Accurately forecasting a tropical cyclone’s (TC) track and intensity remains one of the top priorities in weather forecasting. A dynamical downscaling approach based on the scale-selective data assimilation (SSDA) method is applied to demonstrate its effectiveness in TC track and intensity forecasting. The SSDA approach retains the merits of global models in representing large-scale environmental flows and regional models in describing small-scale characteristics. The regional model is driven from the model domain interior by assimilating large-scale flows from global models, as well as from the model lateral boundaries by the conventional sponge zone relaxation. By using Hurricane Felix (2007) as a demonstration case, it is shown that, by assimilating large-scale flows from the Global Forecast System (GFS) forecasts into the regional model, the SSDA experiments perform better than both the original GFS forecasts and the control experiments, in which the regional model is only driven by lateral boundary conditions. The overall mean track forecast error for the SSDA experiments is reduced by over 40% relative to the control experiments, and by about 30% relative to the GFS forecasts, respectively. In terms of TC intensity, benefiting from higher grid resolution that better represents regional and small-scale processes, both the control and SSDA runs outperform the GFS forecasts. The SSDA runs show approximately 14% less overall mean intensity forecast error than do the control runs. It should be noted that, for the Felix case, the advantage of SSDA becomes more evident for forecasts with a lead time longer than 48 h.
Tropical cyclones (TCs) are among the most devastating natural disasters. They are generally associated with extreme winds and torrential rain, which often lead to inland flooding, huge sea surface waves, and high storm surge. Accurately forecasting TC track and intensity is a very important task in weather forecasting. For TC track forecasts, continuous improvements have been made in the last several decades (McAdie and Lawrence 2000; Aberson 2001), though considerable track forecast error still exists. Over the past 15 yr, the official National Hurricane Center (NHC) 24–72-h track forecast errors for the Atlantic basin have been reduced by about 50% (Franklin 2010). The 5-yr (2005–09) averaged official track forecast errors in the Atlantic basin are 53.4, 96.8, 143.8, 195.6, and 252.1 nautical miles (n mi, where 1 n mi = 1.85 km) at 24, 48, 72, 96, and 120 h, respectively (information online at http://www.nhc.noaa.gov/verification/index.shtml). As for TC intensity forecasts, there has been virtually no net change over the past 15–20 yr despite the recent efforts to enhanced data collection, advance data assimilation, and apply more sophisticated modeling techniques (Franklin 2010). The official NHC 5-yr (2005–09) TC intensity forecast errors in the Atlantic basin are 10.7, 15.2, 18.6, 18.7, and 20.1 knots (kt, where 1 kt = 0.514 m s−1) at 24, 48, 72, 96, and 120 h, respectively. TC intensity forecasting remains a significant challenge, especially for rapidly intensifying storms.
Numerical weather prediction (NWP) models, also referred to as dynamical models, play an important role in TC track and intensity forecasts. Together with statistical models and statistical–dynamical models, they provide objective model guidance for official NHC TC forecasts. NWP models can be classified as global and regional models. Global models cover the entire globe and do not need lateral boundary conditions, thus, they can describe planetary and large-scale features well. Since large-scale environmental flow plays a major role in steering TCs (Harr and Elsberry 1991; Carr and Elsberry 2000), global models can usually be considered to be good guidance models for TC track forecasts. However, global models generally have relatively coarse resolution, so that they are unable to satisfactorily resolve regional-scale features. Global models tend to underpredict TC intensity, but overpredict TC size due to the low horizontal resolution. Limited area models (LAMs), on the other hand, focus on a specific region and usually have finer grid resolution than global models. They can better represent regional-scale characteristics in topography, land-use, land–sea distribution, and sea surface temperature. With smaller grid spacing, LAMs can also better describe regional and small-scale processes and thus, better simulate TC intensity. Conventionally, LAMs are nested in global models by specifying lateral boundary conditions through a “sponge zone” technique using a relaxation procedure (Davies 1976). However, the conventional grid nesting method may distort the information transmitted from the global model into the LAM, leading to a mismatch between the solutions of the LAM and the global model. The large-scale features simulated by the LAM may be better described in the global model (Waldron et al. 1996). Thus, downscaling from global to regional models sometimes degrades the accuracy of TC track forecasts.
Generally, large-scale features are more accurately simulated in global models while small-scale features are usually better captured in high-resolution LAMs. Several alternative downscaling approaches in addition to the conventional sponge zone technique were developed in regional modeling studies. The “perturbation method,” combining the perturbation obtained from the regional model with the large-scale base state from the global model to compose the full field in the regional model, was used in the National Centers for Environmental Prediction (NCEP) Regional Spectral Model nested within a Global Spectral Model (Juang and Kanamitsu 1994; Juang et al. 1997; Juang and Hong 2001). Another similar approach, referred to as spectral nudging (Waldron et al. 1996; von Storch et al. 2000) was utilized to nudge the large-scale solution in the LAM toward that from the global forcing and allow the LAM to develop its small-scale dynamics freely. This approach has been widely used in regional climate dynamical downscaling studies (e.g., Weisse et al. 2005; Miguez-Macho et al. 2005; Meinke et al. 2006; Kanamaru and Kanamitsu 2007a,b; Kanamitsu and Kanamaru 2007; Xue et al. 2007), in seasonal TC activity simulations (Knutson et al. 2007; Feser and von Storch 2008b), as well as in case studies of individual TCs (Feser and von Storch 2008a). In addition, the analysis-nudging four-dimensional data assimilation (FDDA) technique, which nudges all scales in the regional model toward the global model, was used in regional weather and climate simulations (Stauffer and Seaman 1990, 1994; Stauffer et al. 1991; Deng and Stauffer 2006; Castro et al. 2005). Recently, Peng et al. (2010) presented a scale-selective data assimilation (SSDA) approach to downscale from global models to LAMs by driving the LAMS from the regional model domain interior as well as by specifying the lateral and lower boundary conditions. Application of the SSDA approach to a seasonal climate hindcasting for the North Atlantic basin and eastern United States indicates that the large-scale components from the global analyses can be effectively transmitted into the regional model, resulting in improvements in the overall regional model simulations. Xie et al. (2010) applied the SSDA approach to simulate the track of Hurricane Katrina (2005) driven by Global Forecast System (GFS) analyses. Substantial improvements were obtained in the TC track forecasts when the SSDA approach assimilated the large-scale information from global analyses into the regional model. In addition, it was demonstrated that both large- and small-scale flows benefited from the SSDA procedure.
In this study, the SSDA approach will be extended to study its feasibility in TC track and intensity forecasts using Hurricane Felix (2007) as an example. Instead of using the GFS analyses, the GFS near-real-time global forecasts will be utilized to drive the regional model, providing large-scale information as well as boundary conditions. The rest of this paper is organized as follows. Section 2 describes the SSDA approach, the regional model used in this study, and the corresponding three-dimensional variational data assimilation (3DVAR) data assimilation system. The background of Hurricane Felix and the experiment design are given in section 3. Section 4 presents the results and analyses, followed by conclusions in section 5.
2. The scale-selective data assimilation system
To improve the track and intensity forecasts for TCs, the SSDA approach is employed to assimilate the large-scale information from global model forecasts into the LAM, driving the regional model from both the lateral boundaries and the domain interior. The SSDA system consists of the Weather Research and Forecasting Model (WRF; Skamarock et al. 2005; Wang et al. 2010), a 3DVAR technique (Barker et al. 2004) from the WRF’S data assimilation (WRFDA) system, and a low-pass filter to separate large- and small-scale components for both global and regional model forecasts.
Version 3.2 of the WRF with the Advanced Research WRF (ARW) core is employed as the regional weather prediction model in this study. It features a fully compressible, Eulerian, and nonhydrostatic control equation set. The model uses the Arakawa-C grid and the terrain-following, hydrostatic-pressure vertical coordinate system with the top of the model being a constant pressure surface. The time integration scheme is the third-order Runge–Kutta scheme, and second–sixth-order advection schemes are available for the spatial discretization. WRF incorporates various physical processes including microphysics, cumulus parameterization, planetary boundary layer (PBL), surface layer, land surface, and long- and shortwave radiation, with several options available for each process. For more details about the WRF, the reader is referred to Wang et al. (2010). WRF-3DVAR from WRFDA is used to assimilate the large-scale information from global forecasts into the regional model. It is based on an incremental variational data assimilation technique. WRF-3DVAR combines observations with WRF initial or forecast fields (the first-guess fields) to provide improved estimates or analyses. This is achieved through the iterative minimization of a prescribed cost function. Differences between the analysis and observations or first guess are penalized according to their perceived errors. The filter used to separate large- and small-scale components employs the discrete fast Fourier transform (FFT) together with a detrending program dealing with aperiodic lateral boundary.
The assimilation of large-scale information from global model forecasts into the regional model is achieved through a series of SSDA cycles at a preset time interval (e.g., 6 h) as the regional model integration advances forward in time. Figure 1 depicts the procedure of a SSDA cycle. When the regional model reaches the time for the inclusion of large-scale information from global forecasts, both the forecasts from the regional model restart file (WRFRST) and the GFS forecasts are separated into large-scale components (LWRF and LGFS, respectively) and small-scale components (SWRF and SGFS, respectively) by using a low-pass filter. The large-scale components of GFS forecasts (LGFS) and the small-scale components of WRF forecasts (SWRF) are combined in wavenumber space to form the full field (COMOBS). Next, WRF-3DVAR assimilates the combined field (COMOBS, being sampled as input observations) into the original regional model forecasts, obtaining the new restart file for the WRF (NEWRST). WRF then runs forward until reaching the time for the next SSDA cycle. More details about the SSDA system are contained in Peng et al. (2010) and Xie et al. (2010).
3. Hurricane Felix (2007): Model settings and experiments
To verify the performance of the SSDA approach in improving the TC track and intensity forecasts, Hurricane Felix (2007) is used as a test case in this study. Felix was a small, but powerful, category 5 hurricane on the Saffir–Simpson hurricane scale that caused major damage in northeastern Nicaragua (Beven 2008). According to Beven (2008), the powerful storm caused at least 130 deaths in Nicaragua and Honduras, with as many as 70 other people missing. Felix’s landfall in Nicaragua led to severe damage to structures from winds and storm surge along the coast from Puerto Cabezas northward. Thousands of homes and other structures were destroyed. In addition, rain-induced inland flooding occurred in both Nicaragua and Honduras.
Figure 2 shows the “best track” of Hurricane Felix. The time series of maximum sustained winds and minimum sea level pressure (SLP) are shown in Fig. 3. As described in Beven (2008), Felix formed from a tropical wave that departed the African coast, and became a tropical depression around 1200 UTC 31 August about 195 n mi east-southeast of Barbados. As it moved west-northwestward, Felix became a tropical storm around 0000 UTC 1 September about 60 n mi south of Barbados. After passing over Grenada at about 0845 UTC 1 September, it moved across the southern portion of the Caribbean Sea, embedded in deep-layer easterly flow. Felix quickly strengthened and became a hurricane near 0000 UTC 2 September. As Felix moved just north of due west on 2 September, very rapid strengthening occurred during the day. It became a category 5 hurricane with the maximum sustained winds increasing to 145 kt by 0000 UTC 3 September. The central pressure reached a minimum of 929 hPa at 0700 UTC 3 September. Due to the occurrence of an eyewall replacement cycle later that day, Felix then weakened to a category 3 hurricane with the central pressure rising to 953 hPa. This was followed by reintensification at the end of the cycle, and Felix regained its category 5 strength just before landfall near Punta Gorda, Nicaragua, at 1200 UTC 4 September. After landfall, Felix weakened rapidly to a tropical storm over northern Nicaragua in less than 12 h. It then decelerated and turned west-northwestward, and weakened to a remnant low over northern Honduras early on 5 September. More detailed descriptions about Felix are available in Beven (2008).
To perform TC track and intensity forecasts for Hurricane Felix by using the regional WRF, the model domain contains 415 × 271 horizontal grid points with a grid spacing of 12 km (thus it extends 4968 km × 3240 km). The domain is centered at (15°N, 71°W) using the Mercator map projection (see Fig. 2 for the location of the model domain). WRF has 30 sigma levels in the vertical direction with the model top at 50 hPa. The integration time step is 60 s. Modeling results are saved every 6 h. The following physics schemes are chosen: the WRF single-moment five-class (WSM5) microphysics scheme (Hong et al. 2004), the Kain–Fritsch cumulus scheme (Kain and Fritsch 1990), the Yonsei University (YSU) PBL scheme (Hong et al. 2006), the Dudhia shortwave radiation scheme (Dudhia 1989), and the Rapid Radiative Transfer Model (RRTM) longwave (Mlawer et al. 1997) radiation scheme. Sea surface temperature from GFS global forecasts is updated every 6 h. In addition, estimations of air–sea momentum and heat fluxes as well as dissipative heating applicable to hurricane winds (Davis et al. 2008) are used, with the Donelan et al. (2004) relation for sea surface drag coefficient and Garratt’s (1992) parameterization for sea surface enthalpy coefficient.
Two sets of experiments are designed to evaluate the effectiveness of the SSDA approach in TC track and intensity forecasts for Hurricane Felix. The first set of the experiments consists of 17 control (CTRL) runs of the WRF. The model initial time for each of the 17 experiments ranges from 1800 UTC 31 August to 1800 UTC 4 September at 6-h intervals. All 17 control runs end at 0600 UTC 5 September, after which Felix weakened into a remnant low. These simulation time periods are chosen so that they are identical to those of the 17 official (OFCL) NHC forecasts included in the forecast verification report (Franklin 2008). The verification only concerns the forecasts when the TC system is classified as a tropical cyclone (including tropical depression, tropical storm, or hurricane) at both the forecast’s initial time and the forecast’s valid time in the best-track data. For the control runs, the 1° NCEP GFS real-time global forecasts are used to initialize the model and drive the WRF model only through the conventional sponge zone lateral boundary conditions, which are updated every 6 h. In addition, at the initial time of each experiment, a vortex is bogussed according to the NHC’s public advisory valid at the corresponding time (available online at http://www.nhc.noaa.gov/archive/2007/FELIX.shtml?) and implanted into the initial conditions.
The second set of experiments includes 17 SSDA runs with the same forecasting time periods as in the 17 control runs. In addition to the basic settings for the control runs, the SSDA approach described in section 2 is employed to drive the regional WRF model from the domain interior during the model integration, assimilating the large-scale information from the GFS global forecasts into the regional model every 6 h. Since TCs are predominately steered by their large-scale environmental circulation, only the wind field is considered in the SSDA procedure in this study. As it is commonly believed that 13 grid points can resolve a wave reasonably well, the largest wavenumber in the zonal direction that can be well represented by the 1° GFS global forecasts is around four for a domain that extends 4968 km in the zonal dimension (4968 km / 111 km / 12 = 3.7). The cutoff wavenumber of three is thus chosen for the low-pass filter to extract large-scale wind components from the global forecasts, which are well resolved in the global model. Consequently, the wind components with wavelengths longer than 1656 km are extracted and assimilated into the regional model. It should be noted that wavenumber is defined as the model domain extent divided by the wavelength in this study. In addition, only large-scale wind components above the 13th sigma level (about 850 hPa) from global forecasts are used in the WRF-3DVAR data assimilation process. This allows the regional model to adjust its low-level dynamics based on its own regional topography and land–sea characteristics. This practice of only constraining large-scale fields above the PBL in the regional model was commonly used in other downscaling studies (e.g., von Storch et al. 2000). Figure 4 shows the wind vectors at the twentieth sigma level (about 500 hPa) valid at 1200 UTC 3 September for the forecasts initialized at 1200 UTC 2 September including (a) the full field and (b) the large-scale components of the GFS forecast, (c) the full field and (d) the small-scale components of the SSDA experiment before performing the SSDA procedure, (e) the full field of the SSDA experiment after performing the SSDA procedure, and (f) the combined field that consists of the large-scale components of the GFS forecast (b above) and the small-scale components of the SSDA experiment (d above). It is demonstrated that the SSDA procedure can effectively preserve the small-scale features of the regional model and adapt the large-scale features of the regional model to those of the GFS global forecasts.
a. Effects on storm-track forecast
The simulated TC tracks for the control and SSDA experiments are evaluated against the best-track data. Forecast error and forecast skill are used in the verifications for different forecast methods or models. Track forecast error (e, in km) is defined as the great-circle distance between the storm location in the best-track data and the forecast storm center valid at the same time. It can be calculated through (Neumann and Pelissier 1981; Powell and Aberson 2001)
where λo and ϕo and are the latitude and longitude of the storm center in the best-track data and ϕf and λf are the latitude and longitude of the forecast storm center. Track forecast errors from the CTRL and SSDA experiments are compared with the errors from the GFS global forecasts, the NHC official (OFCL) forecasts, and the climatology and persistence model (CLIPER5; Aberson 1998) forecasts. The forecast skill of a forecast model or method represents a normalization of the forecast error against some standard or baseline. It expresses a percentage improvement over the baseline. The skill of a forecast method or model (sf) is given by
where eb is the error of the baseline model and ef is the error of the forecast being evaluated. For track forecast skill, CLIPER5 is used as the baseline model, as it is a climatology and persistence model that contains no information about the current state of the atmosphere (Neumann 1972; Aberson 1998).
Figure 5 and Table 1 give the mean track forecast errors in different forecast periods for the CTRL and SSDA experiments, as well as the GFS global forecasts. Track errors of the OFCL forecasts and the CLIPPER5 (CLP5) model are also shown for comparison. The mean track forecast errors for the control runs increase near linearly from 59 km for 12-h forecasts to 381 km for 96-h forecasts. Due to relatively coarse grid spacing and a poor description of the regional- and small-scale features, the track forecast errors of the GFS global forecasts are larger than those of the control runs for the short-term (less than 24 h) forecasts. However, the GFS global forecasts perform better than the control runs for forecasts longer than 24 h. They even outperform the official NHC forecasts for 3- and 4-day forecasts. This is because the GFS global forecasts quite accurately captured the large-scale environmental flows, which played an important role in the steering of the storm and was crucial to long-term TC track forecasts. Benefiting from the assimilation of large-scale flows from the GFS global forecasts into the regional model, the SSDA experiments clearly outperformed the CTRL experiments. The mean track forecast errors at 24, 36, 48, 72, and 96 h decreased from 124, 173, 203, 260, and 381 km for the CTRL runs to 77, 107, 127, 124, and 136 km for the SSDA runs, respectively. On average, compared to the control runs, the track forecast errors for the SSDA experiments are reduced by over 40%. It should be noted that the track forecast errors of the SSDA runs are also less than those of the GFS global forecasts, with a reduction of approximately 30% in terms of overall mean track forecast error. This may be because, on one hand, the SSDA runs have finer grid resolution and, on the other hand, both large- and small-scale features in the regional model benefited from assimilating large-scale flow from the global forecasts into the regional model by the SSDA approach (Xie et al. 2010). It should also be pointed out that for Hurricane Felix (2007), the track errors for the SSDA runs are very close to, though a little larger than, those of the OFCL forecast for forecasts less than 48 h. However, for forecasts longer than 2 days the SSDA runs outperformed the OFCL forecasts.
In terms of forecast skill, CLIPPER5 performed very well for forecasts less than 24 h, in fact, even better than the official forecasts. Whereas, its track forecast errors increased quickly with the increase of forecast lead time (see Fig. 5). The mean 96-h track forecast error for the CLIPPER5 model reached 722 km, which is much larger than those for other forecast techniques (see Fig. 5 and Table 1). Figure 6 shows the comparison of the track forecast skills relative to the CLIPPER5 model for the CTRL and SSDA runs, the GFS global forecasts, and the OFCL forecasts. It is obvious that the track forecast skill of the SSDA runs is better than the skill of either the CTRL runs or the GFS global forecasts. The forecast skill of the SSDA runs is a little lower than that of the official forecasts for the first 2 days, while higher than that of the official forecasts for the forecasts longer than 2 days.
Figure 7 shows the TC track forecasts initialized at 1200 UTC 2 September for experiments CTRL and SSDA, and the GFS forecasts, together with the storm track from the best-track data. In the CTRL run and the GFS forecasts, the forecast storm tracks are west-northwestward throughout the entire forecast period. However, in the best track, after 0000 UTC 3 September, Felix kept moving nearly due west till shortly after its landfall. Large track errors exist in the CTRL run and GFS forecasts, especially for forecasts longer than 1 day (see Fig. 8 and Table 2). Whereas, the forecast track of the SSDA run lies between the CTRL run forecast and the best track.
The improved track forecast in the SSDA run can be attributed to the improvement in the large-scale circulation as a result of the SSDA procedure. Figure 9 shows the 500-hPa streamline valid at 1200 UTC 3 September for the forecasts (initialized at 1200 UTC 2 September) of the CTRL experiment, the SSDA experiment, and the GFS global forecast, as well as the GFS global analyses. The storm centers and large-scale environmental steering flow vectors (see also in Table 3) are also shown in Fig. 9. It can be seen that the storm is mainly steered to move westward by the anticyclone to its north-northeast. For the CTRL run, the center of the anticyclone is located to the west of that in the GFS analyses, and the storm center is located to the north of that in the GFS analyses. Whereas the SSDA run shows a streamline pattern similar to that of the GFS analyses with the location of the anticyclone also close to that in the GFS analyses. The large-scale environmental steering flow vector in the SSDA run is the closest to that of the GFS analyses. Clearly, the SSDA approach effectively improved the simulation of large-scale features and, thus, improved the storm-track forecast. The SSDA experiment performed better than both the control experiment and the GFS global forecasts. For the forecasts initialized at 1200 UTC 2 September, the mean track forecast errors are reduced from 171 km for the CTRL run and 156 km for the GFS forecast to 93 km for the SSDA run, corresponding to improvements of 46% and 40%, respectively (Table 2).
As the movement of a TC is mainly dominated by the large-scale environmental steering flow, the steering flows from each experiment are then compared with those from the GFS analyses. Table 3 lists the speeds and directions of the large-scale environmental steering flows at each forecast hour for experiments CTRL and SSDA, and the GFS forecasts, which are initialized at 1200 UTC 2 September, as well as for the GFS analyses (GFSA). The steering flows are determined as the averaged wind vectors in the midtroposphere (700–500 hPa) along a 5°–7° radius band from the TC center, which have the best correlation with the TC movement (Chan and Gray 1982). The Cartesian direction is used, with 0° corresponding to moving eastward and 90° corresponding to moving northward. Table 3 indicates that the CTRL and the SSDA experiments have similar translation speeds, which are closer to the mean steering flow speed than that of the GFS forecasts. The mean direction of the steering flows for the SSDA experiment is the closest to that for the GFS analyses. Assuming the environmental steering flow is the only factor that controls the storm track, a hypothetical storm track can be depicted as the trajectory driven by the steering flow. Figure 10 shows the hypothetical storm tracks driven by the steering flows for the CTRL and SSDA experiments, the GFS forecasts, and the GFS analyses (GFSA). Comparing Fig. 10 to Fig. 7, one can find that the environmental steering flow can account for the movement of Felix to a large extent. Among the hypothetical tracks purely due to the steering flows, the one derived from the SSDA run is the closest to that derived from the GFS analyses. Table 4 lists the track errors (km) relative to the hypothetical storm track only due to the steering flows from the GFS analyses for experiments CTRL and SSDA, and the GFS forecasts. It is shown that as a result of the improved steering flow, the mean track errors for the hypothetical tracks are reduced from 163 km for experiment CTRL and 118 km for the GFS forecasts to 83 km for experiment SSDA.
b. Effects on storm size forecast
Storm size is usually measured by the area enclosed by the last closed isobar or the radius of the 34-kt wind in the maximum wind quadrant. Felix is a relatively small and compact system with a radius of approximately 185 km in the maximum wind quadrant during the period from 0000 UTC 2 September to 1200 UTC 4 September based on the best-track data. Figure 11 gives the 48-h forecast SLP and 10-m wind initialized at 1200 UTC 2 September for the CTRL and SSDA experiments and the GFS forecast. One can see that the storm centers in the CTRL run and the GFS forecast are located far away from the best track. The storm center in the SSDA run, however, is much closer to the best track, with a similar storm intensity to that in the CTRL run. The storm size (e.g., the area of SLP < 1004 hPa) for the SSDA run is much less than that for the CTRL run, being more consistent with the observed size of Felix.
Figure 12 gives the vertical cross sections passing through the storm center and the location of the maximum surface wind. It shows the potential temperature and horizontal wind speed valid from 0000 UTC 3 September to 1200 UTC 4 September in a 12-h interval, for both the CTRL and SSDA forecasts initialized at 1200 UTC 2 September. It can be found that the horizontal extent of the 34-kt (17.5 m s−1) wind in the quadrant with strongest wind for the CTRL run is generally larger than that for the SSDA run, though they have identical initial conditions including the initial bogussed vortex. The radial extent of the 34-kt wind for the SSDA run is closer to the 34-kt wind radii (about 185 km) in the quadrant with the strongest wind from the best-track data, which is also close to the mean extent of the 34-kt wind (about 198 km) in the quadrant with the strongest wind from the National Oceanic and Atmospheric Administration/Atlantic Oceanographic and Meteorological Laboratory/Hurricane Research Division (NOAA/AOML/HRD) surface wind analysis (H*wind; Powell et al. 1998) data during the period from 1200 UTC 2 September to 1200 UTC 4 September. This confirms that the inclusion of large-scale flows from global forecasts by the SSDA approach may also improve regional- and small-scale features for the regional model. At this point, whether or not such improvements are incidental and case sensitive is not clear. It is beyond the scope of this study to fully explain the physical causes of the impacts of SSDA on the storm size. For the Felix case, a plausible cause may be that the improved storm track allowed the storm simulated by the SSDA run to follow more closely the coast, thus with reduced moisture supply compared to the control run. Previous studies indicate that moisture supply is an important factor for determining storm sizes (Hill and Lackmann 2009).
c. Effects on storm intensity forecast
Intensity forecast error is defined as the absolute value of the difference between the forecast and best-track intensity (usually minimum SLP and/or maximum surface wind) at the forecast verification time. Forecast skill for an intensity forecast model is defined similarly as in Eq. (2), except the corresponding forecast intensity errors are used instead of the forecast track errors. The baseline model for intensity forecast skill is the Decay-SHIFOR5 (DSHIFOR5; Jarvinen and Neumann 1979; Knaff et al. 2003), which is a climatology and persistence model for intensity that is analogous to the CLIPER5 model for track forecast.
Figure 13 and Table 5 show the mean intensity forecast errors at different forecast periods for different forecast approaches, including the CTRL and SSDA experiments, the GFS forecasts, the DSHIFOR5 forecasts, and the official NHC forecasts. Obviously, the GFS global forecasts have the largest intensity errors because of the relatively coarse grid resolution. Thus, GFS global forecasts do not provide a good guidance model for TC intensity forecasts. Benefiting from higher resolution and being able to represent regional- and small-scale processes, both the CTRL and SSDA runs outperform the GFS global forecasts. The CTRL runs have larger intensity forecast errors for short-term (less than 2 days) forecasts than the official and DSHIFOR5 forecasts, while comparable intensity forecast errors for forecasts longer than 2 days. Similar to the CTRL runs, the SSDA runs have larger intensity forecast errors than the official and DSHIFOR5 forecasts for forecasts within the first 48 h. This may be due to the errors during the model initialization introduced by the vortex bogus scheme. As the forecast time increases, the SSDA runs show the best intensity forecasts, with smallest mean intensity forecast errors for forecasts longer than 2 days. By introducing the SSDA approach, the overall mean intensity forecast error is reduced from 22 m s−1 for the CTRL runs to 19 m s−1 for the SSDA runs, a reduction of 14% (Table 5). Figure 14 shows the intensity forecast skill levels for the CTRL and SSDA runs, the GFS forecasts, and the official NHC forecasts. One can see that the CTRL and SSDA runs are comparable, and both are less skillful than the official forecasts within the first 48 h, while the SSDA runs become more skillful after 48 h.
Figure 15 shows the time series of the forecast minimum SLP and maximum 10-m wind for the CTRL and SSDA runs initialized at 1200 UTC 2 September, as well as their differences from the best-track data. One can see that the forecast intensities in the GFS global forecast are very weak during the whole forecast period, with the minimum SLP being around 1008 hPa and the maximum surface wind being less than 17 m s−1. There are huge differences between the GFS global forecasts and the best-track data (Figs. 15c and 15d). The GFS forecasts totally missed the evolution of Hurricane Felix. In addition, comparison of the 48-h forecast SLP and 10-m wind initialized at 1200 UTC 2 September for the CTRL and SSDA experiments and the GFS forecast (Fig. 11) also indicates that the regional model runs outperform the GFS global forecast in intensity forecasts. Although the forecast intensities are still weaker than the best-track data, downscaling to the regional model forecasts for both the CTRL and SSDA runs significantly improves the intensity forecasts. During the intensification period, the forecast intensities for the CTRL and SSDA runs are comparable. However, the CTRL run did not correctly forecast the weakening stage, because it completely missed the landfall of Felix. The weakening of Felix is captured by the SSDA run, and the forecast landfall is located to the north of the actual landfall location (Fig. 7). The intensity forecast errors for the CTRL run, the SSDA run, and the GFS global forecast initialized at 1200 UTC 2 September are also listed in Table 2. The mean intensity forecast error for the GFS global forecast during the 66-h period is 42.3 m s−1, much larger than that for the CTRL run (23.1 m s−1). The application of the SSDA approach further reduces the mean intensity forecast error from 23.1 m s−1 for the CTRL run to 20.9 m s−1 for the SSDA run, corresponding to a roughly 10% improvement.
It should be noted that a substantial part of the improvements seen in the intensity forecasts is due to the improvements in track forecasts for the Felix case. The improved track forecasts better capture the surface boundary conditions (land–sea distribution, sea surface temperature, ocean heat content, etc.) underneath the storm, which are key factors influencing TC intensity. For example, as for the forecasts initialized at 1200 UTC 2 September, the track of the SSDA run is the closest one to the best track, which mainly moves westward with its landfall in Nicaragua (Fig. 7). With the storm being close to the land, the SSDA run thus reduces intensity forecast errors, especially after the actual landfall of Felix (Table 2 and Fig. 15). Other environmental parameters such as vertical wind shear (measured commonly as the horizontal wind difference between 200 and 850 hPa averaged within a given radius) and upper-level outflow (measured as the 200-hPa divergence averaged within a given radius) may also impact TC intensity change. TC intensity change and vertical wind shear are generally negatively correlated, indicating that strong environmental vertical wind shear usually inhibits TC development (e.g., DeMaria and Kaplan 1994; Zeng et al. 2010). To calculate the environmental parameters of the 200–850-hPa vertical wind shear and 200-hPa divergence for the CTRL and SSDA experiments and the GFS forecasts and analyses, we follow the method used in the Statistical Hurricane Intensity Prediction Scheme (SHIPS; DeMaria and Kaplan 1999). Large-scale fields (with wavenumbers less than four and wavelengths longer than 1242 km) are first obtained by using a low-pass filter described in section 2. The 200–850-hPa vertical wind shear is then calculated by averaging around the TC center within a radius of 600 km, and 200-hPa divergence is averaged within a radius of 1000 km. Tables 6 and 7 list the mean absolute differences of the 200–850-hPa vertical wind shear and 200-hPa divergence between each experiment and the GFS analyses, at different forecast periods for the CTRL and SSDA runs, and the GFS forecasts, respectively. It is shown that the SSDA runs generally have smaller errors for 200–850-hPa vertical wind shear than the CTRL runs for most of the forecast periods except the 24-h forecast period, for which they have comparable vertical wind shear errors. As for the 200-hPa divergence, the SSDA runs have smaller errors than the CTRL runs for forecasts valid at 24, 36, 48, 72 h, while larger errors exist for forecasts valid at 12 and 96 h. The times series of 200–850-hPa vertical wind shear and 200-hPa divergence for the forecasts (initialized at 1200 UTC 2 September) of the CTRL and SSDA runs, the GFS forecasts, and the GFS analyses are shown in Fig. 16. Both the vertical wind shear and the upper-level divergence in the SSDA run are in closer agreement with those in the GFS analyses than the control run. This indicates that the SSDA approach, which assimilates large-scale information from global forecasts into the regional model, also improves the model performance in the simulation of environmental factors that impact TC intensity change for the Felix case.
TCs are causing increasing amounts of destruction, death, and injury due to the increasing population density and economic infrastructure in coastal regions. Economic losses due to landfalling hurricanes on the U.S. mainland have roughly doubled each decade from 1900 to 2005 (Pielke et al. 2008). Increasing the accuracy of TC track and intensity forecasting remains one of the top priorities in weather forecasting, to provide targeted warnings and emergency preparations. While global models have been proven skillful in forecasting TC tracks, regional models with higher resolution have the potential to improve forecasting of TC intensity as well as track. In this study, the SSDA approach, which benefits from the merits of both global models in representing large-scale environmental flows and regional models in describing small-scale characteristics with high resolution, is applied in TC track and intensity forecasting. The idea of the SSDA approach, similar to that of spectral nudging (Waldron et al. 1996; von Storch et al. 2000), is to drive the regional model from the model domain interior as well as through the conventional sponge zone boundary conditions. Large-scale flows from global forecasts are assimilated into the high-resolution regional model through the 3DVAR method, while the small-scale processes are allowed to develop freely.
In the case study of near-real-time forecasting of Hurricane Felix (2007), the regional WRF model was driven by the GFS global forecasts to forecast the storm track and intensity. As for the storm-track forecasting, by assimilating large-scale flows from the GFS global forecasts into the regional model, the SSDA experiments perform much better than either the CTRL experiments or the GFS global forecasts. The mean 1- and 3-day track forecast errors were reduced from 124 and 260 km for the control runs to 77 and 124 km for the SSDA runs, respectively. On average, the track forecast errors for the SSDA experiments are reduced by over 40% relative to the control experiments. The overall mean track forecast error of the SSDA runs is also 29% less than that of the GFS global forecasts. Correspondingly, the SSDA runs have better track forecast skill than the control runs and the GFS global forecasts. In addition, the SSDA runs even perform better than the NHC official forecasts for forecasts longer than 2 days, although the track forecast errors of the SSDA runs are a little larger than those of the OFCL forecasts for short-term (less than 48 h) forecasts.
As for the TC intensity forecast for Felix, both the CTRL and SSDA runs perform much better than the GFS global forecasts, due to their higher grid resolution and better representation of regional- and small-scale processes. Moreover, not only do large-scale environmental flows benefit, but also regional- and small-scale features in the regional model benefit as well from the assimilation of large-scale flows from the GFS global forecasts (Xie et al. 2010). By using the SSDA approach, the overall mean intensity forecast error is further reduced by 14% from 22 m s−1 for the CTRL runs to 19 m s−1 for the SSDA runs. For short-term forecasts, the CTRL and SSDA runs have comparable intensity forecast errors, being less skillful than the NHC official forecasts. In contrast, the SSDA approach becomes the most skillful for extended-range forecasts beyond 48 h. It should be noted that for the Felix case, a substantial portion of the improvements in TC intensity forecasts in the SSDA runs may be due to the improvements in track forecasts, which allowed the SSDA runs to better capture the surface conditions underneath (such as land–sea distribution, ocean heat content). The results also show that assimilating large-scale information from global forecasts into the regional model in the SSDA experiment may improve the representation of vertical wind shear and upper-level divergence, resulting in improvements in TC intensity forecasts. However, additional idealized and real-case studies are needed to thoroughly assess the impacts of the SSDA approach on TC intensity forecasts.
In summary, given that global models usually better capture large-scale information than LAMs, the SDDA approach is an effective downscaling technique for driving the LAM from both the domain interior and the model boundaries, which could improve the performance of the LAM by increasing the accuracy of the descriptions of both the large- and small-scale features. However, if the global model produces a poor large-scale forecast, the SSDA approach might also perform poorly. And in that case it is highly likely that the traditional sponge zone nesting approach also performs poorly. It is necessary to apply the SSDA approach to as many historical cases as possible in order to obtain a statistically meaningful skill assessment of the SSDA approach. In addition, the SSDA approach can be applied within an ensemble framework in different ways. The regional model nested in different global models through the SSDA approach can add ensemble members directly. Alternatively, multiple global model forecasts can form an ensemble forecast, which can then be used to drive different regional models through the SSDA approach to add ensemble members.
The authors appreciate the constructive comments and suggestions from the anonymous reviewers. We are also grateful to Ms. Katie Costa for the English proofreading. The Global Forecast System (GFS) forecast and analysis data for this study are taken from NOAA’s National Operational Model Archive and Distribution System (NOMADS; information online at http://nomads.ncep.noaa.gov). This study is jointly supported by grants awarded by the NOAA Interdisciplinary Scientific Environmental Technology Program through Subcontract NCA&T 270040F, U.S. Department of Energy Award DE-FG02-07ER64448, and National Science Foundation Award AGS-1043125.