a. Model description

The NFS is a nonhydrostatic primitive equation model with a fourth-order finite-difference scheme and positive-definite advection scheme for the moisture field (Hsu and Arakawa 1990). A split-explicit scheme is used for the time integration and a fourth-order diffusion is included to control grid-scale noises. Model physics used for this study include the Kuo scheme for cumulus parameterization (Kuo 1974), a simple cloud–ice explicit scheme for microphysics parameterization (Zhao et al. 1997) on the high-resolution grid, and a TKE–ε closure scheme for the planetary boundary layer processes. There are 30 vertical levels in the terrain-following vertical coordinate, with higher resolution assigned in the planetary boundary layer (Table 1). The optimal interpolation scheme is used for data assimilation.

While the NFS has the multiple-nesting capability, the forecast tracks from the three one-way nested domains with 45-, 15-, and 5-km horizontal grid spacings used operationally (Fig. 1) are very similar in general. However, predictions from the inner-most grid (5-km resolution) can provide better prediction of precipitation and wind fields over Taiwan with its more detailed terrain profile and microphysics. As we are focusing on the track forecast in this study, we will discuss and analyze results from the outer-most domain (45-km resolution) only. In addition, the design of the domain coverage is important for a regional model. Liang et al. (2001) demonstrates that the performance of a low-level jet event is significantly reduced when the southern boundary extends to the tropics, where large forcing errors exist. While it is desirable to have the regional forecast system covering as large an area as possible, significant tests have been carried out to finalize the optimal domain for operational runs of NFS as shown in Fig. 1.

CWBGFS is a spectral model with T179 resolution (approximately 1° resolution) and 30 vertical levels in the σ coordinate. For model physics, similarity theory is used to estimate the surface fluxes. A 1.5-order TKE–ε closure K theory is used to simulate the vertical turbulence mixing. The radiation scheme developed by Harshvardhan et al. (1987) is used in the model with the effects of H₂O, CO₂, and O₃. The cumulus parameterization uses the relaxed Arakawa–Schubert scheme formulated by Moothi and Suarez (1992). The model also includes large-scale precipitation and shallow convection.

The GFS [formerly the Aviation Model (AVN); Kanamitsu (1989)] is a global spectral data assimilation and forecast model system with production every 6 h at 0000, 0600, 1200, and 1800 UTC. Outputs from a horizontal grid spacing of approximately 1° × 1° and 42 vertical layers with a model top at 2 hPa are used in this study. In addition, the NCEP GFS does not use any synthetic bogus data for TC initialization except when the vortex is too weak in the first-guess field. More detailed documentations of the model can be found online (http://www.emc.ncep.noaa.gov/modelinfo).

The lateral boundary condition of the NFS is specified using the tendency of all variables from the global forecast fields with a blending zone covering seven grid points near the boundary of the NFS model domain. The representation of typhoons in the initial state is enhanced by first relocating the circulation associated with the storm to the observed position and then by including synthetic observations in the data assimilation (Liou 2004).

b. Datasets

In the operational run, the initial and lateral boundary conditions of the NFS are provided by the CWBGFS. Note that the amount of daily nontraditional observation data received from the Global Telecommunication System (GTS) at CWB is less than other major meteorology centers (including NCEP), due to the fact that Taiwan is not a member of the World Meteorology Organization, so that the observation data received at CWB are obtained from a private organization. On average, the surface synoptic observation (SYNOP) data are 15% less than those received at NCEP, the number of radiosonde observations (RAOBs) is about the same, and most of the satellite wind and vertical profiles are missing. While many factors contribute to the performance of a numerical model, such as the resolution and model physics, a shortage of data (particularly the satellite radiance) may be a significant one. Figure 2 is the comparison of the 500-hPa anomaly correlation coefficients between NCEPGFS and CWBGFS for the 1-, 2-, and 3-day forecasts in the Northern Hemisphere from May to September 2005. The NCEPGFS clearly shows more forecast skill (higher correlation) than the CWBGFS during the typhoon season, as well as in other seasons, and the difference is more pronounced for 72-h forecasts. In this study, we will examine how the performance of the global model impacts the forecasts of typhoon tracks in the NFS, with experiments using initial fields and lateral boundary conditions from CWBGFS and NCEPGFS, respectively, or a combination of both.

c. Experiment design

Five experiments were designed as listed in Table 2. The notation used in the experiments is specified in the following. The first letter denotes where the initial condition (the first guess in the data assimilation) comes from. A letter U indicates an update cycle, a C indicates a cold start with the first guess coming from CWBGFS, and an N indicates a cold start with the first guess coming from NCEPGFS. The second letter is expressed as a subscript as not all experiments need this notation. It represents an additional treatment in the initial first-guess field in certain areas. In the update cycle of the NFS, there are sometimes spurious small-scale low pressure systems over open oceans and over the Tibetan Plateau. These spurious lows cannot be removed by data assimilation because of the lack of observations. To remedy this, the data from CWBGFS are also used as bogus data over the ocean and over the Tibetan Plateau with 5° resolution in the data assimilation of the update cycle. This feature is denoted as the “5° bogus” in Table 2. This approach is adopted for the NFS as the general purpose regional forecast system and is also used in the operational TC forecast. In this study, this approach is evaluated further for the performance of TC predictions. Therefore, only experiments with an update cycle have a subscripted letter. The last letter indicates the source of the lateral boundary condition, with C and N indicating the forecast fields from CWBGFS and NCEPGFS, respectively.

Following this notation, the control experiment is labeled as U_CC with an update cycle for the first guess and lateral boundary conditions from CWBGFS. The forecasts from the U_CC experiment are slightly different from those in the real-time operational runs due to the different observation dataset used in the latter that has an earlier data cutoff time. In experiment CC, both the initial fields and the lateral boundary conditions are from CWBGFS. In experiment NN, both the initial and lateral boundary data are from NCEPGFS. Experiment U_NC is the same as U_CC (operational run) except that the 5° bogus data over the ocean and the Tibetan Plateau area are from the NCEPGFS. Experiment U_NN has the same initial conditions as in U_NC while its lateral boundary conditions are from NCEPGFS.

All the integrations are carried out to 72 h.

a. Analysis of track errors

The NFS (the version dedicated for typhoon predictions) runs only when a typhoon is in the vicinity of Taiwan. There were 21 typhoons in 2004 and 2005 for which NFS has provided real-time forecasts. The average track errors of the real-time operational NFS for 24, 48, and 72 h are 112, 208, and 304 km, respectively, for all of the 191 cases of the 21 typhoons. Out of these storms, 51 cases for eight typhoons are chosen for our study (Table 3). These cases are the ones with poor performance from NFS during operational runs.

The 72-h-averaged track forecast distance errors from all five experiments are shown in Fig. 3. Note that the U_CC (the control) results are very similar to the real-time operational runs. Among all the experiments, U_NN has the best performance, followed closely by experiment NN. These experimental results indicate that using either initial field or lateral boundary conditions, or both, from NCEPGFS results in a better track prediction than using the CWBGFS fields. The comparison between U_CC (operational run) and CC, where both use CWBGFS forecast fields as the lateral boundary conditions, indicates that a cold start is better than carrying the update cycle in NFS with the 5° bogus data from CWBGFS. This may, in part, provide the reason for the poorer forecasts in the 51 cases during operational runs. Meanwhile, keeping the update cycle and using the 5° bogus from CWBGFS does result in better performance than employing the cold start from CWBGFS completely. When the update cycle is kept while the data in the 5° bogus region are replaced by NCEPGFS analysis (U_NC), the forecast is slightly better than the control (U_CC). However, U_NC is still inferior to CC without the update cycle of NFS. We are currently expanding our experiment sample size to determine whether a cold-start approach should be adopted in NFS for future operational runs.

Using forecast fields of NCEPGFS as the lateral boundary conditions (NN and U_NN) provides the best-track forecasts for our selected cases. Whether the NFS uses a cold start from NCEPGFS as its initial conditions or keeps its own update cycle with 5° bogus from NCEPGFS has little impact on the track forecasts.

In addition, Fig. 3 also contains the track errors from NCEPGFS and CWBGFS themselves. The track forecasts from NCEPGFS are clearly better than those from CWBGFS, fairly consistent with the comparison of their anomaly correlation coefficients in Fig. 2. The track errors from CWBGFS are the worst among all seven categories shown in Fig. 3. In the early stage of the forecast, the performance of the operational NFS is better than that of CWBGFS but is about the same in the later stage. On the other hand, the track simulation exhibited that NCEPGFS and U_NN are comparable. These comparisons further suggest the importance of the lateral boundary influence. Even though the high-resolution regional model has similar forecast skill in track prediction beyond 2 days, it does provide forecast skill in terms of typhoon-associated precipitation and winds. Many studies on numerical experiments demonstrate that a high-resolution mesoscale model can be a useful tool for typhoon prediction (Peng and Chang 2002; Wu et al. 2002; Wang 2007), mainly through a better, more detailed representation of the terrain profile and land–sea contours. For example, the maximum terrain heights on Taiwan are 2215, 2807.6, and 3271.6 m, in the 45-, 15-, and 5-km grid domains, respectively. In addition, a more sophisticated subgrid parameterization is used for fine grids that can better simulate the thermodynamics of typhoons.

For more detailed comparisons, Table 4 lists the percentage differences between two forecasts at different forecast times. As expected, different initial conditions generate large forecast differences in the early stages and the differences decrease with the forecast time. On the other hand, the differences increase with time with different lateral boundary conditions. A cold start from CWBGFS diminishes the 12-h forecast but improves the subsequent forecasts compared with the operational run (U_CC), where the update cycle is retained except in the 5° bogus region. Experiments U_CC and U_NC differ only in their initial data in the 5° bogus region, and their performance differences are small. Experiment U_NC shows significant improvement over CC for a 12-h forecast (31.1%) but it forecasts trails CC at the later stage. As both experiments use the same lateral boundary conditions from the CWBGFS, it is not clear what causes the increase in the track errors beyond 12 h in U_NC. A more clean comparison for the effects of the initial conditions would be between U_CC and U_NC, where the only difference is the replacement of the data in the 5° bogus regions either by the CWBGFS analysis (U_CC) or by the NCEPGFS (U_NC). The U_NC is slightly better than the U_CC. Experiment U_NN performs better than NN for all forecasts, although the differences are very small.

Comparison between the experiment U_NC and U_NN highlights the clear effects of different lateral boundary conditions on the track forecasts. The improvement of the track using the NCEPGFS forecast fields as the lateral boundary conditions increases steadily with time. When the NCEPGFS analysis is used as the initial conditions (in the 5° bogus region) and forecast as the lateral boundary conditions, the largest improvement is obtained (U_CC versus U_NN). The differences in using different fields as the initial conditions are, in general, very small. One result that stands out with different initial conditions is that using the cold start from the CWBGFS is better than keeping the update cycle with blending of the initial field, except at 12 h, as discussed previously.

Based on the superior performance of the NCEPGFS over CWBGFS, using the NCEPGFS analysis as the initial conditions and its forecasts as the lateral boundary conditions (instead of CWBGFS) improves the typhoon track forecast in NFS. In the following section, we diagnose the synoptic fields of the forecasts and the steering flow associated with individual components of the atmospheric circulation to identify features leading to the improvement of the track forecast in different experiments.

Among the eight storms studied, the forecast of Typhoon Talim has the largest average track error, 484 km at 72 h, in the operational run. This large forecast error for Talim contributes significantly to the total track error for NFS for the season. Because of its poor performance, one case starting on 29 August 2005 was chosen as a case study for the PV diagnostics. Another case chosen for individual study is Typhoon Khanun, with the forecast starting at 1200 UTC 17 September 2005. These two cases are discussed in the following sections.

a. Synoptic fields

Talim first formed northwest of Guam on 27 August. As it moved west-by-northwest in the early stage, its intensity increased. Subsequently, Talim moved to the northwest and then passed through the center part of Taiwan to the Fujian Provence of mainland China. The best track and model forecasts of Talim starting at 0000 UTC 29 August are shown in Fig. 4. All of the forecasts for the track have a northwestward bias. In particular, the U_CC (operational) run has the largest track error. Experiment U_NC has the least improvement over U_CC, where the only difference from U_CC is in the use of the NCEPGFS analysis data in the 5° bogus region. When the first guess uses a cold start from the CWBGFS and the lateral boundary conditions from the CWBGFS (CC), a slight improvement in the track forecast is obtained. Experiments NN and U_NN improve the track forecasts more significantly with the lateral boundary conditions coming from NCEPGFS and the initial conditions coming either totally from the NCEPGFS (NN) or partially from NCEPGFS within the 5° bogus region only (U_NN). The track distance errors are 91, 214, and 305 km and 92, 202, and 303 km, respectively, from NN and U_NN experiments for the 24-, 48-, and 72-h forecasts, as compared with 48, 208, and 549 km in U_CC. Note that while the forecast track distance errors for U_NN and NN are very close at 24 h, the directions are different with the U_NN forecast track to the right of the best track and the NN forecast to the left.

The results of our experiments indicate that using both the initial and the lateral boundary conditions from NCEPGFS improves most of the forecast tracks of Talim, with different lateral boundary conditions having the largest impact in the extended forecast. This is consistent with the average of the all cases discussed in section 3. Figure 5 shows the 500-hPa geopotential height from the NCEP analysis during the simulated period from 0000 UTC 29 August to 0000 UTC 1 September. Talim was located to the southwest of the subtropical high between 0000 UTC 29 August and 0000 UTC 30 August. The western flank of the high weakens slightly while its intensity increases after 1200 UTC 30 August. The weakening of the subtropical high may be a result of the intrusion of Talim. During the same period, the trough to the north (between 30° and 40°N) intensified between 29 and 30 August, and a cutoff low formed at 1200 UTC 30 August (shown on 31 August). Meanwhile, another typhoon (Nabi) appeared to have formed in the wake of Talim (Fu et al. 2007) and moved along with Talim. For comparison, Fig. 6 contains the 500-hPa geopotential height of the forecast fields at the 48- and 72-h forecasts (valid on 31 August and 1 September) from the two global models, CWBGFS and NCEPGFS, respectively. The analysis fields from both systems have small differences, with the subtropical ridge stronger in the CWBGFS while Talim was more intense in the NCEPGFS analysis (figure not shown). For the 48-h forecast, the subtropical ridge intensified further in the CWBGFS forecast (Fig. 6a) than in the NCEPGFS forecast (Fig. 6b). The trough to the northwest became a cutoff low in both systems with the one in the NCEPGFS slightly more intense. At the 72-h forecast, the CWBGFS that provides the lateral boundary conditions to the U_CC has a more intense trough, relative to the forecast in NCEPGFS. The 48- and 72-h forecasts of the 500-hPa geopotential height fields from U_CC and U_NN are given in Fig. 7. With the influence from the lateral boundary, the characteristics of the forecasts of the overall synoptic systems are very similar between U_CC and CWBGFS and between U_NN and NCEPGFS, respectively. The trough to the northwest of Talim is more intense in and CWBGFS than in U_NN and NCEPGFS. Meanwhile, the forecasts of the subtropical ridge are also more intense in U_CC and CWBGFS than in U_NN and NCEPGFS. In the next section, we use piecewise PV inversion to identify the major steering responsible for the movement of Talim in different experiments.

b. Piecewise PV diagnosis

The piecewise PV inversion technique was developed by Davis (1992). Conceptually, this technique separates the potential vorticity field into individual pieces bearing different synoptic patterns in different regions. The nonlinear balance equation is then solved for each individual PV field to retrieve the wind field associated with each PV field. The purpose of applying this approach in our study is to identify which and how each individual PV anomaly contributes to the typhoon motion in different experiments. The symmetric average with respect to the typhoon center is treated as the mean field and the piecewise PV inversion is carried out for different parts of the disturbance, as in Wu and Emanuel (1995a,b) and Shapiro (1996). The balance equation is, in spherical coordinates,

View Expanded

where Φ is the geopotential height, Ψ is the streamfunction of the nondivergent flow, a is the earth’s radius, f is the Coriolis parameter, λ is the latitude, and ϕ is the longitude. The PV field is calculated by the following formula:

View Expanded

where κ = R_d/C_p and π = C_p(p/p₀)^κ is the vertical coordinate, η is the vertical component of the absolute vorticity, and the hydrostatic approximation is with θ = −∂Φ/∂π. The total field is separated into the mean and perturbation parts, where the mean is the axisymmetric average centered at the storm and the perturbation is the deviation from the mean. The perturbation PV is then separated into different components associated with different synoptic features in different regions (see the example below). The piecewise PV inversion retrieves the nonlinear balanced mass field associated with individual PV perturbations. The steering flows associated with individual PV disturbances for the cyclone are then computed from the retrieved wind fields. The typhoon advection flow is defined as the balanced flow at the storm center associated with the total PV distribution, excluding the positive PV anomaly of the storm itself. The steering flow (V) is computed as the deep-layer-mean wind vector between 925 and 300 hPa averaged within a 3° latitude circle around each typhoon center (note that we have used 5° latitude as the range and the results are similar); that is,

View Expanded

Our experimental results discussed previously show that different initial fields and lateral boundary conditions can affect the prediction of typhoon tracks in the NFS model. In this section, we apply the piecewise PV inversion to diagnose the impact of different synoptic systems on the prediction of Typhoon Talim (Fig. 4), of which the operational NFS shows the worse typhoon track forecast in 2005. Our diagnostics are intended to find out what impacts the track forecasts most, using the piecewise PV inversion technique.

For the piecewise PV inversion diagnostics of Talim, the total perturbation PV field is divided into four separate regions associated with the subtropical high (SH) in the western Pacific, the midlatitude trough (TR) to the northwest, Typhoon Nabi to the southeast, and the low over the South China Sea (SL) (Fig. 8). These are the major features near Typhoon Talim that may impacts its movement. The five experiments listed in Table 3 for Typhoon Talim at 0000 UTC 29 August are analyzed by the piecewise PV inversion diagnosis.

The time series of the best track [V_BT, V_BT = (X_t+6 − X_t−6)/12 h, where X_t−6 (X_t+6) is the storm center 6 h earlier (6 h later)], and the steering flow computed from four individual PV perturbations and the total perturbation for experiments U_CC and U_NN, are shown in Fig. 8, as U_NN provides the greatest improvement on the track forecast, and we use its forecasts and those from the U_CC for our diagnostics only. The PV perturbations includes the SH, the TR, the SC, Tropical Cyclone Nabi, and the total PV perturbation. First, we compare the steering vector from the total PV perturbation field (q′) with the best track (V_BT). While there are angle differences between the steering and the best track, mainly due to the beta effect (Holland 1983), the steering vectors are, in general, in good agreement with the tracks. There are substantial differences between the best-track movement vectors and the steering vectors from the forecasts of U_CC from 0000 UTC 30 August to 1 September, with the best-track wind vector mostly westward while the steering from the U_CC has a large northward component. The northward steering in U_CC causes large northward bias in its forecast track (Fig. 4). Meanwhile, the total perturbation in experiment U_NN has a steering flow that is in better agreement with the best-track movement vector and it is reflected by its superior forecast of the track (Fig. 4).

Next, we examine the steering vector from individual PV perturbations associated with the SH, TR, SL, and Nabi. The steering vectors from the PV perturbation associated with Nabi and SL are very similar in U_CC and U_NN. They both are small and apparently make little contribution to the total steering of Talim. The steering vectors associated with the midlatitude trough (TR) from U_CC and U_NN are different, especially at 1200 UTC 30 August and 0000 UTC 31 August when the deviation between the U_CC and the U_NN is distinct. Comparing the steering vectors associated with the four individual perturbations with the steering of the total disturbance indicates that the major component of the total steering comes from the one associated with the SH. The two steering vectors from the total disturbance of U_CC and U_NN have large angle differences between them, mainly coming from the steering associated with the SH with some contribution from the steering associated with the TR. On average, the magnitude of the steering vector V_SH is about twice that of the V_TR. Overall, the similarity between the V_SH and V_q′ indicates that the total steering is dominated by the SH and both the SH and TR contribute to the steering of the total disturbance at 1200 UTC 31 August and 1 September. Note that the total steering vector is much weaker than the best-track steering from both U_CC and U_NN on 30 August. This is the time when Talim made the curvature.

In summary, using different initial and lateral boundary conditions in NFS has a large impact on the forecast of the subtropical high that steered Talim. During the period where the track from the U_CC has a large northward bias, both the steering vectors associated with the midlatitude trough (TR) and the subtropical high (SH) from the U_CC have larger southerly components, contributing to the southerly component of the total steering in the U_CC. Meanwhile, the steering vectors in U_NN have smaller southerly components and are mostly from the east. The different steerings from both the subtropical high and the midlatitude trough in U_CC and U_NN contributes to the difference in the total steering that leads to the superior forecast track for Talim in U_NN over the U_CC.