外国数学建模一篇.docx

1、外国数学建模一篇The Interdisciplinary Contest in Modeling 2001 Problem Copyright COMAP 2001Please note that while links are indicated the data is provided on the pages following theproblem.2001 Interdisciplinary Contest in ModelingICM 2001 ProblemZebra mussels, Dreissena polymorpha, are small, fingernail-si

2、zed,freshwater mollusks unintentionally introduced to North America viaballast water from a transoceanic vessel. Since their introduction in themid 1980s, they have spread through all of the Great Lakes and to anincreasing number of inland waterways in the United States and Canada.Zebra mussels colo

3、nize on various surfaces, such as docks, boat hulls,commercial fishing nets, water intake pipes and valves, native mollusksand other zebra mussels. Their only known predators, some diving ducks,freshwater drum, carp, and sturgeon, are not numerous enough to have asignificant effect on them. Zebra mu

4、ssels have significantly impacted theGreat Lakes ecosystem and economy. Many communities are trying tocontrol or eliminate these aquatic pests. SOURCE: Great Lakes Sea GrantNetwork http:/www.sgnis.org/.Researchers are attempting to identify the environmental variablesrelated to the zebra mussel infe

5、station in North American waterways.The relevant factors that may limit or prevent the spread of the zebramussel are uncertain. You will have access to some reference data toi l d li ti f l h i l d b t i th t tOur Waterways - An Uncertain FutureThe Interdisciplinary Contest in Modeling 2001 ProblemC

6、opyright COMAP 2001include listings of several chemicals and substances in the water systemthat may affect the spread of the zebra mussel throughout waterways.Additionally, you can assume individual zebra mussels grow at a rate of15 millimeters per year with a life span between 4 - 6 years. The typi

7、calmussel can filter 1 liter of water each day.Requirement A : Discuss environmental factors that could influence thespread of zebra mussels.Requirement B : Utilizing the chemical data provided at:ap/undergraduate/contests/icm/imagesdata/LakeAChem1.xls,and the mussel population data provided at:ap/u

8、ndergraduate/contests/icm/imagesdata/LakeAPopulation1.xlsmodel the population growth of zebra mussels in Lake A. Be sure toreview the Information about the collection of the zebra mussel data.Requirement C : Utilizing additional data on Lake A from another scientistprovided at:ap/undergraduate/conte

9、sts/icm/imagesdata/LakeAChem2.xlsand additional mussel population data provided at:ap/undergraduate/contests/icm/imagesdata/LakeAPopulation2.xls corroborate the reasonableness of your model from Requirement B. As aresult of this additional data, adjust your earlier model. Analyze theperformance of y

10、our model. Discuss the sensitivity of your model.Requirement D : Utilizing the Chemical data from two lakes (Lake B andLake C) in the United States provided atap/undergraduate/contests/icm/imagesdata/LakeB.xlsandap/undergraduate/contests/icm/imagesdata/LakeC.xlsdetermine if these lakes are vulnerabl

11、e to the spread of zebra mussels.Discuss your prediction.Requirement E: The community in the vicinity of Lake B (in requirementD) is considering specific policies for the de-icing of roadways near thelake during the winter season. Provide guidance to the local governmentofficials regarding a policy

12、on .de-icing agents. In your guidance includepredictions on the long-term impact of de-icing on the zebra musselpopulation.The Interdisciplinary Contest in Modeling 2001 ProblemCopyright COMAP 2001p pRequirement F: It has been recommended by a local community in theUnited States to introduce round g

13、oby fish. Zebra mussels are not ofteneaten by native fish species so they represent a dead end ecologically.However, round gobies greater than 100 mm feed almost exclusively onzebra mussels. Ironically, because of habitat destruction, the goby isendangered in its native habitat of the Black and Casp

14、ian Seas in Russia.In addition to your technical report, include a carefully crafted report (3-page maximum) written explicitly for the local community leaders thatresponds to their recommendation to introduce the round goby. Alsosuggest ways to help reduce the growth of the mussel within and amongw

15、aterways.Information about the collection of the zebra mussel dataThe developmental state of the Zebra mussel is categorized by three stages:veligers (larvae), settling juveniles, and adults. Veligers (microscopic zebra mussellarvae) are free-swimming, suspended in the water for one to three weeks,

16、afterwhich they begin searching for a hard surface to attach to and begin their adult life.Looking for zebra mussel veligers is difficult because they are not easily visible bythe naked eye. Settled juvenile zebra mussels can be felt on smooth surfaces likeboats and motors. An advanced zebra mussel

17、infestation can cover a surface, evenforming thick mats sometimes reaching very high densities. The density of juvenileswas determined along the lake using three 15X15 cm settling plates. The top plateremained in the water for the entire sampling season (S - seasonal) to estimateseasonal accumulatio

18、n. The middle and bottom plates are collected after specificperiods (A . alternating ) of time denoted by .Lake Days. in the data files.The settling plates are placed under the microscope and all juveniles on the undersides of the plate are counted and densities are reported as juveniles/m 2.The Int

19、erdisciplinary Contest in Modeling 2001 ProblemBelow is chemical data that was collected between 1992 and 1999 on Lake A at 10 different sites. The sites range from southern locations (site 1) to northern locations (site 10). The zebra mussel was first introduced in the southern portion of the lake.

20、 Lake Location Test Minimum Value25th PercentilePopulation Median75th PercentileMaximum Value1 Alk 63.8 81.6 86.8 91.9 104.51 Ca 23.2 24.8 26.8 27.2 27.51 Chl-a 0.69 4.13 6.27 9.45 15.551 Cl 9.3 13.1 15.3 17.9 271 Fe 301 381 501 595 9631 K 1 1.2 1.2 1.3 2.31 Mg 5.1 5.7 6.6 6.7 6.71 Na 6.8 9.4 11.4 1

21、2.6 12.91 pH 6.58 7.54 7.68 7.83 8.581 Secchi 0.2 0.6 0.9 1.1 1.81 Temp 8.5 16.1 20.2 21.7 24.2Lake Location Test Minimum Value25th PercentilePopulation Median75th PercentileMaximum Value2 Alk 51.7 66.3 72.4 76.3 88.92 Ca 18 21.6 22.3 22.7 23.22 Chl-a 1.41 3.84 5.52 7.62 22.942 Cl 9.6 13.2 14.9 18.2

22、 31.82 Fe 50 83 143 539 7092 K 1.3 1.4 1.5 1.5 22 Mg 4.5 5.1 5.2 5.4 6.22 Na 9.3 10.6 13.4 15.6 20.62 pH 6.83 7.79 8 8.25 8.68ChlorideIronPotassiumMagnesiumLake TestAlkalinityCalciumChlorophyllMgpHSecchi Disk TranparencyTemperatureSodium mg/LTempAbbreviationAlkCaChl-aClFeKNamg/Lug/Lmg/Lmg/LUNITSmg/L

23、 as CaCO3mg/Lug/LpHmetersoCSecchipHBelow you find zebra mussel population data that was collected at 10 different sites on Lake A. The sites range from southern locations (site 1) to northern locations (site 10). The zebra mussel was first introduced in the southern portion of the Lake A.See File: C

24、ollection for information on collectioning zebra mussel dataLake Test Abbreviation UnitsType of Plate QA A - AlternatingS - SeasonalDays in the Water Lake Days DaysDensity of juveniles Density juveniles/m2Lake Location Date QA Lake Days Density1 7/12/1994 A 31 1331 7/18/1994 A 37 01 9/2/1994 A 46 13

25、31 9/21/1994 A 65 1331 11/2/1994 A 82 5781 11/2/1994 S 154 2,0891 7/12/1995 A 28 2221 7/25/1995 A 13 1781 8/22/1995 A 28 3,3781 9/12/1995 A 21 694,0001 10/18/1995 S 98 498,0001 10/18/1995 S 98 354,0001 10/18/1995 A 36 604,0001 6/24/1996 A 19 01 9/3/1996 A 14 116,0001 9/17/1996 A 28 440,0001 9/30/199

26、6 A 27 22,9781 11/4/1996 A 48 2,3111 11/4/1996 A 35 4,4001 11/4/1996 S 105 386,0001 6/4/1997 A 30 01 6/18/1997 A 27 80,0001 7/2/1997 A 28 42,0001 7/17/1997 A 29 2,6221 8/1/1997 A 30 1,7781 8/18/1997 A 32 52,0001 9/4/1997 A 34 398,0001 9/19/1997 A 32 318,0001 10/8/1997 S 156 146,4891 10/8/1997 A 34 4

27、6,0001 10/8/1997 A 19 11,2001 5/29/1998 A 30 4,2671 6/17/1998 A 34 10,8891 7/7/1998 A 39 5,6001 7/20/1998 A 33 23,4671 8/3/1998 A 27 13,3781 8/20/1998 A 31 80,000Lake A Chem 2 -This chemical data on Lake A was provided by another researcherLake Location Date Stratum T DP Ca Mg TN Temp Chl-a1 5/13/19

28、92 U 0.03 0.01 0.581 5/26/1992 U 0.05 0.02 0.70 15.801 6/11/1992 U 0.05 0.02 0.69 21.30 10.181 6/23/1992 U 0.06 0.02 0.51 20.00 4.691 7/15/1992 U 0.06 0.01 0.73 21.901 7/28/1992 U 0.05 0.01 0.67 22.401 8/11/1992 U 0.05 0.01 0.73 22.501 8/25/1992 U 0.05 0.01 0.54 21.50 6.431 9/17/1992 U 0.06 0.02 0.5

29、7 20.40 7.501 10/6/1992 U 0.06 0.01 0.63 12.201 10/30/1992 U 0.06 0.02 0.571 5/4/1993 U 0.01 0.01 0.42 14.101 6/1/1993 U 0.04 0.01 0.39 17.301 6/8/1993 U 0.04 0.01 0.40 17.501 6/30/1993 U 0.05 0.01 0.491 7/14/1993 U 0.09 0.02 0.791 8/5/1993 U 0.08 0.01 0.571 8/13/1993 U 0.06 0.01 0.361 8/19/1993 U 0

30、.05 0.01 0.481 8/26/1993 U 0.06 0.011 9/2/1993 U 0.08 0.01 0.44 23.501 9/22/1993 U 0.07 0.01 0.54 16.101 10/6/1993 U 0.05 0.01 0.45ug/Lmg/Lug/Lmg/LoCUNITSSamples are obtained from both the Epilimnion (E), (the topmost and warmest layer of water), and the Hypolimnion (H) (the cold deep water layer) a

31、nd Unstratified (U).mg/Lmg/LChlorophyllAbbreviationU / E / HTPDPTNTempChl-aCaMgCalciumMagnesiumTotal NitrogenTemperatureLake TestStratumTotal Phosphorus Dissolved Phosphorus Lake A Population 2-New Researcher Information Below you find zebra mussel population data that was collected at 10 different sites on Lake A. The sites range from southern locations