Meteorol Atmos Phys 98, 269–282 (2007)DOI 10.1007/s00703-007-0265-4Printed in The Netherlands

1 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

2 Institute of Sciences, University of Science and Technology of the Chinese People’s Liberation Army,Nanjing, China

3 International Pacific Research Center and Department of Meteorology, University of Hawaii at Manoa,Honolulu, HI, USA

Initialization and simulation of a landfalling typhoonusing a variational bogus mapped data assimilation (BMDA)

Y. Zhao1;2, B. Wang1, and Y. Wang3

With 12 Figures

Received January 10, 2007; accepted March 4, 2007Published online: June 18, 2007 # Springer-Verlag 2007

Summary

Recently, a new data assimilation method called‘‘3-dimensional variational data assimilation of mapped ob-servation (3DVM)’’ has been developed by the authors.We have shown that the new method is very efficient andinexpensive compared with its counterpart 4-dimensionalvariational data assimilation (4DVar). The new methodhas been implemented into the Penn State=NCAR me-soscale model MM5V1 (MM5_3DVM). In this study, weapply the new method to the bogus data assimilation(BDA) available in the original MM5 with the 4DVar. Bythe new approach, a specified sea-level pressure (SLP)field (bogus data) is incorporated into MM5 throughthe 3DVM (for convenient, we call it variational bogusmapped data assimilation – BMDA) instead of the original4DVar data assimilation. To demonstrate the effective-ness of the new 3DVM method, initialization and simu-lation of a landfalling typhoon – typhoon Dan (1999) overthe western North Pacific with the new method are com-pared with that with its counterpart 4DVar in MM5.Results show that the initial structure and the simulatedintensity and track are improved more significantly using3DVM than 4DVar. Sensitivity experiments also show thatthe simulated typhoon track and intensity are more sensi-tive to the size of the assimilation window in the 4DVarthan that in the 3DVM. Meanwhile, 3DVM takes muchless computing cost than its counterpart 4DVar for a giventime window.

1. Introduction

As numerical weather prediction (NWP) of trop-ical cyclone track and intensity is a typicalinitial value problem, efforts over the years havebeen placed on improving the initial conditions(IC) for NWP models through a variety of dataassimilation techniques. Variational data assimi-lation is one of the most efficient methods to per-form initialization for a NWP model (Bouttierand Rabier, 1997; Courtier et al, 1994; Daley,1991; Navon et al, 1992; Thepaut et al, 1993;Zupanski, 1993; Zou et al, 1995). Three-dimensionvariational data assimilation (3DVar) and Four-dimensional variational data assimilation (4DVar)are two typical representatives of this kind ofmethods, both have been playing more and moreimportant roles in NWP since 1980s when the var-iational principle was introduced to data assimi-lation (Derber, 1989; Le Dimet and Talagrand,1986; Lewis et al, 1985). They produce a bestestimation of model initial state by incorporat-ing observations in the assimilation window withbackground in an optimal way. 4DVar withadjoint technique can produce dynamically and

thermodynamically consistent initial conditionsand allow an optimal comparison between themodel and the observations at different time inthe assimilation window through model trajectory.However, the establishment of the adjoint modelis so tough and the cost of gradient computationis so huge that the development and applicationof 4DVar are limited to some extent at present.Previous experiments with 4DVar have been lim-ited to small domains or relatively coarse spatialresolution models. Many prediction centers andresearch institutions still use 3DVar for model ini-tialization because it is much more inexpensivecompared to its counterpart 4DVar. However,although some constraints of simple dynamicalbalance are utilized in the 3DVar procedure with-out model constraints, the 3-dimensional struc-ture of the IC from assimilation could not beglobally adjusted so that the IC is not necessar-ily consistent with the full-physics predictionmodel. Previous studies clearly point out that atimesaving and efficient data assimilation meth-od is a crucial step toward improving the IC forforecast models.

A new data assimilation approach called‘‘3-dimensional variational data assimilation ofMapped observation (3DVM)’’ has been recentlyproposed by Wang and Zhao (2006). Similar tothe available 4DVar, 3DVM produces an optimalIC that is consistent with the prediction modeldue to the inclusion of dynamical and physicalconstraints of the model and that best fits theobservations in the assimilation window throughthe model solution trajectory. Different from the4DVar, 3DVM does not need the tangent linearand adjoint approximations for calculating thegradient of cost function, and does not generatethe IC at the beginning but the end of the assim-ilation window. It is this change that makes thecomputing cost of 3DVM greatly reduced to alevel equivalent to the 3DVar. The new approachhas been implemented into the Penn State=NCAR mesoscale model MM5V1. This newsystem is named the MM5_3DVM system to dis-tinguish it from the original 4-dimensional varia-tional data assimilation system – MM5_4DVar(Zou et al, 1997).

To apply this new data assimilation method tothe initialization and simulation of typhoons, inthis study the MM5_3DVM system is first testedin the bogus data assimilation (BDA) scheme

available in the original MM5_4DVar (Zou andQingnong, 1999). By this new approach, which isreferred to as variational bogus mapped data as-similation – BMDA, a specified sea-level pressure(SLP) field is assimilated into the MM5 modelwithin a given time assimilation window usingthe MM5_3DVM system instead of the originalMM5_4DVar system. Previous studies have dem-onstrated that the BDA scheme is very efficientin recovering the initial structure of a tropicalcyclone and improves the prediction of tropicalcyclone motion and intensity (Xiao et al, 2000a,b; Wang et al, 2000; Zou et al, 2001; Xiao et al,2002; Pu et al, 2002; Zhang et al, 2003; Parkand Zou, 2004; Zhao et al, 2005). To demonstratethe effectiveness of the new BMDA scheme us-ing 3DVM approach (Wang and Zhao, 2006),initialization and simulation of a landfalling ty-phoon – typhoon Dan (1999) over the westernNorth Pacific is performed and compared withthat using the MM5_4DVar BDA scheme in thisstudy. We will show that the initial structure andthe simulated intensity and track of typhoon Danare improved more significantly using 3DVMthan 4DVar. In the meantime, 3DVM takes muchless computational time than its counterpart4DVar for a given time window. In addition, sen-sitivity experiments also show that the simulatedtyphoon track and intensity are more sensitive tothe size of the assimilation window in the 4DVarthan that in the 3DVM.

The rest of the paper is organized as follows.The MM5_3DVM system and a comparison be-tween 4DVar and 3DVM techniques as initializa-tion schemes of tropical cyclones are discussedin the next section. Details of experimental de-sign are given in Sect. 3. The simulation resultsof storm track and intensity from both 3DVMBMDA and 4DVar BDA are compared in Sect. 4.Section 5 compares the dynamical and thermo-dynamic structure of the typhoon vortices gener-ated by the BDA and BMDA schemes. The majorresults are summarized in the last section.

2. Description of MM5_3DVM system

2.1 Mapped observation

According to the definition given by Wang andZhao (2006), the mapped observation is a kindof data derived from a transform or mapping of

270 Y. Zhao et al

observation. The transform or mapping may be aunit operator, a linear interpolation, a model map-ping, a tangent linear model mapping or itsinverse mapping, observation operator, or a com-posite mapping, and so on. In this paper, themapping we use is the model mapping, whichcan be formulated in the following form:

Mti!tN ðxobsi ; �Þ ¼ xmo

i ; ð1Þwhere Mti!tN ðxobs

i ; �Þ is a mapping from ti to

tNð> tiÞ by the prediction model M, using the

observation xobsi at ti as the IC of the integration

with time step � . xmoi is named the mapped obser-

vation located at tN produced by mapping xobsi .

2.2 Conception of 3DVM

4DVar produces the optimal IC x0a by minimizing

the cost function:

J4DVarðx0aÞ ¼ min

xJ4DVarðxÞ; ð2Þ

J4DVarðxÞ ¼1

2ðx� x0

bÞTB�1

0 ðx� x0bÞ

þ 1

2

XNi¼1

ðHiðxiÞ � yobsi ÞTO�1

i ðHiðxiÞ � yobsi Þ;

xi ¼ Mt0!tiðx; �Þ

8>>>>><>>>>>:

ð3Þwhere x0

b is the background or the first guessat time t0, B0 is the covariance matrix of back-ground error at t0, Hi is an observation operator,yobsi ði ¼ 1; 2; . . . ;NÞ is the observation at ti in

the assimilation window ½t0; tN �ðtN � t0�6 hÞ,Oi is the covariance matrix of observation errorof yobs

i , xi is model state at ti by the predictionmodel ðMÞ integration starting from the initialstate x with time step � . It is clear that the opti-mal IC x0

a produced by 4DVar is located at thetime t0. Comparing with the time location of x0

a,the observations in the window ½t0; tN � are alllocated at the future time, except those at t0. Itis the adjoint model that plays the role in imple-menting the backward integration and therebyfeeds the observations back to the beginning ofthe window.

In the paper by Wang and Zhao (2006), underthe supposition that all variables at the model de-grees of freedom are measured, i.e., yobs

i ¼ xobsi

and Hi is an identical operator, the optimal IC of4DVar from the beginning is moved to the end

of the assimilation window ½t0; tN �ðtN � t0� 6 hÞ.Then, a new conception called 3DVM is derivedfrom this attempt by minimizing the cost function:

J3DVMðxNa Þ ¼ minx

J3DVMðxÞ; ð4Þ

J3DVMðxÞ ¼1

2ðx� xNb Þ

TB�1N ðx� xNb Þ

þ 1

2

XNi¼1

ðMti!tN ðxobsi ; �Þ � xÞT ~OO�1

i

�ðMti!tN ðxobsi ; �Þ � xÞ

or

J3DVMðxÞ ¼1

2ðx� xNb Þ

TB�1N ðx� xNb Þ

þ 1

2

XNi¼1

ðxmoi � xÞT ~OO�1

i ðxmoi � xÞ;

ð5Þ

where xNa is the optimal IC at time tN produced

by 3DVM, xNb ¼ Mti!tN ðx0

b; �Þ is the backgroundat tN with the covariance matrix of backgrounderror BN, the mapped observations xmo

i are lo-cated at tN , produced by mapping the observa-tions xobs

i at ti to the end of the window, the errorcovariance matrix of mapped observation ~OOi isdetermined by

~OOi ¼ Mti!tN ðEi; �Þ �MTti!tN

ðEi; �Þ; ð6Þ

where Ei � ETi ¼ Oi.

Comparing the model state variable x in thecost function of 4DVar (3) with x in the cost func-tion of 3DVM (5), we easily find that the modelstate variable x is no longer expressed implic-itly in (3), but explicitly in (5), and an optimalIC at the time tN can be explicitly calculated asfollowing:

xNa ¼�B�1N þ

XNi¼1

~OO�1i

��1�B�1N xNb þ

XNi¼1

~OO�1i xmo

i

�:

ð7Þ

It is the change of the IC time that makes theadjoint model unneeded any more and the com-puting cost greatly reduced in the 3DVM proce-dure. Furthermore, because the observations arenot at the future time but at the past time of theoptimal IC, 3DVM can be applied to any NWP

operational systems easier than 4DVar.

Initialization and simulation of a landfalling typhoon 271

2.3 MM5_3DVM system

In general, true observations consist of differentkinds of observations with various and irregulardistributions in space and time. How to assimi-late these data using 3DVM becomes the key toevaluating the practicability of the new approachunder the supposition that all variables at themodel degrees of freedom are measured. Here,we use MM5_3DVar system and the predictionmodel adjustment technique to obtain a complete‘‘measured observation’’ xobs

i in (5). In order totest the performance of 3DVM, in this study webriefly construct a MM5_3DVM system basedon the Penn State=NCAR mesoscale modelMM5V1, in which the MM5 4DVar system wasdeveloped by Zou et al (1997). By this method,the irregularly-distributed observations are firstmapped into the regular model grid byMM5_3DVar system. That is

J3DVðxobs�i Þ ¼ minx J3DVðxÞ

J3DVðxÞ ¼1

2ðx� xibÞ

TB�1i ðx� xibÞ

þ 1

2ðHiðxÞ � yobs

i ÞTO�1i ðHiðxÞ � yobs

i Þ

8>>>><>>>>:

ð8Þwhere yobs

i with its error covariance matrix Oi isreal observation irregularly distributes in the as-similation window ½t0; tN �, Hi is an observationoperator, xib is the background field with its errorcovariance matrix Bi.

However, the lack of observational informationat some model grids means that the values of the

increment x0i0 of ðx0i0; x0iobsÞ ¼ xobs�i � x ib obtained

from (8) at these points are zero. The predictionmodel adjustment technique is used to supply thelacking data, namely, some step forward integra-

tions by the prediction model with the IC xobs�i

are performed. That is

ðxnþ1i0 ; xnþ1

iobs Þ ¼ xnþ1i ¼ Mð~xxni ; �Þ

~xxni ¼ ðxni0; xiobsÞ

~xx0i ¼ xobs�

i ¼ ðx0i0; xiobsÞ

8><>: ð9Þ

At each step, the values xniobs of the predictionmodel state variables xni are replaced by the values

xiobs of xobs�i at the model grids where the values

of x0iobs is not zero. In this way, the observationalinformation is transported to those model gridswithout observational information through the dy-

namical and physical constraints of the predictionmodel. When the adjustment kxnþ1

i � xni k is notdescending, all variables at the model degrees offreedom at ti are ‘‘measured’’, and a complete‘‘observation’’ xobs

i is obtained in (9), which meetsthe requirement of the 3DVM supposition.

3. Experimental design

The 3DVM method described in the last sectionis applied to initialization and simulation of a land-falling typhoon – typhoon Dan. Typhoon Dan(9914TC) was initiated over the ocean east ofPhilippines on Oct. 3, 1999. It moved westwardafter its formation as shown in the best track inFig. 1 and intensified rapidly. When Dan enteredSouth China Sea, it moved northward on Oct. 7,and made landfall at Longhai, Fujian on Oct. 9.The maximum surface wind speed was 35 ms�1

and the minimum SLP was 970 hPa when it madelandfall. The strongest winds occurred in the lit-toral province. The storm struck widely the eastof Guangdong, Fujian and Zhejiang provinces,injured more than 500 people, and killed 30 peoplein Fujian province. TY Dan caused economic lossof an estimated 8 billion RMBs in China.

Fig. 1. Observed track (best track map downloaded fromhttp:==agora.ex.nii.ac.jp) of typhoon Dan during the periodfrom 12 UTC 2 Oct. 1999 to 00 UTC 12 Oct. 1999. Thelarge dots indicate the position of the storm at 00 UTC, themiddle dots indicate the position of the storm at 12 UTCand the small dots indicate the 03, 06, 09, 15, 18, 21 UTCstorm positions. The initial time for the numerical simula-tion of typhoon Dan in this study is 00 UTC 6 Oct. 1999

272 Y. Zhao et al

3.1 Vortex specification

The bogused observations for the specified initialvortex consist of only the values of SLP. The bo-gus surface low is specified based on the Fujita’sformula (Fujita, 1952), which is expressed as afunction of r (radial distance from the cyclonecenter) as follows:

PbogusðrÞ ¼ Pc þ�P

�1 �

�1 þ 1

2

�r

R

�2��12�;

r�Rout; ð9Þ

�P ¼ P1 � Pc;

P1 ¼PoutðRoutÞ

�1 þ 1

2

�Rout

R

212 � Pc�

1 þ 12

�Rout

R

212 � 1

; ð10Þ

where Pc is the typhoon’s central pressure, R isthe estimated radius of maximum SLP gradient,and Rout is the radius of the outermost closed iso-bar Pout. The parameters Pc, Pout and Rout arespecified according to the annual tropical cycloneobservational report. R can be determined fromthe radius of the 34-kt wind speed (Park and Zou,2004) or be chosen such that the initial vortexapproximates these characteristics of the actualtyphoon.

At 0000 UTC 06 October 1999, typhoon Danwas located at 18.5� N, 118.9� E with the central

pressure of 970 hPa ðPcÞ and the maximum windspeed of 35 ms�1. The values of PoutðRoutÞ ¼1011 hPa and Rout ¼ 470 km are estimated basedon the NCEP large-scale analysis (Fig. 2). R ischosen to be 90 km.

3.2 Minimization procedure

In this study, the two bogus data assimilationprocedures, one based on 4DVar and the otherwith 3DVM, are carried out in the coarse modeldomain at 36 km resolution with the use of thesame physical processes including bulk planetaryboundary layer, surface fluxes, Kuo-type cumu-lus parameterization.

The cost function in 4DVar system to be mini-mized is written as follows:

JP4DVarðxÞ ¼1

2ðx� x0

bÞTB�1

0 ðx� x0bÞ

þ 1

2

Xti

X�

ðPi � PbogusÞTW

�ðPi � PbogusÞ; ð11Þwhere x0

b is the background analysis from thestandard MM5 analysis field at 0000UTC 06October 1999 with a crudely estimated diagonalerror covariance matrix B0. Pi represents SLP ofthe model atmosphere at time ti, � is a circularhorizontal area surrounding the bogused vortex.The weighting W is treated as constants and de-termined empirically. We takeW ¼ 2:5�10 1=hPa2

for all experiments (corresponding to 0.2 hPa pres-sure error). The gradient check for the 4DVar ismade before the assimilation procedure is applied.

The cost function in 3DVM system is defined as

JP3DVMðxÞ ¼1

2ðx� xNb Þ

TB�1N ðx� xNb Þ

þ 1

2

XNi¼1

ðxmPi � xÞT ~OOiðxmP

i � xÞ; ð12Þ

xmpi ¼ Mti!tN ðxobs

p ; �Þ; ð13Þ

J3DVðxobs�p Þ ¼ minx J3DVðxÞ

J3DVðxÞ ¼1

2ðx� xNb Þ

TB�1N ðx� xNb Þ

þ 1

2ðPN � PbogusÞTWðPN � PbogusÞ

8>>>>><>>>>>:

ð14Þ

where xNb is the background or the first guess atthe end of time window and obtained from the

Fig. 2. Horizontal distribution of sea-level pressure of theNCEP reanalysis at initial time (contour interval: 1 hPa)

Initialization and simulation of a landfalling typhoon 273

standard MM5 analysis field x0b as well, with a

crudely estimated diagonal error covariance ma-trix BN in this study. The mapped observation x

mpi

located at the end of the time window is pro-duced by mapping the ‘‘measured observations’’xobsp located at ti, which is obtained by applying

the algorithm outlined in Sect. 2.3 to the speci-fied surface pressure fields Pbogus. The mappederror ~OOi is simply taken to be the weighting Wused in 4DVar in our application.

3.3 Numerical experiments

In this study, we conducted 7 experiments listedin Table 1 for the 72-h simulation of typhoonDan (1999) using a double nested-mesh MM5.The version we used for this study includes aBurk-Thompson aerodynamic planetary boundarylayer parameterization, Dudhia’s simple ice cloudmicrophysics scheme, dry convective adjustment,and a cumulus parameterization scheme devel-oped by Grell (Grell et al, 1994). The model has15 vertical levels and the model domain is dou-bly nested with horizontal resolutions of 36-kmfor the coarse mesh and 12-km for the fine mesh.The initial and lateral boundary conditions areobtained from the NCEP global reanalysis data(2.5� resolution). The typhoon variational initiali-zation is carried out on the coarse mesh domain.The initial condition for the fine mesh domain isinterpolated from the coarse mesh domain.

CTRL is the control experiment, which is initi-alized with the MM5 analysis without any varia-tional data assimilation. This experiment serves asa benchmark to demonstrate how the variationaldata assimilation improves the typhoon forecast.BDA2m, BDA10m and BDA30m are experimentsstarting from initial conditions obtained by the

4DVar scheme over a 2-min, 10-min or 30-minassimilation window in Eq. (11). BMDA2m,BMDA10m and BMDA30m are experimentsstarting from initial conditions obtained by the3DVM scheme over a 2-min, 10-min or 30-min as-similation window in Eq. (12). The bogused SLP

Pbogus for the BDA scheme and the ‘‘measuredobservations’’ xobs

p for the BMDA scheme is re-peatedly incorporated into MM5. Summationover ti is carried out over 2-min or 10-min win-dows at every 1 min, over 30-min windows atevery 3 min. These experiments are designed totest the prediction skill of MM5 with differentvariational initialization schemes and the sensitiv-ity of typhoon forecast to the size of data assim-ilation window.

4. Track and intensity

There are many factors that affect typhoon motionand intensity. Initial typhoon vortex structure,such as the vortex size (Xiao et al, 2000a), bothhorizontal and vertical structures (Leslie andHolland, 1995; Wang, 1998), and the asymmetricstructure (Ueno, 1995), have significant effects onboth motion and intensity. In this section, we willdiscuss the influence of the size of the assimila-tion time window upon the prediction of trackand intensity of typhoon Dan from the fine meshwith horizontal resolution of 12-km.

The model track and its error at 6-h intervalsfor the entire forecast period are given in Fig. 3with the observed best track, central SLP, and themaximum surface wind from China Meteorologi-cal Administration (1999) as the reference. With acold start without any observed data being as-similated into the initial condition, CTRL failsto capture the initial location, which results in a

Table 1. Summary of numerical experiments

Numericalexperiment

Observationdata

Assimilation time window(Y_M_D-hm!D-hm)

Model initial conditionsat 1999_10_06-00

CTRL NCEP analysisBDA2m 1999_10_06-0000! 06-0002BDA10m Pbogus 1999_10_06-0000! 06-0010 4DVar analysisBDA30m 1999_10_06-0000! 06-0030

BMDA2m 1999_10_05-2358! 06-0000BMDA10m xobs

p 1999_10_05-2350! 06-0000 3DVM analysisBMDA30m 1999_10_05-2330! 06-0000

274 Y. Zhao et al

mean track error of about 259 km in 72-h fore-cast (Table 2) and a delay in landfall with theposition error of about 385 km (Fig. 3b). Otherexperiments with addition of bogus SLP infor-mation by using different initialization methods

improve the prediction of the track and intensityto various extents compared with the CTRL ex-periment. Moreover, the 3DVM experiments im-prove the track simulation more significantlythan the 4DVar experiments. The best track fore-cast is made by the BMDA30m experiment, inwhich the mean track error is greatly reduced to133 km for 72 h integration, and the landfall posi-tion is closer to the observed. Furthermore, thetrack simulation in BDA is more sensitive to thesize of the assimilation window and the densityof the incorporated bogus data than that in theBMDA.

Figure 4 depicts the time evolution of the cen-tral SLP and the maximum wind at the lowestmodel level at 6-h intervals. The simulatedtyphoon intensity in BMDA30m is very simi-lar to that in BDA30m except for the first 6 h.However, the intensity forecast from BDA2mand BDA10m is not as accurate as that from thecorresponding experiments based on 3DVM.Figure 5 shows the first 9 h evolution of the simu-lated center pressure. Three BMDA experimentsall develop strong typhoons with the central SLP

of lower than 970 hPa although their initial cen-tral SLP is about 979 hPa. In contrast, the centralSLP from three BDA experiments increases toabove 975 hPa although the initial central SLP

is about 971 hPa, very close to the observation.Furthermore, the spinup time of the model vortexis about 1 h in 3DVM, while it is 3 h, 2 h, and 5 hin BDA2m, BDA10m, and BDA30m, respectively.These results indicate that the predicted typhoonintensity, including the initial spinup, with BDA

initialization is more sensitive to the size ofassimilation window than that with BMDA initi-alization. In addition, BMDA30m took only 1=9of the computation time of that of BDA30m forthe same initialization with the same bogus data(Table 2). In this sense, the 3DVM might beprior to 4DVar in application to NWP operationsystem.

Table 2. Mean error of typhoon initial central SLP and mean position error of the simulated track from all the experiments

CTRL BDA2m BDA10m BDA30m BMDA2m BMDA10m BMDA30m

Mean PSLV-error (hPa) 41.8 30.5 31.5 22.6 26.2 28.3 23.7Mean track-error (km) 259 190 199 175 146 135 133Computer costof initialization (min)

120 292 878 90 90 91

Fig. 3a. Track of typhoon Dan for the entire 72-h fore-cast period from 00 UTC 6 to 00 UTC 9 October of 1999.The positions of the storm center are given every 6 h.(b) The track position error (km) at 6-h interval in the72-h forecast

Initialization and simulation of a landfalling typhoon 275

5. Structure

5.1 Initial structure

Based on the NCEP reanalysis, the standardMM5 analysis of typhoon Dan gives a weak

vortex with a central SLP of 1008 hPa at the ini-tial time. After BDA, the horizontal distributionof sea-level pressure shows a very smooth vortex(Fig. 6a). However, after BMDA, the horizontaldistribution of sea-level pressure shows a moreintense vortex, especially in the inner core regionof the model typhoon, and a similar pattern in theouter region (Fig. 6b). The radius of maximumSLP gradient is about 90 km as specified. TheBDA scheme assimilates the bogus SLP datadirectly and maintains the initial SLP pressureof the bogus vortex well, while the pressureperturbation above the surface layer has littlechange (Fig. 7a). The BMDA scheme assimilatesthe mapped observation measured by the bogus

Fig. 4. 72-h variations of center sea-level pressure (hPa) (a),and maximum low-level wind speed (m s�1) (b) at 6-h interval

Fig. 5. Time evolution of the simulated typhoon center sea-level pressure (hPa) during the first 9 h of the simulation

Fig. 6. Horizontal distribution of sea-level pressure (SLP)at initial time for (a) BDA30m and (b), BMDA30m.Contour interval for SLP is 3 hPa

276 Y. Zhao et al

SLP data and produces the initial central SLP

of 980 hPa. In contrast to BDA, BMDA generatesnegative pressure perturbation up to the middletroposphere, as seen from the perturbation pres-sure difference in the west-east cross-section be-tween the BMDA30m and CTRL at initial timegiven in Fig. 7b. This indicates that BMDA pro-duces a deeper and more coherent initial vortexthan BDA.

Figure 8 shows the west-east cross-sectionof temperature and humidity fields through the

typhoon center before and after the initializationin experiments BDA30m and BMDA30m. It canbe seen that the NCEP analysis (Fig. 8a1 and a2)shows a quite uniform horizontal distribution intemperature and humidity above the typhoon andthus could not resolve the structure that a maturetyphoon would have. This is mainly due to thefact that there are few or even no radiosonde ob-servations in the typhoon circulation over theopen ocean and thus temperature and humidityanomalies associated with the typhoon could notbe captured in the global analysis. After BDA

or BMDA, temperature and humidity fields inthe typhoon area are modified greatly with a‘‘M’’ shaped structure in specific humidity. Notethat the shading shows the increments of tem-perature and specific humidity in the BDA anal-ysis (Fig. 8b1 and b2) or the BMDA analysis(Fig. 8c1 and c2) from the NCEP analyses. Withthe BMDA procedure, temperature is increasedby as large as about 10 �C near 300 hPa, showinga realistic warm core structure of the model ty-phoon (Fig. 8c1), the maximum increase in spe-cific humidity occurs in the low troposphereabove the typhoon center with a 6 g kg�1 increasenear 750 hPa (Fig. 8c2). With the BDA proce-dure, temperature is increased in the lower tropo-sphere with a maximum temperature anomaly ofabout 11 �C at near 650 hPa (Fig. 8b1), showing atoo low warm core structure. This unrealistic lowwarm core corresponds to the very shallow per-turbation pressure as shown in Fig. 7a. The in-crease in specific humidity in BDA occurs onlyin the lower troposphere above the typhoon cen-ter with a maximum increase of 2 g kg�1 at about950 hPa (Fig. 8c2). The above results demonstratethat the initial structure of the model typhoon ob-tained from the BMDA scheme is more realisticthan that from the BDA scheme. This also ex-plains why the spinup time of model typhoonin the 3DVM BMDA is shorter than that in the4DVar BDA as indicated in Sect. 4.

5.2 Simulated structure

Figure 9 shows the horizontal distributions ofSLP from BDA30m and BMDA30m, respective-ly, after 6 h simulation. The SLP in BMDA fills ra-pidly in the central core region and slowly in theouter region but it possesses a horizontal distribu-tion very similar to initial fields (Figs. 6b and 9b).

Fig. 7. Cross-section of the adjustment of the initial pres-sure perturbation �PP derived from the experiment (a)BDA30m or (b) BMDA30m to NCEP (CTRL). Contourinterval for �PP is 1 hPa

Initialization and simulation of a landfalling typhoon 277

Fig. 8. Cross-section of (a1) temperature and (a2) specific humidity above typhoon Dan before variational initialization(CTRL), cross-section of (b1) temperature (solid line) and its increments (�C, shading), and (b2) specific humidity (solid line)and its increments (g kg�1, shading), above typhoon Dan after 4DVar initialization (BDA30m), and cross-section of (c1)temperature (solid line) and its increments (�C, shading), and (c2) specific humidity (solid line) and its increments (g kg�1,shading), above typhoon Dan after 3DVM initialization (BMDA30m), at initial time. Contour interval for (a1), (b1) and (c1)is 3 �C. Contour interval for (a2), (b2) and (c2) is 2 g kg�1

278 Y. Zhao et al

Much larger adjustment in SLP fields occursin BDA during the first 6 h simulation (Figs. 6aand 9a). This adjustment reflects an imbalancein mass and wind fields in the initial conditionsbased on 4DVar BDA. A detailed analysis of suchan adjustment process has been recently discussedby Wu et al (2006) to some extent. Interestingly,although the initial vortex is much stronger inBDA, the model typhoon becomes very similar inintensity to that in BMDA after 6 h adjustment.This is also true for the vertical structure of

perturbation pressure throughout the troposphereas seen from the difference fields betweenBMDA30m and CTRL, BDA30m and CTRL,respectively, after 6 h simulation (Fig. 10).

The vertical cross-sections of the vertical ve-locity indicate obviously that the typhoon eyeand the eyewall are well developed after 6 hintegration in both BDA30m and BMDA30m(Fig. 11a, b), with descending near the center andascending motion in the eyewall throughout theentire layers of the model atmosphere. Figure 12

Fig. 9. Horizontal distribution of SLP at 6 h time for (a)BDA30m, and (b) BMDA30m. Contour interval for SLP is3 hPa

Fig. 10. Cross-section of the adjustment of the predictedPressure perturbation �PP derived from the experiment (a)BDA30m, or (b) BMDA30m to CTRL at 6 h. Contour in-terval for �PP is 1 hPa

Initialization and simulation of a landfalling typhoon 279

shows the cross-sections of the simulated temper-ature and humidity fields (contours) and the ad-justment from the CTRL experiment in BDA30mand BMDA30m after 6 h simulation. BMDA30mproduces a larger, warmer, and moister core oftyphoon Dan than BDA30m. The temperatureincrease between BDA30m and CTRL reachesabout 5 �C between 850 and 650 hPa (Fig. 12a1),the increase in specific humidity occurs in thelower troposphere above the typhoon center witha maximum increase of 4 g kg�1 near 800 hPa(Fig. 12a2). The temperature increase betweenBMDA30m and CTRL occurs in middle tropo-sphere and reaches a maximum of about 6 �C

at near 600 hPa (Fig. 12b1), and the increase inspecific humidity occurs in the lower tropospherewith a maximum increase of 4 g kg�1 near 850 hPa(Fig. 12b2). Compared with the initial conditions,more significant adjustment occurs in BDA thanin BMDA during the first 6 h simulation. Thisindicates that the evolution of storm structuresfrom BMDA scheme is more consistent with theforecast model than that from BDA scheme.

6. Conclusions

One of the challenging tasks in the operationalnumerical prediction of tropical cyclones is howto design a timesaving and efficient variationaldata assimilation system. In this study, an attempthas been made to apply the 3DVM methodto MM5 and to construct a new 3DVM_MM5system. The system is tested within the frame-work of bogus data assimilation (BDA) with3DVM, namely BDMA, which is compared withthe original 4DVar BDA in MM5 for the initiali-zation and simulation of typhoon Dan (1999).Tests are also made to examine the sensitivity tothe size of assimilation time window. The mostimportant results are summarized as follows:

(1) 3DVM produces the optimal initial conditionat the end of the assimilation window, so that3DVM without the need of an adjoint tech-nique requires much less computational timethan 4DVar. The CPU time of initializationusing BMDA30m is only about 1=9 of thatusing BDA30m;

(2) BMDA scheme uses the typhoon forecastmodel mapping the observed information for-ward to the end of the window, while BDA

scheme uses the adjoint model mapping theobserved information backward to the begin-ning of the window. The results show that theBDA scheme is more sensitive to the size ofassimilation window with the use of the bogusSLP field than the BMDA scheme;

(3) Compared with the available 4DVar in MM5,3DVM produces an optimal initial conditionthat is more consistent with the forecastmodel due to the inclusion of dynamical andphysical constraints of the forecast modeland fits better the observations in the assim-ilation window through the model solutiontrajectory.

Fig. 11. Cross-section of vertical velocity predicted byBDA30m (a), or BMDA30m (b) at 6 h. Contour intervalis 30 cm s�1

280 Y. Zhao et al

(4) The variational initialization experimentsshow that precise typhoon initial structureis critical to the typhoon track and intensityforecasts. BDA and BMDA techniques havedifferent skills in recovering typhoon struc-ture. The BMDA based on 3DVM performsbetter in the track and intensity simulation oftyphoon Dan than the BDA based on 4DVar.

This study is only a step toward improved dataassimilation for typhoon initialization in the fra-mework of bogus data assimilation. To describethe new method, we have only performed a casestudy for a landfalling typhoon in this paper.With the encouraging results herein, we plan toapply the BMDA scheme constructed and tested

in this study to a large number of typhoon casesover the western North Pacific to allow a sys-tematic evaluation of the performance of the newscheme. There are still rooms for further improve-ments of the BMDA scheme presented in thispaper. For example, how to consider the asym-metric structure of the initial bogus vortex andthe initial vortex motion into the new BDMA willbe a topic for future investigation. Another topicfor the general application of the new 3DVMapproach is to use the method to assimilate ob-servations from remote sensing and in-situ mea-surements into high-resolution numerical weatherprediction models to improve the prediction oftropical cyclones and torrential rainfall.

Fig. 12. Cross-section of the predicted temperature (solid line) and its adjustment (�C, shading) from the experiment (a1)BDA30m or (b1) BMDA30m to CTRL at 6 h. Cross-section of the specific humidity (solid line) and its adjustment (g kg�1,shading) from the experiment (a2) BDA30m or (b2) BMDA30m to CTRL at 6 h. Contour interval for (a1) and (b1) is 3 �C.Contour interval for (a2) and (b2) is 2 g kg�1

Initialization and simulation of a landfalling typhoon 281

Acknowledgments

This work was supported by the China National Key Devel-opment Planning Project for Basic Research (Abbreviation:973 Project, Grant No. 2005CB321703), and ChineseAcademy of Sciences for an innovation research project‘‘Application of nonlinear optimum method to studies ofweather and climate predictabilities’’ (Grant No. KZCX3-SW-230). YW has been supported in part by the US Officeof Naval Research grant 000-14-94-1-0493 and in part by theJAMSTEC through its sponsorship of the InternationalPacific Research Center (IPRC) in School of Ocean andEarth Science and Technology (SOEST) at the Universityof Hawaii at Manoa. Numerical experiments were completedon the LASG cluster 1800 computer system.

References

Bouttier F, Rabier F (1997) The operational implementationof 4D-Var. ECMWF Newsletter 78: 2–5

China Meteorological Administration (1999) Tropicalcyclone annals observational report. Beijing: WeatherPress

Courtier P, Thepaut J-N, Hollingsworth A (1994) A strategyfor operational implementation of 4D-Var using an incre-mental approach. Quart J Roy Met Soc 120: 1367–1388

Daley R (1991) Atmospheric data analysis. Cambridge:Cambridge University Press, 457 pp

Derber JC (1989) A variational continuous assimilationtechnique. Mon Wea Rev 117: 2437–2446

Fujita T (1952) Pressure distribution within a typhoon.Grophys Mag 23: 437–451

Grell GA, Dudhia J, Stauffer DR (1994) A description of thefifth generation Penn State=NCAR mesoscale model(MM5). NCAR Tech Note NCAR=TN-3981STR, 138 pp

Le Dimet F-X, Talagrand O (1986) Variational algorithmsfor analysis and assimilation of meteorological observa-tions: Theoretical aspects. Tellus 38A: 97–110

Leslie LM, Holland GJ (1995) On the bogussing of tropicalcyclones in numerical models: A comparison of vortexprofiles. Meteorol Atmos Phys 56: 101–110

Lewis JM, Derber JC (1985) The use of adjoint equations tosolve a variational adjustment problem with advectiveconstraints. Tellus 37A: 309–322

Navon IM, Zou X, Derber J, Sela J (1992) Variational dataassimilation with an adiabatic version of the NMC spec-tral model. Mon Wea Rev 120: 1433–1446

Park K, Zou X (2004) Toward developing an objective4DVAR BDA scheme for hurricane initialization basedon TPC observed parameters. Mon Wea Rev 132:2054–2069

Pu Z-X, Tao W-K, Braun S, Simpson J, Jia Y, Halverson H,Olson W, Hou A (2002) The impact of TRMM data onmesoscale numerical simulation of supertyphoon Paka.Mon Wea Rev 130: 2448–2458

Thepaut J-N, Hoffman RN, Courtier P (1993) Interactions ofdynamics and observations in a 4-dimensional variationalassimilation. Mon Wea Rev 121: 3393–3414

Ueno M (1995) A Study on the impact of asymmetriccomponents around tropical cyclone center on the accu-racy of bogus data and the track forecast. Meteorol AtmosPhys 56: 125–134

Wang Y (1998) On the bogusing of tropical cyclones innumerical models: the influence of vertical structure.Meteorol Atmos Phys 65: 153–170

Wang B, Zhao Y (2006) A new data assimilation approach.ACTA Meteorol Sinica 20(3): 275–282

Wang B, Zou X, Zhu J (2000) Data assimilation and its ap-plications. Proc Natl Acad Sci USA 97: 11143–11144

Wu C-C, Chou K-H, Wang Y, Kuo Y-H (2006) Tropicalcyclone initialization and prediction based on four-dimensional variational data assimilation. J Atmos Sci63: 2383–2395

Xiao Q, Zou X, Wang B (2000a) Initialization and simula-tion of a landfalling Hurricane using a variational bogusdata assimilation scheme. Mon Wea Rev 128: 2252–2269

Xiao Q, Zou X, Kuo Y-H (2000b) Incorporating the SSM=Iderived precipitable water and rainfall rate into a numer-ical model: a case study for ERICA IOP-4 cyclone. MonWea Rev 128: 87–108

Xiao Q, Zou X, Pondeca M (2002) Impact of GMS-5 andGOES-9 satellite-derived winds on the prediction ofa NORPEX extratropical cyclone. Mon Wea Rev 130:507–528

Zhang X-Y, Wang B, Ji Z (2003) Initializations and sim-ulation of a typhoon using 4-dimensional variational dataassimilation-research on typhoon Herb (1996). AdvAtmos Sci 20: 612–622

Zhao Y, Wang B, et al (2005) Improved track forecasting ofa typhoon reaching landfall from four-dimensional va-riational data assimilation of AMSU-A retrieved data.J Geophys Res 110: D14101

Zou X, Qingnong X (1999) Studies on the initialization andsimulation of a mature hurricane using a variational bogusdata assimilation scheme. J Atmos Sci 57(6): 836–860

Zou X, Kuo Y-H, Guo Y-R (1995) Assimilation of atmo-spheric radio refractivity using a nonhydrostatic adjointmodel. Mon Wea Rev 123: 2229–2249

Zou X, Vandenberghe F, Pondeca M, Kuo Y-H (1997)Introduction to adjoint techniques and the MM5 adjointmodeling system, NCAR Technical Note, NCAR=TN-435-STR, National Center for Atmospheric Research,Boulder, CO, 110 pp

Zou X, Xiao A, Lipton AE, Modica GD (2001) A numericalstudy of the effect of GOES sounder cloud-cleared bright-ness temperatures on the prediction of hurricane Felix.J Appl Meteor 40: 34–55

Zupanski M (1993) Regional 4-dimensional variational dataassimilation in a quasi-operational forecasting environ-ment. Mon Wea Rev 121: 2396–2408

Corresponding author’s address: Ying Zhao, State KeyLaboratory of Numerical Modeling for AtmosphericSciences and Geophysical Fluid Dynamics, Institute ofAtmospheric Physics, Chinese Academy of Sciences, Beijing,China (E-mail: zhaoy@mail.iap.ac.cn)

282 Y. Zhao et al: Initialization and simulation of a landfalling typhoon