Summary of the NHC/TPC Tropical Cyclone Track and Intensity Guidance Models

1. Introduction

The National Hurricane Center (NHC) in Miami, Florida issues 72 hr tropical cyclone track and intensity forecasts four times per day for all storms in the north Atlantic and eastern north Pacific east of 140°W. The track forecasts are the storm latitude and longitude (to the nearest tenth of a degree) and the intensity forecasts are the 1-minute maximum sustained surface wind (to the nearest 5 kt) at 12, 24, 36, 48 and 72 hr. The storm structure is quantified by the radial extent of the 34, 50 and 64 kt wind in four quadrants (NE, SE, SW, NW) relative to the storm center. Forecasts of these wind radii are issued four times per day out to 36 hr. The 50 kt wind radii are also forecast at 48 and 72 hr. The Central Pacific Hurricane Center (CPHC) in Honolulu, Hawaii issues similar forecasts for tropical cyclones in the north Pacific from 140°W to 180°W.

The tropical cyclone guidance models that were available to the NHC and CPHC forecasters for the 1997 hurricane season are briefly described in this document. These models range in complexity from simple statistical models to three-dimensional primitive equation models. The statistical and two-dimensional models are maintained by the Tropical Prediction Center (TPC). The three-dimensional models are maintained by the National Centers for Environmental Prediction's (NCEP) Environmental Modeling Center (EMC).

2. Track Models

Table 1 lists all of the operational track guidance models used at NHC. All of these models except CLIPER require output from global forecast models. The global models are usually available about 4 h after synoptic time. However, the official NHC forecast is issued 3 h after synoptic time. To overcome this problem, many of the models use forecast fields from the previous global model run as input, so the track predictions will be available in a timely manner. Models that use forecast fields are listed as "early" in Table 1, and those that wait until the global model run is completed are listed as "late". The late models are typically run twice per day and the early models are run four times per day, although plans are underway to run all of the models four times per day.

As described above, the late models are not available to the forecasters until after the advisories are sent out. To overcome this problem, an interpolation technique was developed to transpose the previous forecast to the current storm position. The forecasts from the interpolated GFDL forecasts are designated by GFDI in Table 1. This technique is applied to all the late models, but for simplicity, only the interpolated GFDL will be included in the verification. Further details on this interpolation technique are described by Horsfall et al (1997).

AVN is the Aviation Run of the NCEP Medium Range Forecast (MRF) model. The MRF is a 28-level sigma vertical coordinate (terrain following) global spectral model with a triangular truncation of 126 waves. It includes parameterizations of convective, radiative and boundary layer processes and has a specialized technique for initializing tropical cyclone circulations where synthetic wind observations are added to the global data assimilation system. The synthetic observations are constructed from the sum of a steering flow and a symmetric vortex. The steering flow is determined from the spectral truncation which produces a vertically averaged wind that is closest to the current motion of the storm. The symmetric vortex at low-levels is constructed from operational estimates of central pressure, radius and pressure of the outermost closed isobar, the radius and value of the maximum low- level winds and the four 34 kt wind radii described above. Synthetic winds are included at about 50 locations within about 200 nm of the storm center at each mandatory level from the surface to the maximum level of the storm circulation (typically 300 hPa). Empirical functions are used to extrapolate the low-level vortex to the upper levels. An automated tracking algorithm which combines six estimates of the storm center (minimum wind speed, maximum relative vorticity, minimum geopotential height at 1000 and 850 hPa) provides a track forecast out to 72 h. Further details on the MRF and the bogussing scheme are described by Surgi et al (1997) and Lord (1991).

Table 1: NHC Operational Track Guidance Models

Model	Type	Timeliness
AVN	Global baroclinic	Late
NOGAPS	Global baroclinic	Late
UKMET	Global baroclinic	Late
GFDL	Limited-area baroclinic	Late
GFDI	Interpolated GFDL	Early
LBAR	Limited-area barotropic	Early
BAM	Trajectory	Early
NHC90/NHC91	Statistical	Early
CLIPER	Statistical	Early

NOGAPS is the U.S. Navy's global spectral forecast model with 18 sigma levels, a triangular truncation of 159 waves, parameterizations of physical processes and a tropical cyclone bogussing scheme. Generally speaking, the NOGAPS bogussing scheme is similar to that described for the MRF model, where synthetic observations that represent the storm circulation are added to the data assimilation system. Similar to the MRF scheme, the observations are created from the sum of an environmental flow and a symmetric vortex. The primary differences from the MRF scheme are that for NOGAPS, the environmental wind is determined from a T20 spectral truncation of the model fields (rather than from a truncation which best matches the storm motion), and that fewer synthetic observations are added, but over larger radial distances from the storm center. In addition, the synthetic observations for NOGAPS are added at the mandatory levels up to 400 hPa, rather than up to a maximum of 300 hPa in the MRF model. Further details of the NOGAPS model and bogussing scheme are described by Hogan and Rosmond (1991) and Goerss and Jeffries (1994).

UKMET is the global forecast model run by the UK Meteorological Office. Similar to NOGAPS and the MRF model, it includes extensive physical parameterizations and a tropical cyclone bogussing system. Further details on forcasting tropical cyclones with the UKMET model are described by Heming (1997).

GFDL (Geophysical Fluid Dynamics Laboratory) is a limited area baroclinic model developed specifically for hurricane prediction. It includes 18 sigma levels and uses a horizontal finite-difference method with three nested grids. The two inner grids move to follow the storm, and the resolution of the inner domain is 1/6 degree. The GFDL model includes convective, radiative and boundary layer parameterizations and has a specialized method for initializing the storm circulation. The initial and boundary conditions are obtained from the Aviation run of the MRF model. The representation of the storm circulation in the global analysis is replaced with the sum of an environmental flow and a vortex generating by nudging the fields in a separate run of the model to an idealized vortex. This idealized vortex is based upon a few parameters of the observed storm, including the maximum wind, radius of maximum wind and outer wind radii. The environmental flow is the global analysis modified by a filtering technique which removes the hurricane circulation. A more detailed description of the GFDL model is given by Kurihara et al (1995).

LBAR (Limited area sine transform BARotropic) is a two-dimensional track prediction model which solves the shallow-water equations initialized with vertically averaged (850-200 hPa) winds and heights from the Aviation Run of the MRF global model (Horsfall et al 1997). An idealized symmetric vortex and a constant vector (equal to the initial storm motion vector) are added to the global model analysis to represent the storm circulation. The boundary conditions are obtained from the global model forecast, and the model equations are solved using the spectral sine transform technique described by Chen et al (1997). To make LBAR timely, initial and boundary conditions are obtained from the 6 hr old MRF forecast. LBAR was developed as an operational version of the experimental VICBAR model (Aberson and DeMaria 1994).

The BAM (Beta and Advection) Model follows a trajectory from the Aviation Run of the MRF model to provide a track forecast. The vertically averaged horizontal wind is used for the trajectory calculation. To remove the global model representation of the storm circulation, a spatial filter is applied to the wind fields. This filter generates fields that are similar to what would be produced by a T25 spherical harmonic truncation. The trajectory also includes a correction term to account for the drift of the storm due to the beta-effect. The BAM model is run with shallow (850-700 hPa), medium (850-400 hPa) and deep (850-200 hPa) vertically averaged winds (BAMS, BAMM and BAMD, respectively). The BAM model is described by Marks (1992) and is based upon the theory developed by Holland (1983).

NHC90/NHC91 and CLIPER are statistical track forecast models. The predictors for CLIPER (CLImatology and PERsistence) include the initial latitude and longitude of the storm, the components of the storm motion vector, the Julian day and the initial storm intensity (Neumann 1972). The CLIPER forecasts are often used to normalize the output from other track models, and as a benchmark for evaluating track forecasting skill. NHC90 is a more general statistical model which uses the output from CLIPER in combination with vertically averaged (1000-100 hPa) geopotential heights from the Aviation Run of the MRF model as predictors (Neumann and McAdie 1991). NHC90 was developed for the Atlantic and NHC91 was developed for the east Pacific.

3. Intensity models

Table 2 lists the operational intensity models available at NHC. The GFDL model was described previously in the context of track prediction. The interpolation technique from the previous GFDL run is also applied to the intensity forecasts (GFDI).

SHIFOR (Statistical Hurricane Intensity FORecast) is a simple statistical model, which uses climatological and persistence predictors to forecast intensity change (Jarvinen and Neumann 1979). Analogous to the CLIPER track model, it is often used as a benchmark for evaluating more general models. However, the developmental sample for SHIFOR excluded cases where storms made landfall, so it is only valid for storms over the ocean.

Table 2: NHC Operational Intensity Guidance Models

Model	Type	Timeliness
SHIFOR	Statistical	Early
SHIPS	Statistical	Early
GFDL	Limited-area baroclinic	Late
GFDI	Interpolated GFDL	Early

SHIPS (Statistical Hurricane Intensity Prediction Scheme) is a statistical model that uses climatological, persistence and synoptic predictors (DeMaria and Kaplan 1997). The primary predictors include the difference between the maximum possible intensity (MPI) and the current intensity, the 850-200 hPa vertical shear of the horizontal wind, persistence (the previous 12 hr intensity change), the 200 hPa eddy flux convergence of relative angular momentum, and the 200 hPa zonal wind and temperature within 1000 km of the storm center. The MPI is estimated from an empirical relationship between sea surface temperature (SST) and intensity (DeMaria and Kaplan 1994). The SSTs are obtained from the weekly analyses described by Reynolds and Smith (1994). The MPI and vertical shear are averaged along the storm track, where the forecast positions are obtained from the LBAR model. Until 1997, only the initial analysis of the aviation run of the MRF model was used to determine the synoptic parameters, due to the difficulty of separating the tropical cyclone and its environment during the forecast period. However, for the 1997 season, the model was generalized to include synoptic predictors from forecasts out to 48 hr. A special filter was developed to remove the vortex circulation from the MRF initial fields. These modified fields were then used to initialize a "no-physics" 11-level limited-area baroclinic model, with boundary forcing from the MRF forecast fields. Similar to SHIFOR, SHIPS was developed from cases where the storm track did not cross land. A version of SHIPS is available for the Atlantic and east Pacific.

4. Model Verification

In principle, all of the baroclinic models forecast track, intensity and structure. However, no systematic procedures have been developed for extracting structure parameters (for example, wind radii) from the model forecasts. Also, the global models do not have adequate horizontal resolution to resolve the inner portion of the storm, so they are not currently used for intensity prediction. Therefore, no verification of the storm structure is available, and the track and intensity verifications will be discussed separately.

After the 1995 Atlantic hurricane season, significant improvements to the NCEP MRF model were implemented (Surgi, et al 1997). Because most of the other NHC models make use of the MRF model output, verification statistics prior to 1996 may not be relevant to the current versions of the models. Therefore, verification results for a sample of cases from the 1996 and 1997 hurricane seasons will be presented. The Atlantic hurricane season of 1996 was very active, while the east Pacific season was unusually quiet. In 1997, the Atlantic was relatively quiet, but the east Pacific was active, so the combination of these two years provides reasonable sample sizes in both basins.

The model forecasts are evaluated by comparison with the best track positions and intensities, which are the post-storm estimates of these parameters based upon all available information. The track error is great circle distance from the forecast to observed storm position, and the intensity error is the absolute value of the forecast and observed maximum surface wind. Only those cases where the storm is of tropical storm strength (maximum winds > 34 kt) or greater are included in the verification sample, and the extra-tropical and subtropical cases are excluded. Also, the verification is restricted to forecasts that were obtained in real-time.

4.1 Track Verification

Table 3 shows the Atlantic track forecast errors for the combined 1996-97 sample for the early models. This table shows that all of the models except the shallow version of BAM (BAMS) have skill at all forecast periods because the average errors are less than those from the CLIPER model. The lack of skill for BAMS is not surprising, since it is only run as a comparison with BAMM and BAMD, and is occasionally used for sheared systems that might be steered by a shallow layer. The track errors from the medium and deep versions of BAM had comparable errors for this sample. Overall, the interpolated GFDL model (GFDI) had the smallest average errors, except at 12 hr, where the LBAR errors were the smallest.

Table 4 shows the Atlantic track forecast errors for the late models, where the CLIPER errors are included for comparison. The sample sizes in Table 4 are considerably smaller than those in Table 3 because the late models are currently only run twice per day, while the early models are available four times per day. Also, the NOGAPS and UKMET forecasts are sent to NHC from remote sites, and transmission problems sometimes prevent the transfer of data. Except at 12 hr, all of the late models had smaller errors than CLIPER. The GFDL and NOGAPS models had smaller track errors than the AVN and the UKMET models.

Table 3: Average Errors (nm) of the Early Track Models for 1996-97 Atlantic Tropical Cyclones

	Forecast Interval (hr)
Model	12	24	36	48	72
CLIPER	51	103	161	220	351
NHC90	46	85	129	180	285
BAMS	61	114	168	222	336
BAMM	49	91	133	177	268
BAMD	47	88	132	183	293
LBAR	41	75	111	159	284
GFDI	42	69	98	128	200
No. Cases	346	310	279	255	207

Table 4: Average Errors (nm) of CLIPER and the Late Track Models for 1996-97 Atlantic Tropical Cyclones

	Forecast Interval (hr)
Model	12	24	36	48	72
CLIPER	51	104	166	237	408
AVN	56	98	139	178	248
NOGAPS	57	81	107	126	193
UKMET	57	92	136	165	244
GFDL	44	70	96	120	178
No. Cases	93	88	77	67	51

Table 5 shows the early model verification for the east Pacific. Comparing Table 5 and Table 3 shows that the average CLIPER errors in the East Pacific are considerably smaller than those in the Atlantic. This reduction is consistent with the relatively smooth tracks and lack of recurvature of the east Pacific storms. In contrast to the Atlantic verification, very few of the models have skill relative to CLIPER. The statistical model NHC91 has the smallest errors, except at 72 hr, where BAMM has the smallest error. The GFDI, which was the best early model in the Atlantic, has the largest errors at 12 and 24 hr, and is only slightly better than CLIPER at 36- 72 hr.

Table 6 shows the late model verification for the east Pacific. Similar to the early east Pacific models, the skill relative to CLIPER is much less than for the Atlantic. Only the GFDL at 48 hr and UKMET at 36-72 hr have errors smaller than CLIPER. This lack of skill is partially due to the smaller CLIPER errors (CLIPER is harder to beat). It might also be due to the relative lack of observations, especially to the west of the storms. A complex numerical model can not make good forecasts with a poor initialization. The lack of observations may also explain why more the baroclinic models generally did not outperform the simpler LBAR and NHC91 models in the East Pacific. These simple models make greater use of the initial storm motion vector. In a data void region, this information may partially compensate for the lack observations.

Table 5: Average Errors (nm) of the Early Track Models for 1996-97 East Pacific Tropical Cyclones

	Forecast Interval (hr)
Model	12	24	36	48	72
CLIPER	42	80	122	165	235
NHC91	41	74	103	135	209
BAMS	51	91	129	163	211
BAMM	47	83	113	144	208
BAMD	48	87	120	152	233
LBAR	43	80	112	148	229
GFDI	55	93	119	154	230
No. Cases	289	244	197	166	110

Table 6: Average Errors (nm) of CLIPER and the Late Track Models for 1996-97 East Pacific Tropical Cyclones

	Forecast Interval (hr)
Model	12	24	36	48	72
CLIPER	40	74	110	151	202
AVN	49	85	131	189	279
NOGAPS	61	98	145	186	262
UKMET	56	82	105	130	186
GFDL	57	89	115	149	227
No. Cases	77	68	49	37	26

4.2 Intensity Verification

As described in Section 2, the SHIFOR and SHIPS models are only valid for storms over water. For this reason, the cases where the storm crossed land were eliminated from the intensity verification sample. Analogous to track models, the SHIFOR errors are used to evaluate the skill of the intensity models.

Table 7: Average Errors (kt) of the Early Intensity Models for 1996-97 Atlantic Tropical Cyclones.

	Forecast Interval (hr)
Model	12	24	36	48	72
SHIFOR	8.2	11.4	14.0	16.9	21.1
SHIPS	8.1	11.0	13.0	15.7	20.5
GFDI	9.3	11.6	13.9	16.6	19.0
No. Cases	305	270	236	211	171

Table 7 shows the early intensity model verification for the Atlantic. The SHIPS errors are smaller than SHIFOR at all forecast intervals, and the GFDI errors are smaller than SHIFOR at 36-72 hr. However, the improvement over SHIFOR was only about 2-10% at 12-72 hr. By comparison, the improvement of the best early Atlantic track models relative to CLIPER was 20-40% at 12-72 hr. This result shows that intensity skill is considerably less than track forecast skill.

Table 8: Average Errors (kt) of the Early Intensity Models for 1996-97 East Pacific Tropical Cyclones.

	Forecast Interval (hr)
Model	12	24	36	48	72
SHIFOR	9.5	15.3	19.8	23.3	26.4
SHIPS	9.6	14.7	17.6	20.4	21.8
GFDI	13.0	19.4	24.5	29.5	37.2
No. Cases	254	214	176	143	99

Table 8 shows the verification of the early intensity models for the East Pacific. The SHIPS forecast improved upon SHIFOR by 4-17% at 24-72 hr, which is better than for the Atlantic. The GFDI forecast errors were larger than SHIFOR at all forecast intervals, which is worse than for the Atlantic.

A verification was also performed for the only late intensity model (GFDL) for the Atlantic and east Pacific (not shown), where SHIFOR and GFDI were included for comparison. The GFDL errors tended to be larger than the GFDI errors at 12-36 hr. This increase appears to be a result of the model initialization, where the vortex circulation goes through an adjustment period during the first 6-12 hr of the forecast, resulting in unrealistic fluctuations in intensity. The interpolation technique tends to smooth these fluctuations. At 48 and 72 hr, the GFDL errors were smaller than those of the GFDI. However, the GFDL errors were greater than or equal to those of SHIFOR at all forecast intervals, except for the Atlantic sample at 72 hr, where the errors were about 13% smaller than those of SHIFOR.

References

Aberson, S.D., and M. DeMaria, 1994: Verification of a nested barotropic hurricane track forecast model (VICBAR). Mon. Wea. Rev., 122, 2804-2815.

Chen, Q.-S., L.-E. Bai, and D.H. Bromwich, 1997: A harmonic-Fourier spectral limited-area model with an external wind lateral boundary condition. Mon. Wea. Rev., 125, 143-167.

DeMaria, M., , and J. Kaplan, 1994: Sea surface temperature and the maximum intensity of Atlantic tropical cyclones. J. Climate, 7, 1324-1334.

DeMaria, M., and J. Kaplan, 1997: An operational evaluation of a statistical hurricane intensity prediction scheme (SHIPS). Preprints, 22nd Conf. on Hurricanes and Tropical Meteorology, Ft. Collins, CO, Amer. Meteor. Soc., 280-281.

Goerss, J., and R. Jeffries, 1994: Assimilation of synthetic tropical cyclone observations into the Navy Operational Global Atmospheric Prediction System, Wea. Forecasting, 9, 557-576.

Heming, J.T., 1997: UK Meteorological Office forecast performance during the unusual Atlantic hurricane season of 1995. Preprints, 22nd Conf. on Hurricanes and Tropical Meteorology, Ft. Collins, CO, Amer. Meteor. Soc., 511-512.

Hogan, T., and T. Rosmond, 1991: The description of the Navy Operational Global Atmospheric Prediction System's spectral forecast model. Mon. Wea. Rev., 119, 1786-1815.

Holland, G.J., 1983: Tropical cyclone motion: Environmental interaction plus a beta effect. J. Atmos. Sci., 40, 328-342.

Horsfall, F.M., M. DeMaria, and J.M. Gross, 1997: Optimal use of large-scale boundary and initial fields for limited-area hurricane forecast models. Preprints, 22nd Conf. on Hurricanes and Tropical Meteorology, Ft. Collins, CO, Amer. Meteor. Soc., 571-572.

Jarvinen, B.R., and C.J. Neumann, 1979: Statistical forecasts of tropical cyclone intensity. NOAA Tech. Memo, NWS NHC-10, 22 pp.

Kurihara, Y., M.A. Bender, R.E. Tuleya, and R.J. Ross, 1995: Improvements in the GFDL hurricane prediction system. Mon. Wea. Rev., 123, 2791-2801.

Lord, S.J., 1991: A bogussing system for vortex circulations in the National Meteorological Center global forecast model. Preprints, 19th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 328-330.

Marks, D.G., 1992: The beta and advection model for hurricane track forecasting. NOAA Tech. Memo, NWS NMC 70, National Meteorological Center, Camp Springs, MD, 89 pp.

Neumann, C.J., 1972: An alternate to the HURRAN tropical cyclone forecast system. NOAA Tech. Memo, NWS SR-62, 22 pp.

Neumann, C.J., and C.J. McAdie, 1991: A revised National Hurricane Center NHC83 model (NHC90). NOAA Tech. Memo, NWS NHC-44, 35 pp.

Reynolds, R.W., and T.M. Smith, 1994: An improved real-time global sea surface temperature analysis. J. Climate, 6, 114-119.

Surgi, N., H.-L. Pan, and S.J. Lord, 1997: Improvement of the NCEP global model over the tropics: An evaluation of model performance during the 1995 hurricane season. Mon. Wea. Rev., in press.