Predictability of the Most Long‐Lived Tropical Cyclone Freddy (2023) During Its Westward Journey Through the Southern Tropical Indian Ocean

This study aimed to explore the predictability of the most long‐lived tropical cyclone (TC) Freddy in 2023 while it traversed westward across the southern tropical Indian Ocean during the first 18 days of its existence. Global ensemble forecasts revealed southward track deflection and intensity underestimation of Freddy. We identified three key factors contributing to the limited predictability of Freddy, which are associated with the Mascarene High, Storm Dingani, and Freddy itself. The large track errors of Freddy can be attributed to the underestimated strength of the Mascarene High, the more northeastern position of Dingani, and the presence of excessively large or small sizes of Freddy. These findings were further validated through a high‐resolution regional model. Specifically, Freddy's track and intensity most closely matched the observations when these three factors were most closely represented. It underscores the pivotal role played by the interaction between TCs and multi‐scale systems in TC forecasts.

• Due to the long lifespan of Storm Freddy, many forecasting challenges across several numerical models arose • The limited predictability of Freddy was related to the underestimated Mascarene High and the more northeastern position of Storm Dingani • The inaccurately forecasted size of Freddy, whether excessively large or small, also contributed to the large track errors

Supporting Information:
Supporting Information may be found in the online version of this article.
TCs tend to form and develop under favorable conditions (Gray, 1968).In the case of Freddy, it was observed to sustain in an environment characterized by weak vertical wind shear and warm sea surface temperature (Figures 1d and 1e).However, one potential hindrance to the development of Freddy was the presence of dry atmosphere along the westward track of Freddy over the southern tropical Indian Ocean (Figure 1f).This adverse condition may have been counteracted by the weak vertical wind shear and small size of a TC (Shimada, 2022).
Additionally, the interaction between binary TCs can influence the track, intensity and structure of TCs (e.g., Ito et al., 2023;J.-D. Lee et al., 2023;Liu et al., 2021;Liu, Gu, & Wang, 2023).During the westward movement of Freddy over the southern tropical Indian Ocean, Storm Dingani (2023) formed to the west of Freddy at 06:00 UTC 9 February, and dissipated at 06:00 UTC 16 February.The average distance between Freddy and Dingani during their coexistence period was 2383 km.
The operational forecasts for TCs provided by Hurricane/Typhoon centers typically focus on a 5-day forecast period (e.g., Cangialosi, 2023;Japan Meteorological Agency, 2022).This is almost comparable to the average lifespan of TCs that is approximately 5.3 days (Figure 1a).However, the performance of numerical models in predicting long-lived TCs remains relatively unknown.Although a grand ensemble simulations of Typhoon Faxai (2019) revealed the cause of errors in TC forecasts for a few weeks (Y.Yamada et al., 2023), their findings are specific to that particular case and it is unknown whether the predictability of other TCs can be extended for longer durations in general.Benefit from the Observing System Research and Predictability Experiment (THOR-PEX) Interactive Grand Global Ensemble (TIGGE) project (Bougeault et al., 2010), global ensemble forecasts with forecast periods exceeding 10 days from some Numerical Weather Prediction (NWP) centers are available, which is comparable to the duration of Freddy during its westward journey over the southern tropical Indian Ocean.In this study, we aim to assess the predictability of Freddy during its 18-day trajectory through the southern tropical Indian Ocean and understand the impacts of multi-scale systems on the forecast errors of Freddy.

Data
We utilized ensemble forecasts with a horizontal resolution of 1° from five global NWP centers that are available in the TIGGE data set (Table S1 in Supporting Information S1).These forecasts were used to derive the predicted tracks and intensities of Freddy and Dingani, as well as the large-scale circulations.The ensemble forecasts were initialized at 00:00 and 12:00 UTC from 5 to 24 February.To assess the forecast results, we obtained the best-track data of Freddy, Dingani and historical TCs from the International Best Track Archive for Climate Stewardship-The World Meteorological Organization (IBTrACS-WMO) v4 data set (Knapp et al., 2010).
This data set provides information on the position and maximum sustained wind speeds of TCs from 1942 up to 14 May 2023.To evaluate the accuracy of the environmental conditions for Freddy, we used the NCEP GFS 0.25-degree Global Forecast Grids Historical Archive and the European Center for Medium Range Weather Forecasts (ECMWF) monthly and hourly reanalysis 5 (ERA5) with 0.25° horizontal resolution.

Verification of Ensemble Forecasts for Freddy
We calculate the track and intensity errors of all ensemble forecasts for Freddy as shown in Figures 2a-2d and Figure S3 in Supporting Information S1.The forecast tracks and intensities of Freddy can be found in Figures S4 and S5 in Supporting Information S1.In the ensemble forecasts, the intensity of Freddy was significantly lower compared to the best-track data (Figure S5 in Supporting Information S1).Therefore, we defined a vortex as a TC when its maximum 10-m wind speed was larger than 10 m s −1 .This is the minimum sustained wind speed of Freddy in the best-track data.Additionally, we calculated the root mean squared error and spread of the ensemble forecasts following the method used in X. Wang and Tan (2023).
The mean track errors of the ensemble forecasts from the five global NWP centers exhibited a rapid increase after around 5 days of forecast (Figure 2e).Specifically, the track errors increased by about 177 km from the third day to the fifth day, and by approximately 284 km from the fifth day to the seventh day.The 120-hr track errors initialized at all times (Figure 2f) were found to be larger than that of the mean National Hurricane Center official forecasts for TCs over the Atlantic basin in 2023 (Cangialosi, 2023).
The large intensity errors and the extreme underestimations of the intensity indicate that the global NWP models struggled to accurately capture the intensity evolution of Freddy (Figures 2c and 2d and Figures S3b,S3d,and S3f in Supporting Information S1).The failure of intensity forecasts for Freddy can be primarily attributed to the coarse resolution of the global ensemble forecasts (Davis, 2018;Gentry & Lackmann, 2010;Gopalakrishnan et al., 2012).Additionally, approximately 23.5% of the forecasts experienced premature dissipation of Freddy, coupled with significant track errors.This can be attributed to the unfavorable surrounding environment (e.g., the region of large vertical wind shear in Figure 1d), which hindered the development of Freddy.Although the NCEP introduced vortex perturbations to reduce the initial errors (Figure 2d), the resulting effect was not as anticipated.
The potential reason is that the intensity of the TC exerts only a minor influence on its movement (Fiorino & Elsberry, 1989).This suggests that improving the initial intensity of Freddy was not a key factor in advancing the predictability during such a long forecast period.
The RMSEs of the track and intensity were far larger than those of the spreads, indicating that the ensemble forecasts were under-dispersive and the model exhibited overconfidence.Therefore, the global NWP forecasts nearly failed to predict Freddy's westward journey through the southern tropical Indian Ocean.

Factors Resulting in the Unsuccessful Forecast Results
To identify the factors contributing to the large forecast errors, we conducted a composite analysis of the ensemble-mean sea level pressure of the 25 smallest (i.e., good) and largest (i.e., bad) track-error results.These  results are the forecasts at the given time but may originate from different NWP centers, or initialize at different time.For example, a good result at 00:00 UTC 7 February may originate from the NCEP or ECMWF, and initialize at 00:00 UTC 5 or 6 February.We used track error rather than intensity error because the intensity forecasts of Freddy were highly inaccurate.In Figures 3a-3d and Figure S6 in Supporting Information S1, we present the differences between the good and bad ensemble forecasts, based on which three key regions that are closely associated with the westward motion of Freddy are highlighted.

The Mascarene High
The first region of significance is located south of 20°S, which corresponds to the area of the subtropical high-pressure system named Mascarene High (Xulu et al., 2020).In the good ensemble results, the Mascarene High was generally stronger, except on the 15, 17, and 19 of February.It suggests that the forecasts of Freddy tended to be less accurate when the Mascarene High was weaker in the global NWP models.This can be confirmed by the negative correlations between the track errors of Freddy and the bias of the Mascarene High index (MHI) most of the time, as shown in Figure 3e and Figure S7 in Supporting Information S1.The MHI is defined as the mean sea level pressure within the region of (40°-110°E, 35°-25°S) following the definition of Nkurunziza et al. (2019), and the bias represents the difference between the MHIs of the forecasts and the GFS reanalysis.The negative bias of the MHI indicates an underestimate of the strength of the Mascarene High in the global WNP models, accounting for over 57% of the ensemble forecasts.Furthermore, we calculated a linear regression equation to analyze the relationship between the track errors of Freddy (Ferr) and the standardized MHI bias as follows, Ferr = −191.4* MHI + 490.9. (1) The negative relationship is reasonable because the Mascarene High could contribute to the easterly steering flow that affected the motion of Freddy.When the Mascarene High was weak, it could slow down the westward motion of Freddy, making it more likely to move southward without encountering strong resistance from the Mascarene High (Figure S8 in Supporting Information S1), as observed in most forecasts.

The Interaction Between Freddy and Dingani
The second significant region is situated near the position of Dingani (its forecast tracks were shown in Figure S9 in Supporting Information S1) and to the east of Dingani at 00:00 UTC on the 11 (75°-95°E, 20°S-0°), 13 (65°-90°E, 25°S-0°), and 15 (65°-75°E, 30°-15°S) of February (Figures 3a-3c).The difference in this region exhibits a negative-positive dipole pattern, extending from the west (or southwest) to the east (or northeast).The negative (positive) anomaly corresponds to the location of Dingani in the good (bad) results, suggesting that when the errors of Freddy were larger, Dingani tended to be positioned more to the east or northeast.This can be supported by examining the relationship between the changes in track errors of Freddy and the track errors, meridional biases, and zonal biases of Dingani during the period of their coexistence (Figures 3f-3h).The linear regression of the Ferr and the standardized track errors of Dingani (Derr) is described as follows, Ferr = 241.4* Derr + 340.5. (2) Therefore, the northeastward bias of Dingani, combined with its larger track errors relative to the observations, aligns with the larger track errors observed for Freddy.
Since Dingani was positioned to the west and southwest of Freddy, its northeastward bias can result in a false northerly steering flow.This northerly flow corresponded to the eastern part of the low-level cyclonic circulation associated with Dingani.As a result, Freddy is influenced to move southward under the steering effect of Dingani, leading to larger track errors.Moreover, the track errors of Freddy after the 16 February were significantly smaller compared to those before (Figure 2f).This timing coincided with the dissipation of Dingani, that further emphasizes the influence of Dingani on the predictability of Freddy.

Vortex Size of Freddy
The third significant region is located near the position of Freddy and to the east of Freddy.Similar to the situation with Dingani, the pattern of the difference in this region exhibits a negative-positive dipole pattern.Considering that the vortex structure can significantly affect TC motion (Carr & Elsberry, 1997;Fiorino & Elsberry, 1989;Tang et al., 2020;Y. Wang & Holland, 1996a, 1996b), it is possible that the vortex size may be another important factor influencing the predictability of Freddy.We define the vortex size of Freddy as the radius at which the azimuthal-mean 10-m azimuthal wind equals 8 m s −1 (R08), a criterion previously used by Benjamin et al. (2017) and Stansfield et al. (2020).Figure 3i illustrates the changes in track errors of Freddy corresponding to variations in R08.The ensemble forecasts exhibited smaller track errors for Freddy with R08 values ranging from 400 to 600 km, which aligns with the visible satellite imagery depicting the rainfall radius (Figure S2 in Supporting Information S1).Additionally, we conducted a linear regression analysis of the Ferr and the standardized R08 as follows, and Ferr = 275.8* 08 + 314.1, (08 > 500 km). (4) These results imply that both excessively small and large sizes of Freddy in the ensemble forecasts contributed to larger track errors.
Although the relative contributions of the three factors to the track errors of Freddy can be quantified by comparing their linear regression coefficients, it is important to consider that these coefficients may be influenced by sample sizes and interaction among the three systems (Text S1 in Supporting Information S1).

Examination in the Regional High-Resolution Simulations
To verify the above findings, we conducted four experiments spanning 17 days using the Weather Research and Forecasting (WRF) model with a finest mesh resolution of 2 km.Further information on the model setup can be found in Text S2 in Supporting Information S1.The first experiment was directly integrated without any modifications (CTRL).In the second experiment (RM_Dingani), the embryo of Dingani (the tropical depression before Dingani was officially named) was artificially removed using the vortex separation method (Liu & Tan, 2016;Liu et al., 2018;Liu, Gu, Wang, & Xu, 2023).The radius of the removed vortex was 1,440 km from the center of the tropical depression, which was large enough to prevent the regeneration of Dingani.In the third experiment (SN), we applied the large-scale spectral nudging (Cha et al., 2011) to force the atmospheric circulations with wavelengths longer than 1,000 km to closely resemble the GFS reanalysis.In the fourth experiment (Large_Freddy), the initial axisymmetric component of Freddy was artificially expanded to be twice the size of the CTRL run.
Figures 4a and 4b illustrate the simulated tracks and intensities of Freddy in the four experiments compared with the best-track data.The simulated track in the SN run closely aligned with the best-track, followed by the RM_Dingani, CTRL, and Large_Freddy runs.Benefiting from the 2-km resolution, the intensity evolutions of Freddy in all experiments were improved compared to the global NWP ensemble forecasts.The SN run performs the best.The Freddy vortices dissipated earlier in the CTRL, RM_Dingani and Large_Freddy runs than that in the SN run.
Figures 4c-4l show the geopotential height at 850 hPa after 6 and 10 days of simulations, compared with the corresponding GFS reanalysis.In the CTRL run, the pattern of the Mascarene High and the position of Dingani differed from those in the reanalysis.As a result, the inaccurate steering flow led to Freddy moving southward against the best-track data.If Dingani did not exist, the simulated track of Freddy would be expected to be better than that of the CTRL run due to the absence of the inaccurate interaction between Freddy and Dingani, as seen in the RM_Dingani run (Figures 4e and 4j).However, in the RM_Dingani run, the pattern of the Mascarene High also differed from that in the reanalysis, resulting in southwestward movement and earlier disappearance of Freddy.
In the SN run, the pattern of the Mascarene High closely resembled that of reanalysis due to the large-scale spectral nudging (Figures 4f and 4k).This appropriate large-scale circulation ensured accurate steering flow of  Freddy and the interaction between Freddy and Dingani, leading to better results for Freddy.In the Large_Freddy run, when the initial size of Freddy was enlarged, Freddy moved southward and turned southeastward toward Australia (Figure 4g).This is reasonable as larger TCs tend to move more poleward due to the stronger beta drift (Fiorino & Elsberry, 1989;Y. Wang & Holland, 1996a, 1996b).Moreover, the large TC may introduce significant changes in the environment structure (Carr & Elsberry, 1997), resulting in the modified steering flow and subsequently altering the motion of Freddy.
These results highlight the importance of accurate representation of the Mascarene High, the interaction between Freddy and Dingani, and the size of Freddy in determining its track and thereby the intensity.

Conclusion and Discussion
This study focused on examining the predictability of the record-breaking long-lived storm Freddy during its westward journey over the southern tropical Indian Ocean in February 2023.The five selected global NWP models demonstrated poor ability to accurately forecast the westward track of Freddy and consistently underestimated its intensity.By analyzing over 7000 NWP ensemble forecasts and the results from the high-resolution regional WRF model, we found that the large track errors of Freddy can be attributed to the underestimated strength of the Mascarene High, the more northeastern position of Dingani, and the presence of excessively large or small sizes of Freddy.The weak Mascarene High resulted in a weak steering flow, which failed to drive Freddy's westward movement effectively.It also caused Dingani to be positioned more to the northeast, leading to northerly steering flow for Freddy.This further resulted in the southward motion of Freddy against the observations.The excessively large or small sizes of Freddy could alter its interaction with its environmental flow and Dingani, thereby affecting its movement.
Therefore, in order to enhance the predictability of long-lived TCs like Freddy, it is essential to improve the representation of multi-scale systems and their interactions.Initialization schemes for TCs can contribute to the improvement of forecasted TC structures (e.g., Cha & Wang, 2013;Kurihara et al., 1993;Liu & Tan, 2016;Liu et al., 2018;Zou & Xiao, 2000), as the initial size of a TC can significantly impact its size evolution (Chen et al., 2023;C.-S. Lee et al., 2010).This relies on improved observations to accurately describe the fine structure of TCs (e.g., Aberson & Franklin, 1999;Bell et al., 2012;Brauer et al., 2020).Moreover, it is crucial to ensure that models have a sufficiently high resolution to accurately capture the intricate structure of TCs.Recent efforts have been made to enhance TC forecasts in global cloud-resolving models (e.g., Nakano et al., 2017;H. Yamada et al., 2016;Y. Yamada et al., 2023).Lastly, the accurate representation of large-scale circulations is fundamental for predicting long-lived TCs, encompassing both weather and sub-seasonal to seasonal time ranges.However, predicting the latter still remains challenging (Jie et al., 2017;Lin et al., 2006;Vitart et al., 2017;Waliser et al., 2003).
Several questions still remain unanswered.We did not resolve what factors led to this long-lived TC.The Mascarene high was not abnormally strong during the lifetime of Freddy (Figure S10 in Supporting Information S1).We speculate that the zonal distribution and the vertical structure of the Mascarene high may play a role in influencing the longer lifespan of Freddy.Freddy encountered five instances of rapid intensification while traversing the southern tropical Indian Ocean before its first dissipation.After its regeneration, Freddy underwent two additional RIs (Figure 1c).It is crucial to investigate the factors contributing to the occurrence of multiple RIs in Freddy and explore the distinctions between them.Moreover, the process by which Freddy regenerated after making landfall in Mozambique remains undisclosed.These aspects warrant further investigation in future studies.

Figure 1 .
Figure 1.(a) Annual frequency (bars), average (black curve), and maximum (red curve) lifespans of tropical cyclones over all basins from 1942 to 14 May 2023; (b) Tracks of Freddy and Dingani, denoted by F and D; (c) Intensity of Freddy; (d) Monthly mean vertical wind shear (m s −1 , shading) between 200 and 850 hPa in February 2023; (e) Monthly mean sea surface temperature (°C, shading) in February 2023; (f) Profiles of specific humidity (g kg −1 ) of the Freddy track (black curve), Western Indian (red curve, Jordan, 1958), and tropical North Atlantic (blue curve, Dunion, 2011).(d-f) Were plotted using the ERA5 monthly analysis.

Figure 2 .
Figure 2. (a-d) Track (km) and intensity (m s −1 ) errors (gray curves) of ensemble forecasts from the European Center for Medium Range Weather Forecasts and NCEP centers.The results of the maximum 10-m wind speed of the vortex less than 10 m s −1 and the forecast time exceeding 12:00 UTC 24 February, were ignored.The red and blue curves denote the mean root mean squared error and ensemble spread, respectively.(e) Mean track errors of all forecasts.(f) Mean 120-hr track errors initialized from 5 to 19 February in 12-hr intervals.The black line in panel (f) denotes the National Hurricane Center official error over the Atlantic basin in 2023.

Figure 3 .
Figure3.(a-d)  Difference of the sea level pressure (hPa) between the best and the worst 25 ensemble forecasts at 00:00 UTC from the 11 to the 17 in 2-day intervals.The dots denote the significance of the difference exceeding 99% confidence level.The symbols of M, F, and D denote the Mascarene High, Freddy, and Dingani, respectively.(e-i) Changes in track errors (dot) of Freddy in relation to the (e) Mascarene High index, (f) track errors, (g) meridional biases, (h) zonal biases of Dingani, and (i) vortex size (R08) of Freddy.The meridional (zonal) biases are calculated as the differences between the forecast latitude (longitude) of Dingani's center and that of the best-track data.A positive meridional (zonal) bias indicates that Dingani was located more northward (eastward) than observed.The black line is the linear regression of the dots.

Figure 4 .
Figure 4. (a) Track and (b) intensity of Freddy in the best-track data (black) and four experiments (colors).Geopotential height at 850 hPa from the (c, h) GFS reanalysis, (d, i) CTRL, (e, j) RM_Dingani, (f, k) SN, and (g, l) Large_Freddy.The black curves denote the best-track data in panel (c, h) and simulated tracks in (d-g, i-l).The symbols of F and D denote Freddy and Dingani, respectively.