9/6/14

1

Statistics and Climate!

Peter Guttorp!University of Washington!

Norwegian Computing Center!peter@stat.washington.edu!

Acknowledgements!

2007 ASA climate consensus workshop! IPCC Fourth Assessment !2009 Copenhagen Diagnosis!2011 NRC: America’s Climate Choices!2012 Detection and attribution workshop in Banff!2013 IPCC Fifth Assessment!NCAR IMAGe/GSP!SMHI modeling group!SARMA and STATMOS network members, particularly Finn Lindgren and Peter Craigmile!

9/6/14

2

Outline!

Difference between weather and climate!Modeling climate!Lines of evidence!Attribution!Data issues and global temperature!Model assessment!

Climate and weather!

Climate 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)!

9/6/14

3

Climate models!

Models of climate and weather!

Numerical weather prediction:!Initial state is critical!Don’t care about entire distribution, just most likely event!

Need not conserve mass and energy!

Climate models:!Independent of initial state!Need to get distribution of weather right!

Critical to conserve mass and energy!!

9/6/14

4

A simple climate model!

!What comes in!!!!!must go out!

Sπr2 (1− a)

4πr2εσT4

Solar constant!1361 W/m2!

Earth’s albedo!0.29!

Effective emissivity!(greenhouse, clouds)!0.615!

Stefan’s constant!5.67×10-8 W/(K4·m2)

Solution!

!!Average earth temperature is T = 288K (15°C)!One degree Celsius change in average earth temperature is obtained by changing!solar constant by 1.4%!Earth’s albedo by 4.5%!effective emissivity by 1.4%!ε = 1 yields T = 255K (-18°C) !

T4 = 1365 × 0.74 × 0.615 × 5.67

× 108

9/6/14

5

But in reality…!

The solar constant is not constant!The albedo changes with land use changes, ice melting and cloudiness!The emissivity changes with greenhouse gas changes and cloudiness!Need to model the three-dimensional (at least) atmosphere!But the atmosphere interacts with land surfaces…!…and 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 vapor!•  carbon dioxide!•  methane!•  nitrous dioxide!•  ozone!

!

9/6/14

6

The climate engine I!If Earth did not rotate:!tropics get higher solar radiation!hot air rises, reducing surface pressure!and increasing pressure higher up!forces air towards poles!lower surface pressure at poles makes air sink!moves back towards tropics!

The climate engine II!

Since earth does rotate, air packets do not follow longitude lines (Coriolis effect)!Speed of rotation highest at equator!Winds travelling polewards get a bigger and bigger westerly speed (jet streams)!Air becomes unstable!Waves develop in the westerly flow (low pressure systems over Northern Europe)!Mixes warm tropical air with cold polar air!Net transport of heat polewards!

9/6/14

7

Climate model history!

Early 1900s Bjerknes (equations)!20s Richardson (numeric solution)!1955 Phillips: first climate model!mid 70s Atmosphere models!mid-80s Interactions with land!early 90s Coupled with sea & ice!late 90s Added sulfur aerosols!2000 Other aerosols and carbon cycle!2005 Dynamic vegetation and atmospheric chemistry!2010 Microphysics!!

Parameterization!

Some important processes happen on scales below the discretization!Typically expressed as regressions on resolved processes!Examples:!

clouds!thunderstorms/cyclones!amount of solar radiation reaching ground!pollutant emissions!

9/6/14

8

Cloud effects!

Low clouds over ocean!more clouds reflect heat (cooling)!fewer clouds trap heat (warming)!

High clouds!more clouds trap heat (warming)!

And neither are well described in GCMs!Some new models produce stochastic clouds!!

Evidence of climate change!

9/6/14

9

Changes in radiation spectrum!

1997"1970"

Observed difference"

Pacific sim."

Global sim."

CO2"O3" CH4"

Harries et al., Nature, 2001"

Sea surface temperature!

1880 1900 1920 1940 1960 1980 2000

-1.0

-0.5

0.0

0.5

Year

Tem

pera

ture

ano

mal

y

9/6/14

10

Ocean heat content!

SPM

Summary for Policymakers

10

1900 1920 1940 1960 1980 2000−20

−10

0

10

20

Year

(1022

J)

Change in global average upper ocean heat content(c)

Global average sea level change

1900 1920 1940 1960 1980 2000−50

0

50

100

150

200

Year

(mm

)

(d)

Arctic summer sea ice extent

1900 1920 1940 1960 1980 20004

6

8

10

12

14

Year(m

illion

km

2 )

(b)

Northern Hemisphere spring snow cover

1900 1920 1940 1960 1980 200030

35

40

45

Year

(milli

on k

m2 )

(a)

Figure SPM.3 | Multiple observed indicators of a changing global climate: (a) Extent of Northern Hemisphere March-April (spring) average snow cover; (b) extent of Arctic July-August-September (summer) average sea ice; (c) change in global mean upper ocean (0–700 m) heat content aligned to 2006−2010, and relative to the mean of all datasets for 1970; (d) global mean sea level relative to the 1900–1905 mean of the longest running dataset, and with all datasets aligned to have the same value in 1993, the first year of satellite altimetry data. All time-series (coloured lines indicating different data sets) show annual values, and where assessed, uncertainties are indicated by coloured shading. See Technical Summary Supplementary Material for a listing of the datasets. {Figures 3.2, 3.13, 4.19, and 4.3; FAQ 2.1, Figure 2; Figure TS.1}

Sea level rise!

9/6/14

11

Other pieces of evidence!

Ocean acidification!Changes in seasons!Increasing global temperature!Heating in upper troposphere and cooling in lower stratosphere!Sea ice decline in Arctic !!

Detection!

Observations 1946-56 Model

ature

1986-96 wie

rs, 2

000,

Na

Wea

ver a

nd Z

w

XYFiltering and projection onto reduced

HE � XY Total least squares regression in reduced dimension space

onto reduceddimension space

Evaluate Evaluate E ˆ

3

amplitudeestimates

goodness of fit

E H

9/6/14

12

Attribution!

Models and data including ghg!

Models and data!with solar and volcanic!forcings only!

Are there alternative explanations?!

9/6/14

13

Solar radiation!

Volcanic eruptions!

Do volcanic eruptions (which cool the tropospheric temperature) produce similar amounts of CO2 to the anthropogenic contribution?!2010 emissions ≈ ! ! !

!8 supereruptions!Last supereruption in Indonesia 74 Kyr ago!Previous in USA 2Myr ago!

9/6/14

14

Cosmic radiation!

Recent 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 concentration!

Feedbacks!

Positive feedbacks: e.g.!! ice-albedo!

Negative feedbacks: e.g.!increased CO2, temperature and precipitation !increases leaf area, !hence evapotranspiration, !leading to cooling!

Model calculations indicate effect 3–7 times smaller than warming!

9/6/14

15

Global temperature!

Global Historical Climatology Network!

9/6/14

16

Some issues!

Homogenization / instrumentation !Combination of data!Non-digitized!Proprietary!Changing network!…and I am not even talking about sea surface temperatures!!!

Gaussian Markov random field model!! ! !Model parameters!! ! !Spatial climate!! ! !Weather anomalies!! ! !Temperature data!

!Data model: temperature ~ elevation + climate + anomaly!

θ

µ(u) θxt(u) θ,µ(u)yt,i θ,µ(ui),xt (ui)

9/6/14

17

Trend estimate!

1880 1900 1920 1940 1960 1980 2000

-1.0

-0.5

0.0

0.5

Year

Anomaly

Comparison with other estimates!

1850 1900 1950 2000

-1.0

-0.5

0.0

0.5

Year

Anomaly

Base period 1970-1989

1850 1900 1950 2000

-1.0

-0.5

0.0

0.5

Year

Anomaly

Base period 1970-1989

1850 1900 1950 2000

-1.0

-0.5

0.0

0.5

Year

Anomaly

Base period 1970-1989

1850 1900 1950 2000

-1.0

-0.5

0.0

0.5

Year

Anomaly

Base period 1970-1989

1850 1900 1950 2000

-1.0

-0.5

0.0

0.5

Year

Anomaly

Base period 1970-1989

1850 1900 1950 2000

-1.0

-0.5

0.0

0.5

Year

Anomaly

Base period 1970-1989

9/6/14

18

Adjusted vs unadjusted!

1880 1900 1920 1940 1960 1980 2000

-0.15

-0.10

-0.05

0.00

0.05

Year

Adj

uste

d m

inus

una

djus

ted

-0.6 -0.4 -0.2 0.0 0.2 0.4

-0.6

-0.4

-0.2

0.0

0.2

0.4

Adjusted

Unadjusted

Model assessment!

9/6/14

19

Comparing climate model output to

weather data!Global models are very coarse!Regional models are driven by boundary conditions given by global model runs!!

Looking for signals in data and models!

Even a regional model describes the distribution of weather!Consider a regional model driven by “actual weather”!!!!!!Annual min temp; 50 km x 50 km grid, 3 hr time res (SMHI-RCA3; ERA40)!!

9/6/14

20

How well does the climate model

reproduce data?!

-25 -20 -15 -10

-20

-15

-10

-5

Observed minimum daily mean

Reg

iona

l min

imum

dai

ly m

ean

Observed minimum temperature 1960-2004

Temperature

Frequency

-25 -20 -15 -10 -5

02

46

810

Regional minimum temperature 1961-2005

Temperature

Frequency

-20 -15 -10 -5 0

02

46

8

Resolution in a regional climate model!

50 x 50 km!

9/6/14

21

Model problem?!

Clouds?!Mean annual temperature about 1.7°C higher in model than Stockholm series!Does the simulation predict observations?!Use more regional series to estimate distribution?!

Is the station really in open air?!

9/6/14

22

Comparison to forested model output!

-25 -20 -15 -10

-25

-20

-15

-10

-5

Observed values

Mod

el p

redi

ctio

ns

Using more data!

SMHI synoptic stations in south central Sweden, 1961-2008 !

12 14 16 18 20 22 24

5658

6062

6466

68Lo

ngitu

de

Latitude

Stockholm

Borlänge

Göteborg

Sundsvall

Lund

Sweden

12 3 456 7

8 1012 13 14

15 1617

9,11*

1960 1970 1980 1990 2000 2010

510

15

Year

Site

ID

(2 missing)

(1 missing)

(30 missing)

(129 missing)

(14 missing)

(66 missing)(6 missing)

(61 missing)

F igure 1: T he left-hand panel displays a map of Sweden indicat ing the 17 locat ions that were

included in the modeling exercise. T he rectangle indicates the spat ial domain of interest ,

D. T he locat ion denoted with an asterisk was kept aside for cross-validat ion purposes. T he

right-hand panel summarizes the data availability. For each of the 17 locat ions, the shaded

9/6/14

23

GEV model!

F(x) = exp − 1+ ξ x − µσ

$%&

'()

$%&

'()

1/ξ$

%&

'

()

ξ < 0

ξ > 0

ξ = 0

Spatial model!

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

−Mt (s) ~ GEV(µ t (s),σ,ξ)

µ t (s) = β0 (s) + β1(s) t − 1961( ) / 50βi (s) ~ GauP(µi,σi (1− ηexp(−θid(s)), i = 0,1

9/6/14

24

Location slope vs latitude!

MLE!!!!!Bayes!

57 58 59 60 61 62 63-1

01

23

45

Latitude

Slo

pe

pa

ram

ete

r

●

●

●●

●●●

●●●

●

58 59 60 61 62

0.00

0.05

0.10

0.15

0.20

Latitude

Cha

nge

per y

ear f

or lo

catio

n

Some references!Guttorp (2012) Climate statistics and public policy. Statistics, politics and policy 3:1. !Guttorp (2014) Statistics and climate. Ann. Rev. Stat. 1:87.!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. !!