This study assesses the skill of four statistical models in hindcasting North Atlantic annual tropical cyclone (TC) frequency over 1950–2008 with the aim of projecting future activity. Three of the models are motivated by operational statistical forecast schemes and are premised on standard hurricane predictors including sea surface temperatures (SSTs) and near-surface zonal winds. The fourth model uses an SST gradient index previously proposed for Caribbean seasonal rainfall prediction. The statistical models, created from backward regression, explain 24–48% of the observed variability in 1950–2008 annual TC frequency. The future state of the predictors is extracted from the ECHAM5, HadCM3, MRI CGCM2.3.2a, and MIROC3.2 global climate model (GCM) simulations under the Coupled Model Intercomparison Project Phase 3. Models utilizing SST and near-surface wind predictors suggest significant increases in mean annual frequency by 2–8 TCs by 2070–2090, compared to a single surface wind predictor model, indicating that positive trends in SSTs under global warming have a larger relative influence on projections than changes in the variability of the surface winds. Wind-only models exhibit declines in TC frequency, while the SST gradient model yields little change relative to the present-day mean. Backward regression reapplied against the 1990–2008 period, analogous to future warmer oceanic and atmospheric state relative to the earlier years in the record, retains only the Caribbean low-level jet (CLLJ)-type predictors, explaining up to 82% of TC frequency variability and suggesting a more dominant role for the CLLJ in a warmer climate. Projections using the new models show either a more conservative increase or a stronger decrease in frequency, consistent with a stronger CLLJ.

Key Points

Statistical models from forecast schemes can explain up to 48% of annual North Atlantic TC frequency
Hindcast period analogous to warmer climate keeps only surface winds and SST gradient in regression
The CLLJ is a major modulator of future North Atlantic TC frequency

1 Introduction

Analyses of extreme events and in particular tropical cyclones (TCs) are particularly important given (i) challenges in predicting their occurrence, duration, and frequency; (ii) their changing characteristics in the face of global warming trends; and (iii) the growing and urgent need to support preparedness and mitigation efforts in order to build climate resilient societies. Losses from hurricanes have increased due primarily to increases in coastal population, wealth per capita, and inflation [Pielke et al., 2008]. Four of the costliest North Atlantic hurricanes on record have occurred within the last decade, with Hurricanes Katrina (2005) and Sandy (2012) producing a combined damage of approximately U.S. $200 billion across the Caribbean, United States, and Canada [Knabb et al., 2006; Blake et al., 2013].

Recent studies have documented some trends in North Atlantic tropical cyclone (TC) frequency over the past century. Studies have noted higher North Atlantic TC activity (+60%°C⁻¹) since 1995 [Goldenberg et al., 2001] and increased frequency of very intense TCs (~ + 17%°C⁻¹) within the North Atlantic region since the 1990s [Emanuel, 2007; Holland and Webster, 2007; Bender et al., 2010]. These trends have been observed in association with long term changes in tropical Atlantic oceanic and atmospheric conditions important to North Atlantic TC development including increased mean surface temperatures (0.12 ± 0.04°C per decade for 1951–2010), increased tropospheric water vapor (7%°C⁻¹ since 1970s), and fluctuations in vertical wind shear (within 6 ms⁻¹ since 1995) [Goldenberg et al., 2001; Intergovernmental Panel on Climate Change (IPCC), 2013]. Changes in some of these local factors as well as the influence of other remote factors such as the variability of sea surface temperatures (SSTs) in the central and eastern equatorial Pacific associated with El Niño–Southern Oscillation and/or multidecadal North Atlantic variations have also been shown to influence TC variability on interannual and decadal timescales [Gray, 1984a; Goldenberg and Shapiro, 1996; Bell and Chelliah, 2006]. Other studies have documented the growing influence of Atlantic SSTs relative to the tropical SST mean on North Atlantic TC frequency variability [Sugi et al., 2009; Murakami et al., 2012]. It is therefore not surprising that statistically premised operational forecast models of North Atlantic TC frequency and intensity incorporate these local and remote factors in one form or another [Saunders and Rockett, 2002; Saunders and Lea, 2005; Klotzbach, 2007; Camargo et al., 2007; Klotzbach, 2011].

Many of the operational statistical models for North Atlantic TC frequency demonstrate reasonable skill in hindcasting North Atlantic TC activity. For example, the National Oceanic and Atmospheric Administration (NOAA) generates seasonal forecasts of North Atlantic TC activity based on two tropical multidecadal modes that capture convective variability over West Africa and the Amazon, and the leading interannual mode (ENSO) [Bell and Chelliah, 2006]. Bell and Chelliah [2006] asserts that the statistical scheme explains 82% of a 5 year running mean North Atlantic accumulated cyclone energy (ACE) index over 1951–2002. Another statistical scheme proposed by Klotzbach [2011] is premised on North Atlantic SSTs, wind shear, and the Niño-3 index and explains 72% of the variance in net tropical cyclone activity from 1982 to 2010. For this study, we investigate what skillful statistical models premised on operational forecast schemes suggest about future (end-of-century) tropical cyclone frequency. While other predictive schemes exist [Ballester et al., 2004; Camargo et al., 2005; Bell and Chelliah, 2006] and for other predictands such as the Genesis Potential Index (GPI) [Emanuel and Nolan, 2004] and the Maximum Potential Index (MPI), this study focuses on the creation of simple models premised on present-day operational schemes. To the authors' knowledge, there is presently no statistically based operational scheme for either GPI or MPI. Furthermore, there is currently no consensus on whether North Atlantic TC frequency will increase or decrease under a climate-changed world [IPCC, 2013]. Whereas several studies, largely using high-resolution dynamical models, have suggested a decrease of up to 20% in global TC frequency toward the end of the century [Yoshimura et al., 2006; Bell et al., 2013; IPCC, 2013], projections over individual basins for which TC activity contributes a significant portion to convective activity and hydrodynamic flow indicate steady declines in TC frequency (~30–50%) for the Pacific [Oouchi et al., 2006; Knutson et al., 2010] but no conclusive trends for the Atlantic, with projections within the range of ±50% [Oouchi et al., 2006; Sugi et al., 2009; Villarini et al., 2011].

We create four statistical models for predicting North Atlantic TC frequency. Three of the models are patterned after existing forecast schemes (see section 2) and use some or all of their atmospheric and oceanic predictors which have been shown to possess significant skill in predicting the observed variability of TC activity over the period 1950–2008. The fourth model attempts to capture the influence of tropical Atlantic SSTs relative to tropical SSTs elsewhere, in this instance the equatorial Pacific. We demonstrate the level of skill of each statistical model in hindcasting annual North Atlantic TC frequency, before utilizing each model to project average annual TC activity for three future time slices. Future values for the model predictors are sourced from four global climate models (GCMs) used in phase 3 of the Coupled Model Intercomparison Project (CMIP3). We note that statistical approaches for projecting future TC frequency have previously been proposed by Villarini et al. [2011], Emanuel [2013], and Camargo et al. [2014]. Villarini et al. [2011] use the difference between tropical Atlantic SSTs (10°–25°N, 20°–80°W) and tropical mean SSTs (30°S–30°N) to project decreasing trends in North Atlantic TC counts toward the end of the century, consistent with the trend from the dynamical studies. Camargo et al. [2014] performed a Poisson regression of four environmental variables to explain the global decreasing trend, while Emanuel [2013] utilized a statistical downscaling approach to similarly project an overall decline of ~7% in global TC frequencies. In the latter instance, however, a change in the direction of the projected trend occurs for Coupled Model Intercomparison Project phase 5 (CMIP5) GCMs (as opposed to CMIP3 GCMs). The concentration of this study is on using statistical models to project changes in North Atlantic TC frequencies.

It is anticipated that the statistical models will not account for potential changes in dynamics under climate change. In particular, based on current understanding of environmental drivers of North Atlantic TCs, projected increases in the SSTs of the north tropical Atlantic will likely result in the lower SST threshold for tropical convection being met year round [Nurse and Charlery, 2014]. That is, monthly mean temperatures will likely exceed the 27°–30°C threshold associated with organized convection and oceanic cooling mechanisms [Waliser et al., 1993] year round. Consequently, in comparison to the present, additional future changes in SSTs may be a less significant determinant of TC occurrence (though still potentially a significant modulator of intensity) relative to atmospheric predictors such as vertical shear. To investigate the likelihood of a shift in the relative influence of SST versus other atmospheric predictors in tropical cyclone prediction schemes and the consequent likely impact, if any, on future projections of TC frequency, the four models are recreated for the period 1990–2008 and again utilized to project future TC frequency. The latter 19 years of the data set are characterized by warmer than normal SSTs in comparison to the original base period [Goldenberg et al., 2001; Holland and Webster, 2007]. We therefore consider these years as a period of time analogous to a future state of warmer SSTs and increased vertical wind shear conditions compared to the earlier years in the record. We discuss this further in the following section. Results from the two sets of models are compared.

Section 2 presents the data sets used and elaborates on the methodology for predictor selection and model creation and validation. Section 3 describes the resulting statistical models obtained for the 1950–2008 period (PERIOD1) and the 1990–2008 period (PERIOD2) and analyzes their projections for three future time slices spanning periods leading up to 2100. Section 4 briefly explores the statistical models that would be constituted if a single pool of predictors across all the forecast schemes were used for 1950–2008 and 1990–2008 and the resulting projections. Section 5 highlights the performance of the combined model and its projections based on the two hindcast periods. Section 6 offers a summary and discussion of the study results.

2 Data, Statistical Models, and Methodology

2.1 Data

The National Hurricane Center's updated Best Track database, HURDAT2, is used to calculate an index of the annual total North Atlantic TC frequencies for the period 1950–2008. The second generation HURDAT incorporates recent updates on the original database and includes all available observations of tropical cyclones and subtropical cyclones occurring within the North Atlantic Ocean [Landsea and Franklin, 2013]. The data set may be accessed at http://www.aoml.noaa.gov/hrd/hurdat/Data_Storm.html. The index used in this study was created by determining the number of storms annually of wind speeds greater than or equal to 18 m/s (or 39 mph), (values equivalent to tropical storm strength or greater), which originated and/or passed through the region bounded by 5°–45°N and 20°–100°W, encompassing the low- to middle-latitude North Atlantic, Gulf of Mexico, and the Caribbean Sea.

The National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) Reanalysis I data set was used to obtain atmospheric predictor variables over the period of interest 1950–2008. NCEP-NCAR Reanalysis 1 extends from 1948 to present and provides 4 times daily, daily, and monthly values of a suite of variables at 17 pressure levels on a 2.5° square grid with inputs from land surface, ship, rawinsonde, pibal, aircraft and satellite, observations, and other sources [Kalnay et al., 1996]. NOAA's Extended Reconstructed sea surface temperatures version 3b (ERSST v3b) data set was used to provide monthly averages of SSTs and SST anomalies on a grid resolution of 2° [Smith et al., 2008]. The Niño-3 index is derived from the ERSST data set and represents SST anomalies averaged over the domain 5°S–5°N and 150°W–90°W.

Baseline and future values of predictors are sourced from four global climate models (GCMs) used in phase 3 of the Coupled Model Intercomparison Project (CMIP3): the 1.5° × 1.5° Max Planck Institute's MPI-ECHAM5 [Roeckner et al., 2003], the 1.25° × 1.25° UK Met Office Hadley Centre's HadCM3 [Gordon et al., 2000], the (0.56°–1.4°) (0.56° at latitudes lower than 8° × 1.4°) Center for Climate System Research (University of Tokyo)/National Institute for Environmental Studies/Frontier Research Center for Global Change (Japanese Agency for Marine-Earth Science and Technology)'s MIROC3.2 [K-1 Model Developers, 2004], and the (0.5°–2.0°) (0.5° at latitudes near the equator) × 2.5° Japanese Meteorological Research Institute's MRI-CGCM2.3.2a [Yukimoto et al., 2001; Yukimoto and Noda, 2002; Yukimoto et al., 2006]. Baseline values are obtained for 1979–1999 and future values are obtained under the Special Report on Emissions Scenarios (SRES) A2 emissions scenario [Nakicenovic and Swart, 2000] for the period 2020–2100. The A2 SRES emissions scenario has been extensively applied to analyses of future climate in the North Atlantic and represents a scenario that is widely considered useful and applicable to small island developing states [Taylor et al., 2012; Karmalkar et al., 2013; McLean et al., 2015]. Though only four CMIP3 models are chosen for use in this study, future work will include a larger suite. The four models chosen have been extensively used in previous TC studies [Sugi et al., 2009; Villarini et al., 2011; Villarini et al., 2010]. The CMIP3 GCMs are used in this study given their extensive use in TC analysis. There have also been suggestions that phase 5 of the Coupled Model Intercomparison Project (CMIP5) show only slight improvements in modeling large-scale features, such as ENSO, and subregional climate dynamics [Ryu and Hayhoe, 2013; Bellenger et al., 2014]. Consequently, the range in model variability is not expected to differ widely between the two suites of GCMs.

2.2 Model Creation

Four statistical models (STAT1 to STAT4) are created. The models are first created over the 1950–2008 period and then for the period 1990–2008 using backward regression where predictors that fail the partial F test at the 1 alpha significance level are eliminated from the regression model [Draper and Smith, 1966]. For STAT1, STAT2, and STAT3, the initial predictor pool in each case is gleaned from an existing statistical model used to forecast TC frequency annually and reported on in the peer reviewed literature. The fourth model (STAT4) is proposed from studies on the dynamics associated with Caribbean late season (August, September, and October (ASO)) rainfall. The original predictor pool for each model is given in Table 1 (second column) and further discussed below. Figure 1 shows the averaging domain for each predictor.

Table 1. Original Predictor Pools and Predictors Selected Using Backward Regression for Two Hindcast Periods, 1950–2008 and 1990–2008a

Model	Original Pool of Predictors	Accepted Predictors for Statistical Schemes
Model	Original Pool of Predictors	Based on 1950–2008	Based on 1990–2008
STAT1	From Saunders and Lea [2015] (Predictand: Running 10 year climatology of hurricane numbers (45%)):	STAT1 = −36.45 + 2.41(Predictor 1) + 1.92 (Predictor 2) (48%)	STAT1 = 20.62 + 3.39 (Predictor 1) (52%)
	1. July–Sept 925 mbar Caribbean and North Atlantic zonal wind speeds (7.5°–17.5°N, 30°–100°W)
	2. August–Sept tropical Atlantic SSTs (10°–20°N, 20°–60°W)
STAT2	From Klotzbach [2011] (Predictand: Post 31 July NTC (85%)):	STAT2 = 31.71 + 3.21 (Predictor 2) (42%)	STAT2 = 45.35 + 4.86 (Predictor 2) (79%)
	1. June–July subtropical Atlantic SSTs (20°–50°N, 15°–35°W)
	2. July tropical Atlantic 10 m zonal wind speeds (10°–17.5°N, 40°–80°W)
	3. European Centre for Medium-Range Weather Forecasts September Niño-3 SST forecast (5°S–15°N, 120°–170°W)
STAT3	From Klotzbach and Gray [2012] (Predictand: Post 31 July NTC (91%)):	STAT3 = −5.89 + 2.388 (Predictor 1) + 1.32 (Predictor 2) (41%)	STAT3 = 39.08 + 4.28 (Predictor1) (82%)
	1. July Caribbean surface zonal wind speeds (10°–17.5°N, 60°–85°W)
	2. July northeastern subtropical Atlantic SSTs (20°–40°N, 15°–35°W)
	3. July northeastern tropical Africa 200 mb zonal winds (5°–15°N, 0°–40°E)
STAT4	From Taylor et al. [2002]:	STAT4 = 4.53 + 1.50 (Predictor 1) (24%)	STAT4 = 4.36 + 2.38 (Predictor 1) (44%)
STAT4	September pacTNA (pacTNA is defined as tropical North Atlantic SST anomalies minus equatorial Pacific SST anomalies (TNA − Niño-3))	STAT4 = 4.53 + 1.50 (Predictor 1) (24%)	STAT4 = 4.36 + 2.38 (Predictor 1) (44%)
COMBINED	All predictors	COMBINED = −79.33 + 3.61 (STAT1 SST) + 1.70 (STAT2 zonal wind) − 0.77 (STAT2 Niño-3) (57%)	COMBINED = −85.95 + 5.51 (STAT1 SST) − 1.53 (STAT2 Niño-3) + 2.9 (STAT3 Caribbean zonal winds) − 1.01 (STAT3 SST) − 2.23 (STAT3 Africa zonal wind) − 11.87 (STAT4 pacTNA) (95%)

^a Statistics in bracket indicate the percentage variance explained by each statistical model for annual TC frequency.

Details are in the caption following the image — **Figure 1**
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Domains of the original predictor pools of each operational forecast scheme and for the SST gradient index. The schemes are from *Saunders and Rockett* [2002] (SR02), *Klotzbach* [2011] (KL11), and *Klotzbach and Gray* [2012] (KG12). The gradient index is from *Taylor et al*. [2002] (TAY02). The predictand domain over which the annual TC count is determined is also shown (HURDAT2 Domain). Shaded region shows area of intense winds speeds associated with the July Caribbean low-level jet.

The initial predictor pool for STAT1 includes July–September averaged 925 mbar zonal winds over the Caribbean Sea and tropical North Atlantic region (predictor 1) and August–September averaged SSTs over the Atlantic Main Development region (MDR) (predictor 2). The STAT1 predictors were first validated for forecasting by Saunders and Rockett [2002] and remain the key predictors in Saunders and Lea's August 2015 forecast issued 5 August 2015. The predictors of STAT1 capture two major environmental dynamics necessary for tropical cyclone formation: SSTs and the requirement of a threshold of at least 26°C to facilitate the amount of water vapor necessary to sustain the TC warm core structure and near-surface (low-level) wind strengths which are in part indicative of the vertical shear environment. Saunders and Lea [2015] assert that surface trade winds show a stronger correlation with Atlantic TC numbers than the total vertical shear and the real-time forecast skill scores for the wind and SST predictors are both 83%, measured with respect to a running 10 year climatology (1980–2014). Their forecasts are also made in relation to deviations above or below a 65 year climate norm extending from 1950–2014. In this study, the correlation between predictors 1 and 2 and the index of annual total Atlantic TC frequency over 1950–2008 is 0.66 and 0.52, respectively.

The predictor pool for STAT2 is premised on the forecast scheme of Klotzbach [2011] which is an update to the Klotzbach [2007] statistical scheme. The predictors are June–July subtropical Atlantic SSTs (predictor 1), July tropical Atlantic 10 m zonal winds (predictor 2), and the September Niño-3 SSTs (predictor 3). Klotzbach [2011] proposes that these predictors represent the following physical dynamics: (i) anomalously warm subtropical Atlantic SSTs are associated with a positive phase of the Atlantic Multidecadal Mode, a northward shift of the Intertropical Convergence Zone, and hence reduced trade wind speeds. The weakening of the trade winds is linked with less mixing and upwelling, resulting in increased SSTs [Kossin and Vimont, 2007]; (ii) anomalous warming of the eastern equatorial Pacific indicates a weakened and eastward-shifted Walker circulation associated with increased vertical wind shear across the Atlantic [Gray, 1984a, 1984b]. Tang and Neelin [2004] highlight that at the delayed onset of ENSO, there is anomalous tropospheric drying over the Atlantic that is linked to a reduction in seasonal TC activity. Predictors 1, 2, and 3 described above, through a stepwise regression against a 1950–2008 annual TC frequency index, explain 18%, 42%, and 11% of the variability of annual TC frequency, respectively.

Klotzbach and Gray [2012] revised the Klotzbach [2011] scheme justified by changes in the linear correlations between the predictors and environmental characteristics prevalent in a given forecast year. The literature does not indicate an improvement of skill of the later models, and both are used in tandem for the purposes of forecasting annual North Atlantic TC activity. The predictors outlined by the revised forecast scheme are (i) Caribbean July surface zonal winds and (ii) northeastern subtropical Atlantic July SSTs, which are similar to those reported on in Klotzbach [2011] but also includes (iii) northeastern tropical Africa July 200 mbar zonal winds as opposed to Niño-3 SSTs. Klotzbach and Gray [2012] indicate that a strong easterly flow of 200 mbar zonal winds over the northeastern regions of tropical Africa is an indicator of more favorable conditions for TC development; the zonal wind predictor is associated with a reduction of vertical wind shear in the Main Development Region and anomalously colder SSTs and higher sea level pressure (SLP) in the equatorial Pacific. Caribbean surface zonal winds, subtropical Atlantic SSTs, and northeastern tropical Africa upper level zonal winds form the initial predictor pool for STAT3.

We note that each of these three schemes includes surface to near-surface wind predictors over or in close proximity to the Caribbean low-level jet (CLLJ) region (see again Figure 1) and with timing which coincides with the summer CLLJ maximum. Whyte et al. [2008] defines the CLLJ as a maximum of easterly zonal winds (>12 m/s) in the south western Caribbean (70°–80°W) with east-west axis along 15°N. It is confined to heights below 600 mbar, and its climatological evolution is characterized by two distinct wind speed maxima in February (the early jet) and July (summer jet) and minima in May and October [Wang, 2007; Whyte et al., 2008; Muñoz et al., 2008].

The lone STAT4 predictor is premised on Taylor et al. [2002] and other studies [Curtis and Hastenrath, 1995; Enfield and Alfaro, 1999; Enfield and Mayer, 1999; Chen and Taylor, 2002] which suggest an influence on Caribbean rainfall via an SST anomaly gradient between the tropical Atlantic and equatorial Pacific. The pacTNA SST gradient is defined as the difference between the eastern equatorial Pacific SST anomalies (6°S–6°N, 150°W–90°W) and tropical North Atlantic SST anomalies (6°S–22°N, 80°W–15°W). Taylor et al. [2002] show that it has a statistically significant correlation with the Caribbean's late rainfall season (ASO) which coincides with the peak in North Atlantic tropical cyclogenesis. Inoue et al. [2002] indicate that the climatology of tropical cyclogenesis shares the same bimodal structure as the Caribbean rainfall profile and that increases in cyclogenesis correspond with large increases in high precipitable water content (on the order of 10 kg m⁻²) from September to October. During ASO, warm Atlantic SSTs are associated with the development of deep westerly anomalies over the Caribbean, weaker trade winds and reduced vertical shear conducive to TC development. The state of the equatorial Pacific may then further enhance or diminish the convective environment of the north tropical Atlantic through (among other things) changes in the vertical shear [Aiyyer and Thorncroft, 2006] and strengthening of the CLLJ [Cook and Vizy, 2010]. The single pacTNA predictor is therefore simultaneously capturing both local and remote influences. Although intraseasonal variations reveal a maximum in SST gradient anomalies in October, it is the September pacTNA gradient which has the strongest intraseasonal correlation with annual TC count (+0.42) and is therefore used as the predictor for STAT4. It is, however, noted that pacTNA has a lower correlation with Caribbean early season rainfall (May–July) (−0.15), which may reduce the gradient's skill at predicting the annual TC frequency.

Finally, we repeat the process of model creation over the 1990–2008 period to explore whether there is a change in model constitution when the atmospheric and oceanic characteristics are analogous to a warmer future state. Glenn et al. [2015] show statistically significant warming of 0.016°C yr⁻¹ and 0.021°C yr⁻¹ in the north tropical Atlantic (including the Caribbean Sea, Gulf of Mexico, and MDR) during the early and late Caribbean rainfall seasons respectively between 1982 and 2012. They note that for the late rainfall season which coincides with peak Atlantic hurricane activity, SST averages for 1998–2012 reflect an increase in magnitude and intensity of the Atlantic Warm Pool (AWP) compared to the earlier 1983–1997 period. The increase may be linked to a shift to the warm phase of the Atlantic Multidecadal Oscillation (AMO) [Enfield et al., 2001; McCabe et al., 2004; Knight et al., 2005; Zhang et al., 2007] and/or to anthropogenic forcing [Elsner, 2006; Trenberth and Shea, 2006; Mann and Emanuel, 2006]. Irrespective of cause, we investigate whether, in the context of relatively higher SST anomalies, there are changes in the predictors retained and/or their relative contribution to explained TC frequency variability.

2.3 Model Validation

The four statistical models are validated using the cross-validation model employed by Alfaro [2002] and Ashby et al. [2005]. The skill of each model is assessed using the coefficient of determination (R²), which is the percentage of variation in the observed data accounted for by the model. Additionally, the model's ability to represent above normal, normal, and below normal TC frequency annually is evaluated using a set of skill scores. They are

The hit rate (HR): The percentage of perfect forecasts of above normal, normal, and below normal annual TC frequency;
The skill score (SS): A variant of the HR where +100 indicates perfect hits and −100% indicates a set of forecasts with no hits;
The root-mean-square error (RMSE): A measure of the spread of the forecast errors and is the square root of the average difference squared between the forecast and observation sets;
The linear error in probability space (LEPS): A measure of how close the forecast and observed values are in terms of the probability density function of the observations [Ward and Folland, 1991; Potts et al., 1996]. LEPS penalizes a forecast that is two categories in error more than another which is only one category in error. Therefore, for a year where below normal activity was observed, a forecast of above normal is penalized more than a forecast of normal.
The probability of detection (POD) above normal (PODAN) and below normal (PODBN): The percentage of correct above or below normal events predicted.
The false alarm rate (FAR) above normal (FARAN) and below normal (FARBN): The percentage of above or below-average forecasts which failed to materialize.

A model is judged to be skillful if the HR, SS, and LEPS are positive, PODs are greater than 50%, and FAR values are less than 33%. An ideal model would achieve HR, LEPS, and PODs of 100% and FARs of zero.

2.4 Future TC Frequency

STAT1, STAT2, STAT3, and STAT4 models determined for both the 1950–2008 and 1990–2008 periods are applied with predictor indices from the four GCMs for a twentieth century base period 1979–1999 and for each year from 2020 to 2100. The projected changes in annual TC frequencies from each of the four statistical models are standardized against the variability of the baseline index by subtracting the baseline mean and then dividing by its standard deviation. Projections of future TC frequency under the A2 scenario are presented as a standardized change for three future time slices (2020–2040, 2045–2065, and 2070–2090) relative to the twentieth century 1979–1999 baseline TC frequency. The change is presented as box plots across the suite of GCMs, statistical models, and future periods. The standardization and use of box plots allows ease of comparison of the distribution of the projected changes and is consistent with the analyses of Villarini and Vecchi [2012].

3 Results for PERIOD1 (1950–2008) Models

3.1 Calibration and Validation

Column 3 of Table 1 summarizes the models created for the period 1950–2008 using the predictor pools noted in Table 1 and after backward regression. Table 2 summarizes the skill scores for each model.

Table 2. Statistical Scores Obtained for Each Statistical Model When Validated Over PERIOD1 (1950–2008) and PERIOD2 (1990–2008)a

	PERIOD1	PERIOD2	PERIOD1	PERIOD2	PERIOD1	PERIOD2	PERIOD1	PERIOD2	PERIOD1	PERIOD2
	STAT1		STAT2		STAT3		STAT4		COMBINED
R²	49	52	42	79	37	82	24	44	57	95
SS	72	64	69	76	57	76	54	68	72	84
RMSE	2.2	2.0	2.1	1.5	2.1	1.4	2.5	2.4	2.1	1.0
HR	81	89	80	84	71	84	69	79	81	89
LEPS	62	81	58	71	40	71	36	61	62	81
FARBN	5	0	5	0	5	0	11	0	5	0
FARAN	0	0	5	0	10	0	10	0	0	0
PODBN	74	100	74	67	58	67	63	83	74	83
PODAN	70	71	65	86	55	86	45	57	70	86

^a Units: %.

Both the July–September Caribbean-Atlantic 925 mbar zonal winds and August–September tropical Atlantic SST predictors motivated by Saunders and Lea [2015] are retained in STAT1 and together explain 48% of the observed variance. This is in comparison to 45% of variability explained for the running 10 year climatology of hurricane numbers modeled by Saunders and Rockett over 1982–2010. STAT1 shows good predictive skill with an SS of 72%, HR of 81%, LEPS of 62%, PODAN of 70%, PODBN of 74%, and FAR values of 5% and less. STAT1 has the highest skill of all four models over 1950–2008. Of the Klotzbach [2011] motivated predictors, the July-averaged tropical Atlantic 10 m zonal wind is the only predictor retained for the STAT2 model and accounts for 42% of the variability. When the STAT2 model is forced to keep all three predictors, the model's performance against the TC frequency index indicates only a 2% improvement in the variability explained. Klotzbach's model explained 85% of post 31 July net tropical cyclone activity (NTC) for 1982–2010. Two of the three predictors from Klotzbach and Gray [2012] were retained in STAT3—the Caribbean July surface zonal winds and the northeastern subtropical Atlantic July SSTs. The rejected predictor was the northeastern tropical Africa July 200 mbar zonal winds. The model explains 41% of the variance and has an SS score of 57%, HR of 71%, LEPS of 40%, PODAN of 58%, PODBN of 55%, and FAR values of 10% and less. The Klotzbach and Gray model explained 91% of post 31 July NTC for 1979–2011. It is not surprising that the skill of the models with respect to TC frequency is lower than that for an aggregate measure such as NTC since our approach is utilizing predictors originally retained for hindcasting NTC to model another TC metric.

The STAT4 model comprising the September Pacific-Atlantic SST anomalies gradient index explains 24% of the observed variability and exhibits the least skill of all the models. SS, LEPS, PODBN, PODAN, and FARBN are 54%, 36%, 63%, 45%, and 11%, respectively. All the statistical models obtained are considered to be skillful given the criteria presented in section 2.3.

We note that it is the low-level zonal wind predictors defined over or near the CLLJ region which are retained in STAT1, STAT2, and STAT3. We will refer to these predictors as CLLJ-type predictors. The results suggest the usefulness of CLLJ-type indices as indicators of historical TC frequency.

3.2 Projections From the 1950–2008 Calibrated Statistical Models

Standardized changes in TC frequency relative to a 1979–1999 base period were determined for three 21 year time slices (2020–2040, 2045–2065, and 2070–2090). Table 3 shows the standardized changes per year averaged over each 21 year time slice over all future realizations from all GCMs, while Table 4 shows a breakdown by forcing GCM for the end of century time slice (2070–2090).

Table 3. Mean Change in TC Frequency Projected Using Statistical Models Obtained Over PERIOD1 (1950–2008) Versus PERIOD2 (1990–2008)a

	STAT1	STAT2	STAT3	STAT4	COMBINED	STAT1	STAT2	STAT3	STAT4	COMBINED
	PERIOD1-Based Statistical Models					PERIOD2-Based Statistical Models
2020–2040	+3.6	−0.4	−1.5	+0.2	+5.4	+0.7	−0.6	−1.7	+1.2	+5.8
2045–2065	+5.2	−0.4	−0.5	0.0	+8.4	+1.1	−0.6	−1.0	+0.9	+9.2
2070–2090	+6.4	−0.3	+0.7	−0.1	+12.7	+0.3	−0.4	−0.7	+0.8	+12.9

^a The mean change expressed as a standardized anomaly from the 1979 to 1999 model consensus mean. Values in italic (bold) indicate a statistically significant increase (decrease) at the 90% confidence level.

Table 4. Change in Mean TC Frequency for the 2070–2090 Period Relative to the 1979–1999 Baseline Period, as Projected for the PERIOD1-Based (1950–2008) and PERIOD2-Based (1990–2008) Statistical Models by Each GCMa

	STAT1	STAT2	STAT3	STAT4	COMBINED	STAT1	STAT2	STAT3	STAT4	COMBINED
	PERIOD1-Based Statistical Models					PERIOD2-Based Statistical Models
ECHAM5	+6.1	−0.9	+3.2	+0.5	+12.3	−1.8	−1.1	+1.6	+1.6	+16.4
HadCM3	+4.4	−1.4	+1.7	−0.4	+12.2	−2.5	−2.2	−0.2	−0.2	+10.8
MIROC3.2	+8.1	−0.1	+3.3	−0.3	+12.9	+6.6	+1.3	+2.9	−0.3	+13.7
MRI CGCM2.3.2a	+6.4	+0.9	−5.5	+0.1	+12.2	+0.5	+0.2	−6.7	+1.3	+10.8

^a Values in italic (bold) indicate a statistically significant increase (decrease) at the 90% confidence level.

STAT1 (Caribbean-Atlantic zonal wind + Atlantic SST) shows statistically significant increases in TC frequency for all three time slices, with the greatest magnitude of standardized change (+6.4 TC per year) toward the end of century (Table 3). For 2070–2090, an annual absolute change of between four and eight more TCs per year is projected dependent on GCM (Table 4). In contrast, STAT2 (Atlantic wind) projects no statistically significant change (or very small reductions) in TC frequencies over the entire 2020–2100 period when averaged for the entire GCM ensemble (Table 3). Of the four GCMs, only MRI CGCM2.3.2a suggests increased frequency (+1 TC per year) at the end of the century using STAT3. Projections from STAT 3 (Caribbean zonal wind + Atlantic SST) exhibit (standardized) decreases of 2 TC per year and 1 TC per year for the two earlier time slices but an increase of 1 TC per year for the 2070–2090 period (Table 3). All the changes are statistically significant. All GCMs with the exception of MRI CGCM2.3.2a indicate higher TC frequencies (of up to approximately 3 TC per year) by the end of the century for STAT3 (Table 4). STAT4 (Pacific-Atlantic SST anomalies gradient) suggests very little or no change in the mean number of TCs annually across the three time slices (Table 3) and no change for the end of century irrespective of the forcing GCM (Table 4).

We note that it is the statistical model which utilizes tropical Atlantic SSTs as a predictor relative to tropical SSTs elsewhere (in this instance the equatorial Pacific) (STAT4) and the model which includes only a CLLJ-type predictor (STAT2) that suggest small or no changes in future TC frequency across the entire future period. This contrasts with the results from the two other models incorporating SSTs from the Atlantic. In general, by the 2070–2090 period, the models comprising CLLJ-type and SST indices (STAT1 and STAT3) indicate statistically significant increases, while the model with only a CLLJ-type predictor suggests a slight decrease (STAT2). The gradient model suggests no change.

Figure 2 illustrates the box plots for each GCM-STAT combination for each time slice. The boxplots underscore the state of projections of future TC numbers. With the exception of STAT1, most GCM-STAT combinations have ranges across negative and positive values with the uncertainty persisting through the end of century. The spread makes it difficult to make definitive statements concerning future TC count from this subset of statistical and dynamical models, however, things to be noted are as follows:

STAT1 (wind + AtlanticSST) projections are systematically positive and exhibit the strongest increases, likely due to the influence of the strong positive trends in Atlantic SSTs.
MRI-STAT3 (wind + subtrop.AtlanticSST) combinations exhibit the largest decrease in TC frequency relative to the 1979–1999 period. The large declines in TC frequency are due to the MRI-CGCM's representation of SSTs in the subtropical North Atlantic region (Figure 3c). According to the GCM, subtropical Atlantic SSTs are projected to be 3–5% colder across the three future time slices compared to the 1979–1999 baseline mean of 27.6°C.

Figure 4 shows the mean spread of TC frequencies obtained for each statistical model considering all GCM inputs for the various time slices. It is also noted that

The GCM predictors reasonably reproduce the mean statistics of the present-day period. The distribution of the twentieth century TC frequency using GCM inputs versus the observed annual TC frequency index are quite similar, particularly for STAT1. The other statistical models yield slightly higher means but within 0.5 TCs of the observed.
While STAT1 yields progressively larger positive changes in TC frequency with consecutive time slices, more conservative or little mean changes in TC frequency are projected by STAT2 and STAT4. STAT3 shows progressive increases in TC frequency with each future time slice but after a decrease in 2020–2040. The projected end of century frequency from STAT3 is consequently only slightly larger than for the baseline period.

4 PERIOD2 (1990–2008) Models

4.1 Calibration and Validation

The calibration and validation of each statistical model were repeated over 1990–2008 (PERIOD2), a period marked with anomalously higher SSTs relative to preceding decades [Glenn et al., 2015].

For PERIOD2, only a single predictor is retained for STAT1 (CLLJ-related winds) (Table 1, fourth column) and the model accounts for 52% of the observed TC frequency variability (Table 2). This is higher than the 48% explained variance by the PERIOD1 model that also included Caribbean-Atlantic SSTs. STAT1 exhibits a smaller SS (64% versus 72%), higher HR (89% versus 81%), similar PODAN (70% versus 71%) but lower PODBN (74% versus 100%), and zero FAR. For STAT2, the CLLJ-type winds is again the only Klotzbach [2011] predictor retained but the model now accounts for 79% of the variability in comparison to 42% for the 1950–2008 period. One of the reasons for the improvement in skill may be due to better measurements of low-level and upper level zonal wind in recent years. STAT2's performance under PERIOD2 regression is similar to the Klotzbach [2011]'s model performance of 72% explained variability for a post 1 August NTC hindcast. The model exhibits improved skill with higher HR, LEPS, and PODAN scores of 84%, 71%, and 86%, respectively. PODBN was, however, lower (67% versus 74%).

For PERIOD1, STAT3 originally retained two predictors (CLLJ-related wind + Atlantic SST) but the SST predictor was rejected for PERIOD2. The PERIOD2 model explains 82% of the variance (in comparison to 41% for the PERIOD1 model), equal to the variability explained by Klotzbach and Gray [2012]'s statistical scheme over the 1979–2011 NTC hindcast. All skill scores are higher for PERIOD2 with HR, LEPS, PODAN, and PODBN of 84%, 71%, 86%, and 67%, respectively. For STAT4 its single predictor is again retained. The hindcast skill of the pacTNA gradient improves for PERIOD2 with 44% variance explained in comparison to 24% for PERIOD1. All skill scores indicate improved model skill with SS of 68%, HR of 79%, and zero FAR.

Each of the models obtained for PERIOD2 exhibits greater skill than the models obtained for PERIOD1 with three of these models conditioned only on CLLJ-type predictors. STAT2 and STAT3 models explain approximately twice as much variability in the latter period (up to 82%), and we again note that the domains of their low-level wind predictors converge closely to the region of CLLJ maximum core and at the time of its climatological maximum in July. The suggestion is that in a warmer climate, Atlantic SST thresholds for TC development are likely being met and changes in the CLLJ may become a more significant factor in future TC activity. We discuss this further in the final section. The increased variance explained by the SST gradient index in PERIOD2 also suggests that atmospheric circulation changes linked to the difference in oceanic basin warming [see, e.g., Fuentes-Franco et al., 2014; Gouirand et al., 2012] will likely influence TC frequency. This is also discussed further in section 6.

4.2 Projections From the 1990–2008 Calibrated Statistical Models

Predictors obtained from the four GCMs for the future periods and a baseline period 1979–1999 are utilized in the PERIOD2 models. Figure 5 illustrates the consensus of the four GCMs for each statistical model. STAT1 now projects more conservative standardized increases in TC frequency over the three future time slices with the first two time slices exhibiting statistical significance (Table 3). For the 2070–2090 period, projections from STAT1 range from −2 to +6 TC per year. Predictors obtained from the ECHAM5 and HadCM3 are the inputs for which STAT1 yields decreasing frequency (Table 4 and Figure 6). STAT2 is consistent with respect to indicating a decrease in the standardized TC frequency in all three future time slices, as observed in PERIOD1, with changes for the first two time slices now statistically significant. The consistency is not surprising as the CLLJ-type predictor was also the lone predictor retained in the PERIOD1 analyses but with differing coefficients. The absolute change projected by the end of the century across the GCMs is −2 to +1. STAT3 also projects steady declines in the standardized TC frequency for the 2020–2040 and 2045–2065 periods, with no significant change for the 2070–2090 period. The sensitivity of STAT1-3 to the domain size, pressure level, and season over which the zonal winds are defined is evident where an increase in TC frequency is suggested by STAT1 versus the decrease suggested by STAT2 and STAT3. STAT4 yields stronger positive standardized changes of approximately 1 TC per year for all time slices relative to PERIOD1 (Table 3). The ECHAM-STAT4 is the only combination to suggest a statistically significant change in TC frequency of +2 TC per year by 2070–2099.

5 A Combined Model

A final model is explored using a combined predictor pool drawn from the four original predictor pools used in STAT1-4. Backward regression is then applied to determine retained predictors. The analysis is done separately for PERIOD1 versus PERIOD2. While it is anticipated that the correlation between some predictors would be high, all predictors are still included in the analyses. Table 1 indicates the final model obtained for both periods.

For PERIOD1, the predictors retained were the STAT1 Atlantic SSTs and the STAT2 Atlantic zonal winds and Niño-3. The model accounts for 57% of the observed variability. For PERIOD2, STAT1 Atlantic SSTs and STAT2 Niño-3 are again retained in addition to all STAT3 predictors (Caribbean zonal winds and Africa zonal winds) and STAT4 pacTNA. This model represents 95% of the observed variability (see Table 1). The combined models are of comparable skill to the four original statistical models and for some skill scores particularly for the 1990–2008 that represents greatly improved skill. The HR, LEPS, and PODs are all greater than 86% (Table 2). The retention of five of the predictors in the 1990–2008 model and almost perfect fit of the hindcast suggests predictors are overfit.

The projections are investigated for both models. Interestingly, the 1950–2008-based model suggests heightened mean TC frequency (not shown) to the order of 9 to 16 TC per year due to the dominant effect of the Atlantic SSTs as suggested by the regression coefficients (Table 1) and the relatively large increases suggested by the GCMs (Figures 3a–3c). The 1990–2008-based model suggests increased TC frequency to the order of 6 to 13 TC per year. Note as well that the STAT2 winds are among the predictors retained for PERIOD1 and STAT3 winds for PERIOD2.

It is important to note that it is unlikely that Atlantic TC frequencies will increase by 13–16 TCs per year in the future. Such values, as well as the overfitting that was observed for PERIOD2, are likely linked to the heavy weighting on the tropical Atlantic SSTs in the combined models. Interestingly, if the analysis periods were extended to 2014, the impact of including the additional 6 years of further significant warming is to remove SST as a predictor in the initial STAT1 and combined models. That is, for 1950–2014, the predictors retained in the models remain the same for all models except STAT1 (where the zonal wind predictor is now the only predictor retained; R² = 0.36 versus our original R² = 0.41 and other skill scores are comparable) and the combined model (where the STAT2 zonal wind predictor is the only predictor retained; R² = 0.44 versus our original R² = 0.49 and other skill scores are comparable). For a 1990–2014 period, the predictors remain unchanged for all the models except the combined model (where the STAT2 zonal wind predictor is now the only predictor retained; R² = 0.65 versus our original R² = 0.92 and other skill scores for new model are lower). These results seem to underscore the point that in a warmer era, it is the relative SSTs (e.g., tropical Atlantic versus remainder of the tropics) and/or the CLLJ type predictors that are the more useful predictors as opposed to Atlantic SST itself.

6 Discussion and Conclusion

Future trends in global and regional TC frequency have largely been investigated using dynamical models whose results suggest higher degrees of uncertainty for regional domains like the North Atlantic. This is because the reliability of projections from dynamical models is influenced by their sensitivity to grid resolution, the ability of the models to accurately simulate the large-scale atmospheric conditions and internal variability of the climate system, and the choice of parameterizations [Hawkins and Sutton, 2009; Sugi et al., 2009; Villarini et al., 2011]. The variety of GCMs with varying model structures therefore makes it difficult to form a consensus between the projections. At the same time, statistical models are currently used with reasonable success to hindcast and forecast TC activity in the North Atlantic. They can potentially offer additional insight into future North Atlantic TC frequency provided that suitable statistical predictors can be identified that (i) account for (most of) the observed variability of TC frequencies, (ii) are realistically represented in the GCMs of interest and (iii) have “a climate change signal” (i.e., respond to a warmer climate), and (iv) the dynamics of hurricane formation do not change in the future climate regime. Statistical models also have the added advantage that they are computationally and financially less demanding than dynamical models.

The performance of four statistical models (STAT1–STAT4) is first assessed over two observational periods: 1950–2008 (PERIOD1) and 1990–2008 (PERIOD2). PERIOD2 is characterized by an increase in SSTs in the north tropical Atlantic including over the main development region for TC development [Glenn et al., 2015]. The proposition is that PERIOD2 (when compared to the prior decades) may be considered analogous to the future which is projected to be characterized by a warmer atmospheric and oceanic environment over the North Atlantic by the end of the century. The investigation therefore hints at possible alternate futures in TC activity as suggested by the “new” models and also highlights the sensitivity of the statistical models to different calibration periods and by extension dominant environmental conditions during those periods.

All the models created possessed reasonable to very good skill in hindcasting TC annual frequency over both periods of analyses. For PERIOD1, two of the four statistical models (STAT1 and STAT3) retained combinations of Atlantic SSTs and Atlantic and Caribbean zonal winds as predictors. Of the other two models, STAT2 retains only a zonal wind predictor while STAT4 retained the gradient index representative of SST differences between the tropical Pacific and Atlantic basins. The initial predictor pools for STAT1-3 were previously explained as being representative of current operational forecast schemes of TC frequency. For PERIOD2, the SST predictors that were retained in STAT1 and STAT3 for PERIOD1 were rejected leaving only zonal wind predictors. The PERIOD1 predictors for STAT3 (also zonal wind) and STAT4 (the SST gradient) are also retained in PERIOD2. If, as previously noted, the SST gradient predictor is a proxy for atmospheric circulation, then in tandem the results suggest that in a warmer climate, zonal winds become the more useful and/or primary indicator of TC frequency. This is probably because the SST thresholds to support convection are already largely being met, and any intensification or diminishing in strength of the low-level winds changes the shear environment and influences TC activity. The low-level winds explain up to 82% of the variability in annual TC frequency for 1990–2008 (see again Table 2).

The significance of the zonal wind to TC activity is further indicated by the fact that it is utilized in all models premised on operational forecast schemes, irrespective of analysis period. The zonal wind predictors used are located over (or near) the domain of the CLLJ and coincide with the timing of its summer maximum. Linear associations between the predictors are captured in Table 5 as well as the correlation of the wind predictors with a July CLLJ index fashioned after Whyte et al. [2008]. Correlation coefficients exceed +0.73 between the zonal winds in STAT1-3 and are as high as +0.92 between STAT2 and STAT3 winds. Significantly, correlations are equally strong (exceed +0.60) with the CLLJ summer index. It is also noteworthy from Table 5 that there are significant correlations between the SST gradient index of STAT4 and both STAT1 wind speeds (+0.62) and the CLLJ index (−0.63). We suggest that CLLJ summer variability is strongly associated with Atlantic TC frequency and is being captured by the statistical models. Wang [2007] suggested that the CLLJ-TC link is through its effect on vertical wind shear and that Caribbean 925 mbar zonal wind is a useful proxy for vertical wind shear over the Atlantic sector. Klotzbach [2011] also found that the July 10 m zonal wind speeds (retained in STAT2) has a strong correlation with August–October averaged vertical wind shear indices over the domain (−0.72) and with the size of the Atlantic Warm Pool. Wang et al. [2008] observed a correlation of +0.51 between the AWP and Atlantic tropical cyclones. The study, then, affirms the summer CLLJ manifestation as a significant influence on TC variability and further suggests that its role becomes increasingly more important (potentially becoming the dominant influence) in determining TC activity in a warmer climate.

Table 5. Correlation Coefficients Calculated Between the Predictors of the STAT1, STAT2, STAT3, and STAT4 Models Based on 1950–2008 Analysis and the July-Averaged Caribbean Low-Level Jet (CLLJ)a

	S1-Uwind	S1-SST	S2-Uwind	S3-Uwind	S3-SST	S4-SST Gradient
S1-Uwind	-	-	-	-	-	-
S1-SST	0.53	-	-	-	-	-
S2-Uwind	0.81	0.38	-	-	-	-
S3-Uwind	0.73	0.38	0.92	-	-	-
S3-SST	−0.38	0.75	0.26	0.20	-	-
S4-SST Gradient	0.62	0.10	0.60	0.62	0.06	-
CLLJ	−0.67	−0.28	0.84	−0.95	−0.23	−0.63

^a Values in bold are statistically significant at the 95% level.

When the statistical models are used to project future TC activity, the PERIOD1-based models comprising both absolute Atlantic SSTs and zonal winds (STAT1 and STAT3) suggest an increase in frequency by 2–8 TC per year by the end of century. The magnitude of the increase is strongly associated with the strong positive trend in Atlantic SSTs projected by the GCMs (see Figures 3a and 3c). On the other hand, the two other statistical models premised on the atmospheric circulation variables indicate either declines of approximately 1 TC per year (STAT2 using zonal wind as the only predictor) or no change (STAT4 using the SST gradient as the predictor) by the end of century. The PERIOD2-statistical models suggest more conservative standardized increases by 2070–2090 for STAT1 and STAT4 (an absolute change of −2 to +6 TC per year), while both STAT2 and STAT3 indicate declines over the 2020–2065 period. The STAT2 and STAT3 trends are accounted for by the projected strengthening of their zonal wind predictors in almost all forcing GCMs over 2020–2090 (Figure 7). This is consistent with other studies that have similarly suggested a strengthening of the CLLJ in a warmer future [Campbell et al., 2011; Martin and Schumacher, 2011; Taylor et al., 2013; Rauscher et al., 2008]. Interestingly, we suggest that even for STAT1, the projected conservative increases for PERIOD2 may be linked to sensitivity of its zonal wind predictor to domain size and season. That is, though most of the GCMs used in this study indicate future strengthening of zonal wind speed over the CLLJ domain for July (not shown), when the averaging domain and period is extended to mirror that used for the STAT1 predictor (both westward and eastward beyond the CLLJ and covering July through September), three of the four GCMs now project decreases in wind speed (Figures 3c and 7). Taken together, however, the suggestion from the statistical models for the two periods of analysis is that as the CLLJ's dominance as a predictor increases in a warmer future, the tendency is for no or small increases (+1 to +3 TC per year) in TC frequency or declines (−1 to −2 TC per year) by the end of the century.

Finally, this study points to the potential significance of relative SSTs as opposed to (for example) SST anomalies in the tropical Atlantic basin alone, with respect to projecting TC activity, particularly in a warmer future. In this study, the pacTNA SST gradient index was used as a predictor. It may be considered as a circulation index proxy for the Caribbean region, given that it attempts to incorporate changes in the interaction between the Pacific and Atlantic which occur via an atmospheric bridge [see Taylor et al., 2002, 2011; Gouirand et al., 2014]. Significantly, the index does not show the strong upward trends projected for Atlantic SSTs toward the end of the century. Instead the GCMs project increased variability toward the end of the century about the present-day mean (Figure 3c). This likely contributes to the smaller projected changes in the future annual TC count (comparable to the projections from the CLLJ-type models) when using the gradient index, in comparison to the higher projections from the statistical models that incorporate tropical north Atlantic SST anomalies. Villarini and Vecchi [2012] similarly report the lack of significant response of cyclone counts to relative SSTs (defined as the difference between local and tropical mean SSTs). The gradient index exhibits a correlation of 0.48 with an index of relative SSTs created using tropical North Atlantic SSTs minus tropical SSTs [Villarini et al., 2011]. Villarini et al. [2011]'s Poisson regression of relative SSTs also explains 33% of the variability observed in 1950–2008 annual TC counts which is 9% more than what is accounted for by the linearly regressed gradient index used in this study. When instead a Poisson regression is applied to the pacTNA gradient index over 1950–2008 with annual TC counts as predictand, the variance explained increases to 39% (as opposed to 24%) which is comparable to the skill of the Villarini et al. [2011] model. This suggests the possibility of further work where the methodology used for model creation and/or the definition of the gradient index is varied. There is likely a sensitivity to the areas of the Atlantic and Pacific used to create the index. A useful analysis would therefore involve identifying the areas that maximize the predictability of TC frequency.

The study also highlights some areas for further work using the statistical models or methodologies employed in this study to provide additional insight into future projections of TC frequency under global warming. Future studies will firstly utilize the suite of Coupled Model Intercomparison Project Phase 5 (CMIP5) GCM and the Coordinated Regional Downscaling Experiment regional climate model simulations to expand the range of future scenarios of TC frequency generated with the statistical models. In particular, models that show skill in representing observed relevant regional dynamics will target, for example, those which accurately represent the North Atlantic Subtropical High and its seasonal east-west migration. The movement of the North Atlantic subtropical high sets up a semiannual variation in meridional sea level pressure gradients which in turn gives rise to the summer and winter maximum in the CLLJ [Wang, 2007; Muñoz et al., 2008].

Another focus of the future research will be on model SST biases. The focus in this study on future change reduced but likely did not eliminate altogether the influence of systematic biases in how the GCMs represented both the SST and zonal wind predictors. For example, Figure 3 shows that STAT1 and STAT3 SST predictors were largely underestimated by the GCMs (except for ECHAM5 which is reasonable for STAT1), while the MRI CGCM overestimated STAT3 SSTs to the order of 4°C. Additionally, the GCM representation of the SST gradient index varied about the observed gradient index but did not capture the amplitudes of the annual variations. The SST cold bias noted in this study is consistent with the observations of Misra et al. [2009] who noted that eight of the CMIP3 models exhibited a mean cold bias for July–September. Cold biases over the western Atlantic have also been noted by Davey et al. [2002], Richter and Xie [2008], and Li and Xie [2012]. The GCMs also generally underestimated the STAT1 zonal wind speeds and in some cases overestimated the STAT2 zonal wind speeds but reasonably simulated STAT3 zonal wind speeds. Future investigations will therefore include a validation of predicted TC frequencies from the statistical models using 20th century GCM data against observed variability, as one of the means of fine tuning the initial choice of GCMs eventually used.

Finally, future analyses will also investigate (i) how the statistical models created with some modifications may be used for investigating TC activity over even smaller domains like the Caribbean; (ii) other predictive schemes conditioned for aggregate measures of TC activity such as the accumulated cyclone energy (ACE) and net tropical cyclone (NTC) activity [Klotzbach, 2007, 2011; Villarini and Vecchi, 2012], recognizing that named storms can form in more marginal environments; (iii) an expanded predictor pool that incorporates measures such as the MPI; and (iv) the relative influence of anthropogenic forcing versus the current phase of the AMO on present-day predictability of TC frequency using the CLLJ, as this may have implications for the next AMO phase shift.

This study suggests that atmospheric circulation-based indices (for example, zonal winds and SST gradient indices) emerge as the primary predictors in statistical models for projecting future TC frequency premised on present-day TC prediction schemes. These models forced by GCM projections project conservative small increases to small decreases in TC count per year by the end of the century. The study provides an example of a seamless prediction methodology where models used for seasonal prediction are applied on climate change timescales.

Acknowledgments

The authors wish to thank Phil Klotzbach and the anonymous reviewers for their insightful comments that significantly enhanced the paper. Data used to create the statistical models are freely sourced from the NOAA's Extended Reconstructed Sea Surface Temperatures (ERSST) v3b (http://www.esrl.noaa.gov/psd/data/gridded/data.noaa.ersst.html), NCEP/NCAR Reanalysis I (http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.html), and NOAA's “Best Track” (HURDAT2) database (http://www.aoml.noaa.gov/hrd/hurdat/Data_Storm.html). For future projections, data obtained from the Coupled Model Intercomparison Project Phase 3 (CMIP3) (ftp://ftp-esg.ucllnl.org) are applied to the statistical models that are provided in the paper. Some of the results discussed in this article were presented at the 31st Conference on Hurricanes and Tropical Meteorology, American Meteorological Society, 30 March 30 to 4 April 2014, San Diego, USA. Participation in the conference was funded by the Caribbean Weather Impacts Group (CARIWIG) Project and by the University of the West Indies.

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Citing Literature

Volume121, Issue8

27 April 2016

Pages 3741-3758

Statistical downscaling of North Atlantic tropical cyclone frequency and the amplified role of the Caribbean low-level jet in a warmer climate

Abstract

Key Points

1 Introduction