statistical challenges in climatology chris ferro climate analysis group department of meteorology...
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Statistical Challenges in Climatology
Chris Ferro
Climate Analysis Group
Department of Meteorology
University of Reading
‘Climate is what we expect, weather is what we get.’ Mark Twain (?)
RSS Birmingham Local Group, Coventry, 11 December 2003
Overview
• History and general issues
• Examples of research topics
• Climate change simulations
• Concluding remarks
History
Jule G.Charney
VilhelmBjerknes
The Earth SimulatorLewis FryRichardson
1950
computerforecasts
1922
manualforecast
‘primitive’equations
1904 2002
GilbertWalker
40 Tflops10 Tbytes
southernoscillation
1923
General Issues
Dependent
Nonstationary
Huge datasets
Limited data
space and time: many scales
space and time: periodicities,
shocks, external forcings
station, satellite, simulation
short record, no replication
Examples of Research Topics
• Observations
• Climate modes
• Numerical models
• Data assimilation
• Forecast calibration
• Other topics
Observations
• Buoys• Field Stations• Ships & Aircraft
• Satellites• Radiosondes• Palaeo-records
• homogeneity, missing data, errors and outliers• network design and adaptive observations• statistical models to reconstruct past climates
Climate Modes
• Principal components: multi-site observations
• Identifies patterns of simultaneous variation
• Physical significance• Reduces dimension• Rotated, simplified etc.
North Atlantic Oscillation,courtesy of Abdel Hannachi
General Circulation Models
• Differential equations• Physical schemes• External forcings• Initial conditions• Numerical scheme• Deterministic output:
temp, precip, wind, pressure etc.
Data Assimilation
State
Observation
Solution
• Assumptions, approximations, choice of
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Forecast Calibration climate model
combinedregression model
Caio Coelho & Sergio Pezzulli
Prior: climate-model forecastLikelihood: regression model
Other Topics
• Model validation
• Forecast verification
• Statistical downscaling
• Climate change attribution
• Stochastic models of processes
Climate Change Simulations
• The PRUDENCE project
• Temperature and precipitation
• Distributional changes
• Extreme values
• Model uncertainty
PRUDENCE
• European Climate• 30-year control
simulation, 1961-1990• 30-year A2 scenario
simulation, 2071-2100• 10 high-resolution
regional models• 6 global models
From www.ipcc.ch
Mean Daily Rainfall
mm mm
Control (1961-1990) Scenario – Control
Mean Daily Rainfall
DJF MAM
SONJJA
Control (1961-1990) Scenario – ControlDJF MAM
JJA SON
mm mm
Simultaneous Confidence Intervals
such that ) ,( Find change. where
,ˆ/)ˆ(let ,point grideach For
iii
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uld
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Bb,Z ibi 1 }{ bootstrapblock sample-2 *)(
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Mean Daily Rainfall Response
DJF JJA
Mean Daily Rainfall Response
DJF JJA
Mean Temperature
ºC
Control (1961-1990) Scenario – Control
ºC
Mean TemperatureControl (1961-1990) Scenario – Control
ºC ºC
SONJJAJJA SON
DJF MAMDJF MAM
Distributional Changes
.)r(av of quantiles- usecan
, somefor )(: test To
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re. temperatu(scenario) control be )( Let
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Daily Rainfall ResponseDJF
Temperature ResponseDJF
Model Uncertainty
ikkijjiijk SYYSMMSGX )()()(E
Scenario YearModelAnnual Mean
Global model 1 2Regional model 1 2 3 4 5 … 1 2Control x x x x xA2 Scenario x x x x xB2 Scenario
Temperature: R2
Temperature: Model Effects
°C
Temperature: Model Response
°C
Extreme Values
./1)Pr(
satisfies ,,levelreturn period- The
.}/)(1{exp)Pr(
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Rainfall 10-DJF Return LevelsControl A2 Scenario / Control
GEV Parameter Estimates
Scale-change Model
p-value
Concluding Remarks
Need for sophisticated statistical techniques to help to analyse large amount of complex data.
‘There is, to-day, always a risk that specialists in two subjects, using languages full of words that are unintelligible without study, will grow up not only, without knowledge of each other’s work, but also will ignore the problems which require mutual assistance.’ Sir Gilbert Walker, 1927
Further Information
PRUDENCE
Climate Analysis Group
9th International Meeting
on Statistical Climatology,
Cape Town, 24-28 May 2004
prudence.dmi.dk
www.met.rdg.ac.uk/cag
www.csag.uct.ac.za/IMSC