Weather Module SE - COMAP

PS-FutureMathematical and Computational Methods for

Planning a Sustainable Future

Weather GeneratorsA Module in Planning for Sustainability

STUDENT EDITION

Lisa Rodgers, Grandview High SchoolSteve Sain, Jupiter Intelligence

Funded by the National Science Foundation,Proposal No. 1503414

This material was prepared with the support of the National Science Foundation. However, any opinions, findings, conclusions, and/or recommendations herein are those of the authors and do not necessarily reflect the views of the NSF.

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Front Cover Photographs: Zonsopkomst Weegje2.jpg (Sunset) By Dick Mudde [Public domain], from Wikimedia CommonsTall Tree Corridor: Public Domain Picture by Chelsea Bock chelseabock (https://unsplash.com/photos/S-U6ipzt4Lw) [CC0], via Wikimedia Commons

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DIMACS

Weather GeneratorsA Module in Planning for Sustainability

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WeatherGeneratorsA Module in Planning for Sustainability

What is sustainability? The most frequently quoted definition related to sustainability is from the World Commission on Environment and Development’s 1987 report Our Common Future. It says, “…sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs.” At the heart of sustainability is the need to assure the long-term persistence and vitality of both humans and the natural environment. Sustainability focuses on interactions between nature and society. These interactions are complex and do not abide disciplinary boundaries. They require understanding of physical and biological processes that are overlaid by human social, political, and economic concerns.

A popular view is that sustainability balances on three pillars—environmental, social, and economic—and that failure or weakness of any one compromises future sustainability. To be sustainable, a practice must be environmentally, economically, and socially sustainable. Sustainable behaviors and practices are those that can be continued (or sustained) indefinitely. To do this they must balance limits imposed by human systems with those imposed by environmental ones.

What is planning for sustainability? Sustainability is forward-looking, and natural resources are finite. Planning for sustainability therefore involves making decisions about how we use limited resources in light of the continuing future needs for those resources. Planning for sustainability seeks to identify practices that can continue indefinitely without critically damaging natural resources, people, or economies, especially those that are at risk.

While it is tempting (and simpler) to base decisions purely on their immediate economic impacts, doing so can easily overlook the long-term environmental (and social) consequences that can undermine sustainability. In planning for sustainability, it is important to consider that human economic and social systems exist within and are dependent on the environment. Decision makers need to identify how their choices impact both human and environmental systems, as well as, whether such choices could persist indefinitely into the future.

Who is involved in planning for sustainability? Planning for sustainability involves everyone. It is reflected not only in decisions made by world leaders, but also in choices made by individual consumers. It is important to note that planning for sustainability can be done at any level—global, national, municipal, or individual.

The men and women who contribute to planning for sustainability as a part of their job have diverse positions in government and industry. These jobs may include various types of Environmental Scientists, various types of Engineers, Architects, Surveyors, Planners, Lawyers, Communication Specialists, Construction Workers, and Government Officials. Their decisions

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impact our daily lives through choices about how we get our water, where bridges are built, when and where to harvest trees for timber, and what materials to use in designing energy-efficient buildings. These jobs often require mathematical and critical thinking skills to measure and model real-world systems and to simulate the impact of a wide range of future scenarios.

Contents

Lesson1:TheWaterCycle....................................................................................................................3 Lesson1:Homework..........................................................................................................................9Lesson2:Statistics...............................................................................................................................11 Lesson2:Homework........................................................................................................................15Lesson3:WeatherandStatisticalPersistence....................................................................................17 Lesson3:Homework........................................................................................................................21Lesson4:IntroductiontoWeatherGenerators..................................................................................23 Lesson4:Homework........................................................................................................................27Lesson5:NaturalVariabilityinData...................................................................................................29 Lesson5:Homework........................................................................................................................31Lesson6:PredictingtheFuture...........................................................................................................33Glossary...............................................................................................................................................37

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Lesson1:TheWaterCycle

Objective 1: Introduce themodule question. Then review thewater cycle and introduce the conceptthatwarmerairholdsmorewatermolecules.This unit’s driving question is: “Global temperatures are rising. What does this mean aboutprecipitation?”What thoughts do you have on this question beforewe begin?Do you think the twotopics (temperature increase and precipitation) are completely unrelated? Do you think they areindirectly related,butwewon’tnoticeadifference?What initiallycomestomindwhenyoureadthisquestion?It’sokayiftheansweris“notmuch.”

TheWaterCycle1. Whatarethethreedifferentstatesofwater?Howareallthreestatesofwaterpresentonthe

planetatanygiventime?

2. Doesthewatercyclehaveabeginningoranend?

3. Doallwatermoleculesfollowthesamepath?Explain.

4. Whatpowersthewatercycle?Explain.

Source:http://www.exploringnature.org/db/detail.php?dbID=27&detID=1188,9/22/2012.Usedwithpermission.

5. Whereinthiscycleiswatercreated?Destroyed?

Thisdataandgraphshowthatwarmeraircanholdagreaterquantityofwaterthancancoolerair.Examinethegraphandconsiderthequestionsthatfollow.Gramsofwatervaporperkgofairvs.ambienttemperature

Temp(deg.Celsius) -40 -35 -30 -25 -20 -10 0 5 10 15 20 25 30 35 40

WaterVapor(g/kg) 0.1 0.2 0.3 0.5 0.8 1.8 3.8 5 7.8 10 15 20 28 35 50

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Datafrom:http://web.gccaz.edu/~lnewman/gph111/topic_units/Labs_all/Water%20Vapor%20Capacity%20of%20Air.pdf,9/21/13.

1. Whatdoesthisgraphshowus?2. Basedonwhatthisgraphisshowingus,wherearewatermoleculesgetting“stuck”inthewater

cycleastemperaturesincrease?

3. Whatformofwaterisusablebyorganismslikeplantsandanimals(solid,liquid,orgas)?

4. Ifmorewatermoleculesaregetting“stuck”intheatmosphere,whatimpactcouldthathaveonorganismsandecosystems?

0

10

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60

70

-40 -30 -20 -10 0 10 20 30 40 50

Gram

sofw

atervaporperkgofair(g/kg)

Temperature(OC)

Gramsofwatervaporperkgofair(g/kg)vs.temperature

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Objective2:Developaconceptofsustainabilityasrelatedtowateruse.Asweworkthroughtoday’slesson,wewillbeworkingonthequestion,“Whatissustainability?”Startbyprovidingananswerforyourself,butfeelfreetoaddtoyourresponseaswediscussthisasaclass.Nowconsiderthisdefinition:

Source:http://www.epa.gov/sustainability/basicinfo.htm,9/22/2012.

1. Whatdoweneedforoursurvivalandwell-being?

2. Whatresourcesdependdirectlyonournaturalenvironment?

3. Whatresourcesdependindirectlyonournaturalenvironment?

4. Whatis“productiveharmony?”

5. Ifwaterexistsinacyclethathasnobeginningandnoend,whydoestheconceptofsustainabilityincludelimitationsofwateravailability?”

6.

Source:http://www.nsf.gov/pubs/2010/nsf10524/nsf10524.htm,9/22/2012.

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Think-Pair-ShareIfwaterexistsinacyclethathasnobeginningandnoend,whydoestheconceptofsustainabilityincludelimitsofwateravailability?Think:Pair:Share:

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Objective3:Identifythatthewatercycleisn’tchanging,butwhenandhowwaterisfallingischangingAsyourteachergoesthroughtheanimations,considerthefollowingquestions:

• Whatdothechangesincolormean?

• Doesthewholeglobegetdrieratthesametime?

• Whydosomeareasactuallygetwetter(moreblue)whilesomeareasgetdrier(morered)?Canweexplainthisintermsofthewatercycle?

Homework:ReadtheNewYorkTimesarticle“StudyIndicatesaGreaterThreatofExtremeWeather,”andwritearesponse.

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Thispageintentionallyleftblank.

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Name_______________________________________________Date________Period________WeatherGenerators

Lesson1:HomeworkDirections:Readthearticle.Onyourownpaper,respondtothepromptfoundattheend.April 26, 2012

Study Indicates a Greater Threat of Extreme Weather By JUSTIN GILLIS New research suggests that global warming is causing the cycle of evaporation and rainfall over theoceans to intensifymore thanscientistshadexpected,anominous finding thatmay indicateahigherpotentialforextremeweatherincomingdecades.Bymeasuringchanges insalinity(amountofsalt inthewater)ontheocean’ssurface,theresearchersinferredthatthewatercyclehadacceleratedbyabout4percentoverthe lasthalfcentury.Thatdoesnot sound particularly large, but it is twice the figure generated from computerized analyses of theclimate.Iftheestimateholdsup,itimpliesthatthewatercyclecouldquickenbyasmuchas20percentlaterinthis century as the planet warms, potentially leading to more droughts and floods. “This providesanother piece of independent evidence that we need to start taking the problem of global warmingseriously,”saidPaulJ.Durack,aresearcherattheLawrenceLivermoreNationalLaboratoryinCaliforniaandtheleadauthorofapaperbeingpublishedFridayinthejournalScience.Theresearchers’analysisfoundthatoverthehalfcenturythatbeganin1950,saltyareasoftheoceanbecamesaltier,while freshareasbecame fresher.That changewasattributed to strongerpatternsofevaporationandprecipitationovertheocean.Thenewpaperisnotthefirsttofindanintensificationofthewatercycle,noreventhefirsttocalculatethatitmightbefairlylarge.Butthepaperappearstomarshalmorescientificevidencethananypapertodateinsupportofahighestimate.“Iamexcitedaboutthispaper,”saidRaymondW.Schmitt,aseniorscientistattheWoodsHoleOceanographic Institution inMassachusetts,whoofferedacritiqueoftheworkbeforepublicationbutwasotherwisenotinvolved.“Theamplificationpatternthatheseesisreallyquitedramatic.”Thepaperisthelatestinstallmentinalong-runningeffortbyscientiststosolveoneofthemostvexingpuzzlesaboutglobalwarming.Whilebasicphysicssuggeststhatwarmingmustacceleratethecycleofevaporationandrainfall, ithasbeendifficulttogetahandleonhowmuchaccelerationhasalreadyoccurred,andthustoprojectthechangesthatarelikelytoresultfromcontinuedplanetarywarming.The fundamental problem is thatmeasurements of evaporation and precipitation over the ocean—which covers 71 percent of the earth’s surface, holds 97 percent of its water and is where most

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evaporationandprecipitationoccurs—arespottyatbest.Toovercomethat,scientistsaretryingtousethechangingsaltinessoftheocean’ssurfaceasakindofraingauge.Thatworksbecause,asrainfallsonapatchoftheocean,itfreshensthesurfacewater.Conversely,inaregionwhereevaporationexceedsrainfall,thesurfacebecomessaltier.Thevariationsinsalinityarelargeenoughthattheycanbedetectedfromspace,andNASArecentlysentupanewsatellite,Aquarius,forthatpurpose.Butitwilltakeyearstoobtainresults,andscientistslikeDr. Durack are trying to get a jump on the problem by using older observations, including salinitymeasurementstakenbyshipsaswellasrecentmeasurementsfromanarmyofroboticfloatslaunchedinaninternationalprogramcalledArgo.Dr.SchmittcautionedthattheworkbyDr.Durackandhisco-authors,theAustralianresearchersSusanE.WijffelsandRichardJ.Matear,wouldneedtobescrutinizedandreproducedbyotherscientists.Anotherexpertnotinvolvedinthework,KevinE.TrenberthoftheNationalCenterforAtmospheric Research in Boulder, Colo., said that Dr. Durack had produced intriguing evidence thatglobalwarmingwasalreadycreatingchanges in thewatercycleata regional scale.ButDr.TrenberthaddedthathedoubtedthattheglobalintensificationcouldbeaslargeasDr.Durack’sgrouphadfound.“Ithinkhemighthavegoneabittoofar,”hesaid.Assuming that the paper withstands scrutiny, it suggests that a global warming of about 1 degreeFahrenheitoverthepasthalfcenturyhasbeenenoughtointensifythewatercyclebyabout4percent.That ledDr. Durack to project a possible intensification of about 20 percent as the planetwarms byseveraldegreesinthecomingcentury.Thatwouldbeapproximatelytwicetheamplificationshownbythecomputerprogramsusedtoprojectthe climate, according to Dr. Durack’s calculations. Those programs are often criticized by climate-changeskepticswhocontendthattheyoverestimatefuturechanges,butDr.Durack’spaperisthelatestofseveralindicationsthattheestimatesmayactuallybeconservative.Thenewpaperconfirmsalong-expectedpatternfortheoceanthatalsoseemstoapplyoverland:areaswithalotofrainfallintoday’sclimateareexpectedtobecomewetter,whereasdryareasareexpectedtobecomedrier.In theclimateof the future, scientists fear, a largeaccelerationof thewater cycle could feedgreaterweather extremes. Perhaps the greatest risk from global warming, they say, is that importantagriculturalareascoulddryout,hurtingthefoodsupply,asotherregionsgetmoretorrentialrainsandfloods.Writing prompt: On your own paper, write a paragraph explaining how measurements of salinity(saltiness) are used to infer the rate of thewater cycle.What impacts are suggested thatmay resultfromthechangeintherateofthewatercycle?

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Lesson2:Statistics

Objective1:Studentslearnmethodsofbasicprobability.Whydoyouthinkwearesobadatpredictingtheweather?Weatherforecastsusuallyassociateapercentagewithpredictionsofrainorsnow.Whydon’tforecastersknowwhat’sgoingtohappen?Whenyouflipacoin,whatisthechanceitwillcomeupheads?Howcanyoushowthatmathematically?Astandarddeckofcardshas52cards,with13ofeachof4suits.Whatarethechancesofpullingonecardfromthedeckthatisaspade?Howcanyoushowthatmathematically?PracticeProblems:1.Usingastandarddeckof52cards(nojokers),whatarethechancesyouwilldrawa5fromthedeck?2.Whatarethechancesofrollinga2onacommon,six-sideddie?3.Arethechancesofrollingeachnumberonthediethesame?4.Whatarethechancesofrollinganevennumberonacommon,six-sideddie?5.Whenyourteacherasksyouto,rollyourdie6timesandwritedownthenumberyourolleachtime.

Roll 1 2 3 4 5 6Result

Ifthechancesofrollingeachnumberare1/6andyourollthediesixtimes,whyareyounotguaranteed

torolloneofeachnumber?

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7. Whyisitsoimportantforstatisticianstouselargesamplesizes?

8. IfIamflippingacoinandhappentoflip10headsinarow,whatarethechancesthatmynextflipwillresultinheads,forthe11thtimeinarow?Howisthispossible?Usetheterm“independent”inyouranswer.

Objective2:Studentslearnmethodsofconditionalprobability.Let’sstartsimple:Yourmompurchasedabagof24Starburstcandies.Thebagcontains6ofeachcolor:red,orange,pink,andyellow.Let’ssupposeyourfavoriteflavoristhepink,soyoureallywantapinkone.Ifyoureachinandgraboneofthepiecesatrandom,whatarethechancesyouwilldrawapinkone?

• Well,let’sfurthersupposeyourtwooldersistersalsowantpinkStarburstandtheygettodrawtheirsrandomlyfromthebagbeforeyoudo.Doesthisaffectyourchancesofgettingwhatyouwant?How?

• Whatisconditionalprobability?

• “WhathappensifyoursistersbothdrawpinkStarburstbeforeyou?Now,whatarethechancesyouwilldrawapinkone?

• Whathappensifneitheroneofthemdrewapinkcandybeforeyou?Whatarethechancesyouwilldrawapinkone?

• Whatisa“string?”

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Objective3:Studentslearnwhatitmeansfordatapointstobeindependent.Ingeneralterms,whatisthedifferencebetweendependentandindependentdatapoints?Giveanexampleofeach.Whatisthedifferencebetweenindependentandconditionalprobability?Isrollingadiemultipletimesorrollingmanydicesimultaneouslyanexampleofindependentorconditionalprobability?Explain.Thereare52playingcardsinastandarddeck.Astheyarebeingdealtout,youcan’treceivethecardsthathavealreadybeendealt.Thatchangestheprobabilityofwhatcardyouwillreceivewhileplayingthegame.Isthisanexampleofanindependentoraconditionalsituation?Explain.Thisunitinvolvesperformingstatisticalanalysesontheweather.Doyouthinkdeterminingtheweatherfromonedaytothenextisindependentofordependentonwhathashappenedinthepast?Why?Isweatherpredictionbasedonindependentordependentstatisticalprocedures?Explainyourchoice.

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Lesson2:Homework

1. Calculatethechancesofrollinga1or2onastandard,six-sideddie.Showyourwork.

2. Calculatethechancesofpullingaredcardfromastandarddeckof52cards.Showyourwork.

3. Supposeyouareplayingacardgamewiththreeotherpeopleandastandarddeckof52cards.Inthisgame,theaceisthehighcard.Eachpersonisdealt13cardssothatallcardsaredistributedamongtheplayers.Therearefouracesinthedeckandfourplayers.Whyisn’titguaranteedthateachoftheplayerswillreceiveoneoftheaces?

4. Inyourownwords,describethedifferencebetweenpredictedprobabilitiesandresults.

5. Foreachscenario,statewhetherthesituationdescribedwouldgeneratedatathatisindependentorconditional.Thenexplainyourchoice.

a. Flippingacoin100times

b. Drawingacardfromadeck,checkingthesuit,placingitbackinthedeck,andthendrawinganother

c. Drawingacardfromadeck,checkingthesuit,settingitaside,anddrawinganother

d. Rollingtwodicesimultaneously

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Lesson3:WeatherandStatisticalPersistence

Objective1:Watchavideoonhowfrontsmove,toexplaintheconceptofstatisticalpersistence.Asyouwatchthevideo,considerthequestion:Doyouthinktheweathertodayisrelatedtotheweatherwe’llhavetomorrow?Isweathercompletelyindependentdaytoday?Whatdoesitmeantobe“persistent?”Objective2:Createaflowchartthatdescribesstatisticalpersistencewithrelationtodice,includinga

definitionofwetanddrydays.Forourpurposes,whatarewetdays?Drydays?Whatisaflowchart?Developasimpleflowchartthatguidesyouthroughthedecisionofwhenyouwilldoyourhomeworktonight.

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Examinethisflowchart.

Answerthefollowingquestionstohelpyouunderstandhowthisflowchartaboutrainshowspersistence.

Spendsometimeworkingwiththisflowchart,addressingthefollowingquestions:

1. Whatdoesrollingthedierepresent?

2. Howdoesthisshowpersistence?

3. Whydidn’twedoeven/oddorflipacoin?

4. Whatdoesthisflowchartaccomplishthatacointossdoesn’t?

5. “Wearestuckinaweatherpattern”issaidbyweatherforecastersonthenews.Whatsortofdicethrowswouldindicatewearestuckinaweatherpattern?

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Objective3:Collectdatawithpersistence;summarizeitina2x2grid.Rollyourdie30times.Keepitsimple:ifyourolla1,2,3,or4,theweatheristhesameasthepreviousday.Ifyourolla5or6,theweatherswitchestothealternate,eitherwetordry.Remember:Rollingthediedoesn’tindicatewhetheritwillrain,itindicateswhethertheweatherwillchange.

Data:StartingweatherisDry

Roll Today'sWeather

2x2DataSummaryGrid1

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Today

2

17

Yesterda

y Wet Dry3

18 Wet

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19 Dry 5

20

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Now,summarizeyourdatabytallyinghowmanytimestheweatherchangedfromwettodryorviceversainthe2x2grid.

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1. Bylookingatyour2x2grid,howcanyoutellthatthereispersistenceintheweather?

2. Whatwouldthesummarygridlooklikeifthereweren’tpersistenceintheweather?

3. Eventhoughthewholeclassstartedwiththesamematerialsandinformation(startingweatherisdry)yourdataisdifferent.Whyisthat?

Homework:Collectdatawithoutpersistence;summarizeitina2x2grid.(Thiswillbeusedtoseeifourpersistencemodelisworking.)Note:Youdonotneedtotakethediehome.Nopersistenceisachievedbyflippingacoin.

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Lesson3:HomeworkFlowchartfordeterminingprecipitationwithoutpersistence,byflippingacoin.

Data:StartingweatherisDry

Roll Today'sWeather

2x2DataSummaryGrid1

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Today

2

17

Yesterda

y

Wet Dry3

18 Wet

4

19 Dry 5

20

6

21 7

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Explainwhythisdatadoesn’tshowpersistence,eventhoughyoumaynothaveexactly½thedaysaswetand½thedaysasdry.

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Lesson4:IntroductiontoWeatherGenerators

Objective1:Introducetheweathergeneratorandtransitionprobabilityfiles.Explainwhatthegeneratoris doing and connect it to thedice lesson.Generateone setof data for a location inNorthAmerica.

Openthe“WeatherGenerator”Excelfilesonyourcomputer.Noticethefollowingcomponentsonthe“WeatherGenerator”tab:

• Transition Probabilities: These are the probabilities that reflect the chance of a change inweather.wet|drymeans “The probability of tomorrow beingwet given that todaywas dry.”wet|wetmeans“Theprobabilityoftomorrowbeingwetgiventhattodaywaswet.”

• Yearsarelistedacrossthetop;studentsmayhavethegeneratorprepareasmanyyearsatonceastheywouldlikebychangingthenumberontheleft.

• Youmayalsochange thenumberofdaysgeneratedperyear.Sinceeachmonthhasdifferenttransition probability it makes sense to have a number ~30, but it can be manipulated forshorterorlongermonths.

• Scrollingdownwillrevealthetotalnumberofwetdaysanddrydayseachmonth.Scrollbackuptorecalculateorchangetransitionprobabilities.

Nownotice theother twotabsonthebottomof thespreadsheet, titled,“Current”and“Future.”Thetwotabslookquitesimilarbutcontaindifferentinformation.

• The Current tab gives transition probabilities thatwere actually experienced over the last 30yearsorso.

• TheFuturetabgivestransitionprobabilitiesthatscientistsbelievemayhappenbasedonclimatemodels.

• Noticethatonbothtabsyouwillseetwodifferenttransitionprobabilities:oneforwet|wetandoneforwet|dry.Whenstudentsworkwiththedata, it is importantthattheyunderstandthattheymustusethevalues forthesamemonthandthesame location inordertoobtainusefuldata.

Put some fake numbers in for transition probabilities and see what happens.What patterns do youobserve?Obtain a location and month assignment from your teacher. Then, go to the “Current” transitionprobabilitytabandfindthetwotransitionprobabilitiesforthatassignment.Recordthemhere:wet|dry___________wet|wet___________Enterthosevaluesintheweathergeneratorandclick“Calculate.”1.Youhavejustusedtheweathergeneratorforthefirsttime,creating5yearsofdataforonemonthinonelocation.Describetheresults:

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Objective2:Discusssummarystatisticsthatarecommonlyusedbutareinappropriateforthisdataset.2.Countandrecordthenumberofdrydaysforeachyearofdata.Then,calculatethemeannumberofdrydaysforyourdata:

Year1 Drydays:Year2 Drydays:Year3 Drydays:Year4 Drydays:Year5 Drydays:

Meannumberofdrydays:

3.Explainwhythemean,oraverage,ofasetofnumbersisoftenausefuldescriptorofdata,butitsusefulnessislimitedinthiscontext.Objective3:Identify,defend,andapplyappropriatesummarystatisticsforthisdata.Poolthesummary

statisticsfromtheclass.4.Thinkingquestions:

• Doyouthinkthepatternofthewetanddrydaysmatters?

• Explainhowit’spossiblethatinoneyearthetotalnumberofwetdayswouldbehighbutthatplantswouldstillstruggletogetenoughwatertosurvive.

• Whichpatternofwaterismostusefulforyourlawn—watereveryfewdaysorallthewetdaysinarowfollowedbyallthedrydaysinarow.

• Whatsortsofinformationmightafarmerwanttoknowaboutrainfall?(Remember,weonlyhave“wet”and“dry,”notamounts.)

• Whichpatternofrainfallismoreimportanttomostpeople—theaveragenumberofdaysthatrainfallsorthelongeststringofwetanddrydays?

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Objective4:Assignonemonthoftheyeartoeachstudent.StudentsuseseeddatafromNCARandrun

theweather generator. They then use the summary statistics fromObjective 3 to describetheirfindingsofwetanddrydaysforeachmonthoftheyear.

5.Asaclass,chooseonelocationfromthe“Current”tabthatyouwishtoinvestigatetogether.

• Recordwhichmonthyou’vebeenassignedtoinvestigate:____________________________• Runthesimulationfor5yearswiththeappropriatetransitionprobabilitiesforyourmonth.For

eachyear,collectdata:totalnumberofwetdays,totalnumberofdrydays, longestwetspell,andlongestdryspellforyourmonth.Recordthesevaluesinthedatatablebelow.Last,computethemeanforeachsummarystatistic.

• Compare the summary statisticswith thoseofother studentswhohave the samemonthandreportyouroverallmeantotheclassdatatable.

Year1 Year2 Year3 Year4 Year5 Mean

Total#ofwetdays

Total#ofdrydays

Longestwetspell

Longestdryspell

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Lesson4:Homework

Directions: Using the wet/dry data generated by hand with persistence vs. without persistence,computethesamesummarystatisticswediscussedinclass:totalnumberofwetdays,totalnumberofdrydays, longestwet spell, and longestdry spell. (Thesearehandouts titled Lesson3:ClassworkandLesson3:Homework.)Forthedatasetwithpersistence(Lesson3:Classwork):

1. Whatisthetotalnumberofwetdays?_______

2. Whatisthetotalnumberofdrydays?_______

3. Whatisthelongestwetspell?_______

4. Whatisthelongestdryspell?______Forthedatasetwithoutpersistence(Lesson3:Homework):

5. Whatisthetotalnumberofwetdays?_______

6. Whatisthetotalnumberofdrydays?_______

7. Whatisthelongestwetspell?_______

8. Whatisthelongestdryspell?______Compareandcontrastthestatistics.Whatissimilaraboutthestatisticsforthetwodifferentdatasets?Whatisdifferent?All studentsusedthesamematerials togeneratedata (identical flowcharts,die,pennies,andstartingdata). Ifwewereall tocomparedatasheets,what shouldweexpect toseeas similarordifferentondifferentstudents’data?Shouldweallexpecttohavethesamedata?Shouldweallexpecttohavethesamesummarystatistics?Whichismorelikelytobethesameamongdifferentstudents?

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Lesson5:NaturalVariabilityinDataSummary:Studentsworktounderstandthedifferencebetweennaturalvariabilityandvariabilitythatis

theresultofhidden,andpossiblyproblematic,variables.Studentsusetheweathergeneratoragaintoexamineandsummarizevariabilitythatisnatural.

Objective1:Examinethehomeworkfromthenightbefore.Howwerethesummarystatisticsdifferent

forthedatawithvs.withoutpersistence?Lookagainatyourhomework.Howcouldwerepresentthisdatagraphicallysothatitiseasiertounderstand?Whatisahistogram?Whatisitusedfor?Aftertheclasshasbuiltahistogramoftheirdata,considerthefollowingquestions:

• Inwhichhistogramistheshortestwetordryspell?

• Dothereappeartobeanytrendsinthelengthofthewetanddryspells?(Thedatawithpersistenceshouldshowlongerwetanddryspells.)

• Whydoesthisdatareflectourdata-collectiontechnique(independentvs.withpersistence)?

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Objective2:Usetheweathergeneratortoreplicate15yearsofonemonth’sdata.Usingtwohistograms(oneforlongestwetspellandoneforlongestdryspell),examinevariabilitythatisnatural.

Location:____________________________Month:____________TransitionalProbabilities(from“Current”tabintheweathergenerator):

wet|dry________ wet|wet________

Remembertoenterthevalueshereaswellasintheappropriatecellsintheweathergeneratorbeforeyouclick“Calculate.”

Trial #wetdays #drydaysLongeststringofwet

daysLongeststringof

drydays1 2 3 4 5 6 7 8 9

10 11 12 13 14 15

Averages Representyourfindingsbycreatingtwohistograms:oneforlengthoflongestwetstringandoneforlengthoflongestdrystring.

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Lesson5:Homework

Consideringthefuture:Howcouldachangeinthewatercyclechangetheday-to-dayexistenceoftheorganismslistedbelow?Imagineyouareeachoftheorganisms.Basedonyourcurrentknowledgeleveloftheseorganisms,predicthowachangeinthewatercyclemightaffecteach.Startbyidentifyingthechiefmannerinwhichyoubelievetheorganismuseswaterandthenidentifywhatmighthappentotheorganismifthequantityofwatereitherincreasedordecreased.Remember:thereislessavailablewaterandsomeareaswillgetwetterwhilesomewillgetdrier.Itispossiblethatsomeorganismswillbenefitfromthis!

1. Arivertrout.

2. Acoralreeffish.

3. Atreeintherainforest.

4. Acactusinthedesert.

5. Acottonfarmer.

6. Acattlerancher.

7. Amigratorybird.

8. Amosquito.

9. Apersonlivinginyourhometownwhoworksindoors.

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Lesson6:PredictingtheFuture

Summary: Students use theweather generator again to predictwhat the future holds. Using outputfromNCARmodelstoseedtheirownweathergeneratormodels,studentsexaminedataandwork to determine how future weather patternsmight be different from current patterns.Finally, themodule endswith students acknowledging themerits and limitations ofmodel-building.

Objective1:RuntheweathergeneratorwithfuturetransitionprobabilitiesfromNCAR.SummarizethedatausingtechniquesdevelopedinLesson5.Untilnow,wehaveonlyexploredtheimplicationsoftransitionprobabilitiesfromthepast.Inessence,scientistshavetakentheactualstringsofdryandwetdaysfromthepastandproducedthetransitionprobabilities based on the actualweather.Wewill now use theweather generator forwhat climatescientistsmoreoftenareinterestedin:predictingthefuture.In the Excel file, the “Future” tab on the weather generator provides another set of transitionprobabilities. This time, though, rather thanusinghistorical dataofwet anddrydays, scientists haveusedapredictiveclimatemodeltodeterminewhatthefuturetransitionprobabilitieswillbebasedoncurrent trends. Scientists continue to collect data every day, and asmore data is collected, updatedinformation becomes available. What we are interested in is using these transition probabilities topredicthowtheoverallweatherpatternswillshiftinthefuture.Today’swork issimilar toyesterday’swork,exceptnowweareusingthetransitionprobabilities fromthe“Future”tabratherthanthe“Current”tab.Thereisobviouslyuncertaintywithpredictingthefuture.JustasinLesson2,welearnedhowrealityisdifferentfrompredictedprobability.(Remember,ifIrolladiesixtimes,I’mnotguaranteedtogeteachnumberonetime.)Whiletheweathergeneratorispredictiveoftheclimatewemayexperienceinthefuture,wedon’texpectthatanymonthwillactuallyhaveaseriesofwet/drydaysexactlylikewhatwearepredicting.The whole class will work on one location, with each student being assigned onemonth—the samemonththeyworkedontheperiodbefore.Thistime,collectdatafor30years.Wewanttocollectmoredata to predict the future thanwhenwewere looking at the past becausemore data leads tomoreaccuratepredictions.

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Location:____________________________Month____________TransitionalProbabilities(from“Future”tabintheweathergenerator):

wet|dry________ wet|wet________

Remembertoenterthevalueshereaswellasintheappropriatecellsintheweathergeneratorbeforeyouclick“Calculate.”

Trial#wetdays

#drydays

Longeststringofwetdays

Longeststringofdrydays

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Averages

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Representyourfindingsbycreatingtwohistograms:oneforlengthoflongestwetstringandoneforlengthoflongestdrystring.

Objective2:Compareandcontrastthefuturedatawithpastdata.Nowcomparethehistogramsfromthe“current”data(fromLesson5:Classwork)withthosefromthe“future”datayoujustcreated.Whatarethedifferencesandsimilarities?Arethehistogramscenteredonthesameplace?Whatdoesthisindicateaboutthefuture?Thismodule’sdrivingquestionis:“Globaltemperaturesarerising.Whatdoesthismeanaboutprecipitation?”Whatthoughtsdoyouhaveonthisquestionnowthatyouhavecompletedthemodule?Ifyourteacherhadyourecordaresponsetothisquestionatthebeginningofthemodule,gobackandreadyouroriginalresponse.Howhasyourunderstandingofthisquestionchanged?

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Objective3:Connectthisdatatoourdailylives.Iftheweatherpatternschangeforthelocationtheclassinvestigated,whatarethepossiblerepercussions?Lookatthedata:Iseachmonthgoingtobewetter,bedrier,orhavenochange?Thinkseasonally:Willeachseasonbewetterordrier?Whataretheimplicationsofthis?Example:InDenver,weexperiencethemajorityofourmoistureintheformofsnowthatfallsinthelatewinterandspring.Thissnowpackthenmeltsthroughthelatespring,summer,andfallmonthsandprovidesthesurroundingareaswithwater.Iftheweatherpatternschangedsuchthatwinterandspringbecamedrier,wewouldbefacedwithalackofwatertofillourreservoirs.Thiswouldresultinareductioninavailablewaterfordrinkingandirrigation,andalossofrecreationalareas,sinceweusethereservoirsforboating,fishing,andaquaticrecreation.Whataretheimplicationsofthechangeinweatherpatternsforthelocationyouinvestigated?Objective4:Discusstheusefulnessandlimitationsofmodel-building.Whatarethebenefitsofusingmodel-buildingtoanswerdifficultquestions?Whatarethelimitationsofusingmodel-buildingtoanswerdifficultquestions?

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GlossaryCondensation—Theconversionofgastoliquid;inthecaseofwater,thegasiswatervapor.Conditionalprobability—Theprobabilityofaneventgiventhatanothereventhasalreadyoccurred.Evaporation—Theconversionofliquidtogas.Histogram—Agraphicaldisplayofdata.Dataistypicallygroupedinto“bins,”orranges,andthenplotted

asverticalbars.Mean—syn.Average.Thesumofthevaluesofasetdividedbythenumber.Median—Themiddlevalueinaseriesofvalues.Mode—Thevaluethatoccursmostfrequentlyinaparticulardataset.Molecule—Agroupofatomsbondedtogether.NCAR—NationalCenterforAtmosphericResearch.Persistence—Whendataoccursinawaysuchthateachdatapointisnotindependentoftheprevious

one.Rather,eachdatapointissomewhat,thoughnotentirely,dependentonthepreviousdatapoint.

Precipitation—Rain,snow,sleet,orhailthatfallsfromthesky.Salinity—Thedissolvedsaltcontentofwater.Simpleprobability—Thechance,orlikelihood,ofaparticulareventoccurring.Sustainability—Theenduranceofsystemsorprocesses.Transitionprobability—Theprobabilityofgoingfromagivenstatetothenext,oralternate,state.Transpiration—Theprocessofwaterbeingabsorbedbyaplant’sroots,movingupwardthroughthe

shoots,andevaporatingaswatervaporfromtheleaves.Weathergenerator—Statisticalmodelthataimstopredictparticularaspectsoffutureweather

conditions.

Weather Module SE - COMAP

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