11/2/16
1
Dynamic Meteorology 2016 (Exercise session 8)
([email protected]) (http://www.phys.uu.nl/~nvdelden/dynmeteorology.htm)
Topics
Evaluation of the weather forecast of 30 October 2016 by “4-cast”
Introduction to project 2 (couples; hypothesis due next 18 Nov.)
Weather discussion by Michiel Baatsen
Exercises from lecture 7, in particular problem 1.18
DynamicMeteorology(Project2)
(h9p://www.staff.science.uu.nl/~delde102/dynmeteorology.htm)
Introduction to project 2 (problem 1.24, p. 152) Principal component analysis (Box 1.11)
Forinspira*on:readsec*ons1.26-1.29
11/2/16
2
IntroducEontotheproject
FormulateahypothesisabouttheconnecEon(correlaEon)betweenthree(ormore)differentatmospheric(oroceanic)variables(aso-calledateleconnec*on)
ExampleofateleconnecEon:(1) RelaEonbetweenwintertemperatureinWesternEurope,wintertemperature
inEasternCanadaandsea-levelpressuredifferencebetweenIcelandandtheAzores(box1.11)
(2) RelaEonbetweensealevelpressureinDarwinandsealevelpressureinTahiE(nextslide)
SendmeyourhypothesisbeforeoronFriday18November2016.
Collectdata(fromtheinternet)ofthesevariables.InvesEgatethisconnecEonwithastaEsEcalanalysistechniquecalledprincipalcomponentanalysis(box1.11).
Evaluateanddiscusstheresultsinanoralpresenta:onofabout15minutesonWednesday18January2016.
(Incouples)
TropicalteleconnecEon
J.Bjerknes,1969:AtmosphericTeleconnecEonsfromtheequatorialPacific.MonthlyWeatherReview,97,163-172.
11/2/16
3
FigurefromWallaceandGutzler,1981:Mon.Wea.Rev.,109,784
“BeltsofAcEon”
“Teleconnec*on”betweenArcEcandlowermiddlelaEtudes
NorthernhemisphereteleconnecEonOne-pointcorrelaEonmapforthenorthernhemisphere
Cross-correlaEonmatrixsealevelpressure
FIGURE1.58.CorrelaEonbetweenzonal-meanandmonthlymeansealevelpressureanomaliesinthenorthernhemisphere(1958-2000).Thecontourintervalis0.3forposiEvevaluesand0.15fornegaEvevalues.NegaEvevalueslowerthan-0.3areshaded.Notethatthemapissymmetricaboutthediagonal,asexpected.Source:J.LiandJ.X.L.Wang,2003:Amodifiedzonalindexanditsphysicalsense.Geophys.Res.LeM.,30,1632.
DefiniEonoftheNAM-indexisbasedonthecross-correlaEonmatrixofmonthlymean(mm)zonalmean(zm)valuesofsealevelpressure(slp)inthenorthernhemisphere.HighestcorrelaEonisfoundformm,zmslp-valuesat65°Nand35°N(forDJF)
NorthernAnnularMode(NAM)
GraphicalrepresentaEonofcross-correlaEonmatrix
65°N
35°N
11/2/16
4
Averageseasonalcycleofzonalmeanmonthlymeansea-levelpressure
FIGURE1.54.Annualmarchofthezonalmeanandmonthlymeansealevelpressureat36°Nandat66°N,averagedovertheyears1979-2012.BasedonERA-Interimreanalysis(h9p://data-portal.ecmwf.int/data/d/interim_moda/).
Zonalmean,monthlymeansealevelpressureanomaliesat66°Nand36°NinDecember–March(phase2)1979-2012(136months)
ERA-Interim1979-2012
PosiEveanomaliesrepresenttheposiEvephaseoftheNorthernAnnularMode(NAM),whilenegaEveanomaliesrepresentthenegaEvephaseofNAM
11/2/16
5
NorthernAnnularModeIndex
FIGURE1.68.Plotofthemonthlymeannorthernhemispherezonalindex(theNAMindex)asfuncEonofEmefrom1873to2011.Source:h9p://ljp.lasg.ac.cn/dct/page/65544.
Definedasthenormalized(dividedbythestandarddeviaEon)differencebetween35°Nand65°Nofthezonalmeansealevelpressureanomalies.
LowpressureinArc9c
HighpressureinArc9c
LongtermvariaEonmayhavetodowithocean(AMO)(figure1.69)
ResearchquesEonInhowfarisincreaseofjanuarytemperatureduetoincreaseoftheNAM-index?
IncreaseoftemperatureinDeBiltmaybefullyexplainedbyenhancedgreenhouseeffect.
Box1.11
11/2/16
6
Hypothesis
Hypothesis:LowwintertemperaturesinCanadaareassociatedwithhighAnnularModeIndex(lowsea-levelpressureinArc*c)andhighwintertemperaturesinCanadaareassociatedwithlowAnnularModeIndex(highsea-levelpressureinArc*c)
Physicalinterpreta*on:WintertemperatureinWesternEuropeisrelatedtoaveragestrengthofwesterlywind
Averagestrengthofwesterlywindisdeterminedbythemeridionalgradientofsea-levelpressureovertheNorthAtlanEcOcean,i.e.bytheNorthernAnnularModeIndex
IfpressureisrelaEvelowovertheArcEcandNorthAtlanEc,westerlywindisstrong,temperaturesarerelaEvehighiswesternEuropeandrelaEvelowinEasternCanada.
Example:
Data
Collectdata:
TimeseriesofmonthlymeantemperatureinwinterinWesternEurope,inEasternCanadaandcorrespondingEmeseriesofmonthlymeanNAM-index
Example:
11/2/16
7
CorrelatethreeEmeseries:temperatureDeBilt,temperatureGooseandNAM-Index
w
Therefore,lowwintertemperaturesinGoose(Canada)areassociatedwithhighannularmodeindex(lowsea-levelpressureinArcEc),whilehighwintertemperaturesinCanadaareassociatedwithlowannularmodeindex(highsea-levelpressureinArcEc).AretemperaturesGooseandDeBiltreallyan*-correlated??
Goose(Canada)isatthesamelaEtudeasDeBilt
Jan.1950-2011Jan.1950-2011
CorrelatethreeEmeseriesExample:
TemperatureDeBiltisanEcorrelatedwithtemperatureGoose,butnotvery.
Goose(Canada)isatthesamelaEtudeasDeBilt
TheupwardtrendinNAM-indexshouldinduceanegaEvetrendintemperatureatGoose,whichisnotthecase
Jan.1950-2011Jan.1950-2011
11/2/16
8
PrincipalComponentAnalysis(PCA)maybringsomeclarity
Thisanalysis(redline)representsaPCAontwovariables
€
y = 0.48x + 2.1FirstPrincipalComponent(PC):
Explains57%ofthetotalvariance
HowdowedothisifwehavemorethantwoEmeseries?
€
M =
1.000 0.5669 −0.50360.5669 1.000 −0.3217−0.5036 −0.3217 1.000
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
NAM DeBilt Goose
DeBilt
Goose
NAM
Cross-correlaEonmatrix:
PrincipalComponentAnalysis(PCA)maybringsomeclarity
Thisanalysis(redline)representsaPCAontwovariables
€
y = 0.48x + 2.1FirstPrincipalComponent(PC):
Explains57%ofthetotalvariance
11/2/16
9
Eigenvaluesofcross-correlaEonmatrixExample:
€
! x 1 ≡ −0.630, −0.565, 0.533( )
€
! x 2 ≡ 0.077, 0.638, 0.766( )
€
! x 3 ≡ 0.773, −0.524, 0.358( )
λ1=1.935; λ2=0.682; λ3=0.383
First eigenvector explains 64.5% of total variance in data
NAM T,DeBilt T,Goose
64.5%
22.7% CO2??
Eigenvectors:
12.8%
NegaEveNAMiscorrelatedwithnegaEvetemperatureanomalyatDeBiltandposiEvetemperatureatGooose
Projectdataonfirsteigenvector(PC)Example:firstprincipalcomponent
€
! x 1 ≡ −0.630, −0.565, 0.533( ) 64.5%
NAM DeBilt Goose
11/2/16
10
Reanalysiswebsites:h9p://apps.ecmwf.int/datasets/h9p://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis2.htmlh9p://www.esrl.noaa.gov/psd/data/Emeseries/h9p://disc.sci.gsfc.nasa.gov/daac-bin/FTPSubset.pl
Data-sources
import numpy as Nimport netCDF4 as Simport matplotlib.pyplot as P
year_len = 36.0mon_len = 12.0
#open filea = S.Dataset("T2m-mm-52N05E.nc", mode='r') #ERA-Interim data: temperature at 2 m at 52N and 5E (one grid point)
#create arrayslat = a.variables["latitude"][:] lon = a.variables["longitude"][:] time = a.variables["time"][:]time = year_len * (time - N.min(time)) / ( N.max(time) - N.min(time))+1979
# T2mT2m = a.variables["t2m"][:,:,:]
y = T2m[:,0,0] # make one-dimensional array
P.plot(time, y)P.scatter(time, y, s=20, color='red', marker=u'o') P.axis([1979,2014,270.0,300.0]) # define axes P.xlabel('year') # label along x-axesP.ylabel('Temperature at 2 m [K]') # label along x-axesP.title('Monthly mean temperature at 52N, 0E') # Title at top of plotP.grid(True)P.show() # show plot on screen
Pythonscripttoreadandplotanetcdf-filewhichhasbeendownloadedfromh9p://apps.ecmwf.int/
Theresult:
NextFriday,4November2015,11:00-12:45BBG201
LectureontheuseofpressureorpotenEaltemperatureasaverEcalcoordinate(isobaricorisentropiccoordinates)
PotenEalvorEcityinisentropiccoordinates
IsentropicpotenEalvorEcitymixingby“planetarywaves”
Week45:examonFriday11November,9-12,roomBBG209.
TheexamisaboutsecEons1.1-1.22(exceptsecEon1.13),andalsoboxes1.1and1.2ofthelecturenotes(thepartthathasbeencoveredinthefirst7lectures).YoudonothavetoknowequaEonsbyheart,butitisofcoursegoodtobefamiliarwithequaEons,sothatyoucanrecognisethetermsandinterprettheequaEon.
11/2/16
11
PROBLEM 1.18 An approximate model of the horizontal distribution of velocity in a tropical cyclone (box 1.6) is the so-called "Rankine vortex". This is an axisymmetric circular vortex with an azimuthal velocity, vθ, which is a function of the radius, r (the distance from the centre of the vortex), as follows.
Here v0 is the maximum wind velocity and R is the radius of maximum wind velocity.
(a) Calculate and plot the relative vorticity as a function of r for a Rankine vortex with v0=40 m s-1 and R=40 km.
(b) Estimate the inertial period “inside” the radius of maximum wind.(c) Is the inertial stability in the core of hurricane Alicia large or small?
€
vθ =v0rR
for r ≤ R and vθ =v0Rr
for r > R