Mathematics of Planet Earth: Protecting Our Planet, Learning from the Past, Safeguarding for the Future

385 Pages·2019·10.496 MB·English

by  Hans G. Kaper, Fred S. Roberts

Mathematics of Planet Earth Series 5
Hans G. Kaper
Fred S. Roberts
Editors
Mathematics
of Planet Earth
Protecting Our Planet, Learning from
the Past, Safeguarding for the Future
Mathematics of Planet Earth
Volume 5
SeriesEditors
KenGolden,DepartmentofMathematics,TheUniversityofUtah,
SaltLakeCity,UT,USA
MarkLewis,UniversityofAlberta,Edmonton,AB,Canada
YasumasaNishiura,TohokuUniversity,Sendai,Miyagi,Japan
JosephTribbia,NationalCenterforAtmosphericResearch,Boulder,CO,USA
JorgePassamaniZubelli,PuraeAplicada,InstitutodeMatemáticaPuraeAplicada,
RiodeJaneiro,Brazil
Springer’s Mathematics of Planet Earth collection provides a variety of well-
written books of a variety of levels and styles, highlighting the fundamental role
played by mathematics in a huge range of planetary contexts on a global scale.
Climate,ecology,sustainability,publichealth,diseasesandepidemics,management
of resources and risk analysis are important elements. The mathematical sciences
playakeyroleintheseandmanyotherprocessesrelevanttoPlanetEarth,bothasa
fundamentaldisciplineandasakeycomponentofcross-disciplinaryresearch.This
createstheneed,bothineducationandresearch,forbooksthatareintroductoryto
andabreastofthesedevelopments.
Springer’s MoPE series will provide a variety of such books, including mono-
graphs, textbooks and briefs suitable for users of mathematics, mathematicians
doingresearchinrelatedapplications,andstudentsinterestedinhowmathematics
interactswiththeworldaroundus.Theserieswelcomessubmissionsonanytopic
of current relevance to the international Mathematics of Planet Earth effort, and
particularly encourages surveys, tutorials and shorter communications in a lively
tutorialstyle,offeringaclearexpositionofbroadappeal.
Moreinformationaboutthisseriesathttp://www.springer.com/series/13771
Hans G. Kaper (cid:129) Fred S. Roberts
Editors
Mathematics of Planet Earth
Protecting Our Planet, Learning from the
Past, Safeguarding for the Future
123
Editors
HansG.Kaper FredS.Roberts
MathematicsandStatistics DIMACSCenter
GeorgetownUniversity RutgersUniversity
Washington,DC,USA Piscataway,NJ,USA
ISSN2524-4264 ISSN2524-4272 (electronic)
MathematicsofPlanetEarth
ISBN978-3-030-22043-3 ISBN978-3-030-22044-0 (eBook)
https://doi.org/10.1007/978-3-030-22044-0
MathematicsSubjectClassification:60Gxx,62–07,62Pxx,86Axx,90Bxx,91Dxx,92Bxx,92Dxx
©SpringerNatureSwitzerlandAG2019
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Foreword
This book is an invitation. Since the winter of 2009, when I first had the idea
of Mathematics of Planet Earth, it has become a passion for me to learn how
the mathematical sciences can help us understand our planet, its ecosystems, and
its organization, and how we as pure and applied mathematicians can contribute
to protecting our planet from the effects of climate change, extreme events, and
otherriskfactors.Forapuremathematicianlikeme,itisnotalwayseasytomake
one’s way through the relevant literature, which—too often—is either targeting
specialists or too elementary on the mathematical side. This book fills the gap.
It is an invitation to our professional community to explore the new challenges
for mathematics related to planet Earth and, at the same time, enrich the cultural
heritageofscienceonourplanet.Thesubjects—notsostandardandverydiverse—
are likely to pique everyone’s interest, as they did for me. Did you know that the
surfaceoftheEarthisnotsosolid andreactstotheslidingofglaciers?Orthatthe
sea-level rise can vary substantially from one region of the globe to another? The
book addresses these and many other interesting questions, like how to measure
biodiversity and what mathematics can say about the sixth mass extinction, which
is being driven by current human behavior. Other chapters are focused on how to
optimizethelong-termhumanuseofnaturalcapitalorhowtoplanforinfrastructure
restoration after an extreme event. The reader is introduced to the mathematics of
foodsystemsandfoodsecurity—newtopicsthatarelikelytobecomeparamountas
theworldpopulationexperiencesthelimitsofsustainabledevelopment.Thesubject
ofinfectiousdiseasesistreatedwithnewexamples,whichcanbringnewideasinto
a modeling course or motivate modeling projects for the students. I hope that this
bookwilldrawyouin,asitdidme.
Montreal,QC,Cananda ChristianeRousseau
November2018
v
Preface
Planet Earth offers a wealth of challenges to science. The planet is at risk, and as
scientists,wehavearesponsibilitytogetinvolvedandapplytheparticularskillsof
ourdisciplinetofacethesechallenges.
Mathematics of Planet Earth is a concerted effort to identify these challenges
and bring them to the attention of the mathematical sciences research community.
Conceived by Christiane Rousseau (Université de Montréal, Canada) in 2009, the
first manifestation of this effort was a yearlong program, Mathematics of Planet
Earth2013.MPE2013startedoutasagrassrootsorganization,whichgrewquickly
intoaninternational partnershipofmorethan150 scientificsocieties,universities,
researchinstitutes,andorganizations.Itbroughtthechallengesfacingourplanetto
theattentionofthemathematicsresearchcommunityandorganizedmanyoutreach
activities to show the public how mathematics contributes to our understanding of
planetEarth,thenatureofthechallengesourplanetisfacing,andhowmathematical
scientistsaddressthesechallenges.Itunderscoredthemultidisciplinarynatureofthe
problemsfacingtheplanetandemphasizedmultidisciplinarypartnershipstoaddress
these problems. An anthology of blogs posted during MPE2013 was published in
2015bytheSocietyforIndustrialandAppliedMathematics(SIAM).1
Attheendof2013,MPE2013morphedintoMathematicsofPlanetEarth(MPE).
Anewstructurewasdesignedtosupporttheongoingresearcheffortsandmaintain
the momentum created by MPE2013. A program of technical and educational
workshops,MPE2013+(supportedbyDIMACSatRutgersUniversity2 andbythe
NationalScienceFoundation,grantDMS-1246305),wasinstrumentalinfurthering
thegoalsofMPE.SowastheformationofaSIAMActivityGrouponMathematics
ofPlanetEarth(SIAG/MPE).3 TheeditorsalsorecognizetheinitiativebySpringer
VerlagtoinitiateabookseriesonthethemesofMPE.
1http://bookstore.siam.org/ot140.
2http://dimacs.rutgers.edu/archive/SpecialYears/2013_MPE/.
3https://www.siam.org/membership/Activity-Groups/detail/.
vii
viii Preface
From the beginning, MPE has been interpreted in the broadest possible sense.
While the geosciences have long been concerned with our planet as a physical
system,thereisagrowingawarenessofthehumanimpactontheecosystemanda
gradualrealizationthatnaturalresourcesarenotinfinite.Sustainabilityhasbecome
a concern, and risks, both social and economic, are receiving increased attention.
ThesethemesdefinethecoreactivitiesofMPE.
The purpose of this book is to introduce challenging problems in MPE-related
topic areas to the mathematical sciences research community, to demonstrate
the application of a wide range of mathematical ideas to these challenges, and
to raise awareness in the application disciplines that the mathematical sciences
offer novel opportunities for quantitative and qualitative analysis. The book is
potentially of interest to scientists in academia, the private sector, government,
and nonprofit organizations active in application areas, such as the geophysical
sciences, climate science, ecology, environmental science, public health, and
socioeconomics.
The book covers some but by no means all topics of interest to MPE; it is
meanttogiveaflavorofselectedtopicsofcurrentinterest.AsProfessorRousseau
states in her Foreword, it is an invitation to explore new challenges. Among the
topics covered are climate change, the spread of infectious diseases, multistability
of ecosystems, biodiversity, infrastructure restoration after extreme events, urban
environments and the Internet of Things, food security, and food safety. These
topics illustrate the wide range of challenges for mathematical modeling. They
also highlight the variety of mathematical techniques brought to bear on these
challenges, from differential equations and dynamical systems theory, optimiza-
tion, statistics, operations research, discrete mathematics, graph theory, and data
analytics.
The prerequisite mathematics for the various chapters varies, but much of the
material should be accessible to advanced undergraduate and graduate students.
Selected chapters can be used as a text for seminars or self-study. Application
scientists (including graduate students) and decision-makers with background
knowledge in one or more of the mathematical topics listed in the previous
paragraph will find a wealth of tools that they may wish to explore for practical
purposes.
The chapters in this book were solicited from a diverse group of experts. Each
chapterofthebookwaspeer-reviewed.Theeditorsworkedwiththeauthorstorevise
theirchaptersandtoputthemallintoacommonlanguageandapproach.Theeditors
thank the (anonymous) reviewers for their extensive efforts to improve the quality
ofthepresentations.
Wehopethatthisvolumewillstimulatethereaderstoexplorethechallengesof
MPEandapplythetoolsofthemathematicalsciencestosolvetheproblemsofour
planet.
Preface ix
Acknowledgments The editors express their appreciation for many enlightening
discussions (technical and otherwise) with colleagues in the Mathematics and
Climate Research Network (funded by the National Science Foundation, grant
DMS-0940363). Fred Roberts acknowledges the support from the NSF through
grantDMS-1246305.
Washington,DC,USA HansG.Kaper
Piscataway,NJ,USA FredS.Roberts
November2018
Road Map
Mathematics of Planet Earth (MPE) views our planet through multiple lenses.
Broadly speaking, it considers our planet as a physical system, as a system
supportinglife,asasystemorganizedbyhumans,andasasystematrisk.Eachlens
providesadifferentperspectiveandmayrequiredifferenttoolsandtechniquesfrom
the mathematical sciences. But the common goal is to gain a better understanding
ofhowthestateofourplanetinfluencesandisinfluencedbyhumanactivities.
Thechaptersinthisvolumearegroupedintofourparts.Thefollowingisabrief
introductiontoeachpartandanoverviewofthechaptersselected.
PartI:Geo-and PhysicalSciences
InPartI,weconsiderplanetEarthasaphysicalsystem.Here,thefocusisonEarth’s
climatesystem,thephysicalprocessesthatoccurinthevariouscomponentsofthe
system(atmosphere,oceans,etc.),theirdynamics,andmutualinteractions.Wehave
selectedthreecasestudiesofphysicalsystemswhichpresenttypicalchallengesfor
mathematicalandstatisticalmodelingandanalysis.
Chapter1discussesaconceptualmodelofthecoupledatmosphere-oceansystem
which emphasizes the critical role of atmospheric carbon dioxide (CO ) in the
2
dynamics of glacial-interglacial cycles during the Pleistocene Epoch. The chapter
also offers an interesting application of techniques from the theory of dynamical
systems.
Chapter 2 presents a closely related problem from geophysics, namely, the
GlacialIsostaticAdjustmentproblem—thatis,theadjustmentoftheEarth’ssurface
to a varying load due to the waxing and waning of ice sheets during a glacial-
interglacialcycle.
Chapter3addressesapracticalproblem,namely,howtomeasureprecipitation.
Unlike temperature, precipitation is highly variable, both in space and in time.
The chapter also describes various statistical methods to identify precipitation
xi