1. Introduction
Subseasonal forecasts of tropical cyclone (TC) activity bridge the prediction gap between weather (1–7 days) forecasts of hourly TC tracks, intensity, size, storm surge, and rainfall (Emanuel 2018; Cangialosi et al. 2020) and seasonal forecasts (3–9 months) of seasonal-mean basinwide activity such as the number of TCs (NTCs) or accumulated cyclone energy (ACE; Bell et al. 2000; Camargo and Barnston 2009; Klotzbach et al. 2019). At the subseasonal-to-seasonal (S2S) range (2–6 weeks), several studies have evaluated weekly averaged probabilistic forecasts of TC genesis, occurrence, and ACE (Vitart et al. 2010; Camargo et al. 2019; Schreck et al. 2023), finding skill in forecasts beyond 2 weeks lead time in case studies (Elsberry et al. 2014; Gregory et al. 2019; Kolstad 2021) and forecast verification metrics (Belanger et al. 2010; Yamaguchi et al. 2015; Switanek et al. 2023). However, several outstanding issues for S2S TC prediction remain such as defining uniform forecast verification methodologies and determining the sources of predictability and model skill (Camargo et al. 2019; Schreck et al. 2023, and references therein).
The expectation that some aspects of TC activity are predictable at the S2S range arises from the observed intraseasonal variability of TCs and its modulation by the Madden–Julian oscillation (MJO; Camargo et al. 2009; Huang et al. 2011; Hansen et al. 2022), equatorial waves (Schreck et al. 2012; Schreck 2016; Feng et al. 2023), extratropical Rossby wave breaking (Li et al. 2018), and subtropical high pressure systems (Camp et al. 2018; Xiang et al. 2022). Evidence for the role of the MJO in S2S TC predictions is that probabilistic forecasts of TC genesis and occurrence have higher skill in models that better simulate the MJO–TC relationship (Camp et al. 2018; Lee et al. 2018a) and forecasts initialized under MJO phases that are favorable for TC genesis in a particular basin are more skillful (Belanger et al. 2010; Lee et al. 2020). However, this evidence is based on prediction skill scores rather than predictability.
Predictability in the climate system based on models can be defined through the difference between a forecast distribution and a climatological distribution (Shukla 1998; Palmer 2000; DelSole and Tippett 2022). S2S predictability can be inferred from model forecasts by checking if a condition, e.g., an MJO phase, significantly modifies the forecast probability of an event from its climatological probability (see, e.g., DelSole and Tippett 2018; Tippett and Lepore 2021; Tippett et al. 2022), and thereby creates a window of forecast opportunity (Mariotti et al. 2020; Domeisen et al. 2022). Model-based assessments of S2S TC predictability can better highlight the extent to which sources of predictability such as the MJO can impact the forecast probability of TC occurrence.
S2S TC prediction skill is hampered by global (GL) model errors in the TC climatology (Camargo and Wing 2016; Lee et al. 2020), environmental conditions (Camargo et al. 2020), and storm-scale processes (Kim et al. 2018; Vannière et al. 2020), as well as in the MJO and its associated teleconnections (Camp et al. 2018; Stan et al. 2022). Partially due to these biases, probabilistic S2S forecasts from dynamical models cannot skillfully predict anomalies from the seasonal cycle of TC genesis beyond 1 week (Lee et al. 2018a) or TC occurrence beyond 2 weeks (Lee et al. 2020). However, calibrating the S2S forecasts to account for model biases in TC frequency can extend the prediction skill of TC activity for an additional 1 or 2 weeks (Camargo et al. 2019; Lee et al. 2020; Camargo et al. 2021; Li et al. 2022).
Model development is one way to improve S2S prediction skill (Camargo et al. 2019; Stan et al. 2022; White et al. 2022). The NASA Global Modeling and Assimilation Office (GMAO) developed and continues to improve the Goddard Earth Observing System (GEOS) S2S forecast system (Borovikov et al. 2019). In 2018, GEOS-S2S-1 was updated to GEOS-S2S-2 (Molod et al. 2020), which has been operating in near–real time (1–2 days behind real time) since then. GEOS-S2S-1 was a part of the North American Multimodel Ensemble (NMME) project for operational seasonal forecasts (Kirtman et al. 2014), and GEOS-S2S-2 expanded this role into subseasonal forecasting by providing forecasts to the NOAA Subseasonal Experiment (SubX; Pegion et al. 2019). The most recent version of GEOS-S2S, GEOS-S2S-3, includes several enhancements, such as higher spatial resolution over the ocean, new atmosphere–ocean interface layer, the proper initialization of the interactive aerosol model, and a substantially larger ensemble size for subseasonal prediction. The GMAO is currently running the retrospective forecasts, and GEOS-S2S-3 is expected to replace the current GEOS-S2S-2 by the middle of 2024.
Several aspects of the climatology and prediction skill of GEOS-S2S-2 have been analyzed in previous studies (Molod et al. 2020; Lim et al. 2021; Aquila et al. 2021; Massoud et al. 2023). For instance, GEOS-S2S-2 can skillfully predict the evolution of the MJO real-time multivariate (RMM) index for up to 30 days (Lim et al. 2021) and can also predict monthly variations of the major teleconnections, such as the North Atlantic Oscillation (NAO) and the Pacific–North American (PNA) pattern up to 2 ahead. However, the climatology and prediction skill of TC activity have not been analyzed yet in either GEOS-S2S-1 or GEOS-S2S-2.
The purpose of this study is to evaluate the TC climatology, predictability, and prediction skill in GEOS-S2S-2 (hereafter GEOS). The skill of GEOS is compared with models participating in the WMO S2S project (see, e.g., Vitart and Robertson 2018; Lee et al. 2018a, 2020). The remainder of this paper is structured as follows. Section 2 describes the GEOS reforecasts, observational data, and methods. The climatology and biases of TC activity in GEOS is assessed in section 3. Prediction skill of TC genesis and occurrence is evaluated in section 4. Section 5 evaluates MJO-related predictability in TC occurrence. Section 6 summarizes and discusses the main findings of this study.
2. Data and methods
a. GEOS-S2S and forecasts
The GMAO has developed the GEOS system with a seamless prediction approach that aims to improve prediction skill across multiple time scales through the assimilation of NASA’s space-based observations (Molod et al. 2020). GEOS uses a fully coupled global model built using an Earth System Modeling Framework (Hill et al. 2004) that allows improvements in each model component to propagate to the rest of the components (Borovikov et al. 2019; Molod et al. 2020). The model components are the GEOS atmospheric general circulation model (AGCM; Molod et al. 2015), the ocean model Modular Ocean Model (MOM5; Griffies et al. 2012), a land surface model with a catchment-based scheme (Koster et al. 2000), the Goddard Chemistry Aerosol Radiation and Transport model (GOCART) (Colarco et al. 2010), and the Community Ice Code-4 (CICE 4.1) for the sea ice model (Hunke and Lipscomb 2010).
The AGCM is run on a cubed sphere grid with an approximately 0.5° × 0.5° horizontal resolution and 72 vertical levels that extend into the mesosphere (Molod et al. 2015). For details of the convective, cloud microphysics, and turbulent schemes as well as other aspects of the AGCM, see previous studies (Moorthi and Suarez 1992; Rienecker et al. 2008; Molod et al. 2015, 2020). The ocean model MOM5 uses a tripolar grid at an approximately 50-km horizontal resolution with 40 layers extending to 4500-m depth (Griffies et al. 2012). The reforecasts are initialized from a weakly coupled atmosphere–ocean data assimilation system, which includes an ocean predictor and corrector segment where the atmosphere is replayed or nudged toward the atmospheric analysis (Molod et al. 2020).
The GEOS-S2S-2 retrospective subseasonal forecasts consist of a four-member ensemble, initialized every 5 days (reforecast frequency) for 45 days (forecast period). The ensemble members were produced by perturbing the atmospheric and ocean states through a simple scaled-difference approach (Borovikov et al. 2019; Molod et al. 2020). The period of the reforecasts used in this study begins 1 January 1999 and ends 31 December 2020.
b. Tracking method
The TC tracking in the GEOS reforecasts was performed using the objective tracking framework TempestExtremes v2.1 (Ullrich et al. 2021), which has been used extensively for TC tracking in reanalysis (Zarzycki and Ullrich 2017; Jones et al. 2021) and model data (Roberts et al. 2020; Zarzycki et al. 2021). TCs that are included in the initial conditions are not removed from the main analysis, except where otherwise indicated. The TempestExtremes open-source software was used to obtain TC tracks from GEOS using 6-hourly instantaneous data (Ullrich and Zarzycki 2017; Ullrich et al. 2021).
The tracking procedure has two main steps. The first algorithm identifies TC candidates as grid points with a closed contour sea level pressure (SLP), and the SLP away from the minimum SLP must increase by at least 2 hPa within a 5.5° great circle distance. The candidate storm must also exhibit a warm core, characterized as a geopotential thickness between 200 and 500 hPa that must decrease by at least 6 m over a 6.5° radius from the SLP minimum. The original algorithm evaluates the geopotential thickness between the layers of 300 and 500 hPa (Ullrich et al. 2021), but due to the lack of model output at this level for 6-h instantaneous data, the thickness of 200–500 hPa is used in this study. These candidate storms are then stitched into a trajectory if they satisfy the following conditions. Candidate storms must last a minimum of 2 days, and the magnitude of the vector of a 10-m wind must be greater than 10 m s−1 for at least 10 time steps (60 h). The candidate storm must also be found within 50°S–50°N for at least 10 time steps (60 h) to be considered a TC.
In addition, we impose a minimum lifetime maximum intensity (LMI) threshold equivalent to the observed tropical storm threshold for all models including GEOS. The equivalent LMI threshold is found through quantile matching of the observed and GEOS intensity distributions (Camargo and Barnston 2009; Lee et al. 2018a, 2020). In the case of GEOS, only storms with an LMI of at least 24 kt (1 kt ≈ 0.51 m s−1) were analyzed; see García-Franco et al. (2023) for the LMI thresholds of the S2S models.
c. Observational and reanalysis datasets
Observed TC tracks and derived statistics are taken from the International Best Track Archive for Climate Stewardship (IBTrACS; Knapp et al. 2018) version 4 (v04r00) for the period 1999–2020. The information used is only from the United States agencies. To match the 6-hourly resolution of GEOS data, we only use records at 0000, 0600, 1200, and 1800 UTC. We have removed tropical disturbances, waves and extratropical cases (using both IBTrACS labels and all cases poleward of 50°N/S), and all storms with an LMI lower than 34 kt.
The fifth major global reanalysis produced by European Centre for Medium-Range Weather Forecasts (ECMWF) (ERA5) reanalysis is used to evaluate the climatology of environmental fields (Hersbach et al. 2020). This choice was made to evaluate the forecasts with estimates that are independent of the fields used for initialization in the weakly coupled assimilation system, which uses some fields such as the sea surface temperature (SST) from MERRA-2 (Molod et al. 2020). The daily ERA5 data were downloaded at a 0.5° resolution to match the resolution from GEOS including the zonal and meridional components of the wind at 850 and 200 hPa, relative humidity, sea level pressure, SST, air temperature, and absolute vorticity. The observed MJO RMM index was obtained from the Bureau of Meteorology (Wheeler and Hendon 2004; Kiladis et al. 2014) for the period 1999–2020.
d. The WMO S2S dataset
The S2S reforecast dataset is available on a common 1.5° × 1.5° horizontal grid from the S2S prediction database (Vitart et al. 2017). For the purpose of tracking TCs in the S2S dataset, Vitart (2017) tailored the method by Vitart and Stockdale (2001) to the S2S model resolution. TCs are operationally tracked in the S2S dataset using this method so all S2S TC studies have used these tracks (e.g., Lee et al. 2018a; García-Franco et al. 2023). Both tracking algorithms, TempestExtremes and the Vitart and Stockdale (2001), aim to find closed minima SLP with a warm core so their physical basis is similar enough that their results can be reasonably compared. In addition, comparisons between different tracking algorithms show that differences typically occur for weak and short-lived systems (Horn et al. 2014; Bourdin et al. 2022). This study uses the same model versions as in García-Franco et al. (2023). For more detail on the S2S models, tracking algorithm, and skill scores, see Vitart and Stockdale (2001), Vitart and Robertson (2018), and Lee et al. (2018a, 2020). The S2S reforecasts are used to compare with the forecast verification scores for GEOS.
e. Environmental conditions
Prior to the computation of the absolute vorticity and VWS in each reforecast, the TC impact on the flow was removed using the potential vorticity inversion method (Wu et al. 2003, 2004; Galarneau and Davis 2013; Ashcroft et al. 2021). The resulting large-scale flow with the TC circulation removed is used to examine the relationship between the environmental steering flow and storm motion. After the potential vorticity inversion, the steering flow is computed as in Lee et al. (2018b) with the sum of the winds at 200 and 850 hPa, i.e., 0.2U200 + 0.8U850.
The GPI in ERA5 was calculated using monthly averages. For the case of the reforecasts, we construct climatologies using a similar approach to García-Franco et al. (2023) by averaging daily data from all valid forecasts for a given month and lead time. In addition, the storm-scale temperature anomalies were calculated using the average temperature in a 20° × 20° box around the storm center as the environmental temperature.
f. Forecast verification
This study uses a fair-sliding reference climatology where the climatological probabilities are computed using a 20-yr sliding window depending on the target forecast year (Risbey et al. 2021). For example, 2002 occurrence forecasts are compared with the observed climatologies using the period 1982–2001 and 2010 forecasts with a reference from 1990 to 2009. This approach is the most consistent with real-time forecast verification.
g. Ensemble size
h. Calibration
Probabilistic genesis and occurrence forecasts have been shown to exhibit skill for longer lead times when postprocessing, or calibration, methods are applied to raw forecasts (Camp et al. 2018; Lee et al. 2020).
1) Regression methods
Lee et al. (2020) found that removing the mean bias by scaling does not guarantee a better BSS and proposed to use a linear regression calibration method. Linear regression, however, can produce negative probabilities, which can be corrected by constraining the calibrated probability (
2) ReLU calibration
A neural network regression model was used to evaluate whether a multilayer regression can render a better calibration than standard regression methods (Rasp and Lerch 2018; Schaumann et al. 2021). Specifically, the neural network regression model minimizes the Brier score between forecast and observed probabilities. Minimizing the Brier score aims to maximize the BSS as in the standard regression methods described above.
The neural network is constructed, first, through the activation function of the rectified linear unit (ReLU; Glorot et al. 2011; Hein et al. 2019). The ReLU is a ramp function (Rasp and Lerch 2018) that is fitted numerically to pairs of forecast probabilities pi and observed outcomes oi and is commonly used due to its fast computation and relatively simple definition compared to other activation functions. The ReLU activation function is used for the hidden layer of the network and follows the definition of the parametric ReLU of He et al. (2015).
The regression model is a multilayer perceptron regressor that optimizes the Brier score using a stochastic gradient-based optimizer (Kingma and Ba 2014) and three hidden layers with 150, 100, and 50 neurons, respectively. The output layer is also the ReLU activation function, and results may not be bounded by 0 an 1 as in the case of linear regression (Lee et al. 2018a). After calibration, the probabilities are explicitly bounded to the interval [0, 1] as explained above for linear regression.
Figure S1 in the online supplemental material illustrates the linear, logistic, and ReLU regression methods. The fit parameters, which include the slope and intercept for linear regression, are estimated for each model, basin, and lead time individually and then used to compute the calibrated probabilities for each forecast. The fitting of the parameters was done in-sample first and then out-of-sample. In the out-of-sample case, we used 66% of the data for training and evaluated the calibration on the remaining 33%.
3. Climatology
a. Genesis, occurrence, and intensity
The average NTCs and the density of TC occurrence or frequency (TCF) as well as their spatial distribution are typical indicators of model fidelity in the simulation of TC activity (Roberts et al. 2020; Camargo et al. 2020, 2021). In the week-2 climatology, GEOS simulates globally 70.5 TCs yr−1, which is less than the observed 85 TCs yr−1. The low bias in NTCs in GEOS stems primarily from the Atlantic (ATL) and eastern North Pacific (ENP) basins where the NTCs in GEOS are, respectively, 8.8 and 5.5 TCs yr−1 less than observed (see Table 1).
TC climatology statistics in observations and GEOS reforecasts. The average NTCs per year, LMI (kt), and seasonal-mean ACE (104 kt2). The statistics are shown for GL, Northern Hemisphere (NH), SH, and TC basin averages.
The spatial distribution of genesis (Fig. 1) shows that the low Atlantic NTCs in GEOS is due to the low genesis rates in the Gulf of Mexico, the Caribbean, and the subtropical North Atlantic. In the main development region (MDR; Goldenberg and Shapiro 1996), GEOS shows similar values of genesis rates in the near-equatorial North Atlantic compared to observations (0.1 TCs yr−1) but lower genesis rates (less than 0.05 TCs yr−1) than observed (0.15 TCs yr−1) in the Caribbean Sea. The underestimation of NTCs in the ENP is due to too few genesis counts off the western coast of southern Mexico compared to observations. In contrast, in the Southern Hemisphere (SH) basins, as well as in the western North Pacific (WNP), NTCs and their genesis locations are reasonably similar to observations.
Climatological distribution of (a),(c) genesis locations and (b),(d) TC track density or TCF in (a),(b) observations (1999–2020) and (c),(d) week 2 GEOS forecasts. The average NTCs globally, and per hemisphere, is found in (b) and (d). The PCC and NRMSE are also shown in (c) and (d).
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
The bias in NTCs in GEOS depends primarily on the location and to a lesser extent on lead time (Table 1). There is a lead-time dependence of the NTC bias in the ENP and southern Indian (SIN) basins where the NTCs decrease from week 1 to week 3, which is partially due to storms that are in the initial conditions, and increases again in weeks 4 and 5. In contrast, the NTCs in the ATL, South Pacific (SP), and northern Indian (NIN) basins do not vary with lead time.
The spatial pattern of genesis frequency biases (Fig. 2) shows little lead-time dependence and a meridional structure characterized by higher than observed genesis closer to the equator (5°–10°) and underestimation of genesis at higher latitudes (>16°). In the ENP, this dipole pattern in genesis biases grows with lead time from week 1 to week 5. Negative genesis count biases are also diagnosed in the western coast of Australia, the northwestern coast of Mexico, and the Bay of Bengal. The global pattern of TCF (Fig. 1d) and its biases (Fig. 2) suggest a better representation of TCF than genesis based on the skill score metrics [pattern correlation coefficient (PCC) and normalized root-mean-square error (NRMSE)].
Biases in (left) genesis and (right) occurrence (TCF) in GEOS reforecasts as a function of lead time. Dots indicate differences that are higher than the observed interannual std dev for each grid point.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
The representation of the TC intensity in GEOS shows a significant low bias in LMI (see Table 1 and Fig. S2). The GEOS model struggles to simulate storms with an LMI > 80 kt, and their simulated frequency is very low compared to observations (Fig. S2). A few global climate models of comparable resolution, including those used for S2S prediction, are able to simulate TCs with an intensity greater than 64 kt at the observed frequency (Camargo and Wing 2016; Davis 2018; Camargo et al. 2021).
The interbasin differences in the TC LMI distributions in GEOS are similar to observations. Simulated and observed TCs in the WNP have a higher LMI than in any other basin and the lowest LMI is diagnosed in the NIN (Fig. S2). According to a Kolmogorov–Smirnov test, the only statistically significant difference (at the 5% significance level) between forecast LMI distributions per lead time is from week 1 onward in the ATL and WNP. In these basins, the LMI reduction is due to the removal of the TCs that were in the initial conditions, and when these TCs were removed from the analysis, there was no change in the LMI distribution with lead time.
ACE combines the impact of TC occurrence, duration, and intensity and is defined as
b. Storm structure
Figures 3 and 4 show radial pressure composites of azimuthally averaged kinematic and thermodynamic fields of simulated storms over the most active TC basin, the western Pacific, including tangential and radial velocities, and warm core temperature anomalies and relative humidity, respectively. Figure 5 shows surface fluxes, precipitation, and column moisture. Only TCs occurring at lead times of 2 weeks were used for these composites.
Composites of the azimuthally averaged pressure radial TC structure for WP storms with sustained winds of 35–45 kt for (a),(b) vertical velocity (shading) and (c),(d) tangential component of velocity (shading) and radial velocity (contours) for observed TC tracks with environmental data from (left) ERA5 and (right) GEOS TCs. The maroon lines in (a) and (b) represent the radius of maximum vertical velocity at each pressure level and in (c) and (d) the radius of maximum tangential wind (RMW).
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
As in Fig. 3, but showing relative humidity (% in shading) and temperature anomalies (K in contours).
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
Azimuthally averaged precipitation rate, total precipitable water, and evaporation rate with respect to the distance from the center of the storm for TC snapshots where the maximum sustained wind is 35–45 kt for GEOS simulation (orange) and ERA5 observed TC tracks (black).
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
Qualitatively, GEOS simulates many aspects of the TC structure correctly. The tangential velocity shows a cyclonic rotation around the center, while the radial velocity shows an overturning circulation with inflow at lower levels and outflow aloft (Fig. 3). A warm core appears at around 300 hPa with high relative humidity near the storm center (Fig. 4), consistent with high precipitation and precipitable water at the center of the storm (Fig. 5).
As in the storms simulated by many global models at 0.5° or lower horizontal resolution (Kim et al. 2018; Moon et al. 2020), GEOS fails to simulate a pronounced eyewall in vertical velocity, precipitation, or precipitable water. Instead, vertical velocity and moisture peak at the center of the storms. Moon et al. (2020) showed that an off-center peak vertical wind velocity appears in a model with a 0.5° resolution when the storm intensity reaches 30–33 m s−1 (58–64 kt), although very few storms reach that intensity. The pressure level of maximum vertical wind speed in GEOS coincides with that in ERA5, peaking somewhere between 750 and 500 hPa.
The tangential velocity profile shown in Fig. 3 peaks off the center as in observations and other models. The radius of maximum wind (RMW) simulated by GEOS is consistent with other models at 0.5° resolution, occurring around 100 km from the center. This is seemingly better than ERA5’s estimation of the RMW (∼200 km) but worse than higher-resolution GCMs, which simulate RMWs close to 75 km from the center (Kim et al. 2018). Aircraft observations consistently report the RMW to occur within 1° of the storm center (Weatherford and Gray 1988).
The tangential velocity in GEOS weakens quickly above 800 hPa in comparison to the ERA5 TC structure. This may suggest that the momentum drag in the planetary boundary layer is too efficient. The magnitude of the simulated tangential wind in GEOS is overall much lower than in ERA5 and other models where tangential winds of similar maximum sustained a wind speed peak closer to 30 m s−1 (Kim et al. 2018; Russotto et al. 2022). This result is consistent with the systematically low LMI observed in section 3a. The radial velocity profiles are quite similar between the model and reanalysis although the inflow is stronger in GEOS.
As in ERA5, the simulated warm core peaks just below 250 hPa. The strength of the warm core seems to be overestimated in GEOS compared to ERA5, since the warm core in GEOS reaches a near 1.5-K anomaly from the surrounding environment. The simulated TCs of the same intensity show a 2-K anomaly at the center of the warm core (Fig. 4). A notable difference between GEOS and ERA5 is that warm core temperature anomalies in GEOS are much stronger and extend further into the lower troposphere than in ERA5, exhibiting a second maximum temperature anomaly above 750 hPa (Fig. 4d), but are qualitatively similar to other GCM warm cores of storms of similar intensities (Kim et al. 2018). The shape of the relative humidity profiles is similar between GEOS and ERA5, with similar radial gradients as well. However, GEOS also appears to overestimate relative humidity near the center of the storm, especially below about 800 hPa and between 200 and 100 hPa.
Figure 5a shows that the peak precipitation rate for GEOS TCs is more than double that of ERA5 TCs. Moon et al. (2020) showed that GCMs tend to overestimate rain rates near the center of TCs. Interestingly, precipitable water (Fig. 5b) is comparable between ERA5 and GEOS, suggesting that GEOS TCs are more efficient at converting water vapor into rain than the TCs in ERA5. The surface evaporation in the model is larger than that in ERA5 (Fig. 5c), likely due to the stronger-than-observed inflow near the surface or to the differences in the parameterized dependance of stress on wind speed.
c. Genesis potential index
The GPI of Emanuel and Nolan (2004) is used to compare key environmental fields in GEOS with ERA5 and diagnose the extent to which biases in the GPI or its components [Eq. (1)] are related to the magnitude, spatial distribution, or temporal variation of biases in TC genesis in GEOS. Figures 6a and 6b show that GEOS reasonably simulates the spatial pattern but greatly underestimates the magnitude of GPI compared to observations. The largest biases are found in the northern coast of Australia, the western coast of Mexico, the central-eastern part of the Atlantic MDR, and the east of the Philippines in the WNP basin. The GPI in the model is higher than observed in only a few regions such as the Bay of Bengal and Caribbean Sea and only in week 1.
GPI (m s−5/2) (a) climatology and (b) biases in GEOS week 2 reforecasts. Biases in individual fields are then shown for (c) η, (e) RH (%), (g) PI (m s−1), and (i) VWS (m s−1). The GPI calculated using the fields from ERA5 but replacing (d) absolute vorticity, (f) RH, (h) PI, and (j) VWS using GEOS week 2 forecast data. Results are shown for JASO in the Northern Hemisphere and for DFJM in the SH, and biases are differences with respect to ERA5.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
Following several previous studies (e.g., Camargo et al. 2007b; Li et al. 2022), the GPI biases are decomposed by replacing terms of the ERA5 GPI with the corresponding field from GEOS one at a time. Figure 6 shows the contribution of each field to the total GPI bias and the bias of each field individually and suggests that GEOS simulates slightly lower than observed PI and η. These biases lead to a slight underestimation of GPI. In contrast, the magnitude of the GPI biases stemming from the RH and VWS biases are higher but with opposite signs. GEOS simulates a higher than observed VWS, which leads to a lower than observed GPI, whereas a larger than observed RH leads to a larger than observed GPI. Similar results are found for other lead times. Li et al. (2022) found that the reforecasts from the Community Earth System Model, version 2, have GPI biases that arise from a similar combination of higher than observed VWS and RH. Both for GEOS and CESM2, the VWS bias dominates and the resulting simulated GPI is lower than observed.
The comparison of Figs. 2 and 6 highlights that the spatial distribution of biases in GPI is inconsistent with biases in genesis rates. For example, genesis rates in the WNP and ENP show a dipole pattern that is not seen in the GPI biases. To examine more closely the spatial relationship between GPI and genesis, Fig. 7 shows the scatter of GPI versus genesis rates averaged over different basins and regions.
Scatterplot of the relationship between GPI and genesis rates. (a) Basinwide averaged GPI vs genesis rates (NTCs per season) in ERA5 (dots) and GEOS (squares). Each square is the average quantity of each week lead time in GEOS. (b) ERA5 GPI vs observed genesis counts. Each dot represents the average GPI and genesis counts within a 20° × 15° moving window for each grid point. (c) As in (b), but for GEOS week 2 forecasts. (d) As in (b), but each triangle represents the bias of the GPI vs genesis averaged in a 20° × 15° moving window.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
The basinwide GPI and genesis counts have a clear relationship in the observations (Fig. 7a). However, the differences of the genesis rates with lead time in GEOS, discussed in the previous sections, are not related to GPI differences with lead time as the GPI varies relatively little with forecast lead time (Fig. 7a). When computed over moving spatial windows of 15° × 20°, the GPI from ERA5 seems to better describe the variability in genesis from IBTrACS (Fig. 7b) than in the GEOS simulations (Fig. 7c). The basin where GPI seems unrelated to genesis in GEOS is the ATL in which there is almost no relationship between the genesis rates and the GPI in GEOS. Moreover, the spatial distribution of biases in GPI appears unrelated to biases in genesis counts (Fig. 7d).
This result means that the genesis biases in GEOS are not explained by the biases in GPI. These results broadly agree with the findings of Li et al. (2022) who also found that the spatial distribution of GPI biases appears unrelated to spatial biases in genesis counts and their lead-time dependence in the CESM2 S2S reforecasts. Several studies have shown that in global models, the relationship between the large-scale environment and the TC activity is weaker than in observed TCs and that indices, such as the GPI, are not well correlated with biases or the simulated interannual variability in TC activity (Camargo et al. 2007a; Camargo and Wing 2016; Camargo et al. 2020; Cavicchia et al. 2023). The seasonality of genesis and GPI is well captured by GEOS (Fig. S7). The sharp peak in the TC season in the ATL and the relatively longer active TC season observed in the WNP are well reproduced in GEOS.
d. Storm motion and steering flow
Biases in track density or TCF (Fig. 2) may be due to the environmental steering flow, which guides the storm motion vector. Figure 8 shows the climatology and biases of the storm translation vector and the steering flow in GEOS, as well as in observations and reanalysis (IBTrACS/ERA5). The storm motion direction and speed are reasonably represented by GEOS, except for negative biases in the storm translation speed in the central Pacific, east of the Philippines, and in the North Atlantic (Fig. 8e). This negative bias may indicate that simulated storms stall in these regions compared to observations which may have important consequences in accurately representing landfall impacts.
(a),(c) Climatology of storm motion vector (arrows) and speed (shading, m s−1). Results are shown in a 2° × 2° grid, and only grid points with an average frequency above 0.1 TCs yr−1 are plotted. (b),(d) Climatology of the large-scale steering flow shown as streamlines and magnitude (shading, m s−1). (e) GEOS biases in storm motion direction (vector) and speed (shading). (f) GEOS forecast biases in steering flow and steering flow magnitude relative to ERA5. Zonal mean zonal wind (m s−1) averaged in the (g) ATL and (h) WNP basins. Vertical dotted lines are drawn at the latitude zero wind speed, where translation motion on average reverses from westward to eastward. Results are shown for GEOS week 2 forecasts.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
Biases in the steering flow are largest in the SH as an easterly bias is observed at equatorial latitudes and at the subtropics (20°S–20°N, Fig. 8f). This bias coincides with positive track density biases in the near-equatorial SIN (Fig. 2). The negative bias in the storm motion speed in the ATL and WNP basins may also indicate that the storms recurve at a different latitude in the model compared to observations. Figure 8g shows that the latitude of recurvature of Atlantic TCs is 29°N in observations, but in GEOS, Atlantic TCs recurve at 27°N, slightly south of observations.
The relationship between the steering flow direction and storm motion direction was examined through the normalized dot product of the two vectors (i.e., the cosine of the differences in the vector direction; Fig. S6). Results show that the steering flow and storm motion vectors are close to being parallel in GEOS and observations. The storm motion direction simulated by GEOS is nearly parallel to the observed storm direction. The biases in storm motion, albeit small, seem unrelated to the steering flow biases in most basins. In the subtropical ATL and WNP, however, the vectors of the storm motion and steering flow biases are nearly parallel, suggesting that mean biases in the environmental wind relate to mean biases in storm motion direction and speed in these regions.
e. Interannual variability
Molod et al. (2020) showed that the interannual variability of the GPI in GEOS-S2S-2 is better correlated with observations than GEOS-S2S v1. However, this result does not necessarily mean a good representation of the interannual variability of TC activity. Table 2 reports the correlation coefficient between the observed and simulated time series (1999–2020) of seasonal ACE per basin (see also Fig. S4). This coefficient can be interpreted as a performance metric of the interannual TC variability. The results show relatively high and statistically significant correlation coefficients for the ATL, WNP, and ENP basins, whereas relatively weaker and statistically insignificant correlations were found for the SIN, NIN, and Australia (AUS) basins.
Interannual variability of basinwide ACE. For the selected five basins, the Pearson correlation coefficient r and the average seasonal ACE anomalies for El Niño (EN) and LN conditions are given in percent (%). Significant correlations to the 5% significance level, according to a Wald test, are highlighted in bold.
The influence of ENSO, measured by the percent change in seasonal ACE associated with warm or cool conditions, is also shown in Table 2. GEOS reasonably replicates the ENSO influence on TC activity in the ATL, ENP, and WNP basins. In the SIN and AUS, the influence of ENSO is less clear in the observations when considering basinwide statistics, which may explain the weaker ENSO–TC connection simulated by the model in these basins.
There is some indication that the ENSO influence is lead time dependent. For example, the effect of the cool phase of ENSO in the ATL increases with lead time since ACE is +70% higher during La Niña (LN) events than in neutral conditions in week 5. These changes with lead time in the ENSO TC connection may be 1) because at short leads, the initial conditions matter, and at long leads, the ENSO phase is more important, and 2) biases in the mean state of TCs or the environment are changing with lead time (as found in the previous section). The analysis of the ENSO–TC connection requires further work beyond the simple basinwide seasonal-mean statistics since the influence of ENSO in some basins can be bimodal such as AUS and the WNP (Camargo et al. 2007b).
4. Prediction skill of TC genesis and occurrence
This section evaluates the prediction skill of probabilistic forecasts of TC genesis and occurrence in GEOS and compares the results with those of the reforecasts from the S2S project. Skill is measured through the BSS using a monthly varying reference climatology (BSSm).
a. Raw skill scores
Figure 9 shows that the BSSm of the TC genesis of GEOS and most S2S models is negative at all lead times, which means that these forecast systems are unable to skillfully predict genesis anomalies with respect to the seasonal cycle. The exception is the ECMWF model, which is skillful in three out of seven basins in week 1. These results are consistent with Lee et al. (2018a).
Basinwide BSS (BSSm) as a function of lead time (days) for (a),(c),(e) TC genesis and (b),(d),(f) occurrence forecasts verified against a monthly varying climatology. Results are shown for the (a),(b) ATL, (c),(d) WNP, and (e),(f) SIN basins.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
The BSSm of GEOS is higher than the median model in the S2S project for all basins. GEOS reforecasts show the highest week 1–2 BSSm in the SIN among all the S2S models considered in this study. Similarly, GEOS shows the second highest week 1 and 2 BSSm in the WNP. In the remaining basins, ENP and ATL, GEOS has a BSSm that is in the top 5 of the 11 models considered.
TC occurrence prediction skill is higher than for TC genesis (Fig. 9). Several models (ECMWF, UKMO, and GEOS) exhibit skill up to day 10 in some basins, consistent with Lee et al. (2020). The prediction skill of occurrence in GEOS is also above average when compared to the S2S cohort. For instance, GEOS is the model with the second highest BSSm in the WNP for weeks 1–4.
ECWMF reforecasts have the highest BSSm globally, but they are particularly skillful in the ENP, SPC, and WNP basins, when compared to the other models. Positive BSSm values are found beyond day 15 in these basins, making ECMWF the only forecast system capable of providing skillful predictions of anomalies with respect to the seasonal cycle beyond week 2. In contrast, many S2S models are not skillful in any basin at any lead time.
b. The impact of ensemble size
Ensemble size is a key feature that explains why some forecast systems are more skillful than others (Domeisen et al. 2022; Schreck et al. 2023). Lee et al. (2018a) showed that the BSSm values of models with relatively large ensemble sizes (ECMWF and BoM) are reduced notably when considering only four ensemble members. GEOS also only has four ensemble members, suggesting that the differences in skill shown in the previous two sections may be sensitive to the ensemble size. To examine this possibility, Fig. 10 illustrates how forecast skill is affected once the ensemble size has been considered using the debiased BSSD.
As in Fig. 9, but showing (left) both BSSm and BSSD for a selection of models and (right) the BSS for raw (BSSm) and calibrated forecasts in GEOS.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
Forecast systems with a relatively small ensemble size, such as GEOS and JMA, show significant increases in skill when using the BSSD in basins where the raw forecasts show no skill such as the ATL, NIN, and AUS. In models with relatively large ensemble sizes, such as ECMWF and CNRM, the correction factor results in a smaller increment of the BSS. According to the average BSSD across all basins, GEOS is the second best model compared to the S2S models. Another way to measure the impact of ensemble size is to use the same ensemble size across models (Lee et al. 2018a). The BSS values of TC occurrence in most models with relatively large ensembles (ECMWF, BoM, and CNRM) noticeably decrease when using only four ensembles (Fig. S8). In all basins, except the ATL, GEOS shows above average skill compared to the S2S models when using only four ensemble members.
These results suggest that the low ensemble size in GEOS is limiting its prediction skill and a larger ensemble size will likely have a positive impact on skill. It is important to note that the correction factor D is artificially increasing the error in the climatological reference forecast and the BSSD values do not imply “real” skill because the real ensemble system is run with four ensemble members. Rather, the BSSD values represent the potential skill if a bigger ensemble was used. It is also noteworthy that the correction factor D may depend on the ensemble size for unreliable forecasts (Tippett 2008), which is often the case for these TC occurrence forecasts.
c. The impact of calibration
Figure 10 shows the impact of the three calibration methods used in-sample, the mean occurrence bias and linear regression (BSSm,lin), the logistic regression (BSSm,log), and the ReLU regression (BSSm,rel). Calibrating the mean occurrence bias (BSSm,mean) does not always lead to better skill, as found by Lee et al. (2020), but rather, the effect of this calibration method is a function of the sign and relative magnitude of the TC occurrence bias. The BSSm,mean is higher than the BSSm only in three out of seven basins.
The three regression methods, fitted in-sample, render higher BSS values than the raw forecasts, and the three methods result in virtually the same BSS values for all basins. Similar results are found when evaluating out-of-sample (Fig. S9). The BSS values of linear, ReLU, and logistic regression methods are very similar despite the fact that the individual calibrated forecast probability is different for the three methods. Even though the functional form of each fitted function to the data is different, all the regression methods aim to maximize the BSS.
The neural network model based on the ReLU activation function renders very similar results to the linear and logistic regression methods. This means that, for the purpose of maximizing the BSS, i.e., minimizing the mean-squared probability error, the linear regression method is sufficient. Figures 10c and 10e and Table 3 show that the calibrated GEOS reforecasts are skillful in all basins up to 15 days lead time, except for the ATL, where the calibrated BSS values are only positive up to day 9.
BSS of TC occurrence probabilistic predictions for each basin in GEOS and ECMWF reforecasts. BSS are shown using a monthly varying climatology (BSSm) and forecasts calibrated through linear regression (BSSm,lin).
To evaluate the spatial distribution of skill in raw and calibrated forecasts, the BSS was calculated using verification areas spanning 20° in longitude and 15° in latitude (Camp et al. 2018; Lee et al. 2020). Each region overlaps in 10° in longitude and 7.5° in latitude creating a total grid of 303 regions (Lee et al. 2018a). Figure 11 shows the resulting spatial distribution of the BSS in GEOS and ECMWF week-2 forecasts. The raw GEOS forecasts are not skillful at this lead time (Fig. 11a). The ECMWF model raw forecasts, in contrast, are skillful in the SIN, WNP, SPC, and ENP at these lead times. Both models have negative BSSm values in the ATL (Fig. 11a).
Maps of BSS of TC occurrence forecasts for GEOS and ECMWF for (a),(b) BSSm and (c),(d) BSSm,lin. The BSS from (e) logistic and (f) ReLU regressions on GEOS forecasts are shown. The BSS is calculated over 20° × 15° boxes centered on each plotted grid point. Only grid points with a mean TC frequency of 0.25 (NTC yr−1) were verified.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
Regression methods result in higher skill globally for the calibrated forecasts when compared to the raw forecasts. In particular, notable increases in skill are observed in the west SIN, NIN, and WNP for GEOS and in AUS and the NIN for the ECMWF (Figs. 11c,d). Despite the fact that the regression methods improve skill globally, in the Atlantic, the GEOS BSS values are negative and only marginally positive in the ECMWF forecasts (Fig. 11). The BSS values in the calibrated forecasts validated out-of-sample lead to the same ranking of the calibration methods but with lower BSS values.
5. The MJO–TC relationship and its impacts on predictability and prediction skill
The MJO–TC relationship in GEOS and its influence on prediction skill and predictability is examined in this section. The MJO amplitude and phases are defined using the RMM index (Wheeler and Hendon 2004) at the moment of forecast initialization. The results are grouped into pairs of MJO phases, as in previous studies (Camargo et al. 2009; Camp et al. 2018).
Figure 12 shows the TC–MJO relationship in GEOS and observations as anomalies in the TC frequency for combined MJO phases. GEOS reforecasts are able to reproduce the MJO–TC relationship in SH and NH basins. In DJFM, the progression of the positive TCF anomaly found in the SIN at phases 2–3, moving eastward toward Australia during phases 4–5, and the SPC for phases 6–7 and 8–1 is well reproduced by GEOS. During JASO, the anomaly pattern in the WNP is also well reproduced by the model. In the ENP, the model anomaly patterns agree well with observations except for phases 2–3 when the model suggests a strong negative anomaly that is not seen in observations. The MJO signal is weaker in the ATL for both forecasts and observations. The overall good representation of the MJO impact on TC frequency on intraseasonal time scales suggests that the MJO may indeed be an important source of S2S TC predictability in GEOS.
Anomalies in the TCF (TCs per season) for pairs of MJO phases 8–1, 2–3, 4–5, and 6–7 in (left) GEOS week 2 forecasts and (right) observations (1998–2020). Anomalies are computed on a common 4.5° × 3°. Results are shown for JASO for the Northern Hemisphere and DJFM for the SH.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
Figure 13a shows the candy plots (Lee et al. 2018a) for the observed probability change of TC occurrence conditioned on the MJO phase. These changes in the probability of TC occurrence in the candy plots correspond well with the maps in Fig. 12. Using Eq. (6) and the observed TC occurrence distribution, the STR was computed for each basin and the MJO phase pair (Fig. 13b). In observations, the highest STR appears in the WNP during phases 6–7. In each basin, high STR values appear in at least two MJO phase pairs. The slight differences between Figs. 13a and 13b are due to the different reforecast periods and frequency in GEOS compared to ECMWF.
Candy plots of the MJO influence on the TC activity and predictability. (a) Percent TC occurrence rate in each pair of MJO phases for each TC basin in observations (1999–2021). (b) STR of the probability shift conditional on the MJO phase pair in observations. (c)–(f) As in (b), but for reforecasts indicating the STR given the probability shifts in week 2 for a given basin. Significant STR (marked with a × to the 5% significance level) is found by bootstrapping observed and forecast distributions.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
The forecast STRs (Figs. 13c–f) are model, basin, and MJO phase pair dependent. However, a few common features appear, such as high STRs in the WNP for forecasts initialized in phases 4–5 (found in three out of four models). The relatively high STRs indicate that forecasts initialized in phases 4–5 by week 2 are likely showing a signal consistent with phases 6–7, which is the phase pair when observations show the highest STR. The relatively high STR in the SIN basin for phases 2–3 is associated with a strong positive shift in the TC occurrence probability (Fig. 14). Similarly, GEOS and ECMWF forecasts initialized in phases 2–3 show significantly high STRs in the ENP by week 2, also due to a strong positive shift in the TC probability in the subsequent phases 2–3 (Fig. 13).
(a),(b) Observed and simulated (top) signal, (middle) STR, and (bottom) BSSm as a function of lead time and MJO phase pair at the initialization of the forecast in (a) GEOS and (b) ECMWF reforecasts for SIN basin. Significance is shown as ★ based on a bootstrap of the forecast distributions at the 5% significance level. (c),(d) Scatterplots of the (c) observed (Sc,o) vs simulated signal (Sc) and (d) skill vs predictability for week 2 forecasts shown as STR vs BSSm|c.
Citation: Weather and Forecasting 39, 9; 10.1175/WAF-D-23-0208.1
A high STR is observed in the SPC for phases 2–3 and the NIN for phases 6–7, which emphasizes that forecasts initialized under a strong MJO in the phases prior to the phases of highest MJO influence can extend predictability into weeks 2 and 3 when models are able to retain the MJO signal. In other basins, however, such as the ATL and AUS, there seems to be no robust footprint of the MJO in the STR.
To examine the relationship between predictability (STR) and skill (BSS), Fig. 14 shows how the model MJO–TC signal Sc relates to the observed MJO–TC signal Sc,o and how the STR relates to the BSS for each pair of MJO phases for the SIN basin. The GEOS signal is very similar to observations for all MJO phase pairs (Fig. 14a) as the model is able to replicate periods of anomalously high and low TC activities. The STR values are high up to lead times of 40 days in phases 2–3 and 6–7, indicating that the initial phase of the MJO provides predictability at the S2S range in this model in SIN beyond week 2.
In contrast, the ECMWF model shows a weaker signal, particularly for phase pairs 4–5 and 6–7, where the model signal is very low despite a strong observed signal. The lack of a negative signal from ECMWF compared to observations is associated with a negative BSSm, i.e., poor week-2 skill for forecasts initialized in these phases. For forecasts initialized in phases 2–3 and 8–1, a positive skill is diagnosed during periods where observations and the forecasts show a positive signal. This means that despite the model exhibiting no signal, the resulting skill depends on the sign of the observed signal.
To explain the diagnosed skillful ECMWF forecasts despite a lack of signal and the unskillful GEOS forecasts despite a significant signal, the BSS was decomposed into three terms: the potential skill, the conditional bias, and the unconditional bias (see the supplemental material and Bradley et al. 2008; Lee et al. 2018a; Tippett et al. 2019, for further details). The results show that the BSS may become negative due to the unconditional and conditional biases and positive due to a positive correlation or potential skill (Fig. S10). The comparison of the two forecast models in SIN shows that ECMWF has a higher skill for MJO phases 8–1 and 2–3 despite having a weaker signal due to low conditional and unconditional biases. In contrast, GEOS shows a higher conditional bias compared to ECWMF, which decreases the BSS. These results emphasize the difference between predictability (defined as the STR) and the skill (defined as the BSS).
Overall, these two forecast models are able to reproduce the observed MJO–TC relationship (Fig. 14c). However, the STR is not well related to the conditional BSSm|c (Fig. 14d). For very high-predictability cases, i.e., STR > 0.2, the BSSm|c is positive. However, there are also several cases where there is skill but no predictability and other cases with some predictability (0.05 < STR < 0.15) but negative BSSm|c. This means that there are cases where skill is greater than predictability and others where predictability does not relate to skill.
6. Summary and discussion
This paper examined the climatology, prediction skill, and predictability of TC activity in the GEOS-S2S-2 reforecasts. The climatological assessment shows that the model is able to reasonably reproduce basic statistics of TC activity such as the number of TCs, except in the Atlantic where the model simulated too few TCs due to low genesis rates in the Caribbean Sea and the Gulf of Mexico. The seasonality of the TC activity is well represented, as evidenced by the seasonal cycle of genesis, ACE, and the GPI.
Several aspects of the kinematic and thermodynamic storm structure are well represented in the GEOS reforecasts, such as the existence of primary and secondary TC circulations. However, GEOS also shows a number of storm-structure biases typical of global climate models of similar and coarser resolutions such as the lack of an eyewall in vertical velocity, precipitation, and moisture. The storm-structure biases are consistent with the lower-than-observed values of LMI for most storms.
The analysis of the environmental conditions highlighted that biases in the VWS and RH are the biggest contributions to biases in the GPI in GEOS. However, relating the biases in the environment to the explicit TC activity was not possible. In global models, biases in the TC activity are difficult to diagnose simply through biases in the mean environmental conditions (Camargo et al. 2019, 2020; Cavicchia et al. 2023). The GPI, as most environmental indices, was developed using the observed monthly climatology of the TC activity and reanalysis environmental fields, which may not be adequate to assess biases in a subseasonal forecast model.
GEOS shows comparable prediction skill of TC genesis and occurrence with most S2S models. Skill in predicting genesis is lower than for TC occurrence, as found previously (Lee et al. 2018a, 2020). The GEOS raw forecasts only provide skillful TC occurrence predictions in the WNP and SIN in week 1. After a regression-based calibration, however, the predictive skill of GEOS can be extended up to week 3 in most basins. The linear regression method for calibrating TC occurrence probabilities, used in Lee et al. (2020), renders very similar results to logistic regression and neural network calibrations.
The ensemble size is diagnosed as a potential limitation of GEOS. The debiased BSSD and limiting all the model ensembles to a size of four show that GEOS is generally more skillful than most S2S models, except for the ECMWF. However, this is not indicative of true skill, given that real-time forecasts use all the available ensembles. This result points to potential improvements in GEOS skill if the ensemble size is increased.
The predictability of TC occurrence was investigated through a measure of predictability known as the STR (Tippett et al. 2022), which is also the perfect model BSS. This analysis demonstrated that the MJO phase can be a key source of S2S TC predictability. When a forecast is initialized under active MJO conditions, a significantly higher STR is found in weeks 2 and 3 for at least half the basins and MJO phases. However, the STR conditioned on the MJO phase depends strongly on the model and basin.
The analysis of the relationship between our measures of predictability (STR) and skill (BSS) shows evidence of forecasts with high skill but no predictability and other cases where there is predictability but no skill. For example, GEOS shows a reasonable simulation of the ENSO impact on TC occurrence in the ATL yet GEOS is not skillful in this basin. The mean occurrence bias in the ATL (Table 1) is penalized by the BSS such that these unreliable forecasts are unskillful despite their good representation of ENSO anomalies.
Another example is illustrated by the GEOS MJO-conditioned forecasts of SIN TCs (Fig. 14a), which show signs of model-based predictability but poor skill. Conditional biases in this basin reduce skill notably. In addition, even if a model has a good representation of one predictable component, there are other sources of predictability, so a good representation of a signal (ENSO and MJO) does not mean skill. Overall, these results imply that the gap between model-based predictability and skill exists due to the biases in the forecast distribution, which negatively impact the BSS. These examples show that predictability may not correspond to forecast skill because predictability only depends on the forecasts and skill depends on the similarity between forecasts and observations (DelSole and Tippett 2022).
Biases in the MJO–TC relationship (Lee et al. 2018a), MJO propagation speed (Lim et al. 2021) and amplitude (Lim et al. 2018) or its teleconnections (Stan et al. 2022) may be the sources of model errors that could explain why predictability does not always result in prediction skill. Furthermore, this study used the MJO RMM for all basins and seasons, but several studies have shown that in boreal summer, the boreal summer intraseasonal oscillation (BSISO) is a strong modulator of TC activity and prediction skill in basins such as the WNP (Wang et al. 2023). Further work is needed to understand the relationship between the MJO and BSISO predictability and prediction skill.
This study shows that despite being able to capture the observed climatology of TC activity and some aspects of TC structure, subseasonal TC predictions from GEOS-S2S-2 reforecasts have less skill than climatological predictions. Applying postprocessing calibration methods can improve model prediction skill up to week 4. An exception is the Atlantic basin, where the calibrated TC prediction remains less skillful than climatological predictions. Real-time bias correction of TC environmental biases may improve TC prediction skill. Among TC-related environmental conditions, vertical wind shear dominates the biases in the GPI, but there seems to be no direct link between GPI biases and the model’s TC genesis. Numerical experiments with tendency-bias correction (Chang et al. 2019) may provide insight on ways to improve the representation of TC activity. Further improvement of the MJO (Lim et al. 2018) and the MJO–TC connections will likely help bridge the gap between predictability and prediction skill.
Acknowledgments
This study was funded by the NASA MAP program (80NSSC21K1495). D. K. was supported by the New Faculty Startup Fund from Seoul National University, the NASA MAP program (80NSSC21K1495), NOAA MAPP program (NA21OAR4310343), NOAA CVP program (NA22OAR4310608), and KMA R&D program (KMI2022-01313). The authors thank Dr. Treng-Shi Huang for assistance with the code for the potential vorticity inversion and Dr. Colin Zarzycki for assistance using the TempestExtremes software.
Data availability statement
The S2S data are publicly available at https://apps.ecmwf.int/datasets/data/s2s/levtype=sfc/type=cf/. The S2S data and S2S TC tracks are available to the research community at http://s2sprediction.net. The IBTrACS dataset is publicly available (Knapp et al. 2018) at https://www.ncei.noaa.gov/products/international-best-track-archive. The ERA5 reanalysis is available from the Copernicus Climate Change Service (C3S) Climate Data Store (CDS; Hersbach et al. 2019) at https://doi.org/10.24381/cds.6860a573.
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