math, models, and climate change · the “ozone hole,” was first observed in the early 1980s....

Math, Models, and Climate Change How shaving cream moved a jet stream, and how mathematics can help us better understand why

Edwin P. GerberCenter for Atmosphere and Ocean ScienceCourant Institute of Mathematical SciencesNew York University

9 October 2013 - Wichita State University

Support for this research was provided by the U.S. National Science Foundation.

Anthropogenic Climate Change

Global Warming Ozone Holevs.

chlorofluorcarbons(CFCs such as freon)

greenhouse gasesCO2, CH4, N2O

Global Warming Ozone Hole

[IPCC 2013 Assessment Report]

vs.


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Global Warming Ozone Hole

[IPCC 2013 Assessment Report]

vs.


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Do Not Cite, Quote or Distribute& 0A23,& B@*$%&7$C/=D&2E3&

&

Figure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

The severe depletion of Antarctic ozone, known asthe “ozone hole,” was first observed in the early 1980s.The depletion is attributable to chemical destruction byreactive halogen gases, which increased in the strato-sphere in the latter half of the 20th century (see Q16).Conditions in the Antarctic winter stratosphere are highlysuitable for ozone depletion because of (1) the longperiods of extremely low temperatures, which promotepolar stratospheric cloud (PSC) formation; (2) the abun-dance of reactive halogen gases, which chemically destroyozone; and (3) the isolation of stratospheric air during thewinter, which allows time for chemical destruction tooccur (see Q10). The severity of Antarctic ozone deple-tion can be seen using satellite observations of total ozone,ozone altitude profiles, and long-term average values ofpolar total ozone.

Antarctic ozone hole. The most widely used imagesof Antarctic ozone depletion are those from space-basedmeasurements of total ozone. Satellite images madeduring Antarctic winter and spring show a large regioncentered near the South Pole in which total ozone is highlydepleted (see Figure Q11-1). This region has come to becalled the “ozone hole” because of the near-circular con-tours of low ozone values in the images. The area of theozone hole is defined here as the area contained withinthe 220-Dobson unit (DU) contour in total ozone maps(light blue color in Figure Q11-1). The maximum areahas reached 25 million square kilometers (about 10 mil-lion square miles) in recent years, which is nearly twicethe area of the Antarctic continent (see Figure Q11-2).Minimum values of total ozone inside the ozone hole aver-aged in late September have reached below 100 DU,which is well below normal springtime values of about200 DU (see Figure Q11-2).

Altitude profiles of Antarctic ozone. Ozone withinthe “ozone hole” is also measured using balloonborneinstruments (see Q5). Balloon measurements showchanges within the ozone layer, the vertical region thatcontains the highest ozone abundances in the stratosphere.At geographic locations where the lowest total ozone

values occur in ozone hole images, balloon measurementsshow that the chemical destruction of ozone is completeover a vertical region of several kilometers. Balloon

TWENTY QUESTIONS: 2006 UPDATE

Q.22

III. STRATOSPHERIC OZONE DEPLETION

Q11: How severe is the depletion of the Antarctic ozone layer?

100 300 400 500Total OzTT one (Dobson units)

4 October 2001

200

Antarctic Ozone Hole

Figure Q11-1. Antarctic “ozone hole.” Total ozonevalues are shown for high southern latitudes as meas-ured by a satellite instrument. The dark blue and purpleregions over the Antarctic continent show the severeozone depletion or “ozone hole” now found during everyspring. Minimum values of total ozone inside the ozonehole are close to 100 Dobson units (DU) compared withnormal springtime values of about 200 DU (see Q4). Inlate spring or early summer (November-December) theozone hole disappears in satellite images as ozone-depleted air is displaced and mixed with ozone-rich airtransported poleward from outside the ozone hole.

Severe depletion of the Antarctic ozone layer was first observed in the early 1980s. Antarctic ozone depletionis seasonal, occurring primarily in late winter and early spring (August-November). Peak depletion occurs inearly October when ozone is often completely destroyed over a range of altitudes, reducing overhead totalozone by as much as two-thirds at some locations. This severe depletion creates the “ozone hole” in imagesof Antarctic total ozone made from space. In most years the maximum area of the ozone hole far exceeds thesize of the Antarctic continent.

Antarctic Ozone Hole

[WMO 2006 Ozone Assessment]

How does anthropogenic forcing affect the atmospheric circulation?

[Image from wikipedia]

But first, what drives the atmospheric circulation?

r=6371 km

troposphere ~ 10 km

But first, what drives the atmospheric circulation?

(not drawn to scale)

But first, what drives the atmospheric circulation?Short answer: differential heating!

solar radiation: heat from below,

and more at the equator

But first, what drives the atmospheric circulation?Short answer: differential heating!

atmosphere transportsenergy (heat and moisture)upwards and polewards

Early ideas: George C. Hadley (1735)

a cell that transportsheat in the meridional

direction

↺

Early ideas: George C. Hadley (1735)

as low level winds approach equator,

they will turn westwardto conserve momentum:

the trade winds

What about the upper level winds?

(no one really worried aboutupper level winds until the

20th century)

.

What about the upper level winds?

x

xx.

osurface windskept in check

by friction

x but upper levelwinds are generate

strong eastward (westerly) jets,

generating strongvertical shear

o.

.

An unstable situation...

⚡Hadley’s singlecell is unstable

(baroclinic instability)

[Charney, 1947; Eady 1949]

Flow is fundamentally not zonally symmetric

⚡Hadley’s singlecell is unstable

(baroclinic instability)

Generates Rossby waves, whose

restoring force is the differential rotation of

the planet.[Rossby et al. 1939]

Meridional structure of the atmospheric circulation

Hadley Cell

Ferrel Cell

Polar Cell

Instability breaks upthe meridional circulation

into three cells

⚡

Hadley Cell

Ferrel Cell

Polar Cell

William Ferrel (1817-1891)

Instability breaks upthe meridional circulation

into three cells

⚡

Meridional structure of the atmospheric circulation

The “eddies,” or deviations from the zonal mean play a critical role in the circulation

Hadley Cell

Ferrel Cell

Polar Cell

⚡

Rossby waves andeddies transport heat and momentum - necessary

to explain the zonal mean.

[Lorenz, 1967]

The circulation in all its glory ...

The brightness (equivalent blackbody) temperature

Latitude

80S 60S 40S 20S EQ 20N 40N 60N 80N

20

50

200

500

8501000 20

15105

0510152025303540455055

ERA40 DJF zonal mean zonal wind [u]

20 km

pres

sure

(hP

a)

10 km

0 km

=120 mph

The jet streams in austral summer (Dec.-Feb.)

m/s

The jet streams in austral summer (Dec.-Feb.)Recent trends

2000–2079 in the CCMVal!2 REF!B2 and AR4 A1B sce-nario integrations. An exception is section 3.1, where trendsare calculated for the period 1979–1999 to be comparedwith reanalysis data, and for the period 2001–2050 to becompared with the previous CCMVal activity (CCMVal!1).Past climate changes are analyzed for a relatively longperiod of 40 years, mainly because O3 depletion beganbefore 1979; observations have shown that O3 concentrationstarted to decrease in the late 1960s, although early trendsare quite weak [e.g., Solomon, 1999, Figure 1]. The longerperiod also allows us to obtain better statistics and compareour results with previous studies. The analysis length forfuture climate change is twice as long as that for past climatechange because O3 recovery is predicted to be slower thanits depletion in the past. The CCMVal!2 models predict thattotal column O3 over the Antarctic will likely reach its 1980value around 2060 [Austin et al., 2010]. Although the

analysis period is somewhat subjective, results are onlyweakly sensitive to the choice of time period. It is found thattrends over 2000–2049 are quantitatively similar to thoseover 2000–2079, although the intermodel standard deviationis somewhat larger.[13] Stratospheric O3 has strong seasonality and its long!

term trend is largest in the late spring. Its impact on the tro-pospheric circulation, however, is delayed by a few monthsand reaches a maximum in the summer, December–February(DJF) [Gillett and Thompson, 2003; Shindell and Schmidt,2004; Perlwitz et al., 2008; Son et al., 2008]. Hence, mostanalyses in this study are carried out for the SH summer.

3. Results

[14] We first evaluate the CCMVal!2 models by com-paring the spatial and temporal structure of the zonal mean

Figure 1. The long!term mean (thick orange) and linear trend (thin black contour) of DJF [u] over1979–1999: (a) CCMVal!2 REF!B1 multimodel mean, (b) ERA40, and (c) NCEP!NCAR reanalysisdata. (d) Future trends over 2000–2079 as simulated by the CCMVal!2 REF!B2 models. Contour intervalsof climatological wind and trend are 10 m s!1 starting from 10 m s!1 and 0.4 m s!1/decade, respectively. InFigures 1a and 1d, multimodel mean values exceeding 1 standard deviation are shaded. In Figures 1b and1c, trends which are statistically significant at the 95% confidence level are shaded. Zero contours are omit-ted in all plots.

SON ET AL.: OZONE AND SOUTHERN HEMISPHERE CLIMATE D00M07D00M07

4 of 18

[Son et al. 2010]

20 km

pres

sure

(hP

a)

10 km

0 km

DJF Trends in zonal mean zonal wind

late 20th century

[Son et al. 2008;Gerber et al. 2011]

reanalysis


reanalysis

late 20th century

models w/GHGs models w/ GHGs+O3



late 20th century

predictions 2000-2079

?


reanalysis models w/GHGs models w/ GHGs+O3

Questions

• What are the relative roles of greenhouse gases and ozone in forcing Southern Hemisphere circulation changes?

• What causes uncertainty in the circulation response? (That is, why is there such variance in model projections?)

• How can we reduce the uncertainty in the circulation response?

• Coupled Models (CMIP3,5 Coupled Model Intercomparison Project, phases 3,5)

• simulate the atmosphere, ocean, and land surface (a “coupled” simulation between the key components of the climate system)

• our best tool for quantitative prediction of climate change

• Chemistry Climate Models (CCMs)

• simulate interactive ozone chemistry in the stratosphere: can predict ozone hole and its recovery

• generally specify the surface ocean temperatures (not a coupled simulation)

• Idealized Atmospheric Models

• primitive equation dynamics on the sphere (guts of an atmospheric model)

• simplified climate physics (no radiation, clouds, moisture)

Century II Performing Arts Center

(cast, in order of decreasing CPU time)

Temperature Signature of Anthropogenic Forcing

hPa (a)

Temperature change, 1960 1999

Mod

els

with

fixe

d oz

one 200

400

600

800

1000

(b)


hPa

latitude

(c)

Mod

els

with

var

ying

ozo

ne

60S 30S 0 30N 60N

200

400

600

800

1000

latitude

°C

(d)

60S 30S 0 30N 60N

10 8 6 4 2 0 2 4 6 8

hPa (a)


Mod

els

with

fixe

d oz

one 200

400

600

800

1000

(b)


hPa

latitude

(c)M

odel

s w

ith v

aryi

ng o

zone

60S 30S 0 30N 60N

200

400

600

800

1000

latitude

°C

(d)

60S 30S 0 30N 60N

10 8 6 4 2 0 2 4 6 8

hPa (a)


Mod

els

with

fixe

d oz

one 200

400

600

800

1000

(b)


hPa

latitude

(c)

Mod

els

with

var

ying

ozo

ne

60S 30S 0 30N 60N

200

400

600

800

1000

latitude

°C

(d)

60S 30S 0 30N 60N

10 8 6 4 2 0 2 4 6 8

Temperature Signature of Anthropogenic Forcing

Circulation responds to changes in temperature gradients

Butler et al. 2010

FIG. 2. The zonal-mean response to tropical tropospheric heating. Bold black lines in all plots represent the control run tropopauseheight. (left) The thermal forcing (K day21). (middle) The total eddy heat flux response (shading) (K m s21) and the temperature re-sponse (contours) (K). (right) The total eddy momentum flux response (shading) (m2 s22) and the zonal-mean zonal wind response(contours) (m s21). (a) Results for tropical upper-tropospheric heating; (b) results for shallow tropical upper-tropospheric heating;(c) results for narrow tropical upper-tropospheric heating; (d) results for tropical heating centered at 500 hPa. Note the forcings are shownpole–pole but the responses are shown for only one hemisphere. The thermal forcings are detailed in Table 1.

1 JULY 2010 BUTLER ET AL . 3481

GHG-likewarming

Butler et al. 2010





GHG-likewarming

The circulation response to thermal forcing in an idealized, dry atmospheric model

the cooling while continuing to allow the upper bound ofthe cooling to extend through the top of the stratosphere.When the center of the heating is lifted by 25 hPa (Fig.5b), the amplitude of the response is damped by ;50%,but the structure of the response is unchanged and thekey features remain significant: the heat fluxes are stillanomalously positive in the polar stratosphere, the upper-tropospheric momentum fluxes are still anomalouslypoleward across 508 latitude, and the surface zonal flow isstill anomalously easterly along ;408 and westerly along;608 latitude (see also Table 4). However, when thecenter of the heating is lifted by 50 hPa (Fig. 5c), thebarotropic component of the tropospheric responselargely vanishes.The sensitivity of the tropospheric response to polar

stratospheric cooling is investigated further in Fig. 6. We

again examine the effect of lifting the cooling, but in thiscase the depth of the cooling is only;100 hPa. Figure 6ashows results for shallow cooling centered at 200 hPa.The structure of the response is largely unchanged fromthat shown in the top of Fig. 5, albeit the amplitude ofthe response is weaker. Note that in the case of shallowcooling the increased heat fluxes in the polar strato-sphere are confined to the levels where cooling is oc-curring (Fig. 6a, middle panel). Figures 6b,c show resultsfor the same shallow cooling, but in these cases thecooling has been lifted by 25 hPa (Fig. 6b) and 50 hPa(Fig. 6c). Lifting the cooling has little effect on the changesin polar stratospheric temperatures (middle column), but ithas a dramatic effect on the changes in the troposphericcirculation (right column). When the cooling is liftedby 25 to 175 hPa (Fig. 6b), the tropospheric response

FIG. 5. As in Fig. 2, but for (left) the responses to the polar stratospheric thermal forcings. The forcings are documented in Table 1 and arecentered at (a) 100, (b) 75, and 50 hPa (c). (right) Note the shading scaling is about half that for Fig. 2.

3484 JOURNAL OF CL IMATE VOLUME 23

The circulation response to thermal forcing in an idealized, dry atmospheric model

Butler et al. 2010



the cooling while continuing to allow the upper bound ofthe cooling to extend through the top of the stratosphere.When the center of the heating is lifted by 25 hPa (Fig.5b), the amplitude of the response is damped by ;50%,but the structure of the response is unchanged and thekey features remain significant: the heat fluxes are stillanomalously positive in the polar stratosphere, the upper-tropospheric momentum fluxes are still anomalouslypoleward across 508 latitude, and the surface zonal flow isstill anomalously easterly along ;408 and westerly along;608 latitude (see also Table 4). However, when thecenter of the heating is lifted by 50 hPa (Fig. 5c), thebarotropic component of the tropospheric responselargely vanishes.The sensitivity of the tropospheric response to polar

stratospheric cooling is investigated further in Fig. 6. We

again examine the effect of lifting the cooling, but in thiscase the depth of the cooling is only;100 hPa. Figure 6ashows results for shallow cooling centered at 200 hPa.The structure of the response is largely unchanged fromthat shown in the top of Fig. 5, albeit the amplitude ofthe response is weaker. Note that in the case of shallowcooling the increased heat fluxes in the polar strato-sphere are confined to the levels where cooling is oc-curring (Fig. 6a, middle panel). Figures 6b,c show resultsfor the same shallow cooling, but in these cases thecooling has been lifted by 25 hPa (Fig. 6b) and 50 hPa(Fig. 6c). Lifting the cooling has little effect on the changesin polar stratospheric temperatures (middle column), but ithas a dramatic effect on the changes in the troposphericcirculation (right column). When the cooling is liftedby 25 to 175 hPa (Fig. 6b), the tropospheric response

FIG. 5. As in Fig. 2, but for (left) the responses to the polar stratospheric thermal forcings. The forcings are documented in Table 1 and arecentered at (a) 100, (b) 75, and 50 hPa (c). (right) Note the shading scaling is about half that for Fig. 2.

3484 JOURNAL OF CL IMATE VOLUME 23



GHG-likewarming

ozone-likecooling

Which forcing has dominated to date?

A Simple Model of the Jet Response

jet shift = ozone pull + GHG push

model simulations give us the forcings and response

∆Ulat = rO3 · ∆T03 + rGHG · ∆TGHG

Quantifying the temperature forcing

hPa (a)


Mod

els

with

fixe

d oz

one 200

400

600

800

1000

(b)


hPa

latitude

(c)

Mod

els

with

var

ying

ozo

ne

60S 30S 0 30N 60N

200

400

600

800

1000

latitude

°C

(d)

60S 30S 0 30N 60N

10 8 6 4 2 0 2 4 6 8

ΔTO3

ΔTGHG



model simulations give us the forcings and response


2000–2079 in the CCMVal!2 REF!B2 and AR4 A1B sce-nario integrations. An exception is section 3.1, where trendsare calculated for the period 1979–1999 to be comparedwith reanalysis data, and for the period 2001–2050 to becompared with the previous CCMVal activity (CCMVal!1).Past climate changes are analyzed for a relatively longperiod of 40 years, mainly because O3 depletion beganbefore 1979; observations have shown that O3 concentrationstarted to decrease in the late 1960s, although early trendsare quite weak [e.g., Solomon, 1999, Figure 1]. The longerperiod also allows us to obtain better statistics and compareour results with previous studies. The analysis length forfuture climate change is twice as long as that for past climatechange because O3 recovery is predicted to be slower thanits depletion in the past. The CCMVal!2 models predict thattotal column O3 over the Antarctic will likely reach its 1980value around 2060 [Austin et al., 2010]. Although the

analysis period is somewhat subjective, results are onlyweakly sensitive to the choice of time period. It is found thattrends over 2000–2049 are quantitatively similar to thoseover 2000–2079, although the intermodel standard deviationis somewhat larger.[13] Stratospheric O3 has strong seasonality and its long!

term trend is largest in the late spring. Its impact on the tro-pospheric circulation, however, is delayed by a few monthsand reaches a maximum in the summer, December–February(DJF) [Gillett and Thompson, 2003; Shindell and Schmidt,2004; Perlwitz et al., 2008; Son et al., 2008]. Hence, mostanalyses in this study are carried out for the SH summer.

3. Results

[14] We first evaluate the CCMVal!2 models by com-paring the spatial and temporal structure of the zonal mean

Figure 1. The long!term mean (thick orange) and linear trend (thin black contour) of DJF [u] over1979–1999: (a) CCMVal!2 REF!B1 multimodel mean, (b) ERA40, and (c) NCEP!NCAR reanalysisdata. (d) Future trends over 2000–2079 as simulated by the CCMVal!2 REF!B2 models. Contour intervalsof climatological wind and trend are 10 m s!1 starting from 10 m s!1 and 0.4 m s!1/decade, respectively. InFigures 1a and 1d, multimodel mean values exceeding 1 standard deviation are shaded. In Figures 1b and1c, trends which are statistically significant at the 95% confidence level are shaded. Zero contours are omit-ted in all plots.


4 of 18



two unknowns




two equations1960-1999 trends 2000-2079 trends

[Perlwitz et al. 2008]

specified at the lower boundary of the model. Aspects ofstratospheric ozone-temperature coupling and the climatol-ogy of the SH polar vortex have been evaluated by Stolarskiet al. [2006], Eyring et al. [2006] and Pawson et al. [2008].The model captures the main aspects of the global couplingbetween ozone and temperature. As with other CCMs, theAntarctic vortex breaks down too late in the season. Otherweaknesses of the GEOS CCM are too much year-to-yearvariability in the vortex structure, a high initial bias in totalozone and a warm bias in lower stratospheric temperaturewhen there is no chlorine-induced ozone loss, which meanthat Antarctic ozone loss and ozone-induced cooling areoverestimated [Pawson et al., 2008].[6] We analyze two simulations of the recent past (P-1

and P-2) and three C21 simulations (C21-HSST, C21-CSSTand C21Cl1960). The atmospheric and lower boundaryforcings of these transient simulations are summarized inTable 1. Simulations P-1 and P-2, starting from differentinitial conditions, are forced with observed changes in SSTand sea ice (HadISST [Rayner et al., 2003]), GHG concen-trations and halogens. GHG concentrations in the C21 runsfollow IPCC scenario A1b (medium, SRESA1B). In C21-HSST and C21-CSST, the halogens are prescribed accord-ing to the Ab scenario [World Meteorological Organization/United Nations Environment Programme, 2003], while inC21Cl1960, chlorine is fixed at 1960 values. SST and seaice distribution for the C21 simulations are taken fromsingle AR4 SRESA1b simulations with the coupledocean-atmosphere models HadGEM1 (C21-HSST) andCCSM3.0 (C21-CSST, C21Cl1960). Run C21-HSST wasincluded in the multi-model analysis of Eyring et al. [2007].

3. Results From GEOS CCM

[7] Figure 1 shows the time series of 70-hPa minimumzonal mean ozone mixing ratio (OMR-min) reached be-tween 90!S and 60!S on any day in October. Around year1960, OMR-min is about 2.7 ppmv. Stratospheric halogenincreases cause the strong decline of OMR-min to less than0.1 ppmv. Although 1980 is commonly used as a baselineagainst which ozone depletion and recovery are evaluated,some Antarctic ozone is lost as halogen emissions increasein the 1970s. In the GEOS simulations, about 10% of thetotal Antarctic ozone is lost between 1970 and 1980[Pawson et al., 2008, Figure 14]. As the stratospherichalogen loading decreases through the C21, the Antarcticozone hole recovers. By the end of the C21, OMR-minreaches 1970 values. In C21Cl1960, OMR-min variesaround 2.8 ppmv.[8] Figure 2 compares SH climate change for 1969 to

1999 (period I) and 2006 to 2094 (period II). The change foreach period is defined as the difference between 11-year

means centered on 1999 and 1969 (Period I) and 2094 and2006 (period II). Monthly changes in polar cap (90!S to64!S) ozone and temperature, and in mid-latitude (70!S to50!S) zonal-mean zonal wind are investigated. In addition,three-month overlapping changes in the SAM index basedon the surface pressure difference between 65!S and 40!S[Gong and Wang, 1999] are shown.[9] Figures 2a, 2c, 2e, and 2g (Figures 2b, 2d, 2f, and 2h)

show the results for period I (II) based on the ensemblemean of simulations P-1 and P-2 (C21-HSST and C21-CSST). The results discussed are very similar for the twoindividual simulations. They are significant on the monthlytime scale in the stratosphere (99% level) and on theseasonal time scale in the troposphere (95% level).[10] Between 1969 and 1999 in P-1 and P-2, ozone loss

over the polar cap migrates down from near 10 hPa inAugust to near 200 hPa in November, with largest lossbetween 50 and 70 hPa during October (Figure 2a). (Tro-pospheric ozone in GEOS CCM is represented by relaxationto climatology, so no trends are expected.) Polar ozone lossforces lower stratospheric cooling in the polar cap(Figure 2c), most pronounced at 100 hPa in December.[11] The polar cooling increases the meridional tempera-

ture gradient and causes westerly zonal wind anomalies inthe stratosphere (Figure 2e). Changes in tropospheric west-erlies maximize during December and January, lagging thestratospheric zonal wind changes by one month. The SAM

Table 1. Time Period, SST Data Set, Scenarios for Halogens and GHGs for GEOS CCM Experiments

Experiment Time Period SST Halogens Greenhouse Gases

P-1 1950–2004 Had1SST Observed ObservedP-2 1951–2004 Had1SST Observed ObservedC21-HSST 1996–2099 HadGEM1 WMO Baseline scenario Ab IPCC/GHG scenario A1b (medium)C21-CSST 2000–2099 CCSM3.0 WMO Baseline scenario Ab IPCC/GHG scenario A1b (medium)C21Cl1960 2001–2099 CCSM3.0 Chlorine fixed at 1960 values IPCC/GHG scenario A1b (medium),

with chlorine fixed at 1960 values

Figure 1. Time series of 70-hPa minimum zonal meanozone mixing ratio [ppmv] over SH polar cap area (between90!S and 60!S) during October (using daily model output).

L08714 PERLWITZ ET AL.: OZONE HOLE RECOVERY AND CLIMATE CHANGE L08714

2 of 5


Regression Coefficients: Estimate of Sensitivity

CCMVal2 Models

1 2 3 4 5 6 7 8 9 10

0.4

0.2

0

0.2

0.4

0.6

model

regr

essio

n co

effic

ient

s (d

eg./

K)

strat. polar cap temp. (O3)tropical temp. (GHG)



CCMVal2 Models

1 2 3 4 5 6 7 8 9 10

0.4

0.2

0

0.2

0.4

0.6

model

regr

essio

n co

effic

ient

s (d

eg./

K)


mea

n


1 2 3 4 5 6 7 8 9 10

0.4

0.2

0

0.2

0.4

0.6

model

regr

essio

n co

effic

ient

s (d

eg./

K)



CCMVal2 Models CMIP3 Models

1 2 3 4 5 6 7 8 9 10

0.4

0.2

0

0.2

0.4

0.6

model

regr

essio

n co

effic

ient

s (d

eg./

K)


mea

n

mea

n



1 2 3 4 5 6 7 8 9 101

0.8

0.6

0.4

0.2

0

model

trend

s (d

eg./d

ecad

e)

total

Attribution of 20 Century Climate Trends


mea

n1 2 3 4 5 6 7 8 9 101

0.8

0.6

0.4

0.2

0

model

trend

s (d

eg./d

ecad

e)

total

mea

n

1 2 3 4 5 6 7 8 9 101

0.8

0.6

0.4

0.2

0

model

trend

s (d

eg./d

ecad

e)

O3totalGHG

Attribution of 20 Century Climate Trends


1 2 3 4 5 6 7 8 9 101

0.8

0.6

0.4

0.2

0

model

trend

s (d

eg./d

ecad

e)

O3totalGHG

mea

n

mea

n


Summary of Model Trends

1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)

c) jet shift, 1960 99

1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)

e) jet shift, 2000 79

3

2

1

0

1C

CM

Val2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad

e)b) T trends, 1960 99

3

2

1

0

1

CC

MVa

l2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad

e)

d) T trends, 2000 79

0.6

0.4

0.2

0

0.2

0.4

CM

IP3

CC

MVa

l2

CM

IP5

r 03

andr GHG

(°/K

)

a) regression coef.



1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)


1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)


3

2

1

0

1C

CM

Val2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad


3

2

1

0

1

CC

MVa

l2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad

e)


0.6

0.4

0.2

0

0.2

0.4

CM

IP3

CC

MVa

l2

CM

IP5

r 03

andr GHG

(°/K

)

a) regression coef.


Shaving cream moved the jet stream!


1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)


1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)


3

2

1

0

1C

CM

Val2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad


3

2

1

0

1

CC

MVa

l2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad

e)


0.6

0.4

0.2

0

0.2

0.4

CM

IP3

CC

MVa

l2

CM

IP5

r 03

andr GHG

(°/K

)

a) regression coef.


But what about the black bars?

But what about the black bars?A Tale of Two Models (London and Paris)

Jet shifts equatorward

2010 2020 2030 2040 2050 2060 2070 2080

3

2

1

0

1

2

3

year

Ula

t (° la

titud

e)

GFDL CM3IPSL CM5A MR

Jet shifts poleward

Changes in Jet PositionPrinceton

1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)


1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)


3

2

1

0

1C

CM

Val2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad


3

2

1

0

1

CC

MVa

l2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad

e)


0.6

0.4

0.2

0

0.2

0.4

CM

IP3

CC

MVa

l2

CM

IP5

r 03

andr GHG

(°/K

)

a) regression coef.


Two Sources of Model Spread:Differences in the thermal response to GHG, O3

Returning to our case study...

2010 2020 2030 2040 2050 2060 2070 2080

3

2

1

0

1

2

3

year

Ula

t (° la

titud

e)


change in jet position

RCP4.5 Changes in Jet Position


2010 2020 2030 2040 2050 2060 2070 2080

3

2

1

0

1

2

3

year

Ula

t (° la

titud

e)



2010 2020 2030 2040 2050 2060 2070 20802

0

2

4

6

8

10

12

year

TG

HG

(K)


change in tropical temperature



2010 2020 2030 2040 2050 2060 2070 2080

3

2

1

0

1

2

3

year

Ula

t (° la

titud

e)



2010 2020 2030 2040 2050 2060 2070 20802

0

2

4

6

8

10

12

year

TG

HG

(K)


2010 2020 2030 2040 2050 2060 2070 20802

0

2

4

6

8

10

12

year

T03

(K)


change in tropical temperature


change in polar temperature

Uncertainty in global warming a poor predictor...

0.2 0.4 0.6 0.8−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3a) ! Ulat vs. ! Ttrop

! Ttropical (K/decade)

! U

lat (°

/dec

ade)

CCMVal2, R=−0.18CMIP3, R=−0.52CMIP5, R=−0.24

−0.5 0 0.5 1 1.5

b) ! Ulat vs. ! Tpolar

! Tpolar (K/decade)

CCMVal2, R=0.62CMIP3, R=0.81CMIP5, R=0.73

Fig. 9. The relationship between the 21st century shift in the austral jet stream !Ulat and(a) tropical upper tropospheric temperatures !Ttrop or (b) polar stratospheric temperatures!Tpolar. Circles, squares, and triangles refer to CCMVal2, CMIP3, and CMIP5 models,respectively. The shading of each symbol reflects the temperature trends of the other com-ponent: !Tpolar in (a) and !Ttrop in (b), with redder shades reflecting a warmer signal, andbluer symbols a colder signal. For example, in (a) there is a shift from blue to red as onegoes from bottom to top: for a given change in tropical temperatures, the jet shifts moreequatorward the more the polar stratosphere warms.

49

Uncertainty in global warming a poor predictor...rather, key is what is happening over the pole!

0.2 0.4 0.6 0.8−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3a) ! Ulat vs. ! Ttrop

! Ttropical (K/decade)

! U

lat (°

/dec

ade)

CCMVal2, R=−0.18CMIP3, R=−0.52CMIP5, R=−0.24

−0.5 0 0.5 1 1.5

b) ! Ulat vs. ! Tpolar

! Tpolar (K/decade)

CCMVal2, R=0.62CMIP3, R=0.81CMIP5, R=0.73

Fig. 9. The relationship between the 21st century shift in the austral jet stream !Ulat and(a) tropical upper tropospheric temperatures !Ttrop or (b) polar stratospheric temperatures!Tpolar. Circles, squares, and triangles refer to CCMVal2, CMIP3, and CMIP5 models,respectively. The shading of each symbol reflects the temperature trends of the other com-ponent: !Tpolar in (a) and !Ttrop in (b), with redder shades reflecting a warmer signal, andbluer symbols a colder signal. For example, in (a) there is a shift from blue to red as onegoes from bottom to top: for a given change in tropical temperatures, the jet shifts moreequatorward the more the polar stratosphere warms.

49

1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)


1

0.8

0.6

0.4

0.2

0

0.2

CC

MVa

l2

CM

IP3

CM

IP5

Ulat

(°/d

ecad

e)


3

2

1

0

1C

CM

Val2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad


3

2

1

0

1

CC

MVa

l2

CM

IP3

CM

IP5

T 03

and

T GHG

(K/d

ecad

e)


0.6

0.4

0.2

0

0.2

0.4

CM

IP3

CC

MVa

l2

CM

IP5

r 03

andr GHG

(°/K

)

a) regression coef.


Two Sources of Model Spread:Differences in the circulation response to temperature

Uncertain Forcing vs. Uncertain Dynamics

• Variability in modeled circulation response due to

• differences in thermal forcing by ozone and GHGs

• differences in “circulation sensitivity”

Jet position in historical simulation (degrees)

21 C

entu

ry J

et S

hift

(deg

rees

)

[ Kidston and Gerber 2010]

Connection between 21st Century Jet Shift and20th Century Climatology

equatorward bias



position of jet in reanalyses

21 C

entu

ry J

et S

hift

(deg

rees

)


position of jet in reanalyses

equatorward bias

larger jet shift



21 C

entu

ry J

et S

hift

(deg

rees

)


Connection between the Climatological Jet Position and Time Scales of Internal Variability

Ann

ular

Mo

de

Tim

e S

cale

(day

s)

equatorward bias

long

er ti

me

scal

es

[ Kidston and Gerber 2010]Jet position in historical simulation (degrees)

What does this annular mode time scale represent?

latitude80 60 40 20

J

F

M

A

M

J

J

A

S

O

N

D

J

latitude

80 60 40 20

70 30 10 10 30 70

a) model w/ short time scales b) model w/ long time scales

500 hPa geopotential height anomalies in two models

[ Gerber et al. 2010]

January

time

Connection between the Climatological Jet Position and Time Scales of Internal Variability

Ann

ular

Mo

de

Tim

e S

cale

(day

s)

equatorward bias

long

er ti

me

scal

es

[ Kidston and Gerber 2010]Jet position in historical simulation (degrees)

Internal Variability - Jet Shift Connection

Annular Mode Time Scale (days)

larger jet shift

longer time scale


21 C

entu

ry J

et S

hift

(deg

rees

)

Similar Connections in CCMVal2 Models (20th Century)

equa

torw

ard

bias

[44] The geometry of the sphere and the equator!to!poletemperature difference establish a high!latitude limit to theextent of the extratropical jet. If the jet changes its locationin response to external forcing, the poleward displacement(and intensification) may preferentially occur when the cli-matological jet is located in the latitudes lower than thishigh!latitude limit. In models where the climatological jet islocated in high latitudes, it is likely difficult to move the jetfarther poleward. In contrast, in models where the climato-logical jet exhibits an equatorward bias, there is much moreroom for the jet to move poleward. This simple, likelyoversimplified, argument amounts to a geometric constraint.[45] The dynamic constraint is linked to a connection

between internal variability and background flow. A seriesof idealized modeling studies by Gerber and Vallis [2007],Son et al. [2008] and Simpson et al. [2010] have shown thatthe e!folding time scale of zonal mean flow variability orannular mode (hereafter simply “the time scale”) is highlysensitive to the background flow. They found that it isshorter in integrations where the climatological eddy!drivenjet is located in higher latitudes. Figure 10b shows therelationship between the time scale and the location of cli-matological jet for the CCMVal!2 models. Here, the timescale is estimated by e!folding time scale of the SAM index,derived from the Empirical Orthogonal Function (EOF)analyses of daily zonal mean geopotential height. Thise!folding time scale is first calculated at each model leveland then integrated from the surface to 250 hPa. (See Gerberet al. [2010] for further details.) It is found that the timescale is highly correlated with the location of climatologicaljet, decreasing as the jet is located in higher latitudes. This isconsistent with idealized model experiments. A similarrelationship is also found in the AR4 model integrations[Kidston and Gerber, 2010].

[46] The fluctuation!dissipation theorem links the inter-nal variability of a system to its response to externalforcing [e.g., Leith, 1975]. Proper application of fluctua-tion!dissipation theory requires knowledge of the correla-tion structure between all modes of the system, or at least asubset sufficient to represent the dynamics [e.g., Majdaet al., 2010], but such an analysis is beyond the scope ofthis study. As discussed by Leith [1975], however, a simplerrelationship may apply if the annular mode is sufficientlyuncorrelated with other modes in the system. In this case onemight expect that for models with more persistent internalvariability (e.g., longer time scale), the jet should respondmore to external forcing, as found by Gerber et al. [2008]and Ring and Plumb [2008] in idealized model integra-tions. This is to a large degree in agreement with thefindings of Figure 10.[47] Why is the e!folding time scale shorter as the jet is

located in higher latitudes? It may arise from meridionalpropagation of baroclinic eddies [Son et al., 2007; Simpsonet al., 2010]. The summer hemisphere jet is essentiallydriven by eddies and generally forms at the region ofmaximum baroclinicity as discussed in section 3.3 (see alsoFigure 9a). Given that baroclinicity in the subtropics is fixedby the Hadley circulation, the extratropical jet at higherlatitudes implies a broader baroclinic zone where baroclinicwaves can propagate. This may allow eddies to propagatelatitudinally more effectively, weakening the stability of theeddy fluxes which maintain the zonal mean flow anoma-lies. The result would be a less stationary zonal mean flowanomaly in time, leading to shorter time scale. The oppo-site would be the case for the jet located in lower latitudes.Eddy activity would be confined to a more limited latitudeband, and would increase the chances that eddy fluxescontinuously occur at similar latitudes, making zonal mean

Figure 10. The relationship between the climatological jet location in the CCMVal!2 REF!B1 scenarioand (a) the tropospheric jet response to ozone depletion and (b) time scale of the SAM index in the SHsummer as simulated by the CCMVal!2 REF!B1 models. In Figure 10a the tropospheric [u]max trend isnormalized by the hO3i50 trend. Only 15 models are used here excluding two outliers which show tooweak hO3i50 trend or negative [u]max trend (see Figures 7 and 8). In Figure 10b, only 11 models areused, as others have not archived sufficiently daily data. Time scale based on the NCEP!NCAR reanalysis[Baldwin et al., 2003] is indicated with error bar in Figure 10b.


14 of 18

larger jet shiftlonger time scale

long

er ti

me

scal

e

[ Son et al. 2010]

What connects variability and change?

Springs: An (imperfect) analogy

Hooke’s LawF = −kx


Hooke’s Law

{x F=kx

pull spring down

it pullsback!

F = −kx


F = ma

Hooke’s Law

Newton’s Second Law

F = −kx


− k

mx =

d2x

dt2

−α2x =d2x

dt2

F = ma

Hooke’s Law

−kx = md2x

dt2

let α =�

k

m


F = −kx

F = −kx


− k

mx =

d2x

dt2

−α2x =d2x

dt2

F = ma

Hooke’s Law

−kx = md2x

dt2

d2x

dt2= −α2x(t)

So, period of oscillation is 2π

α=

2π√

m√k

Look for solution of form:

then:


x(t) = A cos(αt) + B sin(αt)


{x

pull spring down

Fspring = Fexternal

The response to “external” forcing: in equilibrium,

Period of oscillation is 2π

α=

2π√

m√k

Fexternal

Fspring=kx

it pullsback


{x Fspring=kx

pull spring down

it pullsback

Fspring = Fexternal

−kx = Fexternal

The response to “external” forcing: in equilibrium,

Period of oscillation is 2π

α=

2π√

m√k

Fexternalx = −Fexternal

k

L is related to the timecorrelation structure of x, properties of the natural

variability.

Fluctuation-Dissipation Theory (in brief!)

= −Lx + N(x)

= −Lx + W

∂x∂t

= B(x)


= −Lx + N(x)

= −Lx + W

+f

+f

+f

external perturbation

∂x∂t

= B(x) L is related to the timecorrelation structure of x, properties of the natural

variability.

∂x∂t

= B(x)


= −Lx + N(x)

= −Lx + W

+f

∂x∂t

= −Lx + W + f

0 = −Lx + 0 + f

x = L−1f

+f

+f

external perturbation

L is related to the timecorrelation structure of x, properties of the natural

variability.


= −Lx + N(x)

= −Lx + W

+f

∂x∂t

= −Lx + W + f

0 = −Lx + 0 + f

x = L−1f

In most simple case,

L−1 =� ∞

0ρ(τ)dτ

ρ(τ) = x(t)x(t + τ)

+f

+f

∂x∂t

= B(x) L is related to the timecorrelation structure of x, properties of the natural

variability.

Does it work?

latitude

pres

sure

(hPa

)

5

30

−5

0

−80 −60 −40 −20

100

200

300

400

500

600

700

800

900

zonal mean zonal wind, u

Idealized Atmospheric Model Experiments

latitude

pres

sure

(hPa

)

−80 −60 −40 −20

100

200

300

400

500

600

700

800

900 −5

−3

−1

1

3

5

u and the annular mode

Idealized Atmospheric Model Experiments

Apply torque that projects on internal variability

latitude

pres

sure

(hPa

)

−80 −60 −40 −20

100

200

300

400

500

600

700

800

900 −5

−3

−1

1

3

5

[Ring and Plumb, 2008]

u and the annular mode

System responds modally: strong projection on to internal variability

latitude

pressure

01530456075

200

400

600

800

torque

shading: annular mode positive and negative

contours: response ofmodel to the torque,uforced - ucontrol(negative dashed)

[after Ring and Plumb 2008]

Model with greater persistence more sensitive to external forcing

−0.1 −0.05 0 0.05 0.1 0.15−5

0

5

projection of forcing

proj

ectio

n of

resp

onse

m=17

m=89

NH, L20NH, L40SH, L20SH, L40

[Gerber, Voronin, and Polvani 2008]

τ = 33 days

τ = 96 days

Conclusions

• In austral summer, the Southern Hemisphere jet stream is pushed poleward by greenhouse gas induced tropical warming and pulled poleward by ozone induce cooling of the polar stratosphere. To date, ozone loss has been the most important driver.

• Uncertainty in climate forecasts stems from differences in the thermal response to anthropogenic forcing (primarily differences in ozone) and the circulation sensitivity to temperature changes.

• A model’s ability to simulate today’s climate and variability is an important measure for determining if its climate change projections are trustworthy.

math, models, and climate change · the “ozone hole,” was first observed in the early 1980s....

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