semester planning & project planning review from nov 1...

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Wednesday15Nov,2017Lecture#33

Today’sTopics•Semesterplanning&Projectplanning•ReviewfromNov1lecture!•Gaia-biogeophysicalfeedbacks•Gaia-nonlineardynamics

•ForestFireexample•Summary

SemesterSchedule• Wed11/15lect33UmaGaia-modeling• Fri11/17AMlect34Danlecture• Friday11/17PM‘Howtogiveabad/goodtalk’• Mon11/20lect35Danlecture• Wed11/22lect36Danlecture• ThanksgivingBreak• Mon11/27lecture37DanLecture• Wed11/29lecture38Umalecture• FriAM/PM12/1studentpresenta[onsallonthisday,5presenta[ons.Thisis2weeksfromthisFriday.

• Mon12/4lecture39Umalecture• Wed12/6lecture40Umalecture• Fri12/9FinalpartaAM(Paleo),partbPM(climatedyn.)

ProjectDeadlines

Presentation DayGo over slides by today with Dan or Uma

Go over talk outline with Dan or Uma

How to give talks

Deadline 3: Key project papers, 20 pointsDeadline 4: Presentation outline, 11/22, 40 pointsDeadline 5: go over slides, 11/29, 30 pointsabove early deadlines are 20% of your grade

Review•Whatisaparameteriza?on?•Whatisamodel?•Whatisaclimatemodel?

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Daisyworld• Originatedin1983byA.WatsonandJ.

Lovelock.

• Thisverysimplemodelwasdevelopedtorespondtothecri?cismsoftheGaiaHypothesis.

• Imaginarygreyworld;samedistancefromsunasearth

• TheenvironmentofDaiseyworldhasonevariable,Temperature.

• ThebiotahasblackandwhitedaisiesTheplanetiswellwateredandhasnutrientssotemperaturedeterminesthegrowthofdaisies.

• AkeypointaboutDaisyworldisthatthedaisiesalterthesameenvironmentalvariable(temperature)inthesamedirec?onatthelocallevelandthegloballevel.

• Muchofthetheore?calinterestsismodelcentersonestablishingthecondi?onsinwhichregula?ondoes,anddoesnot,emerge.

http://www.gingerbooth.com/flash/daisyball/DaisyBall.htmlDaisyworld online model you can play with:

Daisyworld• Twotypesofdaisiescompeteforspaceonaplanetandgrowsimilarlyasafunc?onoftemperature.

• Becauseofthealbedoeffecttheycantoleratedifferentamountsofsolarradia?on.

• Blackdaisiescantoleratelowersolarluminositywhilewhitedaisiescantoleratehighersolarluminosity.

• Thealbedogovernslocaltemperaturewhichcontrolstheamountofareacovered.

h_p://www.gingerbooth.com/flash/daisyball/DaisyBall.htmlModelonweb:Companion website: www.wiley.com/go/mcguffie/climatemodellingprimer

Daisyworldα g = fbareαbare + fWαW + fBαB

• Globalalbedoisafunc?onofbareground,whitedaisiesandblackdaisies.

• Asthelocaltemperaturechangesinresponsetochangesinsolarluminosity,thegrowthratesofthedaisieschangeandthischangesthealbedooftheplanet.

• Daisiescangrowtocoverarablelandbasedonagrowthratethatdependsontemperature.

• Thegrowthrateislargestatop?maltemperatureanddropsoffatlocaltemperaturesthatarewarmerorcolder.

Gr =1−kg(Toptimum −Tlocal )2• Whenluminosityislowblackdaisiesdominatebutasluminosityincreases,whitedaisies

begintodominate.

• Thismodelprovidesaframeworkfortheexpira[onofhoworganismscanself-regulatetheirenvironment.

The‘CLAW’paper• ConsideredthefirsttestableGaiaHypothesis

(thatlivingthingsworktomodifytheclimate)

• TocounteractthewarmingduetodoublingCO2,weneedtodoublethenumberofCCN.

DMSMechanism

• Dimethylsulfide(DMS),producedbyoceanplanktonandoxidizedinatmospheretoformasulfateaerosol.

• Aerosolscoolclimateoverallbyincreasingalbedo

• ‘InGaianterms,theplanktonacttoreducethedisturbancetotheclimate.'

Measurable Quantities

Processes

Sign here uncertain

RootsoftheDMSMechanism

Dr. Glenn Shaw, Prof Emeritus UAF

Dr. Robert Charlson, Prof Emeritus UW

Aside

Gaia• ThefieldhasnowmaturedtotheextentthattheviabilityoftheGaia

theoryisnolongerdirectly?edtothevalidityoftheDaisyworldmodel,aswassome?mesthecaseintheearlyyearsa^eritsincep?on.HencewetreatDaisyworldasaninteres?ngmathema?calmodelinitsownright.ItmayinformthedebateonGaia,buttheyarenotinextricably?ed.Therehavebeenmanyoffshootstootherareasofscience,includingnonlineardynamics,ecosystemandfoodwebtheory,evolu[onarytheory,physiology,maximumentropyproduc[on,andar[ficiallife.Thankstoitsrela?velysimplemathema?calformula?on,DaisyworldisalsowidelyusedintheteachingofEarthsystemscience[e.g.,Kumpetal.,1999;McGuffieandHenderson-Sellers,1997;Ford,1999].(fromWoodetal.2008)

• Nowitis?metomoveontodevelopnewconceptualmodelstoaddressques?onsregardingplanetaryself-regula?onandthecouplingoflifeandtheenvironment.

Reference:Wood,A.J.,G.J.Ackland,J.G.Dyke,H.T.P.Williams,andT.M.Lenton(2008),Daisyworld:Areview,Rev.Geophys.,46,RG1001,doi:10.1029/2006RG000217

Gaia• Howdaisiesadaptwithintheboundsoffeedbackloops

definedintheoriginalmodel.Butwhatthenatureofthefeedbacksinthemodelarealteredtoseehowthiseffectstheevolu?onofthecomponentsofthesystem.

•WatsonandLovelock[1983]reversedthesignofinterac?onbetweendaisycolorandplanetarytemperaturebyassumingthatconvec[ongeneratedoverthewarmspotsoftheblackdaisyclumpsgenerateswhitecloudsabovethem.Inthiscasetheblackdaisiesares?lllocallywarmerthanthewhitedaisies,butbothdaisytypesnowcooltheplanet.Hencetheblackdaisiesalwayshaveaselec[veadvantageovertheirwhitecompatriots,whichtheydrivetoex[nc[on.Yetplanetarytemperatureiss[llregulated,albeitonthecoldsideoftheop?mumforgrowth.

Non-linearDynamics:BasinsofA_rac[onstable state A or B

Change environmentso basin is shallowerso A is less stable, a small push moves it to B.

A big push needed to move it to B.

ForestFireModelsasanotherExample

• DrosselandSchwablforest-firemodel:– Aburningtreebecomesanemptysite.– Agreentreebecomesaburningtreeifatleastoneofits

neighborsisburning.– Atanemptysiteatreegrowswithprobabilityp.– Atreewithoutaburningnearestneighborbecomesaburning

treebylightningwithaprobabilityf.

Cri?calparameterisf/p(forp<<f/p)anditissmall

ForestfiremodelslidesthankstoDavidNewman

ForestFireModels

• Forestfiremodelbecomescri?calbytheintroduc?onofthelightningparameterf.

• Thereisonlyonerelevantparameterinthesystemf/p.• Ifρistheaverageddensityoftreesinsteadystate,theaveragenumberoftreesdestroyedbyalightningstrokeis

• Thereisaself-organizedcri?calstateforf→0.

s = fp

⎛ ⎝ ⎜ ⎞

⎠ ⎟ −11−ρ

ρ


Spreadingrateanddynamicsgovernedbyf/p(andp)

Smallf/pleadstofrontlike(ordered)propaga[ngfires,probabilityofgrowthislarge

f:probabilityoflightning

p:probabilityofregrowth

Notaveryrealis?clookingforest.


Forestwithpatchydistribu[on

Largerf/p(throughreduc[oninp)givesamorephysicalpictureofaforest

Morerealis[clookingforestthanpreviousslide.ForestfiremodelslidesthankstoDavidNewman

LowRiskControlStrategycanbeCounterProduc[ve

Systemundergoesdynamicalself-organiza[on

Controlofsmallfires(firefigh[ng)canleadtoincreaseddensityandincreasedchanceofmajorfires

similartodecreasedf/pfigure

0

20

40

60

80

100

0 5000 1 104 1.5 104 2 104 2.5 104 3 104

Trees burned-control1Trees burned-nocontrol

Tree

s burn

ed

TimeForestfiremodelslidesthankstoDavidNewman

Self-similarinthepatchinessandinthenumberoffires.Thesystemorganizesitselftositatacri[calpoint.

Aside:Self-similarityPropertyinNature• Inmathema?cs,aself-similarobjectisexactlyorapproximatelysimilartoapartofitself

(i.e.thewholehasthesameshapeasoneormoreoftheparts).

• Youseethisinstreamstorivers,similarshapesbutdifferentscales.Youseethisincoastlines.

AFernorRomanescuBroccoliareexamplesofsomethingself-similar.

IfyoucontrolForestFires=>MoreBigfires

1

10

100

1000

104

0 20 40 60 80 100


Even

ts

Size

0

2000

4000

6000

8000

1 104

0 20 40 60 80 100


Even

ts

Size

TailofProbabilityDistribu[onFunc[onoffiresgetslarger


RegularScale LogScale

MoreBigfires

Mul[pleTimeScalesintheDynamicsSystemhascorrela[onsovermany[mescales

dynamicalnotprobabilis[ceffect

0.00

0.10

0.200.30

0.400.50

0.60

0510152025303540

1 104 1.5 104 2 104 2.5 104 3 104

Density Trees burned

Dens

ity o

f gr

een

tree

s Number of trees burned per stepTime steps

Thisisanexampleofaselfregula[ngsystem.


AddSeasonalitytoGaia

Conclusions• ItisnotjustlifealonethatbutthewholeEarthsystemthat

tendstoregulateclimate.

• ThisideaofGAIAmakescompletesensetononlineardynamicscommunitybuttheyviewitsomewhatdifferentlythanmotherearth&Unicorns&macrameetc..Butself-regula?onwithinacertainparameterspace,beyondwhichyouwillgointoadifferentstatewhichcouldbeormaynotbeok.

semester planning & project planning review from nov 1...

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