Washington WASHINGTON UNIVERSITY IN ST LOUIS [email protected] MSR Tutorial Group Exercises.
Exercises tutorial-7 (31-10-2018)
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Tutorial 7 - Dynamical Meteorology Exercises tutorial-7 (31-10-2018) Problems 1.20 (p. 144), 1.21 (p.157) and 1.22 (p.158) Results of the weather predicGon 28 October 2018 PresentaGon by team “Tempestas”
Transcript of Exercises tutorial-7 (31-10-2018)
Tutorial7-DynamicalMeteorology
Exercisestutorial-7(31-10-2018)Problems1.20(p.144),1.21(p.157)and1.22(p.158)
ResultsoftheweatherpredicGon28October2018PresentaGonbyteam“Tempestas”
PROBLEM1.20(p.144).Determiningthecross-isentropicmassfluxThecross-isentropicmassflux(figure1.60)isnotastandardproductofanyre-analysisdata-set.Itcanbedeterminedfromthepressureandvelocityattheearth’ssurfaceandonisentropicsurfaces.Isentropicvelocityandpressureisgivenonaregularlat-longrid(“plate-carrée”projecGon)atregularintervals(0,6,12,18UTC)onthefollowingstandardisentropes:265K,275K,285K,300K,315K,330K,350Kand370K.WhichequaGonismostsuitabletodeterminethecross-isentropicmassfluxfromthisdatasetandhowwouldyouproceedtoproducefigure1.60?
Figure1.60.Timemean,zonalmeancross-isentropicmassfluxinJanuary2007asafuncGonoflaGtudeandpotenGaltemperature.
PROBLEM1.21(p.157).AsimplerelaKonbetweenthemeridionalPotenKalVorKcitySubstancefluxandzonalmeanacceleraKonordeceleraKon.PotenGalvorGcitycanbeinterpretedasbeingthemixingraGoofasubstance,called“potenGalvorGcitysubstance”,PVS,whichisidenGcaltoabsolutevorGcity.ThelocalGmeratechangeofPVSisgovernedbyeq.1.236a,wherethefluxofPVSisdefinedineq.1.236b.#(a)Figure1.59indicatesthatthezonalmeanzonalwind,[u],at60°NishighlycorrelatedwiththeintegratedfluxofPVS,ΔPVS,acrossthe60°Nparallel.Why?(HINT:readBox1.12)(b)Assumethatdθ/dt=0andthatthezonalmeanvalueof[vσZ]at60°Nduringonedayhasavalueof5×10-5ms-2.Calculatetheassociatedchangeofthezonalmeanzonalvelocity,[u],at60°Nduringthisday,assumingadiabaGcandinviscid(fricGonless)condiGons?(RememberfromthefirstpartofthecoursethatvorGcity,averagedoverthearea,S,isequaltocirculaGonaroundSdividedbyareaenclosedbyS)(Theradiusoftheearthis6371km.).
FIGURE1.59:RunningdailymeanpolewardisentropicPVS-flux(upperpanel)(redlines),atθ=350Kandatφ=60°N,between1December2006and18February2007.ThethickredlinerepresentsthefluxduetothemeancirculaGon,whilethethinredlinerepresentstheeddyflux.TheblacklinerepresentstheGmeintegratednetfluxofPVS.Thebluelinerepresentsthezonalmeanzonalwind,[u],atφ=60°N. Figure1.59
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PROBLEM1.22(p.158).RelaKonbetweenisentropicmeridionalpressuregradientandthethermalwindInwhichway(deriveanequaGon)isthezonalmeanisentropicmeridionalpressuregradientrelatedtothezonalmeanzonalwindinanatmosphereinthermalwindbalance?DoesthisrelaGonexplainthelowerpanelsoffigure1.74?
Figure1.74(onlylowerpanels).Monthlymean,zonalmeanisentropicmeridionalpressuregradient(redshading;firstcontourcorrespondsto3×10-5Pam-1)andmonthlymean,zonalmeanzonalwindvelocity(bluecontoursat5m/sintervals;zerocontournotshown).
