Dr.DavidDiMarcoDr.RyanSavitz

NeumannUniversity

How a River’s Length and Discharge Relate to the

Precipitation in its Basin

Abstract

•  The authors wish to find out how a river’s length and basin’s precipitation relate to its discharge. This will be accomplished by dividing the discharge rate at its mouth by its length, generating the river’s discharge gain per kilometer (DGPK), essentially how rapidly the river gains flow as it progresses to its mouth.

AbstractCon;nued

•  Then the Pearson product-moment correlation coefficient (PCC) will be used to measure to what degree the DGPK correlates to the mean precipitation over the river basin over the 14 rivers studied in this paper. Since the correlation turns out to be significant, the corresponding regression line will be generated.

Data

•  Inthetablebelowriverlengthsarecitedfromthe2010WorldAlmanac.Theprecipita;onfiguresforallriversexcepttheMagdalena,Po,VolgaandYukonarefrom(Lakshmietal.,2018).Thevirginmeanannualdischarge(VMAD,thedischargebeforeanysubstan;alhumanmanipula;ons)dataarefromanar;cleinScienceMagazine(Nilsson,2005).

Data Ave. Monthly River Length(miles/kms) Precip.(mm) VMAD(m3/sec) Amazon 3,900/6,276 190.42 200,000 Colorado 1,450/2,334 24.54 550 Congo 2,720/4,377 124.61 41,000 Danube 1,770/2,849 77.26 6,450 Ganges 1,560/2,511 112.6 22,102 Magdalena 1,000/1,609 170.83* 7,500 Mekong 2,700/4,345 135.46 15,900 Mississippi 2,340/3,766 71.7 18,400 Murray 1,609/2,589 40.31 775 Nile 4,160/6,695 54.79 3,000 Po 405/652 100.0* 1,460 Volga 2,290/3,685 55.17** 8,050 Yangtze(Chang-Jiang) 3,450/5,552 86.92 29,460 Yukon 1,979/3,185 40.22*** 6,370 * Institute for Technology and Resources Management in the Tropics and Subtropics (See reference list) ** The Volga River Basin Report (See reference list) *** U.S. Geological Survey, Water-Resources Investigations Report 99-4204 (See reference list)

Table 1: River Data

LiteratureReview

•  Changesinriverdischargecanhavegreatprac;calimpacts.Theseimpactsincludetherela;velyobviouspossibilityoffloodingwithintheriver’sproximity.Inaddi;ontoimpactssuchasthese,morecompleximpactsexist.Inpar;cular,Nohara,Kito,Hosaka,andOki(2006)notethatchangesinriverdischargecanaffectthermohalinecircula;on,which,inturn,canhaveglobalclima;cimpacts.

LiteratureCont.

•  Giventheseimportantimpacts,developingamodelofchangesinriverdischargeduetochangesintheclimatewouldbeofgreatvalueand,indeed,workhasbeendoneinthisarea.Mostofthesemodels,however,arebasedoncomplexcoupledatmosphere-oceangeneralcircula;onmodels,andareuniquetopar;cularregionsoftheglobe(Noharaetal.2006).

LiteratureCont.

•  Itisthegoalofthispapertopresentaparsimoniousandeasytounderstandmodelthatcanbeusedtohelppredictriverdischargeatanyloca;on.

•  Foreachriver,wewillcalculatethequan;tyVMAD/length,andcallthisquan;tythedischargegainperkilometer(DGPK).

DataRiver DGPK Amazon 31.867 Colorado 0.236 Congo 9.367 Danube 2.264 Ganges 8.802 Magdalena 4.661 Mekong 3.659 Mississippi 4.886 Murray 0.299 Nile 0.448 Po 2.239 Volga 2.185 Yangtze(Chang-Jiang) 5.306 Yukon 2.000

Table 2: River DGPK

Analysis

•  Wewillnowinves;gatehowcloselytheDGPKcorrelateswithprecipita;onusingthePearsonproduct-momentcorrela;oncoefficient(PCC).Lengthwillbeinkms,VMADinm3/secandprecipita;oninmms.Andtheresul;ngPCCis0.720.WealsonotetheT-testis3.5958witha1-sidedp-valueof0.00734.Theseresultsarefromtheonlinecalculatorat(WessaP.,2017).

Analysis

•  Thisprovidesconvincingevidencethatasta;s;callysignificantposi;verela;onshipexistsbetweenDGPKandbasinprecipita;on.Thisresultisintui;ve,inthatitshowsthatthereisasignificantandposi;verela;onshipbetweenariver’sdischargeandtheamountofprecipita;onovertheriver’sbasin.

Analysis

Analysis

•  Theini;alregressionrunwasusedtopredictdischargegainasafunc;onofprecipita;on.Thisregression,however,appearedtoresultinerrorsthatwerenotnormallydistributed,andanon-constanterrorvariance(heteroskedas;city).Thiswasmostlikelyduetothecurvatureofthedata,aswellastheskewnessofthedatasetsthemselves.

Analysis

•  Hencethenaturallogarithm(ln)ofeachvariablewastaken,andanewregression,withln(precipita;on)usedtopredictln(dischargegain)wasperformed.Thisregressionwasfoundtocloselysa;sfytherequirementsofhavingaconstanterrorvarianceandnormallydistributederrors.

Analysis

•  Equa%on1:DGPK=0.00055*P1.94,whereDGPKisdischargeandPisprecipita;onoverthebasin.Unlikeothercurrentlyusedandcomplexmodels,thisequa;onprovidesaneasytouseandunderstandmodelthatcanquicklyes;matethedischargeofariver.

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Golosov, V., and Belyaev, V. The Volga River Basin Report. UNESCO International Sediment Initiative, http://isi.irtces.org/isi/rootfiles/2017/07/04/1496391629451299-1498713525725099.pdf Retrieved 29 May 2019. Institute for Technology and Resources Management in the Tropics and Subtropics, http://www.basin-info.net/ Retrieved 5/29/19. Kriauciuniene, J., Meilutyte-Barauskiene, D., Reihan, A., Koltsova, T., Lizuma, L., & Sarauskiene, D. (2012). Variability in temperature, precipitation and river discharge in the Baltic States.

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