Semester planning & Project planning Review from Nov 1...
Transcript of Semester planning & Project planning Review from Nov 1...
1
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?
4
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
ForestfiremodelslidesthankstoDavidNewman
Spreadingrateanddynamicsgovernedbyf/p(andp)
Smallf/pleadstofrontlike(ordered)propaga[ngfires,probabilityofgrowthislarge
f:probabilityoflightning
p:probabilityofregrowth
Notaveryrealis?clookingforest.
ForestfiremodelslidesthankstoDavidNewman
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
Trees burned-control1Trees burned-nocontrol
Even
ts
Size
0
2000
4000
6000
8000
1 104
0 20 40 60 80 100
Trees burned-control1Trees burned-nocontrol
Even
ts
Size
TailofProbabilityDistribu[onFunc[onoffiresgetslarger
ForestfiremodelslidesthankstoDavidNewman
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.
ForestfiremodelslidesthankstoDavidNewman
AddSeasonalitytoGaia
Conclusions• ItisnotjustlifealonethatbutthewholeEarthsystemthat
tendstoregulateclimate.
• ThisideaofGAIAmakescompletesensetononlineardynamicscommunitybuttheyviewitsomewhatdifferentlythanmotherearth&Unicorns¯ameetc..Butself-regula?onwithinacertainparameterspace,beyondwhichyouwillgointoadifferentstatewhichcouldbeormaynotbeok.