2021年高中数模美赛B题中文及解法思路
解法思路：
1)用多元回归模型求出米德湖流入、流出和损失的因素。讨论这些因素之间的关系及其对米德湖水量和水位的相对影响。
问题B：应对干旱
背景,米德湖（LakeMead）是位于内华达州-亚利桑那州边界的科罗拉多河水库，是美国最大的水库（图1）。2021夏天，米德湖达到了自20世纪30年代首次蓄水以来的最低水位。气候变化引发的干旱，加上米德湖服务的2500万人口对水的需求不断增加，使得这座水库的蓄水量减少到了其全部容量的36%左右。20218月16日，垦务局宣布科罗拉多河首次出现缺水情况[1]。最初，这一一级缺水宣言导致亚利桑那州、内华达州和新墨西哥州的供水量减少，农业社区最先感受到削减。
图1：米德湖概况（国家公园管理局[2]）
随着世界各地的干旱不断加剧，研究人员继续开发更有效地回收水的方法。一种方法是回收流动的废水.我们的水槽、厕所和淋浴间。你可能认为这是不可能的（也许恶心），但这项技术已经存在并正在改进。在最大电流下在这种情况下，这些废水在排放到当地水道之前要经过几个处理过程。图2显示了水源和使用应用的示例。处理设施使用各种技术来满足适用规范。这些规范是从特定水源取水、处理水以使其达到特定目的所需的质量水平，然后使其可用于该目的所必需的要求。一些用途包括农业灌溉、生活用水供应（包括饮用水）、工业和商业用途以及补充地下水。
图2.再生水的水源和使用应用示例（环境保护局）
要求
您的团队决定使用米德湖调查和了解干旱对水库的影响，并考虑将废水循环利用作为解决水资源短缺的方法。在您开始调查时，我们提供以下信息：
米德湖的水位是以平均海平面以上英尺为单位的水面高度来衡量的。
米德湖的面积以英亩为单位。
米德湖的水量以英亩-英尺为单位。
表1显示了2010年垦务局计算的米德湖高程、面积和体积之间的关系[4]。
海拔（英尺）湖泊面积（英亩）湖泊体积（英亩-英尺）
1229.0159,86629,686,054
1219.6152,82828,229,730
1050.073,61510,217,399
895.030,0842,576,395
表1.米德湖的面积和体积（按海拔高度）
1.米德湖容量。米德湖的水量是流入、流出和损失的函数。科罗拉多河为超过96%的流入量提供了来自其他三条支流的额外水，以及湖面上的直接降水。流出是通过释放水（例如，通过水坝）和直接从湖泊中消耗而发生的。损失通过蒸发发生。确定并描述影响米德湖流入、流出和损失的因素。讨论这些因素之间的关系及其对米德湖水量和水位的相对影响。
b、米德湖的形状非常不规则，整个湖的深度也各不相同。考虑如何验证表1中所示的高程、面积和体积关系。描述您需要的信息和数据，并讨论如何使用数学计算这些测量值。注：您无需获取这些数据或计算度量值。
2.米德湖水位。这两个问题数据文件提供了有关米德湖水位的信息，这些信息由平均海平面以上的英尺高度给出。
b、根据一年的变化，开发两个米德湖水位模型。使用每个模型预测2025年、2030年和2050年米德湖的水位。比较并评估两个模型及其预测。
模型1：仅考虑最近干旱期的数据，并假设最近干旱期模式持续。
模型2：使用2005-2020年的水位数据，并假设这一时期的模式
2021HIMCM
ProblemB:TacklingtheDrought
Background
LakeMead,aColoradoRiverreservoirontheNevada-Arizonaborder,isthelargestwaterreservoirintheUnitedStates(Figure1).Inthesummerof2021,LakeMeadregistereditslowestlevelonrecordsinceitsinitialfillinginthe1930s.Drought,fueledbyclimatechange,alongwithincreasingdemandforwaterbythe25millionpeopleLakeMeadserves,hasshrunkthisreservoirtoapproximately36percentofitsfullcapacity.OnAugust16,2021,theBureauofReclamationannouncedthefirst-everwatershortagedeclarationontheColoradoRiver[1].Initially,thisTier1watershortagedeclarationresultsinreducedwaterdeliveriestothestatesofArizona,Nevada,andNewMexicowithagriculturalcommunitiesbeingthefirsttofeelthecuts.
Figure1:LakeMeadOverview(NationalParkService[2])
Asdroughtsaroundtheworldhavebeenincreasing,researcherscontinuetodevelopmeanstorecyclewatermoreefficientlyandeffectively.Onemethodistorecyclewastewaterthatflows
outofoursinks,toilets,andshowers.Youmaythinkthisisimpossible(andperhaps
disgusting),butthistechnologyalreadyexistsandisimproving.Undermostcurrent
circumstances,thiswastewatergoesthroughseveraltreatmentprocessespriortobeingreleasedintolocalwaterways.Figure2showsexamplesofwatersourcesanduseapplications.Atreatmentfacilityusesvarioustechniquestomeetfit-for-purposespecifications.Thesespecificationsaretherequirementsnecessarytobringwaterinfromaparticularsource,treatittogetittothequalitylevelneededforaparticularpurpose,andthenmakeitavailableforthatpurpose.Somepurposesincludeagriculturalirrigation,domesticwatersupply(toincludedrinkingwater),industrialandcommercialuse,andrecharginggroundwater.
Figure2.Examplesofwatersourcesanduseapplicationforrecycledwater(EnvironmentalProtectionAgency)
Requirements
YourteamdecidestouseLakeMeadtoinvestigateandlearnmoreaboutdroughtimpactonwaterreservoirs,andtoconsidertherecyclingofwastewaterasasolutiontowatershortages.Asyoubeginyourinvestigation,weprovidethefollowinginformation:
·ThelevelofLakeMeadismeasuredbyelevationofthewatersurfaceinfeetabovemeansealevel.
·TheareaofLakeMeadismeasuredinacres.
·ThevolumeofwaterinLakeMeadismeasuredinacre-feet.
Table1showstherelationshipofelevation,area,andvolumeofLakeMeadascalculatedbytheBureauofReclamationin2010[4].
Elevation(feet)AreaofLake(acres)VolumeofLake(acre-feet)
Table1.AreaandVolumeofLakeMeadbyElevationLevel
1.LakeMeadVolume.TheamountofwaterinLakeMeadisafunctionofinflow,outflow,andloss.TheColoradoRiverprovidesover96%oftheinflowwithadditionalwatercomingfromthreeothertributaries,aswellasdirectprecipitationonthelakesurface.Outflowoccursthroughreleasingwater(forexample,throughadam)andconsumptiondirectlyfromthelake.Lossoccursthroughevaporation.
info@comap.com|a.Identifyanddescribefactorsthatimpactinflow,outflow,andlossinLakeMead.DiscusstherelationshipofthesefactorsandtheirrelativeinfluencesonthevolumeandwaterlevelofLakeMead.
b.LakeMeadhasaveryirregularshapeandvaryingdepthsthroughout.Considerhowyouwouldverifytheelevation,area,andvolumerelationshipsshowninTable1.Describewhatinformationanddatayouwouldneedanddiscusshowyouwouldusemathematicstocalculatethesemeasures.Note:YouareNOTrequiredtoobtainthesedataorcalculatethemeasures.
2.LakeMeadWaterLevel.ThetwoproblemdatafilesprovideinformationaboutLakeMeadwaterlevelsgivenbyelevationinfeetabovemeansealevel.
a.Considerthedataprovided.BrieflydiscussoverallpatternsinthehistoricaldataforLakeMeadwaterlevels.Defineyourcriteriafordroughtperiodsandidentifythebeginningsandendsofperiodsofdrought.Commentonhowthemostrecentdroughtperiodcomparestoearlierones.
b.DeveloptwomodelsforthewaterlevelinLakeMeadasafunctionoftheyear.UseeachmodeltopredictthewaterlevelinLakeMeadintheyears2025,2030,and2050.Compareandevaluateyourtwomodelsandtheirpredictions.
·Model1:Considerdatafromonlythemostrecentdroughtperiodandassumethemostrecentdroughtperiod’spatterncontinues.
·Model2:Usewaterleveldatafrom2005-2020andassumethisperiod’spattern
continues.
3.BasedonyourmodelsandwaterlevelpredictionsinPart2,addresstheimpactonfuturewaterusagedemandsandconsideriftherecyclingofwastewatercouldmakeupallorapartofanyfutureshortfalls.
a.Identifyanddescribethefactorsyouwouldincludeinaplantorecyclewastewater.
Considerthedecisionslocalleaderswouldneedtomakeandtheprioritiestheymightsetthatwouldimpactyourplan.
b.Describeyourplanandhowyouwouldmeasuretheimpactofimplementingyourplan.
4.Writeaone-pagenon-technicalnewsarticlereportingthekeytakeawaysandrecommendationsfromyourinvestigation.
YourPDFsolutionofnomorethan25totalpagesshouldinclude:
·One-pageSummarySheet.
·TableofContents.
·Yourcompletesolution.
·One-pageArticle.
·Referenceslist.
Note:TheHiMCMContestnowhasa25-pagelimit.Allaspectsofyoursubmissioncounttowardthe25pagelimit(SummarySheet,TableofContents,ReferenceList,andanyAppendices).
info@comap.com|Attachments
AttachmentA:2021_HiMCM_LakeMead_MonthlyElevationData.xlsx
ElevationofwateratLakeMead(infeetabovesealevel)attheendofeachmonthbyyearfrom1935to2021.BureauofReclamationdatafoundat
AttachmentB:2021_HiMCM_LakeMead_LowHighElevationData.xlsx
Glossary
BureauofReclamation:agovernmentagencythatmanages,develops,andprotectswaterandrelatedresourcesintheseventeenwesternstatesoftheUnitesStates.
Elevation:ameasureofheightindicatedbythenumberoffeetabovemeansealevel.
FitForPurposeSpecifications:adescriptionofconstructiondesignthatindicatesthefacility(inthiscaseaparticulartypeofwatertreatmentfacility)meetstherequirementsforitsspecificintendeduse.
Inflow:thewaterenteringabodyofwater.
MeanSeaLevel:anaveragelevelofthesurfaceoftheseausedasareferenceorbaseleveltomeasureheightordepthonEarth.
Outflow:thewaterleavingabodyofwater.
Wastewater:thepollutedformofwaterthatcomesfromhomes,businesses,industrialprocesses,orrainwaterrunoff.Wastewaterincludeswaterfromhouseholdusessuchasshowering,dishwashing,laundryand,ofcourse,flushingthetoilet.
References
release/3950.
[2]NationalParkService.“OverviewofLakeMead.”UpdatedSeptember2,2020.Foundat
[3]UnitedStatesEnvironmentalProtectionAgency.“BasicInformationaboutWaterReuse.”
reuse.
[4]NationalParkService.“StorageCapacityofLakeMead.”UpdatedAugust5,2019.Foundat