Table Of ContentSpringer INdAM Series 38
Piermarco Cannarsa
Daniela Mansutti
Antonello Provenzale Editors
Mathematical
Approach
to Climate
Change and its
Impacts
MAC2I
Springer INdAM Series
Volume 38
Editor-in-Chief
GiorgioPatrizio,UniversitàdiFirenze,Florence,Italy
SeriesEditors
ClaudioCanuto,PolitecnicodiTorino,Turin,Italy
GiulianellaColetti,UniversitàdiPerugia,Perugia,Italy
GrazianoGentili,UniversitàdiFirenze,Florence,Italy
AndreaMalchiodi,ScuolaNormaleSuperiore,Pisa,Italy
PaoloMarcellini,UniversitàdiFirenze,Florence,Italy
EmiliaMezzetti,UniversitàdiTrieste,Trieste,Italy
GiocondaMoscariello,UniversitàdiNapoli“FedericoII”,Naples,Italy
TommasoRuggeri,UniversitàdiBologna,Bologna,Italy
SpringerINdAMSeries
This series will publish textbooks, multi-authors books, thesis and monographs
in English language resulting from workshops, conferences, courses, schools,
seminars, doctoral thesis, and research activities carried out at INDAM - Istituto
Nazionale di Alta Matematica, http://www.altamatematica.it/en. The books in the
series will discuss recent results and analyze new trends in mathematics and its
applications.
THESERIESISINDEXEDINSCOPUS
Moreinformationaboutthisseriesathttp://www.springer.com/series/10283
Piermarco Cannarsa (cid:129) Daniela Mansutti (cid:129)
Antonello Provenzale
Editors
Mathematical Approach
to Climate Change and its
Impacts
MAC2I
Editors
PiermarcoCannarsa DanielaMansutti
DepartmentofMathematics IstitutoperleApplicazionidelCalcolo
UniversityofRome“TorVergata” ‘M.Picone’,CNR,Rome,Italy
Rome,Italy
AntonelloProvenzale
InstituteofGeosciences&Earth
Resources(IGG)
NationalResearchCouncil(CNR)
Pisa,Italy
ISSN2281-518X ISSN2281-5198(electronic)
SpringerINdAMSeries
ISBN978-3-030-38668-9 ISBN978-3-030-38669-6(eBook)
https://doi.org/10.1007/978-3-030-38669-6
©SpringerNatureSwitzerlandAG2020
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In Mathematicstheartofproposinga
questionmustbeheld ofhighervaluethan
solvingit.
(Georg Cantor)
Mathematicsallowsfor nohypocrisyand no
vagueness.
(Stendhal)
Preface
Climate change and the associated critical problems, which might impact on the
well-beingandpotentiallythesurvivalofhumansonplanetEarth,areattractingthe
attentionofboth the scientific communityand the generalpublic,sometimeswith
conflictual approaches. We believe that Mathematics can provide tools to address
these problems, raising well-posed questions and framing them in conceptual
models.Themodelsolutionscanthenbeanalyzedandcomparedwithobservations,
toproviderelevantinformationforbothdiagnosticandprognosticpurposes.
Inthisapproach,itisimportanttofullyacknowledgethe difficultiesassociated
with trying to address phenomena that are part of an extremely complex system
and may still be beyond our current conceptual and computational capabilities.
Suchcomplexity,however,shouldnotpreventusfromexploringthesubjectusing
mathematicalmodelling, which is especially suitable to tackle issues that are still
poorlyunderstood.
The current volume was conceived in this spirit. The aim here is to provide
ideas, suggestions, and motivations, inviting researchers in Applied Mathematics
andrelateddisciplinestoengageandenterintodialoguewitheach otherandwith
environmentalscientistsinthisfundamentalareaofresearch.
The volume includes contributions relating to the outcomes of the interna-
tionalINDAM Workshop “MathematicalApproachto Climate Change Impacts—
MAC2I”, held in Rome at the INDAM Headquarters on 13–17 March 2017. It
comprises a collection of original, peer-reviewed articles on research issues that
emergedfromdiscussionsineachsubjectarea.
Thecontentsofthisbookincludethefollowingtopics:
– accurate parameter determination supported by rigorous existence, regularity,
uniqueness, and stability results in the case of Energy Balance Models with
Memory,whicharerelevanttoclimatedynamicsinvestigations;
– three innovative mathematical modelling approaches to complex ice state (sea
ice) and composition (morainic ice), two of them related to real cases, and
experimentaldata;
vii
viii Preface
– anovelmethodforeventscreeningcategorizationofcarbondioxideconcentra-
tiontimeseries;
– differentcomplementarymathematicalformulationsof the problemof control-
lingthespreadofinvasivespecies,withnumericaltestingonrealsituationsand
data;
– influenceofbedloadtransportprocessesinacoastalsand-bedriveruponbeach
changes,withafocusontheFiumiUnitioutletintotheAdriaticsea;
– a tutorialonmathematicalmodellingoflarge-scalemotionsof atmosphereand
oceans,includingshallowness,Earthrotation,andwindeffects.
Mostcontributionsinthebookrelatetoactualcasestudies:mathematicalmodels
and/or methods are embedded into a real physical set-up, using observational
dataformodelvalidationand/oraddressingspecificdiagnostic/prognosticqueries.
This aspect justifies structuring the table of contents into thematic parts, namely
GeophysicalFluidsandClimate,Hydrology,Glaciology,andEcosystems.
We hope that this book can be used for doctoral programs in Applied Mathe-
matics,withcoursesrangingfrommathematicalproblem-solvingtoolstothestudy
ofthecomplexitiesofclimateandenvironmentalchange,therebyattractingcritical
andvaluableattentiontothiscrucialfield.
Rome,Italy PiermarcoCannarsa
Rome,Italy DanielaMansutti
Pisa,Italy AntonelloProvenzale
September2019
Acknowledgements
TheworkshopMathematicalApproachtoClimateChangeImpacts—MAC2Istems
fromofthehomonymthematicsectionoftheexcellenceprojectofappliedmathe-
matics,MATH-TECH,fundedbytheItalianMinistryofEducation,Universityand
Research(MIUR)andawardedtotheIstitutoperleApplicazionidelCalcolo(IAC)
‘M. Picone’ of the National Research Council (CNR) and to the INDAM (2015–
2017)(coordinator:RobertoNatalini,IAC-CNR).Editorsacknowledgethefinancial
support for that event, of which the present scientific paper collection is a direct
consequence.
ix
Contents
PartI Theme:GeophysicalFluidsandClimate
GeophysicalFluidDynamics,NonautonomousDynamicalSystems,
andtheClimateSciences........................................................ 3
MichaelGhilandEricSimonnet
ParameterDeterminationforEnergyBalanceModelswithMemory ..... 83
PiermarcoCannarsa,MartinaMalfitana,andPatrickMartinez
PartII Theme:Hydrology
BedloadTransportProcessesinaCoastalSand-BedRiver:The
StudyCaseofFiumiUnitiRiverintheNorthernAdriatic.................. 133
SilviaCilli,PaoloBilli,LeonardoSchippa,EdoardoGrottoli,
andPaoloCiavola
PartIII Theme:Glaciology
MathematicalModelingofRockGlacierFlow
withTemperatureEffects ....................................................... 149
KrishnaKannan,DanielaMansutti,KumbakonamR.Rajagopal,
andStefanoUrbini
AModeltoDescribetheResponseofArcticSeaIce......................... 163
RezaMalek-MadaniandKumbakonamR.Rajagopal
Modelling Sea Ice and Melt Ponds Evolution: Sensitivity
toMicroscaleHeatTransferMechanisms..................................... 179
AndreaScagliarini,EnricoCalzavarini,DanielaMansutti,
andFedericoToschi
xi
