1. Introduction
The Joint Typhoon Warning Center (JTWC; see appendix A for acronyms used within this work) in Pearl Harbor, Hawaii, forecasts tropical cyclone (TC) track, intensity, and wind radii for U.S. assets in their area of responsibility (AOR) west of 180° in the Northern Hemisphere and for the entire Pacific and Indian Oceans in the Southern Hemisphere. JTWC track errors have gradually improved in the last 20 years (Francis and Strahl 2022), with seasonal mean track errors at longer forecast periods such as 120 h dropping by nearly 50% so that the 5-yr mean track errors are approximately 180 n mi [1 n mi ≈ 1.86 km; n mi and kt (1 kt ≈ 0.51 m s−1) are used for the remainder of this work as they are operational units used by the U.S. Navy]. The track error improvements are smaller in recent years, especially at shorter lead times. The 5-yr mean 24-h track errors only improved from approximately 48 to 43 n mi between 2011 and 2020, an improvement of just 5 n mi in 10 years.
One of the products generated with each official JTWC forecast is a wind forecast error swath that is commonly used as a ship avoidance area. This “traditional error swath” shown in Fig. 1 incorporates the largest quadrant of 34-kt (17.5 m s−1) wind radii in the current forecast and the 5-yr mean track error at each forecast time to construct a cumulative or 120-h error swath. An optional convex hull routine is available to increase the area slightly while eliminating abrupt changes in the swath. The traditional error swath algorithm has been in operation at JTWC for 20 years with only minor modifications. It is a predecessor to probabilistic products such as the operational wind speed probabilities (WSPs; DeMaria et al. 2013) also produced routinely at the JTWC. A question that arises is whether a WSP product could replace the traditional error swath to simplify the JTWC product suite. We focus our attention on the 34-kt threshold because the traditional error swath is based on 34-kt radii, and a probability threshold that retains the desired qualities of the traditional error swath is preferred.
The 120-h JTWC error swath (hatched area); 34-kt cumulative WSP areas (color-filled areas defined by the color key at bottom); 0-, 12-, 24-, 36-, 48-, 72-, 96-, and 120-h track positions (purple line with typhoon symbols); 34- (red) and 50-kt (blue) wind radii; and historical 6-h track positions (black line and typhoon symbols) for a Kirogi (WP112023) forecast issued at 1200 UTC 31 Aug 2023.
Citation: Weather and Forecasting 40, 6; 10.1175/WAF-D-24-0173.1
The purpose of this effort is to investigate the use of different 34-kt cumulative WSP thresholds as a proxy for the traditional error swath. To do so, we define objective verification of bulk data in the data and methods section, show and discuss both individual cases and bulk statistics in the results section, and summarize findings, recommendations, and future work in the summary and discussion.
2. Data and methods
a. Best tracks, traditional error swaths, and WSP swaths
Real-time runs for the traditional error swaths and postseason analyzed best tracks used in this work were collected at JTWC for the 2022 season (January–December 2022 for the Northern Hemisphere and July 2021–June 2022 for the Southern Hemisphere) on the Automated TC Forecast (ATCF) System (Sampson and Schrader 2000). The operational track positions, intensities, and 34-kt wind radii (R34 estimates) are all scrutinized and corrected in the postseason best track review process. Documentation of uncertainties of the best track quantities is discussed in Torn and Snyder (2012) and Sampson et al. (2018). The WSP swaths were generated using real-time analyses and forecasts to simulate real-time performance expected in operations.
The traditional error swath specifically provides the area where the potential for gale force winds exists. Computation of the traditional error swath follows a rather simple formulation, where the 5-yr mean track forecast error from the JTWC western North Pacific forecasts (normally hundreds of cases at 120 h) is added to the forecast maximum 34-kt wind radius at each of the JTWC forecast times (e.g., 0, 12, 24, 36, 48, 72, 96, and 120 h) to form traditional swath error circles. Then, the individual error circles at JTWC forecast times are summed using a general polygon clipper routine (https://github.com/rickbrew/GeneralPolygonClipper/blob/main/gpc.c, accessed 17 December 2024) and 25 passes of a three-point filter to smooth the result. The swath then represents the summation of the maximum size (R34) and 5-yr mean error along the entire forecast track. When the radii are missing at a forecast point (e.g., a decaying TC with less than 35-kt intensity or a TC over land with no wind radii), the computed error swath only includes the 5-yr mean track forecast error at those forecast points. The traditional swath ignores real-time track, intensity, and wind radii uncertainties (e.g., spread–skill relationships such as those in Goerss 2007; Goerss and Sampson 2014; Sampson et al. 2018) and does not explicitly address landfall or TC forecast asymmetries. Further information on the traditional error swath can be found in Strahl et al. (2016).
The development of WSPs addressed the operational needs to account for track, intensity, and surface wind structure forecast variations and bounding the official forecast. A random walk or Monte Carlo method samples the 5-yr basin-specific forecast errors of track and intensity that accounts for serial error correlations. Wind radii errors, on the other hand, are based on variations about a climatology and persistence model (Knaff et al. 2007). Given official forecast inputs and terciles of track uncertainties (Goerss 2007), the method creates somewhat realistic yet random forecast realizations that bound the official track and intensity forecast and provides climatological variations in wind field size, e.g., Fig. 2 (left). For realizations whose centers become located over land, a simple reduction in intensities is applied that affects the resulting modeled wind radii. Using 1000 realizations, cumulative (to a lead time) and incremental (within a time span) probabilities of 34, 50, and 64 kt are determined within the domain by counting the number of points that exceed these thresholds. Although there is plenty of room for improvement, the WSPs address many of the shortcomings of the traditional error swaths.
The 36-h forecast wind radii (brown) from 20 random members of the 1000 generated by the WSP algorithm (left) before and (right) after modifications to use JTWC wind radii forecast asymmetries. Six-hourly best track (black) and JTWC forecast track and 34-kt radii (orange) included for reference. Case is for WP262022 (Nalgae) at 0000 UTC 31 Oct 2022.
Citation: Weather and Forecasting 40, 6; 10.1175/WAF-D-24-0173.1
b. WSP 34-kt wind radii with forecast asymmetries
In the original WSP algorithm, the wind radii realizations were prescribed using a climatology and persistence model and without official forecast wind radii or forecast wind radii asymmetries (Fig. 2, left). The wind radii were also only weakly correlated with forecast time, resulting in large fluctuations in size through the forecast. Although neither behavior is necessarily a detriment to the WSP product performance (e.g., the cumulative WSP product shown in Fig. 1), the fluctuations are likely detrimental to downstream applications that rely on individual realizations that have time-consistent radii and asymmetries such as wave model ensembles driven with WSP realizations (Sampson et al. 2021) and to the credibility of the WSP algorithm since the probability plumes tend to be symmetric even in asymmetric TCs.
To address both the asymmetry and time-continuity issues in the WSP algorithm, developers added routines to sample the deterministic forecast R34 estimates from each of the four quadrants and then add random errors to produce asymmetric and time-consistent realizations (Fig. 2, right) that are discussed further in appendix B. Because these realization files are intended for downstream applications, the 50-kt (25.7 m s−1) and 64-kt (32.9 m s−1) wind radii, radius of maximum wind, and central pressure are all prescribed to maintain structural and time consistency in the forecast realizations.
The wind radii realizations have been visually inspected for approximately 3 years and demonstrate the desired properties, but that is no guarantee of reasonable performance in the cumulative wind probabilities that result from the asymmetries. Validation of the WSPs using the new asymmetries is done using the evaluation metrics discussed below. The verification is independent as the WSP model used was developed using historical data only up to and including 2020.
c. Evaluation metrics
Bulk evaluation metrics include calibration and average swath area for both the cumulative probabilities and traditional error swath. Both of these swaths are retained as polygons, and so the calibration and average swath areas are computed by routines that operate on polygons. The JTWC best tracked R34, which represents the maximum extent of 34-kt winds in compass quadrants (northeast, southeast, southwest, northwest), is used as ground truth, and it is assumed that 34 kt or higher winds fill the entire quadrant. For this study, calibration is the percentage of the JTWC R34 that is outside of the area defined by the cumulative wind speed probability threshold. For example, only about 30% of the best track radii area in the lower-left case of Fig. 3 is within the 5% WSP contour, so the calibration for that specific case is 70%. To compute swath area for this same case, sum the entire area within the 5% WSP contour. The optimal error swath would have the smallest swath area that does not have too much of the observed radii area outside of the swath (calibration metric). Using very low WSP thresholds would reduce the amount of area outside of the swath area but would further restrict the area available for naval operations.
Examples of verifying R34s partially outside of swaths. (top) Traditional error swaths (black) and verifying best track radii (purple) for 120-h forecasts for (left) WP142022 (Muifa) initiated at 0600 UTC 30 Jun 2022, (center) WP122022 (Himmamnor) initiated at 1200 UTC 1 Sep 2022, and (right) WP052022 (Aere) initiated at 0600 UTC 4 Jul. (bottom) Corresponding 34-kt cumulative 5% WSP swaths for the same cases. JTWC 120-h forecast track (solid orange to 72 h, dashed to 120 h) and 120-h R34 if it existed (also orange) are included for reference.
Citation: Weather and Forecasting 40, 6; 10.1175/WAF-D-24-0173.1
Some notable cases where cumulative probabilities missed large percentages of the swath or differed greatly from the traditional error swath are also presented to assist with diagnostics (Fig. 3). Common themes among these cases are that they include landfall and/or are weak TCs that are dissipating. The leftmost panels show traditional (top) and WSP (bottom) both missing about 30% of the final R34s for a landfalling TC in China; the middle panels show both completely missing the final R34s of an accelerating TC undergoing extratropical transition between the Asian Continent and Hokkaido, Japan; and the rightmost panels show the traditional error swath capturing the final R34s for a TC dissipating east of Japan, while the WSP swath captures about 15%. Since TC landfall issues represented a large fraction of the cases where the WSP missed the verifying radii or differed greatly from the traditional error swath, bulk verification is also performed with rudimentary land removal (removing cases where the TC center is over land). The WSP algorithm currently uses a simple landfall decay model (Kaplan and DeMaria 1995), while the traditional error swath has no landfall effects as visually apparent in the cases in Fig. 3.
3. Results
Average cumulative 34-kt wind probability verification (percent forecast vs percent verified) and average swath areas for the 24-, 48-, 72-, 96-, and 120-h forecast periods are shown in Fig. 4. For these cases, the WSP algorithm is run only to the verifying forecast time so that it provides an indication of the cumulative WSP calibration at selected cumulative probability thresholds (2%, 5%, 25%, and 50% missed) compared with the size of the swath at each forecast time. Immediately noticeable is that the percent missed area for all thresholds increases with increasing forecast period. Although this tendency is not particularly desirable (i.e., we prefer that the cumulative probability swaths have a relatively constant calibration metric), it is not terribly surprising since the data include landfall cases in terrain that the WSP does not yet address and for which the JTWC R34 in quadrants is an oversimplification of the complex flow behavior (i.e., overland portions of radii are not representative of the overocean conditions, or are conservatively too large). If cases in which TC centers over land are removed from the dataset, the issue is less severe as the dashed lines (without landfall cases) are generally below the solid lines of the same color. The problem still exists for 50% and to a lesser extent the 25% probabilities. But for mariners at seas, the issues at the higher probabilities are likely not a concern because lower probabilities are more likely useful in navigation (e.g., mariners avoiding areas where the probabilities exceed 10%). For bases and other inland assets, the WSP products have only been applied at lower thresholds for guidance. For example, the 50-kt WSP thresholds for Conditions of Readiness in Sampson et al. (2012) at 12, 24, 48, and 72 h were derived from watches and warnings in the Gulf of Mexico and Atlantic Seaboard to be 12%, 8%, 6%, and 5%, respectively. Visual inspection of the two products showed that the traditional error swath in JTWC operations is also more similar to low WSP swaths (e.g., rather large as seen in Fig. 3).
(left) Cumulative 34-kt WSP calibration and (right) swath area covered for selected thresholds. Solid lines are 2022 season means for JTWC’s AOR. Dashed lines are for subset eliminating cases with TC centers over land. There are 730 total cases for the entire season (solid lines). There are 676, 676, 682, 689, and 696 cases, respectively, for cases with landfall removed at 24, 48, 72, 96, and 120 h.
Citation: Weather and Forecasting 40, 6; 10.1175/WAF-D-24-0173.1
An interesting finding in Fig. 4 is that although the 2% cumulative WSP swath is 4% larger than the 5% cumulative WSP swath, the gain in verifying 34-kt wind speeds is only on the order of 0.5%. This means that the WSP swath’s increase in area with lower thresholds is not providing much additional verifying 34-kt wind speed area. There is also an issue of contour smoothness at the lower thresholds since we are only running 1000 realizations on a 1° grid due to computational restraints. Even the 5% cumulative WSP swaths shown in Fig. 3 will need to be smoothed for a final product.
Figure 3 highlights more glaring differences between the 5% cumulative 34-kt WSP product and the traditional error swath. For WP142022 (left), both swaths miss the majority of the 120-h verifying R34 even with large differences in swath shapes. For the WP122022 case (middle panels of Fig. 3), the swaths are similar, and both miss the verifying R34 entirely. And for the WP052022 case (right panels of Fig. 3), the traditional error swath encompasses the entire verifying R34 with a much larger swath. The verifying R34 estimates for the WP052022 case are entirely outside the WSP swath in this case because the TC was expected to remain 35 kt or less for the entire forecast with an extended period over land. In all three of these cases, some of the WSP algorithm forecast realizations are affected by landfall, and verifying R34 estimates are the last analyzed in their specific best track. These are admittedly difficult cases chosen specifically to highlight limitations of the algorithm.
The forecast in Fig. 1 also shows large differences in the swaths at 120 h when a TC dissipates. In this case, the JTWC 120-h forecast intensity is 30 kt, and the 5% cumulative 34-kt WSP swath, represented by the dark green area in Fig. 1, extends just beyond the 96-h forecast position. The traditional error swath extends the entire length of the track forecast and includes a large area around the 120-h forecast position. Incidentally, the verifying intensity from JTWC for this case was 30 kt, but this does highlight the fact that the traditional error swath does extend the entire length of the forecast as it is prescribed to do.
Figure 5 shows results from an objective evaluation of the traditional error swath with the 5% cumulative 34-kt WSP product for the entire length of the forecast, as it is applied in operations. The total area that includes land cases (solid lines in the right panel of Fig. 5) remains constant through the forecast because the error swath is the same for evaluation of all forecast periods. For both algorithms, the overall verification shows that the short and intermediate forecast swaths miss verifying 34-kt winds approximately 1%–7% of the time but increase to about 10% at 120 h. The WSP swath at 120 h has a mean area missed of just over 10%, while the traditional error swath is about 3% less. Removing cases with verifying TC centers over land reduces the average area missed to 3% for the traditional error swath and 5% for the WSP-based swath. This demonstrates the well-calibrated nature of the WSP-based swath.
Homogeneous comparisons of (left) mean missed 34-kt wind areas for the traditional error swath and 5% cumulative WSP threshold and (right) mean swath area forecasted through forecast time. Comparisons are for the 2022 season in JTWC’s AOR.
Citation: Weather and Forecasting 40, 6; 10.1175/WAF-D-24-0173.1
Figure 5 demonstrates the calibration differences, but this can be further investigated by plotting individual cases to determine where the outliers exist (Fig. 6). Figure 6 (left) shows an analysis of the differences for the individual cases as a function of traditional error swath size. Some of the more interesting cases are shown in Fig. 3, and it is apparent that the largest size differences are for smaller error swaths. For the largest error swaths, the differences are generally within 20%–30% of each other. For example, the largest absolute difference in the dataset is 1 449 911 n mi2 for WP162022 at 0600 UTC September 16, and that is only −23.36% of the traditional error swath (2 378 400 n mi2). Figure 6 (right) shows all the cases where the verifying JTWC best tracked R34 was either partly or fully outside a swath. A blue dot along the diagonal indicates the two algorithms missed approximately the same area for that given case, while one far from the diagonal indicates differences in that individual case. Most cases are at 0, 0 since the two swaths include the verifying JTWC best tracked R34. Of the 25 of 717 (3%) traditional and 48 of 717 (7%) WSP cases that are found to have JTWC best tracked R34 partially or completely outside the error swaths, most were of areas less than 5000 n mi2. There are a few large area misses for both algorithms, but those are for the same forecast cases (they lie along the diagonal in the Fig. 6, right panel).
(left) Distribution of swath size differences as a function of swath size, where the y axis is 100 × (traditional error swath area − WSP error swath area)/(traditional error swath area). (right) Best track R34 area missed by WSP vs traditional error swaths. Blue dots indicate the individual (717 total) cases, most of which are 0, 0.
Citation: Weather and Forecasting 40, 6; 10.1175/WAF-D-24-0173.1
Figure 7 shows two circles anchored to the same lower latitude with average areas for two error swaths. The average traditional error swath for the entire dataset (∼1 120 000 n mi2) is approximately 15% larger than the average 34-kt WSP-based swath based on the 5% probability threshold (960 000 n mi2). Therefore, the average WSP-based swath is 15% smaller in area and (from Fig. 5) only includes 3% less of the JTWC best track R34 area. This is likely a reasonable trade-off between swath size and performance since many of the largest discrepancies involve landfalling and/or dissipating TCs. In absolute terms, that is an average of 26 000 n mi2 extra area for navigation at sea around a 120-h WSP swath compared with a traditional error swath.
Circles representing the average traditional error swath area (blue) and the average 34-kt WSP swath based on the 5% probability threshold (red).
Citation: Weather and Forecasting 40, 6; 10.1175/WAF-D-24-0173.1
4. Summary and discussion
This work investigates the performance of the JTWC traditional error swath and a potential replacement based on the WSP algorithm. Some initial work to add JTWC R34 asymmetries and forecast time consistency to the realizations is performed (appendix B). Then, the WSP algorithm is rerun for the 2022 season to collect WSP-based swaths based on several probability thresholds. The 34-kt WSP-based swath based on the 5% probability threshold is found to be a reasonable proxy for ship avoidance swath when applied to the 2022 season, is on average 15% smaller in area, and includes 3% less of the JTWC best track R34 area. Tests removing cases with TC centers over land result in more analyzed wind speed area covered, especially for the 120-h WSP swath. Testing a lower 34-kt WSP threshold of 2% results in only 0.5% more 34-kt wind speed area covered, which the authors consider a poor trade.
There are other advantages to using the WSP algorithm. Among them are that the WSP algorithm is in development with hopes for improvements in landfall (see Santos et al. 2024); improvements in operational center forecasts; improvements in track, intensity, and wind radii model spread/skill relationships (e.g., Goerss 2007; Goerss and Sampson 2014; Sampson et al. 2018); and machine learning applications (e.g., Meng and Song 2024; DeMaria et al. 2023). All these improvements will likely reduce the wind risk swath, but mariners also need to avoid high seas associated with tropical cyclones, so there is a need for pairing the wind and seas risks. For the U.S. Navy, this effort requires real-time wave height probabilities that are consistent with TC wind probabilities as outlined in Sampson et al. (2021). The dilemma that needs to be resolved is computing the consistent wave probabilities (and swaths) in time to distribute with the wind probabilities (and swaths), and there is hope that this might be mitigated through use of machine learning.
Acknowledgments.
The authors would like to acknowledge funding provided by the Office of Naval Research under ONR Award N0001420WX00517 to NRL Monterey and a grant to CIRA (N00173-21-1-G008). We would also like to thank all the people at NRL, FWC-Norfolk, and JTWC who keep the ATCF running in operations and James Hansen for his constructive comments. Rabi Rivett and anonymous reviewers are also acknowledged for their careful reviews. The scientific results and conclusions, as well as any views or opinions expressed herein, are those of the authors and do not necessarily reflect those of NOAA or the Department of Commerce. ATCF is a registered trademark of the Naval Research Laboratory.
Data availability statement.
The best track data used in this study are freely available from the Joint Typhoon Warning Center (https://www.metoc.navy.mil/jtwc/jtwc.html?best-tracks). Traditional error swaths and WSP swaths are available from both JTWC and NRL pending public release.
APPENDIX A
List of Acronyms
| AOR |
Area of responsibility |
| ATCF |
Automated Tropical Cyclone Forecast System |
| JTWC |
Joint Typhoon Warning Center |
| PACOM/J3 |
Pacific command operations |
| R34, R50, R64 |
Radii of 34-, 50-, 64-kt winds |
| TC |
Tropical cyclone |
| vmax |
Maximum 1-min wind speed |
| WSP |
Wind speed probability |
APPENDIX B
Wind Radius Realization Modifications
The wind radii realizations used in this work deviate from the DeMaria et al. (2009, 2013) descriptions. The changes ensure that the individual realizations lack sudden and unrealistic size variations and contain asymmetries and inner-core structures more consistent with the official forecast.
The first change restricted the shape factor “x” errors to values between 0.1 and −0.1. This change restricts the 12-h changes in x to physically realistic values. The tails of the error distribution, if used, could result in errors larger than typical observed values of x that range between 0.2 and 1.2. And large variations in x can overwhelm the built-in serial correlation that is desired between time steps. An x shrinkage factor of 0.0669 based on best track data as in Knaff et al. (2007) is prescribed at each time step to prevent overdispersion. Tests without this factor demonstrate that its removal allows too much dispersion and very large areas warned.
The second modification ensures that asymmetries observed in the CLIPER forecast are maintained in each of the realizations. This is accomplished by calculating the initial quadrantwise ratio between each realization’s wind radii with the CLIPER-based radii associated with the official track and intensity forecast. Applying these ratios plus a random error to each quadrant creates final wind radii that better maintain quadrantwise asymmetries through the multiple realizations that have different intensities, motions, and locations.
The third change involves calculating the quadrantwise wind radii assuming an overland exposure for use when the storm center is over land. Application of a reduction factor of 0.8 CLIPER-based vortex winds reduces the size of wind radii in these cases. The mix of overland and oceanic cases close to land provides a computationally efficient compromise to determine land proximity for each point surrounding every realization.
This forces R50 and R64 to grow and shrink with R34 and to maintain the general structure of a TC throughout the forecast. Then, the radii are used to estimate both the radius of maximum wind via Chavas and Knaff (2022) and Avenas et al. (2023). And finally, central pressure is prescribed via Courtney and Knaff (2009). These realization file changes correct known shortcomings with inconsistencies between R34 and the inner core (R50, R64, and the radius of maximum wind) that occasionally occur if not addressed. They also provide a physically consistent radius of maximum wind and mean sea level pressure (MSLP). Additional validation is desired before including the realization file changes in the wind speed probability calculations, but the authors see potential applications for the realization files in downstream applications.
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