Table Of ContentMathematics
Planet Earth
of
OT140_Kaper_Rousseau_FM-02-04-15.indd 1 2/19/2015 11:12:02 AM
Edited by
Hans Kaper Christiane Rousseau
Georgetown University Université de Montréal
Washington, DC Montréal, Quebec
Canada
Mathematics
Planet Earth
of
Mathematicians Reflect on
How to Discover, Organize, and
Protect Our Planet
Society for Industrial and Applied Mathematics
Philadelphia
OT140_Kaper_Rousseau_FM-02-04-15.indd 3 2/19/2015 11:12:02 AM
Copyright © 2015 by the Society for Industrial and Applied Mathematics
10 9 8 7 6 5 4 3 2 1
All rights reserved. Printed in the United States of America. No part of this book may be reproduced,
stored, or transmitted in any manner without the written permission of the publisher. For information,
write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor,
Philadelphia, PA 19104-2688 USA.
Publisher David Marshall
Acquisitions Editor Elizabeth Greenspan
Developmental Editor Gina Rinelli
Managing Editor Kelly Thomas
Production Editor David Riegelhaupt
Copy Editor Matthew Bernard
Production Manager Donna Witzleben
Production Coordinator Cally Shrader
Compositor Bytheway Publishing Services
Graphic Designer Lois Sellers
Cover image of sea ice to the west of Adelaide Island photographed from RRS James Clark Ross
on passage to Rothera, December 1997. Reprinted with permission from Peter Bucktrout/British
Antarctic Survey.
Library of Congress Cataloging-in-Publication Data
Mathematics of planet Earth : mathematicians reflect on how to discover, organize, and protect our
planet / edited by Hans G. Kaper, Georgetown University, Washington, DC, Christiane Rousseau,
Université de Montréal, Montréal, Quebec, Canada.
pages cm. -- (Other titles in applied mathematics ; 140)
Includes bibliographical references and index.
ISBN 978-1-611973-70-9
1. Ecology--Mathematics. 2. Environmental sciences--Mathematics. I. Kaper, H. G., editor. II.
Rousseau, Christiane, editor.
QH541.15.M34M385 2015
577.01’51--dc23
2014048797
is a registered trademark.
OT140_Kaper_Rousseau_FM-02-04-15.indd 4 2/19/2015 11:12:02 AM
We dedicate this volume
to the members of the
SIAM Activity Group for
Mathematics of Planet Earth.
OT140_Kaper_Rousseau_FM-02-04-15.indd 5 2/19/2015 11:12:02 AM
Contents
Preface xi
I APlanettoDiscover 1
1 PlanetEarth 3
1.1 HowOldIstheEarth? ChristianeRousseau . . . . . . . . . . . . . . . 3
1.2 TheEquationofTime ChristianeRousseau . . . . . . . . . . . . . . . 4
1.3 HowIngeLehmannDiscoveredtheInnerCoreoftheEarth
ChristianeRousseau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Why Do Earthquakes Change theSpeed of Rotation of the Earth?
ChristianeRousseau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 MathematiciansListenastheEarthRumbles ChristianeRousseau . 7
1.6 Flow through Heterogeneous Porous Rocks: What Average Is the
CorrectAverage? ToddArbogast . . . . . . . . . . . . . . . . . . . . . . 9
1.7 ImagingwithGaussianBeams NickTanushev . . . . . . . . . . . . . . 13
1.8 ThinkingofTrees IlyaZaliapin . . . . . . . . . . . . . . . . . . . . . . . 15
2 OceanandAtmosphere 19
2.1 AtmosphereandOceanDynamicsthroughtheLensofModel
Systems GregLewis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 AtmosphericWavesandtheOrganizationofTropicalWeather
JosephBiello . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 NonlinearWavesandtheGrowthofaTsunami EstelleBasor . . . . 23
2.4 UniversalityinFractalSeaCoasts ChristianeRousseau . . . . . . . . 24
2.5 IceFloes,CoriolisAcceleration,andtheViscosityofAirandWater
RobertMiller. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 ThereWillAlwaysBeaGulfStream—AnExerciseinSingular
PerturbationTechnique RobertMiller . . . . . . . . . . . . . . . . . . . 28
2.7 The Great Wave and Directional Focusing John M. Dudley and
FrédéricDias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.8 ControllingLightning? ChristianeRousseau . . . . . . . . . . . . . . . 33
2.9 MathematicianSteppingonThinIce DeborahSullivanBrennan . . 35
3 WeatherandClimate 37
3.1 NumericalWeatherPrediction WeiKang . . . . . . . . . . . . . . . . 37
3.2 Lorenz’sDiscoveryofChaos ChrisDanforth . . . . . . . . . . . . . . 39
3.3 PredictingtheAtmosphere RobertMiller. . . . . . . . . . . . . . . . . 40
vii
viii Contents
3.4 ArcticSeaIceandColdWeather HansKaper . . . . . . . . . . . . . . 41
3.5 ExtremeWeatherEvent WilliamJ.Martin. . . . . . . . . . . . . . . . 44
3.6 WimpyHurricaneSeason BrianMcNoldy . . . . . . . . . . . . . . . . 45
3.7 ExtremeEvents HansKaper . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.8 TheNeedforaTheoryofClimate AntonelloProvenzale . . . . . . 48
3.9 MathematicsandClimate HansKaper. . . . . . . . . . . . . . . . . . . 50
3.10 ClimateSciencewithoutClimateModels HansKaper . . . . . . . . 53
3.11 SupermodelingClimate JamesCrowley . . . . . . . . . . . . . . . . . . 54
3.12 ReconstructingPastClimates BalaRajaratnam. . . . . . . . . . . . . 55
3.13 (Big) Data Science Meets Climate Science Jesse Berwald, Thomas
Bellsky,andLewisMitchell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.14 HowGoodIstheMilankovitchTheory? HansKaper . . . . . . . . 58
3.15 Earth’sClimateattheAgeoftheDinosaurs ChristianeRousseau . 60
3.16 TwoBooksonClimateModeling JamesCrowley. . . . . . . . . . . . 61
4 BeyondPlanetEarth 65
4.1 ChaosintheSolarSystem ChristianeRousseau . . . . . . . . . . . . . 65
4.2 KAMTheoryandCelestialMechanics AlessandraCelletti. . . . . . 66
4.3 NewWaystotheMoon,OriginoftheMoon,andOriginofLifeon
Earth EdwardBelbruno . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4 Low-FuelSpacecraftTrajectoriestotheMoon MarianGidea . . . . 71
4.5 WhereDidtheMoonComeFrom? ChristianeRousseau. . . . . . . 73
4.6 DataAssimilationandAsteroids RobertMiller . . . . . . . . . . . . . 75
4.7 UnderstandingtheBigBangSingularity EdwardBelbruno . . . . . 76
II APlanetSupportingLife 79
5 Biosphere 81
5.1 TheMysteryofVegetationPatterns KarnaGowda . . . . . . . . . . 81
5.2 HowVegetationCompetesforRainfallinDryRegions
FrankKunkleandKarthikaMuthukumaraswamy . . . . . . . . . . . . . 83
5.3 BiologicalEventsinOurWaterSystems MatthewJ.Hoffmanand
KaraL.Maki. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.4 BirdWatchersandBigData WesleyHochachka . . . . . . . . . . . . . 86
5.5 It’saMath-Eat-MathWorld BarryCipra . . . . . . . . . . . . . . . . . 89
5.6 OceanAcidificationandPhytoplankton ArvindGupta . . . . . . . 90
5.7 OceanPlanktonandOrdinaryDifferentialEquations HansKaper 91
5.8 ProspectsforaGreenMathematics JohnBaezandDavidTanzer. . 93
6 EcologyandEvolution 97
6.1 MathematicsandBiologicalDiversity FrithjofLutscher . . . . . . . . 97
6.2 WhyWeNeedEachOthertoSucceed ChristianeRousseau . . . . . 98
6.3 TheUnreasonableEffectivenessofCollectiveBehavior
Pietro-LucianoBuono . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.4 FromIndividual-BasedModelstoContinuumModels HansKaper 102
6.5 OptimalControlandMarineProtectedAreas KentE.Morrison . . 104
6.6 LinearProgrammingforTreeHarvesting PeterLynch . . . . . . . . 105
Contents ix
III APlanetOrganizedbyHumans 107
7 CommunicationandRepresentation 109
7.1 TheChallengeofCartography ChristianeRousseau . . . . . . . . . . 109
7.2 WhatDoesAltitudeMean? ChristianeRousseau . . . . . . . . . . . . 110
7.3 DrawingConformalMapsoftheEarth ChristianeRousseau . . . . 111
7.4 ChangingOurClocks HansKaper . . . . . . . . . . . . . . . . . . . . . 113
7.5 High-ResolutionSatelliteImaging PaulaCraciunand
JosianeZerubia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.6 MicrolocalAnalysisandImaging GaikAmbartsoumian,Raluca
Felea,VenkyKrishnan,CliffNolan,andToddQuinto. . . . . . . . . . . 116
7.7 HowDoestheGPSwork? ChristianeRousseau. . . . . . . . . . . . . 120
8 Energy 123
8.1 IntegratingRenewableEnergySourcesintothePowerGrid
WeiKang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.2 MathematicalInsightsYieldBetterSolarCells ArvindGupta . . . 124
8.3 MathematicalModelingofHydrogenFuelCells BrianWetton . . 126
8.4 MathematicalModelsHelpEnergy-EfficientTechnologiesTakeHold
inaCommunity KarthikaMuthukumaraswamy . . . . . . . . . . . . 130
8.5 GeothermalEnergyHarvesting BurtS.Tilley. . . . . . . . . . . . . . 132
8.6 OfCatsandBatteries RussCaflisch. . . . . . . . . . . . . . . . . . . . . 133
9 EconomicsandFinance 135
9.1 DynamicProgrammingforOptimalControlProblemsinEconomics
FaustoGozzi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.2 SolarRenewableEnergyCertificates MichaelCoulon . . . . . . . . . 137
9.3 HowMuchforMyTonofCO ? MireilleBossy,NadiaMaïzi,and
2
OdilePourtallier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
9.4 TheSocialCostofCarbon HansEngler . . . . . . . . . . . . . . . . . 141
9.5 MeasuringCarbonFootprints HansKaper. . . . . . . . . . . . . . . . 142
9.6 MusingsonSummerTravel DavidAlexandreEllwood . . . . . . . . 143
9.7 TheCarbonFootprintofTextbooks KentE.Morrison . . . . . . . . 146
9.8 SustainableDevelopmentandUtilizationofMineralResources
RoussosDimitrakopoulos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
9.9 Scientific Research on Sustainability and Its Impact on Policy and
Management MarkLewis . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
10 HumanBehavior 151
10.1 PredictingtheUnpredictable—HumanBehaviorsandBeyond
AndreaTosin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
10.2 BudgetChicken KentE.Morrison . . . . . . . . . . . . . . . . . . . . . 152
10.3 MathematicsandConflictResolution EstelleBasor . . . . . . . . . . 154
10.4 Modelingand UnderstandingSocial Segregation Laetitia Gauvin
andJean-PierreNadal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
10.5 ModelingtheEvolutionofAncientSocieties EstelleBasor . . . . . . 157
10.6 NetworksintheStudyofCultureandSociety ElijahMeeks. . . . . 157
IV APlanetatRisk 161
11 ClimateChange 163
11.1 TheDiscoveryofGlobalWarming HansKaper . . . . . . . . . . . . 163
x Contents
11.2 LettertoMyImaginaryTeenageSister–1 SamanthaOestreicher . 164
11.3 LettertoMyImaginaryTeenageSister–2 SamanthaOestreicher . 166
11.4 GlobalWarmingandUncertainties JuanM.Restrepo . . . . . . . . . 167
11.5 How to Reconcile the Growing Extent of Antarctic Sea Ice with
GlobalWarming HansKaper . . . . . . . . . . . . . . . . . . . . . . . . 169
11.6 RisingSeaLevelsandtheMeltingofGlaciers ChristianeRousseau. 170
11.7 GlobalWarming—RecommendedReading HansKaper. . . . . . . 170
12 Biological Threats 173
12.1 MathematicsbehindBiologicalInvasions–1 MarkLewis . . . . . . 173
12.2 MathematicsbehindBiologicalInvasions–2 JamesCrowley . . . . 174
12.3 Surges in Latent Infections: Mathematical Analysis of Viral Blips
KarthikaMuthukumaraswamy . . . . . . . . . . . . . . . . . . . . . . . . . 175
12.4 PreventionofHIVUsingDrug-BasedInterventions
JessicaM.Conway. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
12.5 RandomNetworksandtheSpreadofHIV EstelleBasor . . . . . . . 179
12.6 TalkingacrossFields PersiDiaconisandSusanHolmes . . . . . . . . 180
12.7 UsingMathematicalModelingtoEradicateDiseases RobertSmith? 182
12.8 NeglectedTropicalDiseases—HowMathematicsCanHelp Robert
Smith? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
12.9 ContagiousBehavior EstelleBasor . . . . . . . . . . . . . . . . . . . . . 185
13 PredictingCatastrophesandManagingRisk 187
13.1 EarthquakeModelingandPrediction DarkoVolkov . . . . . . . . . 187
13.2 SeismicRiskProtection AlfioQuarteroni . . . . . . . . . . . . . . . . 189
13.3 FireSeason JamesCrowley . . . . . . . . . . . . . . . . . . . . . . . . . . 190
13.4 PlowingFieldsofData KentE.Morrison . . . . . . . . . . . . . . . . . 191
13.5 FindingaSensibleBalanceforNaturalHazardMitigationwithMath-
ematicalModels KarthikaMuthukumaraswamy. . . . . . . . . . . . . 191
13.6 ModelingtheEffectsofStormSurgesonCoastalVegetation
CatherineCrawley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
13.7 Königsberg’s Bridges, Holland’s Dikes, and Wall Street’s Downfall
ChristianGenestandJohannaG.Ne˘slehová . . . . . . . . . . . . . . . . . 194
13.8 SystemicRiskinComplexSystems JamesCrowley . . . . . . . . . . 196
ContributorIndex 199
NameIndex 201
SubjectIndex 203
Preface
In2013,thecommunityofmathematicalscientistsandeducatorsfocuseditscollective
attention on the mathematics of planet Earth. In the course of the year, a grassroots
organization grew toan international partnership of more than 150 scientific societies,
universities, research institutes, and organizations. The project, known as Mathematics
of Planet Earth 2013 or MPE2013, received the patronage of UNESCO in December,
2012.
MPE2013wasauniqueevent. Itbrought thechallengesfacingour planet totheat-
tention ofthemathematicsresearch community innumerous lectures, seminars, work-
shops, and special sessions at conferences of the professional societies; it sponsored the
development of curriculum materials for all educational levels; it organized many out-
reachactivities,includinganinternationaljuriedexhibitofvirtualandphysicaldisplays
foruseinmuseumsandschools;anditpresentedaseriesofpubliclecturesbyrenowned
scientistswhoshowedthepublichowmathematicscontributestoourunderstandingof
planetEarth,thenatureofthechallengesourplanetisfacing,andhowmathematicians
helpsolvethem. AlistofitspartnersandprogramscanbefoundontheMPE2013home
page,http://mpe2013.org/.
Fromthebeginning,“MathematicsofPlanetEarth”wasinterpreted inthebroadest
possibleterms. Inadditiontoclimatechangeandsustainability, itincludedgeophysics,
ecology, epidemiology, biodiversity, as well as the global organization of the planet by
humans. Thedifferenttopicswereclassifiedintofourthemes:
A PLANET TO DISCOVER: planetEarth,Earth’sclimatesystem,weatherandcli-
•
mate,beyondplanetEarth;
APLANET SUPPORTING LIFE: biosphere,ecology,evolution;
•
A PLANET ORGANIZED BY HUMANS: communication and representation, en-
•
ergy,humanbehavior,economicsandfinance;
A PLANET AT RISK: climate change, invasive species, infectious diseases, natural
•
disasters.
Aspart oftheoutreach, MPE2013featured twoblogs—an English-languageblog1 anda
French-languageblog.2 Someindividualcountriesfeaturedtheirownblogs;forexample,
“MathsofPlanetEarth”inAustralia.3 TheMPE2013blogswereinitiatedin2012. Posts
appearedsomewhatirregularlyduringtheFallof2012,butstartingonJanuary1,2013,
the English-language blog posted entries seven days a week until the beginning of the
summerbreakonJuly14. BloggingresumedonAugust15onaMondaythroughFriday
1http://mpe2013.org/blog/
2http://www.breves-de-maths.fr/
3http://mathsofplanetearth.org.au/category/blog/
xi
xii Preface
scheduleuntiltheendoftheyear. Altogether,270postswerepublished,coveringawide
rangeoftopicsreflectingthebroadscopeofMPE.
ThevolumeathandisananthologyoftheEnglish-languageblogpostspublishedon
the website of MPE2013. We have omitted posts announcing workshops, conferences,
and special lectures, unless they included information of lasting value to the themes of
MPE2013, and edited the posts to streamline the text where necessary. The posts are
groupedinfourparts,followingthefourMPEthemeslistedabove. Eachpostisidentified
by its original contributor(s). Many of the entries are accessible to a general audience,
some require a bit of scientific knowledge, and a few include mathematical jargon that
willonlyappeal totheinitiated. Thisrangeofentrystylesreflectsthebreadth ofMPE
andthediversityofthecontributorstotheblog.
MPE2013wasanunusuallysuccessfuleffort,withalegacythatwilllastwellbeyond
2013. Itcreatedexceptionalopportunitiesforlong-termcollaborationswithinthemath-
ematicalsciencescommunityandwithotherrelatedscientificdisciplines. Itintroduced
anewgenerationofresearcherstothescientificproblemsconnectedwithclimatechange
andsustainability,andstimulatedinitiativestoanswerquestionslike“Whatismathemat-
ics useful for?” Its outreach activities brought the role of the mathematical sciences in
addressingsomeoftheplanet’smostpressingproblemstotheattentionofaworldwide
audience. Wehopethatthiscollectionofblogpostswilldemonstratethatthemathemat-
ical sciences communityis aware ofthe issues around planet Earth and standsready to
applyitsexpertisetothesolutionoftheproblemsfacingourplanet.
Acknowledgments
WethankourmanyfriendsandcolleagueswhowereinvolvedintheplanningofMPE2013
andworkedsohardtoimplementtheprogramandmakeitasuccess. Wethank,inpar-
ticular,allthosecolleagueswhocontributedtotheMPE2013DailyBlog. Wehopethat
thisanthologyisatangiblereminderofaworthwhileeffortandtimewellspent.
WesincerelyappreciatetheencouragementandadvicewereceivedfromJimCrowley,
ExecutiveDirectorofSIAM,andrecognizethetechnicalexpertiseofthestaffatSIAM.It
wasapleasuretoworkwithElizabethGreenspan,GinaRinelli,andDavidRiegelhaupt,
whocollectivelymanagedthetimelyproductionofthisvolumewhilemakingsurethat
itwouldmeetthehigheststandardsofthepublishingtrade.
HansG.Kaper ChristianeRousseau
GeorgetownUniversity UniversitédeMontréal
Washington,DC Montréal,Canada
January27,2015
