GEOS22060/32060–Spring2019–Homework4DueinKitemailbox(whichisinthemailroomonthe1stflooroftheHindsbuilding)4pmFriday17thMay.Togettothemailroomonthe1stflooroftheHindsbuilding,turn leftonenteringHinds through themain (East)entrance,walkpast thesofas,andjustafterenteringawindowlesscorridor,themailroomwillbethefirstroomonyour left.Nocreditwillbegiven foranswerswithoutworking. It isOK tousee.g.Mathematica,butifyoudo,pleaseprintoutthework. Q1. Effect of Supercontinent Formation.Mountains are important to theglobalweathering budget. This is because mountain uplift increases the amount ofmaterial available forweathering per year (the sedimentmass flux). Because thetotal planet-integrated weathering must be constant (averaged over >107 yrtimescales) inordertoavoidaclimaterunaway, the increase inmaterialavailableforweatheringmustbecompensatedbyadecreaseintheamountofweatheringperunit sediment. The easiest way to decrease the amount of weathering per unitsediment is to lower the planet temperature. (The lowering of temperature isaccommodatedbyatransientpulseofincreasedweathering.ThistransientincreaseinweatheringlowerstheCO2concentration,whichlowerstemperature.Theplanetis now less efficient at weathering each sediment parcel, and so the climate re-equilibratesatanew,lowertemperature).Thepurposeofthisquestionistoworkthroughtheorder-of-magnitudeeffectonplanetaryclimateofformingnewmountainbelts.

Earth280Ma.Credit:RonBlakey(NAU).The most recent global supercontinent, Pangea, was completed ~280 Ma bycollision of North America with Africa. The collision (the Alleghenian orogeny)created a mountain chain, the Central Pangean Mountains. The AppalachianMountains approximately correspond to a remnant of this mountain belt. In thisquestion,use thepaleogeographic reconstructionabove (grid spacing30degrees)andEarthradius=6x106m.

Assume weathering efficiency (cations/yr/km^3 of sediment flux) scales as

whereE isactivationenergyandR isthegasconstant,8.314J/mol/K,andsurfacetemperature T is in K. Assume an effective activation energy for weathering(“effective”includingtheeffectoftemperatureonrainfall)ofE=74kJ/mol(Westetal.,Earth&PlanetaryScienceLetters,2005).

(a) Supposepaleomagneticdata1indicateAfricatravelledNat5cm/yrandcollidedwithastationaryNorthAmerica.Assumecontinentalcrustis35kmthick.Becausecontinentsarebuoyantrelativetothemantle,neithercontinentsubducts.Atsteadystate,continentalcrustismovinguptothesurface atmountain belts, undergoingweathering and erosion, and themass is being redistributed away from the mountain-belt, all at equalrates.What is themass flux? Suppose thepre-collision eroded fluxwasequaltoEarth’smodernsedimentfluxof8km3/yr;whatisthefractionalchangeinerodedflux(i.e.,mass/volumeavailableforweathering)?

(b) Assumeanactivationenergyforthetemperatureeffectonweatheringof74kJ/mol(Westetal.,Earth&PlanetaryScienceLetters2005).Whatisthesignandmagnitudeofplanetarytemperaturechange?

(c) SupposethattheicesheetintheSHemispheregrows.Isthisapositiveornegativefeedbackonthechangeyoucalculatedinpart(b)?Why?

(d) Itisoftensaidofwarmingclimatesthat“wetareasgetwetter,dryareasgetdrier.”2Giventhatweatheringratedependsonbothtemperatureandrainfall,explainqualitativelyhowchangesinrainfallontheCentralPangeanMountainsduetothewarmingyoucalculatedinpart(b)wouldfeedbackon(andthusmodify)youranswertopart(b).

(e) Supposethatcollisionhadoccurredinthedesertbeltat25°Ninsteadofatthehumidequator.Explainhowyouanswertopart(d)woulddiffer.

TheformationoftheHimalayasandTibetisoneleadinghypothesisforthecoolingofEarththatledtotheonsetoficesheetsonAntarctica~35Myrago.Q2. Tidally Locked Exoplanet.Many, perhapsmost, of the rockyhabitable-zoneplanets in the Universe orbit M-dwarf stars; these are also the easiest habitable-zonerockyplanetstodetectandcharacterize.However,becauseM-dwarfsarefaint,

1 Paleomagnetic data provide great constraints on latitudinal drift rates, butconstrainingpaleo-longitudinaldriftrequireslessdirectmethodssuchasmatchingupgeologicprovincesoneithersideofariftzone,orlookingforevidenceofhotspotvolcanism(hotspotsareunderlainbymantleplumes,whichmoveslowlyrelativetoplatesandsodefinea“hotspotreferenceframe”).2This is not always exactly true. For example, an expanding Hadley cell underwarming (the Hadley cells are currently expanding due to anthropogenic globalwarming)canturnthelow-latitudeedgeofthedesertbeltintoawetzone.

the habitable zone is located close to the star (i.e. the ratio of planet radius r toorbital radius a ismuch smaller than on Earth). Because tidal locking timescalesscaleasa-5forconstantr,suchplanetsareveryvulnerabletotidallocking.

Surface temperature on a tidally locked planet, calculated using an idealized 1Dclimatemodel. Thenumbers 0.001à10 correspond to atmospheric pressure in bars.Localtemperature iscontrolledbythegreenhouseeffect,butalsobythetendencyofthickeratmospheres to redistributeenergy fromthe lightside to thedarkside. (FromKiteetal.ApJ2011)Considerthetidallylockedplanetfromthefigure.

(a) Asinpreviousquestion,assumeweatheringratescalesas

where E is activation energy and R is the gas constant. Assume aneffectiveactivationenergyforweathering(“effective”includingtheeffectof temperatureonrainfall)of74kJ/mol,as fortheprevioushomework.Forthe0.01bartidallylockedplanetcase,whatistheratioofweatheringrateatthesubstellarpointtoweatheringrateat60°fromthesubstellarpoint?

(b) Assumingmountainbelts/tectonicupliftzonesarerandomlydistributedwithdistancefromthesubstellarpoint,commentonwhereontheplanetmostweatheringoccurs.Considerthelikelyeffectoficecover.

(c) Now assume that the gas that is the principal constituent of theatmosphere is also the principal greenhouse gas. (This assumptionwasusedtocalculatethetemperaturesshownintheplot.Thisassumptionisnot true for theEarth,but is true forMars,Venus,Triton, andarguablyalsoTitan).Explainhowtheplanet-integratedweatheringratechangesasweincreasepressurefrom0.001à10bars.

(d) Isthishypotheticalplanetstabletoasuddentwo-foldstepincreaseinthevolcanicoutgassingrate?Why?

(e) Now assume that everything is the same as in (e), but the effectiveactivationenergyisnow1000kJ/mol.Isthishypotheticalplanetstabletoa sudden two-fold step increase in the volcanic outgassing rate?Why?Hint: Recall that the threshold surface temperature for runawaygreenhouseonaplanetwithwateroceansis~330K.