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Statistics and ClimatePeter GuttorpUniversity of WashingtonNorwegian Computing Centerpeter@stat.washington.edu

Acknowledgements2007 ASA climate consensus workshop IPCC Fourth Assessment 2009 Copenhagen Diagnosis2011 NRC: Americas Climate Choices2012 Detection and attribution workshop in BanffNCAR IMAGe/GSPSMHI modeling groupSARMA and STATMOS network members, particularly Finn Lindgren and Peter CraigmileOutlineDifference between weather and climateModeling climateLines of evidenceAttributionData issues and global temperatureModel assessmentClimate and weatherClimate is the general or average weather conditions of a certain region.American Heritage Science Dictionary (2002)

Climate is what you expect; weather is what you get.Heinlein: Notebooks of Lazarus Long (1978)

Climate is the distribution of weather.AMSTAT News (June 2010)Climate modelsModels of climate and weatherNumerical weather prediction:Initial state is criticalDont care about entire distribution, just most likely eventNeed not conserve mass and energyClimate models:Independent of initial stateNeed to get distribution of weather rightCritical to conserve mass and energy

Same basic fluid dynamics equationsA simple climate modelWhat comes in

must go out

Solar constant1361 W/m2Earths albedo0.29Effective emissivity(greenhouse, clouds)0.61Stefans constant5.6710-8 W/(K4m2)SolutionAverage earth temperature is T = 289K (16C; 61F)One degree Celsius change in average earth temperature is obtained by changingsolar constant by 1.4%Earths albedo by 4.5%effective emissivity by 1.4% = 1 yields T = 255K (-18C; 0F)

Natural variability of solar constant 0.1-0.2%But in realityThe solar constant is not constantThe albedo changes with land use changes, ice melting and cloudinessThe emissivity changes with greenhouse gas changes and cloudinessNeed to model the three-dimensional (at least) atmosphereBut the atmosphere interacts with land surfacesand with oceans!So what is the greenhouse effect?What comes in is concentrated in shorter wavelengths than what must go out. The greenhouse gases in the atmosphere absorbs much of the energy in these longer outgoing waves, thus warming the atmosphere.Most abundant greenhouse gases:water vaporcarbon dioxidemethanenitrous dioxideozone

Circulation time: water vapor 9 days, carbon dioxide 30-1000 yearsmethane 12 yrs, N2O 114 yrsMethane conc up 2.5 times over preind, CO2 40%

10The climate engine IIf Earth did not rotate:tropics get higher solar radiationhot air rises, reducing surface pressureand increasing pressure higher upforces air towards poleslower surface pressure at poles makes air sinkmoves back towards tropics

The climate engine IISince earth does rotate, air packets do not follow longitude lines (Coriolis effect)Speed of rotation highest at equatorWinds travelling polewards get a bigger and bigger westerly speed (jet streams)Air becomes unstableWaves develop in the westerly flow (low pressure systems over Northern Europe)Mixes warm tropical air with cold polar airNet transport of heat polewardsClimate model historyEarly 1900s Bjerknes (equations)20s Richardson (numeric solution)1955 Phillips: first climate modelmid 70s Atmosphere modelsmid-80s Interactions with landearly 90s Coupled with sea & icelate 90s Added sulfur aerosols2000 Other aerosols and carbon cycle2005 Dynamic vegetation and atmospheric chemistry2010 Microphysics

Richardson took 6 weeks to calculate 8 hours of weather. Wrong answer!ParameterizationSome important processes happen on scales below the discretizationTypically expressed as regressions on resolved processesExamples:cloudsthunderstorms/cyclonesamount of solar radiation reaching groundpollutant emissionsCloud effectsLow clouds over oceanmore clouds reflect heat (cooling)fewer clouds trap heat (warming)High cloudsmore clouds trap heat (warming)And neither are well described in GCMsSome new models produce stochastic clouds

high: 5-14 km; low < 2kmEvidence of climate changeChanges inradiation spectrum

19971970Observed differencePacific sim.Global sim.CO2O3CH4Harries et al., Nature, 2001Sea surface temperature

trends are increasing in all oceans except north atlanticData from buoys, ship logs, stations, sonds etc.18Ocean heat content

Sea level rise

Not uniformeg larger at north Atlantic coastPredictions from TAR and CMIP220Other pieces of evidenceOcean acidificationChanges in seasonsIncreasing global temperatureHeating in upper troposphere and cooling in lower stratosphereSea ice decline in Arctic

Detection

Attribution

Models and data including ghgModels and datawith solar and volcanicforcings only90% ranges of uncertaintyAre there alternative explanations?Solar radiation

Mechanism?Friis-Christensen and Lassen, 1991.25Volcanic eruptionsDo volcanic eruptions (which cool the tropospheric temperature) produce similar amounts of CO2 to the anthropogenic contribution?2010 emissions 8 supereruptionsLast supereruption in Indonesia 74 Kyr agoPrevious in USA 2Myr agoSupereruption = 450 km^3 or 108 cubic miles of magma ejectedMount St Helens .05 cubic miles26Cosmic radiationRecent experiments at CERN show that interaction between water vapor, ammonium and cosmic radiation increases cloud production.No change observed in rate of cosmic radiation, increase in atmospheric ammonium concentrationFeedbacksPositive feedbacks: e.g. ice-albedoNegative feedbacks: e.g.increased CO2, temperature and precipitation increases leaf area, hence evapotranspiration, leading to coolingModel calculations indicate effect 37 times smaller than warmingData issues and global temperatureDaily temperature

maxmin08:0014:0021:00Global Historical Climatology Network

Oldest record Berlin cts from 170131Some issuesHomogenization / instrumentation Combination of dataNon-digitizedProprietaryChanging networkand I am not even talking about sea surface temperatures!

Gaussian Markov random field modelModel parametersSpatial climateWeather anomaliesTemperature data

Data model: temperature ~ elevation + climate + anomaly

Trend estimate

Inner CI, outer pred int, RW2 smoother34Comparison with other estimates

HadCRU red NOAA green GISS purple 35Adjusted vs unadjusted

Model assessmentComparing climate model output to weather dataGlobal models are very coarseRegional models are driven by boundary conditions given by global model runs

Looking for signals in data and modelsEven a regional model describes the distribution of weatherConsider a regional model driven by actual weather

Annual min temp; 50 km x 50 km grid, 3 hr time res (SMHI-RCA3; ERA40)

Stockholm observations since 175639How well does the climate model reproduce data?

Reason for minimaResolution in a regional climate model

50 x 50 km41Model problem?Clouds?Mean annual temperature about 1.7C higher in model than Stockholm seriesShould look at the part of simulation that predicts forested area?Use more regional series to estimate distribution?Comparison to forested model output

How compare two distributions in nonstationary and dependent case?43Using more dataSMHI synoptic stations in south central Sweden, 1961-2008

Not homogenized44GEV model

Spatial modelwhere

Parameters describe distribution (i.e. nonstationary climate)No model for simultaneous minima (i.e. weather)

Location slope vs latitudeMLE

Bayes

Some referencesGuttorp (2012) Climate statistics and public policy. Statistics, politics and policy 3:1. Guttorp, Sain and Wikle (eds.) (2012) Special issue: Advances in statistical methods for climate analysis. Environmetrics 23:5. NAS (2012) Climate change: Lines of evidence. Weart (2011) The Discovery of Global Warming.