Three-dimensional visualization of ensemble weather forecasts

23 Pages·2015·17.53 MB·English

Geosci.ModelDev.,8,2355–2377,2015
www.geosci-model-dev.net/8/2355/2015/
doi:10.5194/gmd-8-2355-2015
©Author(s)2015.CCAttribution3.0License.
Three-dimensional visualization of ensemble weather forecasts –
Part 2: Forecasting warm conveyor belt situations for aircraft-based
field campaigns
M.Rautenhaus1,C.M.Grams2,A.Schäfler3,andR.Westermann1
1ComputerGraphics&VisualizationGroup,TechnischeUniversitätMünchen,Garching,Germany
2InstituteforAtmosphericandClimateScience,ETHZürich,Zurich,Switzerland
3DeutschesZentrumfürLuft-undRaumfahrt,InstitutfürPhysikderAtmosphäre,Oberpfaffenhofen,Germany
Correspondenceto:M.Rautenhaus([email protected])
Received:4February2015–PublishedinGeosci.ModelDev.Discuss.:27February2015
Revised:23June2015–Accepted:7July2015–Published:31July2015
Abstract. We present the application of interactive three- 1 Introduction
dimensional (3-D) visualization of ensemble weather pre-
dictions to forecasting warm conveyor belt situations dur- Weatherforecastingduringaircraft-basedfieldcampaignsre-
ing aircraft-based atmospheric research campaigns. Moti- quiresthemeteorologisttoexplorelargeamountsofnumeri-
vated by forecast requirements of the T-NAWDEX-Falcon calweatherprediction(NWP)datainashortperiodoftime.
2012 (THORPEX – North Atlantic Waveguide and Down- Atmosphericfeaturesrelevanttoaresearchflighthavetobe
stream Impact Experiment) campaign, a method to predict identifiedquickly,andfindingshavetobecommunicatedto
3-Dprobabilitiesofthespatialoccurrenceofwarmconveyor colleagues.Furthermore,assessingtheforecast’suncertainty
belts (WCBs) has been developed. Probabilities are derived has become indispensable as flights frequently have to be
from Lagrangian particle trajectories computed on the fore- plannedseveraldaysbeforetake-off.
cast wind fields of the European Centre for Medium Range A challenging element in forecasting methodology is to
Weather Forecasts (ECMWF) ensemble prediction system. create clear and intuitive visualizations that allow the me-
Integration of the method into the 3-D ensemble visualiza- teorologist to perform these tasks in a timely manner. To
tion tool Met.3D, introduced in the first part of this study, advance forecasting techniques for research flight planning,
facilitatesinteractivevisualizationofWCBfeaturesandde- this work presents a new approach using interactive three-
rived probabilities in the context of the ECMWF ensemble dimensional (3-D) visualization of ensemble weather pre-
forecast. We investigate the sensitivity of the method with dictions (the latter a major source of information on fore-
respecttotrajectoryseedingandgridspacingoftheforecast castuncertainty;GneitingandRaftery,2005;Leutbecherand
windfield.Furthermore,weproposeavisualanalysismethod Palmer,2008)toforecastwarmconveyorbelt(WCB)situa-
toquantitativelyanalysethecontributionofensemblemem- tions.
berstoaprobabilityregionand,thus,toassisttheforecaster The article is the second part of a two-paper study. The
in interpreting the obtained probabilities. A case study, re- first part (Rautenhaus et al., 2015, hereafter “Part 1”) intro-
visitingaforecastcasefromT-NAWDEX-Falcon,illustrates duces“Met.3D”,atoolprovidinginteractive3-Dtechniques
thepracticalapplicationofMet.3Danddemonstratestheuse for the visual exploration of ensemble weather prediction
of3-Danduncertaintyvisualizationforweatherforecasting data. This article focuses on the specific application case of
and for planning flight routes in the medium forecast range forecastingWCBs:strong,ascendingandoftenrainproduc-
(3to7daysbeforetake-off). ing airstreams associated with extratropical cyclones. The
term“WCB”wasintroducedbyHarrold(1973)andBrown-
ing(1971)andconsolidatedinaconceptualairstreammodel
for extratropical cyclones (also including the cold conveyor
PublishedbyCopernicusPublicationsonbehalfoftheEuropeanGeosciencesUnion.
2356 M.Rautenhausetal.:Three-dimensionalvisualizationofensembleweatherforecasts–Part2
beltandthedryairstream)byCarlson(1980).Exampleref- A. Howwillthelarge-scaleweathersituationdevelopover
erencesforWCBsincludeBrowning(1990)foranoverview, the next week, and will conditions occur that favour
Eckhardtetal.(2004)andMadonnaetal.(2014)foraclima- WCBformation?
tology,andBrowning(1986)andPfahletal.(2014)forrele-
B. Howuncertainaretheweatherpredictions?
vanceinlarge-scaleprecipitation.WCBsareanatmospheric
feature that has been in the focus of several aircraft-based C. Where and when, in the medium forecast range and
campaigns (e.g. Pomroy and Thorpe, 2000; Vaughan et al., within the spatial range of the aircraft, is a WCB most
2003;Schäfleretal.,2014;Vaughanetal.,2015). likelytooccur?
A recent campaign that targeted WCBs is T-NAWDEX-
Falcon 2012 (THORPEX – North Atlantic Waveguide and D. HowmeaningfulistheforecastofWCBoccurrence?
DownstreamImpactExperiment,hereafterTNF),whichtook
E. WherewilltheWCBbelocatedrelativetocyclonicand
place in October 2012 in southern Germany. Schäfler et al.
dynamicfeatures?
(2014) described the TNF flight-planning process. WCBs
(as well as other atmospheric features targeted by research ThetechnicalbasisforquestionsAandBislaidinPart1.
flights) are of an inherently 3-D nature. However, although This article addresses questions C to E and presents a case
the atmosphere is 3-D, the forecasting and flight-planning studythatdemonstrateshowthemethodsdevelopedinboth
toolsemployedduringTNFreliedontwo-dimensional(2-D) papersareappliedtoforecasting.
visualization methods. This is a common property not only Thepaperisstructuredasfollows.InSect.2,wepropose
ofcampaigntools(Flatøyetal.,2000;Blakesleeetal.,2007; a technique to compute 3-D probabilities of WCB occur-
He et al., 2010; Rautenhaus et al., 2012) but also of me- rence. Our approach is put into relation to previous work
teorological workstations in general (e.g. Heizenrieder and in the field, and its integration into the Met.3D architec-
Haucke,2009;Russelletal.,2010).3-Dvisualizationmeth- ture is described. During TNF, we followed the approach
ods are not commonly usedin forecasting. While 3-D tech- of Wernli and Davies (1997) and used Lagrangian particle
niqueshavebeenusedinresearchsettingsasearlyasinthe trajectories computed on the forecast wind field to objec-
1980s(e.g.GrotjahnandChervin,1984;Hibbard,1986;Hib- tively detect WCB airstreams. Using wind forecasts from
bardetal.,1989;Wilhelmsonetal.,1990)andcontinuetobe the European Centre for Medium Range Weather Forecasts
used in recent visualization tools (e.g. Hibbard, 2005; Nor- (ECMWF) Ensemble Prediction System (ENS; comprising
ton and Clyne, 2012; Dyer and Amburn, 2010; Murray and 50 perturbed forecast runs and an unperturbed control run;
McWhirter,2007),onlyfewreportsonapproachesusing3-D e.g. Buizza et al., 2006), trajectories were started from the
techniquesforforecastinghavebeenpublishedinthepast2 atmosphericboundarylayer(ABL)foreachensemblemem-
decades(TreinishandRothfusz,1997;Koppertetal.,1998; ber.ThosetrajectoriesfulfillingaWCBcriterionweregrid-
McCaslinetal.,2000).Part1,Sect.2,providesfurtherdetails dedinto2-Dgridsanddisplayedasprobabilitymapsshow-
onthelistedreferencesandon3-Dvisualizationinmeteorol- ingtheoccurrenceofeitherorallofWCBinflow,ascentand
ogy. outflow.However,generalisingthisapproachtothreedimen-
Similarly, while the use of ensemble predictions has sions poses challenges, as discussed in Sect. 2. We present
been reported for recent field campaigns (e.g. Wulfmeyer anadaptedapproachusingdomain-fillingtrajectories,which
et al., 2008; Elsberry and Harr, 2008; Ducrocq et al., 2014; ismoreaccurate,albeitcomputationallymoreexpensive.In
Vaughan et al., 2015), they have, to the best of our knowl- order to find the best method that is still computationally
edge,notbeenusedtocreatespecific3-Dforecastproducts tractableinaforecastsetting,bothapproachesarecompared
for flight planning. However, in particular the possibility to inSect.3.Weanalysetheirsensitivitytothegridspacingof
use ensembles to compute 3-D probability fields of the oc- the forecast wind fields and to the number and locations of
currenceoffeaturesoreventsisvaluableforflightplanning. thetrajectoryseedingpoints.
FortheWCBcase,aprobabilityofWCBoccurrencecanbe To facilitate quantitative interpretation of the obtained
usedtoplanflightroutesinregionsinwhichtheprobability probabilities, we further propose a visual analysis method
toencounteraWCBisatamaximum. forcasesinwhichonlylowprobabilitiesoftheoccurrenceof
Theworkpresentedinthisarticleismotivatedbytheques- WCBsareencountered(Sect.4).Insuchcasesaflightoften
tionsof(1)howinteractive3-Dvisualizationcanbeusedto mightnotbeplannedduetotheinterpretedhighuncertainty.
improvetheexplorationof3-Dfeaturesofinteresttoaflight However,lowprobabilitycanhavetwocauses.Eitherindeed
campaign,and(2)howensembleforecasts(inparticularde- only a small percentage of the ensemble members predict
rived probabilities) can be used to improve research flight aWCBfeature,orlargespatialvariationofthefeaturesinthe
planninginthemediumforecastrange(thatis,threetoseven individual ensemble members causes only marginal overlap
daysbeforetake-off).Ourdevelopmentshavebeenguidedby and thus low probabilities. In the latter case the probability
anumberofforecastquestionsthatreflecttheTNFrequire- thataWCBwilloccurisactuallymuchlargerthansuggested
ments.TheyarerepeatedherefromPart1forcompleteness: bythevisualizedprobabilities.However,thereisalargeun-
certaintyinwhereitwilloccur.Tohelptheuserdistinguish
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M.Rautenhausetal.:Three-dimensionalvisualizationofensembleweatherforecasts–Part2 2357
betweenthesecauses,weproposeamethodthatidentifiesthe airstreamsinamodellingcasestudyofthe1979“President’s
contributionofindividualmemberstoaprobabilityregion. Daystorm”andrelatetheairstreamstotheconceptualmodel
After the introduction of all methods that are required to byCarlson(1980).Furthercasestudies,includingKuoetal.
exploreaforecasttoanswerforecastquestionsAtoE,Sect.5 (1992), Schultz and Mass (1993), Mass and Schultz (1993)
revisitstheTNFforecastcaseof19October2012.Thecase and Reed et al. (1994), also interpret computed trajectories
study shows how the proposed 3-D ensemble visualization inconsiderationoftheCarlson(1980)model;however,note
workflowisappliedtocampaignforecasting,andillustrates thattheyareabletoidentifyratheracontinuumofflowpaths
theuseandaddedvalueofthepresentedmethods. thandiscreteairstreams.
Thepaperisconcludedwithasummaryanddiscussionin Inmorerecentstudies(seediscussionbelow),Lagrangian
Sect.6. particletrajectoriesarefrequentlyusedtoobjectivelydetect
WCB structures in numerical model output. For our work,
we are interested in the specific ways trajectories are used
2 Probabilityofwarmconveyorbeltoccurrence in the literature to detect WCBs. In particular, this includes
theemployedobjectivedetectioncriteriaandthespatialand
WCBs are Lagrangian airstreams in extratropical cyclones temporalspacingofthetrajectoriesaswellastheemployed
(e.g. Harrold, 1973; Carlson, 1980; Browning, 1990). They windfields.
transport warm and moist air from the ABL in a cyclone’s Wernli and Davies (1997) introduced objective criteria
warm sector upward and poleward towards the tropopause. to extract what they call “coherent ensembles of trajecto-
The inflow region in the lower troposphere typically ex- ries” (CET; a bundle of trajectories started at different lo-
tends over several hundred kilometres in diameter. WCB cations; not to be confused with the meaning of “ensem-
airmassescommonlyascendbyabout500–600hPain48h, ble”in“ensembleforecasts”)fromasetoftrajectoriescover-
therebycoveringhorizontaldistancesofupto2000km(e.g. ingtheentiredomainofinterest.Theyusewindfieldsfrom
WernliandDavies,1997;Eckhardtetal.,2004).Duetothe the ECMWF global atmospheric model, interpolated (from
strongascent,condensationleadstostronglatentheatrelease aspectraltruncationofT213)toaregularlatitude–longitude
andtheformationofcloudsandprecipitation(e.g.Browning, grid of 0.75◦×0.75◦ with 31 levels in the vertical and a
1986).Therefore,WCBsarehighlyrelevantforprecipitation 6h time interval. Trajectories are started on every model
extremesintheextratropics(e.g.Pfahletal.,2014).Oncethe gridpointbelow800hPa(approx.sevenlevels).Wernliand
air masses reach jet level, an outflow region forms near the Davies show that nearly identical CETs are obtained by se-
tropopause.Thisregionischaracterizedbycirruscloudsthat lectingtrajectoriesthatexperienceeitheramoisturedecrease
extendoverseveralthousandkilometresalongthejetstream. of 12gkg−1 in 48h or an ascent of more than 620hPa in
Readers interested in furtherdetail are referred to Madonna 48h. The approach allows one to focus on the dynamically
et al. (2014), who give a comprehensive introduction to the mostrelevantcoresofanextratropicalcyclone’sairstreams.
field. Inasubsequentarticle,Wernli(1997)appliedthesuggested
To plan a flight that allows for aircraft measurements method to the case study of Browning and Roberts (1994)
within a WCB, we are interested in the spatial and tempo- and relates the obtained CETs to the WCB model. Unlike
ral distribution of WCB features in the ensemble forecast. the analysis of a continuum of airstreams in a cyclone, this
As a summary measure of the uncertainty information, the methodselectsthestrongestascendingairmasseswithinthe
probabilityofWCBoccurrence,p(WCB),isofparticularin- WCB.
terest.Itprovidesforagivenlocationin3-Dspaceatagiven Stohl (2001) and Eckhardt et al. (2004) computed clima-
time the probability of encountering a WCB air mass. To tologies of WCBs. Stohl (2001) seeded the trajectories on
compute p(WCB) from an ensemble weather forecast, we a 1◦×1◦ grid in the horizontal and on two vertical levels
firstneedtodetectWCBfeaturesintheindividualensemble at500and1500ma.s.l.(abovesealevel).Henotedthatthe
members. results of his climatology are sensitive to the WCB selec-
tion criterion, and settled for the – as he writes – “some-
2.1 WCBdetectionbasedonobjectivelyselected whatarbitrary”criterionof8000min48h(theapproximate
Lagrangianparticletrajectories timescale at which air flows through a single synoptic sys-
tem).Similarly,Eckhardtetal.(2004)startedtrajectorieson
In early studies of, for instance, Harrold (1973), Carlson a 1◦×1◦ grid at 500ma.s.l. They noted that “any criterion
(1980)andBrowning(1986),conveyorbeltairstreamshave used for an automatic classification of WCBs is necessarily
been identified by manual inspection of satellite imagery subjective”. In their work, trajectories travelling more than
or by isentropic analysis. Subsequent studies have used La- 10◦ eastward and 5◦ northward and ascending more than
grangianparticletrajectoriescomputedwithwindfieldsfrom 60%oftheaveragetropopauseheightwithin48hareclassi-
numerical model output to investigate case studies of extra- fiedasWCBtrajectories.
tropical cyclones. For example, Whitaker et al. (1988) and A number of studies use the trajectory model “La-
Hibbard et al. (1989) show the existence of three distinct grangian analysis tool” (LAGRANTO) (Sprenger and
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2358 M.Rautenhausetal.:Three-dimensionalvisualizationofensembleweatherforecasts–Part2
Wernli, 2015), originally introduced by Wernli and Davies dictaWCBfeatureatthatgridpoint.Inamoreformalway,
(1997). Spichtinger et al. (2005) analysed ice supersatura- themethodtocomputep(WCB)attimetcanbesummarized
tioninthevicinityofaWCB’soutflowregion,Gramsetal. asfollows:
(2011) presented a case study of an extratropical transition.
Schäfler et al. (2011) analysed aircraft measurements and 1. For every ensemble member m and every available
Madonnaetal.(2014)presentedaclimatologyofWCBs.All forecasttimestept0∈(t−48h...t),integrate3-DLa-
four studies settle for a criterion of an ascent of more than grangian particle trajectories, started at a fixed set of
600hPain48htoselectWCBtrajectories.Intermsofseed- seedingpoints,fromt0forwardintimefor(cid:49)t =48h.
ing, Schäfler et al. (2011) started their trajectories on every
2. SelectthosetrajectoriesthatfulfilaspecifiedWCBcri-
modelgridpointbetweenthesurfaceand850hPaofthede-
terion(e.g.anascentof(cid:49)p=600hPain(cid:49)t =48h).
terministic ECMWF T799L91 forecast (spectral truncation
of T799, with 91 vertical levels), interpolated to a regular 3. For each member m, create a 3-D binary grid Bm that
latitude–longitude grid of 0.25◦×0.25◦, and using the ap- for every grid point with indices k,j,i, Bm , contains
kji
proximately 17 lowest levels. Madonna et al. (2014) seed a set bit (Bm =1) if the grid point is located “inside”
their trajectories at 80km distance in the horizontal and at kji
a WCB air mass at time t, where “inside” needs to be
20hPaverticaldistanceonlevelsbetween1050and790hPa.
determinedfromthetrajectorypositionsatt.
Theirwindfieldisavailableat1◦×1◦gridspacing.
DuringTNF(Schäfleretal.,2014),LAGRANTOhasbeen 4. ForeachgridpointcomputetheprobabilityofWCBoc-
used with wind fields from the ECMWF ensemble forecast currencebycountingthenumberofmemberswithaset
covering the North Atlantic and Europe. To keep the com- bitforthepoint:p(WCB) =1/MP Bm ,whereM
kji m kji
putationaldemandtractablefortheoperationalforecastset- denotesthenumberofensemblemembers.
ting, the available ENS spectral resolution of T639 was in-
terpolated to 1◦×1◦ in latitude and longitude. In the verti- For trajectories seeded approximately in the atmospheric
cal, all available 62 levels were used. A 6h time step was boundary layer, we call this method an “ABL-T method”.
used. Trajectories were started for each member at 1◦ hor- Note that the grid topology of B needs to be identical for
izontal spacing at five levels constant in pressure between eachmemberinordertoavoiderrorsduetovariationsingrid
1000 and 800hPa. The selection criterion was set to an as- point positions, as is the case for probabilities derived from
centof500hPain48h. ECMWFNWPoutput(cf.Sect.5inPart1).
In summary, the reviewed studies have all restricted tra- Themethodposesseveralchallenges.Withrespecttostep
jectory seeding to lower atmospheric levels. The horizontal (1),trajectoryseedingneedstobesufficientlydensetospa-
distancebetweenstartpointsmostlycorrespondstothegrid tially sample the WCB features. The literature reviewed in
spacingofthedrivingwindfields.Whiletheexactselection Sect. 2.1 indicates that grid spacings of 1◦ or less should
criterion for WCB trajectories varies, all studies use a cri- be sufficient. For step (2), the WCB criterion must be care-
terion that filters trajectories according to a given ascent in fullychosen,astheascentthatatrajectoryexperiencesmay
atwodayperiod. dependonfactorsincludingseasonalvariabilityorthehori-
zontal andvertical grid spacingof the employedwind fore-
2.2 Computationofp(WCB) casts.Also,interactivitymustbeconsideredtoenableauser
to change (cid:49)p and (cid:49)t during forecasting to judge the sen-
We follow the approach of Wernli and Davies (1997) and sitivity of p(WCB) on these parameters. Third, we need to
detectWCBfeaturesbyselectingLagrangianparticletrajec- find a suitable gridding strategy that determines in step (3)
toriesaccordingtoagivenascent(cid:49)p inagiventimeperiod whether a grid point is located inside a WCB air mass. The
(cid:49)t.TrajectoriesarecomputedwithLAGRANTO.Weusethe simplestapproachistoextract,foreachmember,theparticle
sameECMWFENSwindfieldsdescribedindetailinPart1, positions of all WCB trajectories at time t, and to compute
Sect.4.1.FromtheavailablespectraltruncationofT639,the foreachparticlethegridcellBm inwhichitiscontained.
kji
windforecastsarehorizontallyinterpolatedbytheECMWF During TNF, this simple approach was applied in 2-D to
Meteorological Archive and Retrieval System (MARS) to computep(WCB)fortotalgridcolumns,aswellasforthree
a regular latitude–longitude grid of 1◦×1◦ (the same data verticalintervalstodistinguishinflow,ascentandoutflow.In
used during TNF) and (additionally) 0.25◦×0.25◦. In the thehorizontal,aregulargridwithaspacingof1◦×1◦inlati-
vertical,theECMWFmodeluseshybridsigma-pressureco- tudeandlongitudewasused.However,withthisapproachno
ordinates(UntchandHortal,2004,alsocf.Fig.9inPart1), physical assumptions are made about the air volume repre-
ofwhichallavailable62modellevelsareused. sentedbyeachparticle.Theresultissensitivetobothtrajec-
Oncetrajectorieshavebeencomputedandselected,agrid- toryseedingpointsandgridtopologyofB,andthepositions
dedfieldofp(WCB)canbederivedbyrelatingeachensem- oftheWCBparticlesareonlycapturedwithanaccuracyof
blemember’strajectoriestoabinarygrid,andbycomputing theorderofthegridspacingofB.Also,duetothechanging
foreachgridpointtherelativenumberofmembersthatpre- areaofthegridcellswithlatitude,theresultisbiasedtowards
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M.Rautenhausetal.:Three-dimensionalvisualizationofensembleweatherforecasts–Part2 2359
shapeoftheparticlevolumeneedtobemade.Afterapplying
a WCB selection criterion to the trajectories, the bits of the
gridpointsfromwhichWCBtrajectorieswerestartedareset.
However,theapproachrequiresincreasedcomputationalre-
sources.Seedingpointsarenowrequiredonalltropospheric
layersandhencealargernumberoftrajectoriesisrequired.
Also,trajectoriesadditionallyhavetobecomputedbackward
(a)
intimetoalsocapturethosesituationsinwhichaWCBtra-
jectorypassesitsseedingpointintheascentoroutflowphase.
Step(1)inthemethoddescriptionaboveishenceextendedto
alsointegratethetrajectoriesbackwardintimefor(cid:49)t hours
fromtimet.
Asanexample,Fig.3showsresultsofselectingdomain-
filling trajectories that ascend more than 500hPa in 48h
(Fig.3a–c)andmorethan600hPain48h(Fig.3d–f).Note
(b)
howthe30%isosurfaceofp(WCB)overtheEnglishChan-
nelalmostvanisheswith600hPafiltering(Fig.3f).
In Sect. 3, we compare four DF-T and ABL-T set-ups
withvaryinggridtopologywithrespecttoobtainedp(WCB)
Figure 1. Total column probability of WCB occurrence (%), as
andtocomputationaldemand.Thecomparisonallowstofind
availableduringTNF.ProbabilitiesarecomputedfromABL-started
trajectoriesfilteredforanascentof500hPain48h.Forecastsfrom aset-upwell-suitedforusageincampaignforecasting.
(a)00:00UTC,15October2012andfrom(b)00:00UTC,17Oc-
tober2012,bothvalidat18:00UTC,19October2012.Compareto 2.3 Implementation
Fig.3inSchäfleretal.(2014).
Trajectories computed with LAGRANTO are stored in
NetCDF files. Trajectory selection and the computation of
lowerprobabilitiesclosetothepoles.Examplesoftheresult- p(WCB) take place in Met.3D and have been implemented
ingtotalcolumnp(WCB)fieldareshowninFig.1andcan in a number of modules in the Met.3D data processing
alsobeenfoundinSchäfleretal.(2014,theirFig.3).Dueto pipelinedescribedinPart1,Sect.4.2.AnalogoustoFig.10
thedescribedissues,theresultsshouldonlybeinterpretedin inPart1,Fig.4showsanexampleset-up.Separatepipeline
aqualitativemanner. modules are responsible for reading trajectory data from
In 3-D, more complexity is added as the vertical extent disk, filtering the data according to the selection criterion,
of the grid cells also has to be taken into account. To elim- gridding and probability computation. This architecture al-
inatebiasandsensitivity,onepossibilityistoassumeanair lowsmodulestobeexchangedwhen,forexample,datafrom
parcel mass and geometry for the trajectory particles, as il- adifferenttrajectorymodelshouldbereadoradifferentse-
lustrated in Fig. 2a. In the example, the particle is associ- lectioncriterionshouldbeapplied.
ated with a spherical air parcel. Given the required thermo- Hardware permitting, parts of the pipeline (for example,
dynamicvariablesattheparticlepositionatstarttimet0 and trajectory selection) can be executed in parallel. Intermedi-
gridding time t, the volume and thus radius of the parcel at ateresultsinthepipelinearecachedbyamemorymanager.
t can be computed and the overlapping grid points found. Bothparallelexecutionandcachingincreasetheinteractivity
However,duetothelargedifferenceinverticalandhorizon- ofthesystemwithrespecttochangingtheselectionparam-
talscaleofourgrids(oftheorderof100kminthehorizontal eters(cid:49)p and(cid:49)t.ForfurtherdetailsontheMet.3Dpipeline
and100minthevertical),theusageofsphericalgeometryre- architecture,wereferthereadertoPart1,Sect.4.2.
quiresthecomputationofaverylargenumberoftrajectories. To select trajectories according to the ascent criterion,
Yet, geometry that reflects the different scales (for example themaximumpressurechangeoccurringwithinatrajectory
ellipses,cylindersorsimplerectangularboxes)isdifficultto over the time interval (cid:49)t is required. For the grid spacings
motivatephysically.Also,usageoflargeairparcelsneglects used here, the data volume of the trajectories of all mem-
potentialdeformationoftheparcelsbythewindfield. bersamountstomultipleGBpertimestepifstoredinbinary
Anapproachnotrequiringanysuchassumptionsistouse NetCDFformat(approximately2.4GBfor1◦horizontalgrid
domain-filling trajectories (in the following referred to as spacingifaverticalregionofinterestof52levelsisselected,
“DF-Tmethod”).Here,wefirstspecifythegridtopologyfor andapproximately38GBifthehorizontalgridspacingisde-
B. Next, as illustrated in Figs. 2b, c and 3, for every mem- creased to 0.25◦). Reading the data from disk and perform-
ber and each grid point Bm , a trajectory starting on Bm ingtheselectioncanhencebeslow.Wethusmakeuseofthe
kji kji
is computed. This way, we can be certain that each Bm is factthattheonlyinformationrequiredtocomputetheprob-
kji
placedexactlyonatrajectoryandnoassumptionsaboutthe abilities is whether the trajectory started from a grid point
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2360 M.Rautenhausetal.:Three-dimensionalvisualizationofensembleweatherforecasts–Part2
Figure2.Methodstocomputep(WCB).(a)ABL-Tmethodusingtrajectoriesstartedintheatmosphericboundarylayerandintegrated48h
forwardintime.Toget3-DgriddedinformationonWCBlocation,anairparcelvolumeneedstobeassumedforeachparticlesothatgrid
pointsoverlappingwiththevolumecanbedetermined.(b)DF-Tmethodusingdomain-fillingtrajectoriesstartedfromeverygridpointof
thep(WCB)gridandintegratedboth48hforwardandbackwardintime.NovolumehastobeassumedasselectedWCBtrajectoriesare
locatedexactlyongridpoints(c).
Figure3.Derivationofp(WCB)withDF-Tset-up(S3).(a,d)Trajectoriesstartedat18:00UTC,19October2012,computedwithwindfields
fromtheensemblecontrolforecastfrom00:00UTC,17October2012,integratedforwardandbackwardintimefor48heach.Trajectories
areselectedaccordingtoanascentof(a–c)500and(d–f)600hPain48h.Colourencodesaltitude(hPa).(b,e)Volumerenderingofthe
binarygridB,representingthestartpositionsoftheselectedtrajectories.(c,f)ProbabilityofWCBoccurrencederivedfromall51members
of the ensemble. The red opaque isosurface shows 30% probability, the purple transparent isosurface 10% probability. Vertical axes are
labelledwithpressurealtitude(hPa).
fulfilstheselectioncriterion.Thedatavolumethatneedsto 3 Choiceofp(WCB)methodandgridspacingfor
beloadedcanbelargelyreducedbypre-computingthemax- forecasting
imum pressure change (cid:49)p for a range of time intervals (cid:49)t.
Now,foragiven(cid:49)t,onlythemaximum(cid:49)pforeachtrajec- Touseap(WCB)methodforforecastingduringacampaign,
tory(i.e.gridpoint)needstoberead.Theselectionprocess anumberofcriterianeedtobefulfilled:
is reduced to comparing each trajectory’s (cid:49)p to the given
thresholdvalue.Thisway,weareabletoprovideaninterac- a. Thetrajectoriesneedtobecomputedinashortperiodof
tivelyadjustableselectioncriteriontotheuser. time(forourapplicationthisispreferablylessthanone
hour), so that results are available soon after the fore-
castwindfieldsbecomeavailablefromECMWF(with
“available” we mean that the retrieval of the forecast
datafromMARS,yieldingtheinterpolatedwindfields
describedinPart1,Sect.4.1,hasfinished);
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M.Rautenhausetal.:Three-dimensionalvisualizationofensembleweatherforecasts–Part2 2361
Figure4.SampleMet.3Ddataprocessingpipelinetovisualizep(WCB),depictedanalogoustoFig.10inPart1.Differentpipelinemodules
(yellow)areresponsibleforreadingandselectingtrajectories,andforcomputingthep(WCB)field.Intheexample,avolumeactor(green;
fordetailsseePart1,Sect.3)visualizestheresultingp(WCB)data.Arequestfortheprobabilityofoccurrenceoftrajectories,emittedby
thevolumeactor,triggersfurtherrequestsupthepipeline.Intermediateresultsarecachedbythememorymanger,connectedtoeachpipeline
module(indicatedbytheblacklines).Pipelineexecutioncanbeparallelandiscontrolledbyataskscheduler,alsoconnectedtoallpipeline
modules(fordetailsseePart1,Sect.4.2).
b. theamountoftrajectorydataneedstobesmallenough S2. Thesameset-upas(S1),butwithhorizontalwindfield,
tobehandledinteractivelyinMet.3D; B, and p(WCB) grid spacing reduced to 1◦×1◦. As
in(S1),thelower52verticallevelsareusedforB and
c. thegridspacingneedstobefineenoughtocapturethe
p(WCB).
important features that are present in a “best-possible”
forecast.
S3. Thesameset-upas(S2),butwithB andp(WCB)grids
definedbyaconstantsurfacepressureof1000hPa,not
3.1 Evaluatedset-ups
by the ensemble minimum surface pressure. The wind
forecast data remain as in (S2). The advantage of this
We evaluate four different set-ups with respect to the given
set-up is that the p(WCB) grid can be interpreted as
criteria:
a structured pressure level grid and thus be visualized
S1. Asthe“best-possible”p(WCB)forecast,weuseaDF- muchmoreefficiently(Part1,Sect.4.3).Thisway,the
T set-up with trajectories computed on the ECMWF interactivityinMet.3Dcanbeimproved.Thedrawback,
ENS wind fields at the highest available grid spacing however,isthatsomeofthelower-levelgridpointsare
(T639L62spectralresolution,horizontallyinterpolated nowlocatedbelowthesurfaceandbecomeinvalid.This
by MARS to a regular grid of 0.25◦×0.25◦ in lati- reduces the vertical grid spacing in the lower tropo-
tudeandlongitude,with62hybridsigma-pressurelev- sphereabovemountainousterrain.
els in the vertical). Care must be taken with respect to
the choice of the Bm and p(WCB) grids. A straight- S4. An ABL-T set-up using a grid B that is regular in the
forward choice is to use the ECMWF grid on which horizontalwithagridspacingof1◦×1◦ asin(S2)and
thewind fieldsare available. However,the verticalpo- (S3).Inthevertical,thegridisregularinpressurewith
sition of the grid points on all but the uppermost hy- a grid spacing of 10hPa. This spacing is of the order
bridsigma-pressurelevelsdependsonthesurfacepres- of the average spacing of the model level grids used
sure field (Untch and Hortal, 2004, also cf. Part 1, in (S2) and (S3), and results in a comparable number
Sect.4.1),whichvariesbetweenensemblemembersand of vertical levels in the region of interest (90 levels
timesteps.Hence,ifforagiventimesteptheindividual between 1000 and 100hPa). Usage of a regular pres-
members’windgridsareusedfortheBm,theproblem surelevelgridcanbemotivatedphysically;fromhydro-
describedinPart1,Sect.5,arises:thegridpointsarelo- staticbalance(e.g.WallaceandHobbs,2006,Sect.3.2),
catedatdifferentverticalpositionsacrosstheensemble, we know that for a column of air with constant mass
and hence an error is introduced when computing the m the difference in pressure δp between top and bot-
probability.Toavoidthisproblemwhilestayingasclose tomboundaryofthecolumnstaysconstantwithheight:
aspossibletotheECMWFgrid,weusethegriddefined −δp=gρδz=mgA,wheregistheaccelerationdueto
bythetimestep’sensembleminimumsurfacepressure gravity (assumed to be constant), ρ the density of the
fortheBm ofallmembers.Theminimumsurfacepres- air, δz the geometric height of the column and A the
sure is chosen to ensure that all grid points are located cross sectional area of the column. We start the trajec-
abovethesurface(ifthemeansurfacepressureisused, tories on those grid points of B that are located below
gridpointsinthelowestlevelscanbelocatedbelowthe 700hPaandclassifyagridpointasbelongingtoaWCB
surfaceinsomemembers).Wefocusonaverticalregion ifaparticleispositionedinthecorrespondinggridcell.
of interest of up to approximately 100hPa and for the Thisway,whileweimplicitlyassumeaparticlegeome-
Bm and p(WCB) grids discard the model levels above trythatisrectangularinlongitude,latitudeandpressure,
thiselevation(retainingthelower52levels). the mass represented by the particle remains constant
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2362 M.Rautenhausetal.:Three-dimensionalvisualizationofensembleweatherforecasts–Part2
whenrisingatconstantlatitude.Theartefactofdecreas- turetheshapeandlocationofthep(WCB)featuresequally
inggridcellareaAtowardsthepolesremains,though. wellas(S1).
For trajectory integration, the same forecast data as in The differences between set-ups (S2) and (S3) are negli-
(S2)and(S3)areused. gible.Whilevirtuallynodifferencescanbefoundinthevi-
sualizationsoftheWCBascentat410hPa(Fig.6c),thedif-
ferencesbecomemorepronouncedintheloweratmospheric
For all trajectory computations, LAGRANTO is driven
layers (Fig. 6d). This can be explained with the grid topol-
withECMWFENSforecastdataat6htimesteps.Themodel
ogy:athigheraltitudes,theelevationofthemodellevelsbe-
internallyusesa30mintimestepfortheintegration,trajec-
comesincreasinglyindependentofsurfacepressure(cf.Part
torypositionsareoutputat6hintervals.
1, Sect. 4.1) and hence the difference in the p(WCB) grids
vanishes.However,evenatlowaltitudestheobserveddiffer-
3.2 Set-upcomparison encesinp(WCB)remainwithinafewpercent.
ThebottomrowsofFigs.5and6showtheresultsforthe
Intermsofcomputationalresources,set-up(S1)isthemost ABL-T set-up (S4). Despite the crude assumption with re-
demandingconfiguration.Onourtestsystem(six-coreIntel specttoairparcelgeometry,themajorp(WCB)featuresare
Xeonrunningat2.67GHz;24GBRAM;512GBsolidstate capturedwell.However,thisset-uptendstopredictslightly
drive), the computation of the trajectories of a single time higherprobabilitiescomparedto(S2)and(S3)intheatmo-
steptakesabout50CPUminutespermember.Thedataout- spheric boundary layer, and slightly lower probabilities at
putforatimestepofallmembers,storedinbinaryNetCDF higheraltitudes.
format,amountstoapproximately38GB.Whilesuchsimu- Results for other time steps are similar (not shown). We
lations are feasible for research settings, they are not suited concludethatfromthepresentedcandidates,set-ups(S3)and
forforecasting.Forset-ups(S2)and(S3),thenumberoftra- (S4) are best suited to be used in a forecast setting. While
jectories decrease by a factor of 16. The time required to showing small differences with respect to the absolute pre-
compute the trajectories reduces to about 3 CPU minutes dicted values, both capture the shape and locations of re-
per time step and member, about 2.4GB of trajectory data gions of elevated p(WCB). Also, both are feasible to com-
areproducedpertimestepfortheentireensemble.Withthe puteinlessthananhourandtheresultscan,duetothestruc-
current ENS size of 51 members, this setting is feasible for turedverticalgridlayout,bevisualizedmoreefficientlythan
forecasting if a small compute cluster is available. For set- the results computed by the set-ups based on hybrid sigma-
up(S4),thetimefurtherreducestoabout1CPUminuteand pressureverticalcoordinates(cf.Part1,Table2)1.
datavolumereducestoapproximatelyoneGB.
InFigs.5and6,thefourset-upsarecomparedbymeans
offourtypicalvisualizationsoftheMet.3Dworkflow:(a)the
4 Probabilityregioncontribution
volume rendering of p(WCB) isosurfaces already used in
Fig.3c,(b)avolumerenderingofWCBfeaturesinforecast The methods introduced so far allow one to visualize the
member12(ascapturedbythebinarygridB12),(c)ahori- computed p(WCB) fields and to find regions in which the
zontalsectionat410hPathroughtheascentregionassociated occurrenceofaWCBismostlikely.However,itremainsan
with precipitation and (d) a horizontal section through the open question how the magnitudes of the displayed proba-
inflow region at 950hPa. The TNF forecast case of 19 Oc- bilities should be interpreted. A distinct property of the ex-
tober 2012 that already served for the examples in Part 1 amples presented in Sect. 3 are relatively low probabilities.
is used. The main features (cf. Fig. 1 in Part 1: inflow over For instance, in Fig. 3c maximum values only reach about
theMediterraneanSea,ascentovertheEnglishChanneland 30%.Asmentionedintheintroduction,suchlowmagnitudes
southern England, outflow over Scandinavia and Russia, as can have two causes: either indeed only 30% of all ensem-
well as a strong ascent associated with former Hurricane ble members predict the WCB event, or large spatial varia-
Rafael over the North Atlantic) are well represented by all tion of the features in the individual members causes only
set-ups.However,intheregionsofmaximump(WCB),set- marginal overlap and thus low probabilities. Also, noise in
ups(S2)and(S3)predictprobabilitiesthataredecreasedby theindividualbinaryvolumescancauseemptygridcellsin
about 10% compared to the “reference” set-up (S1). This thefeaturesanddecreaseprobabilityvalues.Interpretingthe
is visible in the smaller extent of the 30% isosurface in data correctly and being able to distinguish between these
Fig.5aaswellasinthehorizontalsections(Fig.6c,d).Also,
singlememberWCBstructuresaremoresolidinset-up(S1),
1Toprovideanorderofmagnitudeoftherenderingtimes,using
asillustratedinthe3-Dviewofthebinaryvolumeofmember
the same hardware set-up as in Part 1, Table 1 (Nvidia GeForce
12(Fig.5b).Thedecreaseiscausedbythelowerhorizontal
GTX560Tigraphicscardwith2GBofvideomemoryonasix-core
gridspacingofthedrivingwindfields,inwhichfewertrajec- Intel Xeon running at 2.67GHz) and a sampling step size of 0.1,
toriesexperiencestrongascent–potentiallyduetosmoothed the isosurface visualizations in Fig. 5a require on average 361ms
vertical velocities. Nevertheless, set-ups (S2) and (S3) cap- forset-up(S2)and102msfor(S3).
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M.Rautenhausetal.:Three-dimensionalvisualizationofensembleweatherforecasts–Part2 2363
Figure5.Comparisonofset-upstocomputep(WCB).SameforecastasinFig.3.Theselectioncriterionissetto500hPain48h.(a)Volume
renderingofp(WCB)(redopaqueisosurfaceshows30%probability,purpletransparentisosurface10%probability).(b)Volumerendering
ofthebinarygridB ofasinglemember(member12),representingtheWCBfeaturesforthismember.(S1)DF-Tset-upwithahorizontal
gridspacingof0.25◦×0.25◦,intheverticalthelower52(of62)hybridsigma-pressurelevels(uptoapproximately100hPa)definedbythe
ensembleminimumsurfacepressureareused.(S2)As(S1)butwith1◦×1◦ horizontalgridspacing.(S3)As(S2)butwithverticallevels
definedbyaconstantsurfacepressureof1000hPa.(S4)ABL-Tset-upwith1◦×1◦horizontalgridspacingandaregularverticalgridwith
agridspacingof10hPa.
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2364 M.Rautenhausetal.:Three-dimensionalvisualizationofensembleweatherforecasts–Part2
(c, S1.) (d, S1.)
(c, S2.) (d, S2.)
(c, S3.) (d, S3.)
(c, S4.) (d, S4.)
Figure6.SameasFig.5,butshowing(c)horizontalsectionofp(WCB)at410hPa;(d)horizontalsectionofp(WCB)at950hPa;colour
codingin%;greencontourlinesshowensemblemeangeopotentialheight.
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