	j.k.jensen@dnmi.no
Cathrine Myrmehl	cathrine@nrsc.no
Alf Kirkevåg	alf.kirkevag@geofysikk.uio.no
Idar Barstad	idar@gfi.uib.no
Helge Drange	helge@nrsc.no
Nils Gunnar Kvamstø	nilsg@gfi.uib.no
Kjetil Lygre	kjetil@nrsc.no
Øvind Breivik	breivik@nrsc.no
Tore Furevik	tore@gfi.uib.no
Jan Erik Stiansen	jan.erik.stiansen@imr.no
Odd Helge Otterå	oddho@nrsc.no
Lasse Dretvik	lasse.dretvik@start.no
Paul Skeie	paul@gfi.uib.no
Gard Hauge	gard@gfi.uib.no
Vibeke W Thyness	vibeke@gfi.uib.no
Even Nilsen	even@gfi.uib.no
Kristian Nielsen	kristian@gfi.uib.no
Anne Britt Sandoe	annebrit@nrsc.no
Knut Barthel	barthel@gfi.uib.no
Anne D Sandvik	anne@gfi.uib.no
Øyvind Sætra	o.saetra@dnmi.no
Morten Skogen	morten@imr.no
Ina T Kindem	ina@gfi.uib.no
Helge Strand	helge@gfi.uib.no
Martin Miles	martin.miles@geog.uib.no
Stig Nilsen	stig@gfi.uib.no
Øyvind Byrkjedal	oyvindb@gfi.uib.no
Mats Bentsen	mats@nrsc.no

 

• Contents
• Introduction
  • Purpose of this course
  • Brief history of statistics
  • What is statistics ?
  • General philosophy
  • Statistical software
  • Further reading
  • Exercises
• Descriptive statistics
  • Tabulation and the data matrix
  • Summary measures for univariate data
  • Resistant measures
  • Graphical representation
    • Dotplot
    • Boxplot (box-and-whiskers plot)
    • Stem-and-Leaf plot
    • Histogram
  • Transformation of data
  • Further reading
  • Exercises
• Probability Distributions
  • Probability distribution and density functions
    • What is probability distribution and why use it?
      • Probability
      • Distributions
      • Cumulative probability and probability density functions
  • Normal/Gaussian distribution
  • Binomial distribution
    • Example Coin-flipping
  • Gamma distribution
  • Poisson distribution
  • Higher order moments: skewness, kurtosis, etc.
    • Skewness
    • The Kurtosis
  • Further reading
  • Exercises
• Outliers and Extremes
  • Robustness and Resistance
  • Location, Spread and Quantiles
    • Location
    • Spread
    • Example: outliers in the September temperature in Bergen
  • Rank correlation
  • Extreme values
  • Further reading
  • Exercises
• Statistical inference
  • The Null and alternative hypotheses
    • Some definitions
  • Confidence intervals for rejection
  • Student's t-test
  • F-statistics
  • Wilcoxon-Mann-Whitney type tests
  • Chi-squared test
    • Kolmogorov-Smirnov tests^*
    • The Chi-squared distribution^*
  • Monte Carlo tests
  • Test for trends^*
    • Trend testing based on Spearman rank coefficient^*
    • Mann-Kendall rank correlation statistics^*
    • Trend testing based on student's t-test^*
  • Further reading
  • Exercises
• Linear Regression I: Introduction
  • A few words on modelling strategy ...
  • Linear regression
  • ANalysis Of VAriance (ANOVA)
  • Model fit validation using residual diagnostics
  • Weighted and robust regression
  • Further sources of information
  • Exercises
• Linear Regression II: Extensions
  • Multiple regression
  • Multivariate regression
  • Non-linear response
  • Parametric and non-parametric regression
  • Further sources of information
  • Exercises
• Multivariate methods
  • The geographical distribution of correlation
    • Hovmöller plots
  • Problem of multiplicity^*
  • The data matrix and SVD
    • S-mode
    • T-mode^*
  • Empirical Orthogonal Function analysis
    • Example of use: Spatial correlation maps based on EOF products
    • Geographical weighting
    • Rotated EOFs^*
    • Complex and frequency-domain EOFs^*
      • Complex EOFs^*
      • Frequency-domain EOFs^*
    • Extended EOFs^*
  • CCA, SVD and Multivariate regression^*
    • Classical CCA^*
    • Barnett-Preisendorfer CCA^*
    • SVD^*
    • MVR^*
  • Common EOFs^*
  • Cluster analysis^*
  • Further reading
  • Exercises
• Time series I: time-domain
  • Introduction
  • Time series components
  • Filtering and smoothing
  • Serial correlation
  • ARIMA(p,d,q) time series models
  • Further sources of information
  • Exercises
• Time series analysis II: frequency-domain
  • Fourier and Fast Fourier Transforms
    • FT and filtering^*
    • FT and Monte Carlo testing^*
  • Estimating power spectra
  • Red and white noise characteristics
    • FT and the problem of multiplicity^*
  • Advanced topics
    • Multi-taper, maximum entropy, and SSA^*
      • Multi-taper
      • Maximum entropy method
    • Coherence and Cross-spectra^*
    • Singular Spectrum Analysis^*
    • Wavelet analysis^*
    • 2-D FT^*
  • Further reading
  • Exercises
    • Getting started with MINITAB
    • Dataset 1: rdgmorph.txt
    • Dataset 2: darwin.txt
    • Dataset 3: darwinraw.txt
    • Dataset 4: atldjf.dat
• Bibliography
• About this document ...