1. Introduction
Tropical cyclones (TCs) form when sustained convection becomes focused near the center of a precursor disturbance in which the flow is in near-solid-body rotation and the inertial stability is high (e.g., Dunkerton et al. 2009; Montgomery et al. 2010; Wang et al. 2010a,b; Wang 2012; Tory et al. 2013d). Before TC formation is successful, convection in the precursor disturbance must moisten the typically dry middle troposphere (e.g., Nolan 2007; Wang 2012 and references therein) so that, on the system scale, condensational heating dominates over evaporative cooling. In the high inertial stability core, sustained heating leads to a system-scale spinup of the circulation (e.g., Eliassen 1951; Willoughby 1979; Shapiro and Willoughby 1982; Schubert and Hack 1982; Hack and Schubert 1986). The scale and the duration of the heating necessary to drive the system-scale spinup of the storm is in turn a function of the inertial stability (e.g., Nolan and Montgomery 2002; Nolan and Grasso 2003; Willoughby 2009), such that the weaker the precursor circulation, the larger the extent and longer lived the diabatic heating must be for the system-scale circulation to intensify.
The diabatic processes of condensation and freezing that provide this convective heating are fueled by the release of lower-troposphere conditional instability, which develops in part from sea surface fluxes of heat and moisture, producing an accumulation of lower-troposphere moist entropy. Conditional instability is consumed by convection during the TC formation process, as convection moistens the troposphere and drives the intensification of the system-scale circulation. Conditional instability can also be reduced in localized areas by downdrafts that cool and dry the surface layer. This loss of conditional instability during TC formation is to some extent offset by surface moist entropy fluxes and by some contribution through horizontal transport into the convective region. However, for the mature TC, which is considered to be self-sustaining, it has been suggested that the majority or all of the storm’s energy (sufficient to maintain the circulation against friction and enable it to intensify) is derived locally from the surface moist entropy fluxes (e.g., Rotunno and Emanuel 1987). It follows that the role of in situ energy extraction from the sea surface becomes increasingly important during the TC formation process.
Palmén (1948) suggested that a SST threshold of about 26°–27°C might be necessary for TC formation. There are many references in the literature to this SST threshold. Some refer back to the original Palmén source (e.g., Gray 1968; Dengler 1997), while in many later papers the threshold had become so widely accepted that no reference was required (e.g., Rodgers et al. 2000; Tory and Frank 2010). It is only very recently that any attempts at testing the validity of the Palmén threshold have appeared in the literature (Dare and McBride 2011, hereafter DM11), who incidentally, concluded that the SST threshold was 25.5°C. To understand the SST threshold concept, it is worth revisiting its history in more detail. Palmén’s (1948) threshold is dependent on one main assumption that TC formation requires upper-tropospheric instability (about 10–12 km above the surface); that is, TC formation requires deep convection. The instability was measured as the temperature difference between a lifted hypothetical air parcel and the environment at 300 hPa. The hypothetical air parcel was assumed to have an initial surface temperature equal to the sea surface and 85% relative humidity. It was raised from the surface adiabatically to saturation and then moist adiabatically to 300 hPa. Applied to the September North Atlantic Ocean climatology, Palmén found that the geographic distribution of the 300-hPa instability region matched quite well the known Atlantic TC formation regions. An examination of the SST showed that the edge of the unstable region roughly coincided with the 26°–27°C isotherms. Palmén then plotted the 26°–27°C warm-season SST isotherms globally and noted that the tropical regions where TC formation did not occur were characterized by lower SSTs. This was fairly strong evidence for the necessity of warm SSTs for TC formation, although the result is somewhat qualitative. Palmén noted that TCs did not form near the equator as a result of insufficient background absolute vorticity, which demonstrates awareness that warm SSTs might be necessary, but they are not sufficient for TC formation. Twenty years later, the SST threshold became more specific when Gray (1968) plotted the 26.5°C warm-season SST isotherms onto his global map of tropical storm (TS) development regions (see his Fig. 3), and added a 26.5°C line1 to a latitude versus SST line plot for various ocean basins (his Fig. 18).
Given the largely qualitative arguments for the SST threshold, DM11 decided to test the concept by investigating the actual observed SSTs in the vicinity of TC formation over a 28-yr period. They defined TC formation as the time the storm reached TS intensity,2 which is consistent with previous SST threshold studies [Palmén (1948) focused on “tropical hurricanes” and Gray (1968) considered storms that reached sustained winds of 40 mi h−1 (1 mi h−1 ≈ 0.45 m s−1)]. In this paper, we also consider TC formation to be complete when the storm reaches TS intensity. DM11 combined the International Best Track Archive for Climate Stewardship (IBTrACS) TC database (Knapp et al. 2010) with the National Oceanic and Atmospheric Administration/National Climatic Data Center (NOAA/NCDC) SST dataset, and found numerous exceptions in which TCs do form over sea surfaces less than 26°–27°C and at times 4°–5°C cooler. One might question whether a threshold exists if there are exceptions to the rule. If potential errors in the TC database (e.g., TC intensity estimations) are considered, then allowances for a small number of exceptions may be justified. However, there remain in the IBTrACS TC database unambiguous cases of storms that acquired TS intensity above cooler sea surfaces. These include storms that have been flagged as subtropical and extratropical at the time they reached TS intensity, which one may argue are not truly tropical in nature. DM11 removed these storms plus any additional storm that formed poleward of 35° latitude, and found 37 additional exceptions to a SST threshold of 25.5°C at the time of formation. They recognized that most of these storms passed over water that exceeded this threshold at some time in the previous 48 h, which led them to conclude that an SST threshold does exist. However, their threshold is 1° lower than the long-accepted 26.5°C-SST threshold of Gray (1968), and they specified that SST in excess of 25.5°C needs to be encountered by the precursor storm for at least one 6-hourly observation in the previous 48 h (a typical gestation period noted by DM11).
In this paper we reconsider the SST threshold concept, and note that it is based on the assumption that the majority of the storm energy is sourced from the release of conditional instability, within the deep tropical troposphere (Palmén 1948). We hypothesize that if enough energy is derived from another energy source, such as the release of baroclinic instability, then the SST threshold concept may not apply. While McTaggart-Cowan et al. (2013) have shown that approximately 30% of TCs in the IBTrACS database formed in a somewhat baroclinic environment, with 21% associated with some upper-tropospheric disturbance, we expect most will have only benefited from enhanced convection in associated regions of isentropic ascent, or increased upper-troposphere instability, rather than from any significant release of baroclinic instability. Many storms that formed in the vicinity of strong upper-tropospheric disturbances developed in the relatively deep tropics but some formed in stronger baroclinic environments at relatively high latitudes. Those that formed in the vicinity of a well-defined subtropical jet could benefit from the release of baroclinic instability. One might question whether such storms are truly “tropical.”
Lucas et al. (2014) define as tropical any location with a tropopause height greater than 14.5 km. Tory et al. (2013c) used an alternative definition for application to model data with insufficient vertical resolution to define the tropopause height. They defined the poleward extent of the tropical region by the position of the subtropical jet (STJ) at 200 hPa, and deemed any storm to have formed poleward of their estimated subtropical jet to be subtropical. As the location and structure of the tropical edge evolves from day to day, it is important to use an instantaneous rather than a fixed or seasonal definition of the tropical edge, when determining whether a storm formed in a tropical environment.
In this paper we reexamine the SST threshold concept by removing storms from the database deemed to have formed outside the tropics, using a modified version of the Tory et al. (2013c) definition of the poleward edge of the tropics. We use the same dataset as DM11, but a different methodology. While DM11 considered 1°C threshold bins (centered on integer degrees Celsius values) and counted the number of occurrences of formation over SST corresponding to each bin, we consider in this paper threshold values as points rather than bins, and count the number of storms that form on the cool side of the threshold value (i.e., the number of storms that become an exception to the threshold rule). Furthermore, we consider threshold values at 0.5°C intervals, in combination with potential gestation time periods ranging from 0 to 48 h at 6-hourly intervals. This introduces a second dimension to the SST threshold concept, such that all thresholds are presented as a SST–gestation period combination, which allows for a time lag between any surface flux–based conditional instability recovery, and the storm reaching TS intensity. Since it is not clear what that time lag should be, or how long the storm needs to be in contact with the warm sea surface, we consider a time-lag parameter space that extends to DM11’s 48 h, at 6-hourly intervals (the highest time frequency of the available data). We follow the DM11 gestation period concept and consider the threshold SST condition to be satisfied if the threshold SST is exceeded for any 6-h SST observation in the gestation period. Consequently, the SST thresholds increase with longer gestation periods, since the likelihood of the threshold being exceeded increases as the number of observation periods considered increases. For simplicity we decided to let the point source SST observation at the storm center represent the SST over the entire storm’s entropy source region. This assumes weak SST gradients in the immediate vicinity of the storm.
In the next section we revisit the DM11 results using the smaller SST intervals and a greater temperature range. In section 3 we introduce the tropical edge definition of Tory et al. (2013c) and present the results with and without the subtropical storms removed. In section 4 we consider the thresholds obtained after the removal of borderline TCs and TCs that formed under obvious baroclinic influence. The results are discussed in section 5, and the paper is summarized in section 6.
2. Dare and McBride results revisited
DM11 used the IBTrACS TC database to define 6-hourly observations of TCs globally. They considered only storms with at least one observation in which the 10-min-averaged sustained wind reached or exceeded 17 m s−1. This value is a compromise between the TS definitions used by the Regional Specialized Meteorological Centers throughout the world.3 Wind speed estimates in the IBTrACS TC database appear in 5-kt increments (1 kt ≈ 0.51 m s−1), for both 10- and 1-min-averaged winds. Using the traditional conversion factor of 0.871 to convert from 1- to 10-min-averaged winds, 35-kt 10-min-averaged winds and 40-kt 1-min-averaged winds are very similar in magnitude (18.0 and 17.9 m s−1, respectively) and are the lowest 5-kt increments that exceed the 17 m s−1 threshold. [The result does not change if the Harper et al. (2010) conversion factor of 0.93 is used.]
To exclude storms with baroclinic features, DM11 also removed any storm that was flagged to be subtropical or extratropical, or was located poleward of 35° latitude, at the time it first reached 17 m s−1. For the remaining TCs in the database, the SST at the time of formation was assessed using the NOAA/NCDC daily SST dataset, which has a grid spacing of 0.25° × 0.25° (Reynolds et al. 2007). From a population of more than 2000 TCs they found only 37 were located over water cooler than 25.5°C at the time of formation, and of these 28 had experienced SSTs greater than 25.5°C at some time in the previous 48-h gestation period.
Here, we reproduce and extend the DM11 results and present them in tabular form in Table 1. In this table we consider eight threshold values ranging from 24.5° to 28.0°C at 0.5°C intervals. Note that there were a total of 2049 storms analyzed in Table 1, but only those that formed over water less than the SST thresholds appear in the table. The number of TCs that were located over water less than each threshold temperature value at the time of formation (time = 0 h) are listed in the top row. Successive rows below list the number of TCs that were located over water less than the threshold temperature during the entire gestation period, for the range of gestation periods shown in the left column. We consider in this study the possibility that the SST threshold may need to be reached at some time closer to formation than the 48-h gestation period considered by DM11. The resulting range of possible SST and gestation period threshold combinations are evident in Table 1. Each threshold value has two columns in Table 1. Storms that fail to meet the threshold for which there is track information available over the full gestation period are included in the left column of each threshold value (labeled with “C” for complete SST history). These storms have a known SST history over the full gestation period. Storms with track data that do not extend back over the entire gestation period are listed in the right column of each threshold value (labeled with “NC” for not complete SST history). Some part of the SST history during the gestation period is unknown for these storms. This style of presentation gives readers the opportunity to draw their own conclusions regarding threshold values, and to arrive at their own threshold definitions, based on the choice of gestation period and the number of exceptions readers are willing to accept. Last we note that counts for most storms appear in multiple rows and columns, because an SST threshold exception for one threshold temperature must also be an exception for higher threshold temperatures, and a threshold exception at one gestation time period must also be an exception at all shorter gestation time periods. For illustration consider TS Arlene (1999), which experienced the highest preformation SST of 25.3°C at 24 h prior to formation, which means it was counted in the complete (C) columns for all thresholds of 25.5°C and greater, for all gestation history times between 0 and 24 h. There is no track and hence no SST data prior to this time, which means TS Arlene was also counted in the not complete (NC) columns for all thresholds of 25.5°C and greater, for gestation history times longer than 24 h.
Number of “exception” TCs out of 2049 storms in the IBTrACS database from July 1981 to December 2008 that formed over sea surfaces of temperature less than a range of SST thresholds (top row), and over a range of gestation periods (hours prior to formation). The number of exception TCs for each SST–gestation period threshold is divided into two categories. In the left position are the numbers of TCs with complete (C) track and SST data over the entire gestation period, and in the right position the number of TCs with track and SST data that is not complete (NC) over the gestation period. For a TC to be included in a particular SST–gestation period threshold position the SST threshold in the vicinity of the storm has not been exceeded at any time during the gestation period. SST–gestation period threshold combinations with the total number of storms between 1 and 10 are indicated by boldface text. Following DM11, all storms labeled as subtropical or extratropical in the IBTrACS database have been excluded, as have all storms that formed poleward of 35° latitude. The formation time is the time at which the 10-min mean wind first reaches or exceeds 17 m s−1.
For the SST < 25.5°C threshold there are 32 storms in Table 1 with SSTs at formation time (zero gestation period considered) that did not exceed this threshold. This is five less than DM11 identified, as a careful examination of the database revealed these five records were fragments of tracks associated with other storms, and were therefore discarded. All storms with track information stretching back 48 h experienced SSTs that exceeded the 25.5°C threshold at some time in the 48 h leading up to formation, and there were only six storms with less than 48-h track information prior to formation that did not have this SST threshold satisfied [25.5°C–48 h; Table 1]. Interestingly, five of those six were deemed to be subtropical using the tropical–subtropical interface definition presented in the next section, which suggests the DM11 threshold is quite robust.
Table 1 also shows that in moving from lower to higher SST threshold values, the number of storms forming at SSTs below each threshold increases slowly at the lower threshold values and rapidly increases above about 26.5°C, which is consistent with Figs. 1 and 3 of DM11. Furthermore, if one is willing to consider up to 10 exceptions (i.e., total number of C + NC storms, indicated by boldface text in Table 1) the 25.5°C SST–18-h gestation threshold is quite prominent.
3. Exclusion of nontropical storms
a. Subtropical filter
In an attempt to eliminate storms with baroclinic features, DM11 chose to exclude storms, which at the time they first exceeded 17 m s−1, were labeled subtropical or extratropical in the IBTrACS database, and storms that formed poleward of 35° latitude (hereafter we label this the DM11 subtropical filter). However, many TCs identified by McTaggart-Cowan et al. (2013) as having strong baroclinic influence at formation time were located at latitudes equatorward of 35°, and indeed equatorward of 30° latitude. Furthermore, many of these were not identified in the IBTrACS database as subtropical or extratropical, which means storms that are potentially strongly baroclinic and of questionable tropical origins were included in the DM11 analysis.
It is clear that a fixed latitude for defining the tropical–subtropical interface is not ideal (e.g., Tory et al. 2013c), especially for climate change studies where tropical expansion is a likely possibility in a warming climate (e.g., Lucas et al. 2014; Kossin et al. 2014). Thus, a dynamically based definition is arguably more appropriate for SST threshold studies. In this paper we use the tropical–subtropical interface definition of Tory et al. (2013c) with some minor modifications. In Tory et al. (2013c) the intention was to identify the STJ axis and use that to define the poleward edge of the tropics. However, for strong and broad STJs, the jet axis was often located hundreds of kilometers poleward of where the tropopause began to slope downward (i.e., hundreds of kilometers from the edge of the subtropical baroclinic zone). In this paper we define the poleward edge of the tropics to be the lowest latitude, poleward of 7° (to avoid incorrectly identifying monsoon jets as subtropical), with a 200-hPa wind speed equal to or exceeding 25 m s−1. [This brings the tropical edge slightly more equatorward compared to the definition used by Tory et al. (2013c).] An additional condition used requires the 200-hPa zonal component of the wind to exceed +5 m s−1.
The latitude of the poleward tropical edge was calculated in European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) data for each 6-h time period and each longitude. If the observed TC track was found to be poleward of any part of the “tropical edge” within ±1° longitude of the storm, at any time during the 48 h prior to the formation time, the TC was deemed to be subtropical and excluded from the analysis. Hereafter, we refer to this method for separating tropical from subtropical storms as the STJ subtropical filter.
Table 2 provides a comparison of the number of storms that fall into the various categories used to identify tropical and subtropical storms using the DM11 and STJ subtropical filters. The columns in Table 2 contain the IBTrACS categories plus the excluded storms that failed to meet the latitude threshold of DM11, while the rows represent the tropical and subtropical storms as defined by the STJ subtropical filter. The numbers in boldface (italic) text indicate the number of storms in each category in which there is agreement (disagreement) in the subtropical–tropical designation. Interestingly about ¼ of the storms flagged to be subtropical or extratropical in the IBTrACS database were not identified as subtropical by the STJ subtropical filter; that is, this relatively large proportion of flagged storms was located equatorward of the objectively determined STJ at the formation time. One can also see from Table 2 that the tropical edge as determined by the STJ filter must often deviate from the DM11 fixed 35°-latitude tropical edge, since seven of the eight storms that DM11 excluded (poleward of 35° latitude) were deemed to be tropical by the STJ filter, and eight storms identified as subtropical by the STJ filter formed equatorward of 35° latitude.
Comparison of storm categorization used to separate tropical from subtropical storms by DM11 and this study. The DM11 categories are based on the IBTrACS storm categories and the formation latitude: NR is not reported; DS is disturbance; TS is tropical in nature; SS is subtropical; and ET is extratropical. Only the TS category was separated into storms that formed on either side of 35° latitude, because all of the NR and DS storms formed equatorward of 35°, and the SS and ET storms were considered to be subtropical by DM11 regardless of formation latitude. Boldface numbers indicate agreement between the two methods for separating tropical and subtropical storms, and italic numbers indicate disagreement.
b. Impact of the DM11 and STJ subtropical filters
To give an indication of how the exclusion of subtropical storms affects the results, we show in Table 3 the number of threshold exceedances with all storms included, and in Table 4 the results with subtropical storms excluded using the STJ filter. The impact of excluding the DM11 subtropical storms can be ascertained from a comparison between Tables 1 and 3, and the impact of excluding the STJ-determined subtropical storms can be ascertained from a comparison with Tables 4 and 3. This latter comparison shows that 24 of the 31 storms that were located over water cooler than 24.5°C at the formation time in Table 3 were subtropical. Furthermore, all of the 22 (=9 + 13; 1.0%) storms located over water that did not exceed 24.5°C during the entire 18 h prior to formation were subtropical. A comparison of Table 3 with Table 1 shows that the DM11 subtropical filter eliminated fewer storms that formed over cooler SSTs than the STJ subtropical filter. Table 4 shows that there is only one exception to the DM11 conclusion that the SST threshold for TC formation is >25.5°C at some time in the previous 48 h. If we assume the STJ subtropical filter is superior to the DM11 equivalent, then Table 4 suggests the DM11 conclusion is actually more robust than they showed (cf. with the six exceptions for the 25.5°C SST–48-h gestation threshold in Table 1). An examination of the individual storms showed that the one exception in Table 4 is TS Arlene (1999), which actually formed quite close to the STJ (but not close enough to be eliminated by the objective STJ subtropical filter). With this storm removed, the 25.5°C SST–42-h gestation threshold would be true (i.e., zero exceptions to the rule) for all remaining storms in the database.4 Indeed, if we remove Barry (1995), which formed downstream of an amplifying 200-hPa trough, and Malakas (2004), a very weak, short-lived TC that formed close to the STJ, a 25.5°C SST–24-h gestation threshold would be valid.
As in Table 1, but for the entire IBTrACS database (2100 storms) from July 1981 to December 2008.
As in Table 3, but for TCs in the IBTrACS database from July 1981 to December 2008, with the exception of the 47 storms that formed poleward of the objectively determined subtropical jet (defined in section 3). SST–gestation period threshold combinations with total number of storms between 0 and 10 are identified by boldface text.
Again if one is willing to consider up to 10 exceptions (i.e., total number of C + NC storms, indicated by boldface text in Table 4) the 26.0°C SST–24-h gestation threshold is quite evident. However, 10 exceptions represent only 0.5% of the total number of storms in the database for the period examined. A greater number of exceptions might be expected given the following: imperfect storm intensity and location estimates, SST errors, and errors in the assumption that point SST values near the diagnosed storm center are representative of the storm as a whole. As it is difficult to determine the expected number of exceptions due to these combined errors, we instead make note of the number of exceptions for the 26.5°C-SST threshold with gestation periods of 48, 24, 12, and 6 h. Expressed as a percentage of the total number of storms analyzed, these are 0.7%, 1.4%, 2.6%, and 4.0%, respectively. An alternative to just accepting a certain exception percentage is to individually assess the exception storms. This is considered in the next section.
4. Exclusion of borderline TCs and baroclinic storms
The selective removal of borderline TCs, or TCs with suspected baroclinic influences (not identified by the STJ subtropical filter) discussed in the previous section, raises the following question: how many other borderline TCs or TCs with potentially significant baroclinic origins should perhaps be eliminated from the analysis? To identify these suspect TCs, a laborious and time-consuming manual analysis of more than 2000 storms would be required. Instead, we begin by manually investigating those storms that if eliminated would have an influence on the results, by considering progressively higher SST thresholds and shorter gestation periods, until we encounter storms with no obvious reasons for elimination. In total we consider the 28 (=22 + 6; 1.4%) storms that appear in the 26.5°C SST–24-h gestation threshold position in Table 4. These storms are listed in Table 5, with the possible reasons for their exclusion listed as codes, which are defined in Table 6.
List of TCs that have been considered for exclusion from the analysis. (The exclusion codes refer to reasons for excluding the storms given in Table 6.) Explanations for the IBTrACS rating codes (rightmost column) are given in the caption of Table 2. Storms in this table that were excluded in the DM11 analysis and the reason for their exclusion are indicated by boldface text. Note that the storm name Josephine was used twice for the North Atlantic basin storms.
List of potential reasons for excluding storms from the analysis, grouped into three categories: 1) the first five reasons represent borderline and thus minimal threat TCs, 2) the next two reasons represent TCs with likely baroclinic influences to their development, and 3) the last two reasons represent storms that have no or minimal circulation evident in ERA-Interim data, which suggests they are either too small to have been resolved, or that they have been declared before a coherent deep vortex has developed or the location data is incorrect.
With Barry (1995) and Arlene (1999) removed, all remaining storms in the database satisfy the 26°C SST–48-h gestation threshold (not shown). So we skip this threshold and consider next the 26.5°C threshold. One can see from Table 4 that there are 14 (=5 + 9) storms that do not satisfy the 26.5°C SST–48-h gestation threshold. These storms, which include Barry (1995) and Arlene (1999), are listed in the first 14 rows of Table 5. (The five C storms are listed first followed by the nine NC storms.) The manual analysis of these storms identified doubts regarding their validity as TCs, and/or whether they were free from strong baroclinic influences that might negate the validity of the SST threshold. The arguments for excluding the storms in Table 6 have been grouped into nine categories. Categories 1–5 relate to weak or short-lived storms that could fall into the error margins of the subjective process of declaring TCs. Categories 6 and 7 identify TCs with likely baroclinic influences, and categories 8 and 9 are TCs that had little or no evidence of their circulation in the lower and/or middle troposphere in the ERA-Interim data, using the Okubo–Weiss–zeta (OWZ)5 thresholds of Tory et al. (2013d) to define the circulation. These OWZ values are weaker than would be expected in a marginal TC. The reason why the relevant circulation patterns are not apparent in the reanalysis data is uncertain. It is possible that the storms were legitimate, but too small to be adequately resolved in the reanalysis wind data at 850 and/or 500 hPa. Other possibilities, although less likely, might be incorrect TC identification or errors in the track location data.
An updated threshold table with the 14 storms removed is presented in Table 7, where it can be seen that a number of potential SST–gestation period threshold combinations exist (i.e., the shortest gestation period for each SST threshold column that has zero entries in the table). These SST–gestation period threshold combinations are: 24.5°C–18 h, 25.0°C–24 h, 25.5°C–30 h, 26.0°C–42 h, and 26.5°C–48 h. Table 7 shows that there are only six storms that exceed the 26.5°C SST–36-h gestation threshold. These six are located in rows 15–20 of Table 5. There are potential reasons for excluding all six and multiple reasons for five of the six. When the six storms are excluded, only 8 (=14 − 6) storms remain that exceed the 26.5°C SST–24-h gestation threshold (rows 21–28 in Table 5). However, arguments could not be found for excluding two of the eight storms [Ana (1985) and Tip (1989)], which prompted an end to the progressive exclusion exercise. The threshold table with the 12 storms removed is provided in Table 8, which offers five potential SST–gestation period threshold combinations: 24.5°C–6 h, 25.0°C–12 h, 25.5°C–18 h, 26.0°C–24 h, and 26.5°C–36 h. If two exceptions [Ana (1985) and Tip (1989)] are allowed, the gestation period for the final combination is reduced by 12 h (i.e., 26.5°C SST–24 h). Table 8 also shows that ever-increasing number of exceptions need to be found if the SST thresholds are to be raised and gestation periods reduced further. Thus, we conclude that reasonable arguments can be made for SST thresholds up to 26.5°C, but not above.
As in Table 4, but with the 14 storms that are counted in the 48-h gestation row (C + NC) of the 26.5°C threshold column of Table 4 (these are the first 14 storms in Table 5) excluded.
As in Table 7, but with the exception of 12 of the 14 storms that are counted in the 24-h gestation row of the 26.5°C threshold column in that table (i.e., these are the last 14 storms in Table 5, with the exception of Ana and Tip). The contribution of Ana and Tip to the 26.5°C threshold at −24 and −30 h is indicated by an asterisk.
The impact on SST thresholds from the exclusion of, first, the storms that formed poleward of the STJ and, then, the borderline and baroclinic storms is summarized in Fig. 1, which shows the number of TCs that form below a range of threshold SST values for the 24- (Fig. 1a) and 48-h (Fig. 1b) gestation periods. Figure 1 is especially useful for identifying practical SST thresholds, in which small number of exceptions might be considered. Figure 1 shows that any threshold that does exist, when all TCs in the IBTrACS database are considered (thin solid line; data from Table 3), must be less than 24.5°C as the line does not cross the abscissa for either gestation period. Applying the STJ filter (dashed line, data from Table 4), one can see that the DM11 threshold of 25.5°C with a 48-h gestation period (Fig. 1b) is valid and almost valid for a 24-h gestation period (Fig. 1a). Removing the first 14 storms in Table 5 from the analysis (dotted line, data from Table 7) raises the SST threshold with a 48-h gestation period by about 1°C (cf. the dotted and dashed lines in Fig. 1b), but has little impact on the thresholds with a 24-h gestation (Fig. 1a). Removing the final 12 storms (thick solid line, data from Table 8) has a significant impact on the SST threshold with a 24-h gestation period (cf. the thick solid with the dashed line in Fig. 1a), but no impact on the SST threshold with a 48-h gestation period (Fig. 1b).
Number of storms that form over sea surfaces cooler than the threshold SST values for (a) 24- and (b) 48-h gestation periods. The thin solid line includes all storms in the IBTrACS database that exceed 17 m s−1. The dashed line includes all storms after the STJ filter has been applied (see section 3), and the dotted and thick solid lines represent all storms after the STJ filter has been applied minus the 14 and 26 storms removed, respectively, discussed in section 4 and listed in Table 5.
Citation: Journal of Climate 28, 20; 10.1175/JCLI-D-14-00637.1
The thresholds obtained from Table 8, after the STJ filter was applied and the 26 storms removed, are illustrated in Fig. 2 for gestation periods ranging from 0 to 48 h at 12-h intervals. If one is willing to accept a small number of storms failing to meet the SST thresholds, then 25° and 26°C become practical SST thresholds for 0- and 12-h gestation periods, respectively, and 26.5°C becomes a practical threshold for 24-h gestation and longer. Figures 1 and 2 also help illustrate the large number of exceptions that would be required before a 27.0°C threshold could be considered.
Number of storms that form over sea surfaces cooler than the threshold SST values for all remaining storms after the STJ filter has been applied minus the 26 storms listed in Table 5 that have been removed (i.e., data from Table 8). Each line represents a gestation period between 0 and 48 h at 12-h intervals.
Citation: Journal of Climate 28, 20; 10.1175/JCLI-D-14-00637.1
5. Discussion
All storms in the IBTrACS database that reached the 17 m s−1 wind speed threshold (2100 storms in this study) are potentially dangerous, including the subtropical and hybrid storms. These latter storms can develop over sea surfaces at temperatures much less than 26.5°C. For example, 31 (1.5%) storms were located over sea surfaces less than 24.5°C at the formation time, and 19 (=2 + 17; 0.9%) of these had not experienced SST in excess of 24.5°C at any point along their recorded track in the previous 48 h (Table 3). Fortunately, these storms only account for a small fraction of the database. An understanding of the position of the subtropical jet during the formation of all but 5 of these 31 storms would flag the potential for baroclinic assistance in their development [24 identified by the STJ subtropical filter, and 2 identified manually to be close to the subtropical jet: the unnamed storm labeled D19798:HSK2498 (1998) and Malakas (2004) that were also weak and short lived]. Of the above five exception storms, two experienced SST > 26.5°C in the previous 24 h, and from Table 5 we can see that of the remaining three storms one was barely a TC [Josephine (2002)] and two had subjectively determined baroclinic influences [Barry (1995) and the unnamed storm labeled 0720002001 (2001)]. The further elimination from consideration of the remaining storms in Table 5 identifies a 26.5°C SST–36-h gestation threshold. However, with only two exceptions [Ana (1985) and Tip (1989)] a 26.5°C SST–24-h gestation threshold might be considered more practical.
Returning to the complete IBTrACS database (Table 3), one can see that in reaching the 26.5°C SST–24-h gestation threshold, a total of 60 (=34 + 26; 2.9%) storms were excluded or excused from the analysis. The application of the STJ subtropical filter excluded 32 (1.5%) of these 60 storms (cf. Tables 3 and 4) and the subjective assessment of the remaining 28 (=22 + 6) storms led to arguments for excluding 26 (1.2%), based on the storms being either questionable TCs or having suspected baroclinic assistance in their formation.
These results suggest that an analysis of SST in the vicinity of persistent cloud clusters could offer useful insight into TC formation potential. If the SST has exceeded the 26.5°C threshold, then TC formation within 24 h is a possibility. For SST less than the threshold an analysis of the 200-hPa wind field could offer useful insight into whether a dangerous storm has the potential to develop by tapping into baroclinic potential energy.
6. Summary
There are many references to a SST threshold for TC formation of 26°–27°C in the literature (e.g., Gray 1968; Dengler 1997; Rodgers et al. 2000; Tory and Frank 2010). This threshold was based on Palmén’s (1948) visual comparison of the warm-season SST distribution and TC formation maps of the time. The threshold was further refined to 26.5°C by Gray (1968) in what appears to be an arbitrary decision to use the average value of Palmén’s threshold temperature range. However, it is only recently that the SST threshold was first tested by examining the SST in the vicinity of TC formations (DM11). Of more than 2000 storms investigated, DM11 found numerous cases of TC formation over SSTs below the Palmén threshold (reproduced in our results presented in Table 3).
The SST threshold concept is based on the assumption that the developing TC sources the majority of its energy from the release of lower-troposphere conditional instability, which must be replenished by the heat and moisture fluxes from the underlying sea surface. At SSTs less than some threshold it is assumed that the energy transfer from the sea to the atmosphere is not sufficient to maintain sufficiently deep convection on the spatial and temporal scales necessary to power TC formation. It follows that storms that are supplemented by energy from the release of baroclinic instability are capable of forming over sea surfaces cooler than the threshold temperature, which suggests the SST threshold concept applies only to developing storms with minimal baroclinic influence.
Here, we have reexamined the SST threshold of DM11 using their subtropical filter, and compared the SST threshold results that emerge after applying the STJ subtropical filter. The DM11 subtropical filter eliminated storms flagged as subtropical or extratropical in the IBTrACS TC database, in addition to storms that formed poleward of 35° latitude, whereas the STJ subtropical filter eliminated storms forming on the poleward side of the STJ. Both methods considered only storms that exceeded 17 m s−1 at some point in their lifetime. The DM11 conclusion of a 25.5°C-SST threshold encountered at some time in the 48 h prior to formation was found to be robust. The concept of SST threshold coupled with a gestation period was introduced to describe this type of threshold.
After applying the STJ subtropical filter the DM11 25.5°C SST–48-h gestation threshold was found to be even more robust (i.e., fewer exceptions in Table 4 than in Table 1). Furthermore, Table 4 showed that other SST–gestation period combinations are valid: 24.5°C–18 h, 25.0°C–36 h, and with one exception 25.5°C–42 h.
Recognizing that the simple STJ subtropical filter is not perfect and that some of the weak and short-lived TCs in the database perhaps never reached TC intensity [because of the somewhat subjective application of the Dvorak (i.e., Dvorak 1973) technique for assessing TC intensity], we reassessed the thresholds after considering more exceptions. Arguments were presented to exclude 26 storms as either questionable TCs or having suspected baroclinic assistance in their formation. The resulting SST–gestation period threshold combinations are as follows: 24.5°C–6 h, 25.0°C–12 h, 25.5°C–18 h, 26.0°C–24 h, and 26.5°C–36 h. The latter combination would be reduced to a 24-h gestation but for the presence of two storms [Ana (1985) and Tip (1989)], in which we found no obvious reason for exclusion.
This study supports the long-held notion of the 26.5°C-SST threshold necessary for TC formation, provided the storm is not receiving significant additional energy from the release of baroclinic instability. However, this threshold only emerges after consideration of a TC formation gestation period of about 24 h.
Acknowledgments
We thank Sally Lavender and Noel Davidson, for their contributions in reviewing an early draft of this paper, and two anonymous reviewers, whose suggestions greatly improved the clarity of the central message.
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Gray (1968) cited Palmén (1948) and Palmén (1956) as the source of the 26.5°C SST necessary condition for TC formation (p. 675), although we could not find this specific value in those papers.
The wind speed threshold that defines the TS differs between TC warning centers, and ranges from about 15 to 17 m s−1 when expressed as a 10-min-averaged sustained wind.
A 10-min-averaged sustained wind of 34 kt (17.5 m s−1) is used to define the following: tropical storms in the northwestern Pacific by the Japanese Meteorological Agency, category-1 tropical cyclones in the Australian region and the South Pacific, moderate tropical storms in the southwestern Indian Ocean, and cyclonic storms in the northern Indian Ocean. A 1-min-averaged sustained wind of 34 kt (15.2 or 16.7 m s−1 depending on the conversion factor used to convert to 10-min-averaged wind) is used to define tropical storms in the North Atlantic and the northeastern Pacific and is used by the Joint Typhoon Warning Center in the northwestern Pacific.
Note that these tables are constructed such that storms are counted in more than one column, and the “1” for each entry in the NC column of the 25.5°C threshold represents TS Arlene.
OWZ, which is a function of the Okubo–Weiss parameter (Okubo 1970; Weiss 1991), has been used by Tory et al. (2013a–d) to identify regions of enhanced absolute vorticity in low-deformation flow (i.e., flow in near-solid-body rotation). The core of any TC should contain enhanced values of OWZ greater than the thresholds used by Tory et al.
