Review Article WRF-ARW Variational Storm-Scale Data Assimilation

14 Pages·2013·3.05 MB·English

HindawiPublishingCorporation
AdvancesinMeteorology
Volume2013,ArticleID815910,13pages
http://dx.doi.org/10.1155/2013/815910
Review Article
WRF-ARW Variational Storm-Scale Data Assimilation:
Current Capabilities and Future Developments
JuanzhenSunandHongliWang
NationalCenterforAtmosphericResearch,P.O.Box3000,Boulder,CO80307-3000,USA
CorrespondenceshouldbeaddressedtoJuanzhenSun;[email protected]
Received6May2013;Accepted18June2013
AcademicEditor:JidongGao
Copyright©2013J.SunandH.Wang.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
ThevariationalradardataassimilationsystemhasbeendevelopedandtestedfortheAdvancedResearchWeatherResearchand
Forecasting(WRF-ARW)modelsince2005.Initialeffortsfocusedontheassimilationoftheradarobservationsinthe3-dimensional
variationalframework,andrecentlytheeffortshavebeenextendedtothe4-dimensionalsystem.Thisarticleprovidesareviewof
thebasicsofthesystemandvariousstudiesthathavebeenconductedtoevaluateandimprovetheperformanceofthesystem.
Futureactivitiesthatarerequiredtofurtherimprovethesystemandtomakeitoperationalarealsodiscussed.
1.Introduction Doppler Radar Analysis System), was later expanded to
include microphysical retrieval, as well as short-term fore-
In the past two decades active research was conducted casts initialized by these retrieved fields [6–9]. Another
on the development of techniques to initialize storm-scale variational-based radar DA system was developed by Gao
numerical prediction models. It has been recognized that et al. [4] using a 3-dimensional variational data assimi-
the success will critically depend on the optimal use of the lation (3D-Var) technique in the framework of the ARPS
nationaloperationalWSR-88Dradarnetworkthatcoversthe (Advanced Research and Prediction System [10]) model. A
United States with single Doppler coverage in most areas. so-called3.5-dimensionalvariationalradardataassimilation
Althoughthenetworkprovidesobservationsataresolution basedonNavy’sCOAMPS(TheCoupledOcean/Atmosphere
thatisabletoresolveatmosphericconvection,theyareonly Mesoscale Prediction System) was developed and demon-
limitedtoradialwindandreflectivity.Thereforeseveralearly stratedthroughanumberofstudies[11,12].Thesevariational
studiesfocusedonthefeasibilityofretrievingmeteorological systems showed great potentials in the use of radar obser-
fields from these single Doppler observations. Techniques vations for initializing high-resolution numerical models
with different complexities have been developed which aim through several case studies and real-time demonstrations
at obtaining the unobserved meteorological variables such [13,14].
as3-dimensional(3D)wind,temperature,andmicrophysical The demonstrated potential motivated the development
fields from the radar observations of radial velocity and ofaradarDAschemeinthevariationalDAsystemWRFVAR
reflectivity(e.g.,[1–5]). of the community model ARW-WRF (Advanced Research
Thetechniquesthatmakeuseofanumericalmodelina WeatherResearchandForecasting;hereafterrefertoWRF).
dataassimilation(DA)contextreceivedparticularattention WRFVAR includes both 3D-Var [15, 16] and 4D-Var [17]
because they combine the retrieval, initialization, and fore- components. The radar DA scheme was first developed for
castinonesystem.ThefirstradarDAsystemforthestorm- WRF 3D-Var [18, 19] and recently expanded to 4D-Var [20,
scalewasdevelopedbasedonthe4-dimensionalvariational 21]. Unlike the ARPS 3D-Var system and VDRAS whose
data assimilation (4D-Var) technique and a boundary layer developments were motivated by the assimilation of radar
fluid dynamics model for the retrieval of the 3D wind and observationsforconvective-scaleanalysis,theWRFVARsys-
temperature[1].Thissystem,knownasVDRAS(Variational temwasstartedwithconventionaldataassimilationwithout
2 AdvancesinMeteorology
theconvective-scaleanalysisasapriority.Itthusemphasized (ADM) to reduce the computational cost and a simplified
thesynoptic-scalebalancethroughtheuseofmodelforecast representationofphysicalprocessesinTLMandADMinthe
backgroundanditserrorcovariance.Italsousedthestream dataassimilationcycle.
function and velocity potential as the momentum control The cost function of the incremental formulation can
variables instead of the direct velocities as in VDRAS and be derived from the standard cost function with some
ARPS3D-Var.Inaddition,theincrementalformulation[22] assumptionsthatwillbedescribedlater.Firstweexpressthe
that is commonly used in large-scale data assimilation sys- standardcostfunctionasfollows:
temswasadoptedbyWRFVAR,whichmightnotbesuitable
forthestorm-scaleapplicationsbecauseofthelinearization 𝐽(x )= 1(x −x𝑏)𝑇B−1(x −x𝑏)
0 2 0 0 0 0
required in the formulation. Therefore, the addition of a
radardataassimilationcapabilitytoWRF,whichisaforecast 1 𝐾
systemaimingatbroadresearchandoperationalapplications, + ∑{y𝑜−𝐻 [𝑀 (x )]}𝑇 (1)
2 𝑘 𝑘 𝑘 0
presentsnewchallengesthatdonotexistinthesystemsthat 𝑘=0
focusonthestorm-scaleanalysisandforecasting.
×R−1{y𝑜−𝐻 [𝑀 (x )]}.
Inrecentyearsseveraloperationalcentersthroughoutthe 𝑘 𝑘 𝑘 0
world have also been developing and testing capabilities of
This cost function assumes that the assimilation window
assimilating radar observations to initialize high-resolution
covers𝐾observationwindowswitheachrepresentedbythe
convection-permitting NWP models. One of the notable
efforts was taken by the Met Office of the United Kingdom subscript 𝑘. The variables of x0, x0𝑏, and y𝑘𝑜 represent the
usingtheunifiedmodelanditsvariationaldataassimilation initialatmosphericstate,thebackgroundstatewhichcanbe
system[23].Thelessonslearntinunderstandingandfinding previousmodelforecast,andtheobservedstate,respectively.
solutionstotheaforementionedchallengesinWRFVARhave 𝑀𝑘isthenonlinearpredictionmodeltopropagatetheinitial
a wide application to the operational community because atmosphericstatetothatatthe𝑘thobservationtimeinthe
some operational data assimilation systems use the similar case of 4D-Var. It should be noted that 3D-Var is regarded
frameworkasWRFVARandwillhencefacethesamechal- as a special case in which 𝐾 can simply set to 0 and 𝑀𝑘
lenges. set to the identity matrix. 𝐻𝑘 is the nonlinear observation
The purpose of this paper is to provide a review of the operator. B and R arethebackgroundandobservationerror
progress of the WRFVAR system and its planned future covariancematrices,respectively.
developments. Since the initial development of the system, Toderivethecost functionoftheincrementalformula-
a good number of studies have been conducted which tion, we first introduce the innovationvariable d at the 𝑘th
either aim at the further development of the system or at observationtimeas
answeringsomechallengingscientificquestions.Areviewof
thesestudieswillbenefitthefutureusersofthecommunity d𝑘 =y𝑘𝑜−𝐻𝑘[𝑀𝑘(x0)] (2)
system. In Section2, we provide a review on the overall
system design, including the fundamental framework of andthenlinearizetheoperators𝐻𝑘and𝑀𝑘in(1)asfollows:
WRFVAR,radarobservationoperators,controlvariablesand
theirbackgrounderror(BE)estimates,andautomatedradar 𝐻𝑘[𝑀𝑘(x0𝑛)]≈𝐻𝑘[𝑀𝑘(x0𝑛−1)]+H𝑘M𝑘[x0𝑛−1]𝛿x0𝑛, (3)
dataqualitycontrol.Theperformanceofthe3D-Varsystemis
reviewedinSection3andofthe4D-VarsysteminSection4. wherethesuperscripts𝑛and𝑛−1representthecurrentand
Atthelastsection,wediscusstheplannedfutureeffortsfor previousouterloopiterations,respectively.H𝑘andM𝑘arethe
theDAsystem. tangentlinearoperatorof𝐻𝑘and𝑀𝑘.Using(2)and(3),the
costfunction(1)canbechangedto
2.SystemDesignofWRFVARRadarDA 𝐽𝑛[𝛿x𝑛]= 1{𝛿x𝑛−[x𝑏−x𝑛−1]}𝑇B−1{𝛿x𝑛−[x𝑏−x𝑛−1]}
0 2 0 0 0 0 0 0
f2o.1l.loFwusndthaemeinnctarelmFreanmtaelwvoarrkiaotifonWalRFfoVrAmRu.laThtioenW[2R2F]VtAhaRt + 1∑𝐾{H M [x𝑛−1]𝛿x𝑛−d𝑛−1}𝑇
2 𝑘 𝑘 0 0 0
is commonly used in operational systems. In the standard 𝑘=0
variational formulation, the optimal analysis is obtained by
×R−1{H M [x𝑛−1]𝛿x𝑛−d𝑛−1}.
minimizing a cost function measuring the misfit between 𝑘 𝑘 0 0 𝑘
observation and prediction by a nonlinear model. In the (4)
incremental variational formulation, however, a linearized
modelisusedtogeneratethepredictionneededinthecost When the increment 𝛿x0𝑛 at the 𝑛th outer loop iteration is
function.Theadvantageoftheincrementalapproachisthat obtained,theestimateoftheatmosphericstateisupdatedby
itnotonlyreducesthecomputationalcostof4D-Varbutalso x𝑛 =x𝑛−1+𝛿x𝑛andusedtoproducethefirstguesstrajectory
0 0 0
improvesthemathematicalconditioningofthecostfunction 𝑀𝑘[x0𝑛]forthenextouterloop𝑛+1.Thebasicassumption
(i.e., a quadratic cost function) because of the linearization of the incremental approach is that the solution of the cost
of the forward operator. It facilitates the use of a coarser function(4)graduallyapproachesthatofthenonlinearcost
resolution tangent linear model (TLM) and adjoint model function(1)givenenoughnumberofouterloopiterations.
AdvancesinMeteorology 3
Assuming the background error covariance matrix is where(𝑥𝑑,𝑦𝑑, 𝑧𝑑)representsthelocationoftheobservation
given by B = UUT and a control variable transform by point and (𝑥𝑟,𝑦𝑟,𝑧𝑟) represents the location of the radar
𝛿x0 = Uk, the background term of the cost function (4) station.𝑉𝑡iscalculatedfromtherainwatermixingratiowith
issimplifiedto(1/2)(∑𝑁 k𝑖)T(∑𝑁 k𝑖),where𝑁isthetotal a height correction following Sun and Crook [6]. Relation
number of outer loops𝑖,=1whereby𝑖=a1voiding the difficulty in (6) is linear except that 𝑉𝑡 is nonlinearly dependent on 𝑞𝑟,
computing the inverse of B. The control variable transform whichneedstobelinearizedtoobtainthelinearobservation
𝛿x0 = Uk is implemented through a series of operations operatorfor𝑉𝑟.Notethattheearthcurvatureeffect[25]must
U=UpUkUh[15].ThehorizontaltransformUhisperformed be considered when mapping the radar observations to the
usingarecursivefilter[24].TheverticaltransformUkapplies model grid, which is done in the radar data preprocessing
an EOF (empirical orthogonal function) decomposition on packagethatisdescribedinthenextsubsection.
theverticalcomponentofthebackgrounderrorcovariance. The formulation of the reflectivity operator is not as
ThephysicaltransformUpconvertstheincrementincontrol straightforward because it depends on the assumption of
variablespacetoanalysisvariablespace.Thecontrolvariables drop size distribution in a microphysical parameterization
oftheWRFVARsystemwillbedescribedlaterinthissection. schemeandtheclassificationofhydrometeors.FollowingSun
Theoptimalanalysisisobtainedbyminimizingthecost and Crook [6], Xiao et al. [19] used the following relation
function (4) by iterating in both the outer and inner loops. forWRF3D-VarbyassumingtheMarshall-Palmerdropsize
Thenumberofinnerloopiterationsisdeterminedeitherby distributionforrain:
aconvergencecriterionoraprespecifiedfixednumber.The
number of the outer loop iterations is typically 2 to 6. The 𝑍=43.1+17.5log10(𝜌𝑞𝑟), (8)
gradient of the cost function required in the minimization where 𝜌 is the air density (kgm−3) and 𝑞𝑟 is the rainwater
processiscomputedbytheadjointmethod.Forthe4D-Var −1
mixingratio(gkg ).Zhangetal.[26]examinedadifferent
system with the incremental formulation, a forward model
relationbyassumingaconstrainedgammadropsizedistri-
and its TLM and ADM are needed. The forward model is
butionandfoundsomeimprovementintheanalysisoflow
the same as the WRF forecast model but currently only
precipitation.
with the physical schemes of the Kessler microphysics and
Equation(8)wasusedinthecostfunction(5)toassim-
the diffusion. More schemes will be added to the forward
ilatereflectivityintheWRF3D-VardevelopedbyXiaoetal.
modelinthefutureastheadjointoftheseschemeshasbeen
[19].However,Wangetal.[27]showedthatthelinearization
developed.
of (8)asrequiredbytheincrementalformulationofthecost
functioncanresultinadrybiasinrainwateranalysis.Thus
2.2.RadarObservationOperators. Toassimilateradarobser-
theyproposedtoindirectlyassimilatethederivedrainwater
vations, the following observation terms are added to the mixingratio𝑞𝑟from(8)byreplacing𝑍with𝑞𝑟in(5).
existingcostfunction:
𝐽= 𝐽 + 1∑𝑘 [(V −V ob)𝑇R−1(V −V ob) s2t.a3n.dCaorndtcroolnVtraorlivaabrlieasbalensd(CBVac)k[g15ro]ufonrdWERrrFor3DE-sVtiamraatned. 4ThDe-
old 2 𝑟𝑘 𝑟𝑘 k 𝑟𝑘 𝑟𝑘
𝑘=0 Var are the stream function 𝜓, the unbalanced component
(5)
+21(Z𝑘−Zo𝑘b)𝑇Rz−1(Z𝑘−Zo𝑘b)], pofervaetluorceit𝑇y𝑢p,othteenutinalb𝜒al𝑢a,ntcheeducnobmalpaonnceendtcoofmsuprofnaecnetporfestseumre-
𝑃 , and “pseudo” relative humidity Rhs. The unbalanced
su
where 𝐽 is used to represent the existing cost function component for each of the three variables is the residual
old
beforeradardataassimilationisdeveloped.ThevariablesV𝑟 after subtracting the respective correlated component with
standfortheradialvelocityandZforthereflectivityfactor. 𝜓 which is obtained by a statistical fitting. The “pseudo”
Thesuperscript“ob”indicatestheobservations.Thesymbols relativehumidityisthewatervapormixingratiodividedby
R−1andR−1standforobservationerrorcovariancematrices itssaturatedvalueinthebackgroundstate.Toassimilateradar
k z
radial velocity and reflectivity associated with warm rain,
forradialvelocityandreflectivity,respectively.Notethatthe
summationovertheobservationtimelevels𝑘isnotneeded vertical velocity and the microphysical parameters of cloud
inthecaseof3D-Var.Theobservationoperator𝐻𝑘inthecost water and rainwater must be added as control variables. In
thecurrentWRFVARsystem,nocross-correlationwithother
function(1)linksthemodelvariablesinamodelcoordinate
variables is considered for relative humidity, cloud water
totheobservationvariablesinanobservationspace.Forthe
mixing ratio, rain water mixing ratio, and vertical velocity.
radar radial velocity, this linkage is formulated with the 3D
windfield(𝑢,V,and𝑤),thehydrometeorfallspeed𝑉𝑡,and The4D-VartechniquethroughtheuseoftheWRFmodelcan
thedistance𝐷betweenthelocationofadatapointandthe implicitlyproducemultivariatecorrelationsfortheanalysis.
Oneissuethatraisesconcernsfortheconvective-scaleDA
radarantenna:
is the selection of momentum control variables. The use of
𝑉 = 1 [(𝑥 −𝑥 )𝑢+(𝑦 −𝑦 )V+(𝑧 −𝑧 )(𝑤−𝑉)], streamfunctionandvelocitypotential(𝜓and𝜒)waswidely
𝑟 𝐷 𝑑 𝑟 𝑑 𝑟 𝑑 𝑟 𝑡
acceptedbyglobaloperationalmodels(e.g.,NationalCenter
(6) ofEnvironmentalPrediction’sGridpointStatisticalInterpola-
tionandUnitedKingdomMetOfficeUnifiedModel3D-Var
𝐷=√(𝑥𝑑−𝑥𝑟)2+(𝑦𝑑−𝑦𝑟)2+(𝑧𝑑−𝑧𝑟)2, (7) system).However,arecentstudybyXieandMacDonals[28]
4 AdvancesinMeteorology
suggestedthattheuseofstreamfunctionandvelocitypoten- 400
tial as momentum control variables might not be suitable
foranalysisoveraregionaldomainforsmall-scaleproblems.
OthermesoscaleDAsystemsthatinvolveradarobservations,
suchasVDRASandARPS3D-Var,usedu-windalongx-grid 300
direction and v-wind along y-grid direction as momentum
controlvariables.Aneffortisbeingundertakentocompare m)
theimpactofthechoiceofmomentumcontrolvariableson k
e (
high-resolution analysis. Some preliminary results will be cal 200
showninSection5. h s
Forcontrolvariableswithoption5(CV5)inWRFVAR, ngt
e
arecursivefilterandEOFs(empiricalorthogonalfunctions) L ∗
are used to model background error covariance. The hor-
100
izontal autocovariance, which is assumed to be spatially
homogeneousandisotropic,ismodeledbytherecursivefilter.
The vertical error correlations are modeled using the diag-
nosedEOFs(empiricalorthogonalfunctions)fromestimated
0
background errors. Since convective-scale data assimilation
usingradarobservationsiscommonlydoneonlimitedarea 10 20 30
domains,itispreferabletoderivebackgrounderrorstatistics Vertical EOF mode
overthedomainofinterestaswellastheseasonofinterest. rh 𝜒u
T 𝜓
Therearetwoapproachestoestimatethebackgrounderror u
statisticsofthecontrolvariablesinWRFVAR:theensemble
Figure1:LengthscalesofforecasterrorsoftheWRFVARcontrol
method[20,29]andtheNMCmethod[30].Bothmethods variablesofstreamfunction(𝜓),unbalancedvelocitypotential(𝜒𝑢),
are included in the utility GEN BE [15] of the standard unblancedtemperature(𝑇𝑢),andrelativehumidity(rh),withrespect
releasedWRFdataassimilationsystem.Bothalgorithmswere totheverticalEOFmode,computedusing3kmWRFforecastsover
usedinpreviousWRFVARstudies. adomainthatcoversaregionofN24∘–N49∘andW116∘–W74∘inthe
Anexampleoftheestimatedbackgrounderrorstatisticsis USA.Notethatthesurfacepressurehasonlyonemode(indicated
giveninFigure1,whichshowsthehorizontallengthscalesof bythepurple∗)becauseitisa2Dfield.
thecontrolvariableswithrespecttotheverticalEOFmodes.
Theerrorstatisticsiscomputedonadomaincoveringalarge
∘ ∘ ∘ ∘
part of the USA (N24 –N49 and W116 –W74 ) using the
NMC method and the June 2012 data from the real-time coupled with the 4D-Var radar data assimilation in which
WRF 3km runs. The plot shows that the length scales are the frequently updated wind analysis through a continuous
a few hundred kilometers for the dynamical variables and cyclingisusedasthereferencewindforthedealiasing.Lim
temperature in the first few modes and reduced to below andSun[32]demonstratedthatthecouplingofthevelocity
100kilometersinhighfrequencymodes.Thelengthscaleof dealiasing algorithm with the radar DA system improved
relativehumidityisbelow50kilometersforallEOFmodes. theaccuracyofthereferencewindandhenceresultedinan
improved dealiased velocity field by significantly reducing
the percentage of the improperly dealiased data from using
2.4.AutomatedRadarDataQualityControl. Anautomated areferencewindfieldthathadnoradardataassimilation.
radar data quality control and error estimate system that The velocity dealiasing can be particularly challenging
can be executed in real-time is an essential component of during hurricane events because of the strong wind and
an operational radar DA system. The automated radar data the large error in the reference wind, especially near the
preprocessingsystemembeddedinNCAR’sreal-time4D-Var center where a slight offset of center location can cause a
systemVDRASthatisbasedonacloud-scalemodel(different large difference in wind direction. Recent applications of
fromWRF)[6]producesqualitycontrolledradardataforuse the coupled dealiasing scheme in VDRAS suggest that the
by WRFVAR. The system along with its radar data quality scheme is effective to automatically unfold severely aliased
control package has been used in real-time since 2001. The velocityobservations.Figure2showsanexamplefromalarge
VDRAS data preprocessing system includes several quality numberofradarvolumesthatweresuccessfullydealiasedfor
control algorithms as well as filtering, superobbing, and Typhoon Morakot that affected Taiwan during 7–9 August
errorcomputation.InSun[31],someofthesepreprocessing 2008.
methods were described. One of the challenging issues in
theuseofradarradialvelocityforvariousapplicationsisthe
data quality control of aliased velocities, known as velocity 3.Reviewofthe3D-VarPerformances
dealiasing. Radial velocity is aliased when the true radial
velocity is larger than the unambiguous velocity of a radar TheperformanceandimpactofradarDAusingWRF3D-Var
or Nyquist velocity [25]. A unique feature of the VDRAS wereexaminedthroughstudiesofindividualcasesaswellas
datapreprocessingsystemisavelocitydealiasingalgorithm multiplecases/daysunderoperationalsettings.Thefirstcase
AdvancesinMeteorology 5
Aliased radial velocity Dealiased radial velocity
(a) (b)
∘
Figure2:Radialvelocityobservationsat0.5 elevationfromRCHLradaroftheCentralWeatherBureau(CWB)ofTaiwanbefore(a)and
after(b)thedealiasingschemeinVDRASwasapplied.Thethinwhitecontoursarecostallines.
studywithradarradialvelocitydataassimilationinWRF3D- theuse of a linearized form of the 𝑍-𝑞𝑟 equation (8) as the
Var was reported by Xiao et al. [18] using a heavy rainfall observation operator and the warm-rain partition scheme.
case that occurred over the Korean Peninsula. They found Asaforementioned,theWRF3D-Varappliestheincremental
that the assimilation of the radial velocity data from Jindo approach that requires the linearization of the forward
radaroperatedbytheKoreanMeteorologicalAdministration model. The logarithm 𝑍-𝑞𝑟 equation (8) has a high degree
improvedthewindanalysis(especiallythenorthwardcom- of nonlinearity especially when 𝑞𝑟 is small. They found
ponent)resultinginsubstantialimprovementfor3hrainfall a dry bias was introduced because of the errors in the
forecastsandnoticeableimprovementfor6hforecasts.Ina linearization. In addition, the performance of the partition
follow-up paper, Xiao et al. [19] described a methodology scheme largely depends on quality of relative humidity in
to assimilate radar reflectivity data into the WRF 3D-Var. the first guess state because the switches that initiate the
Although the reflectivity is linked to the rain water mixing warm rain processes may never be turned on during the
ratio, they chose the total liquid water 𝑞𝑡 as the control minimization of the cost function. Moreover, as noted by
variableinsteadof𝑞𝑟notonlybecausethedistributionoftotal Xiaoetal.[19],thewarm-rainpartitionschemeisnotsuitable
waterismoreGaussian-likebutalsothemultivariateanalyses for winter storms in which cold rain process may play an
canbeachievedbyuseofapartitionscheme.Inthisscheme, importantrole.Wangetal.[27]describedanewschemefor
theanalysisincrementof𝑞𝑡ispartitionedintothewatervapor theassimilationofreflectivityinwhichthederivedrainwater
mixingratio𝑞V,thecloudwater𝑞𝑐,andtherainwater𝑞𝑟using mixing ratio from (8) was assimilated instead of the direct
a warm rain microphysical scheme. The method was first assimilation of the reflectivity observations. In addition, an
tested withthelandfallingtyphoonRusa(2002)overSouth extraobservationtermwasaddedtothecostfunction(5)that
Korea.Theirresultsindicatedthatthepositiveimpactofradar measures the misfit between the water vapor mixing ratios
reflectivitylastedonlyfor3hours.However,whenbothradial fromthemodelandanestimatedfieldfromradarreflectivity
velocityandreflectivityradarobservationswereassimilated, observations. The estimated water vapor was obtained by
noticeableimprovementlastedupto12hours. assumingsaturationwhereradarreflectivityishigherthana
The above 3D-Var radar data assimilation system was specifiedthresholdabovethecloudbase.Inthisnewscheme,
further evaluated by Pu et al. [33] in a case study of the thecontrolvariablesforthemicrophysicsarepseudorelative
HurricaneDennisnearlandfallthatoccurredduring2005in humidityandrainwatermixingratios.Thepartitionscheme
southeasternCuba.Inthisstudy,theeastwardandnorthward usedinXiaoetal.[19]isnotneeded.
velocities synthesized from an airborne Doppler radar as The performance of the new reflectivity assimilation
well as reflectivity were assimilated into the WRF 3D-Var. scheme was demonstrated using an operational WRF 3D-
Theydemonstratedthattheradardatasignificantlyimproved Var DA and forecasting system with rapid update cycles
the short-term (18 hours) forecasts of the intensity, track, by Wang et al. [27]. Four heavy-rain-producing convective
and precipitation. However, similarly as in Xiao et al. [19], casesthatoccurredduringsummer2009inBeijing,China,
the impact was mainly attributed to the assimilation of the werestudiedusingthenewsystem.Resultsshowedthatthe
Dopplerwindobservations. indirectassimilationofreflectivitysignificantlyimprovedthe
Therelativelysmallimpactofthereflectivitydatainthe short-termprecipitationforecastskillupto6hours,extended
scheme developed by Xiao et al. [19] motivated a further fromthe3hoursshowninXiaoetal.[19].Figure3compares
examination of the reflectivity assimilation. Wang et al. the 4-hour forecasts from two experiments that assimilate
[27] pointed out some issues with this scheme, namely, radialvelocityaloneandbothradialvelocityandreflectivity,
6 AdvancesinMeteorology
3 h forecasts 4 h forecasts
43∘N 43∘N
0.1
42∘N 42∘N
5
41∘N 41∘N
on on 10
ati 40∘N ati 40∘N
v v
Obser 39∘N Obser 39∘N 25
50
38∘N 38∘N
37∘N 37∘N 100
112∘E 114∘E 116∘E 118∘E 120∘E 112∘E 114∘E 116∘E 118∘E 120∘E
(a) (b)
3 h forecasts 4 h forecasts
43∘N 43∘N
0.1
42∘N 42∘N
5
41∘N 41∘N
10
Vr 40∘N Vr 40∘N
25
39∘N 39∘N
50
38∘N 38∘N
37∘N 37∘N 100
112∘E 114∘E 116∘E 118∘E 120∘E 112∘E 114∘E 116∘E 118∘E 120∘E
(c) (d)
3 h forecasts 4 h forecasts
43∘N 43∘N
0.1
42∘N 42∘N
5
41∘N 41∘N
10
+qr 40∘N +qr 40∘N
Vr Vr 25
39∘N 39∘N
50
38∘N 38∘N
37∘N 37∘N 100
112∘E 114∘E 116∘E 118∘E 120∘E 112∘E 114∘E 116∘E 118∘E 120∘E
(e) (f)
Figure3:Hourlyaccumulatedprecipitation(unit:mm)fortheconvectivecasethatoccurredonJuly23,2009,inBeijing,China.The3-hour
(leftcolumn)and4-hour(rightcolumn)forecastsareinitializedat0600UTCbya3hourlycycledWRF3D-Var.TheradarQPE((a)and(b))
isusedtoverifytheexperimentsthatassimilateradarradialvelocity((c)and(d))onlyandthatassimilatebothradialvelocityandrainwater
mixingratioderivedfromreflectivity((e)and(f))(from[27]).
AdvancesinMeteorology 7
respectively,foroneofthefourcasesstudiedinWangetal. 1.4E+06
[27]. It is evident from this comparison that the addition 1.2E+06
of the reflectivity data assimilation improves the forecast n 1.0E+06 2
bismcyhpmermoavkeeiwndgapsothasleistoiavreceoaimnofipframtchteedopfbrtyehceSiupninetawettiroaenlfl.em[c3t4oi]rveibtyycoarmussnpimnaicintla.gtThitohnee ost functio 864...000EEE+++000555 3 4 5 6
3D-Varoveraconsecutiveone-weekperiodovertheUSGreat C
2.0E+05
Plainsregion.
0.0E+00
All of the studies reviewed previously assimilated radar
1 11 21 31 41 51 61 71 81 91 101111121
observationswithonecycleormultiple3hourlycycles.Sunet
Number of iterations
al.[34]demonstratedthattheimprovementoftheshort-term
precipitationforecastcouldbeachievedbyrunningtheWRF 4DVT30
3D-Varwith3hourlyrapidupdatecyclesevenwithoutradar 4DVT15
observations, although adding radar data further improved 4DVT05
theforecasts.Itisdesirabletorun3D-Varwithmorefrequent
Figure 4: Cost functions with respect to the number of total
cycles(lessthanonehour)fornowcastingapplications,given
iterationsaccumulatedbythe6outerloopsindicatedontopofthe
thefactthatradarsprovidefrequentobservations.However, solid curve. The three cost functions are from three experiments
initialexperimentsyieldedmixedresultswithhourlycycles. thatusetheassimilationwindowlengthof5minutes(4DV T05),
Digital filter initialization [35] was used in an attempt to 15minutes(4DV T15),and30minutes(4DV T30)(from[20]).
reducenoisesthatmayhavebeenthereasonforthedifficulty
withthehourlycycles,butnosignificantimpactwasfound.
Some technical issues need to be resolved and will be
discussedinthelastsection. the updated WRF version 3.3. These upgrades along with
someothersoftwareenhancementsweredescribedinZhang
etal.[44].Wangetal.[20]describedthelatestdevelopment
4.SomeEarlyResultsofthe4D-VarSystem ofthesysteminregardtoradardataassimilationandshowed
the results of a case study from a squall line precipitation
The ultimate goal of the WRFVAR radar data assimilation event.Usingthesamecase,SunandWang[21]comparedthe
system is the development of a 4D-Var scheme that is performanceofthe4D-Varwiththatof3D-Varandfoundthat
capableofusingthefrequentradarobservationsatmultiple theprecipitationforecastinitializedbythe4D-Varnoticeably
time levels. In their OSSE (Observation System Simulation improvedoverthatof3D-Var.
Experiments)study,Sugimotoetal.[36]showedthatthe3D- One question sought to answer by Wang et al. [20] was
Varhadonlylimitedabilityinretrievingthetangentialwind whether the incremental formulation would be feasible for
component that was not observed by radar. Using the 4D- theapplicationattheconvective-scale.Theyconcludedthat
Var of a cloud-scale model, Sun and Crook [37], Sun and the incremental formulation worked well in the context of
Crook[38],andCrookandSun[39]allshowedthatthe4D- radardataassimilationwithahigh-resolutionconfiguration
Var technique was able to retrieve the tangential wind with whenthetypicalassimilationwindowlengthsoflessthan30
reasonable accuracy. We therefore anticipate that the WRF minuteswereused.Figure4showsthereductionofthecost
4D-Var can improve the 3D wind retrieval and hence the function(5)whenthewindowlengthsof5,10,and30minutes
convectiveforecastingoverits3D-Var. are used. Note that the frequency of the data is the same
The 4D-Var technique is used in the global operational (5min) in all the three experiments. In these experiments,
systemsbyseveralmajoroperationalweatherservicecenters six outer loop iterationsfor the nonlinearbase state update
throughout the world. The European Center for Medium- wereused,and20innerloopiterationsfortheminimization
Range Weather Forecasts (ECMWF) is the first center that ofthecostfunctionwereperformed.Itisseenthatthecost
implementeda4D-Varoperationalsystem[40–42].Follow- function is smoothly reduced when the 5-minute window
ingthesuccessofECMWF,other4D-Varsystemsbasedon wasused.Somediscontinuitiesareshownasthebasestateis
operationalNWPmodelsweredevelopedandimplemented updatedinthecaseof15-and30-minutewindowlengths,but
atseveraloperationalcentersthroughouttheworldastheir thecostfunctionissteadilyreducedattheendofeachouter
dataassimilationsystemsforglobalorregionalNWPwithout loopfromthepreviousloop.Figure4alsosuggeststhatthe
the convective-scale radar data assimilation. Recently the 30-minuteassimilationwindowresultsinalargestreduction
Met Office has run a real-time demonstration with an of the cost function despite of the discontinuity caused by
hourlycycling4D-Varsystemanda1.5kmresolutionovera the mismatch between the linearized forward model and
domaincoveringSouthernEnglandandWales.Thissystem the nonlinear base state. Wang et al. [20] showed that the
currentlyassimilatesradarradialvelocityinthe4D-Var,but forecastinitializedbythe4D-Varwiththe30-minutewindow
the reflectivity is assimilated with a diabatic initialization producedprecipitationwithsmallestbias.
followingJonesandMacpherson[43]. The performance of WRF 4D-Var was compared with
ThebasicframeworkoftheWRF4D-Varwasdescribed 3D-VarbySunandWang[21]inacasestudy.Theyshowed
byHuangetal.[17]andtestedusingaTyphooncase.Recently, thatthe4D-Varsubstantiallyimprovedtheprecipitationskill
theTLManditsADMofthesystemwereupgradedtomatch over the 3D-Var for the 0–6h forecasts of the squall line
8 AdvancesinMeteorology
Validated at 2002061306 Validated at 2002061306
38∘N 38∘N 0.1
0.2
0.4
37∘N 37∘N
0.8
1.6
36∘N 36∘N 3.2
6.4
12.8
35∘N 35∘N 25.6
51.2
99∘W 98∘W 97∘W 96∘W 95∘W 94∘W 99∘W 98∘W 97∘W 96∘W 95∘W 94∘W
(a) StageIV (b) 3DV
Validated at 2002061306 Validated at 2002061306
38∘N 38∘N 0.1
0.2
0.4
37∘N 37∘N
0.8
1.6
36∘N 36∘N 3.2
6.4
12.8
35∘N 35∘N 25.6
51.2
99∘W 98∘W 97∘W 96∘W 95∘W 94∘W 99∘W 98∘W 97∘W 96∘W 95∘W 94∘W
(c) 3DVQV (d) 4DV
Figure5:6-hourforecastsofhourlyaccumulatedprecipitation(mm)from(b)thebasicWRF3D-Var(3DV),(c)theenhancedWRF3D-Var
(3DVQV),and(d)the4D-Var(4DV).TheStageIVprecipitationanalysisisshownby(a)forverification.
studied.Figure5comparesthe6-hourprecipitationforecasts forecasts compared to the 3D-Var, suggesting that the 4D-
(hourlyaccumulation)ofa4D-Varexperimentwithtwo3D- Varhasabetterabilityinretrievingthe3Dwindasexpected.
Var experiments from their study. The difference between Diagnosticanalysesintheirstudysuggestedthatthe4D-Var
the two 3D-Var experiments 3DV and 3DVQV is that the producedmorerealisticlow-levelcoldpool,itsleadingedge
latter accounts for the effect of latent heat by assimilating convergence, and mid-level latent heating when compared
saturated in-cloud humidity as described in Wang et al. withtheradaranalysesproducedbyVDRAS.
[20,27].Theimprovementoftheprecipitationforecastfrom
the 4D-Var over the basic 3D-Var (Figure5(b)) is clearly
shownwhencomparedwiththeStageIVdata(Figure5(a)). 5.FutureDevelopmentsfor
Although the line structure is forecasted in the experiment WRFVARRadarDA
3DVQV(Figure5(c)),thesqualllinehasslowerpropagation
speed and the precipitation is overforecasted. It is clearly Theencouragingresultsproducedinthepaststudieswarrant
seenthatthe4D-Varexperiment(Figure5(d))hastheclosest further development and improvement of the WRFVAR
agreementwiththeobservations.Thequalitativeverifications radardataassimilationsystem.Animmediatenextstepisto
oftheforecastsarecomparedinFigure6usingtheFractions investigatetheimpactoftheanalysisandforecastwithregard
Skill Score (FSS) [45] with the radii of influence of 8km, totheselectionofmomentumcontrolvariables.Oneofthe
24km,and48km.Thesuperiorperformanceofthe4D-Var motivations for investigating the impact of the momentum
is shown by the improved FSS and the elimination of the control variables is that we have found that WRF 3D-Var
initial skill drop that is present in the 3D-Var techniques. tended to produce degraded results when an hourly cycle
Sun and Wang [21] also found that the radial velocity frequencywasused.Anewoptionthatusestheu-windand
observationshadgreaterimpactonthe4D-Varanalysesand v-windisbeingaddedtotheWRFVARsystemandcompared
AdvancesinMeteorology 9
1.0 1.0
0.8
0.8
0.6
SS SS 0.6
F F
0.4
0.4
0.2
0.2
1.0 2.0 3.0 4.0 5.0 6.0 1.0 2.0 3.0 4.0 5.0 6.0
3DV 3DV
3DVQV 3DVQV
4DV 4DV
(a) 5mmROI=8km (b) 5mmROI=24km
1.0
0.9
0.8
SS 0.7
F
0.6
0.5
0.4
1.0 2.0 3.0 4.0 5.0 6.0
3DV
3DVQV
4DV
(c) 5mmROI=48km
−1
Figure6:Fractionsscalescore(FSS)versusforecasthourofhourlyaccumulatedprecipitation(mmh )forthethresholds5mmwiththe
radiusofinfluence(ROI)of8km(a),24km(b),and(c)48km,respectively.
withtheexistingschemeusing𝜓and𝜒momentumvariables. observationerrorof1ms−1.Thebackgrounderrorcovariance
Notethattheunbalancecomponentofthevelocitypotential values for the two tests were calculated using an ensemble
is used in WRF 3D-Var although, for simplicity, we use the of short-term WRF forecasts. Apparently, the test using the
notation 𝜒 in the following description. Preliminary results 𝜓-𝜒 control variables (Figures 7(a) and 7(d)) gives larger
indicatethatthetwooptionscanyieldsignificantdifferences horizontalspreadthanthetestusingtheu-vcontrolvariables
in the characteristics of background error covariance and (Figures7(b)and7(e)).Byplottingtheincrementsalongthe
henceaffectthefinalanalysis.Figure7comparestheanalysis x-direction on the observation level (Figures 7(c) and 7(f))
increments of u-wind and v-wind from single observation it is clearly shown that the magnitudes of the wind incre-
tests using the two momentum control variable options. mentsaresubstantiallydifferentandmuchlargervalueshave
These single observation tests were conducted by assuming resultedfromtheuseofthe𝑢-Voptionthanthe𝜓-𝜒option.In
an observation of u (left column) and v (right column) at addition,the𝜓-𝜒controlvariableschemeproducesnegative
thepointmarkedby“+”inFigure7withaninnovationand increments in the distance far away from the observation
10 AdvancesinMeteorology
18.3 .0 18.3 .0
.0
16.3 16.3
.0 .0 .0 .0 .0
14.2 14.2
m) 12.2 m) 12.2
k k
ht ( 10.2 .0 ht ( 10.2 .0
g g
Hei 8.1 .1 Hei 8.1 .0 .1
6.1 .0 + 6.1 +
4.1 .0 4.1
.0
2.0 .0 2.0 .0
0.0 0.0
0 30 60 90 120 0 20 40 60 80 100
x-wind component contours:−0.25 to 0.25 by 0.05 y-wind component contours:−0.25 to 0.25 by 0.05
(a) (d)
18.3 .0 18.3 .0 .0
16.3 16.3
.0 −.1 .0
.0
14.2 14.2
m) 12.2 .0 m) 12.2
ght (k 10.2 .1 ght (k 10.2 .0 .1 .0
Hei 8.1 Hei 8.1 .2
6.1 6.1 +
.0 .2
4.1 .0 4.1
.1
.0 .0
2.0 2.0
0.0 0.0
0 30 60 90 120 0 20 40 60 80 100
x-wind component contours:−0.15 to 0.45 by 0.05 y-wind component contours:−0.45 to 0.55 by 0.05
(b) (e)
0.5 0.5
0.4 0.4
ent 0.3 ent 0.3
n n
o o
p p
m m
o 0.2 o 0.2
c c
d d
n n
wi 0.1 wi 0.1
x- y-
0.0 0.0
−0.1 −0.1
0 30 60 90 120 0 20 40 60 80 100
(c) (f)
Figure7:Verticalsectionsofanalysisincrementsfromexperimentsthatassumeasingleobservationofu-wind(leftcolumns)andv-wind
(rightcolumns)with1ms−1innovationlocatedatthepointmarkedby“+”in(a)and(d).The𝑢andVincrements(unit:ms−1)resultingfrom
theanalysesthatuse𝜓and𝜒asmomentumcontrolvariablesareshownin(a)and(d),respectively,andfromthedirectuseof𝑢andVas
controlvariablesthatareshownin(b)and(e),respectively.Themagnitudesof𝑢andVincrementsontheobservationlevel(6km)areplotted
asafunctionofx-andy-gridpoints.Thehorizontalgridspacingis4km.
point, which is questionable for the convective-scale. The arethecausesofthedifferenterrorcharacteristicsandisalso
impact of the different momentum control variables in the beingstudiedusingrealobservations.
contextofradardataassimilationforconvectiveforecasting AlthoughtheinitialresultsfromSunandWang[21]are
isbeingcurrentlystudiedinmoredepthtoinvestigatewhat encouraging, it is obvious that the WRF 4D-Var should be