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  • View in gallery

    Model domain and topography with 10-km resolution. Contour interval is 100 m.

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    (a) Observed rainfall amount (mm) accumulated from 1500 to 2100 UTC 14 Jul 2001 [0000 to 0600 local standard time (LST) 15 Jul in figure]. (b) Hourly precipitation (mm) at the Seoul station. (c) GMS-enhanced IR image at 18 UTC 14 Jul 2001.

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    Power spectra density (Press et al. 1996) for temperature selected at a land point, which is displayed in wave period and vertical sigma levels. (a), (b) Power spectra density after (daytime) and during the 12-h nudging period (nighttime) from 1200 UTC 8 Dec to 0000 UTC 9 Dec 2003, respectively. (c), (d) Same as (a), (b) except for IAU with 12-h window.

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    (a) Averaged absolute tendency of surface pressure (MASP) by 3DVAR system without IAU as a control (R3DV in thin line) and with IAU (thick line). (b) Surface pressure tendency at an ocean point for R3DV and IAU experiment

  • View in gallery

    Same as Fig. 4a except for the addition of 3-h nudging experiment (FDDA) at 1200 UTC 14 Jul 2001.

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    Time–height section of time tendency of u wind for a land grid point. (a), (b) The 3DVAR system without IAU, and with IAU, respectively.

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    Response function of IAU increment according to 6-, 3-, and 1-h IAU windows. Amplitude of IAU increments comes from Bloom et al. (1996).

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    (a) Domain-averaged precipitation in 10-min intervals during 12 h, overlapped 3DVAR without IAU (R3DV) and with IAU (IAU). (b) Domain-integrated cloud water amount during 6 h from 1200 UTC 14 Jul 2001.

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    (a) Domain-integrated cloud water amount in forecasted minutes with only Qc and Qr (only Qc + Qr), and Qc, Qr, Qi, Qg, and Qs from previous forecast (All), and no hydrometeors (None); and (b) domain-averaged temperature (solid line) and domain-integrated mixing ratio (dotted line) according to approximately 850–500 hPa. This is performed by the R3DV experiment without IAU initialization.

  • View in gallery

    The 6-h accumulated rainfall amount from 1500 to 2100 UTC 14 Jul 2001 from 3-h cycling 3DVAR system (a) without IAU (R3DV), and (b) with IAU (IAU in figures). Winds are represented at 0.995 sigma.

  • View in gallery

    CSI for (a) 10- and (b) 30-mm threshold during 3-h according to forecast time. (c) CSI for first 6 h of accumulated rain in different threshold rainfall amount. The lack of a bar implies that no events occurred for that run that met the threshold criterion for that forecast time.

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    (a) Time series of hourly rainfall summarized over all stations in Korea according to different IAU forcing variables. IAU means a case with every forcing variable produced from 3DVAR. NTG and NLBC mean IAU run without skin temperature forcing and lateral boundary forcing, respectively. (b) CSI for 60-mm threshold values during 6 h for experiments with different forcing.

  • View in gallery

    The 6-h accumulated rainfall amount from 1500 to 2100 UTC 14 Jul 2001 for (a) 1-h 3DVAR cycling (RUC1), (b) same as (a) except for with IAU (IAU1), (c) 2-h 3DVAR cycling (RUC2), and (d) same as (c) except for with IAU (IAU2).

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    (a) The 3D-integrated cloud water during 20 h from cycling start time, and (b) cost function from 3DVAR minimization in terms of iteration number for 2-h updates of 3DVAR system without IAU (RUC2) and with IAU (IAU2).

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    (a) Rmse of RH (%) for 12-h forecast and (b) T for 24 forecast over 10 Jun and 10 Jul 2003. ETS over 5 mm/3 h (c) for the period of 12 Jun to 17 Jul 2003, and (d) for 1 Sep to 30 Nov 2003.

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Incremental Analysis Updates Initialization Technique Applied to 10-km MM5 and MM5 3DVAR

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  • 1 Korea Meteorological Administration, Seoul, South Korea
  • 2 National Center for Atmospheric Research, Boulder, Colorado
  • 3 Korea Meteorological Administration, Seoul, South Korea
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Abstract

An incremental analysis updates (IAU) technique is implemented for 3-h updates of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) three-dimensional variational data assimilation (3DVAR) and model system with a 10-km resolution to remove spurious gravity waves. By gradually incorporating analysis increments, IAU affects only the removal of high frequencies, leaving the waves related to diurnal processes. IAU appears to be efficient in reducing the moisture spinup problem in the MM5 3DVAR cycling system. The advantage of the IAU is the most significant in improving precipitation forecasts. Rapid update cycle (RUC) with 1- and 2-h intervals in conjunction with the IAU indicates a rapid minimization and less spinup and -down problems because of greater balancing between the moisture and dynamic variables. Impact studies are performed on a heavy rainfall case that occurred in the Korean Peninsula. Verification results with a 3-h cycling system are presented on operational environments.

Corresponding author address: Dr. Ying-Hwa Kuo, MMM/National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: kuo@ucar.edu

Abstract

An incremental analysis updates (IAU) technique is implemented for 3-h updates of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) three-dimensional variational data assimilation (3DVAR) and model system with a 10-km resolution to remove spurious gravity waves. By gradually incorporating analysis increments, IAU affects only the removal of high frequencies, leaving the waves related to diurnal processes. IAU appears to be efficient in reducing the moisture spinup problem in the MM5 3DVAR cycling system. The advantage of the IAU is the most significant in improving precipitation forecasts. Rapid update cycle (RUC) with 1- and 2-h intervals in conjunction with the IAU indicates a rapid minimization and less spinup and -down problems because of greater balancing between the moisture and dynamic variables. Impact studies are performed on a heavy rainfall case that occurred in the Korean Peninsula. Verification results with a 3-h cycling system are presented on operational environments.

Corresponding author address: Dr. Ying-Hwa Kuo, MMM/National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: kuo@ucar.edu

1. Introduction

Even though a variational system has practical advantages, such as the ability to assimilate observations directly, thereby imposing balance constraints through preconditioning, and finding an optimal solution and the minimization of the cost function, there are still issues associated with spinup and initialization. These issues become more severe with a rapid update cycle, which incorporates more frequent observations. Usually variational assimilation methods employ a background error covariance that spreads the influence of the observation in space, and filter analysis increments through dynamic balance or statistical relationship. However, linear balance constraints are often insufficient to prevent the development of spurious energy on the fastest time scale of numerical forecast (Polavarapu et al. 2004). Thus, a separate filtering procedure is required to remove spurious high-frequency gravity wave noise, which can have a detrimental effect on the first few hours of the forecast, and on the data assimilation cycle as a whole. These initialization and spinup problems are extremely harmful in 3D variational method without model constraints. Even though 4D methods, such as the four-dimensional variational data assimilation (4DVAR), often adds additional constraints on smoothness or balance, resulting in a relatively balance analysis, filtering issues remain.

A number of approaches have been developed to address the initialization problem including: nonlinear normal mode initialization (Daley 1979); bounded derivative initialization (Semazzi and Navon 1986); damped time-differencing scheme (Baker et al. 1987); diabatic initialization (Puri 1985); National Centers for Environmental Prediction (NCEP) Spectral Statistical Interpolation (SSI; Parrish and Derber 1992) using a linear balance constraints, nudging technique (Grell et al. 1995); digital filter initialization technique (DFI; Lynch and Huang 1992); and incremental analysis updates (IAU; Bloom et al. 1996). The digital filter (DF) method has been known as an applicable technique to the variational technique that has been used in the rapid update cycle (RUC) system (Benjamin et al. 2004), in a high-resolution model system in eight European countries (Lynch et al. 1999). The U.K. Met Office (UKMO) has used the digital filter technique and IAU as an alternative initialization technique (Clayton 2003).

The main purpose of this paper is to investigate the impacts of the IAU process to reduce the gravity wave noise as the simplest way to couple a model with high-resolution three-dimensional variational assimilation (3DVAR). Then we will investigate whether or not the precipitation forecast skill can be improved by moisture spinup as a side effect of the IAU process. Section 2 briefly describes the model, the 3DVAR system, and a heavy rainfall case used in this study. Nudging and IAU techniques as initialization schemes will be compared in section 3. A comparison between the IAU and the DFI will be briefly discussed as well. Section 4 will describe the behavior of the IAU in a cycling data assimilation system in terms of initialization performance and impacts on precipitation forecast. Section 5 will introduce verification results based on an operational framework at the Korea Meteorological Administration (KMA), where the IAU technique was launched as an operational system on 29 January 2004. In section 6, we present a summary and conclusions.

2. MM5 3DVAR and case

a. The 3DVAR and IAU coupling

The main characteristics of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (NCAR) Mesoscale Model (MM5) 3DVAR are included in Barker et al. (2003, 2004) in detail. The 3-h continuous assimilation system with 10-km resolution was used in this study. Backgrounds are generated by MM5 version V3.6, which use the Reisner 2 microphysics, the Kain–Fritsh convection scheme, and a nonlocal boundary layer. The model has horizontal mesh of 178 (x direction) × 160 (y direction) grid points and 33 vertical layers. Figure 1 shows the domain and topography with a 10-km resolution that resolve the very complex terrain over the Korean Peninsula. The 3-h lateral boundary conditions (LBCs) are provided by forecasts from a 30-km resolution model at KMA.

A summary of observational data available in this experiment is shown in Table 1. High-frequency automatic weather station observations (METAR in table), which have approximately 25-km resolution, over South Korea are assimilated by the 3DVAR at every update cycle. The cutoff time for the availability of observations is about 90 min before and after the analysis time. To make effective use of METAR data, we use surface-layer similarity theory to match 2-m temperature and moisture observations and 10-m winds to the cycling 3DVAR background. This procedure has been verified to effectively use more surface observations for a KMA model with a complex terrain (Guo et al. 2002).

To apply the IAU technique to the 3DVAR cycling system, we treat analysis increments as additional forcing terms in the model equation,
i1520-0493-134-5-1389-e1
i1520-0493-134-5-1389-e2
where all prognostic fields (X) are updated for an arbitrary prognostic field by leapfrog steps with the Asselin filter (Grell et al. 1995). Here, X is the model variable at a given model time step, (∂X/∂t) includes all dynamic and physical tendencies in Eq. (1); δX is the fractional increments obtained by dividing the total increment (ΔX) by the total number of time steps using the assimilation window. Updates of forecast variables in the model are performed using the fields in the 3DVAR increment file. This is affected by reading each increment and adding the appropriate fraction. The analysis increments are added onto the corresponding wind fields, temperature, specific humidity, pressure perturbation, vertical motions, and surface ground temperature. In our sensitivity tests, IAU on pressure perturbation and vertical motions has very little impact on the heavy rainfall case of 15 July 2001. However, because the MM5 3DVAR system has generated the pressure perturbation and vertical motion in addition to the winds, temperature, and specific humidity, we have used a consistent treatment for every increment. The IAU has a 3-h window from −1.5 to +1.5 h centered at each analysis time. A total of 360 steps are used to add the whole increments during the window because of Δt = 30 s. One day forecast is produced at 1200 UTC after four update cycles (0000, 0300, 0600, 0900 UTC) from 0000 UTC 14 July 2001.

b. A heavy rainfall case

This paper intends to apply an IAU and a 3DVAR system to a heavy rainfall case in Seoul, South Korea, that occurred on 14 July 2001. The major reason for choosing this case is that the operational forecast (MM5 forecast with 10-km nested domain at that time) at KMA failed to predict the amount of precipitation and rainband. Even though the forecast for this case was improved when the 3DVAR cycling system and METAR data were introduced, there was still a northward-shifted rainband (Guo et al. 2002). Therefore, we will focus our investigation on how much forecasts can be improved by the application of both the IAU and the 3DVAR cycling system in this case.

Figures 2a,b show the 6-h accumulated rainfall amount and hourly rainfall on 15 July 2001. The rainfall was roughly 250 mm during 6 h in Seoul and the heavy rainfall was mainly concentrated from 1500 to 1800 UTC 14 July 2002 with a very narrow rainband. Maximum rainfall amount was located in northeast area of Seoul at 383.5 mm. Hourly precipitation at the Seoul station was approximately 30 to 40 mm. Geostationary Meteorological Satellite-5 (GMS-5) enhanced IR at 1800 UTC on 14 July 2001 indicates that convective systems around Seoul at 1200 UTC moved northeastward during that time (Fig. 2c). The size of the most intensive convection system, as indicated in black, is approximately 400–800 km2, which corresponds to the mesogamma scale convective system.

Similar to most heavy rainfall cases that have occurred in Korea, this case also had synoptic environments favorable for a heavy rainfall occurrence (Lee and Lee 2003). The upper-level northwesterly flow east of the trough brought enough cold air for the depression underneath to intensify. The lower-level moist air originating from the Yellow Sea west of the Korean Peninsula increased convective instability. The mean sea level pressure indicated that a localized low pressure system in the Yellow Sea, which was the strongest at 1500 UTC July 14 at the beginning of the heavy rainfall in the Seoul. This low pressure system over the ocean supported the development of the convective system by providing a moist inflow at lower levels (not shown here).

3. Comparison of initialization techniques

a. IAU and nudging

Without the proper control of spurious gravity waves, an intermittent cycling data assimilation system can generate noise and imbalance, resulting in poor performance. Imbalances in the analysis can be removed through initialization procedures, but the resultant changes to mass and winds may be significant compared to the analysis increment. This poses a challenge to high-temporal resolution mesoscale assimilation systems, such as the rapid update cycle, because the mesoscale dynamic balance in the analysis increments is difficult to achieve.

The easiest way to overcome this problem is to apply the nudging technique because this technique is already in the MM5 community model. The MM5 nudging technique known as four-dimensional data assimilation (FDDA; Grell et al. 1995) has the following simple equation:
i1520-0493-134-5-1389-e3
where X, F(X), αD are model variables, the original model forcing term, and nudging coefficient, respectively. Nudging is designed to force the model state (X) gradually to the (Xa). However, because the forcing term in Eq. (3) is directly related to the current model state (X), the nudging forcing is operative at every point of the model independent of observations. There is a great possibility of removing low frequency waves generated by the model with forcing term including X. The filtering of background state (e.g., the removal of diurnal or tidal signals) is highly undesirable. In general, numerical weather prediction (NWP) centers around the world filter only analysis increments rather than analyses in order to preserve the physical signal in the background state (Polavarapu et al. 2004).
On the other hand, the IAU technique can be expressed in Eq. (4):
i1520-0493-134-5-1389-e4
where Xb is the background, αIAU is the predefined weighting coefficient, and XaXb indicates the analysis increment. In Eq. (4), if the analysis increment is zero at a specific location, IAU forcing will be zero. This means that IAU forcing is significant only in regions where observations induce an analysis increment.

Figure 3 indicates one piece of evidence for the filtering properties of FDDA and IAU, which are expressed by the power spectral density of temperature per wave period (Press et al. 1996) at a land point with vertical layers. The top of Fig. 3 shows power spectra by nudging (Fig. 3a) after assimilation window and (Fig. 3b) during assimilation window. The bottom panels are the same as Figs. 3a,b except for IAU. To compare the same frequency over the same period, we applied the whole IAU window before model initial time such as nudging. The 12-h nudging and IAU window were applied from 1200 UTC 8 December to 0000 UTC 9 December 2003. Therefore initialized initial conditions are used from 0000 UTC 9 December 2003. After the application of nudging initialization, a time series during the day over a 12-h period (0000 to 1200 UTC 9 December) indicates a strong semidiurnal spectra near the surface as measured by longwave radiation (Fig. 3a). However, the temperature trend during the nudging relaxation period, that is, night time, was filtered out for the low frequency waves, such as semidiurnal waves (spectra at 12 h), as well as high frequency waves (Fig. 3b). Nudging severely reduces wave amplitude for stationary waves and diurnal waves at a longer relaxation time than 6 h. However, Figs. 3c,d indicate the IAU filtering properties that show the strong peak near the surface after the IAU initialization similar to those of Fig. 3a. Even though spectra densities seem to be similar during assimilation window in Figs. 3a,c, the spectra in lower and middle level (850–300 hPa) are still smaller than IAU. But the temperature time series during the IAU initialization keeps the strong spectra at the upper troposphere and lower stratosphere by short wave radiation during the night (Fig. 3d). Compared with Fig. 3b, we found that the one advantage of the IAU initialization properties affected only the high frequency through analysis increments and remains the waves related to daily variation during the assimilation period.

b. The IAU and digital filter

Because the mathematical relationship between IAU and DFI was recently demonstrated in Polavarapu et al. (2004), we will briefly summarize only practical aspects. Several variations of the DFI have been proposed, including adiabatic DFI (Lynch and Huang 1992), diabatic DFI (Lynch and Huang 1993), and modified diabatic DFI (Lynch et al. 1997). Adiabatic DFI uses the adiabatic model for a backward and forward model from the initial time. Diabatic DFI demonstrates that the time series of the model variables processed by the digital filter are produced by a diabatic integration of the model. Lynch and Huang (1993) showed that the diabatic scheme has slightly better noise reduction properties than the adiabatic scheme. However, because the backward integration is adiabatic, this could create the diabatic discrepancy. For these reasons, Lynch et al. (1997) suggested filtering the backward integration as well as the forward integration so that some of the gravity wave noise would be removed before the forward integration begins. However, to apply backward integration of DFI to a limited area mode; moisture physics, dissipation, and boundary conditions should be controlled carefully. Thus, if there is no overriding requirement to have balanced fields available at the analysis time, it is usually better to exclude the backward integration and use a pure digital filtering scheme that produces valid balanced fields after the analysis period. This technique was proposed by Fillion et al. (1995) and is known as digital filter finalization (DFF). DFF performs a 12-h forward integration to generate a time series of forecast variables that are then filtered with a centered digital filter. This allows diabatic effects to be treated more consistently. DFF can be applied incrementally so that the background evolution is left unaffected. This scheme, known as the incremental DFF (IDFF) is applied to both the analysis and the background. And then, the difference is taken to obtain a time-filtered increment that can be added onto the background evolution. The IAU has similar filtering properties but without the optimal filter design and backward integration of the DFI in the linear case (Clayton 2003).

4. Results

a. Initialization performance

In this section, the results of applying the IAU technique to the initialization of the analysis will be described. Figure 4a shows the evolution of the absolute tendency of surface pressure averaged over the forecast domain. The average absolute surface pressure and surface pressure tendency are indicators of the level of noise in the external gravity wave component. R3DV and IAU mean 3DVAR without and with IAU. The initialization performance for the IAU experiment at 0300 UTC is very similar to that of R3DV because the IAU uses the same forecasts as those of R3DV and only METAR data are present at that time. The inclusion of sounding data at 0600 and 1200 UTC cause a fluctuating curve, indicating the presence of gravity waves for initialization in the R3DV simulation. However, the excessive noise present in the uninitialized forecast (thin curve) is effectively removed by the IAU scheme (thick curve). Figure 4b, the surface pressure tendency at an ocean point, yields the similar conclusion. A chosen ocean point is located in (150, 100) in Fig. 1, approximately 500–600 km away from the east coast of the Korean Peninsula. Even though there is no sounding station over the ocean, increments over the land were spread by a recursive filter with a scale length that is noted by horizontal correlation (Barker et al. 2004). Scale lengths are usually several hundred kilometers. That means that the imbalance over the land can be spread over the ocean. Large gravity wave fluctuation near 1200 UTC in the R3DV experiment is greatly reduced by IAU. This rapid reduction in gravity wave activity by IAU will help to reduce aliasing in subsequent analyses. Two questions remain: Why does R3DV with balanced constraints generate the gravity wave noise? and Why is this noise more severe at 0000 and 1200 UTC in assimilating sounding data? There are possible imbalance sources by some assumptions in the 3DVAR system. The first possible source is the process for the calculation of linearized balanced pressure. Barker et al. (2004) used cyclostrophic terms for the linearized balanced pressure [Eq. (4)] to permit an improved balance in regimes of high curvature like hurricanes. However, geostrophic mass and wind balance were imposed in KMA 3DVAR system. After achieving an unbalanced pressure by minimizations, hydrostatic density is derived from the total pressure (unbalanced + balanced pressure by the balance equation). As a result, the hydrostatic temperature increments are calculated by hydrostatic density and geostrophic balanced equation.

There is another aspect of rationale for IAU that shows good performance of initialization. All models employ parameterizations of thermodynamic processes of some sort. These parameterizations typically act on changes in profile of temperature and moisture caused by other model process like advection. These changes are typically much smaller in amplitude than those produced by analysis increments. The result of the sudden insertion of such large changes (as much as a few degrees K at some levels) likely causes a large nonlinear response from the parameterization such as wildly inappropriate rainfall and attendant latent heating, even though analysis increments come from balanced constraints. IAU, by greatly reducing the amplitude of the analysis forcing seen by the various parameterizations, allows the overall model a chance to respond more linearly to the information coming from the analysis.

Now we focus on IAU initializations relative to the nudging technique with a 3-h relaxation time. To have a clean comparison, we first look at the differences between the first application of the nudging technique (FDDA) and IAU at 1200 UTC 14 July 2001. FDDA is started from the analysis at 0900 UTC and then nudged the model state into analyses at 1200 UTC. On the other hand, the IAU with a 3-h window starts at 1050 UTC using +1.5-h forecast based on analysis at 0900 UTC. Figure 5 shows the evolution of absolute tendency of surface pressure from the starting time of each initialization technique. The first finding is the trend by FDDA and IAU come nearly to the same level after 4-h integration, around 1500 UTC. The other point is the jump of the curve in FDDA at 1200 UTC. We suspect that this small jump results from the uninitialized LBCs from 3DVAR analysis at 1200 UTC and sudden switch off of the nudging term at 1200 UTC.

An important consideration is the computational cost in operational implementation of the IAU. Because only a half window of IAU covers a 1.5-h forecast before the initial time, the IAU is less expensive than FDDA with whole window before the initial time to get same forecast length.

To gain further insight into the model processes affected by the data assimilation methodology, we show the tendency of the u component of wind at a land grid point as a function of height and time over the land area in Fig. 6. The top and bottom panel indicate the tendency generated by the 3DVAR without (R3DV) and with IAU, respectively. In general, the R3DV and IAU show a similar tendency pattern. The tendency plot (Fig. 6a) or the R3DV indicates that model shock (or noise) is excited at each analysis time (0300, 0600, 0900, 1200 UTC) throughout the vertical column of the model. The shocks appear to be the strongest at about 23rd sigma layer (approximately 500–300 hPa) at 0600 and 1200 UTC. These shocks propagate and gradually weaken after the analysis time. The METAR (Table 1) data assimilation near the lower levels shows little imbalance tendency at 0600 and 0900 UTC in the R3DV experiment as well. However, the tendency of the IAU seems to overcome this weakness of the R3DV. In other words, the IAU gradually inserting increments on the model is very effective for creating a dynamic balance in the forecast model. However we should point out that a lot of changes are happening, too. For example, some increments seem to disappear from the lower half of the domain in IAU. Some medium-scale patterns are also affected around 11 sigma level (900–800 hPa) at 0500–0600 UTC. According to Eq. (6) in Bloom et al. (1996), the amplitude of the response function with 3-h IAU window and constant weights is shown in Fig. 7. We can see time scales below 3 h such as 1 or 2 h may be damped above 50%. However we need to investigate further the degree to which waves having time scales shorter than 3 h are filtered in the nonlinear case, since the response function in Fig. 7 was derived in linear sense.

b. Spinup of moisture variables

The impacts of IAU initialization on the precipitation forecast were attributed to the improvement in the spinup of the water cycle due to the fast production of cloud water during the initial forecast time. The spinup of the precipitation processes is a major problem during the initial integration period of almost every numerical model (Kasahara et al. 1988). This is due to the inconsistency between the velocity divergence and the moisture fields (Puri and Miller 1990). Another possible source of spinup problems could be the lack of balance among analyzed mesoscale wind, temperature, and moisture. Note that the moisture spinup following the initialization procedure is likely to be closely associated with the specific moisture schemes used in the forecast model. In our experiments, cloud, rain, ice water, and graupel in addition to the water vapor mixing ratio are passed from backgrounds to 3DVAR analysis according to Reisner 2 microphysics in MM5. As we pointed out in section 4, one other consideration for spinup is that the magnitude of the analysis increments lead to adjustments that may violate assumptions underlying the parameterizations used in the model.

Figure 8a shows the tendency of area-integrated precipitation between R3DV without IAU in a 12 h period. Spinup time in R3DV is approximately 30 min to 1 h with all hydrometeors being passed from the background. The precipitation tendency from the IAU experiment shows a smooth transition from one cycle to another. This correlates well with Fig. 6, indicating that the non-IAU adjustment processes trigger sharp, intense responses from the MM5 parameterization of moisture-related process. The nonzero precipitation amount by IAU at analysis time was mostly attributed to model integration through half the IAU window defined before the initial time. One remarkable feature in R3DV is that the large increase of rain after a few minutes integration is reduced in the next steps of integration. This probably is caused by an imbalance between moisture and dynamic variables. The current 3DVAR system used a specific humidity as the control variable, which belongs to the univariate analysis independent of temperature increment.

Figure 8b shows another piece of evidence for the spinup of moisture variables in terms of 3-dimensional integrated cloud water. The strong convective system around 1500 UTC near the Korean Peninsula should lead to a continuous increase in cloud and rainwater. In particular, more hydrometeors in IAU are caused by a cloud band over the ocean around the Korean Peninsula (not shown here). However, R3DV shows a spinup and -down before and after 1300 UTC, which resulted from an adjustment between the moisture and dynamic variables.

Figure 9 makes possible further investigation of the spinup and spindown in R3DV experiment (Fig. 8). Every experiment in Fig. 9 is performed with 3DVAR without IAU. Figure 9a shows the impact of spinup and spindown according to the different hydrometeors backgrounds. The “All” experiment appears to imply all hydrometeors (Qc, Qr, Qi, Qg, and Qs according to Reisner 2 microphysics) come from a previous forecast, while the “None” experiment has zero values for all hydrometeors. Only specific humidity from 3DVAR analysis is used in initial condition in the None experiment. The Qc + Qr experiment has only cloud and rainwater from previous forecast in addition to analyzed specific humidity. First, we can find that the moisture variables passed from previous forecasts significantly impact spinup problem. Experiments with only cloud and rainwater (only Qc + Qr in Fig. 9) do not provide significant help in reducing the spinup and spindown when compared with an experiment having no hydrometeors (None in Fig. 9). Even though the R3DV experiment with all hydrometeors (All in Fig. 9) indicates a weaker spinup and -down phenomena around 10–50 min than those of the other experiments (only Qc + Qr and None), the drying of the hydrometeors still exists after 60 min. A possible explanation for the drying of moisture variables about 1 h is related to the imbalance of the temperature and moisture variable around 30–60 min in Fig. 9b. This figure describes the average temperature and specific humidity approximately 850–500 hPa in vertical at which cloud water is mainly concentrated. The general trend of temperature and moisture is cooling and drying in the middle atmosphere owing to the increase in hydrometeors in time. However, a slight increase in temperature occurred before one hour of integration. The temperature increase may lead to the evaporation of the hydrometeors and decrease of hydrometeors amount in the All experiment in Fig. 9. However IAU may show the gradual decrease both of temperature and moisture. One advantage of using the IAU is that the humidity fields are consistently initialized along with the other prognostic variables. This allows the IAU to significantly improve precipitation spinup.

c. Skill of precipitation forecast

In this section, we will investigate the spinup impact on short-term forecast skill. Figures 10a,b show a 6-h accumulated rainfall generated by R3DV and the IAU experiment from 1500 to 2100 UTC after cycling 4 times without and with the IAU, respectively. The major differences between R3DV and IAU are in the orientation of the rainband near Seoul, precipitation in the northeastern part of the Korean Peninsula and the maximum rainfall amounts. With regard to the rainband orientation, it is difficult to assess which experiment performs better, since there are no rainfall observations over the ocean. However, in comparison with the observations (Fig. 2), we can see that the rainfall was overestimated at Tae-An Peninsula in R3DV. The 6-h accumulated rainfall in observation was roughly 20 mm in this region, while the R3DV shows precipitation above 100 mm during 6 h. IAU shows only about 40 mm. Furthermore, the rainfall over the northeastern part of the Korean Peninsula can be confirmed from the satellite images, as convective systems were located over that region (see Fig. 2c). This rainfall pattern is consistent with the strong easterly from the East Sea toward the Taebak mountain located near the east coast (Fig. 1). Maximum rainfall amounts for IAU at the center of Seoul are roughly 80 mm greater than that of R3DV.

To investigate the model’s skill in quantitative precipitation forecast, threat score (or Critical Success Index; CSI) are calculated. Figures 11a,b show the CSI for 10 and 30 mm during a 3-h period. Figure 11c shows CSI with different threshold values (0.1, 1, 5, 10, 30, and 60 mm) for 6-h precipitation ending at 2100 UTC. In this case heavy rainfall took place during the 12-h period from 1200 UTC 14 July to 0000 UTC 15 July 2001. As a result, the CSI is in general high during the first 12 h forecast from 1200 UTC 14 July 2001, and low afterward. The IAU shows higher CSI than R3DV at 3- and 6-h forecast times, with the exception at 9-h integration. Figure 11c shows the dominant impact of IAU is on heavier precipitation. Bias scores for IAU are generally better than R3DV (not shown here) too. For this heavy rainfall case, IAU demonstrates an improved short-range forecast skill of heavy precipitation.

d. Sensitivities of IAU forcing

In this section, we also investigate the sensitivities of IAU forcing variables on this heavy rainfall case. The IAU forcing used in this study is described in section 2a. Figure 12 shows the time series of hourly rainfall summarized over all the stations in Korea and the CSI score. Because rainfall above 1 mm occurred in the middle of the Korean Peninsula, the integrated rainfall amount is directly related to those around Seoul. In these figures, NTG is an experiment excluding skin temperature forcing, and NLBC experiment has IAU forcing only at interior points except for the lateral boundary zone. For any limited area model, forecast skill is increasingly controlled by the lateral boundary conditions over time as the duration of a forecast increases. Boundary update frequency for IAU application is 1.5 h because we have a 3-h IAU window centered at the 3DVAR analysis time. Boundary conditions (BCs) after 3-h IAU window are exactly same in NLBC and IAU. The only differences in the NLBC and IAU is that fractional increment is added to the lateral boundaries in integrating model and interpolated BCs from the mother domain (30 km) are modified to make consistent boundary values and tendencies during IAU window.

We discovered two characteristics in this time series. First, an experiment without ground (skin) temperature forcing (NTG in Fig. 12) had reduced rainfall at 1900 UTC, even though the distribution of 1-h accumulated rainfall of each experiment is very similar to that from the IAU experiment with skin temperature forcing. When skin temperature is added as the IAU forcing, both ground (Tg) and air temperature (Ta) have similar distribution in forecasts. However, upward heat flux by Tg–Ta [Eqs. (5a), (11), (12) in Zhang and Anthes 1982] with Tg forcing becomes little bit larger than NTG experiment before the maximum rainfall occurrence (1700 UTC 14 July 2001). Larger upward heat flux makes lower specific humidity distribution in lower atmosphere, which result in larger latent heat flux by the vertical distribution of specific humidity. That is why greater rainfall occurs in the IAU experiment with skin temperature forcing than in the NTG experiment. Second, the NLBC without lateral forcing by the IAU during the IAU integration showed the delayed maximum rainfall amount. The precipitation distribution by NLBC is an approximately 10–20-km northward-shifted rainband. Our experiment has a relaxation boundary condition with five grid points. Thus, IAU forcing over the entire domain of the model assisted in the better positioning of the rainband in this case. Increments of vertical motion derived by 3DVAR using the Richardson equation (Xiao et al. 2003) have little impact on this rainfall prediction.

On the other hand, Fig. 12b shows verification results in terms of CSI with different IAU forcing for a 60-mm threshold during 6 h. In comparing NTG and NLBC, IAU with every IAU forcing including skin temperature and LBCs forcing has the better skill score.

e. Rapid update cycles

The RUC procedure falls within a class of schemes that include all sequential data assimilation methods. It can be interpreted in the general framework of Kalman filtering (Daley 1991). Because Kalman filtering in its original formulation is not practical for application in the present-day numerical forecasting systems, some simplifications are necessary. Optimum interpolation and 3DVAR-based intermittent assimilation applied in the RUC are special cases of the Kalman filtering with empirically deduced forecast error covariance matrices (Benjamin et al. 2003). Because our experiments are based on the 3-h cycling system, we have examined the validation of IAU with more frequent cycling.

Figure 13 shows 6-h accumulated rain (1500 to 2100 UTC) from forecast performed in 1200 UTC 14 July after the cycling. This is the same as Fig. 10 except for 1- and 2-h cycling intervals. IAU window sizes for 1- and 2-h RUC system are same as update interval in this experiment. First, 3DVAR cycling with 1-h update interval (RUC1) does not produce the correct precipitation band and amount, when we compare the observed rain (Fig. 2). RUC1 generates the northward shifted rainband and considerably weaker rainfall amount. However, using IAU with 1-h cycling (IAU1) generates the correct rainband even though the amount of rainfall is still weak over Seoul. The 3DVAR cycling in a 2-h interval (RUC2) produces a rainband that is still shifted northward. However, the amount of rainfall in the western part of Seoul is increased. The IAU with 2-h cycling (IAU2) produces almost the same rainband as that with 3-h cycling with the 3-h IAU window (Fig. 13d is very similar to Fig. 10b) but with weak rainfall over the northeastern part of the Korean Peninsula. Furthermore, we found that 1-h 3DVAR cycling with IAU (IAU1) demonstrates a more accurate precipitation forecast than those of the 2-h cycling 3DVAR without the IAU procedure (RUC2).

The reason for the improved precipitation forecast for IAU with 1- and 2-h cycling can be found in Fig. 14. Figure 14a represents the cloud water integrated over the 3D model domain for 2-h RUC with (IAU2) and without IAU (RUC2). The 3DVAR analysis time is 0200, 0400, 0600, 0800, 1000, 1200 UTC in the 2-h updated cycle system. We found that RUC repeatedly has a moisture adjustment through spinup and -down during the assimilation period until 1200 UTC. However, the IAU2 has a smooth increase both for cloud and rainwater. Therefore, the IAU with a 1-h preintegration contributes to solving the spinup and -down by an adjustment between dynamic and hydrometeor variables. Furthermore, Fig. 14b shows the cost function in terms of iteration numbers between RUC2 and IAU2. The definition of cost function is the same as Barker et al. (2004). Owing to better moisture adjustment, IAU2 shows faster convergence in minimization. Slower convergence in minimization for the cost function resulted from the fluctuating gradients (not shown here). This implies the irregular decent direction for the minimization algorithm owing to dynamic imbalances. IAU in more frequent updates of the 3DVAR system contributes to reducing the balance time between dynamic and moisture variables as well as the removal of gravity waves.

5. Operational performance

The MM5 3DVAR with IAU became operational frame on 29 January 2004 after a 6-month testing period at KMA. The coupling procedure of IAU into MM5V3 and assimilating observations are the same as shown in this paper. As pointed out in a previous section, KMA MM5 3DVAR is characterized by a 3-h continuous cycling system and 10-km resolution to focus on the forecasting for the Korean Peninsula. Figure 15 shows the verification result based on an operational system. Even though these results cover a different verification period due to the testing environment at KMA in 2003, we can draw a positive conclusion. First, we could not see large differences in synoptic verification in term of rms and bias. However, IAU has showed smaller errors in the lower atmosphere, especially in the temperature and moisture field. This could be important in summer season forecasting (Figs. 15a,b). Figure 15c compares the equitable threat score (ETS) of the operational system (10 km nesting from 30 km mother domain without 3DVAR, OPR in figure) with 3DVAR (R3DV) without the initialization technique. Generally the R3DV shows a larger ETS except around the initial time (3- and 6-h forecast). This was caused by the moisture variable’s imbalance in terms of spinup. However, Fig. 15d, which has the results from OPR and R3DV with IAU, shows the improvement of the skill of the initial precipitation forecast around the 3- to 6-h forecast.

Even if R3DV with IAU was successfully implemented as the operational system, we need to further investigate the weighting of IAU in time. The current time weighting in distributing the increments is constant over the window. Because most of the observations are observed at the center of the assimilation window, more weighting using a bell or triangle shape would be desirable. However, we didn’t find any large differences between the constant and triangle shape of weighting in our sensitivity.

6. Summary and discussion

This study targets the application of the IAU to improve initialization performance and short-term forecast. The theoretical backgrounds of the IAU already are demonstrated in Bloom et al. (1996) and Polavarapu et al. (2004) against nudging or digital filter technique.

The incremental analysis updates (IAU) technique is implemented for 3-h updates of the MM5 3DVAR system with 10-km resolution to remove the spurious gravity waves in this study. IAU in 3-h updates of the 3DVAR system represents a significant improvement over the 3DVAR system without any initialization scheme in terms of the gravity wave removal and the improvement of spinup. The IAU filtering properties focusing on analysis increments are more desirable than those of the nudging method, especially for a longer assimilation window. The IAU affects only the high-frequency features caused by analysis increments, and leaves diurnal process unaffected. However, the nudging technique filters out too much meaningful wave information such as the semidiurnal wave.

The IAU scheme avoids using physically unsound backward time integration, unlike that used for the digital filter initialization. The outstanding characteristics of the IAU are computational cost, without backward integration and regardless of the use of the adiabatic and diabatic model, and a simple implementation without the use of an optimal digital filter. IAU and incremental digital filter scheme can be approximately equivalent to the incremental digital filter (Clayton 2003; Polavarapu et al. 2004) in linear sense, with a less expensive and more simple implementation.

IAU also appears to reduce the initial noise level and moisture spinup efficiently because of the gradual incorporation of analysis increments. The humidity fields are consistently initialized along with the other prognostic variables. The advantage of the IAU is most significant in improving precipitation spinup problem. Thus, a clear improvement of precipitation forecast is indicated using the IAU approach.

With an application of the IAU scheme to 1- and 2-h updated cycles, the possibilities of its use in a RUC are indicated in terms of fast minimization and less spinup and -down through more balancing between moisture and dynamic variables.

In this study, the term balance has been used rather loosely to mean a model-state free of gravity wave noise. Another aspect of the balance is how rapidly the balance of hydrometeors variables is improved without oscillation (without overmoistening due to spinup, or overdrying due to spindown). This balance is essentially the consistency between humidity and dynamic variables such as divergence (i.e., vertical motion fields).

The major disadvantage of the IAU application in an operational sense is that the initialized analysis is not available at the analysis hour because the center of the IAU window is located at the analysis time. This means that the initialized IAU with full forcing can be retrieved one and a half hours later in the 3-h IAU window.

Our latest data assimilation experiments based on an operational frame at KMA indicate a clear improvement of precipitation forecast using the IAU approach, while the observation verification scores for other quantities seems to be insensitive to initialization. More systematic investigation on the application of the IAU, including the combination of more asynoptic data such as radar and satellite data and the IAU scheme, will be carried out in the near future.

Acknowledgments

The development of MM5 3DVAR has been supported by many NCAR/MMM scientists and KMA/NWPD colleagues, including the collaboration projects from 2001 to 2003. The authors wish to express their thanks to Adam Clayton at the Met Office who provided extensive discussion on the implementation of the IAU scheme. This research was supported by the Post-Doctoral Fellowship Program (2002) of the Korea Science & Engineering Foundation (KOSEF). We thank Xiang-Yu (Hans) Huang and two reviewers for providing comments that helped to improve this manuscript.

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Fig. 1.
Fig. 1.

Model domain and topography with 10-km resolution. Contour interval is 100 m.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 2.
Fig. 2.

(a) Observed rainfall amount (mm) accumulated from 1500 to 2100 UTC 14 Jul 2001 [0000 to 0600 local standard time (LST) 15 Jul in figure]. (b) Hourly precipitation (mm) at the Seoul station. (c) GMS-enhanced IR image at 18 UTC 14 Jul 2001.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 3.
Fig. 3.

Power spectra density (Press et al. 1996) for temperature selected at a land point, which is displayed in wave period and vertical sigma levels. (a), (b) Power spectra density after (daytime) and during the 12-h nudging period (nighttime) from 1200 UTC 8 Dec to 0000 UTC 9 Dec 2003, respectively. (c), (d) Same as (a), (b) except for IAU with 12-h window.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 4.
Fig. 4.

(a) Averaged absolute tendency of surface pressure (MASP) by 3DVAR system without IAU as a control (R3DV in thin line) and with IAU (thick line). (b) Surface pressure tendency at an ocean point for R3DV and IAU experiment

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 5.
Fig. 5.

Same as Fig. 4a except for the addition of 3-h nudging experiment (FDDA) at 1200 UTC 14 Jul 2001.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 6.
Fig. 6.

Time–height section of time tendency of u wind for a land grid point. (a), (b) The 3DVAR system without IAU, and with IAU, respectively.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 7.
Fig. 7.

Response function of IAU increment according to 6-, 3-, and 1-h IAU windows. Amplitude of IAU increments comes from Bloom et al. (1996).

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 8.
Fig. 8.

(a) Domain-averaged precipitation in 10-min intervals during 12 h, overlapped 3DVAR without IAU (R3DV) and with IAU (IAU). (b) Domain-integrated cloud water amount during 6 h from 1200 UTC 14 Jul 2001.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 9.
Fig. 9.

(a) Domain-integrated cloud water amount in forecasted minutes with only Qc and Qr (only Qc + Qr), and Qc, Qr, Qi, Qg, and Qs from previous forecast (All), and no hydrometeors (None); and (b) domain-averaged temperature (solid line) and domain-integrated mixing ratio (dotted line) according to approximately 850–500 hPa. This is performed by the R3DV experiment without IAU initialization.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 10.
Fig. 10.

The 6-h accumulated rainfall amount from 1500 to 2100 UTC 14 Jul 2001 from 3-h cycling 3DVAR system (a) without IAU (R3DV), and (b) with IAU (IAU in figures). Winds are represented at 0.995 sigma.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 11.
Fig. 11.

CSI for (a) 10- and (b) 30-mm threshold during 3-h according to forecast time. (c) CSI for first 6 h of accumulated rain in different threshold rainfall amount. The lack of a bar implies that no events occurred for that run that met the threshold criterion for that forecast time.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 12.
Fig. 12.

(a) Time series of hourly rainfall summarized over all stations in Korea according to different IAU forcing variables. IAU means a case with every forcing variable produced from 3DVAR. NTG and NLBC mean IAU run without skin temperature forcing and lateral boundary forcing, respectively. (b) CSI for 60-mm threshold values during 6 h for experiments with different forcing.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 13.
Fig. 13.

The 6-h accumulated rainfall amount from 1500 to 2100 UTC 14 Jul 2001 for (a) 1-h 3DVAR cycling (RUC1), (b) same as (a) except for with IAU (IAU1), (c) 2-h 3DVAR cycling (RUC2), and (d) same as (c) except for with IAU (IAU2).

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 14.
Fig. 14.

(a) The 3D-integrated cloud water during 20 h from cycling start time, and (b) cost function from 3DVAR minimization in terms of iteration number for 2-h updates of 3DVAR system without IAU (RUC2) and with IAU (IAU2).

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Fig. 15.
Fig. 15.

(a) Rmse of RH (%) for 12-h forecast and (b) T for 24 forecast over 10 Jun and 10 Jul 2003. ETS over 5 mm/3 h (c) for the period of 12 Jun to 17 Jul 2003, and (d) for 1 Sep to 30 Nov 2003.

Citation: Monthly Weather Review 134, 5; 10.1175/MWR3129.1

Table 1.

Observation data number according to observation type on 14 Jul 2001.

Table 1.
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