Digital filter initialization for MM5

Digital Filter Initialization for MM5

MIN CHEN

Institute of Urban Meteorology, CMA, Beijing, China

XIANG-YU HUANG*

National Center for Atmospheric Research,� Boulder, Colorado

(Manuscript received 11 October 2004, in final form 15 July 2005)

ABSTRACT

In this paper several configurations of the fifth-generation Pennsylvania State University–National Cen-ter for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5), which is implemented at BeijingInstitute of Urban Meteorology in China, are used to demonstrate the initial noise problem caused eitherby interpolating global model fields onto an MM5 grid or by using MM5 objective analysis schemes. Animplementation of a digital filter initialization (DFI) package to MM5 is then documented. A heavy raincase study and intermittent data assimilation experiments are used to assess the impact of DFI on MM5forecasts. It is shown that DFI effectively filters out the noise and produces a balanced initial model state.It is also shown that DFI improves the spinup aspects for precipitation, leading to better scores forshort-range precipitation forecasts. The issues related to the initialization of variables that are not observedand/or analyzed, in particular those for nonhydrostatic quantities, are discussed.

1. Introduction

The fifth-generation Pennsylvania State University–National Center for Atmospheric Research MesoscaleModel (MM5) (Dudhia 1993) has been widely usedboth in the research community and at operational cen-ters. The initial model state for MM5 can be obtained inseveral ways. In most research applications, analysesfrom global models or large-scale models are interpo-lated onto the MM5 model grid to create the initialmodel states (e.g., Dudhia 1993). Operationally ori-ented applications of MM5 often involve observationsbefore launching a forecast. There are two types ofanalysis that assimilate observations into the model:continuous and intermittent (Daley 1991). The four-

dimensional data assimilation (FDDA) approach(Grell et al. 1994) is a continuous scheme nudging ob-servations into the MM5. Intermittent data assimilationschemes for MM5 include the Cressman scheme (Ben-jamin and Seaman 1985), the three-dimensional varia-tional data assimilation (3DVAR) scheme (Barker etal. 2004), and the four-dimensional variational data as-similation (4DVAR) scheme (Zou and Kuo 1996).

As the model is used as a constraint of data assimi-lation, FDDA and 4DVAR for MM5 can generate ini-tial model states that are consistent with the model dy-namics. The interpolation and the three-dimensionalschemes, however, unavoidably introduce imbalancesbetween mass and wind fields to the initial states. Theuse of high-resolution orography together with the in-terpolated model fields could lead to further imbal-ances. In the MM5 model integrations, the imbalancestrigger spurious high-frequency oscillations, consideredas “noise,” which may cause numerical instabilities andforecast failures. They are detrimental for data assimi-lation systems with rapid update cycles, because a noisyshort-range forecast against which new observationsare checked would lead to rejection of good observa-tions. There are also MM5 variables such as cloudwater, rainwater, and vertical velocity that are difficult

* Additional affiliation: Danish Meteorological Institute,Copenhagen, Denmark.

� The National Center for Atmospheric Research is sponsoredby the National Science Foundation.

Corresponding author address: Min Chen, Institute of UrbanMeteorology, CMA, Beiwaxili 55, Haidian District, 100089Beijing, China.E-mail: [email protected]

1222 M O N T H L Y W E A T H E R R E V I E W VOLUME 134

© 2006 American Meteorological Society

MWR3117

to be initialized by the interpolation or by the currentlyavailable analysis schemes.

There is evidence that an initialization procedure forMM5 should be beneficial, especially when the initialstates for MM5 are from a large-scale model interpo-lated to the MM5 grid or from an objective analysisscheme like 3DVAR. For example, the initial imbal-ance and rapid model adjustment excite acoustic andgravity waves that last several hours in the model inte-grations (Manning et al. 2002). Filtering the optimalinitial condition at the end of an MM5 4DVAR mayreduce the noise by 20% (De Pondeca and Zou 2001).Introducing a digital filter as a weak constraint into theMM5 4DVAR is shown to improve the observationhandling, the minimization convergence, and the as-similation quality (Wee and Kuo 2004).

In this study, several configurations of MM5 (version3.6.1), as implemented on the SGI ORIGIN2000 at theBeijing Institute of Urban Meteorology (IUM), areused (section 2). The current IUM operational setup isused to determine the noise characteristics caused byinterpolations and objective analyses (section 3). Thena digital filter initialization (DFI) package is imple-mented in MM5 (section 4). A heavy rain case is chosento demonstrate how DFI filters out the noise and im-proves the dynamic consistency of the model fields, forexample, vertical velocity and pressure perturbation,which are not analyzed or interpolated from the globalforecasts (section 5). Intermittent cycling data assimi-lation experiments using the same framework are thenpresented and discussed (section 6). Concluding re-marks are given in the end (section 7).

2. MM5 at IUM

The first mesoscale numerical forecasting systembased on MM5, version 2, was implemented at IUM in1997. It became operational in 1999. The current op-erational configuration is based on MM5, version 3.6.1.Preoperational tests started in 2000, and it became op-erational in July 2004.

In the IUM standard configuration, MM5 runs onthree domains with horizontal resolutions of 27, 9, and3 km, all having 37 vertical levels. The model domainsand terrain height for domain 1 are shown in Fig. 1. Themodel grid points for the three domains are 151 � 151� 37, 142 � 184 � 37, and 172 � 199 � 37, and the timesteps for each domain are 80, 27, and 9 s, respectively.Simple but full model physics schemes are used:Blackadar PBL (Blackadar 1976), Grell cumulus pa-rameterization (Grell et al. 1991), Dudhia radiation(Dudhia 1989), simple ice microphysics (Dudhia 1989),and five-layer soil scheme (Dudhia 1996).

The current IUM operational setup runs in a so-called cold-start fashion. Two operational runs at 0000and 1200 UTC are carried out each day. For every run,the background fields are obtained by interpolating theT213 global model forecasts of the National Meteoro-logical Center of the China Meteorological Administra-tion (NMC/CMA) to the MM5 grids. Conventionaldata are collected from the Global TelecommunicationSystem and the IUM local network. A series of qualitycontrols, including vertical check, error-max check, andbuddy check (Dudhia et al. 2000), are performed beforethe observations are assimilated. A modified Cressmanscheme, which includes noncircular influence functions(Benjamin and Seaman 1985), is used to combine thebackground fields and the observations. The resultinganalyses are used directly as initial model states to startthe operational MM5 forecasts.

The next IUM operational setup will run in data as-similation cycles, using its own short-range forecastsfrom previous cycles as background for analyses. Boththe Cressman scheme and the MM5 3DVAR (Barkeret al. 2004) are under evaluation. The main features ofMM5 3DVAR include (Barker et al. 2004) the follow-ing:

1) quasi-Newton minimization algorithm developed atArgonne National Laboratory,

2) analysis increments on an unstaggered Arakawa Agrid (The input background wind fields for 3DVARare interpolated from an Arakawa B grid used bythe MM5 forecast model. The unstaggered analysiswind increments need to be interpolated back to theArakawa B grid before being used to initialize aforecast.),

3) analysis performed on the nonhydrostatic modelsigma-height levels of MM5,

4) preconditioned control variables using streamfunc-tion, velocity potential, unbalanced pressure, andspecific/relative humidity, and

5) linearized mass–wind balance (including both geo-strophic and cyclostrophic terms) used to define abalanced pressure.

As in the cold-start cycles, the analyses are used di-rectly as initial model states to start the MM5 forecasts.To enable an easy comparison with the current opera-tional setup, 12-h cycles are used at the moment, withthe analysis performed also at 0000 and 1200 UTC. Thegoal for the next operational setup is to run rapid up-date cycles with 3-h cycling or even 1-h cycling (Ben-jamin et al. 2004a). All of the experiments in this paperare performed under the operational framework as de-scribed above.

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3. Initial noise

The mean absolute surface pressure tendency N, de-fined as

N �1IJ �i�1

I

�j�1

J ��ps

�t �ij,where ps is the surface pressure and the summationdenotes calculation over the whole model domain, is a

characteristic quantity that reflects directly the overallbalance of the model states (Lynch and Huang 1992).

Investigation on N in the operational database re-veals severe imbalances in the first 6–12 h of the fore-casts. As an example, a few MM5 24-h forecasts of theoutermost domain (D01) starting from 1200 UTC 21August 2002 are selected. All of these experiments usean identical 12-h forecast from the previous data assimi-lation cycle as their first guess against which the experi-

FIG. 1. (a) Model domains (D01, D02, and D03) and (b) D01 terrain height (m) used inthe operational setup at the Beijing Institute of Urban Meteorology in 2004.


ment named as NODFI-3DVAR uses MM5/3DVARand NODFI-CRSM uses the Cressman method fortheir analyses, respectively. To set a reference of a“noise free” level of N, we made a forecast, denotedNODFI-BG, with its initial condition directly from theprevious cycle’s 12-h forecast and without any analysisprocedure involved.

The evolutions of N from these MM5 forecasts areshown in Fig. 2. It is clear that the initial noise levelusing 3DVAR analysis is much lower than that usingCressman analysis. One possible reason is the analysisgenerated by 3DVAR would intrinsically have betterbalance than Cressman analysis, as balance (i.e., weakgeostrophic, hydrostatic) constraints are built into thepreconditioning of the cost-function minimization(Barker et al. 2004).

To isolate the noise introduced by vertical interpola-tion between � and pressure levels, we have made an-other run denoted as NODFI-VINT, whose initialmodel state is obtained by first interpolating theNODFI-BG’s noise-free initial state to pressure levels,then interpolating it back to model � levels. No analysisis involved in NODFI-VINT. From Fig. 2, NODFI-VINT has the similar noise level as NODFI-3DVAR,suggesting that severe noise would be introduced to thenoise-free model state, even if the coordinate transfor-mation between � and pressure levels is the only pro-cedure to be considered. For the Cressman scheme andother analysis methods performed on pressure levels,this part of the noise would be as significant as thatbrought by analysis.

To explore the noise problem of cold-start runs with-out any analysis, an extra experiment of NODFI-GTOM is designed. The initial state of NODFI-GTOMis interpolated from the T213 global analysis at 1200UTC 21 August 2002 instead of the forecast of the pre-vious cycle. It is clearly shown in Fig. 2 that NODFI-GTOM has the highest initial noise level.

Another way to demonstrate the imbalances of theinitial conditions is to use maps of the initial surfacepressure tendencies. For a noise-free model state, asshown in Fig. 3a, the initial surface pressure tendenciesare below 3 hPa (3 h)�1 over most model points. Thevisible small-scale pressure tendency centers are relatedto weather systems. The differences between Figs. 3band 3a indicate that significant noise is generated whenthe analysis procedure combines observations and thefirst guess. For NODFI-3DVAR the maximum/minimum initial surface pressure tendencies’ centersseem to relate to sounding stations, suggesting thatmost of the initial noise is generated by 3DVAR. Butfor NODFI-VINT (Fig. 3c), obvious orographic fea-tures can be identified from the initial surface pressure

tendencies of NODFI-VINT, which could be a reflec-tion of terrain height as a factor of surface pressurecalculation (Grell et al. 1994).

For the Cressman scheme in MM5, analysis and thevertical interpolation between � and pressure levels arethe two major procedures responsible for the genera-tion of noise. As shown in Fig. 3d, a gross pattern oforography and minimum/maximum centers related tosounding stations can be identified.

The interpolation from a large-scale model to theMM5 grid generates noise through horizontal interpo-lation, grid changes (e.g., A grid to B grid), verticalinterpolation, and adjustment of the model fields to thenew high-resolution orography. From Fig. 3e it is evi-dent that the vertical interpolation and orography havethe main contribution.

4. Digital filter initialization

It is evident from the previous section that an initial-ization scheme for MM5 is desirable if its initial modelstates are produced by interpolating large-scale modelanalysis to the MM5 grid or by using a three-dimensional analysis (the Cressman scheme or theMM5/3DVAR). There are many initialization schemes,including dynamic initialization (Miyakoda and Moyer1968), nonlinear normal-mode initialization (Machen-hauer 1977), and DFI (Lynch and Huang 1992), that allcould be considered for MM5 implementations.

In this study, DFI is chosen for its simplicity and

FIG. 2. The 12-h evolutions of the mean absolute surface pres-sure tendency N [hPa (3 h)�1] of five MM5 forecasts, all started at1200 UTC 21 Aug 2002.


FIG. 3. (a) The initial surface pressure tendency for NODFI-BGat 1200 UTC 21 Aug 2002. The contour interval is 3 hPa (3 h)�1.(b) Same as in (a), but for NODFI-3DVAR. The contour intervalis 10 hPa (3 h)�1. In addition to the pressure tendency, the distri-bution of the sounding stations used by 3DVAR analysis is alsoshown. (c) Same as in (a), but for NODFI-VINT. The contourinterval is 20 hPa (3 h)�1. (d) Same as in (c), but for NODFI-CRSM. (e) Same as in (c), but for NODFI-GTOM. Positive con-tours are solid, negative contours are dashed, and the zero contouris suppressed.


flexibility. A thorough review on the DFI theory anddifferent applications was given by Huang and Yang(2002). Following the review we have made a diabaticDFI (DDFI) implementation for MM5. The Dolph fil-ter (Lynch 1997) has been chosen for all the experi-ments presented in this paper. The details of DDFI andthe Dolph filter can be found in Huang and Lynch(1993) and Lynch (1997).

5. A case study

The heavy rain case chosen for the demonstration isa local torrential rainfall incident that occurred in thelate afternoon of 1 August 2002. It was caused by twomeso-�-scale convective systems developed in Miyun, anortheast county of Beijing, China. The total accumu-lated precipitation in Miyun County (40.58°N,116.85°E) during 6 h reached 280.2 mm, which causedsevere mud-rock flow, flooding, and loss of lives.

A number of simple cold-start runs of the outermostdomain (D01) with different DFI configurations havebeen performed. In Table 1, a summary of the testedinitialization schemes is given. NODFI-CRSM is thecontrol experiment without any initialization proce-dure. DFI-CRSM is the corresponding DFI experimentwith 2-h time span. DFI4H-CRSM uses a longer filterspan. NODFI-GTOM and DFI-GTOM are designedwith the initial conditions directly from the interpolatedglobal analysis to the MM5 27-km grid without anyobjective analysis involved, one without initializationand the other with DFI. All of the DFI experiments usethe Dolph filter and a 1-h stop-band edge period. Thefilter spans are given in Table 1.

a. Noise level

As shown in Fig. 4, all DFI schemes successfully re-duce the spurious high-frequency oscillations to a rea-sonable level. After 12-h integration the time series ofall initialized forecasts converge toward that ofNODFI-CRSM. Because of the lack of analysis,NODFI-GTOM has a lower noise level than NODFI-CRSM and DFI-GTOM has a slightly different asymp-

totic value than that of DFI-CRSM and DFI4H-CRSM.DFI4H-CRSM may bring a little more filtering effectsthan DFI-CRSM at the cost of doubling computationalexpense for backward and forward integrations withlonger filtering time span. If the noise control is not theonly concern, DFI-CRSM should be preferred.

b. Moist spinup features

The spinup feature of moisture fields is another im-portant factor that needs to be considered when evalu-ating the impact of an initialization scheme. Huang andSundqvist (1993) demonstrated that as full physical pro-cesses are incorporated in the forward filtering proce-dure, unanalyzed hydrometeor fields could be pro-duced at the initial time. Accordingly, spinup effectscould be reduced.

In Fig. 5, time series of the domain-averaged precipi-tation rate R are compared. For NODFI, R is shown tostart from nearly 0 and increase rapidly during the fol-lowing 3-h integration. For the DFI-CRSM test, spinupproblems seem to be alleviated as R values are im-proved to the value greater than 4 mm day�1 at theinitial time, and then increase gradually in the followingintegrations. It is quite evident that the spinup processhas not been completed during the forward diabaticDFI integration, because R still increases at the earlystage of the forecast. DFI4H-CRSM has a larger initialprecipitation rate of 7 mm day�1, indicating that whenfilter span is longer, the spinup process starts earlier

TABLE 1. List of runs for the case study.

Expt InitializationFilter

span (h)Filtertype Analysis

NODFI-CRSM None — — CressmanDFI-CRSM DFI 2 Dolph CressmanDFI4H-CRSM DFI 4 Dolph CressmanNODFI-GTOM None — — NoneDFI-GTOM DFI 2 Dolph None

FIG. 4. The evolution of the mean absolute surface pressuretendency N [hPa (3 h)�1] of MM5 forecasts, all started from 0000UTC 1 Aug 2002.


during the forward integration of DFI, leading to ashorter spinup process after initialization.

c. Changes made by DFI to the model fields

A requirement of any initialization procedure is thatthe changes made by the procedure are acceptablysmall. In general, they should be smaller than thechanges made by analysis (Daley 1991). The initializa-tion increment, defined as the difference between theinitialized field and analysis, and the analysis incre-ments, defined as the differences between analysis andbackground, are shown in Table 2. As Cressman analy-sis and initialization perform on different kinds of ver-tical coordinate systems in MM5, analysis incrementsare calculated from the difference between the initialconditions of NODFI-CRSM and NODFI-GTOM,while the initialization increments are estimated fromthe difference between the filtered (e.g., DFI-CRSM/DFI4H-CRSM) and unfiltered (e.g., NODFI-CRSM)initial conditions. In this way, the analysis increments ofvertical velocity w and pressure perturbation pp can

also be estimated, although both of them are not di-rectly analyzed.

Evidently, the initialization increments for the regu-lar model prognostic variables such as the x componentof velocity u, y component of velocity �, temperature T,and specific humidity q are definitely smaller than theanalysis increments. DFI4H-CRSM has larger initial-ization increments than DFI-CRSM due to their longerfilter spans. Therefore, longer filter spans may lead tobetter filtering effects at the cost of larger initializationincrements in addition to their higher computationaldemands.

In addition to the above-mentioned variables, w andpp are needed by the nonhydrostatic MM5. In MM5,the initial w is simply calculated from the pressure ve-locity, which is obtained by integrating horizontal ve-locity divergence vertically while still on the hydrostatic� levels (Dudhia et al. 2000). During the procedure ofthe generation of MM5 initial conditions, the modelequation for vertical velocity in finite-difference form isused with the acceleration and advection terms set tozero once virtual temperature T�(z), where z is the ver-tical height coordinate, is known on the nonhydrostaticmodel levels. This leaves a relation between T�(z) andthe vertical gradient of pp. Given the sea level pressure,pp at the lowest � level can be estimated. Using T�(z),pp at other levels is obtained by vertical integrations.This balance ensures that the initial vertical accelera-tion is zero in each model column. During the DFIbackward and forward integrations w and pp are ad-justed significantly due to the nonhydrostatic dynamics.That is why the initialization increments of these non-hydrostatic variables are of comparable or even greaterthan the analysis increments.

d. Initialized nonhydrostatic variables

We can investigate whether the initialization incre-ments for w and pp are reasonable. The initial verticalvelocity fields at a sigma (� � 0.5) level for NODFI-CRSM and DFI-CRSM are shown in Figs. 6a and 6b,respectively. The initial vertical velocity field ofNODFI-CRSM has many small-scale updraft/down-draft centers. In DFI-CRSM some updraft centers havedeveloped in places with vigorous convective activities,

FIG. 5. The evolution of domain-averaged precipitation rate R(mm day�1). All forecasts are started at 0000 UTC 1 Aug 2002.

TABLE 2. Root-mean-square of initialization and analysis increments of domain 1 at 0000 UTC 1 Aug 2002. Note that the analysisincrements for DFI4H-CRSM are the same as that for DFI-CRSM.

Expt Increment u (m s�1) � (m s�1) T (K) q (g kg�1) w (m s�1) pp (hPa)

DFI-CRSM Initialization 0.67 0.67 0.52 0.63 0.036 0.667— Analysis 2.15 2.02 0.95 2.94 0.024 0.615

DFI4H-CRSM Initialization 1.06 1.12 0.71 0.74 0.047 0.793


identified on satellite images (Fig. 6d), for example, inthe area to the northwest of Japan. In fact as shown inFig. 6c, a similar pattern of w is also generated after 1-hintegration from NODFI-CRSM. Therefore, the ame-lioration of spinup due to DFI, as discussed in previoussections, may be not only due to the adjustment of themoisture fields at initial time, but also due to the gen-eration of vertical velocity fields leading to the precipi-tation at the start of the following forecast.

The pp initialization increments for DFI-CRSM (Fig.7b) are nearly the opposite of the pp analysis incre-ments for NODFI-CRSM (Fig. 7a), indicating that mostof pp information introduced by the analysis has beenlost during the procedure of DFI. However, the pp dif-ference between the NODFI-CRSM 1-h forecast andinitial analysis (Fig. 7c) is very similar to the DFI-CRSM initialization increment (Fig. 7b). In other

words, the analysis increments in pp are also lost in thefirst hour of an uninitialized forecast. From this point ofview, using the hydrostatic assumption to construct ini-tial nonhydrostatic variables may not be the best ap-proach. Alternatively, DFI can be used for the con-struction of nonhydrostatic variables.

6. Data assimilation experiments

a. The data assimilation system

To assess the impact of DFI on forecasts, data as-similation experiments are performed over a 7-day pe-riod, from 0000 UTC 21 August to 1200 UTC 27 Au-gust 2002. The synoptic situation was characterized bymany vigorous convective activities in the model do-main. Each cycle covers a time span of 12 h and gen-erates a 24-h forecast. The background for analysis is

FIG. 6. The initial vertical velocity (m s�1) at level � � 0.5 valid at 0000 UTC 1 Aug 2002 (a) for NODFI-CRSM and (b) forDFI-CRSM. (c) The vertical velocity (m s�1) at t � 1 h for NODFI-CRSM valid at 0100 UTC 1 Aug 2002. Positive contours are solid,negative contours are dashed, the zero contour is suppressed, and the contour interval is 0.02 m s�1. (d) Infrared image of GeostationaryMeteorological Satellite (GMS) valid at 0000 UTC 1 Aug 2002.


the 12-h forecast from the previous cycle, and the lat-eral boundaries come from the interpolated NMC/CMA T213 forecasts available at the analysis time. Theobservation types used in the data assimilation systeminclude conventional surface and radiosonde reports.Hydrometeor variables, such as rainwater, cloud watercontent, etc., are not analyzed. Their values from thebackground are kept.

A series of data assimilation experiments with Cress-man or 3DVAR have been carried out using DFI. Par-allel runs without initialization have also been per-formed for comparisons. The results of the case studyindicated that the Dolph filter with 2-h span and 1-hstop-band edge period is a good choice for controllingnoise with little damage to the analysis. Therefore, thisfilter configuration is used in data assimilation experi-ments. The forecast model and forecast domain are thesame as those of the case study stated above.

b. Noise level

Figure 8 shows the time series of N for each time stepof the first 12 h averaged over 14 consecutive cycles ofall experiments starting on 0000 UTC 21 August 2002.In general, NODFI-3DVAR has a lower noise levelthan NODFI-CRSM. It takes around 6-h integrationfor N of NODFI experiments to descend to a reason-able value. On the other hand, both DFI experimentshave a low noise level from the beginning of the fore-casts. For rapid updated cycles with a time span shorter

FIG. 8. The evolution of the mean absolute surface pressuretendency N [hPa (3 h)�1] in the first 12-h forecasts averaged from14 cycles from 0000 UTC 21 Aug to 1200 UTC 27 Aug 2002.

FIG. 7. (a) Analysis increments, (b) initialization increments,and (c) changes after 1-h integration of NODFI-CRSM of pres-sure perturbation (hPa) at sigma � 0.5. The contour interval is 0.4hPa. Positive contours are solid, negative contours are dashed,and the zero contour is suppressed.


than 6 h, initialization should be necessary for the pur-pose of keeping cycles steady.

c. Moist spinup features

The time evolutions of the mean total R averagedover the 14 cycles of all experiments are shown in Fig.9. For NODFI-CRSM, “spindown” caused by the im-balances between hydrometeors and other analyzedfields during the first stage of integration is a pro-nounced feature; R may on the average drop from 7 to0.7 mm day�1 during the first 15-min integration.Thereafter, a spinup process starts.

For NODFI-3DVAR, the spindown is not quite clearon average. One possible reason is that for the dataassimilation cycles using 3DVAR, during the assimila-tion procedure, the vertical velocity on � levels is alsokept untouched along with the hydrometeors. The bal-ance between vertical motion and moisture fields fromthe previous forecast is kept, leading to less initialshocks in precipitation.

For both analysis methods, time series of R for ini-tialized forecasts start at a lower precipitation level andincrease gradually during the following hours. Their ini-tial low rain rate can be considered as the results of theincomplete spindown/spinup process taking place dur-ing the diabatic forward integration of DFI.

On the average, DFI-initialized forecasts have alarger rain rate than NODFI, especially during the first6 h. This is consistent with the conclusions drawn fromthe case study that the DFI procedure can adjust thehydrometeors and vertical velocity, which can be ex-pected to lead to better precipitation forecasts.

d. Initialization increment

To have an idea about the effect of the DFI proce-dure on the analysis, the initialization increments ofDFI-CRSM and DFI-3DVAR are shown in Table 3,which are root-mean-squares (rms) of u, �, t, q, w, andpp vertically integrated over 37 � levels and horizontallyaveraged over the whole model domain. Analysis in-crements of these two DFI experiments are calculatedin the same way as a reference.

Table 3 shows that for conventional variables such asu, �, t, and q the initialization increments are one-thirdto one-half of the analysis increments for both schemes,indicating that the changes brought by DFI are accept-able. For the Cressman scheme in each cycle, w and pp

are diagnosed from the analysis transformed from pres-sure levels to � levels. As stated for the case study, theirinitialization increments are of the comparable magni-tudes with the analysis increments. For 3DVAR analy-sis the situation is different. The forecasted w from theprevious cycle is used directly as the analysis field ofnew cycle. In this way the previous nonhydrostatic fea-ture is retained, although it is not in consistent withother analyzed variables. However, pp is diagnosedbased on the hydrostatic assumption. In general,3DVAR has smaller initialization increments thanthose of Cressman.

e. Observation verification

In each data assimilation cycle a 24-h forecast is runto assess the impact of initialization schemes on theforecast quality. Upper-air model fields are directly

FIG. 9. The evolution of domain-averaged precipitation rate R(mm day�1) in the first 12-h forecasts averaged from 14 cyclesfrom 0000 UTC 21 Aug to 1200 UTC 27 Aug 2002.

TABLE 3. Root-mean-square of initialization and analysis increments averaged over 14 consecutive cycles started at 0000 UTC 21Aug 2002.

Expt Analysis Increment u (m s�1) � (m s�1) T (K) q (g kg�1) w (m s�1) pp (hPa)

DFI-CRSM Cressman Analysis 2.95 2.99 1.29 1.49 0.56 1.34— Cressman Initialization 1.08 1.03 0.51 0.76 0.56 0.95

DFI-3DVAR 3DVAR Analysis 1.12 1.11 0.78 0.62 0 1.04— 3DVAR Initialization 0.56 0.57 0.32 0.42 0.04 0.46


verified against radiosonde observations at 0000 and1200 UTC. The verified forecasted elements are chosenas geopotential height, temperature, wind, and relativehumidity at 925, 850, 700, 500, 400, 300, 250, 200, 150,and 100 hPa, respectively. Figure 10 presents the verti-

cal profiles of rms difference between model variablesand radiosonde observations averaged over the 14cycles. Surface model fields are directly verified againstsurface station observations every 3 h. The surface veri-fication includes 2-m temperature, 10-m wind, 2-m rela-

FIG. 10. Rms differences between (left) analyses at t � 0 h, (middle) forecasts at t � 12 h, and (right) forecasts at t � 24 h andradiosonde observations, averaged over 14 consecutive cycles started on 0000 UTC 21 Aug 2002.


tive humidity, and sea level pressure. Figure 11 showsthe time series of rms difference between model variablesand surface observations averaged over the 14 cycles.

Using observations as reference, CRSM has betterforecast skill than 3DVAR, which is expected to beimproved by tuning the background error in the3DVAR analysis in future work. The discrepancies be-tween NODFI and DFI are quite evident at the initialtime for both upper-air and surface variables. It is ap-parent that DFI pushes the initial state away from ob-servations, particularly for the relative humidity fore-casts. However, the differences introduced by DFI areless than the assumed errors for radiosonde observa-tions. For instance, the noticeable difference found inthe 850-hPa temperature is around 0.2 K, less than 0.5K, the assumed observation error of temperature (Ben-

jamin et al. 2004b). We even speculate that it is theCressman scheme that overfits observations. For3DVAR the inconsistency of rms between the analysesof NODFI and DFI is quite small.

Considering forecast performance at t � 12 h and t �24 h, the rms profiles of DFI experiments for bothanalysis methods are quite similar to those of NODFIexperiments. For the rms time series of surface fore-casted fields, the differences in scores for forecasts ofDFI and NODFI are generally insignificant. In otherwords DFI works satisfactorily and does not degradethe forecasts of these selected variables.

f. Precipitation verification

The impact of DFI on the precipitation forecasts hasalso been assessed. The 6-h rainfall observations from

FIG. 11. Rms differences between analyses (t � 0) or forecasts (t 0) and surface observations, averaged over 14 consecutive cyclesstarted on 0000 UTC 21 Aug 2002: (top left) 2-m temperature, (top right) 2-m relative humidity, (bottom left) 10-m wind, and (bottomright) sea level pressure.


about 2000 stations are processed to yield the observa-tions of 6- and 12-h accumulated rainfall of each station.The precipitation forecasts of each cycle are interpo-lated to surface stations and verified directly against theobservations.

Figure 12 shows the threat and bias scores of precipi-tation forecasts averaged over 14 cycles for three fore-cast lengths of 0–6, 0–12, and 0–24 h, respectively. Forboth analysis methods, the 0–6 h threat scores of DFIare significantly better than those of NODFI, particu-larly for larger rainfall thresholds beyond 1 mm. That is,the precipitation forecast skill can be improved by usingDFI. Correspondingly, the bias scores larger than 1 forlight precipitation below 5 mm shrunk while the valuesless than 1 for larger rainfall thresholds are improved.Therefore, it revealed that the frequencies of bothoverprediction for light precipitation and underpredic-

tion for larger rainfall beyond 5 mm are remarkablyovercome by using DFI. For 0–12 and 0–24 h forecasts,both scores are also slightly improved. In general, usingDFI may lead to more skillful precipitation forecasts.These improvements are in good agreement with theshortened spinup time and larger precipitation rate dueto DFI, as discussed above.

7. Conclusions

In this paper, it is shown that imbalances betweenmass and wind in initial conditions can trigger spurioushigh-frequency oscillations, considered as noise, in theMM5 model integrations. The imbalances are mainlycaused by two procedures, interpolations and dataanalyses. A diabatic DFI package is implemented forMM5 to control the noise.

FIG. 12. Average threat scores (a) for forecasts based on Cressman analysis, (b) for forecasts based on 3DVAR analysis and biasscores, (c) for forecasts based on Cressman analysis, and (d) for forecasts based on 3DVAR analysis from 14 consecutive cycles startedon 0000 UTC 21 Aug 2002.


A heavy rain case is chosen to evaluate DFI, which isshown to remove the noise efficiently. The unanalyzedmoisture fields can be adjusted during the diabatic for-ward integration of DFI, and the spinup problem isreduced. For regular prognostic variables, the initializa-tion increments are acceptably small compared with theanalysis increments. Vertical velocity and pressure per-turbation, which are related to the nonhydrostatic dy-namics, are also adjusted during the backward and for-ward integrations of DFI. Compared with their initialvalues calculated under the hydrostatic balance as-sumption, the filtered nonhydrostatic variables aremore realistic and dynamically consistent with othermodel variables. In other words, DFI can be consideredas a good method for initializing nonhydrostatic prog-nostic variables that are not analyzed by current analy-sis schemes.

For 14 consecutive intermittent data assimilationcycles covering a 7-day period in August 2002, noisecontrol, spinup features, initialization increments, andimpact on forecast quality are studied extensively. DFIhas been demonstrated to provide well-balanced initialconditions, reduced spinup time, and improved precipi-tation forecast skills.

In applications of FDDA, the initial noise has notbeen considered as a serious problem. A careful com-parison between FDDA and intermittent data assimi-lation systems using Cressman or 3DVAR with DFIshould be performed, especially for high-resolutionmodels using high-resolution observations.

In recent years, the Weather Research and Forecast-ing (WRF) modeling system, which is the next genera-tion of nonhydrostatic mesoscale models of MM5, hasbeen in the IUM plan for operational implementation.The work about noise control and initialization of non-hydrostatic model variables described in this paper willbe useful for the future operational implementation ofWRF.

The conclusions of the present study are based onexperiments using a 27-km resolution grid and 12-h cy-cling configuration. We have started to look into theinitialization issues in the higher resolution (9 and 3km) and rapid update cycles (3 h). The preliminaryresults indicate that without DFI the high-resolutionanalyses have a much higher noise level than thatshown in this paper and that the rapid update cycleshave a higher demand on the noise level of the back-ground fields. The impact of DFI on the high-resolutionupdate cycle of MM5 is under investigation and will bereported in the near future.

Acknowledgments. The authors thank YingchunWang (IUM) and Ying-Hwa Kuo (NCAR) for their

continuous support, Chaolin Zhang (IUM) for his ini-tial efforts, which led to the current DFI implementa-tion, Shuiyong Fan (IUM) for his work on construc-tions of 3DVAR cycles, Dale Barker (NCAR) andHenrik Vedel (DMI) for their careful comments, PeterLynch (Met Éireann), Xiaohua Yang (DMI), and JimyDudhia (NCAR) for their suggestions, and the anony-mous reviewers for their critical comments, which im-proved the presentation of the manuscript. The studywas partially supported by Beijing Municipal Scienceand Technology Commission under ContractH020620250330, and the Ministry of Science and Tech-nology of PRC under Contracts 2002BA904B05 and2005BA904B05.

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Digital filter initialization for MM5

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