## 1. Introduction

The fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) (Dudhia 1993) has been widely used both in the research community and at operational centers. The initial model state for MM5 can be obtained in several ways. In most research applications, analyses from global models or large-scale models are interpolated onto the MM5 model grid to create the initial model states (e.g., Dudhia 1993). Operationally oriented applications of MM5 often involve observations before launching a forecast. There are two types of analysis 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 observations into the MM5. Intermittent data assimilation schemes for MM5 include the Cressman scheme (Benjamin and Seaman 1985), the three-dimensional variational data assimilation (3DVAR) scheme (Barker et al. 2004), and the four-dimensional variational data assimilation (4DVAR) scheme (Zou and Kuo 1996).

As the model is used as a constraint of data assimilation, FDDA and 4DVAR for MM5 can generate initial model states that are consistent with the model dynamics. The interpolation and the three-dimensional schemes, however, unavoidably introduce imbalances between mass and wind fields to the initial states. The use of high-resolution orography together with the interpolated model fields could lead to further imbalances. In the MM5 model integrations, the imbalances trigger spurious high-frequency oscillations, considered as “noise,” which may cause numerical instabilities and forecast failures. They are detrimental for data assimilation systems with rapid update cycles, because a noisy short-range forecast against which new observations are checked would lead to rejection of good observations. There are also MM5 variables such as cloud water, rainwater, and vertical velocity that are difficult to be initialized by the interpolation or by the currently available analysis schemes.

There is evidence that an initialization procedure for MM5 should be beneficial, especially when the initial states for MM5 are from a large-scale model interpolated to the MM5 grid or from an objective analysis scheme like 3DVAR. For example, the initial imbalance and rapid model adjustment excite acoustic and gravity waves that last several hours in the model integrations (Manning et al. 2002). Filtering the optimal initial condition at the end of an MM5 4DVAR may reduce the noise by 20% (De Pondeca and Zou 2001). Introducing a digital filter as a weak constraint into the MM5 4DVAR is shown to improve the observation handling, the minimization convergence, and the assimilation quality (Wee and Kuo 2004).

In this study, several configurations of MM5 (version 3.6.1), as implemented on the SGI ORIGIN2000 at the Beijing Institute of Urban Meteorology (IUM), are used (section 2). The current IUM operational setup is used to determine the noise characteristics caused by interpolations and objective analyses (section 3). Then a digital filter initialization (DFI) package is implemented in MM5 (section 4). A heavy rain case is chosen to demonstrate how DFI filters out the noise and improves the dynamic consistency of the model fields, for example, vertical velocity and pressure perturbation, which are not analyzed or interpolated from the global forecasts (section 5). Intermittent cycling data assimilation experiments using the same framework are then presented and discussed (section 6). Concluding remarks are given in the end (section 7).

## 2. MM5 at IUM

The first mesoscale numerical forecasting system based on MM5, version 2, was implemented at IUM in 1997. It became operational in 1999. The current operational configuration is based on MM5, version 3.6.1. Preoperational tests started in 2000, and it became operational in July 2004.

In the IUM standard configuration, MM5 runs on three domains with horizontal resolutions of 27, 9, and 3 km, all having 37 vertical levels. The model domains and terrain height for domain 1 are shown in Fig. 1. The model grid points for the three domains are 151 × 151 × 37, 142 × 184 × 37, and 172 × 199 × 37, and the time steps for each domain are 80, 27, and 9 s, respectively. Simple but full model physics schemes are used: Blackadar PBL (Blackadar 1976), Grell cumulus parameterization (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 0000 and 1200 UTC are carried out each day. For every run, the background fields are obtained by interpolating the T213 global model forecasts of the National Meteorological Center of the China Meteorological Administration (NMC/CMA) to the MM5 grids. Conventional data are collected from the Global Telecommunication System and the IUM local network. A series of quality controls, including vertical check, error-max check, and buddy check (Dudhia et al. 2000), are performed before the observations are assimilated. A modified Cressman scheme, which includes noncircular influence functions (Benjamin and Seaman 1985), is used to combine the background fields and the observations. The resulting analyses are used directly as initial model states to start the operational MM5 forecasts.

The next IUM operational setup will run in data assimilation cycles, using its own short-range forecasts from previous cycles as background for analyses. Both the Cressman scheme and the MM5 3DVAR (Barker et al. 2004) are under evaluation. The main features of MM5 3DVAR include (Barker et al. 2004) the following:

quasi-Newton minimization algorithm developed at Argonne National Laboratory,

analysis increments on an unstaggered Arakawa A grid (The input background wind fields for 3DVAR are interpolated from an Arakawa B grid used by the MM5 forecast model. The unstaggered analysis wind increments need to be interpolated back to the Arakawa B grid before being used to initialize a forecast.),

analysis performed on the nonhydrostatic model sigma-height levels of MM5,

preconditioned control variables using streamfunction, velocity potential, unbalanced pressure, and specific/relative humidity, and

linearized mass–wind balance (including both geostrophic and cyclostrophic terms) used to define a balanced pressure.

## 3. Initial noise

*N*, defined as

*p*is the surface pressure and the summation denotes calculation over the whole model domain, is a characteristic quantity that reflects directly the overall balance of the model states (Lynch and Huang 1992).

_{s}Investigation on *N* in the operational database reveals severe imbalances in the first 6–12 h of the forecasts. As an example, a few MM5 24-h forecasts of the outermost domain (D01) starting from 1200 UTC 21 August 2002 are selected. All of these experiments use an identical 12-h forecast from the previous data assimilation cycle as their first guess against which the experiment named as NODFI-3DVAR uses MM5/3DVAR and NODFI-CRSM uses the Cressman method for their analyses, respectively. To set a reference of a “noise free” level of N, we made a forecast, denoted NODFI-BG, with its initial condition directly from the previous cycle’s 12-h forecast and without any analysis procedure involved.

The evolutions of *N* from these MM5 forecasts are shown in Fig. 2. It is clear that the initial noise level using 3DVAR analysis is much lower than that using Cressman analysis. One possible reason is the analysis generated by 3DVAR would intrinsically have better balance than Cressman analysis, as balance (i.e., weak geostrophic, hydrostatic) constraints are built into the preconditioning of the cost-function minimization (Barker et al. 2004).

To isolate the noise introduced by vertical interpolation between *σ* and pressure levels, we have made another run denoted as NODFI-VINT, whose initial model state is obtained by first interpolating the NODFI-BG’s noise-free initial state to pressure levels, then interpolating it back to model *σ* levels. No analysis is 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 the noise-free model state, even if the coordinate transformation between *σ* and pressure levels is the only procedure to be considered. For the Cressman scheme and other analysis methods performed on pressure levels, this part of the noise would be as significant as that brought by analysis.

To explore the noise problem of cold-start runs without any analysis, an extra experiment of NODFI-GTOM is designed. The initial state of NODFI-GTOM is interpolated from the T213 global analysis at 1200 UTC 21 August 2002 instead of the forecast of the previous cycle. It is clearly shown in Fig. 2 that NODFI-GTOM has the highest initial noise level.

Another way to demonstrate the imbalances of the initial conditions is to use maps of the initial surface pressure tendencies. For a noise-free model state, as shown in Fig. 3a, the initial surface pressure tendencies are below 3 hPa (3 h)^{−1} over most model points. The visible small-scale pressure tendency centers are related to weather systems. The differences between Figs. 3b and 3a indicate that significant noise is generated when the analysis procedure combines observations and the first guess. For NODFI-3DVAR the maximum/minimum initial surface pressure tendencies’ centers seem to relate to sounding stations, suggesting that most of the initial noise is generated by 3DVAR. But for NODFI-VINT (Fig. 3c), obvious orographic features can be identified from the initial surface pressure tendencies of NODFI-VINT, which could be a reflection of terrain height as a factor of surface pressure calculation (Grell et al. 1994).

For the Cressman scheme in MM5, analysis and the vertical interpolation between *σ* and pressure levels are the two major procedures responsible for the generation of noise. As shown in Fig. 3d, a gross pattern of orography and minimum/maximum centers related to sounding stations can be identified.

The interpolation from a large-scale model to the MM5 grid generates noise through horizontal interpolation, grid changes (e.g., A grid to B grid), vertical interpolation, and adjustment of the model fields to the new high-resolution orography. From Fig. 3e it is evident that the vertical interpolation and orography have the main contribution.

## 4. Digital filter initialization

It is evident from the previous section that an initialization scheme for MM5 is desirable if its initial model states are produced by interpolating large-scale model analysis to the MM5 grid or by using a three-dimensional analysis (the Cressman scheme or the MM5/3DVAR). There are many initialization schemes, including dynamic initialization (Miyakoda and Moyer 1968), nonlinear normal-mode initialization (Machenhauer 1977), and DFI (Lynch and Huang 1992), that all could be considered for MM5 implementations.

In this study, DFI is chosen for its simplicity and flexibility. A thorough review on the DFI theory and different applications was given by Huang and Yang (2002). Following the review we have made a diabatic DFI (DDFI) implementation for MM5. The Dolph filter (Lynch 1997) has been chosen for all the experiments presented in this paper. The details of DDFI and the 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 is a local torrential rainfall incident that occurred in the late afternoon of 1 August 2002. It was caused by two meso-*β*-scale convective systems developed in Miyun, a northeast county of Beijing, China. The total accumulated precipitation in Miyun County (40.58°N, 116.85°E) during 6 h reached 280.2 mm, which caused severe mud-rock flow, flooding, and loss of lives.

A number of simple cold-start runs of the outermost domain (D01) with different DFI configurations have been performed. In Table 1, a summary of the tested initialization schemes is given. NODFI-CRSM is the control experiment without any initialization procedure. DFI-CRSM is the corresponding DFI experiment with 2-h time span. DFI4H-CRSM uses a longer filter span. NODFI-GTOM and DFI-GTOM are designed with the initial conditions directly from the interpolated global analysis to the MM5 27-km grid without any objective analysis involved, one without initialization and the other with DFI. All of the DFI experiments use the Dolph filter and a 1-h stop-band edge period. The filter spans are given in Table 1.

### a. Noise level

As shown in Fig. 4, all DFI schemes successfully reduce the spurious high-frequency oscillations to a reasonable level. After 12-h integration the time series of all initialized forecasts converge toward that of NODFI-CRSM. Because of the lack of analysis, NODFI-GTOM has a lower noise level than NODFI-CRSM and DFI-GTOM has a slightly different asymptotic value than that of DFI-CRSM and DFI4H-CRSM. DFI4H-CRSM may bring a little more filtering effects than DFI-CRSM at the cost of doubling computational expense for backward and forward integrations with longer filtering time span. If the noise control is not the only concern, DFI-CRSM should be preferred.

### b. Moist spinup features

The spinup feature of moisture fields is another important factor that needs to be considered when evaluating the impact of an initialization scheme. Huang and Sundqvist (1993) demonstrated that as full physical processes are incorporated in the forward filtering procedure, unanalyzed hydrometeor fields could be produced at the initial time. Accordingly, spinup effects could be reduced.

In Fig. 5, time series of the domain-averaged precipitation rate *R* are compared. For NODFI, *R* is shown to start from nearly 0 and increase rapidly during the following 3-h integration. For the DFI-CRSM test, spinup problems seem to be alleviated as *R* values are improved to the value greater than 4 mm day^{−1} at the initial time, and then increase gradually in the following integrations. It is quite evident that the spinup process has not been completed during the forward diabatic DFI integration, because *R* still increases at the early stage of the forecast. DFI4H-CRSM has a larger initial precipitation rate of 7 mm day^{−1}, indicating that when filter span is longer, the spinup process starts earlier during the forward integration of DFI, leading to a shorter spinup process after initialization.

### c. Changes made by DFI to the model fields

A requirement of any initialization procedure is that the changes made by the procedure are acceptably small. In general, they should be smaller than the changes made by analysis (Daley 1991). The initialization increment, defined as the difference between the initialized field and analysis, and the analysis increments, defined as the differences between analysis and background, are shown in Table 2. As Cressman analysis and initialization perform on different kinds of vertical coordinate systems in MM5, analysis increments are calculated from the difference between the initial conditions of NODFI-CRSM and NODFI-GTOM, while the initialization increments are estimated from the difference between the filtered (e.g., DFI-CRSM/DFI4H-CRSM) and unfiltered (e.g., NODFI-CRSM) initial conditions. In this way, the analysis increments of vertical velocity *w* and pressure perturbation *p*_{p} can also be estimated, although both of them are not directly analyzed.

Evidently, the initialization increments for the regular model prognostic variables such as the *x* component of velocity *u*, *y* component of velocity *υ*, temperature *T*, and specific humidity *q* are definitely smaller than the analysis increments. DFI4H-CRSM has larger initialization increments than DFI-CRSM due to their longer filter spans. Therefore, longer filter spans may lead to better filtering effects at the cost of larger initialization increments in addition to their higher computational demands.

In addition to the above-mentioned variables, *w* and *p*_{p} are needed by the nonhydrostatic MM5. In MM5, the initial *w* is simply calculated from the pressure velocity, which is obtained by integrating horizontal velocity divergence vertically while still on the hydrostatic *σ* levels (Dudhia et al. 2000). During the procedure of the generation of MM5 initial conditions, the model equation for vertical velocity in finite-difference form is used with the acceleration and advection terms set to zero once virtual temperature *T _{υ}*(

*z*), where

*z*is the vertical height coordinate, is known on the nonhydrostatic model levels. This leaves a relation between

*T*(

_{υ}*z*) and the vertical gradient of

*p*

_{p}. Given the sea level pressure,

*p*

_{p}at the lowest

*σ*level can be estimated. Using

*T*(

_{υ}*z*),

*p*

_{p}at other levels is obtained by vertical integrations. This balance ensures that the initial vertical acceleration is zero in each model column. During the DFI backward and forward integrations

*w*and

*p*

_{p}are adjusted significantly due to the nonhydrostatic dynamics. That is why the initialization increments of these nonhydrostatic variables are of comparable or even greater than the analysis increments.

### d. Initialized nonhydrostatic variables

We can investigate whether the initialization increments for *w* and *p*_{p} are reasonable. The initial vertical velocity fields at a sigma (*σ* = 0.5) level for NODFI-CRSM and DFI-CRSM are shown in Figs. 6a and 6b, respectively. The initial vertical velocity field of NODFI-CRSM has many small-scale updraft/downdraft centers. In DFI-CRSM some updraft centers have developed in places with vigorous convective activities, identified on satellite images (Fig. 6d), for example, in the area to the northwest of Japan. In fact as shown in Fig. 6c, a similar pattern of *w* is also generated after 1-h integration from NODFI-CRSM. Therefore, the amelioration of spinup due to DFI, as discussed in previous sections, may be not only due to the adjustment of the moisture fields at initial time, but also due to the generation of vertical velocity fields leading to the precipitation at the start of the following forecast.

The *p*_{p} initialization increments for DFI-CRSM (Fig. 7b) are nearly the opposite of the *p*_{p} analysis increments for NODFI-CRSM (Fig. 7a), indicating that most of *p*_{p} information introduced by the analysis has been lost during the procedure of DFI. However, the *p*_{p} difference between the NODFI-CRSM 1-h forecast and initial analysis (Fig. 7c) is very similar to the DFI-CRSM initialization increment (Fig. 7b). In other words, the analysis increments in *p*_{p} are also lost in the first hour of an uninitialized forecast. From this point of view, using the hydrostatic assumption to construct initial nonhydrostatic variables may not be the best approach. Alternatively, DFI can be used for the construction of nonhydrostatic variables.

## 6. Data assimilation experiments

### a. The data assimilation system

To assess the impact of DFI on forecasts, data assimilation experiments are performed over a 7-day period, from 0000 UTC 21 August to 1200 UTC 27 August 2002. The synoptic situation was characterized by many vigorous convective activities in the model domain. Each cycle covers a time span of 12 h and generates a 24-h forecast. The background for analysis is the 12-h forecast from the previous cycle, and the lateral boundaries come from the interpolated NMC/CMA T213 forecasts available at the analysis time. The observation types used in the data assimilation system include conventional surface and radiosonde reports. Hydrometeor variables, such as rainwater, cloud water content, etc., are not analyzed. Their values from the background are kept.

A series of data assimilation experiments with Cressman or 3DVAR have been carried out using DFI. Parallel runs without initialization have also been performed for comparisons. The results of the case study indicated that the Dolph filter with 2-h span and 1-h stop-band edge period is a good choice for controlling noise with little damage to the analysis. Therefore, this filter configuration is used in data assimilation experiments. The forecast model and forecast domain are the same as those of the case study stated above.

### b. Noise level

Figure 8 shows the time series of *N* for each time step of the first 12 h averaged over 14 consecutive cycles of all experiments starting on 0000 UTC 21 August 2002. In general, NODFI-3DVAR has a lower noise level than NODFI-CRSM. It takes around 6-h integration for *N* of NODFI experiments to descend to a reasonable value. On the other hand, both DFI experiments have a low noise level from the beginning of the forecasts. For rapid updated cycles with a time span shorter than 6 h, initialization should be necessary for the purpose of keeping cycles steady.

### c. Moist spinup features

The time evolutions of the mean total *R* averaged over the 14 cycles of all experiments are shown in Fig. 9. For NODFI-CRSM, “spindown” caused by the imbalances between hydrometeors and other analyzed fields during the first stage of integration is a pronounced feature; *R* may on the average drop from 7 to 0.7 mm day^{−1} during the first 15-min integration. Thereafter, a spinup process starts.

For NODFI-3DVAR, the spindown is not quite clear on average. One possible reason is that for the data assimilation cycles using 3DVAR, during the assimilation procedure, the vertical velocity on *σ* levels is also kept untouched along with the hydrometeors. The balance between vertical motion and moisture fields from the previous forecast is kept, leading to less initial shocks in precipitation.

For both analysis methods, time series of *R* for initialized forecasts start at a lower precipitation level and increase gradually during the following hours. Their initial low rain rate can be considered as the results of the incomplete spindown/spinup process taking place during the diabatic forward integration of DFI.

On the average, DFI-initialized forecasts have a larger rain rate than NODFI, especially during the first 6 h. This is consistent with the conclusions drawn from the case study that the DFI procedure can adjust the hydrometeors and vertical velocity, which can be expected to lead to better precipitation forecasts.

### d. Initialization increment

To have an idea about the effect of the DFI procedure on the analysis, the initialization increments of DFI-CRSM and DFI-3DVAR are shown in Table 3, which are root-mean-squares (rms) of *u*, *υ*, *t*, *q*, *w*, and *p*_{p} vertically integrated over 37 *σ* levels and horizontally averaged over the whole model domain. Analysis increments of these two DFI experiments are calculated in the same way as a reference.

Table 3 shows that for conventional variables such as *u*, *υ*, *t*, and *q* the initialization increments are one-third to one-half of the analysis increments for both schemes, indicating that the changes brought by DFI are acceptable. For the Cressman scheme in each cycle, *w* and *p*_{p} are diagnosed from the analysis transformed from pressure levels to *σ* levels. As stated for the case study, their initialization increments are of the comparable magnitudes with the analysis increments. For 3DVAR analysis the situation is different. The forecasted *w* from the previous cycle is used directly as the analysis field of new cycle. In this way the previous nonhydrostatic feature is retained, although it is not in consistent with other analyzed variables. However, *p*_{p} is diagnosed based on the hydrostatic assumption. In general, 3DVAR has smaller initialization increments than those of Cressman.

### e. Observation verification

In each data assimilation cycle a 24-h forecast is run to assess the impact of initialization schemes on the forecast quality. Upper-air model fields are directly verified against radiosonde observations at 0000 and 1200 UTC. The verified forecasted elements are chosen as geopotential height, temperature, wind, and relative humidity at 925, 850, 700, 500, 400, 300, 250, 200, 150, and 100 hPa, respectively. Figure 10 presents the vertical profiles of rms difference between model variables and radiosonde observations averaged over the 14 cycles. Surface model fields are directly verified against surface station observations every 3 h. The surface verification includes 2-m temperature, 10-m wind, 2-m relative humidity, and sea level pressure. Figure 11 shows the time series of rms difference between model variables and surface observations averaged over the 14 cycles.

Using observations as reference, CRSM has better forecast skill than 3DVAR, which is expected to be improved by tuning the background error in the 3DVAR analysis in future work. The discrepancies between NODFI and DFI are quite evident at the initial time for both upper-air and surface variables. It is apparent that DFI pushes the initial state away from observations, particularly for the relative humidity forecasts. However, the differences introduced by DFI are less than the assumed errors for radiosonde observations. For instance, the noticeable difference found in the 850-hPa temperature is around 0.2 K, less than 0.5 K, the assumed observation error of temperature (Benjamin et al. 2004b). We even speculate that it is the Cressman scheme that overfits observations. For 3DVAR the inconsistency of rms between the analyses of NODFI and DFI is quite small.

Considering forecast performance at *t* = 12 h and *t* = 24 h, the rms profiles of DFI experiments for both analysis methods are quite similar to those of NODFI experiments. For the rms time series of surface forecasted fields, the differences in scores for forecasts of DFI and NODFI are generally insignificant. In other words DFI works satisfactorily and does not degrade the forecasts of these selected variables.

### f. Precipitation verification

The impact of DFI on the precipitation forecasts has also been assessed. The 6-h rainfall observations from about 2000 stations are processed to yield the observations of 6- and 12-h accumulated rainfall of each station. The precipitation forecasts of each cycle are interpolated to surface stations and verified directly against the observations.

Figure 12 shows the threat and bias scores of precipitation forecasts averaged over 14 cycles for three forecast lengths of 0–6, 0–12, and 0–24 h, respectively. For both analysis methods, the 0–6 h threat scores of DFI are significantly better than those of NODFI, particularly for larger rainfall thresholds beyond 1 mm. That is, the precipitation forecast skill can be improved by using DFI. Correspondingly, the bias scores larger than 1 for light precipitation below 5 mm shrunk while the values less than 1 for larger rainfall thresholds are improved. Therefore, it revealed that the frequencies of both overprediction for light precipitation and underprediction for larger rainfall beyond 5 mm are remarkably overcome by using DFI. For 0–12 and 0–24 h forecasts, both scores are also slightly improved. In general, using DFI may lead to more skillful precipitation forecasts. These improvements are in good agreement with the shortened spinup time and larger precipitation rate due to DFI, as discussed above.

## 7. Conclusions

In this paper, it is shown that imbalances between mass and wind in initial conditions can trigger spurious high-frequency oscillations, considered as noise, in the MM5 model integrations. The imbalances are mainly caused by two procedures, interpolations and data analyses. A diabatic DFI package is implemented for MM5 to control the noise.

A heavy rain case is chosen to evaluate DFI, which is shown to remove the noise efficiently. The unanalyzed moisture fields can be adjusted during the diabatic forward integration of DFI, and the spinup problem is reduced. For regular prognostic variables, the initialization increments are acceptably small compared with the analysis increments. Vertical velocity and pressure perturbation, which are related to the nonhydrostatic dynamics, are also adjusted during the backward and forward integrations of DFI. Compared with their initial values calculated under the hydrostatic balance assumption, the filtered nonhydrostatic variables are more realistic and dynamically consistent with other model variables. In other words, DFI can be considered as a good method for initializing nonhydrostatic prognostic variables that are not analyzed by current analysis schemes.

For 14 consecutive intermittent data assimilation cycles covering a 7-day period in August 2002, noise control, spinup features, initialization increments, and impact on forecast quality are studied extensively. DFI has been demonstrated to provide well-balanced initial conditions, reduced spinup time, and improved precipitation forecast skills.

In applications of FDDA, the initial noise has not been considered as a serious problem. A careful comparison between FDDA and intermittent data assimilation systems using Cressman or 3DVAR with DFI should be performed, especially for high-resolution models using high-resolution observations.

In recent years, the Weather Research and Forecasting (WRF) modeling system, which is the next generation of nonhydrostatic mesoscale models of MM5, has been in the IUM plan for operational implementation. The work about noise control and initialization of nonhydrostatic model variables described in this paper will be useful for the future operational implementation of WRF.

The conclusions of the present study are based on experiments using a 27-km resolution grid and 12-h cycling configuration. We have started to look into the initialization issues in the higher resolution (9 and 3 km) and rapid update cycles (3 h). The preliminary results indicate that without DFI the high-resolution analyses have a much higher noise level than that shown in this paper and that the rapid update cycles have a higher demand on the noise level of the background fields. The impact of DFI on the high-resolution update cycle of MM5 is under investigation and will be reported in the near future.

## Acknowledgments

The authors thank Yingchun Wang (IUM) and Ying-Hwa Kuo (NCAR) for their continuous support, Chaolin Zhang (IUM) for his initial efforts, which led to the current DFI implementation, Shuiyong Fan (IUM) for his work on constructions of 3DVAR cycles, Dale Barker (NCAR) and Henrik Vedel (DMI) for their careful comments, Peter Lynch (Met Éireann), Xiaohua Yang (DMI), and Jimy Dudhia (NCAR) for their suggestions, and the anonymous reviewers for their critical comments, which improved the presentation of the manuscript. The study was partially supported by Beijing Municipal Science and Technology Commission under Contract H020620250330, and the Ministry of Science and Technology of PRC under Contracts 2002BA904B05 and 2005BA904B05.

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The 12-h evolutions of the mean absolute surface pressure tendency *N* [hPa (3 h)^{−1}] of five MM5 forecasts, all started at 1200 UTC 21 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The 12-h evolutions of the mean absolute surface pressure tendency *N* [hPa (3 h)^{−1}] of five MM5 forecasts, all started at 1200 UTC 21 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The 12-h evolutions of the mean absolute surface pressure tendency *N* [hPa (3 h)^{−1}] of five MM5 forecasts, all started at 1200 UTC 21 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

(a) The initial surface pressure tendency for NODFI-BG at 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 interval is 10 hPa (3 h)^{−1}. In addition to the pressure tendency, the distribution of the sounding stations used by 3DVAR analysis is also shown. (c) Same as in (a), but for NODFI-VINT. The contour interval 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 contours are solid, negative contours are dashed, and the zero contour is suppressed.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

(a) The initial surface pressure tendency for NODFI-BG at 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 interval is 10 hPa (3 h)^{−1}. In addition to the pressure tendency, the distribution of the sounding stations used by 3DVAR analysis is also shown. (c) Same as in (a), but for NODFI-VINT. The contour interval 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 contours are solid, negative contours are dashed, and the zero contour is suppressed.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

(a) The initial surface pressure tendency for NODFI-BG at 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 interval is 10 hPa (3 h)^{−1}. In addition to the pressure tendency, the distribution of the sounding stations used by 3DVAR analysis is also shown. (c) Same as in (a), but for NODFI-VINT. The contour interval 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 contours are solid, negative contours are dashed, and the zero contour is suppressed.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of the mean absolute surface pressure tendency *N* [hPa (3 h)^{−1}] of MM5 forecasts, all started from 0000 UTC 1 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of the mean absolute surface pressure tendency *N* [hPa (3 h)^{−1}] of MM5 forecasts, all started from 0000 UTC 1 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of the mean absolute surface pressure tendency *N* [hPa (3 h)^{−1}] of MM5 forecasts, all started from 0000 UTC 1 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of domain-averaged precipitation rate *R* (mm day^{−1}). All forecasts are started at 0000 UTC 1 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of domain-averaged precipitation rate *R* (mm day^{−1}). All forecasts are started at 0000 UTC 1 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of domain-averaged precipitation rate *R* (mm day^{−1}). All forecasts are started at 0000 UTC 1 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The initial vertical velocity (m s^{−1}) at level *σ* = 0.5 valid at 0000 UTC 1 Aug 2002 (a) for NODFI-CRSM and (b) for DFI-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 Geostationary Meteorological Satellite (GMS) valid at 0000 UTC 1 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The initial vertical velocity (m s^{−1}) at level *σ* = 0.5 valid at 0000 UTC 1 Aug 2002 (a) for NODFI-CRSM and (b) for DFI-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 Geostationary Meteorological Satellite (GMS) valid at 0000 UTC 1 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The initial vertical velocity (m s^{−1}) at level *σ* = 0.5 valid at 0000 UTC 1 Aug 2002 (a) for NODFI-CRSM and (b) for DFI-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 Geostationary Meteorological Satellite (GMS) valid at 0000 UTC 1 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of the mean absolute surface pressure tendency *N* [hPa (3 h)^{−1}] in the first 12-h forecasts averaged from 14 cycles from 0000 UTC 21 Aug to 1200 UTC 27 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of the mean absolute surface pressure tendency *N* [hPa (3 h)^{−1}] in the first 12-h forecasts averaged from 14 cycles from 0000 UTC 21 Aug to 1200 UTC 27 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of the mean absolute surface pressure tendency *N* [hPa (3 h)^{−1}] in the first 12-h forecasts averaged from 14 cycles from 0000 UTC 21 Aug to 1200 UTC 27 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of domain-averaged precipitation rate *R* (mm day^{−1}) in the first 12-h forecasts averaged from 14 cycles from 0000 UTC 21 Aug to 1200 UTC 27 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of domain-averaged precipitation rate *R* (mm day^{−1}) in the first 12-h forecasts averaged from 14 cycles from 0000 UTC 21 Aug to 1200 UTC 27 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

The evolution of domain-averaged precipitation rate *R* (mm day^{−1}) in the first 12-h forecasts averaged from 14 cycles from 0000 UTC 21 Aug to 1200 UTC 27 Aug 2002.

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

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

Citation: Monthly Weather Review 134, 4; 10.1175/MWR3117.1

List of runs for the case study.

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

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

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+ The National Center for Atmospheric Research is sponsored by the National Science Foundation.