To improve the initial conditions of tropical cyclone (TC) forecast models, a dynamical initialization (DI) scheme using cycle runs is developed and implemented into a real-time forecast system for northwest Pacific TCs based on the Weather Research and Forecasting (WRF) Model. In this scheme, cycle runs with a 6-h window before the initial forecast time are repeatedly conducted to spin up the axisymmetric component of the TC vortex until the model TC intensity is comparable to the observed. This is followed by a 72-h forecast using the Global Forecast System (GFS) prediction as lateral boundary conditions. In the DI scheme, the spectral nudging technique is employed during each cycle run to reduce bias in the large-scale environmental field, and the relocation method is applied after the last cycle run to reduce the initial position error. To demonstrate the effectiveness of the proposed DI scheme, 69 forecast experiments with and without the DI are conducted for 13 TCs over the northwest Pacific in 2010 and 2011. The DI shows positive effects on both track and intensity forecasts of TCs, although its overall skill depends strongly on the performance of the GFS forecasts. Compared to the forecasts without the DI, on average, forecasts with the DI reduce the position and intensity errors by 10% and 30%, respectively. The results demonstrate that the proposed DI scheme improves the initial TC vortex structure and intensity and provides warm physics spinup, producing initial states consistent with the forecast model, thus achieving improved track and intensity forecasts.
Tropical cyclones (TC) are severe weather systems that cause human fatalities and property damage in their affected areas. An accurate prediction of the motion and intensity of a TC is critical to preparedness and evacuation for areas that could potentially be hit by an intense TC. Dynamical prediction by numerical models is a major objective approach to TC forecasting in most major TC centers. Considerable progress has been made in numerical TC forecasts because of the advancements in observations and the rapid increase in computing resources. However, numerical TC forecasts still suffer from considerable errors in both track and intensity due to uncertainties in model physics and initial conditions. One way to reduce TC forecast errors is to improve TC forecast models. There have been a number of efforts in recent years to improve these models in terms of physical processes related to surface flux under TC conditions (Emanuel 2003; Donelan et al. 2004; Moon et al. 2004; Zeng et al. 2010) and convective parameterization (Ma and Tan 2009), ocean feedback processes (Emanuel et al. 2004; Davis et al. 2008), and increased model resolution (Chen et al. 2007; Davis et al. 2010).
Another way to reduce TC forecast errors is to improve the initial condition of the forecast model. An accurate initial condition, particularly for the initial TC structure and intensity, is very important for improving TC forecasts. Uncertainties in initial conditions are unavoidable due to imperfect observations and analysis methods used. In particular, initial conditions for TC forecasts usually have large errors because most TCs occur over open oceans where observations are grossly insufficient, particularly for defining the precise location and inner-core structure. Although observing platforms for TCs, including satellites and radar, have been significantly advanced in the past decade or so, they still have limitations in fully resolving the three-dimensional structure of a TC. Therefore, various initialization methods have been developed to obtain improved initial conditions for TC forecast models.
One TC initialization method involves the use of a synthetic or bogus vortex. In this method the bogus vortex, which is generated by analytic empirical functions for surface pressure and wind, is used to replace the vortex in the global (or regional) analysis. Using this method, however, it is difficult to generate the asymmetric structure of the TC vortex associated with the TC motion. This method might also result in physical and dynamical inconsistencies between the initial condition and the forecast model. Nonetheless, a number of studies have shown that this method can reasonably reproduce TC features with improved track and intensity forecasts (Ueno 1989; Leslie and Holland 1995; Wang 1998; Ma et al. 2007; Kwon and Cheong 2010). Another approach to TC initialization is the bogus data assimilation (BDA), which uses variational data assimilation with synthetic observations of a TC vortex that closely matches the observed TC intensity and structure (George and Jeffries 1994; Zou and Xiao 2000; Davidson and Weber 2000; Pu and Braun 2001; Zhang et al. 2007; Wang et al. 2008).
Another TC initialization method is dynamical initialization (DI) by forecast model integration (Kurihara et al. 1993; Bender et al. 1993; Peng et al. 1993; Nguyen and Chen 2011). This method has the advantage that the initial TC vortex generated by the DI is consistent with the dynamics and physics of the forecast model, while it requires additional model integration for the TC to intensify in the model. Kurihara et al. (1993) proposed a DI method, where an axisymmetric vortex component was generated by the integration of an axisymmetric version of the TC forecast model. The asymmetric vortex component was constructed by integrating the nondivergent barotropic vorticity equation model on a beta plane using the initial conditions from the constructed symmetric vortex flow. A similar DI scheme is currently used in the U.S. Navy regional coupled model for TC prediction (Hendricks et al. 2011) but the vortex is spun up in a different three-dimensional TC model of Wang (2001) under idealized conditions.
Recently, Nguyen and Chen (2011) developed a TC initialization scheme where a TC vortex was spun up through 1-h cycle runs from the initial forecast time and tested the scheme for a TC case. In their work, the initial condition generated from the cycle runs is consistent with the dynamics and physics of the forecast model because the model used in the cycle runs and that in the forecast run are identical. The most important advantage of this scheme is that the TC vortex, generated through the cycle runs, is adapted to the actual large-scale environment in which the TC is embedded. However, to ensure a convergence to the observed TC intensity, they have to specify the surface pressure field for the axisymmetric TC vortex during the cycle runs. The specification of the axisymmetric vortex structure is artificial because no such data are available from observations. In addition, this DI scheme spins up the dynamical fields of the TC vortex only because all model physics are still a cold start for the forecast run.
A real-time TC forecasting system has been operational at the International Pacific Research Center (IPRC) since the 2011 TC season using the Advanced Research Weather Research and Forecasting (WRF) Model. To improve TC forecast skill, we recently developed a new DI scheme and implemented it into the real-time TC forecasting system. This new DI scheme is based on cycle runs as used in Nguyen and Chen (2011) but a 6-h window before the initial forecast time is used for the cycle runs and also a large-scale spectral nudging technique is utilized. We will show that there are several additional advantages to using this new scheme. The objectives of this paper are to introduce the IPRC real-time TC forecasting system, introduce a new DI scheme, and investigate the effect of the scheme on TC forecasts over the northwest Pacific. The real-time forecasting system and a new DI scheme are introduced in section 2. Model setup and experimental design are described in section 3. The results of the forecast experiments for TCs, which occurred in the 2010 and 2011 TC seasons, are verified in section 4 and two case studies are discussed in section 5. Main conclusions are drawn in the last section.
2. The real-time TC forecasting system and a new dynamical initialization scheme
a. The IPRC real-time forecasting system for northwest Pacific TCs
The IPRC real-time TC forecasting system was built based on the WRF Model (Skamarock et al. 2005) and operated since 2011 TC season (see online at http://iprc.soest.hawaii.edu/users/dhcha). In the initial version of the real-time forecasting system, a bogus vortex with empirical idealized vortex specification (Wang 1998) was used for TC initialization and the model was run at the horizontal resolution of 15 km, which was relatively coarse due to the limitation of computing resources at that time. Despite the better skill in the intensity forecasts compared with the global model forecast, the real-time forecasting system still had low skills in track and intensity forecasts due to the low model resolution and the simple TC initialization.
Recently, we improved the real-time forecasting system by implementing a new DI scheme (see section 2b) and employing multiply nested, movable meshes with an innermost domain of 2-km horizontal grid spacing (see section 3). Figure 1 depicts the components of the updated IPRC real-time forecasting system for TCs over the northwest Pacific. If the Joint Typhoon Warning Center (JTWC) provides the warning message for a real TC occurring over the northwest Pacific, the system operates automatically. The real-time forecasting system consists of five procedures: 1) obtaining TC position and intensity from the JTWC, 2) downloading real-time global analysis data and forecast data from the Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) to provide both initial and lateral boundary conditions for the WRF Model, 3) performing DI through repetitive 6-h cycle runs (see section 2b), 4) conducting a 72-h real-time forecast using the WRF Model, and 5) postprocessing and Web displaying of the model forecast.
The model domain is triply nested with resolutions of 18, 6, and 2 km, respectively. Both cycle runs and the forecast run are conducted using the WRF Model with the same model configuration and physics parameterization options except that the large-scale spectral nudging technique is applied to both wind and temperature fields in the outermost domain in the cycle runs to reduce errors in the large-scale environmental flow. In addition, the two inner nested domains with 6- and 2-km grid spacings move following the model TC in the forecast run. However, in order to effectively separate and merge the TC component the 6-km nested domain does not move in the cycle runs.
b. A new dynamical initialization scheme for TCs
The weak initial TC vortex in global analysis and forecast can be dynamically enhanced by cycle runs using a high-resolution model, where the vortex is gradually spun up during the model integration. If the model used in the cycle runs is identical to the forecast model, the spunup vortex will be dynamically and physically consistent with the forecast model. Nguyen and Chen (2011) recently achieved this in a case study using the WRF Model. We extended and improved the method in our real-time TC forecasting system. Instead of 1-h forward-in-time cycle runs used in Nguyen and Chen (2011), our DI scheme generates a realistic TC vortex component comparable to the observed. This is achieved by 6-h cycle runs from 6 h before the initial forecast time (t0 − 6 h) to the initial forecast time t0. The advantage of the 6-h cycle runs between t0 − 6 h and t0 is that more realistic TC features can be generated by the DI because both the observed TC information and the GFS analysis data at t0 − 6 h and t0 are available in real time. This new DI scheme can also spin up all model physics such as the planetary boundary layer and cloud microphysics. This is because at the initial forecast time the model will not be reinitialized since a large-scale spectral nudging technique is used in the cycle runs; namely, a warm startup of the model forecast (see details below).
The new DI scheme consists of four procedures: 1) separation of a TC vortex, 2) repeated cycle runs for TC vortex spinup, 3) spectral nudging to reduce bias in large-scale fields in the cycle runs, and 4) relocation of the spunup TC vortex to the observed position. The spectral nudging is applied only to the outermost domain (DM1), while other procedures are applied to both the outermost domain and the inner-domain with 6-km grid spacing (DM2). In this section, the DI scheme is described by showing results for the Typhoon Kompasu case with the initial forecast time at 0000 UTC 31 August 2010.
1) Vortex separation
The main purpose of the DI is to only spin up the TC vortex component while keeping the environmental component as unchanged as possible after the DI. To enhance only the TC vortex component, the TC vortex separation method of Kurihara et al. (1993) is used. Kurihara et al. (1995) noticed that the domain for the vortex component is not necessarily circular. They then proposed a filtering method to obtain the vortex component while minimizing the removal of important nonhurricane features. In this study, however, a filter with a circular TC domain is used for efficient separation and merging of the TC components at times t0 and t0 − 6 h. The TC vortex component is defined as
where FV is the vortex component, F is the total field of a variable, and FE is the environmental component defined as
where FB is the basic component and FD is the disturbance component. To calculate the basic component, we use the filtering method of Nguyen and Chen (2011) for high-resolution model output, which is modified from Kurihara et al. (1993). Also, the isolation of the TC vortex component from the disturbance component is accomplished with the following cylindrical filter from Kurihara et al. (1993):
In (3), R is the radius of the TC domain used for separation and merging of TC component, l is a parameter controlling the filtering shape (=0.2R), and the overbar denotes an azimuthally average at the radius R defined in (5). To determine R, the azimuthal mean tangential wind profile at 850 hPa is calculated. The R is determined by searching for a radius where the tangential wind profile satisfies one of the two conditions: m s−1 and s−1, or < 3 m s−1 until the search exceeds the outer limit of 600 km. The R in the first cycle is calculated from the GFS analysis data at t0 − 6 h, while R in the Nth cycle is obtained from the WRF output at t0 in the (N − 1)th cycle.
Also, the TC vortex component in (1) is separated into axisymmetric component and asymmetric component :
Note that the vortex center here may deviate from the observed TC center and we consider the axisymmetric vortex as the TC vortex in the GFS analysis, which is relocated to the observed TC center before it is merged with the model spunup TC vortex.
2) Cycle runs
Cycle runs in this study refer to the WRF Model runs, which are repeatedly conducted for the 6-h window immediately before the initial time of the model forecast. To improve the TC vortex structure and intensity for the model forecast, the embedded axisymmetric TC vortex generated at the end of the last cycle (N − 1) run is used as the axisymmetric TC vortex at the initial time of this cycle (N) run. This is the core of the DI scheme proposed in this study.
We assume that the axisymmetric component of the TC vortex can be reasonably reproduced by the cycle runs because the asymmetric TC feature may be randomly generated in the cycle runs. Therefore only the axisymmetric component of the TC vortex spun up through the cycle runs is updated for the initial TC vortex by our DI scheme. Specifically, we extract only the axisymmetric vortex component after each cycle run for the next cycle run. Each 6-h cycle run is initialized at t0 − 6 h with the GFS analysis data as the initial condition except for the axisymmetric TC vortex, which comes from the previous cycle run. This means that both the environmental component and the asymmetric vortex component at initial time t0 − 6 h of each cycle run are identical to the GFS analysis data. Because the asymmetric flow determines the motion of the TC vortex (Fiorino and Elsberry 1989; Kurihara et al. 1993), we implicitly assume that the asymmetric flow over the TC core is well resolved in the GFS analysis, although the axisymmetric TC vortex might be generally weaker compared with the observed TC. Note also that during the cycle runs, the lateral boundary conditions are linearly interpolated from the GFS analysis data between t0 − 6 h and t0.
The initial condition of each cycle run at t0 − 6 h is then defined as
where FN is the total field in the Nth cycle run at t0 − 6 h, FE is the environmental component of the GFS analysis at t0 − 6 h, is the asymmetric vortex component of the GFS analysis at t0 − 6 h, is the axisymmetric vortex component of the GFS analysis at t0 − 6 h (relocated to the observed TC center if the vortex center is away from the observed by more than 10 km), and is the axisymmetric vortex component from the (N − 1)th cycle run at t0 relocated to the observed TC center at t0 − 6 h. That means the axisymmetric vortex component of the (N − 1)th cycle run at t0 is relocated to the observed TC center at t0 − 6 h and merged with the GFS analysis to construct a new vortex at t0 − 6 h for the Nth cycle run. In contrast, the environmental component and asymmetric vortex component are reinitialized as those from the GFS analysis at t0 − 6 h in each cycle run. In (8), ω is a weighting function to merge the axisymmetric vortex component with the large-scale and asymmetric vortex components, which is given as
Because the weighting function is zero within R/2 and gradually increases beyond R/2 (Fig. 2), only the axisymmetric vortex component from the WRF Model run is dominant over the inner part of the TC domain (<R/2), while the axisymmetric vortex component is smoothly merged with that of the GFS analysis over the outer region of the TC domain (>R/2). This implies that the outer circulation of the TC vortex is well resolved in the GFS analysis but the inner core intensity/strength is too weak.
The cycle run is conducted at least twice and is terminated once the simulated maximum surface wind is within 2 m s−1 of that from the JTWC real-time TC warning. The reason why the minimum iterations are conducted twice is that it takes about 12 h for a balance adjustment and the model physics spinup. If a storm does not deepen during the first two cycles (i.e., the difference in central sea level pressure between the first and second cycle runs is within 2 hPa), the following tangential wind VT from the empirical bogus method (Wang 1998) is embedded into the total field of the third cycle at t0 − 6 h:
Here VD is 50% of the difference in maximum surface wind speed between the total field of the third cycle run at t0 − 6 h and observation, rm is the radius of maximum wind of total field of the third cycle at t0 − 6 h, p is pressure, Pt is pressure at the vortex top (100 hPa here), and Ps is surface pressure. The maximum number of the cycle runs is set to 20, and the output of the cycle run with maximum TC intensity is employed as the initial condition of the forecast run if the TC intensity is not comparable to the observed intensity by the 20th cycle run.
Figure 3 shows each component at t0 − 6 h in (8) (i.e., the environmental component, asymmetric vortex component, axisymmetric vortex component, and the total field), which are calculated in the last cycle run for Typhoon Kompasu. The environmental component only has the large-scale feature of geopotential height around TC, and the asymmetric and axisymmetric vortex components are reasonably represented. It should be noted that the axisymmetric vortex component in geopotential height from the cycle runs is much lower than that from the GFS analysis, indicating that the axisymmetric vortex component represents a much stronger TC vortex from the DI.
Figure 4 shows the simulated surface wind at the end (t0) of each cycle run for Typhoon Kompasu. The observed maximum wind speed at 0000 UTC 31 August 2010 is 49 m s−1. However, the maximum wind speed in the GFS analysis is only 18.3 m s−1, indicating that the GFS with 0.5° resolution is not able to capture the intensity of a strong TC. To obtain the realistic initial condition for Typhoon Kompasu, 13 cycle runs are successively conducted during the DI. As the cycle increases, the simulated maximum wind speed intensifies and gets closer to the intensity from the JTWC best-track data. After the last cycle run, the maximum surface wind speed increases to 48.4 m s−1, which is comparable to the observed but much stronger than that in the GFS analysis. The asymmetric feature with stronger surface wind in the northeastern quadrant of the TC circulation appears in all cycle runs, similar to that in the GFS analysis. Figure 5 shows the zonal–vertical cross sections of the tangential wind and potential temperature across the TC center after each cycle run. Although the intensity of Typhoon Kompasu at 0000 UTC 31 August 2010 is almost category 3, the TC structure is not captured well in the GFS analysis. The tangential wind to the west of the TC center is too weak and the eyewall structure is not well resolved. Also, the inner-core size is unrealistically large and the deep TC circulation is not captured. Similar to the GFS analysis, the TC structure is still unrealistic in the earlier cycle runs. As the cycle increases, the eyewall structure is properly reconstructed and the tangential winds around the eyewall are largely increased. Also, the deep cyclonic circulation in the TC core is gradually enhanced, whereas the inner-core size is reduced. Similar to the horizontal distribution of surface wind speeds, the asymmetric feature, such as the stronger wind to the east of the TC center, is maintained throughout the cycle runs.
3) Spectral nudging
By the DI scheme, the model output integrated from t0 − 6 h to t0 is used for the initial condition of the forecast run. This results in a well-developed and realistic TC vortex and has the advantage for a warm startup of the forecast model physics. However, it is possible that the initial condition of the forecast run after the DI can have nontrivial error in the environmental field at t0 against the GFS analysis. To reduce the initial error of the forecast run, the large-scale spectral nudging method (von Storch et al. 2000; Miguez-Macho et al. 2005; Cha et al. 2011) is applied to the integration of each cycle run:
where Q is the model prognostic variables, F is the model operator, α (=0.0003, corresponding to an e-folding damping time of 55.6 min) is a nudging coefficient, and and are the large scale components of the global analysis and the WRF Model forecast, respectively. The spectral nudging can reduce the deviations in the large-scale fields between the WRF Model after the cycle runs and the GFS analysis at t0. It has little effect on mesoscale features developed in the cycle runs. This allows the mesoscale structure of the TC eyewall to develop freely during the cycle runs. In this study, the spectral nudging is applied to the large-scale component with wavelength larger than 1000 km for both wind and temperature fields above the planetary boundary layer.
4) TC vortex relocation
After the last cycle run, the simulated TC center at t0 can have a nonnegligible position error as compared to the observed TC position. To reduce the initial position error of the forecast run, the following relocation method is utilized:
where dx and dy are the position differences in zonal and meridional directions, respectively, between the observed TC center at t0 and the spunup TC center at t0. In the relocation method, cylindrical filtering from Kurihara et al. (1993) is used to divide the total field into TC vortex component and environmental field. After separation, only the TC vortex component is relocated to the observed TC position and it is then merged with the environmental field to construct new total fields. The relocation is applied to all possible variables of the WRF restart file at t0 after the last cycle run. Similar to Hsiao et al. (2010), the relocation is skipped to exclude the topographic effect if high terrain exists within the radius of TC gale-force wind. This is because the restart file is written in sigma vertical coordinate. The axisymmetric structure can be affected greatly by topography if high terrain exists in the inner-core region of a TC. When a TC is close to the high terrain, the axisymmetric circulation of the TC vortex would be largely distorted if the cylindrical filter of the relocation method at t0 is applied to variables on sigma levels. Note that in the DI scheme, the WRF Model outputs are converted from sigma coordinate to pressure coordinate in the relocation procedure after each cycle run. In that case, the effect of high terrain on the converted output is relatively weak; thus, we can use the relocation procedure after each cycle run in the DI scheme. An example of the relocation for Typhoon Kompasu is shown in Fig. 6 where a 30-km position error is prominently reduced after the relocation.
3. Model setup and experimental design
To evaluate the effectiveness of the new DI scheme, two sets of forecasts are conducted for TCs occurred over the northwest Pacific in 2010 and 2011 (Table 1): a forecast run without the use of the DI scheme (hereafter referred to as the CTL run), and a forecast run using the DI scheme (hereafter referred to as the DI run). The results from the two forecast runs are also compared with those from the GFS forecasts. The initial condition in the CTL run is interpolated from the GFS analysis, while the DI run uses the WRF output from the last cycle run as described in section 2b. Other model configurations in the two runs are identical.
In both forecast runs, the WRF Model contains a mother domain (DM1), an intermediate domain (DM2), and an innermost domain (DM3). The two-way moving nesting method is applied. Domain sizes (horizontal grid spacings) of DM1, DM2, and DM3 are 311 × 251 grid points (18 km), 271 × 271 grid points (6 km), and 211 × 211 grid points (2 km), respectively. The domain sizes are chosen to allow DM2 to cover the primary cyclonic circulation of most TCs while also allowing DM3 to cover the inner-core region of TCs. The center of the mother domain is 5° (7°) to the north (northwest) from the observed TC center if the latitude of the observed TC center is north (south) of 20°N, while the centers of the two subdomains are near the observed TC center. All domains have 28 vertical levels from the surface to the model top at 50 hPa. The time steps for the model integration are 90, 30, and 10 s for DM1, DM2, and DM3, respectively. The forecast runs are initialized at 0000 or 1200 UTC and integrated for 72 h.
The model physics include the WRF single-moment 6-class microphysics scheme (WSM6) (Hong et al. 2004), Dudhia shortwave radiation scheme (Dudhia 1989), Rapid Radiative Transfer Model (RRTM) longwave radiation scheme (Mlawer et al. 1997), Yonsei University (YSU) planetary boundary layer scheme (Hong et al. 2006), and the Noah land surface model (Chen and Dudhia 2001). These schemes are applied for all domains. The Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1990) is applied only to DM1. The parameterizations of surface momentum and heat fluxes over the ocean as well as dissipative heating applicable to strong winds (Davis et al. 2008) are employed with the momentum roughness length from Donelan et al. (2004) and the parameterization for heat and moisture roughness lengths from Garratt (1992).
As mentioned in section 2a, the model configurations for the cycle runs are the same as those for the forecast run except for application of the large-scale spectral nudging in DM1 and the stationary nature of DM2. In the DI run, the initial condition of the forecast run is the output of the DI and the lateral boundary condition is from the GFS forecast, while the initial condition and lateral boundary condition in the CTL run are from the GFS analysis and forecast, respectively. Sea surface temperature (SST) is the same as that used in the GFS forecast.
In total, 14 TCs occurred over the northwest Pacific in 2010, which is below the climatological mean. We selected 9 TCs with their duration longer than 4 days and conducted 38 forecasts for both the CTL and DI runs. We also conducted 31 forecasts for 4 TCs that occurred in 2011, which all had intensities above typhoon intensity [>64 kt (~33 m s−1)] in their lifetime and showed different types of tracks, to demonstrate the robustness of the proposed new DI scheme. Therefore, in total, 69 forecasts for 13 TCs in 2010 and 2011 were conducted in this study (Table 1). If the initial TC intensity in the GFS analysis at the initial forecast time is close to the observed, the DI can result in overintensification of the TC. Therefore, the DI scheme is skipped for cases in which the maximum wind speed in the GFS analysis at the initial forecast time is within 90% of the JTWC best-track data. Of our 69 forecasts there are 4 cases (about 5%) where we skipped the DI. For these cases, the results from the CTL run are used in the verification. To verify the TC forecasts, the JTWC best-track data are used for TCs in 2010 and the JTWC warning information is used for TCs in 2011. This is because the JTWC best-track data for TCs in 2011 was not available at the time we performed the verification.
4. Verification of the forecasts
In this section we evaluate the 69 forecasts using the traditional metrics of TC position and intensity errors to demonstrate the effectiveness of the new DI scheme. The position error and intensity error of the CTL and DI runs are calculated from the results of DM2 because the instantaneous result of DM2 with a time step of 30 s implies a time mean of 30 s to 1 min, comparable to the best-track intensity in terms of the maximum surface wind speed, which is assumed to be a 1-min mean. Figure 7 shows the position and intensity errors averaged for the 69 forecasts. For all runs, the position errors tend to increase as the forecast time increases. At all lead times, the GFS forecasts show the largest position errors, and the DI run has smaller position errors than the CTL run. Based on the Student’s t test and 95% confidence level of correctly rejecting the null hypothesis, the DI run has significantly smaller position errors than the GFS forecasts at all lead times except between 6 and 30 h, while it has significantly smaller position errors than the CTL run only at initial time. The initial position error of the DI run is much smaller than that of the GFS analysis and that of the CTL run as a result of the use of the relocation method. However, the DI run still has small initial position error because the relocation method in the forecast runs was skipped when the TC core was affected by topography as mentioned in section 2. Also, merging the relocated TC vortex component with the environmental component in the relocation method can cause small initial position error as well in the DI run as a result of the asymmetric nature of the environmental pressure field. The improvements from the DI run are obvious in intensity forecasts. The GFS forecast shows the largest intensity biases (reaching as large as 20 m s−1). The CTL run reduces the intensity biases to about 10 m s−1 at all lead times except for the initial time. The DI run further reduces the intensity biases because of the use of the DI scheme, in particular, in the first 24-h forecasts. The smaller intensity biases of the DI run, as compared to the GFS forecasts, are significant at all lead times. The smaller intensity biases of the DI run, as compared to the CTL run, are significant from 0 to 48 h. It is noteworthy that the improvement due to the use of the DI scheme decreases as the forecast time increases.
Compared with the GFS forecast, the CTL run decreases the 72-h mean position and intensity errors by about 10% and 45%, respectively (Table 2). This means that the high-resolution WRF Model can improve the TC forecast in terms of track and intensity even if no specific TC initialization scheme is employed. Compared with the CTL run, the position and intensity errors in the DI run are further reduced by about 15% and 30%, respectively. Therefore, the DI improves both the track and intensity forecasts.
To examine the effect of the DI on each TC case, we analyze the statistics of 72-h mean errors averaged for each TC case as shown in Table 3. Note that Typhoon Malakas is the only case for which all initial intensities in the GFS analysis are comparable to the observed. The DI was skipped for this case and the results of the CTL run were used in the statistics for the DI run. In all TC cases, the position errors from the DI run are smaller than or similar to those from the CTL run. For the TCs where the GFS forecasts show position errors larger than 200 km (e.g., Conson, Kompasu, and Malou), the DI run shows much smaller position errors, indicating more significant improvements from the DI. For other TCs where the GFS forecast shows relatively small position errors, the DI run has position errors slightly smaller than or similar to those of the GFS forecast. This may be due to the fact that the large-scale flow related to TC motion cannot be further improved by the DI if the GFS predicts the large-scale flow realistically. Nevertheless, for all TCs except for Typhoon Malakas, the DI run has much smaller forecast errors for intensity than either the GFS forecast or the CTL run, implying that the DI significantly improves TC intensity forecasts.
It is noteworthy from Table 3 that the improvement due to the use of the DI scheme on the track and intensity forecasts depends on the performance of the GFS forecasts. To examine such dependence, Fig. 8 shows the scatterplots of differences in position and intensity errors between the GFS forecast and the DI run as a function of the GFS forecast errors. The differences in the errors imply the reduced errors by the use of the DI scheme. For both track and intensity, the differences tend to increase as the errors in the GFS forecast increase. This demonstrates that the overall performance/improvement of the model with the DI scheme is strongly related to the large errors in GFS forecasts, in particular intensity error (Fig. 8b).
5. Case studies
As shown in the previous section, the new DI scheme developed in this study has a positive effect on track and intensity forecasts. In this section, we will further investigate why the DI scheme improves the TC forecasts by two case studies for Typhoons Kompasu and Megi.
a. Typhoon Kompasu
Typhoon Kompasu formed over the northwest Pacific near Chuuk State and moved northwestward to the East China Sea. After passing Okinawa, it extraordinarily veered to South Korea and hit the Seoul metropolitan area. Typhoon Kompasu led to significant wind damage in both Japan and Korea. Figure 9 shows the TC tracks from the GFS forecast and the CTL and DI runs. The GFS forecast has relatively large position errors compared with the JTWC best-track data. After passing Okinawa, the predicted TC moves more westward to the east coast of China and turns to North Korea. Similar to the GFS forecast, the CTL run predicts westward biased tracks. In the DI run, the track error is significantly reduced, suggesting a considerable improvement in track forecast with the DI. Also, the initial storm positions in the DI run are in good agreement with those observed due to the application of the relocation method.
The intensity forecasts for Typhoon Kompasu are also improved with the DI. Figure 10 shows the temporal evolutions of TC intensities from the GFS forecast and from the CTL and DI runs with different initial times. The TC intensities of the GFS forecasts are much weaker than the best-track data for all forecast lead times. In particular, the initial intensities are considerably weaker than those observed. For example, at 0000 UTC 31 August 2010, the initial intensity is less than 20 m s−1, which is much weaker than the observed 48 m s−1. The GFS forecast also fails to predict the intensification of the storm because the predicted maximum surface wind does not show any increasing trend. This might be partially due to the too weak initial storm intensity and partially due to the coarse resolution and/or the inadequate physics parameterization of the GFS. In the CTL run, the storm intensifies to some extent but its intensity is still much weaker than the best-track data. That is, the CTL run slightly improves the intensity forecast for Typhoon Kompasu because of the high model resolution, but still fails to predict the intensification most likely due to the too weak initial storm. In contrast, the initial intensities of the DI run are in good agreement with those observed, leading to proper simulation of the intensification process. Therefore, the DI run realistically captures the temporal evolution of TC intensity. This demonstrates that the new DI scheme significantly improves the intensity forecast for Typhoon Kompasu.
To clarify how the DI scheme improves the initial TC features, we show in Fig. 11 the radial–vertical cross sections of the azimuthal mean tangential and radial winds, and potential temperature anomalies of the storm at the initial forecast time in the GFS analysis and the DI run. Although the observed TC at the initial time is almost category 3, the TC intensity in the GFS analysis is quite weak and the TC structure is not well resolved. In the GFS analysis, both the tangential and radial winds are significantly underestimated, and the radius of maximum wind (RMW) is about 200 km, but it is only about 40 km in the best-track data. Also, a very weak warm core structure vaguely appears in the GFS analysis. In contrast, the structure of Typhoon Kompasu is well represented in the DI run, with strong tangential winds throughout the depth of the troposphere with low-level inflow and upper-level outflow, and has a well-developed warm core in the mid- to upper troposphere. The maximum tangential wind in the DI run is over 45 m s−1 at 900 hPa, which is about 3 times of that in the GFS analysis. Also, the RMW decreases considerably from about 200 km in the GFS analysis to about 60 km in the DI run. Although the RMW in the DI run is still larger than the observed, it is significantly improved compared to that in the GFS analysis. These TC features in the DI run are in good agreement with those of a well-developed real TC (e.g., Frank 1977).
To demonstrate the effect of the DI on the predicted TC features during the forecast run, we show in Fig. 12 the horizontal TC structure in the CTL and DI runs at the peak intensity of the observed TC. In the satellite IR image, the storm shows a compact inner-core structure with two outer spiral rainbands, one extending from the west to the northeast and a major one spiraling from the east in the inner core to the southwest outward. In the inner-core region, convection is considerably enhanced in the northeast quadrant. In the CTL run, the inner core structure is quite asymmetric and only the major outer spiral rainband is captured. In contrast, the DI run properly reproduces the horizontal distribution of cloud and precipitation in Typhoon Kompasu. The simulated inner-core structure and two outer spiral rainbands correspond well to the satellite observation.
Figure 13 shows the zonal–vertical cross sections of the total wind speed and potential temperature across the storm center in different runs at the peak intensity of the observed TC (after 24-h forecast). In part because of the underestimated initial TC intensity and large vortex size, the GFS forecast produces unrealistic TC structure with shallow cyclonic circulation, too large inner-core size, and underdeveloped eyewall to the west of the storm center. The CTL run slightly enhances the TC vortex but the intensity is still too weak compared to the observation. In particular, wind speeds to the west of the storm center are too weak. In contrast, the DI run with the enhanced initial TC vortex greatly improves the TC intensity and structure, such as deep cyclonic circulation, well-developed eyewall, and small inner-core size.
As described in section 2, in the DI scheme, the repeated cycle runs allow the TC vortex to spin up, the large-scale spectral nudging reduces errors in the large-scale environmental field, and the relocation reduces the initial position error. To investigate the individual contributions of these methods to the improved track and intensity forecasts, we conduct two auxiliary experiments. In one experiment (the DI_NOSN run), the large-scale spectral nudging is excluded from the DI scheme. In another experiment (the DI_NOREL run), the relocation after the last cycle run is not applied. Figure 14 shows the track and intensity forecasts from five runs with the same initial forecast time. The predicted track from the DI_NOREL run is very close to that from the DI run (Fig. 14a). This indicates that the contribution of the relocation to the improved track forecast is insignificant except for a reduction of position error at the initial forecast time. This also implies that the enhanced TC vortex through the cycle runs contributes much more to the improved track forecast in the DI scheme. The track position error from the DI_NOSN run is larger than that from the DI run, implying that the large-scale spectral nudging reduces the track forecast error. Table 4 shows the root-mean-square errors (RMSEs) of the large-scale environmental components of several atmospheric variables at the initial forecast time from the DI and DI_NOSN runs. For all variables, the DI run has smaller error in the initial environmental fields than the DI_NOSN run. In the DI scheme, the restart file of the WRF Model at the end of the last cycle run from t0 − 6 h to t0 is used for the initial conditions for the 72-h forecast run. This gives the advantage of warm physics start up in the entire model domain. However, the environmental fields of the restart file can be different from those of the GFS analysis at t0, because they are generated by 6-h model integration. The error of large-scale environmental field in the DI_NOSN run is nontrivial, while the error in the DI run is prominently reduced because of the use of the spectral nudging (see Table 4). This means that the spectral nudging contributes positively to the improved track forecast by reducing errors in the large-scale environmental fields, which is the result of the last 6-h cycle run. Therefore, the improved track forecast in the DI run results from both the improved TC vortex by the cycle runs and the reduced error in environmental fields by the spectral nudging. In terms of the intensity forecast, the errors from the DI, the DI_NOSN, and the DI_NOREL runs are similar to each other except that the DI_NOSN run predicts slightly stronger TC after the 48-h forecast because of the delayed landfall (Fig. 14b). Therefore, the repeated cycle runs to enhance the TC vortex directly improves the intensity forecast, while the spectral nudging indirectly improves the intensity forecast by improving the track forecast.
Furthermore, the advantage of the warm startup of model physics can be illustrated by showing the model-predicted precipitation at an early forecast lead time. As we can see from Fig. 15, without the application of the DI scheme in the CTL run, the model radar reflectivity is quite weak and less organized while in sharp contrast, that in the DI run shows great similarity to that observed. This indicates that the warm startup of model physics is critical to the short-term forecast of precipitation, although strong TC vortex in the DI run also contributes to the improved precipitation forecast.
b. Typhoon Megi
Typhoon Megi was the strongest typhoon over the northwest Pacific in 2010 and resulted in significant damage in the Philippines, Taiwan, and mainland China. It formed southeast of Guam and moved westward to the Philippines. After passing over the Philippines, it turned to the north and moved toward south China. The tracks predicted from the three forecasts are similar to each other and close to the best track (Fig. 16). All forecasts capture the landfall over Luzon Island in the northern Philippines and the northward turning after crossing Luzon Island. As seen in Table 3, the 72-h mean position errors averaged for 10 forecasts are less than 100 km in all runs. Nevertheless, the position error from the DI run is about 30% smaller than that from the GFS forecast.
To examine the effect of the DI scheme on the improvement of the TC structure, we analyzed the radii of 34-kt (~17.5 m s−1) winds (R34) for Typhoon Megi in Table 5. The DI run has smaller error of R34 at the initial time of the forecast run as compared with the GFS analysis. The R34 in the GFS analysis is about 20% smaller than that in the best-track data, because the initial TC vortex is much weaker in the GFS analysis because of the low resolution. On the contrary, the R34 from the DI run is in good agreement with the best-track data. This implies that the DI scheme improves the structure of the TC vortex.
Figure 17 shows the temporal evolutions of the maximum surface wind and central sea level pressure predicted for Typhoon Megi from the three runs. It is not surprising that the GFS forecast largely underestimates the intensity of Typhoon Megi. Although the CTL run considerably improves the intensity forecast, the predicted intensity experiences significant initial shocks in the first 6 h. Similar initial shocks also appear in the CTL run for Typhoon Kompasu at a relatively lower level (Fig. 10b). The initial shocks in the CTL run are related to the discrepancies in both the dynamical balance in the interpolated high resolution to the WRF Model from the low-resolution GFS analysis and the spinup of physics of the forecast model (namely the cold startup). It takes about 12 h for the model to achieve dynamical balance and the spinup of model physics in the CTL run. In contrast, the initial shocks do not appear in the DI run because the physical and dynamical inconsistencies and any possible imbalances are damped during the cycle runs in the DI. The warm startup of model physics also contributes to a smooth evolution of the storm intensity in the DI run.
6. Summary and discussion
To improve the real-time forecast of TCs, a new DI scheme was developed and implemented into the IPRC real-time forecast system for TCs over the northwest Pacific using the WRF Model. In this DI scheme, each cycle run was initialized 6 h before the initial forecast time (t0 − 6 h) and integrated for 6 h to the initial forecast time t0 using real-time GFS analysis data for both initial and lateral boundary conditions. To prevent randomly developed asymmetric features, only the axisymmetric vortex component from the cycle run was used to enhance the TC inner-core strength that generally could not be resolved well in the GFS analysis. Namely, the axisymmetric vortex component from each cycle run was used to replace the axisymmetric vortex component in the GFS analysis at t0 − 6 h for the next cycle run. To maintain the large-scale environmental flow during the cycle runs, large-scale spectral nudging was utilized for both the wind and temperature fields in the outermost domain. In our application, the large-scale component with horizontal wavelength longer than 1000 km was kept close to the GFS analysis. The cycle run was terminated once the intensity of the simulated TC was comparable to that of the observed TC and then the TC was relocated to the observed position to reduce the initial position error for the subsequent forecast run. The newly developed DI scheme had been shown to improve not only the TC intensity but also the TC structure, and also provide the warm startup of model physics.
To evaluate the effectiveness of the new DI scheme, 69 forecast experiments with and without the use of the DI scheme were conducted for 13 TCs occurred in 2010 and 2011 over the northwest Pacific. The statistics for the 69 forecasts indicated that the CTL run without the DI scheme had smaller 72-h mean position and intensity errors than the GFS forecast, implying the importance of the high model resolution required for TC forecast. The DI run with the use of the DI scheme further reduced the position and intensity errors of the CTL run by 10% and 30%, respectively, indicating the positive effect of the DI scheme on the TC forecast accuracy.
Two typhoon cases among the 13 TCs were analyzed in some detail to demonstrate the impacts of the DI scheme and the spectral nudging on the track and intensity forecasts. In the Typhoon Kompasu case, forecasts using the DI scheme significantly reduced both the position and intensity errors by improving the initial TC intensity and structure, which were not well captured in the GFS analysis. In particular, the enhanced initial TC vortex by repeated cycle runs and the reduced error of environmental fields by the large-scale spectral nudging contributed significantly to the improved track and intensity forecasts. In the Typhoon Megi case, the CTL run displayed significant initial shocks in the time evolution of the maximum surface wind and the central sea level pressure in the first 6-h forecast, most likely due to the discrepancies in dynamical balance from the interpolation to the high-resolution WRF Model from the low-resolution GFS analysis and also the spinup of physics of the forecast model. In contrast, the initial shocks were mostly eliminated using the DI scheme because the physical and dynamical inconsistencies and any possible imbalances were damped during the cycle runs in the DI. The warm startup of model physics was also an advantage of the new DI scheme. As a result, overall the new DI scheme has a significant positive effect on both track and intensity forecasts of TCs because it improves the three-dimensional TC structure and intensity at the initial forecast time, provides a warm startup of model physics, and reduces the imbalance in the initial state of model forecast. The DI scheme is currently being applied to the IPRC real-time forecasts for TCs over the northwest Pacific.
The main purpose to perform a DI is to minimize any dynamical imbalance at the initial time of a forecast model. This is particularly important for TC forecast model since TCs are very strong synoptic weather systems, any imbalance at the initial time may lead to numerical instability. As mentioned in section 1, Kurihara et al. (1993) first proposed to use a balanced TC vortex spun up from an axisymmetric version of their three-dimensional forecast model to replace the weak axisymmetric vortex in global analysis at the initial time. However, this spunup axisymmetric vortex did not reflect any effect of the storm environment on the storm structure since only the mean vertical sounding was used as the basic state in the axisymmetric model. In Hendricks et al. (2011), a three-dimensional model that was different from the forecast model was used to spin up a three-dimensional TC vortex by forward time integration. Similar to Kurihara et al. (1993), the environmental effect on the intensification of the TC vortex could not be included.
This shortcoming has been avoided by the DI scheme recently proposed by Nguyen and Chen (2011), where a TC vortex was spun up through 1-h cycle runs from the initial forecast time by using the forecast model. Since the cycle runs used the global analysis fields as the initial condition, all environmental effect on the spinning up of the TC vortex was included in their DI scheme. Furthermore, because the model used in the cycle runs and that in the forecast run were identical, the initial TC vortex generated from the cycle runs was consistent with the dynamics of the forecast model. Compared with Kurihara et al. (1993) and Hendricks et al. (2011), the most important advantage of the DI scheme of Nguyen and Chen (2011) was that the TC vortex, generated through the cycle runs, was adapted to the actual large-scale environment in which the TC was embedded. However, the scheme of Nguyen and Chen (2011) had some weaknesses as well. First, to assure a convergence of the cycle runs to the observed TC intensity, they had to assimilate the surface pressure field for an axisymmetric vortex during the cycle runs. The specification of the axisymmetric vortex structure was not constrained by observations. Second, their DI scheme only spins up the dynamical fields of the TC vortex and does not spin up the model physics at the initial time of the forecast run. Third, the effectiveness of their scheme was demonstrated for a TC case only.
In our new DI scheme, we have avoided some of the above shortcomings while keeping the advantages of the earlier schemes. Instead of 1-h cycle runs from t0 in the scheme of Nguyen and Chen (2011), 6-h cycle runs from t0 − 6 h are performed in our new scheme. This has the following advantages. First, the dynamical balance can be achieved not only for TC vortex but also for the non-TC fields because of the 6-h dynamical adjustment during the cycle runs. Second, since the model forecast starts from the integration of the last 6-h cycle run, all model physics are spun up at the initial forecast time, thus the model features a warm startup for the forecast run. Third, the use of the large-scale spectral nudging during the cycle runs ensures that the non-TC large-scale fields are nearly conserved during the cycle runs, which is important for the warm startup of the model physics and the track prediction. Furthermore, similar to the scheme of Nguyen and Chen (2011), the TC vortex constructed by the proposed DI scheme has better dynamical and physical balances and is better adapted to the environment in which the TC is embedded than that from the DI schemes of Kurihara et al. (1993) and Hendricks et al. (2011). In addition, the new DI scheme is easy to be implemented into any other high-resolution models since we have developed a module that is independent of the rest of the forecast model. Indeed, we have recently implemented the new DI scheme into the NCEP Hurricane WRF (HWRF) Model already. Results from our preliminary tests are very encouraging as well.
Finally, we would like to mention that the high-resolution WRF Model without the DI can improve TC forecasts to some extent compared to the much coarser resolution GFS forecast. This implies that the improvements in TC forecasts from the DI run result not only from the use of the DI scheme but also from the use of the high-resolution WRF Model. Therefore, for real-time dynamical TC forecasts, the improvements in the forecast model are equally important to the advancements in the TC dynamical initialization. It is believed that there is still room to further improve the performance of the real-time forecast system that we have developed by some extra model tunings, such as the improvements in model physics and the optimal combination of different model physics parameterization schemes.
As mentioned in section 2b, the simple cylindrical filter of Kurihara et al. (1993) is used in the current version of our real-time forecast system to separate the TC component at t0 and t0 − 6 h. We notice that the TC domain is important for TC forecast and that the method of Kurihara et al. (1995) is better for the removal of non-TC disturbance component. Therefore, we plan to modify the vortex separation algorithm in our DI scheme for the next version of the real-time forecast system using the updated method documented in Kurihara et al. (1995). Also, we will investigate the possible effect of the spectral nudging on the forecast run as designated by Liu and Xie (2012). They showed that the application of the scale-selective assimilation, similar to the large-scale spectral nudging, for the entire forecast time can lead to an improved track forecast. In addition, the new DI scheme can be combined with a four-dimensional data assimilation system during the cycle runs. These will be our next research topics.
This study has been supported in part by NSF Grant ATM-0754039 and by NOAA Grant NA09OAR4310081, and in part by the China Department of Science and Technology International Collaboration Grant 2008DFA22180. Additional support has been provided by the JAMSTEC, NASA, and NOAA through their sponsorships of the International Pacific Research Center (IPRC), School of Ocean and Earth Science and Technology (SOEST) at the University of Hawaii at Manoa.
School of Ocean and Earth Science and Technology Publication Number 8767 and International Pacific Research Center Publication Number 921.