formulate the hypothesis of tropical cyclone

1. Introduction
a. Experimental setup
b. Tracking algorithm
c. Vorticity budget
3. General overview of the simulations
a. Midtropospheric vortex structure and evolution
b. Vorticity budget
c. The importance of the upshear-left quadrant
5. Summary, hypothesis, and open questions

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Time series of (a) maximum 10-m wind speed, (b) symmetricity, and (c) number of convective bursts (CBs) after applying a 6-h running mean for each ensemble member (gray), the early member (green), and the late member (purple). Dots indicate the onset of intensification. See text for details about symmetricity and CBs.

Domain-centered simulated composite reflectivity below 1.5 km (shading; every 5 dB Z ) for (a)–(d) the early and (e)–(h) the late members. Panels show (a),(e) 24, (b),(f) 72, (c),(g) 84, and (d),(h) 102 h. Shear direction is indicated at the lower-left corner of each panel.

(a) Evolution of the 400–900-hPa tilt vector after applying a 6-h running mean from 1 h until the onset of intensification of each member. Dots appear every 24 h, dashed circles are every 50 km, and stars appear at the onset of intensification of each member. (b),(c) Comparison of onset of intensification against (b) duration and (c) average magnitude of downshear left tilt (defined as a mathematical tilt angle between 0° and 90°). Colors are as in Fig. 1 .

Azimuth–time evolution of (a),(c),(e) 400-hPa absolute vorticity (shading; every 1 × 10 −4 s −1 ); (b),(d),(f) saturation fraction (shading; every 0.025); and total column condensate (contours; plotted at 0.5, 1.0, 5.0, 10.0, and 20.0 mm) averaged within a 50-km-wide ring centered on the total column rain centroid for (a),(b) the early member, (c),(d) the late member, and (e),(f) the ensemble mean with respect to the onset of each member. Thick black lines mark the onset of intensification. A 6-h running mean was applied. Azimuths are defined with respect to the 200–850-hPa shear vector and represent the following: DR (315°), DL (45°), UL (135°), and UR (225°).

Vertical cross sections of absolute vorticity (shading; every 0.3 × 10 −3 s −1 ) and diabatic heating (contours; only plotted at 5 K h −1 ) along the 400–900-hPa tilt vector and centered on the 900-hPa center of circulation of the early member. Distance increases from point A to point B as indicated by the insets on the lower-left corner of each panel. Panels show 6-h-averaged fields with a center time of (a) 36, (b) 60, (c) 82, and (d) 97 h.

Pressure–time depiction of absolute vorticity (shading; every 1 × 10 −4 s −1 ) and density potential temperature anomaly (contours; every 0.5 K) averaged within a 50-km radius from the midtropospheric center of circulation for (a) the early member, (b) the late member, and (c) the ensemble mean with respect to the onset of intensification of each member. Thick solid lines mark the onset of intensification and thick dashed lines mark the arrival of the midtropospheric vortex to upshear left. A 6-h running mean was applied.

As in Fig. 6 , but for vertical mass flux (shading; every 0.05 kg m −2 s −1 ) and equivalent potential temperature (contours; every 2.5 K).

Pressure–time depiction of area-averaged vorticity tendencies (shading; every 1.25 × 10 −5 s −1 ) following the midtropospheric vortex of (a),(c),(e),(g),(i) the early and (b),(d),(f),(h),(j) the late members. Panels show (a),(b) the actual vorticity tendency calculated from center differentiation, (c),(d) the sum of individual tendencies, (e),(f) the combination of mean stretching and friction, (g),(h) eddy vorticity flux, and (i),(j) tilting of horizontal vorticity. Thick solid lines mark the onset of intensification and thick dashed lines mark the arrival of the midtropospheric vortex to upshear left.

As in Fig. 8 , but for the tendencies with respect to the lower-tropospheric center of circulation.

Horizontal snapshots of 500–700-hPa layer-averaged vertical velocity (shading; every 10 Pa s −1 ) and horizontal vorticity (vectors) centered on the 900-hPa center at (a) 60 and (b) 90 h. Black dots indicate the positions of the 400-hPa center. (c) As in (a) and (b), but centered on the 900-hPa center at 81 h. (d) Horizontal snapshot of 950-hPa absolute vorticity (shading; every 0.3 × 10 −3 s −1 ) and storm-relative winds (vectors) centered on the 900-hPa center at 81 h. Black boxes depict the vorticity budget integration domain relative to the midtropospheric center in (a) and (b) and the lower-tropospheric center in (c) and (d). Shear direction is indicated at the lower-left corner of each panel. Notice the different domains in (a) and (b).

(a)–(c) Horizontal snapshots of 900-hPa nondivergent winds (black arrows), 400-hPa nondivergent winds (magenta arrows), 900-hPa radial wind (shading; every 5 m s −1 ), and 400–900 layer-averaged vertical velocity exceeding 1 m s −1 (gray shading) centered on the lower-tropospheric center of the early member at (a) 60, (b) 82, and (c) 97 h. (d)–(f) As in (a)–(c), respectively, but for 900-hPa irrotational winds (black arrows) and absolute vorticity (shading; 10 −3 s −1 ). Black boxes depict the vorticity budget integration domain following the midtropospheric vortex. Shear direction is indicated at the lower-left corner of each panel.

Time–radius depiction of azimuthally averaged eddy radial vorticity flux (shading; every 0.625 m s −1 h −1 ) averaged below 1-km height of (a) the early and (b) the late members. (c) Ensemble distributions of eddy radial vorticity flux averaged below 1-km height and within a 50-km radius from the lower-tropospheric center of each member. Standard boxplots are used, where whiskers indicate minima and maxima, boxes extend from the 25th to the 75th percentiles, and middle lines depict the medians.

Ensemble-mean CFADs of vertical mass flux (shading; % in a semilogarithmic scale) during a 12-h period when the midtropospheric vortex is (a) UL or (b) DL in each member. (c) The differences between (a) and (b).

Pressure–azimuth depiction of backward trajectories released from 300 hPa at (a),(c) 82 h of the early member and (b),(d) 117 h of the late member for (a),(b) buoyant and (c),(d) dynamic accelerations (shading; every 0.025 m s −1 ) along the trajectories only during parcel ascent. Black lines indicate the location from where parcels were released. Distance is given relative to the midtropospheric center, where negative (positive) values represent azimuthally upwind (downwind) distance.

Pressure–azimuth depiction of backward trajectories released from 900 hPa and within a 50-km radius from the midtropospheric vortex of the early member. Colors depict equivalent potential temperature (shading; every 2 K) for parcels released backward at (a) 66 and (b) 84 h. (c) Ensemble distributions of downward entropy fluxes averaged below 900 hPa and within a 50-km radius from the midtropospheric center. Standard boxplots are used, where whiskers show the minima and maxima, boxes extend from the 25th to the 75th percentiles, and middle lines depict the medians.

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A Hypothesis for the Intensification of Tropical Cyclones under Moderate Vertical Wind Shear

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A major open issue in tropical meteorology is how and why some tropical cyclones intensify under moderate vertical wind shear. This study tackles that issue by diagnosing physical processes of tropical cyclone intensification in a moderately sheared environment using a 20-member ensemble of idealized simulations. Consistent with previous studies, the ensemble shows that the onset of intensification largely depends on the timing of vortex tilt reduction and symmetrization of precipitation. A new contribution of this work is a process-based analysis following a shear-induced midtropospheric vortex with its associated precipitation. This analysis shows that tilt reduction and symmetrization precede intensification because those processes are associated with a substantial increase in near-surface vertical mass fluxes and equivalent potential temperature. A vorticity budget demonstrates that the increased near-surface vertical mass fluxes aid intensification via near-surface stretching of absolute vorticity and free-tropospheric tilting of horizontal vorticity. Importantly, tilt reduction happens because of a vortex merger process—not because of advective vortex alignment—that yields a single closed circulation over a deep layer. Vortex merger only happens after the midtropospheric vortex reaches upshear left, where the flow configuration favors near-surface vortex stretching, deep updrafts, and a substantial reduction of low-entropy fluxes. These results lead to the hypothesis that intensification under moderate shear happens if and when a “restructuring” process is completed, after which a closed circulation favors persistent vorticity spinup and recirculating warm, moist air parcels.

A major impediment of accurate tropical cyclone (TC) forecasts is the interaction of TCs with environmental vertical wind shear (VWS). Although VWS is one of the most inhibiting factors of TC intensification ( Merrill 1988 ; DeMaria and Kaplan 1994 ; Paterson et al. 2005 ; Hendricks et al. 2010 ), TCs can intensify under VWS magnitudes that are neither too weak nor too strong (moderate shear hereafter; Molinari et al. 2004 , 2006 ; Molinari and Vollaro 2010 ; Montgomery et al. 2010 ; Foerster et al. 2014 ; Stevenson et al. 2014 ; Rios-Berrios et al. 2016b , a ; Zawislak et al. 2016 ; Rios-Berrios and Torn 2017 ; Nguyen et al. 2017 ). Consequently, intensity changes are more difficult to predict for moderate VWS scenarios than for weak or strong VWS ( Bhatia and Nolan 2013 ; Finocchio and Majumdar 2017 ). This issue represents a major forecasting challenge as recognized by a former hurricane specialist who stated that “one of [their] biggest challenges is trying to sort out what’s going to happen at intermediate levels of shear ” ( Sumwalt et al. 2017 , p. 3). Motivated by this challenge and its important implications, this study aims at identifying physical processes preceding TC intensification under moderate VWS.

Several theories exist to explain TC intensification; however, various limitations prevent their applications to the TC–VWS problem. Most theories describe intensification as a feedback between surface fluxes, near-surface convergence of energy and angular momentum, and latent heat release ( Ooyama 1964 , 1969 , 1982 ; Charney and Eliassen 1964 ; Emanuel 1986 ). Such feedback, however, is based on an axisymmetric view of mature TCs. An alternate paradigm was proposed by Van Sang et al. (2008) to account for asymmetric features manifest as buoyant, rotating updrafts. According to that paradigm, intensification follows the merger and symmetrization of vertical vorticity associated with those updrafts. The resulting vortex structure aids intensification via concentrated near-surface convergence and latent heat release within a closed circulation ( Van Sang et al. 2008 ; Smith et al. 2017 ). Sheared TCs are characterized by asymmetric moisture distributions and asymmetric secondary circulations ( Reasor et al. 2013 ; DeHart et al. 2014 ; Rios-Berrios and Torn 2017 ), which may influence the symmetrization process or may hinder the feedback between near-surface convergence and latent heat release (e.g., Molinari et al. 2004 , 2013 ).

Existing theories can be expanded to VWS scenarios by hypothesizing that sheared TCs must overcome the effects of VWS (e.g., tilt, asymmetric precipitation) in order to establish robust tangential and overturning circulations capable of driving intensification. Molinari et al. (2004) identified such evolution from aircraft observations of Hurricane Danny (1997) under shear magnitudes between 5 and 11 m s −1 . Intensification happened when individual rotating updrafts merged into a dominant surface vortex and the equivalent potential temperature θ e exhibited a dramatic radial gradient. Their results led to the proposal of a two-stage process explaining intensification under VWS. During the first stage, the asymmetric TC is characterized by buoyant updrafts as well as strong downdrafts that flood the boundary layer with cool, dry air. Intensification happens during the second stage because near-surface convergence and deep latent heat release happen within the high- θ e region of a symmetric, closed surface circulation.

Although this two-stage process has not been further explored, other studies agree that symmetrization of precipitation is a key process preceding intensification under moderate VWS. Sheared TCs are characterized by a wavenumber-1 precipitation asymmetry, with updrafts dominating in the downshear half and downdrafts in the upshear half ( Corbosiero and Molinari 2002 ; Chen et al. 2006 ; Hence and Houze 2011 ; Reasor et al. 2013 ; DeHart et al. 2014 ). Consequently, an azimuthal extension of precipitation from downshear to upshear is a hallmark of intensifying TCs under moderate VWS ( Rappin and Nolan 2012 ; Ge et al. 2013 ; Onderlinde and Nolan 2014 , 2016 ; Tao and Zhang 2014 ; Finocchio et al. 2016 ; Rios-Berrios et al. 2016a ; Zawislak et al. 2016 ; Nguyen et al. 2017 ). Such extension is often preceded by deep convective updrafts in the upshear-left quadrant (e.g., Stevenson et al. 2014 ; Chen and Gopalakrishnan 2015 ; Rogers et al. 2016 ; Rios-Berrios et al. 2016b , a ; Smith et al. 2017 ; Wadler et al. 2018 ). An outstanding issue is what drives symmetrization; possible explanations include vortex alignment (e.g., Zhang and Tao 2013 ) or humidification of the upshear half (e.g., Rios-Berrios et al. 2016a ; Rios-Berrios and Torn 2017 ). However, those processes could be the result—rather than the cause—of the azimuthal extension of precipitation.

Another outstanding issue, not accounted for in the two-stage process of Molinari et al. (2004) , is the role of vortex tilt during intensity changes of sheared TCs. Vortex tilt emerges after the center of circulation is displaced along a vertical axis by the sheared environmental flow. This VWS effect limits ascent above the lower-tropospheric center of circulation via thermodynamic stabilization ( Jones 1995 ; DeMaria 1996 ) or via cool, dry air fluxes ( Riemer et al. 2010 ; Tang and Emanuel 2012 ; Riemer and Laliberté 2015 ). Consequently, another hallmark of intensifying TCs under moderate VWS is a small vortex tilt ( Davis et al. 2008 ; Reasor and Eastin 2012 ; Rappin and Nolan 2012 ; Ge et al. 2013 ; Zhang and Tao 2013 ; Onderlinde and Nolan 2014 ; Tao and Zhang 2014 ; Finocchio et al. 2016 ; Munsell et al. 2017 ; Leighton et al. 2018 ). In some cases, however, intensification begins when the vortex is tilted (e.g., Raymond and López Carrillo 2011 ; Stevenson et al. 2014 ; Rios-Berrios et al. 2016b ) or when a new, vertically aligned vortex emerges within shear-organized convection ( Molinari et al. 2004 , 2006 ; Davis et al. 2008 ; Molinari and Vollaro 2010 ; Nguyen and Molinari 2015 ). Those discrepancies suggest that not all TCs follow the same pathway to intensification under moderate shear or that intensification is favored by a combination of factors including, but not limited to, a small vortex tilt. Explaining how and why a TC vortex realigns, remains vertically aligned, or reforms under VWS is of utmost importance ( Jones 1995 ; Reasor et al. 2004 ; Reasor and Montgomery 2015 ; Elsberry and Park 2017 ; Rogers et al. 2017 ). Equally important is clarifying why intensification is more likely when the vortex is aligned than when it is tilted.

These open issues motivate this study, with the purpose of diagnosing physical processes preceding TC intensification under moderate VWS. An ensemble of idealized simulations, described in section 2 , was employed to diagnose processes from multiple realizations of the same TC with prescribed environmental conditions and without complexities added by external factors (e.g., upper-tropospheric disturbances, land interactions). The ensemble confirms that small vortex tilt and symmetric precipitation are necessary conditions for intensification ( section 3 ). A detailed analysis focused on a midtropospheric vorticity maximum ( section 4 ), shows a two-stage process akin to the hypothesis of Molinari et al. (2004) combined with the vortex merger paradigm of Van Sang et al. (2008) . The results lead to the hypothesis ( section 5 ) that intensification in sheared environments follows after deep updrafts initiate a “restructuring” process, consisting of a transition from strong, yet asymmetric ascent in the vicinity of a midtropospheric vortex to nearly symmetric ascent within a vertically aligned, closed circulation. Intensification follows thereafter because the resulting TC structure promotes a feedback between near-surface convergence and ascent within a closed circulation.

Simulations with the modified Rankine vortex were integrated forward using the Weather Research and Forecasting (WRF; Skamarock et al. 2008 ) Model, version 3.4.1. Three nested domains were used with grid spacing of 18, 6, and 2 km, respectively, and horizontal domains of 4320 km × 4320 km, 2160 km × 2160 km, and 720 km × 720 km, respectively. Both innermost domains followed the TC throughout the simulation. All domains contained 40 vertical levels with a model top around 56 hPa. Several tests with different domain sizes and vertical resolutions showed only small sensitivities to those specifications. A cumulus parameterization was not used in any domain because the 2-km domain covered the main region of precipitation. Radiative feedbacks were not included, but a forthcoming publication will explore the sensitivity of results to radiation. All other physics parameterizations are listed in Table 1 .

Physics parameterizations employed in the WRF idealized simulations.

Environmental winds were kept constant during the integration to isolate structural changes of a TC-like vortex within a specific environment. Nolan (2011) introduced the point downscaling method, which keeps constant environmental winds by applying the Coriolis torque only onto the perturbation winds. Point downscaling was applied here, in combination with analysis nudging, to retain the initial environmental wind profile in the 18-km domain, while allowing all fields to evolve in the 6- and 2-km domains. A drawback of this method is that the environment is not adjusted for thermal wind balance. Another drawback is that constant wind profiles are not realistic representations of observed TC environments ( Rios-Berrios and Torn 2017 ); however, constant wind profiles were used here to eliminate processes associated with the evolving environment. TC intensification within temporally evolving environments should be explored in the future to confirm the findings of this work in a more realistic framework.

An ensemble of 20 idealized simulations was generated to account for variability in the timing of intensification. Zhang and Tao (2013) demonstrated that, in a similar modeling setup as employed here, the timing of intensification varies substantially under moderate VWS magnitudes. Their approach—following from Van Sang et al. (2008) —was used here to generate the ensemble with uncorrelated, random perturbations sampled from a uniform distribution of water vapor mixing ratio between −0.5 and 0.5 g kg −1 . Random perturbations were added only below 950 hPa and within the 2-km domain. All members used the same background conditions specified by Zhang and Tao (2013) : 27°C sea surface temperature everywhere, constant planetary vorticity corresponding to 20°N, 5 m s −1 westerly VWS, and 2 m s −1 easterly surface wind. This shear magnitude is at the lower end of moderate VWS ( Rios-Berrios and Torn 2017 ), but larger magnitudes preclude intensification in this modeling setup ( Zhang and Tao 2013 ). Because of the westerly shear, storm-relative quadrants will represent the following: downshear right (DR) is southeast, downshear left (DL) is northeast, upshear left (UL) is northwest, and upshear right (UR) is southwest of the domain center.

Consistent with the findings of Zhang and Tao (2013) , the ensemble simulates an intensifying TC with large variability in the timing of intensification ( Fig. 1a ). All members exhibit a gradual intensification during the first 48 h, followed by a period of nearly steady-state intensity. Ensemble members diverge after 96 h when some members simulate rapid intensification, whereas other members simulate steady-state intensity. All members ultimately simulate rapid intensification, but there is substantial variability around the onset of intensification. Following Judt and Chen (2016) , the onset was defined as the first lead time that met two criteria: 1) the intensity over the following 24 h increased by at least 15.1 m s −1 and 2) the intensity over the following 6 h increased by at least 3.8 m s −1 (nearly equivalent to a continuous intensification of 15.1 m s −1 in 24 h). Within the ensemble, the objectively determined onset happens anywhere between 97 and 130 h (black dots in Fig. 1a ). Despite this variability, all members cluster together after intensifying and reaching their maximum simulated intensity by 192 h.

Citation: Journal of the Atmospheric Sciences 75, 12; 10.1175/JAS-D-18-0070.1

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The large variability in the onset of intensification offers an opportunity to explore why some members simulate intensification earlier than others. Following the approach of Zhang and Tao (2013) , this issue was investigated by comparing two members that predict the earliest and latest onset of intensification (early and late members hereafter). This comparison revealed that their main difference was the timing of symmetrization of precipitation ( Fig. 2 ). Domain-centered plots of composite reflectivity show that precipitation initially organizes in the downshear half of the simulated TCs ( Figs. 2a,e ), followed by a cyclonic motion around a lower-tropospheric center of circulation ( Figs. 2b,f ). These members diverge from each other as precipitation moves through the downshear-left quadrant; precipitation moves faster and, consequently, reaches upshear left sooner in the early member than in the late member ( Figs. 2c,g ). Shortly after precipitation reaches upshear left, the early member is characterized by nearly symmetric precipitation ( Fig. 2d ). The late member, however, is still highly asymmetric by 102 h ( Fig. 2h ). Intensification begins quickly after precipitation transitions from an upshear-left maximum to a nearly symmetric distribution.

The different precipitation evolutions are related to different tilt evolutions. Vortex tilt was diagnosed via the distance between the lower- and midtropospheric centers of circulation determined from the object-tracking method described in section 2 . The lower-tropospheric center was tracked at 900 hPa, whereas the midtropospheric center was tracked at 400 hPa because that level was characterized by a clear vorticity maximum within precipitation (not shown). Figure 3a shows the evolution of 400–900-hPa tilt after applying a 6-h running mean to remove short-term variability. All members simulate increasing tilt magnitude during the first 24 h, which corresponds to the timing of convective organization in the downshear half ( Figs. 2a,e ). After 24 h, the midtropospheric vortex begins an azimuthal motion through the downshear-left quadrant. The early and the late members diverge after 24 h when the midtropospheric vortex remains radially closer to the lower-tropospheric center in the early than in the late member. This small difference grows over time such that the early member reaches upshear left approximately 26 h earlier than in the late member (72 vs 98 h). The tilt magnitude quickly decreases thereafter until reaching a minimum just before the onset of intensification.

All members depict the same tilt evolution, albeit with different azimuthal motions through the downshear-left quadrant. This result is illustrated in Fig. 3b , which compares the onset of intensification against the duration of downshear-left tilt (defined as a mathematical tilt angle between 0° and 90°). A strong correlation exists between those two quantities (Pearson’s correlation coefficient of 0.97). The duration of downshear-left tilt depends on the average downshear-left tilt magnitude, resulting in a strong correlation between the onset of intensification and the average downshear-left tilt magnitude (Pearson’s correlation coefficient of 0.93; Fig. 3c ). In this study, tilt magnitude depends on the initial location of downshear convective organization, which randomly varies between members because of the initial boundary layer water vapor perturbations. Members with convective organization closer to the lower-tropospheric center of circulation develop smaller downshear-left tilts for shorter durations, thus leading to earlier onsets of intensification ( Figs. 3b,c ). This study will not explore the mechanisms governing the azimuthal tilt motion through the downshear-left quadrant; instead, the analysis will focus on the upshear-left tilt reduction that happens over a 24–32-h period in all members despite their different downshear-left tilts.

Previous modeling studies also identified symmetrization of precipitation and tilt reduction as necessary for intensification (e.g., Ge et al. 2013 ; Zhang and Tao 2013 ; Onderlinde and Nolan 2014 ; Tao and Zhang 2014 , 2015 ; Finocchio et al. 2016 ; Munsell et al. 2017 ); however, the following questions remain unanswered:

Why are upshear-left precipitation and tilt important for intensification?

What drives the symmetrization of precipitation and vortex tilt reduction?

Why is the symmetric, aligned structure more conducive to intensification than the asymmetric, tilted structure?

4. Diagnosis of physical mechanisms

A key aspect of the idealized simulations is the coevolution of precipitation and a midtropospheric vorticity maximum. This coevolution, hinted by the symmetricity and tilt diagnostics, was confirmed with a time–azimuth framework depicting averaged variables within a 50-km ring located at the radial position of the precipitation centroid at each lead time ( Fig. 4 ). A region of positive 400-hPa absolute vorticity is collocated with the asymmetric precipitation before the onset of intensification. Both fields undergo a similar evolution: A maximum first appears downshear, gradually moves through the downshear-left quadrant, accelerates in the upshear-left quadrant, and finally spreads over all azimuths just before the onset of intensification ( Figs. 4a,c,e ). This evolution happens faster in the early member than in the late member, especially because of their different evolutions through the downshear-left quadrant ( Figs. 4a,c ). An ensemble mean with respect to the onset of intensification confirms that tilt reduction and symmetrization happen in unison during the 24 h preceding intensification of all members ( Fig. 4e ).

The midtropospheric vorticity maximum emerges as a separate entity within the shear-organized convection. This result is illustrated in Fig. 5 through cross sections of 6-hourly averaged vorticity and diabatic heating along a line passing through both the lower-tropospheric and midtropospheric centers of circulation of the early member. A small-scale, nearly aligned vortex first appears within a region of large diabatic heating located 100 km away from the lower-tropospheric center ( Fig. 5a ). The small-scale vortex weakens in the lower troposphere, but a conglomerate of small-scale, positive vorticity remains with peak values around 400 hPa and latent heat release over a deep layer ( Fig. 5b ). This conglomerate of vorticity forms a mesoscale midtropospheric vortex that is detected by the tilt vector as it travels azimuthally around the lower-tropospheric center (cf. Fig. 3a ); however, this midtropospheric vortex is not directly connected to the main TC vortex in the sense of a single tilted “cylinder.” The midtropospheric vortex persists and strengthens upon reaching upshear left ( Fig. 5c ), followed by a transition to a single vertically aligned vortex before the onset of intensification ( Fig. 5d ).

Although environmental shear induces storm-scale asymmetries in strong TCs ( Corbosiero and Molinari 2002 ; Chen et al. 2006 ; Reasor et al. 2013 ; DeHart et al. 2014 ), our simulations suggest that a midtropospheric vortex modulates asymmetries in weak, sheared TCs. In addition to the vorticity and precipitation asymmetries before intensification, clear moisture asymmetries also exist as demonstrated by the vertically integrated saturation fraction ( Figs. 4b,d,f ). Near-saturated air only exists in the vicinity of the midtropospheric vorticity maximum and its associated precipitation. All other regions remain dry until symmetrization, after which time all azimuths become nearly saturated within the 50-km ring centered on the precipitation centroid of each member ( Fig. 4f ). Other kinematic and thermodynamic fields are also modulated by the presence (or lack) of the midtropospheric vortex in each quadrant (not shown), which agrees with the tilt-relative circulations identified by Jones (1995) .

The aforementioned findings motivate an analysis of the structure and evolution of the midtropospheric vortex to elucidate why its arrival to upshear left precedes intensification. To this end, a pressure–time framework was employed to diagnose area-averaged quantities within a 50-km radius of the midtropospheric vortex. That area captures the main region of evolving precipitation and vorticity, while considering the midtropospheric vortex separately from the lower-tropospheric vortex even though both contribute to the same TC-scale system.

Noteworthy changes happen after the midtropospheric vortex enters upshear left, or 12–24 h before the onset of intensification ( Fig. 6 ). Vorticity increases first near the level of maximum vorticity, followed by a rapid increase of lower-tropospheric vorticity and a transition to a vorticity maximum near the surface. At the same time, the thermal anomalies weaken or even disappear. These structural changes happen as the TC vortex transitions from tilted to aligned, which suggests that those changes simply represent the decreasing tilt magnitude. However, vertical profiles following the 900-hPa center of circulation also indicate increasing vorticity at all levels (not shown) only after the midtropospheric vortex enters upshear left.

Given the link between the midtropospheric vorticity and precipitation, a possible explanation for the increasing lower-tropospheric vorticity is a change in the vertical mass flux profile. The vertical mass flux profile relates to vorticity tendencies via the stretching term, which is proportional to divergence or the vertical gradient of the vertical mass flux [Eq. (2) ]. A top-heavy profile favors vorticity spinup over a deep layer, whereas a bottom-heavy profile favors vorticity spinup near the surface. A shift from a top-heavy to a bottom-heavy profile happens during tropical cyclogenesis when a lower-tropospheric center of circulation forms from a disturbance with a midtropospheric vorticity maximum (e.g., Raymond and López Carrillo 2011 ; Gjorgjievska and Raymond 2014 ; Davis 2015 ; Tang et al. 2016 ). Potential explanations for the shift in the vertical mass flux profile include lower-to-midtropospheric stabilization (e.g., Raymond and Sessions 2007 ) or midtropospheric saturation (e.g., Davis 2015 ; Tang et al. 2016 ), both of which are thought to facilitate lower-tropospheric ascent and increasing lower-tropospheric vertical mass flux.

The previous subsection described processes associated with the evolution of the midtropospheric vortex; however, it is unclear how those processes influence intensity changes. Based on the vorticity and vertical mass flux profiles, a potential hypothesis is that the shift from a predominantly top-heavy to a more bottom-heavy mass flux profile represents increased near-surface convergence, which favors vorticity spinup via vortex stretching. This hypothesis was tested through an area-averaged vorticity budget calculated on a 100 km × 100 km box centered on either the lower- or midtropospheric centers of circulation. The domain size is consistent with the previous analyses and with the radius of maximum winds at the onset of intensification (not shown). Budget calculations with respect to both centers were used to quantify the role of each vortex. Only the early and the late members were considered because high-frequency output was required to balance the budget. All calculations show strong agreement between the actual tendencies ( Figs. 8a,b , 9a,b ) and the sum of individual tendencies ( Figs. 8c,d , 9c,d ), thus lending confidence to this analysis.

The vorticity budgets further highlight the role of the midtropospheric vortex before the onset of intensification. Total vorticity tendencies are of comparable magnitude when calculated with respect to either the midtropospheric ( Figs. 8a–d ) or lower-tropospheric centers ( Figs. 9a–d ) of both early and late members. A persistent vorticity spinup happens underneath the midtropospheric vortex 12–24 h before the onset of intensification of both members, or around 84–96 h in the early member and 108–132 h in the late member ( Figs. 8a–d ). A persistent vorticity spinup happens at all levels within the lower-tropospheric vortex only after the onset of intensification ( Figs. 9a–d ). The main difference between members is that the late member has more frequent periods of negative vorticity tendencies at all levels, which likely weaken and delay the azimuthal motion of its midtropospheric vortex.

Individual tendencies illustrate the processes leading to the persistent vorticity spinup following the midtropospheric vortex ( Figs. 8e–j ). Consistent with the top-heavy vertical mass flux profile before intensification, the net mean stretching term (mean stretching plus friction) depicts persistent vorticity spinup above 850 hPa ( Figs. 8e,f ). That spinup, however, is partially offset by negative tilting of horizontal vorticity ( Figs. 8i,j ). Downdrafts collocated with outward horizontal vorticity induced by the main TC vortex, as well as updrafts collocated with inward horizontal vorticity, result in negative tilting when the midtropospheric vortex is downshear left ( Fig. 10a ). This pattern changes after the midtropospheric vortex enters upshear left, or around 84 h in the early member and 120 h in the late member; the tilting term becomes positive ( Figs. 8i,j ) as inward horizontal vorticity induced by the stronger midtropospheric vortex is collocated with downdrafts ( Fig. 10b ). At the same time, the net mean stretching substantially increases in the boundary layer ( Figs. 8e,f ). Despite vorticity spindown via eddy vorticity fluxes ( Figs. 8g,h ), a persistent vorticity spinup happens after 84 h in the early member and after 120 h in the late member. That spinup happens through both vorticity convergence and tilting of horizontal vorticity above the boundary layer after the midtropospheric vortex enters upshear left.

Importantly, the substantial and persistent vorticity spinup happens before the 400–900-hPa tilt magnitude reaches a minimum in both the early and the late members (cf. Fig. 3 ). That vorticity spinup happens locally because of vortex stretching and tilting above the boundary layer and not because of eddy vorticity fluxes as would be expected if the midtropospheric and lower-tropospheric vortices were aligning through differential vorticity advection. These processes—which also appear in the vorticity budget of observed sheared TCs ( Rios-Berrios et al. 2016b , a )—are consistent with a large-ensemble study of TC intensification ( Miyamoto and Nolan 2018 ). A new question emerges from these findings, Is tilt reduction solely a result of advective alignment between the lower- and midtropospheric centers or a result of other processes?

The vorticity budget with respect to the lower-tropospheric vortex favors the latter view. A large vorticity spinup happens above 600 hPa after 84 h of the early member and 120 h of the late member ( Figs. 9a–d ). If that midtropospheric vorticity spinup signaled alignment, then the positive tendency should be contributed primarily by eddy fluxes. Integrated tendencies, however, show negative eddy fluxes above 800 hPa except for a brief 6-h period just before the onset ( Figs. 9g,h ). Instead, vorticity spins up via tilting of horizontal vorticity above 950 hPa ( Figs. 9i,j ) and occasional positive eddy fluxes below 800 hPa ( Figs. 9g,h ). Those tendencies are facilitated by the flow configuration when the midtropospheric vortex is upshear left. Positive tilting mainly happens at the northwestern edges of the integration domain, where upward motion associated with asymmetric convection is collocated with outward-pointing horizontal vorticity induced by the midtropospheric vortex ( Fig. 10c ). Likewise, positive eddy vorticity fluxes happen near the surface as the storm-relative inflow is collocated with vorticity anomalies generated below the midtropospheric vortex ( Fig. 10d ).

Snapshots of irrotational and nondivergent winds show the contrasting flow configurations when the midtropospheric vortex is downshear left or upshear left. In the former, the surface vortex is broad and composed of multiple mesoscale circulations ( Fig. 11a ). Updrafts exceeding 1 m s −1 happen over a broad region ( Fig. 11a ), and both convergent and divergent flow appear beneath the midtropospheric vortex ( Fig. 11c ). In contrast, a single and more compact circulation appears near the surface ( Fig. 11b ), predominantly convergent flow appears in the vicinity of near-surface vorticity exceeding 3 × 10 −3 s −1 ( Fig. 11e ), and updrafts exceeding 1 m s −1 happen within a region of strong vorticity near the surface and a closed circulation aloft after the midtropospheric vortex enters upshear left ( Figs. 11b,e ). Although near-surface inflow accompanies the midtropospheric vortex at all times, that inflow is radially closer and near stronger vorticity when the midtropospheric vortex is upshear left.

Vortex merger has been recognized as important during tropical cyclogenesis (e.g., Ritchie and Holland 1993 ; Simpson et al. 1997 ; Hendricks et al. 2004 ; Montgomery et al. 2006 ) and intensification ( Van Sang et al. 2008 ). Recent work on this subject suggests that vortex merger is facilitated by both nondivergent and irrotational vorticity fluxes ( Schecter 2017 ). Development of a TC following the merger, however, depends on the distance between the vortices, among other factors ( Schecter 2016 ). Here, vortex merger happened once the midtropospheric vortex moved close enough to the lower-tropospheric vortex to provide an enclosed region of recirculation by the nondivergent flow and coalescence by the irrotational flow. This sequence of events points at an indirect role of shear, where advection by the westerly sheared flow slows down the upshear migration of the midtropospheric vortex, forcing instead a radially inward migration. Following that indirect influence, vortex merger ultimately led to the establishment of a single vertically upright vortex ( Figs. 11c,f ) accompanied by latent heat release within a closed circulation ( Fig. 5d ).

These results support a two-stage process as initially proposed by Molinari et al. (2004) : 1) a tilted, asymmetric stage and 2) an aligned, symmetric stage. During the first stage, the lower-tropospheric vortex cannot spin up because the convergence of absolute vorticity and latent heat release happen below the midtropospheric vortex, but the midtropospheric vortex cannot build downward because the asymmetric vertical motions are anticorrelated with the horizontal vorticity induced by the main TC vortex. After the midtropospheric vortex and associated precipitation reach upshear left, the flow configuration facilitates vortex stretching and vorticity merger akin to the Van Sang et al. (2008) paradigm. A single vertically aligned vortex emerges and spins up during the second stage via near-surface convergence of absolute vorticity, free-tropospheric tilting of horizontal vorticity, and latent heat release within a closed circulation—an evolution that is consistent with axisymmetric theories of intensification ( Ooyama 1964 , 1969 , 1982 ; Charney and Eliassen 1964 ; Emanuel 1986 ).

The previous subsection confirmed the influence of structural changes on the simulated intensification; therefore, it is imperative to explain why those changes happened after the midtropospheric vortex reached upshear left. To understand such changes, the statistics of vertical motions within a 50-km radius from the midtropospheric vortex were assessed via contoured frequency by altitude diagrams (CFADs; Yuter and Houze 1995 ). CFADs group variables (in this case vertical mass flux) by their values at each height, thus quantifying individual vertical motion contributions to the area-averaged vertical mass flux profile. CFADs were obtained for each member and averaged during 12-h periods when the midtropospheric vortex was in the upshear-left quadrant ( Fig. 13a ) or in the downshear-left quadrant ( Fig. 13b ). Comparing those CFADs shows that the vertical mass flux profile changes because of a reduction of downdrafts below 600 hPa and an increase of updrafts at all levels—especially above 600 hPa—when the midtropospheric vortex reaches upshear left ( Fig. 13c ). Although it is intriguing that deep updrafts occur more frequently when the midtropospheric vortex reaches a region typically characterized by subsiding air ( Reasor et al. 2013 ; DeHart et al. 2014 ), real-world intensifying TCs also exhibit strong and deep updrafts in the upshear-left quadrant ( Wadler et al. 2018 ).

This result, which appears in all members, is tied to an increase in deep convective updrafts as depicted by a diagnosis of convective bursts (CBs) within a 50-km radius from the midtropospheric center ( Fig. 1c ). Convective bursts represent grid points where the 8–16-km layer-averaged vertical velocity exceeded 5 m s −1 and the 8–14-km layer-averaged reflectivity exceeded 20 dB Z (following Rogers et al. 2015 and Judt and Chen 2016 ). Time series of the number of convective bursts show three key results ( Fig. 1c ): 1) CBs happen more frequently during the tilted, asymmetric stage than during the aligned, symmetric stage; 2) all members experience a CB maximum during the 12–24-h period before the onset of intensification; and 3) all members have nearly zero CBs at the onset of intensification.

The first result is consistent with the vertical accelerations induced by a midtropospheric vorticity maximum and its associated thermodynamic structure during the tilted, asymmetric stage but not during the aligned, symmetric stage. The second result is consistent with the evolution of the vertical mass flux profile when the midtropospheric vortex reaches upshear left, further pointing at structural changes that favor deep convective updrafts in that quadrant. Last, the third result shows that the onset of intensification is characterized by a convective minimum, demonstrating that symmetrization (cf. Fig. 1b ) results from a large azimuthal coverage of shallow convection and stratiform precipitation (consistent with observations; Tao and Jiang 2015 ; Tao et al. 2017 ).

Parcel trajectories examined during the convective bursts maximum demonstrate that both buoyant and dynamic accelerations promote deep convective updrafts in the upshear-left quadrant. Figure 14 shows this result through a pressure–azimuth depiction of the buoyant and dynamic acceleration along parcel trajectories only after the parcels had started ascending. Air parcels begin ascending in the region azimuthally upwind of the midtropospheric vortex. Most air parcels become positively buoyant after they begin ascending above 500 hPa ( Figs. 14a,b ). Such buoyant accelerations are likely aided by latent heat release as warm and moist air parcels rise at a small radius relative to the lower-tropospheric center. At the same time, air parcels experience dynamic accelerations through their entire ascending trajectories ( Figs. 14c,d ). This dynamic forcing for ascent represents an upward-directed nonhydrostatic pressure gradient force associated with the stronger vorticity aloft ( Figs. 5c , 11b ). The presence of the midtropospheric vortex, and its associated low pressure away from the surface, provides a dynamic forcing for ascent.

This analysis provides an explanation for the appearance and impact of upshear-left convective updrafts preceding intensification. Deep updrafts happen within a closed circulation, where the stronger vorticity aloft induces an upward acceleration. The associated strong ascent within the closed region aids lower-tropospheric moistening by suppressing downdrafts, reducing low-entropy downward fluxes, and promoting recirculating warm, moist air parcels. Recirculation happens within an enclosed region where the nondivergent winds are much stronger than the irrotational winds ( Figs. 11c,f ), thus inhibiting cool, dry air intrusions from the environment ( Raymond and López Carrillo 2011 ). The late member experiences those processes much later because of more downdrafts ( Fig. 7 ), fewer convective bursts ( Fig. 1c ), and larger downshear-left tilt ( Fig. 3a ). Following vortex merger initiated by the deep updrafts and associated vortex stretching, the reformed surface-based vortex has favorable kinematic and thermodynamic conditions to undergo intensification.

An ensemble of idealized numerical simulations was used to diagnose physical processes preceding TC intensification under moderate VWS. Consistent with previous studies, the ensemble was characterized by large variability in the simulated intensity, precipitation asymmetry, and vortex tilt. New insights were gained through a process-based analysis centered on the characteristics and evolution of a shear-induced midtropospheric vortex. This analysis showed that intensification followed after tilt reduction and symmetrization of precipitation because that structure promoted persistent vorticity spinup and recirculating warm, moist air parcels. All members exhibited similar processes driving intensification; however, the timing of intensification varied between members because of their initial downshear-left tilt magnitude and subsequent timing of tilt reduction.

The sequence of events in these idealized simulations can be summarized as follows:

A mesoscale midtropospheric vortex emerges within the shear-organized precipitation.

The midtropospheric vortex travels cyclonically around a lower-tropospheric center of circulation at a distance that depends on the precise location of shear-organized convection.

Upon reaching upshear left, shear slows down the upshear migration of the vortex and forces instead a radially inward migration.

Deep convective updrafts emerge and spin up strong, small-scale vortices that coalesce and merge into a single closed circulation over a deep layer.

Vortex merger happens only after the midtropospheric vortex reaches upshear left, where the flow configuration favors near-surface vortex stretching and eddy radial vorticity fluxes toward a common center of circulation.

Recirculating air parcels prevent downdrafts and allow for a warming and moistening lower troposphere within the closed circulation.

Last, the vertically aligned TC intensifies via near-surface convergence of absolute vorticity, tilting of horizontal vorticity, and latent heat release within the closed circulation.

Based on these results, it is hypothesized that intensification under moderate VWS happens if and when a two-stage “restructuring” process takes place. During the first stage, precipitation is asymmetric because rising motions happen predominantly near the midtropospheric vortex, the combination of elevated deep convection and stratiform precipitation yield a top-heavy vertical mass flux profile, and strong downdrafts bring low-entropy air to the boundary layer. This structure changes during the second stage when vortex merger leads to a single closed circulation over a deep layer, vertical mass fluxes increase near the surface, and high-entropy air persists in the boundary layer. Intensification proceeds during the second stage with only minor effects from VWS because precipitation is nearly symmetric and the TC vortex remains nearly aligned. A restructuring process is proposed based on those system-scale structural changes. This hypothesis is similar to the two-stage process proposed by Molinari et al. (2004) , except with the added vortex merger paradigm proposed by Van Sang et al. (2008) .

It is further hypothesized that the likelihood and length of that restructuring process depend on environmental and internal conditions, in agreement with other studies of TC intensification under moderate VWS ( Tao and Zhang 2014 ; Rios-Berrios and Torn 2017 ; Nguyen et al. 2017 ). Sheared TCs within favorable environmental thermodynamics (e.g., abundant moisture, warm sea surface temperature) are more likely to complete the restructuring process because of continuous support for ascent and inhibition of downdrafts (e.g., Tao and Zhang 2014 ; Nguyen et al. 2017 ). Environmental conditions ahead of the midtropospheric vortex and in the upshear half are especially important to ensure the sustainment and propagation of precipitation from downshear left to upshear left ( Rappin and Nolan 2012 ; Ge et al. 2013 ; Onderlinde and Nolan 2016 ; Rios-Berrios et al. 2016b , a ; Rios-Berrios and Torn 2017 ). Likewise, the restructuring process likely applies to weak TCs—depressions, tropical storms, and weak hurricanes—which are more likely to exhibit a tilted, asymmetric structure than strong, mature TCs ( Jones 1995 ; DeMaria 1996 ; Reasor et al. 2004 ; Riemer and Montgomery 2011 ). Further investigation is needed to confirm these hypotheses and to establish how shear-related processes such as ventilation affect the hypothesized restructuring process.

Although idealized, these simulations are consistent with intensification of real-world TCs. Humidification of the upshear half and symmetrization of precipitation are key characteristics of intensifying TCs under moderate VWS ( Molinari et al. 2004 ; Kieper and Jiang 2012 ; Jiang and Ramirez 2013 ; Zagrodnik and Jiang 2014 ; Rios-Berrios et al. 2016a ; Zawislak et al. 2016 ; Nguyen et al. 2017 ; Rios-Berrios and Torn 2017 ). Symmetrization is often preceded by upshear-left convective bursts (e.g., Rogers 2010 ; Stevenson et al. 2014 ; Chen and Gopalakrishnan 2015 ; Rogers et al. 2016 ; Wadler et al. 2018 ), even though upshear-left bursts do not always lead to intensification ( Judt and Chen 2016 ). New insights were gained here about the origin and relevance of those convective bursts: dynamic forcing for ascent appeared below the midtropospheric vorticity maximum, and that ascent promoted increasing near-surface vertical mass fluxes and humidification of the lower and midtroposphere. Observations of upshear-left convective bursts during the intensification of Hurricane Earl (2010) support this result, as those bursts also happened near a midtropospheric vorticity maximum ( Stevenson et al. 2014 ). Tilt reduction is also a common feature of observed intensifying TCs in sheared environments (e.g., Raymond and López Carrillo 2011 ; Reasor and Eastin 2012 ; Rogers et al. 2015 ). Importantly, tilt reduction happened through stretching, tilting, and vortex merger—not solely through advective vortex alignment.

Several questions remain open for future research. For example, what mechanisms inhibit the hypothesized restructuring process? This study focused on intensification, but an equally important problem is TC weakening under moderate or strong VWS. One possibility is that the restructuring process is inhibited by processes that prevent vortex merger and the subsequent establishment of a single closed circulation. Likewise, can the vortex merger process happen in other quadrants? Some TCs intensify after vortex reformation in the downshear half ( Molinari et al. 2004 , 2006 ; Davis et al. 2008 ; Molinari and Vollaro 2010 ; Nguyen and Molinari 2015 ); therefore, vortex merger and reformation may depend on other factors such as the flow configuration, thermodynamic background, or the distance between the deep updrafts and a lower-tropospheric center of circulation. Another question that remains unanswered is, What factors control the azimuthal motion of the midtropospheric vortex and its associated precipitation? The onset of intensification largely depends on that motion (cf. Fig. 3 ), but the ensemble was characterized by large variability induced by small perturbations to the initial boundary layer water vapor. These and other questions should be addressed, especially with observations and with simulations that account for temporal shear variability, to further understand the hypothesized restructuring process.

Acknowledgments

This study would not have been possible without the point downscaling code provided by Drs. David Nolan and Matthew Onderlinde. Comments from three anonymous reviewers helped improve an earlier version of this manuscript. This study also benefited from discussions with Drs. George Bryan, Kristen Corbosiero, John Molinari, and Brian Tang. Dr. Jimy Dudhia, Dr. Wei Wang, and Ms. Kelly Werner from NCAR helped in numerous ways with the modeling experiments. All experiments were performed with an educational allocation in the Yellowstone Supercomputer System administered by NCAR’s Computational Information Systems Laboratory (CISL; CISL 2012 ) during the first author’s visit to NCAR, sponsored by NCAR’s Advanced Study Program Graduate Visitor fellowship. This research also funded through NOAA Grants NA14OAR4830172 and NA16NWS4680025. The National Center for Atmospheric Research is sponsored by the National Science Foundation.

RIP is freely available ( http://www2.mmm.ucar.edu/wrf/users/docs/ripug.htm ).

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Hypothesis on Tropical Cyclone Freddy in Mozambique

Tropical cyclones, also known as hurricanes or typhoons in different parts of the world, are among the most powerful and destructive meteorological events on Earth. Their formation and trajectory are influenced by a complex interplay of geographic and climatic factors. This study focuses on Tropical Cyclone Freddy, which recently wreaked havoc in Mozambique, a southeast African country known for its rich cultural heritage and diverse landscapes.

Tropical Cyclone Freddy provides a unique case study for grade 12 Geography students to explore. By examining various variables such as sea surface temperatures, atmospheric pressure, wind speed and direction, and geographical features of Mozambique, learners can generate and test hypotheses that could explain the cyclone’s characteristics and impacts.

Table of Contents

Guide for Generating a Hypothesis on Tropical Cyclone Freddy in Mozambique

Step 1: Understand the Problem

The first step in any scientific inquiry is to understand the problem at hand. In this case, the problem is Tropical Cyclone Freddy in Mozambique. Research about tropical cyclones, their causes, and impacts. Understand the geographical and climatic conditions of Mozambique. Consider what you already know about the factors that contribute to the formation and the path of a tropical cyclone.

Step 2: Gather Preliminary Data

Find data about Tropical Cyclone Freddy. This could include its path, wind speed, rainfall, damage caused, etc. Also, try to find data about the conditions in Mozambique before, during, and after the cyclone. This could include data about temperature, humidity, atmospheric pressure, and oceanic conditions. Other relevant data might include the time of the year the cyclone occurred, the state of the El Niño/La Niña cycle, and Mozambique’s geographical features that might influence cyclone paths.

Step 3: Identify Variables

From your research and the data gathered, identify the variables that might be connected to the problem. Variables could be anything that could influence the cyclone’s formation, path, or impacts. Examples might include sea surface temperature, atmospheric pressure, humidity, wind speed and direction, Mozambique’s topography, and population density.

Step 4: Formulate Your Hypothesis

A hypothesis is a testable statement that predicts the relationship between variables. Based on your understanding of the problem and the data you’ve gathered, make an educated guess about what might have caused or influenced the cyclone’s formation, path, or impacts. Your hypothesis should clearly state what you think the relationship is between your identified variables.

For example: “If sea surface temperatures were above average in the Indian Ocean off the coast of Mozambique prior to Tropical Cyclone Freddy, then this may have contributed to the cyclone’s formation and intensity.”

Step 5: Test Your Hypothesis

Plan and conduct an investigation to test your hypothesis. This could involve more detailed data analysis, creating models, running simulations, or even conducting experiments if possible.

Step 6: Analyze Your Results and Draw Conclusions

Analyze the results of your investigation to see if they support your hypothesis. If the data supports your hypothesis, then it may be valid. If the data doesn’t support your hypothesis, then it may need to be revised or discarded.

Remember, in scientific inquiry, even a hypothesis that turns out to be incorrect is valuable because it contributes to our understanding of the world. The goal is not necessarily to prove your hypothesis right, but to understand more about the world.

Step 7: Communicate Your Findings

Lastly, communicate your findings in a clear, organized manner. This could be in the form of a report, presentation, or discussion. Include your initial hypothesis, the methods you used to test it, your results, and what those results mean in the context of your hypothesis.

This guide should help you formulate and test a hypothesis about Tropical Cyclone Freddy in Mozambique. Remember, the process of scientific inquiry is iterative and often requires multiple rounds of hypothesis generation, testing, and revision. Good luck!

Example of Hypothesis Related to Tropical Cyclone Freddy in Mozambique

Here are ten possible hypotheses related to Tropical Cyclone Freddy in Mozambique. Remember, these are educated guesses based on what we know about tropical cyclones and the geography and climate of Mozambique. They would each need to be tested using appropriate methods and data.

Hypothesis on Sea Surface Temperature: Higher sea surface temperatures in the Indian Ocean off the coast of Mozambique contributed to the increased intensity of Tropical Cyclone Freddy.
Hypothesis on Atmospheric Pressure: Lower atmospheric pressure in the region where Tropical Cyclone Freddy formed led to the cyclone’s rapid intensification.
Hypothesis on Wind Patterns: The prevailing wind patterns at the time of Tropical Cyclone Freddy’s formation influenced its path, leading it to make landfall in Mozambique.
Hypothesis on Humidity Levels: High humidity levels in the atmosphere over Mozambique contributed to the high rainfall amounts associated with Tropical Cyclone Freddy.
Hypothesis on Topography: The flat coastal plains of Mozambique contributed to the extensive flooding caused by Tropical Cyclone Freddy.
Hypothesis on El Niño/La Niña Cycle: The stage of the El Niño/La Niña cycle at the time of Tropical Cyclone Freddy’s formation influenced its intensity and path.
Hypothesis on Land Use: Deforestation and land use changes in Mozambique have increased the country’s vulnerability to the impacts of tropical cyclones like Freddy.
Hypothesis on Urbanization: Urbanized areas in Mozambique experienced more severe impacts from Tropical Cyclone Freddy due to factors like population density and infrastructure.
Hypothesis on Climate Change: Climate change, as evidenced by rising sea surface temperatures and increased atmospheric moisture, is making tropical cyclones like Freddy more intense and more damaging when they make landfall in Mozambique.
Hypothesis on Coastal Barrier Systems: Degradation of coastal barrier systems, such as mangrove forests and coral reefs, has increased Mozambique’s vulnerability to storm surges associated with tropical cyclones like Freddy.

Each of these hypotheses can be tested using a combination of historical data, climate models, geographical analysis, and potentially ground-based surveys or studies.

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Published: 09 June 2022

An analytic model of the tropical cyclone outer size

Shuai Wang 1 , 2 &
Ralf Toumi ORCID: orcid.org/0000-0002-5203-1883 1

npj Climate and Atmospheric Science volume 5 , Article number: 46 ( 2022 ) Cite this article

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Atmospheric science
Projection and prediction

There are simple conceptual models of tropical cyclone intensification and potential intensity. However, such a framework has been lacking to describe the evolution of the outer circulation. An analytic growth model of the tropical cyclone outer size is derived from the angular momentum equation. The growth model fits a full-physics idealized tropical cyclone simulation. The lifecycle composite of the best-track outer size growth shows a strong super-linear nature, which supports an exponential growth as predicted by the growth model. The climatology of outer size growth measured by the radius of gale-force wind in the North Atlantic and Eastern Pacific during the period 2004–2017, can be understood in terms of four growth factors of the model: the initial size, the growth duration, the mean growth latitude, and the mean top-of-boundary-layer effective local inflow angle. All four variables are significantly different between the two basins. The observed lifetime maximum size follows a lognormal distribution, which is in line with the law of the proportionate effect of this exponential growth model. The growth model fits the observed outer size well in global basins. The time constant of the exponential size growth is approximately equal to the product of the Coriolis parameter and the mean effective inflow angle above the boundary layer. Further sensitivity experiments with the growth model suggest that the interannual variability of the global lifetime maximum size is largely driven by the variation of growth duration.

Climate damage projections beyond annual temperature

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Warning of a forthcoming collapse of the Atlantic meridional overturning circulation

Introduction.

It has been challenging to quantify the overall destructive potential of landfalling tropical cyclones (TCs). Especially after Hurricane Katrina (2005) and Sandy (2012), more attention has been paid on the impact of TC size at landfall and the development of new destructive metrics for public warning 1 , 2 , 3 , 4 . With a similar core intensity, various TC sizes can lead to considerably different destructive potentials 5 , 6 , 7 . After a TC reaches its lifetime maximum intensity, the increase in TC destructive potential can be explained mainly by the expansion of TC size 8 , 9 . Understanding TC size lifecycle is, therefore, of critical importance.

Tropical cyclone outer size can be defined by the radial extent of near-surface cyclonic circulation with a fixed wind speed 10 . It was found that the outer size in the North Atlantic is significantly smaller than that in the western North Pacific 11 which is the basin with the largest mean outer size globally 12 , 13 . Outer sizes with different wind speed thresholds may show opposite changes so that when the intensity decays, the high-wind-speed outer radii can shrink and low-wind-speed ones can expand 14 . Wind profile models can provide a more comprehensive picture of the entire low-level wind structure 15 , 16 , 17 .

Local environmental conditions influence TC outer size, for example, the synoptic flow patterns in both the upper and lower troposphere 18 , relative humidity 19 , 20 , sea-surface temperature 21 and vertical temperature profile 22 . Intuitively the net import of angular momentum from larger radii enhances the local angular momentum and thus the near-surface swirling winds increase 10 . However, it was also found that the outer size may also depend on free-tropospheric air subsidence due to radiative cooling 23 .

Despite the substantial amount of research on size climatology, diagnostic wind field models, and environment controls on size, the size evolution itself has received relatively less attention 10 , 12 , 24 . Progressive growth of TC outer size after the maturity of intensity was simulated with idealized models 25 , which supports a similar finding in the North Atlantic 26 . A recent study 27 reported that: the North Western Pacific typhoons generally grow until the midpoint of their lifetimes whereas the Atlantic hurricanes continue expanding throughout most of their lifecycles (i.e., hurricanes grow for a relatively more extended period than typhoons); hurricanes grow more slowly than typhoons; hurricanes have a smaller initial size at genesis than typhoons; and hurricanes exhibit a smaller lifetime maximum size (LMS) than typhoons. These findings were however only based on reanalysis and climate model data.

In this study, we will use the radius of gale-force wind ( R 34 , 34 kt ≈ 17.5 m s −1 ) from the TC best track data set for the analysis of outer size growth. The period of interest in a TC lifecycle is from the first time when R 34 starts to be recorded in at least one quadrant in the best track, to the time when the quadrant averaged R 34 reaches its lifetime maximum for the first time.

The objectives of this study include: formulating the first growth model of TC outer size; validating the derived exponential model for TC size growth with idealized simulations and observations; comparing the climatology of key growth factors between the North Atlantic (NA) and Eastern Pacific (EP) TCs; exploring the physical reasons for the difference in the LMS climatology between the NA, EP and other basins; and investigating the driving factors for the interannual variability of the global LMS.

Variable definition and assumptions

The growth model is derived for a wind radius that is larger than the radius of maximum wind speed in an axisymmetric cylindrical coordinate. We first define the variables used in the derivation at the top of the boundary layer in Table 1 . There are numerous definitions and methods for defining the top of the boundary layer 28 . Since the growth model will be derived from the momentum equation the dynamical boundary layer height, i.e., the heights of the maximum wind speed varying with radius, is applied in this study to define the top of the boundary layer. The model is established on the assumption that at the top of a TC boundary layer the flow is in gradient wind balance and therefore α V is small and temporally quasi-stationary at R V where V t is fixed.

With flight observations, the TC tangential wind above the boundary layer has been shown in gradient wind balance to a good approximation 29 . Considering the radial momentum equation in the free atmosphere, a gradient wind balance assumes a small radial velocity maintaining a quasi-steady state, i.e., ∂ V r /∂ t ≈ 0. This approximation applies at the top of the boundary layer during the growth time of an outer size R V that is away from the eyewall. A physically plausible mean effective inflow angle \(\overline{{\alpha }_{V}}\) during the growth can be therefore hypothesized. Note that ∂ α v /∂ t ≈ 0 assumes α V following a fixed tangential wind V t at R V is quasi-stationary during the growth phase in the outer rainbands, and only has high-frequency fluctuations around its mean value \(\overline{{\alpha }_{V}}\) during the growth of R V . \(\overline{{\alpha }_{V}}\) can vary from storm to storm. We will further justify this inference with idealized TC simulations. In addition, the Coriolis parameter is treated as a time-invariant variable for each cyclone and calculated as the mean latitude during the growth of each TC.

An exponential growth model for tropical cyclone outer size

The growth model is derived in an axisymmetric framework. The angular momentum at R V can be written as

The angular momentum budget at R V is then given at the top of the boundary layer by

The four terms in Eq. ( 2 ) represent the local rate of change, radial momentum flux, vertical momentum flux, and the impact of diffusion.

By substituting Eq. ( 1 ) in the first two terms, Eq. ( 2 ) can be rearranged as

We next apply Eq. ( 3 ) following R V rather than the air parcel and this approach has also been recently used to study the eyewall contraction and rapid intensification 30 . Such a change requires a coordinate transformation from \(\left(r,z,t\right)\) to \(\left({R}_{V}(t),z,t\right)\) for Eq. ( 3 ). This transformation changes the term \({R}_{V}\frac{\partial {V}_{t}}{\partial t}\) in coordinate ( r , z , t ) to \({R}_{V}(\frac{\partial {V}_{t}}{\partial t}+\frac{\partial {V}_{t}}{\partial {R}_{V}}\frac{\partial {R}_{V}}{\partial t})\) in coordinate \(\left({R}_{V}(t),z,t\right)\) , and also replaces the coordinate r to R V . Note that the transformation above can not be applied to terms containing \(\frac{\partial {R}_{V}}{\partial t}\) or \(\frac{\partial {{R}_{V}}^{2}}{\partial t}\) , otherwise one would obtain incorrect relations, e.g., \(\frac{\partial {R}_{V}}{\partial t}\) in coordinate ( r , z , t ) to \(\frac{\partial {R}_{V}}{\partial t}+\frac{\partial {R}_{V}}{\partial {R}_{V}}\frac{\partial {R}_{V}}{\partial t}=2\frac{\partial {R}_{V}}{\partial t}\) in coordinate \(\left({R}_{V}(t),z,t\right)\) .

The terms affected by the coordinate transformation can be written as follows:

By applying the coordinate transformation above, Eq. ( 3 ) can be rewritten as

We next conduct scale analysis for Eq. ( 4 ). The variable V t is a fixed wind speed used to define the outer wind radius R V , so \(\frac{\partial {V}_{t}}{\partial t}=0\) by definition. The angular momentum tendency will therefore be caused by changes in the radius. However, the radial gradient of tangential wind, \(\frac{\partial {V}_{t}}{\partial {R}_{V}}\) , should vary with the growth of R V . To estimate the scale of \(\frac{\partial {V}_{t}}{\partial {R}_{V}}\) , we use the modified Rankine Vortex 15 at R V considering its simple expression and good ability to present the outer wind profile 31 . The modified Rankine Vortex can be written at R V as

Now the radial gradient of tangential wind, \(\frac{\partial {V}_{t}}{\partial {R}_{V}}\) , can be estimated with

By taking the typical values of x = −0.5 (ref. 31 ), 50 m s −1 for V m , 50 km for R m and 250 km for R V into Eq. ( 6 ) we find a typical scale of 10 −5 for \(\frac{\partial {V}_{t}}{\partial {R}_{V}}\) .

For the other terms, since the growth model is developed for TC outer size, the scales of all quantities at the top of the boundary layer are estimated within the radial distance of about 100–500 km from TC centre, which covers the typical values of, for example, the radii of 18 and 12 m s −1 at surface 12 , 13 . Within this radial range, the height of the boundary layer is about 1000–1500 m (ref. 28 ). By considering the scales found in previous studies as shown in Table 2 , the magnitudes of the terms in Eq. ( 4 ) are:

Scale analysis now suggests that Eq. ( 4 ) may be simplified and rearranged as

where \(\tan {\alpha }_{V}={V}_{r}/{V}_{t}\) is used as previously defined. The term ∂ R V /∂ t on the l.h.s. is the evolution of an outer size defined by a fixed tangential wind speed, V t .

We next apply (1) the assumption given in the last sub-section to replace the time-dependent α V with its mean value \(\overline{{\alpha }_{V}}\) (time-invariant) during the growth and (2) the small-angle approximation \({V}_{r}/{V}_{t}\,\approx \,\tan \,\overline{{\alpha }_{V}}\,\approx \,\,\overline{{\alpha }_{V}}\) (according to the scales in Table 2) and then obtain

Now in Eq. ( 8 ), R V is the only time-dependent variable. Integrating Eq. ( 8 ) with an initial condition of R V = R o at t = 0 results in

Equation ( 9 ) is the full expression of a new analytic solution for TC outer size growth. The derived model depicts an exponential growth with a time constant of \({f}_{o}\overline{{\alpha }_{V}}\) . It is noteworthy that V t / f o is a hypothetical radius for V t when the Rossby number is unity. It can also be regarded as to a inverse- f scale when V t is replaced by the maximum potential intensity, which has dynamical scaling implications for TC size in rotating radiative-convective equilibrium simulations and aqua-planet frameworks 32 . The derived growth model suggests that the TC outer size growth is primarily dominated by four factors:

initial size.

growth duration.

mean latitude during growth.

mean effective inflow angle at the top of boundary layer.

The doubling time is a useful concept to quantify an exponential growth process. Assuming that it takes a TC time T D to grow from R o to 2 R o , the doubling time of Eq. ( 9 ) is then given by:

Figure 1 a shows the fit of the growth model (Eq. ( 9 )) to the outer size ( R 34 ) evolution in the full-physics simulation (see “Methods” for the growth model fit and idealized simulation set-up). The growth model fully captures the simulated outer size growth ( r = 0.99, P value < 0.01). From the fit we infer a mean effective inflow angle \(\overline{{\alpha }_{V}}\) of 1.0° at the top of the boundary layer. Figure 1 b shows that this mean effective inflow angle is seen in the simulation at a height of about 1500 m above the surface R 34 . Therefore, the assumptions for the inflow angle required for the analytic growth model are well-validated by the full-physics simulation. The inflow angle at the top of the boundary layer is therefore excellently predicted by the analytic model. We do not find a statistically significant ( P value > 0.05) change of the inflow angle during the growth period in this simulation, which justifies the steady-state assumption of V r (i.e., ∂ V r /∂ t ≈ 0) and applying a mean effective inflow angle \(\overline{{\alpha }_{V}}\) in one growth event (from Eqs. ( 7 ) to ( 8 )). At this height, the mean wind adjustment factor at R 34 is found to be 0.76 in the simulation, which is very close to 0.75, the value assumed for the R 34 growth fit (see “Methods”).

a The growth of outer size ( R 34 ) at a height of 10 m (black line) and the best fit with the growth model (red line). A wind reduction factor of 0.75 is applied (see “Methods”). b Time series of inflow angles at the lowest model level (brown dashed line) and the top of the boundary layer (blue dashed line) following the growing R 34 in ( a ). The inflow angles are calculated based on the azimuthally averaged tangential and radial winds. The solid lines show the mean inflow angles. The mean effective inflow angle during this growth event is estimated to be 1.1° at the top of the boundary layer.

Observations

We next validate the growth model by compositing the TC outer size to paint a general picture for the observed outer size evolution. Figure 2 shows that on average the TC outer size increases in the NA and EP in a super linear fashion within at least the last 2 days before reaching the LMS. The absolute change of size for every 6 h increases when approaching the LMS. This is qualitatively in line with the prediction by the exponential growth model.

The solid lines show the mean evolution and the shading areas denote one standard error to the mean. The composites are based on 6-h observations (dots). There are 94 and 107 TCs used in the NA and EP, respectively.

We next continue the quantitative validation of the growth model by fitting individual TC outer size growth in the NA and EP. The three inputs—i.e., the initial size R o , growth duration t , and the Coriolis parameter f o calculated with the mean latitude during a growth—are taken from the best-track data. The mean effective inflow angle \(\overline{{\alpha }_{V}}\) is treated as a fitting parameter for each TC (see “Methods”). Figure 3 shows that the Pearson correlation coefficient between all fitted and observed R 34 is 0.93 and 0.90 in the NA and EP, respectively, with a slope of 0.89 and 0.86. Partial correlation analysis reveals that correlation coefficient in Fig. 3 does not change if the mean f o is used for all TCs, and only changes in the NA from 0.93 to 0.91 if the mean R o is adopted. The results in Figs. 2 and 3 suggest that the exponential growth model is a plausible choice to describe the TC outer size growth. The slopes, less than one in Fig. 3 , suggest that the growth model may underestimate the size growth when approaching the LMS.

The solid line denotes the linear least-squares fit. The dotted line shows the y = x line. The r values in the legend are the Pearson correlation coefficient with the total number ( N ) of size observations.

Difference between basins

The growth model suggests that the following factors can depict a TC growth:

Lifetime maximum size,

Initial size,

Growth duration,

Mean growth latitude, and

Mean Effective inflow angle.

We next conduct inter-basin comparisons of factors (1)–(4) with the best-track data, and factor (5) based on the estimates from fits (see “Methods”).

Figure 4 a displays the probability density function (PDF) of the log-transformed LMS in the NA and EP. According to the Kolmogorov–Smirnov (KS) test statistics, the P value from the normality test of the transformed LMS distributions is 0.45 and 0.62, respectively, for NA and EP TCs. This means the distribution of LMS in these two basins has a strong lognormal feature.

PDF of log-transformed ( a ) LMS (km), ( b ) initial size (km), ( c ) growth duration (h), and ( d ) mean growth latitude ( ∘ N) for NA and EP TCs. The solid lines and dots are the observed PDFs based on the best track. The bell-shaped shadings in ( a ) denote the fitted normal distribution. The P value from the lognormal test of LMS is 0.45 in the NA and 0.62 in the EP, respectively, which suggests that the distributions are lognormal. The bin widths are 0.2 in ( a ), 0.2 in ( b ), 0.4 in ( c ), and 2° in ( d ). The mean in each basin is given in the legend.

Figure 4 b shows the log-transformed distribution of initially recorded R 34 . The mean TC intensity at the time when the initial R 34 is measured is 36 kt for both NA and EP TCs. Compared to the distribution of LMS, the log-transformed initial size is still somewhat skewed (Fig. 4 b), but the P value of a normality test is 0.10 in the NA and 0.01 in the EP, respectively. This suggests a much weaker lognormal feature of the initial size than the LMS in both basins. Figure 4 a and b suggests that the exponential growth process enhances the lognormality of the outer size distribution when growing towards the LMS. We will further discuss this point in the next section.

The growth duration, as shown in Fig. 4 c, is defined as the growth period from the initial size to LMS. Positive skewness is found in both basins. A longer growth duration (Fig. 4 c) and higher mean growth latitude (Fig. 4 d) are found in the NA but they are not significantly correlated.

More quantitative comparison of the growth factors is summarized in Table 3 . The statistical significance of the differences between the two basins are also examined by bootstrapping (see “Methods”). The observed LMS in the best track and estimated LMS from the fit show consistent differences between the two basins. Compared to the EP, an NA TC typically has a larger initial size, grows for a longer period at a higher mean latitude, and ends with a larger LMS. The LMS, initial size, growth duration, and mean latitude between the two basins are significantly different at the 99% confidence interval.

The TCs in the EP have a significantly larger inflow angle than NA TCs ( P value = 0.04, Table 3) . However, the doubling time, which is a measure of relative growth rate, is not significantly different between the two basins. This may be because the larger inflow angle in the EP is compensated by a lower mean growth latitude. According to the growth model, a larger LMS in the NA is then determined by a larger initial size and a longer growth duration, given the doubling time is similar in the two basins.

The analytic model in other basins

It is of interest to also validate the growth model in the other basins. Table 4 shows the Pearson correlation coefficient together with the associated P value from the least-squared linear fit between the observed and fitted TC size. The global correlation coefficient is 0.83, with variation between 0.80 and 0.87 in all the basins, and the corresponding P value is consistently less than 0.05. The mean root-mean-square error of the global TCs is 24 km, and this is 15% of the global mean R 34 (157 km). The root-mean-square error varies from 14 to 27 km in all the basins.

Since the model can in general depict the TC outer size growth globally, we next investigate the global model features: the LMS, initial size, growth duration, mean growth latitude, mean effective inflow angle following R 34 , and doubling time (Table 5 ). The inter-basin differences of these variables are also examined by testing the statistical significance of a variable’s distribution in each basin (BASIN) against that in all the other basins (ex-BASINs). If one variable, according to bootstrapping, shows a significant difference between one pair of BASIN and ex-BASINs, it indicates the particularity of this variable in BASIN.

Each basin, apart from the SI and SP, have significantly different mean LMS compared to the rest of the basins (Table 5) . NA and WP TCs show larger LMS, whereas the LMS in the EP and NI are generally smaller. There are different reasons for the uniqueness of LMS in these basins and it can be usefully understood in terms of the growth model. The NA has a significantly longer growth duration at a higher mean latitude, whereas the WP has significantly larger initial size and mean effective inflow angle. The anomalously small LMS in the EP is mainly due to the small initial size and mean effective inflow angle at a lower mean latitude during growth. In the NI the short growth duration at a lower mean latitude leads to a small LMS. All basins have unique combinations of initial size, mean growth latitude and/or mean effective inflow angle. These three factors determine the doubling time (Eq. ( 10 )). The NA and EP have significantly longer doubling time than in the other basins. This is likely due to a smaller mean effective inflow angle as this is the only growth factor in the NA and EP that is different compared to that in the other basins.

Interannual variation of the LMS

The growth model identifies four factors for TC size growth: the initial size, growth latitude, local effective inflow angle, and growth duration. This provides a simple way to understand the interannual variation of the LMS. In this section, we focus on the medians of the LMS and growth factors considering their skewness. We do not find any significant trend of the observed annual median LMS (Fig. 5 ). With the observed four factors of each TC, the model can reproduce the interannual variation of the LMS in a good agreement with the observation. The correlation between the modeled and observed annual LMS time series is 0.86 after detrending (Fig. 5 a). We next perform sensitivity experiments by fixing each of the four growth factors to their global medians to examine their relative importance by comparing the correlation between the observed and modeled LMS time series. The growth latitude is found to contribute little to the interannual LMS variation (Fig. 5 b). The growth duration and initial size (Fig. 5 c, d) show a relatively large influence. However, if the initial size is fixed, the modeled and observed LMS shows an almost perfect synchronous change for some of the period (2004–2013), which does not happen when the growth duration is fixed. This suggests that the growth duration may be the most important and consistent growth factor to the interannual variation of the LMS. The effective inflow angle is relatively less important to the interannual variation, but it does seem to be crucial to push up the modeled LMS to the observed level (Fig. 5 b).

The LMS of each TC is modeled by Eq. ( 9 ) with full variables in ( a ), fixed f o or \(\overline{{\alpha }_{V}}\) in ( b ), fixed t in ( c ), and fixed R o in ( d ). If f o , \(\overline{{\alpha }_{V}}\) , t or R o is fixed, the median values of 4.2 × 10 −5 s −1 , 0.9 ∘ , 90 h or 83 km is used, respectively. The Pearson correlation coefficient ( r ) of the detrended observed and modeled time series are given in the figure legend.

There are simple and useful analytic models for TC intensity change 33 , 34 , 35 . A simple analytic model for TC outer size growth has been lacking. Here we present a growth model developed explicitly for the TC outer size, which can be used to understand the inter-basin difference of the LMS and its interannual variation. The model also explains several empirical findings into a single framework:

that the initial size is important 36 ;

that TC size increases with latitude 26 ;

the inter-basin differences of size 13 ; and

that the TC outer size is log-normally distributed 37 .

The growth model is developed for TC outer circulation, a regime that has different dynamics from the inner-core region where the radius of maximum wind is located 17 . In particular, the vertical advection and diffusion are much less important at the outer circulation than in the eyewall. The growth model suggests that the TC outer size growth is primarily dominated by four factors: the initial size, growth duration, mean growth latitude, and mean effective inflow angle. Numerical studies of idealized TCs showed that an initially large TC is more likely to reach a large size at a later stage 38 , 39 . According to our analysis, WP TCs have both significantly larger initial size and LMS, which supports those idealized simulations. However, the growth model also suggests that the growth duration, mean effective inflow angle and latitude determine the lifetime maximum size for the same initial size. It has been shown that the duration of major tropical cyclones for 1982–2018 has been shortened by 1 day 40 . If we assume the same reduction for the mean growth duration, with the global mean values of R o = 90 km, latitude=18°N/S, \(\overline{{\alpha }_{V}}=1.{0}^{\circ }\) and duration = 100 h (Table 5) , the growth model predicts a reduction of mean LMS by −53 km over 37 years, i.e., −1.4 km per year. This predicted change is close to an observed value in a recent study 41 showing that the global annual mean R 34 (not LMS shown in Fig. 5) is decreasing with a rate of −2.5 km per year based on best-track data. However, no changes of size based on satellite observations have been reported 26 . Our results also reveal that the LMS does not show a significant change, which is consistent with a steady annual mean R 34 inferred from ocean cold wakes 42 . Poleward migration of TC lifetime maximum intensity has been found in recent decades 43 . However, further analysis (not shown) reveals that the growth model is the least sensitive to any latitude change compared to the other growth factors. For example, the LMS would only increase by less than 10% if the growth latitude were to increase by 50% with other factors fixed.

The inflow angle is of crucial importance in our growth model. However, there has been a lack of studies on the inflow angle at the top of the boundary layer in the outer-core region. A previous study 28 finds a boundary layer depth at surface R 34 is about 1400 m, with V t = 31 m s −1 , and V r = 1 m s −1 at this height, which gives an inflow angle of about 1.8° (their Fig. 4). The magnitude of this inferred top-of-boundary-layer inflow angle agrees with our estimates from simulations (1.0°) and observations (also 1.0° globally). It should be noted that the concept of inflow angle in this study is assumed to be axisymmetric. However, for any given time and storm this inflow angle could be asymmetric because of, for example, storm motion and shear 44 .

Based on flight-level datasets, two primary types of growth processes were previously suggested 45 : an internally dominated process relating to secondary eyewall formation and eyewall replacement cycles, and an externally forced process by the synoptic environment. Environmental and internal conditions that have been found to be important to the TC outer size change, e.g., the potential intensity and midlevel relative humidity 46 , the surface fluxes 47 , the dynamics in the boundary layer 48 , and convective processes 49 , 50 , are not directly included in the derived growth model. However, the inflow angle can be taken as a key physical variable linking the effects of internal and external conditions and then directly affecting the growth process (as shown by Eq. ( 8 )). A further opportunity, beyond the scope of this work, may be to establish statistical relationships between the inflow angle and real-time internal and environmental conditions.

The proposed growth model does not predict a maximum equilibrium R 34 (if there is one per se). This is different from other TC intensification models 33 , 34 . Considering the differential form of the growth model (Eq. ( 7 )), the growth process is only terminated when the radial inflow ceases. Applying the model to a decrease of R 34 would require radial outflow at the top of the boundary layer by, for example, the Ekman spin down due to the surface turbulent drag 51 , 52 .

The growth model sheds light on the principal drivers of the interannual variation of LMS. The global LMS variability has so far been primarily driven by the variability in the duration of the growth. Future duration and hence LMS could change by, for example, a change in track length and/or change in translation speed. Predictions of translation speed are not uniform 53 , 54 so it is not clear what the likely changes of LMS could be.

Several studies have shown that the TC size has a positively skewed distribution for the radius of the outermost closed isobar 10 , the radius of 15 m s −1 wind 11 , the radius of 17 m s −1 wind 55 , and the radius of the eye 14 . A previous study 37 shows explicitly that the radius of vanishing storm wind is log-normally distributed when normalized by a relevant TC length scale defined as the ratio of the potential intensity to the Coriolis parameter. It has also been shown that the global distribution of the radius of 12 m s −1 is approximately lognormal only after the same normalization 12 .

In our analysis, the LMS of NA and EP TCs both follow a lognormal distribution without any normalization. This is not contradictory to the previous study 12 since their size climatology covered all sizes during a lifecycle. We show that the initial size distribution does not show a significant lognormal feature, but the lognormality of LMS is asymptotically achieved via exponential growth. Why does exponential growth increase the lognormality of the variable?

The exponential growth model is essentially an expression of the law of proportionate effect that states that according to the Central Limit Theorem, a lognormal distribution will be generated in the asymptotic limit 56 . The accumulation of the proportionate effect through the exponential growth process enhances the lognormal feature of the variate 57 , and in our analysis, this variate is the TC outer size.

The main uncertainty of the current study comes from the best-track data set taken from the National Hurricane Center (NHC) and Joint Typhoon Warming Center (JTWC). Consensus methods 58 are used at both NHC and JTWC for operational R 34 forecast. Most of our analysis is based on the NHC best track in the NA and EP after 2004 when the quality can be relatively more guaranteed after rigorous post-season analysis with more observations and proxies. In the NHC best track, the percentage uncertainty of R 34 in the NA relative to the average value varies from about 25–35% depending on the availability of multiple observations 59 . The EP TC best track from NHC is also post-season quality controlled, but the associated uncertainty is unknown. Most of the R 34 from the JTWC best track used in this study is real-time estimated since the post-season quality control only started at JTWC basins about three years ago. It was reported that the average R 34 in the JTWC basins increases by 25% after the post-season analysis 60 . The mean R 34 uncertainty from both NHC and JTWC has been estimated 61 to be about 15%. This uncertainty can be expected to be further reduced in the future 62 .

An analytic growth model of TC outer size is derived in this study. The proposed model suggests an exponential process for the outer size growth. The observed composite of size growth shows a strong super linear nature, which supports the exponential growth of TC outer size. The analytic growth model can capture the size growth of both modeled and observed individual storm events. A climatology of TC size growth in the NA and EP for 2004–2017 identifies the key factors of size growth as suggested by the analytic growth model, i.e., the initial size, growth duration, mean growth latitude and mean effective inflow angle. These four variables are significantly different between NA and EP TCs. The lifetime maximum size distribution is lognormal, whereas the lognormal characteristic is much weaker for the initial size. It is the law of proportionate effect, a consequence of the exponential growth model, that enhances the lognormality of TC outer size via an exponential growth process.

A global climatology of TC size growth shows that each basin has a unique combination of size growth factors. The model framework presented here links together several previous empirical findings, such as the role of initial size on final size, the dependence of size on latitude, inter-basin size differences, and the lognormal distribution of size. The proposed growth model provides a simple framework to understand the interannual variability of the lifetime maximum size that may be largely driven by the variation of the growth duration.

The TC best-track data for 2004–2017, including the storm type (e.g., tropical storm, extratropical transition), geographical location, intensity, and R 34 measurement, are taken from the International Best Track and Archive for Climate Stewardship 63 Version 4. In the NA and EP, the quality of R 34 observations since 2004 can be relatively more guaranteed after rigorous post-season analysis 46 , but we will also give a brief global climatology of TC size growth to cover the Western Pacific (WP), North Indian Ocean (NI), South Indian Ocean (SI) and South Pacific (SP). The TC best track in the NA and EP are taken from the National Hurricane Center (NHC), and for the other basins from the Joint Typhoon Warming Center (JTWC, Sampson et al. 60 ).

The TC records in IBTrACS are reported regularly at 0000, 0600, 1200, and 1800 UTC. More frequent measurements during landfall are excluded from our analyses. For each best-track subset of individual cyclones, R 34 is calculated as the mean in four quadrants. The quadrants where R 34 equals 0 are excluded from the averaging following previous studies 64 , 65 . Figure 6 shows the full IBTrACS tracks (gray lines) in the NA and EP for 2004–2017. The partial tracks (color lines) used in our analysis are also highlighted in Fig. 6 after the following pre-processing procedures:

no extratropical transition period as labeled in the best-track data is considered,

a record is only considered if the TC center is over water,

only the records from the first R 34 measurement to the lifetime maximum R 34 are selected for each TC, and

TCs must have at least eight consecutive R 34 records for 2 complete days.

Best track of NA and EP TCs for 2004–2017 before (gray tracks) and after (color tracks) data filtering.

Full-physics idealized tropical cyclone simulation

To validate the growth model and examine the steady-state inflow angle assumption we perform idealized TC simulations. We use the full-physics atmospheric Weather Research and Forecasting (WRF) Model 66 in the set-up described in ref. 20 . The run is configured with a triple nesting grid mesh, 4-km grid spacing in the innermost domain, and an initial bogus vortex specified with an analytic wind profile model 7 , 39 . The simulation is conducted in a stationary environment with a constant sea-surface temperature of 27 °C. The run lasts for 9 days, the last 6 days of which is employed for our analysis.

Lognormality test and statistical significance

The P value of a lognormal distribution test is estimated with the Kolmogorov–Smirnov (KS) test. The null hypothesis of the KS test is that the tested and target distributions are identical. A P value approaching unity indicates that the tested distribution becomes close to the target distribution. A bootstrapping method is applied to examine the statistical significance of the difference between two distributions, considering the skewness of the examined growth parameters. First, the two distributions are resampled 10,000 times to generate 10,000 pairs of distributions. Each resampled member has the same sample size as its parent distribution, and the elements in a parent distribution can be repeated during bootstrapping. Second, the difference in the means between the resampled distributions in each pair is calculated to form a new distribution with 10,000 samples. Thirdly, the percentile of zero difference is calculated to get the two-sided P value for the statistical significance. For example, a percentile of zero difference lower than the 2.5th or higher than the 97.5th suggests the two distributions are different at the 95% confidence interval.

Growth model fit

We validate the growth model (Eq. ( 9 )) by fitting both simulated and observed TC outer size evolution with least-squares minimization. For each fit, there are six parameters: three inputs and three estimates. The three inputs are the observed: initial size, mean latitude during growth, and growth duration. Three estimates are made: the mean effective inflow angle \(\overline{{\alpha }_{V}}\) , LMS, and doubling time (Eq. ( 10 )).

The R 34 in the best track is measured by near-surface total wind speed, but the growth model is derived at the top of the boundary layer for a fixed tangential wind speed. To resolve this inconsistency, we assume a wind adjustment factor of 0.75 from the top of the boundary layer to surface 67 , 68 . We will fit the model to the surface R 34 , but with this adjustment factor, the tangential wind of 34 kt at the surface R 34 will be adjusted to 34/0.75 kt ≈45 kt at the top of the boundary layer. A vertical disconnection of lower-troposphere horizontal wind during landfall may happen 69 , and that may significantly change the wind adjustment factor. However, that concern does not apply to our analysis since any landfall period is not included in our analysis. Our general results are not sensitive to the choice of the adjustment factor varying between 0.7 and 1.0.

Data availability

Tropical cyclone best-track data can be downloaded from the National Centers for Environmental Information website ( https://www.ncei.noaa.gov/data/international-best-track-archive-for-climate-stewardship-ibtracs/v04r00/access/csv/ibtracs.ALL.list.v04r00.csv ).

Code availability

The source codes for the analysis of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work was supported by the Natural Environment Research Council/UKRI (NE/V017756/1) and the UK-China Research and Innovation Partnership Fund through the Met Office Climate Science for Service Partnership (CSSP) China as part of the Newton Fund.

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A hypothesis for the intensification of tropical cyclones under moderate vertical wind shear

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A major open issue in tropical meteorology is how and why some tropical cyclones intensify under moderate vertical wind shear. This study tackles that issue by diagnosing physical processes of tropical cyclone intensification in a moderately sheared environment using a 20-member ensemble of ideal... Show more A major open issue in tropical meteorology is how and why some tropical cyclones intensify under moderate vertical wind shear. This study tackles that issue by diagnosing physical processes of tropical cyclone intensification in a moderately sheared environment using a 20-member ensemble of idealized simulations. Consistent with previous studies, the ensemble shows that the onset of intensification largely depends on the timing of vortex tilt reduction and symmetrization of precipitation. A new contribution of this work is a process-based analysis following a shear-induced midtropospheric vortex with its associated precipitation. This analysis shows that tilt reduction and symmetrization precede intensification because those processes are associated with a substantial increase in near-surface vertical mass fluxes and equivalent potential temperature. A vorticity budget demonstrates that the increased near-surface vertical mass fluxes aid intensification via near-surface stretching of absolute vorticity and free-tropospheric tilting of horizontal vorticity. Importantly, tilt reduction happens because of a vortex merger processnot because of advective vortex alignmentthat yields a single closed circulation over a deep layer. Vortex merger only happens after the midtropospheric vortex reaches upshear left, where the flow configuration favors near-surface vortex stretching, deep updrafts, and a substantial reduction of low-entropy fluxes. These results lead to the hypothesis that intensification under moderate shear happens if and when a restructuring process is completed, after which a closed circulation favors persistent vorticity spinup and recirculating warm, moist air parcels. Show less

Rosimar Rios-Berrios-NCAR/UCAR

Christopher A. Davis-NCAR/UCAR

Ryan D. Torn

Journal of the Atmospheric Sciences

http://dx.doi.org/10.1175/JAS-D-18-0070.1

http://n2t.net/ark:/85065/d79p34mp

Tropical Cyclones
Nearest Living Relative Analysis
Oxygen Isotope Analysis
Convective Cloud Feedback
Hadley Cells
Polar Stratospheric Clouds

Following Emanuel's hypothesis about tropical cyclones, other people have investigated the impact of cyclones on OHT and the possibility of cyclones causing equable climates. The other studies have shown that tropical cyclones do increase OHT; however, there are some aspects of the system that Emanuel did not consider in his first paper.

Ryan L. Sriver and Matthew Huber examined SSTs before and after tropical cyclone events to see the effects of cyclones on OHT. They used the difference in temperatures to estimate the amount of vertical mixing that occurred as a result of cyclones, and they assumed that any cooling that occurred on the sea surface was a result of vertical mixing. After they had obtained estimates for the amount of vertical mixing, they assumed that all of the heat diffused downward eventually had to have been translated into OHT. Their results showed that roughly 15% of peak OHT is attributable to mixing induced by tropical cyclones and that about half of the thermohaline circulation may result from this same vertical mixing (Sriver and Huber, 2007). Additionally, they found that tropical SSTs are highly correlated to globally integrated annual ocean heat content (OHC) and OHT (r 2 =0.73). When tropical SSTs decrease, OHC and OHT increase. As a result, their data supports the idea that cyclone activity increases OHT out of the Tropics, but they fail to acknowledge one important aspect of OHT.

Sriver's and Huber's study shows a correlation between cyclone activity, SST, and OHT. (Sriver and Huber, 2007)

The ocean is very good at removing heat from the Tropics and moving it to the mid-latitudes; however, by about 50° latitude, the ocean does not transport much heat further north. Instead, the atmosphere handles most of the heat transport after that point. This fact hurts Emanuel's hypothesis because the ocean does not to bring heat to the high-latitudes, so even if tropical cyclones were to increase in frequency or intensity, the heat would only be transported to the mid-latitudes. Therefore, it seems unlikely that tropical cyclones would be fully responsible for equable climates.

Ocean OHT (green) drops off by about 50°. (MIT's CMI)

Work by Malte Jansen and Raffaele Ferrari also has exposed a problem with Emanuel's idea. In their paper from 2009, Jansen and Ferrari examine the effects on OHT based on where mixing occurs. They argue that cyclones do not mix the entire area around the equator but rather that they generally mix certain latitude bands. They base this idea off of the fact that tropical cyclones rarely tend to happen equatorward of 8° to 10° latitude (Jansen Ferrari, 2009). This trend exists because water slightly north and south of the equator actually tends to be warmer than water at the equator because upwelling of cold, deep water at the equator cools the sea surface there.

Cyclones tend to occur in bands off of the equator. (Jansen and Ferrari, 2009)

Using this fact as a basis, Jansen and Ferrari performed a study to examine the effects of mixing when it occurs in different latitude bands. In the study, they performed four different runs: a control run that simulated normal conditions, a "no gap" run that had mixing between 31°N and 31°S, a run with mixing between 5.6° and 31° latitude, and a run with mixing between 11.2° and 31° latitude. The "no gap" run revealed that when mixing occurs throughout all of the low-latitudes poleward OHT increases. The runs with gaps, however, showed a different result. When mixing did not occur in a gap around the equator, both poleward and equatorward OHT existed. The model demonstrated that two different circulation cells could form with water moving away from the mixing band and sinking in the poles and at the equator. Because some of the heat would move toward the equator, having a gap would reduce poleward OHT. In their own words, "mixing triggered by [tropical cyclones] primarily induces an equatorward transport of heat and results in an overall decrease of poleward OHT out of the equatorial region" (Jansen and Ferrari, 2009). Therefore, their study contradicts Emanuel's thoughts. While it is possible that tropical cyclones could increase poleward OHT, they are more likely to reduce poleward OHT and to increase equatorward OHT because they rarely occur directly over the equator. Using the characteristics of tropical cyclones' locations as their base, Jansen and Ferrari show that it is unlikely that tropical cyclones instigated equable climates.

The "no gap" run increases poleward OHT, while the gap runs show both poleward and equatorward OHT. (Jansen and Ferrari, 2009)

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Original research article, a hypothesis and a case-study projection of an influence of mjo modulation on boreal-summer tropical cyclogenesis in a warmer climate with a global non-hydrostatic model: a transition toward the central pacific.

1 Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokohama-Shi, Kanagawa, Japan
2 Center for Earth Surface System, Atmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa-Shi, Chiba, Japan
3 Computational Climate Science Research Team, Advanced Institute for Computational Science/RIKEN, Kobe, Hyogo, Japan

The eastward shift of the enhanced activity of tropical cyclone to the central Pacific is a robust projection result for a future warmer climate, and is shared by most of the state-of-the-art climate models. The shift has been argued to originate from the underlying El-Ñino like sea surface temperature (SST) forcing. This study explores the possibility that the change of the activity of the Madden–Julian Oscillation (MJO) can be an additional, if not alternative, contributor to the shift, using the dataset of Yamada et al. (2010) from a global non-hydrostatic 14-km grid mesh time-slice experiment for a boreal-summer case. Within the case-study framework, we develop the hypothesis that an eastward shift of the high-activity area of the MJO, as manifested itself as the significant intra-seasonal modulation of the enhanced precipitation, is associated with the increased tropical cyclogenesis potential over the North central Pacific by regulating cyclonic relative vorticity and vertical shear. In contrast, the North Indian Ocean and maritime continent undergo relatively diminished genesis potential. An implication is that uncertainty in the future tropical cyclogenesis in some part of the Pacific and other ocean basins could be reduced if projection of the MJO and its connection with the underlying SST environment can be better understood and constrained by the improvement of climate models.

Introduction

The regional change of tropical cyclones in future warmer climate has been a highly debated area of research. Even the sign of change in cyclone frequency differs from one model to another based on well-coordinated recent model datasets from Coupled Model Intercomparison Project (CMIP) 3 and 5 ( Knutson et al., 2010 ; Camargo, 2013 ; Emanuel, 2013 ; Tory et al., 2013 ). However, the state-of-the art hydrostatic general circulation models all project an overall increase of genesis in the central Pacific, compared to present-day climatic conditions ( Li et al., 2010 ; Murakami et al., 2012 ; Zhao and Held, 2012 ). This change was mostly ascribed to the underlying El-Ñino-type sea surface temperature (SST) forcing which was specified as a warmer climate condition. Notably, a time-slice experiment with the global non-hydrostatic model also projected a similar change of tropical cyclone activity ( Yamada et al., 2010 ; Y2010). It remains unclear however how the change of the tropical cyclogenesis would be influenced by the associated changes of atmospheric phenomena such as the Madden–Julian Oscillation (MJO, Madden and Julian, 1971 , 1972 ). Li et al. (2010) indicated that the enhanced tropical cyclone activity over the central Pacific region can be related to an increased variance of tropical synoptic-scale perturbations. This short article sheds a new light on this problem by focusing on a link between the change in the role and horizontal distribution of the MJO and the tropical cyclogenesis over the North central Pacific under a warmer climate state based on the experiment reported by Yamada et al. (2010) . Note that the boreal-summer season is the focus of this research.

The model used is the Non-hydrostatic ICosahedral Atmospheric Model (NICAM, Tomita and Satoh, 2004 ; Satoh et al., 2008 ), a global model that is capable of calculating meso-scale convection, which is an essential building block of tropical convection, but a most elusive element in traditional hydrostatic models. With these benefits, NICAM simulations captured boreal winter- ( Miura et al., 2007 ; Fudeyasu et al., 2008 ), spring- ( Taniguchi et al., 2010 ), and summer-time ( Oouchi et al., 2009 , 2012 ; Satoh et al., 2012 ) MJO events and associated tropical cyclogenesis as well. The application of NICAM to research on the future change of the MJO and tropical cyclogenesis draws strongly upon these successful case studies. This study does not go beyond the case-study framework. As the model needs large computational resources, we were required to make some compromises with respect to various aspects, e.g., temporal duration and the size of ensembles in order to perform the integration necessary to obtain a greater statistical validity for intra-seasonal phenomenon such as MJO. The time integration is 5 months each of present and future experiments. Among various issues of MJO, this study focuses on the geographical change of the MJO activity that can be related to tropical cyclogenesis. The design of the experiment is explained in section Experimental Design, which is followed by the presentation of the results in section Results. Section Summary and Remarks concludes with a summary and further remarks.

Experimental Design

The NICAM experiments are performed using a grid spacing of around 14-km. The method used is a time-slice experiment ( Bengtsson et al., 1996 ), and details are explained in Yamada et al. (2010) . To be brief, the model is integrated over the five (JJASO) and six (MJJASO)—months period for present-climate (PRESENT) and future (FUTURE) experiment, respectively. The SST in PRESENT is derived from the NOAA Optimum Interporation (OI) SST V2 dataset for 2004 ( Reynolds et al., 2002 ). In FUTURE, the model was spun up during all of May, which is excluded from the analysis. The FUTURE SST forcing is created by adding the differences between PRESENT (1979–2003) and FUTURE (2075–2099) onto the PRESENT SST with the dataset of the World Climate Research Program Coupled Model Inter-comparison Project phase 3 (CMIP3), following the method of Mizuta et al. (2008) . The forcing has an El-Ñino like horizontal pattern (Y2010, Figure 1 ) which, as argued later, affects the interpretation of the results. The projection of tropical cyclone change in the same suite of data is reported in Y2010 along with its comparison with a downscaling method ( Emanuel et al., 2010 ). The tracking methodology of tropical cyclone follows Yamada et al. (2010) . The observational dataset is from the Unisys Corporation ( http://weather.unisys.com/hurricane/ ).

Figure 1. (A) Hovmoller plots of precipitation averaged over 5° S–5° N [mm day −1 ] for PRESENT. (B) Same as (A) except for FUTURE. (C) Blue bars: accumulated precipitation amount [mm] summed over the date with higher precipitation rate (more than 8 mm day −1 ) during JJASO for PRESENT; bottom numerals: tropical cyclone counts for western Pacific, Indian Ocean, Pacific, and Atlantic. Pacific area are divided as 100°–150° E, 150° E–160° W, and 160°–90° W with slash marks, (D) Same as (C) .

We first focus on a comparison of the time series of equatorial precipitation, zonal distribution of its accumulated amount, and zonal-vertical circulation in the tropical region between PRESENT and FUTURE (Figure 1 ). A significant future change in precipitation is the increased precipitation near the dateline, a location which closely coincides with the underlying largest SST forcing (Figures S1A,B). The precipitation undergoes a marked intra-seasonal modulation in FUTURE. Consequently, the main area of upwelling for JJASO is located more eastwardly in FUTURE, and is characterized by the intensified vertical shear in the western and eastern branches with respect to its center (Figures S1C,D).

The change in the zonal circulation pattern is also confirmed by both the Walker Circulation Index (WCI, Wang, 2002 ) and also the tropospheric (from the surface to 150 hPa) moisture convergence flux (MFlx) averaged over the Indian ocean (60–100°E) (Figure S2). The Walker circulation is driven by the temperature difference in the underlying SST along the equatorial Pacific, and the WCI measures the vertical velocity anomaly difference between the eastern and western Pacific region at the 500-hPa level (See Wang, 2002 for a detailed definition).

An overall comparison reveals that throughout the simulation periods, the sign of the temporal WCI variation is almost in phase with that of MFlx in PRESENT, and out of phase in FUTURE. In other words, the zonal circulation pattern over the Indian-Ocean to the entire Pacific sector changes in FUTURE from bimodal to unimodal consisting respectively, of upward/downward motions in the central Pacific and downward/upward motions in the western Pacific and the Indian Ocean.

Figures 1C,D is annotated with tropical cyclone counts during JJASO. Each of the three numbers separated by slash marks are the Pacific counts for 100–150° E, 150 o E–160 o W, and 160–90 o W, respectively. The total number of tropical cyclones decreases in FUTURE, as previously shown by Y2010, and consistent with other previous studies. However, an increase in the FUTURE count is evident over the central Pacific (150 o E–160 o W), in contrast with a decrease over the western side (100–150 o E), showing an eastward shift of tropical cyclogenesis in FUTURE. Figure 1B shows the intra-seasonal variation of precipitation over the central Pacific. This implies that the increase in tropical cyclones over the North central Pacific is related not solely to the change in stationary flows associated with the ENSO-type SST response, but also to changes in intra-seasonal oscillations, i.e., the MJO. It is unclear whether any intra-seasonal variability of precipitation over the central Pacific is associated with the MJO. The next question is in what way the active areas of the MJO and tropical cyclogenesis change in association with these changes in climate state.

The change in MJO activity can be seen in Figure 2 displaying the Hovmoller plots of zonal velocity anomaly at 200 hPa ( A,B ), and Real-time Multivariate (RMM) MJO indices ( C,D ) based on Wheeler and Hendon (2004) (WH04). The indices elucidate the behaviors of MJO over the different longitudes. They are based on extended empirical orthogonal function analysis of zonal velocity anomalies at 200 and 850 hPa in addition to the outgoing longwave radiation (OLR) anomaly derived from the daily outputs. To create anomalies, the climatological mean of the reanalysis dataset for the period 1979–2001 is subtracted from the raw output using NCEP/NCAR daily reanalysis ( Kalnay et al., 1996 ) for velocities and NOAA for OLR. Each anomaly is then divided by its longitudinally-averaged normalization factor (as computed in WH04 to be 15.1 Wm −2 for OLR, 1.81 ms −1 for 850 hPa zonal wind, and 4.81 ms −1 for 200 hPa zonal wind), and then these are projected onto the WH04 EOFs. Estimating the applicability of the indices to the future climate dataset is an important subject for future studies.

Figure 2. (A) Hovmoller plots of zonal velocity anomaly at 200 hPa from the time average over JJASO [ms −1 ] for PRESENT. (B) Same as (A) except for FUTURE. (C) PC1–PC2 phase-space points of JJASO MJO activity for PRESENT based on the method of Wheeler and Hendon (2004) . For each of eight equal-angled phase-space categories, the approximate locations of the enhanced convective signal of MJO are labeled. (D) Same as (C) except for FUTURE.

There are eight phases for categorizing the convectively active signal of the MJO (PH1–8), each of which roughly corresponds to the area of active MJO center. Overall, the eastward movement of the velocity is seen both in PRESENT and FUTURE (Figures 2A,B ), and clear amplifications of its eastward movement are detected in FUTURE (e.g., earlier in August over 120–60 o W, and in late August over 120 o E–180 o ). On the RMM phase space, the eastward movement of the MJO can be seen through the traces moving counter-clockwise across the corresponding geographical location. Figure 2C indicates the presence of an eastward movement from early June to early July which corresponds to the MJO case discussed by Oouchi et al. (2009) . During July and August, no clear eastward movement is present compared to the observations (URL: http://cawcr.gov.au/staff/mwheeler/maproom/RMM/phasediag/pd.2004.6.1.gif ), but it is followed by a stronger signal in October across PH6 and 7, being almost comparable to a western Pacific MJO signal in the early October ( Nakazawa, 2006 ). As we do not expect the model to be skillful at simulating the behavior of the MJO beyond 20 days or so ( Vitart, 2009 ), the apparent similarity of the signals later than mid-July is not examined further here. A comparison between PRESENT and FUTURE reveals a series of suppressed signals during June and July, while a stronger signal is present in August corresponding to the one mentioned above. Among PH1–8, the amplitude in FUTURE increases relatively in PH6 and 7, compared to PH2–4. These results are consistent with the intuitive impressions obtained by the Hovmoller diagrams shown by Figure 1 .

To see a rough linkage between the change of the MJO and the environment of tropical cyclogenesis, Figures 3A,B illustrates the large RMM phase (LRP, eastward propagation only) which we define as the date when the difference of the maximum amplitude of MJO index between the consecutive 6-days period is larger than 1.2 (red triangles) or between 0.8 and 1.2 (blue triangles); ( C,D ) are the meridional-time plot of genesis potential density (GPD) defined as the ratio of genesis potential index (GPI; Emanuel and Nolan, 2004 ) with respect to the entire period and PH regions. In this study, GPI is calculated for each of the following areas for major ocean basins to facilitate discussion: (Indian Ocean, 45–90° E; maritime continent, 90–110° E; Western Pacific, 100–150° E; Central Pacific, 150° E–160° W; Eastern Pacific and Atlantic, 160–20° W. In PRESENT, we cannot see close correspondence between the LRP in excess of 1.2 and a higher GPD. In other words, GPD is not necessarily contributed to by the growth of RMM in PRESENT. On the other hand, in FUTURE the correspondence becomes stronger over the central Pacific (PH6 and 7), and to some degree over the Eastern Pacific and Atlantic, suggesting a closer link between the MJO's amplification, and higher GPD over the central Pacific. Interestingly, the higher GPD is more dominant over the central Pacific and the western hemisphere than it is elsewhere in FUTURE. This may be associated with the bimodal/unimodal circulation patterns in PRESENT/FUTURE (Figure S1).

Figure 3. (A) The large RMM phases defined as the date when the difference of the maximum RMM amplitude between the consecutive 6-days period is larger than 1.2 (red) and 0.8 (blue) for PRESENT. (B) Same as (A) except for FUTURE. (C) Time series of genesis potential index ( Emanuel and Nolan, 2004 ) density [%] for PRESENT for the following regions: Indian Ocean, 45–90° E; maritime continent, 90–110° E; Western Pacific, 100–150° E; Central Pacific, 150°E–160°W; Eastern Pacific and Atlantic, 160–20° W. The density is with respect to whole defined regions and period (JJASO). (D) Same as (C) except for FUTURE.

To investigate the link between MJO and tropical cyclogenesis potential in the North central Pacific, the meridional-time plot of relative vorticity anomaly at 850 hPa over 150 o E–160 o W is shown in the upper panel of Figure 4A for PRESENT and ( B ) for FUTURE. The “central” Pacific region is selected, as defined in the tropical cyclone count in the slash-marked values in Figures 1A,B . The bottom sub-panels ( A,B ) plot the time series of the relative vorticity, RMM amplitude (larger than 0.8), and vertical shear averaged over 0–10° N and the longitudinal region. A comparison between PRESENT and FUTURE reveals that increased cylonic vorticity is more notable in FUTURE. The increase closely coincides with that of the RMM amplitude and also the decrease of the vertical shear, and these features become more pronounced in FUTURE. This suggests that the propagation of the MJO and associated enhancement of vorticity and weakening of vertical shear can contribute positively to tropical cyclogenesis over the North central Pacific region in FUTURE. The tropical cyclogenesis locations are plotted in the upper panels of Figures 4A,B . We can see that the genesis in FUTURE occurs at the timing of the larger RMM phase, and it is associated with larger values of cyclonic vorticity and negative anomaly of vertical shear more clearly than PRESENT. A clear case occurs during first August–mid September. These results suggest a possible connection between the eastward shift of the MJO location and that of tropical cyclogenesis over the North central Pacific in FUTURE.

Figure 4. (A) Top; Meridional-time plot of relative vorticity at 850 hPa averaged over 150° E–160° W (the “central” Pacific region as defined in the tropical cyclone count in the slash-marked values in Figures 1C,D ) for PRESENT, Bottom; the time series of relative vorticity (multiplied by arbitrary factor), RMM amplitude (larger than 0.8), and vertical shear averaged over the above longitudinal region and 0–10° N. The tropical cyclone marks indicate the genesis points in the region. (B) Same as (A) except for FUTURE.

Summary and Remarks

The eastward shift of the enhanced Pacific tropical cyclone activity—from the western Pacific to the central Pacific—under a future warmer climate has been a widely projected result in the global climate models, including the global non-hydrostatic model (Y2010). However, no previous studies have discussed its association with the change of the MJO. This study proposes a hypothesis for this question within a boreal summer case-study framework of Y2010 using the global non-hydrostatic model NICAM. Although the simulation is too short to consider inter-annual variability, numerical results show a common signal of decrease in the total number of tropical cyclones in FUTURE (Y2010). In our result, the increase in tropical cyclones is seen over the North central Pacific; this motivates us to further investigate what causes the enhancement of tropical cyclone activity over the North central Pacific in FUTURE. We found that the simulated MJO becomes active in August in FUTURE, and tropical cyclones are more generated associated with this active MJO.

Our study has the following implications: (1) an eastward shift of the higher activity area of the MJO reaching the central Pacific with its likely association with the underlying SST forcing, enhanced precipitation and Walker circulation; (2) relatively weakened activity over the tropical warm pool across the Indian Ocean to maritime continent; (3) an increase in tropical cyclogenesis potential over the North central Pacific associated to some extent with the propagation of MJO that favorably controls the vertical shear and relative vorticity, and (4) relatively suppressed tropical cyclogenesis potential over the North Indian Ocean and maritime continent, whose association with MJO activity relative to other factors remains to be substantiated. The finding (1) supports the prevailing notion that the warmer SST condition helps sustain or enhance the development of MJO, and is consistent with the observational evidence that convective activity and the atmospheric response to SST propagates more eastwardly into the central Pacific in El-Ñino years ( Dunkerton and Crum, 1995 ; Hendon et al., 1999 ; Kessler, 2001 ). It remains to be completely clarified whether TC genesis under such a condition would be more likely to appear under either or both of the effects of MJO and SST, which may not be competing depending on the time scale of interest.

In the context of the present climate, there is a large body of observational studies on the possible modulation of tropical cyclones by the MJO over the global basins (e.g., Camargo et al., 2009 ), the western Pacific (e.g., Nakazawa, 1986 ; Liebmann et al., 1994 ; Kim et al., 2008 ), and the Atlantic ( Klotzbach, 2010 ). This paper focuses on the potential increase of tropical cyclones through the change of MJO-associated synoptic-scale environmental fields including the parameters relevant to the modulation associated with the MJO (e.g., intensified relative vorticity, and moderated vertical shear, Camargo et al., 2009 ) over the central Pacific. Clarification of the mechanism behind the causal relationship between the activation of the MJO and the net increase of TC awaits further study. One might argue that such a straightforward extrapolation of “present-climate” analogy to future condition needs to be carefully considered. There can be other factors responsible for increase of the total number of TCs that may differ from one basin to another depending on the different background states between future and present climate conditions, and this question is left for future investigation. It should also be noted that much longer-term simulation is necessary to clarify how TC modulation is affected by different MJO-phases (both active- and inactive- MJO periods), in addition to the MJO-active case presented here. These concerns need to be addressed in future.

While our results suggest that our understanding of changes in Pacific tropical cyclogenesis in a future warmer climate may be enhanced by further research on the link between MJO and associated tropical cyclogenesis, much work remains to be done. As only a very few MJO events are simulated in our study, the generality of the results cannot be proven in any climatological sense, and this needs to be investigated in future with longer-period simulations. This study does not consider future changes of the MJO (and evaluation of the MJO index) per se , which would need a larger sample size with extended simulation period, and which could bring new challenges of its own. Additionally, some cautions need to be kept in mind to ensure progress in a suitable direction. Pacific tropical cyclogenesis is known to be substantially affected by other tropical disturbances in addition to the MJO, including equatorial waves (e.g., Li, 2012 ). Even when the MJO apparently controls cyclogenesis, other disturbances can play roles in some way or another, associated with or independent of the presence of the MJO. In this article, the effects of the other disturbances are ignored in favor of the MJO, assuming that the MJO would exert the largest scale first-order control. Identifying the relative effects of the other disturbances will be a priority for future investigation. We also did not address the exact role of the MJO in controlling the frequency: whether it generates or modulates the tropical cyclone activity, and what sub-synoptic pathway is present to the emergent tropical cyclone. Future work should explore this issue. Given the shortness of the time integration spanning 5 months, this study is viewed as a case study for a boreal summer season. We plan to extend the experiment across the seasons to evaluate the statistical reliability of the findings. In the near future, we also plan to expand the temporal boundaries of the research as we get access to greater computing resources via the K-computer ( Yokokawa et al., 2011 ).

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The author thanks development members of NICAM team. The numerical experiments were performed on the Earth Simulator of JAMSTEC under the framework of KAKUSHIN project funded by the Ministry of Education, Culture, Sports, Science, and Technology, Japan. The CMIP3 sea surface temperature and sea ice concentration dataset was provided by the Meteorological Research Institute. The comments from reviewers helped improve the original manuscript.

Supplementary Material

The Supplementary Material for this article can be found online at: http://www.frontiersin.org/journal/10.3389/feart.2014.00001/abstract

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Keywords: central-Pacific tropical cyclone, future MJO, global non-hydrostatic projection, model-derived hypothesis, seamless weather projection

Citation: Oouchi K, Satoh M, Yamada Y, Tomita H and Sugi M (2014) A hypothesis and a case-study projection of an influence of MJO modulation on boreal-summer tropical cyclogenesis in a warmer climate with a global non-hydrostatic model: a transition toward the central Pacific? Front. Earth Sci . 2 :1. doi: 10.3389/feart.2014.00001

Received: 04 December 2013; Accepted: 28 January 2014; Published online: 18 February 2014.

Reviewed by:

Copyright © 2014 Oouchi, Satoh, Yamada, Tomita and Sugi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Kazuyoshi Oouchi, Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showamachi, Kanazawa-ku, Yokohama-Shi, Kanagawa 236-0001, Japan e-mail: [email protected]

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Tropical Cyclone Nivar – Geography Grade 12 Research Task

On this page, we have compiled a general guide for Grade 12 Geography Students who are doing their research on Tropical Cyclone Nivar.

In November 2020, Tropical Cyclone Nivar emerged as a significant meteorological event, marking itself as only the third cyclone to make landfall in India since the formidable storm Amphan earlier in May of the same year. This educational article delves into the formation, trajectory, and impacts of Cyclone Nivar, equipping students with a comprehensive understanding of its dynamics and effects.

Table of Contents

Why do tropical cyclones such as Nivar develop in late summer?

Tropical Cyclone Nivar developed in the Bay of Bengal during late November 2020, a period when ocean temperatures are warm enough to support cyclone formation. Warm sea temperatures are crucial for cyclone genesis, providing the energy needed for these systems to develop and intensify.

What is the impact of coriolis force and latent heat on the development of tropical cyclone Nivar?

The Coriolis force and latent heat were instrumental in the development of Tropical Cyclone Nivar. The Coriolis effect, due to the Earth’s rotation, gives the storm its spinning motion, while the release of latent heat during water vapor condensation supplies the energy that fuels the cyclone’s intensification and sustenance.

Discuss the stage of development of the tropical cyclone Nivar.

Forming in the Bay of Bengal, Tropical Cyclone Nivar made landfall between 26 and 28 November 2020, hitting Puducherry and parts of Tamil Nadu, including Chennai, as well as Andhra Pradesh. Initially classified as ‘very severe’, Nivar weakened to ‘a severe cyclonic storm’ after landfall, demonstrating the typical lifecycle of tropical cyclones as they interact with land.

Why can category 1 tropical cyclones be more destructive (damaging) than category 5 tropical cyclones?

Though not explicitly detailed in the reports on Nivar, it is understood that category 1 tropical cyclones can cause significant damage, particularly if they affect vulnerable, densely populated areas, due to prolonged wind, rain exposure, and the heightened potential for flooding, as observed with Nivar’s impact.

How did this tropical cyclone impact the following?

Environment.

Tropical Cyclone Nivar led to extensive environmental damage, including over 1000 uprooted trees, flooding, and blocked waterways, showcasing the significant environmental disruption that can occur with such storms.

Nivar caused substantial economic losses through flooding, destruction of crops and plantations, damage to infrastructure, and the disruption of power supply, underscoring the broad economic impacts of cyclones.

People/Communities

The cyclone claimed four lives, injured several, and displaced thousands, with around 175,000 people taking shelter in rescue shelters. Evacuation efforts and the imposition of prohibitory orders to restrict movement were critical responses to safeguard communities.

What precautions can be implemented/ or has been implemented to reduce the impact of the tropical cyclone.

The local government/government of the country.

Preventive measures included mass evacuations, the deployment of the National Disaster Response Force (NDRF) , and advisories on cyclone preparedness. Tamil Nadu’s government also took measures to prevent metropolitan flooding in Chennai, showcasing proactive disaster management.

The local residents

Local residents were advised to secure their homes, switch off utilities, and heed official warnings. Such preparedness actions are crucial for minimizing personal and property loss during cyclones.

Evaluate the impact of Global Warming on the frequency (regularity) of tropical cyclones such as Nivar.

The warming of oceans, attributed to climate change, is linked to more intense cyclones and dangerous storm surges in the Bay of Bengal, as observed with Nivar. Conditions like La Nina further contribute to favorable cyclogenesis environments, suggesting that global warming may increase tropical cyclones’ frequency and severity.

Conclusion/Summary

Tropical Cyclone Nivar serves as a stark reminder of the devastating potential of tropical cyclones and the importance of preparedness, early warning systems, and effective disaster response mechanisms. The cyclone’s impacts on the environment, economy, and communities highlight the multifaceted challenges posed by such natural disasters, reinforcing the need for comprehensive strategies to mitigate their effects in an era of climate change.

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GEOGRAPHY SCHOOL BASED ASSESSMENT EXEMPLARS - CAPS GRADE 12 LEARNER'S GUIDE

GEOGRAPHY SCHOOL BASED ASSESSMENT EXEMPLARS - CAPS GRADE 12 LEARNER GUIDE

1. Introduction The purpose of this document is to provide learners with a set of benchmarked school- based assessment tasks (SBAs). It contains useful information and guidelines in the form of exemplars on the following aspects of the curriculum:

How to do a research task
Working with sources and source-based questions
Data handling
Marking rubrics as guidelines to completing research tasks

2. Objectives/Aims of the project It is envisaged that this SBA document will provide learners with examples of SBA tasks that are of high quality and a high standard.

A common standard is set as prescribed by the Curriculum and Assessment Policy Statement (CAPS) document.
Quality teaching and learning of FET – Grade 12 Geography is promoted throughout all schools in South Africa.

3. Assessment tasks as outlined by CAPS

4. Assessment tasks 4.1 Term 1 – Data-handling task Two examples of typical data-handling tasks are provided below.

4.1.1 Exemplar: Data-handling task 1

Curriculum content: Physical Geography (tropical cyclones, subtropical anti-cyclones and drainage basins) • Compliant with CAPS.
May be tested in the CAPS final external examination.
One (1) data-handling task must be done.

GRADE 12 SBA (CAPS 2014) DATA-HANDLING TASK PHYSICAL GEOGRAPHY

TIME: 1 hour (60 minutes) MARKS: 60 QUESTION 1 1.1 Refer to FIGURE 1A showing a synoptic weather map of Tropical Cyclone Irina.

1.1.1 Determine the number of tropical cyclones, including Irina, that has occurred during this tropical cyclone season. (1 x 2) (2) 1.1.2 Give a reason to support your answer to QUESTION 1.1.1. (1 x 2) (2) 1.1.3 Describe the surface air circulation within Tropical Cyclone Irina. (1 x 2) (2)

1.2 Refer to FIGURE 1B showing a satellite image of Tropical Cyclone Irina and FIGURE 1C showing the projected path of Tropical Cyclone Irina.

1.2.1 Using the satellite image, determine in which stage of development Tropical Cyclone Irina is. (1 x 2) (2) 1.2.2 Give evidence from the satellite image to support your answer to QUESTION 1.2.1 (1 x 2) (2) 1.2.3 Discuss TWO socio-economic impacts of Tropical Cyclone Irina on areas along the east coast of southern Africa. (2 x 2) (4) 1.2.4 Draw a labelled cross-section of Tropical Cyclone Irina as depicted on the satellite image from X to Y. Clearly indicate the position of the eye and the cumulonimbus clouds on your cross-section. (2 x 2) (4) 1.2.5 State the reason for the use of the words, ‘projected path’ when describing the path of Tropical Cyclone Irina. (1 x 2) (2)

1.3 Refer to FIGURE 1A.

1.3.1 Identify the high-pressure cells labelled P and Q. (2 x 2) (4) 1.3.2 Use evidence from the map to explain whether wind speed will be greater in area P or area Q. (3 x 2) (6)

QUESTION 2 2.1 Refer to FIGURE 2A showing cross-sections of the Tugela River along its course in its drainage basin shown in FIGURE 2B.

2.1.1 Define the term drainage basin. (1 x 2) (2) 2.1.2 Which of FIGURE 2A and FIGURE 2B shows a longitudinal and transverse profile respectively? (2 x 2) (4) 2.1.3 Match each of cross-sections A, B and C (FIGURE 2A) with positions (i), (ii) and (iii) (FIGURE 2B). (3 x 2) (6) 2.1.4 Briefly explain the difference in the width of the river channel at A and C. (2 x 2) (4)

2.2 Refer to FIGURE 2B showing the drainage basin of the Tugela River from its upper to the middle to the lower course.

2.2.1 Determine the stream order of the Tugela River at point X along its course. 1 x 2) (2) 2.2.2 Identify and explain ONE of the stream channel patterns of the Tugela River at (ii) along its course. (3 x 2) (6) 2.2.3 Draw a labelled free-hand cross-section through the river channel along line T–S, showing the position of and the difference in shape between a slip-off slope and an undercut slope. (2 x 2) (4) 2.2.4 Give ONE reason why the Tugela River is more likely to flood in the vicinity of (iii). (1 x 2) (2)

[30] GRAND TOTAL: 60

4.1.2 Exemplar: Data-handling task 2

Curriculum content: People and their needs (gross domestic product, industrial areas, industrial development zones [IDZ])
Compliant with CAPS.
May be tested in the NCS and CAPS final external examination.

GRADE 12 SBA (CAPS 2014) DATA-HANDLING TASK PEOPLE AND THEIR NEEDS

TIME: 1 hour (60 minutes) MARKS: 60 QUESTION 1 1.1 Refer to FIGURES 1A and 1B and answer the questions that follow.

1.1.1 Define the following terms:

Gross domestic product (1 x 2) (2)
Balance of trade (1 x 2) (2)

1.2 Identify the largest and the smallest contributor to the South African GDP. (2 x 2) (4) 1.3 Use FIGURE 1B to describe the trend of the South African GDP from 2010 to 2012. (1 x 2) (2) 1.4 How will the trend mentioned in QUESTION 1.3 affect South Africa’s Balance of Trade? (1 x 2) (2) 1.5 Which economic activity (primary, secondary or tertiary) in FIGURE 1A accounts for the existing trend mentioned in QUESTION 1.3? (1 x 2) (2) 1.6 Discuss the relationship between the percentage contributed by agriculture to the South African GDP and food security in the country. (2 x 2) (4) 1.7 FIGURE 1A indicates that the agricultural sector contributes a very small percentage to the GDP. Write a short paragraph (approximately 12 lines) in which you account for the small contribution of the agricultural sector to the South African GDP. (6 x 2) (12)

2.3 Explain any TWO factors that have led to the growth and development of the industrial area referred to in QUESTION 2.2. (2 x 2) (4)

QUESTION 3 Refer to FIGURE 3 before answering the questions below. 3.1 What is an IDZ? (1 x 2) (2) 3.2 Name the province in which the Coega IDZ is located. (1 x 2) (2) 3.3 Briefly describe TWO aims for the development of the Coega IDZ. (2 x 2) (4) 3.4 As a manufacturer of heavy earth-moving equipment for sale in Asia, explain what would encourage you to open a factory in the Coega IDZ. (2 x 2) (4) 3.5 Suppose you are a South African government official responsible for economic development. State FOUR incen tives you would use to attract foreign investors to the Coega IDZ. (4 x 2) (8)

[20] GRAND TOTAL: 60

FIGURE 3: COEGA IDZ

4.2 Term 3 – Research task Two examples of typical research tasks are provided below. 4.2.1 Learner guidelines for conducting research Research framework for assessment (Guideline on administration of research task)

In choosing a topic for research, isolate topics in specific areas in the Geography CAPS content that you have studied in Grade 12.

4.2.2 Guidelines for research Research Task Step 1: Formulating a hypothesis/problem statement As Geographers we seek to understand and explain the interactions amongst humans, and between humans and the environment in space and time. This is achieved by asking questions or making informed geographical decisions. This entails the development of a hypothesis or a problem statement to be tested.

You have to choose a specific area of study where a geographical problem exists.
During this stage, a geographical question showing a problem is asked.
Identify the problem from a local area.
Formulate a hypothesis or a problem statement. (Hypothesis research is used to prove that certain variables are dependent on or independent of each other. Problem statement research is only to highlight that a specific problem exists in a specific community.)
You should then follow the steps of research to ensure that the geographical question is answered.

Other possible hypothesis-type research examples:

The value of property along north-facing slopes is higher than the value of property along south-facing slopes in Meyersdal, Gauteng (choose local area).
The cause of rural-urban migration in Ndwedwe, KwaZulu-Natal (choose local area), is the lack of service delivery in the health sector.
Climate change will impact negatively on grape farming and related industries in the Western Cape.
The closing down of many primary schools in Lusikisiki (Eastern Cape) (choose a local area) is due to a decline of the population in the age group 7 to 15 years.
The poor condition of roads (specify the names of the roads) leading to/in Harrismith, Free State (choose local area), is due to the lack of proper planning by the local municipality.
The impact of building a dam along the Jukskei River in Gauteng (choose local area) upstream of Alexandra will reduce flooding and the subsequent loss of life in Alexandra.
The e-toll system will impact negatively on the economic position of people using private transport in Gauteng.
The e-toll system will impact positively on traffic flow to the major urban centres in Gauteng.
Informal settlements in the Vhembe district of Limpopo have low levels of development due to the lack of provision of basic needs (choose ONE informal settlement in your local area).
Overcrowding of informal settlements is due to the lack of proper planning by the local government (choose local area).

Step 2: Background information about an area of study

You must explain where in South Africa the study area is located. (This can be indicated on the map.)
Describe the study area in terms of its exact position (degrees, minutes and seconds).
Provide relevant information about the area, for example population of the area or climate of the area.

Step 3: Mapping

You must provide a map of the area in question.
During this stage you must create a buffer zone around the area where the geographical problem exists.
The map should have a clear legend/key and must be drawn to scale. The scale must be indicated on the map.
If the map used covers a wider area, buffer zones around the area of study should be created.
The map used should be the most recent map of the study area.

Step 4: Methods of data collection

The use of questionnaires
Observations
Field trips
Newspaper articles
Government department statistics

Step 5: Analysis and synthesis of data

Use collected data now to formulate a discussion around the existing geographical problem.
At this stage you should represent some of the information graphically where necessary, for example graphs and sketches.
Analyse graphic information during this stage.

Step 6: Recommendations and possible solutions

You should now make recommendations to solve the geographical problem in question.
You should present your original and realistic opinions as far as you possibly can.

Step 7: Conclusion – accept or reject the hypothesis

You should now take a decision to either ACCEPT or REJECT the hypothesis.
Give reasons for either ACCEPTING or REJECTING the hypothesis.

Step 8: Bibliography

You must include a comprehensive bibliography.
List websites in full.
You must include annexures of questionnaires and interviews conducted.

Step 9: Submission

You must include graphs, tables, diagrams and pictures where necessary.
On submission, ensure that a suitable cover page is included.

4.2.3 Compiling a bibliography for a research task

For a book: Author (last name, initials). Title of Book (Publishers, Date of publication). Example: Dahl, R. The BFG. (Farrar, Straus & Giroux, 1982).
For an encyclopaedia: Encyclopaedia Title , Edition date. Volume number, ˈArticle Titleˈ, page number(s). Example: Encyclopaedia Britannica , 1997. Volume 7, ˈGorillasˈ, pp. 50–51.
For a magazine: Author (last name first), ˈArticle Titleˈ. Name of Magazine . Volume number, (Date): page number(s). Example: Jordan, Jennifer, ˈFilming at the Top of the Worldˈ. Museum of Science Magazine . Volume 47, No. 1, (Winter 1998): p. 11.
For a newspaper: Author (last name first), ˈArticle Titleˈ. Name of Newspaper. City, state publication. (Date): Edition if available, Section, page number(s). Example: Powers, Ann, ˈNew Tune for the Material Girlˈ. The New York Times . New York, NY. (3/1/98): Atlantic Region, Section 2, p. 34.
For a website: Quote the name of the website in full and underline. Example: http://www.sahistory.org.za/topic/womens-struggle-1900-1994
For a person: Full name (last name first). Occupation, date of interview. Example: Smeckleburg, Sweets. Bus driver. 1 April 1996.
For a film/documentary: Title, Director, Distribution, Year. Example: Braveheart, Director Mel Gibson, Icon Productions, 1995.

4.2.4 Proposed cover page for a research task

STATEMENT OF AUTHENTICITY I hereby declare that ALL pieces of writing contained in this research task are my own original work and that if I made use of any source, I have duly acknowledged it.

Learner’s signature: __________________________________ Date: _____________

4.2.5 Exemplar: Research task 1

Curriculum content: Key human-environment interactions in urban areas: People and places – inner-city problems
One (1) research task must be done.

Compile your research by completing the activities outlined below.

Step 1: Formulate the hypothesis/problem statement

Formulate your own hypothesis based on a problem you have identified, for example: The increasing number of informal settlements (choose localised informal settlement) in and around urban areas in South Africa has resulted in higher crime rates within the inner city due to higher unemployment. (Focus: More people in surrounding informal settlements result in unemployment causing people to turn to crime.)

Step 2: Background information about the study area Give a brief introduction and description (background information) of the city (study area) you have selected in terms of:

Historical background
Population
Description of the location of informal settlements in relation to the inner city
Other relevant statistical information
Provide a map showing the position of the informal settlement in relation to the city that you have identified for your research task. (It is easier to choose your local area as an area of study.)
The map should clearly indicate buffer zones where informal settlements are located.
The map should include areas of the city that are regarded as crime ˈhotspotsˈ.
The map must have a clear legend/key.
The scale of the map must be indicated.

Step 4: Data collection Collect data using at least THREE methods, for example:

Questionnaires
Interviews
Field trips
Photographs and maps
Literature research (newspapers, magazines, books, et cetera)
Internet research
Analyse the data that you have collected, and formulate a report on your findings. Support your findings with graphs, photos, et cetera.
Briefly discuss how the existence of informal settlements contributes to crime in the inner city.
Briefly discuss the contribution of high unemployment rates in the informal settlement to crime in the inner city.

Step 6: Recommendations and solutions

Provide suitable recommendations and solutions to the problem.

Step 7: Conclusion – accept or reject the hypothesis

Based on your findings in Step 5, you may either ACCEPT or REJECT the hypothesis.
Give reasons for your conclusion.
Compile a bibliography for your research. If you have done any Internet research, you must provide the website(s) that you have used in full.
Collate all your information.
Include a table of contents.
Ensure that you include a copy of the questionnaire and/or questions asked in your interviews as annexures.
Design a suitable cover sheet.
Submit your research.

4.2.6 Exemplar: Research task 2

Curriculum content: Physical Geography (fluvial processes)

Choose a river close to your school or where you live as an area of study, and conduct your research by following the steps outlined below. Step 1: Formulate the hypothesis/problem statement

Formulate your own hypothesis based on a problem you have identified, for example:

Step 2: Background information about the river under study

Describe the provincial location of the river.
Climate – particularly the amount of rainfall that is received.
Vegetation
Relief and topography
Underlying rock structure
Specify the river type, for example permanent, periodic.
Describe the river stage (youth, mature or old age) at your study area.
Provide a map showing the river being studied and the adjacent settlements.
Create a clear buffer zone at the part of the river that is being studied.
The map should have a clear key/legend.
Indicate the scale of the map.
Use the above sets of data collected to determine the extent to which the river is affected by human activities.
Explain in detail how the identified human activities impact on the quality of water and the flow pattern of the river.

Step 6: Recommendations and solutions

In your opinion as a researcher, what would be the possible solution(s) to the negative impact caused by human activities in the river?
Make long-term recommendations to the government department(s) leading to legislature to protect the river.

Step 7: Conclusion – accept or reject the hypothesis

Submit your research.

4.2.7 Proposed marking rubric for a research task

NAME OF LEARNER: _________________________________________________________GRADE: __________

CURRICULUM TOPIC: __________________________________________________________________________

RESEARCH TOPIC: __________________________________________________________________________

EDUCATOR NAME: ______________________________DATE OF ASSESSMENT: __________________

MODERATOR NAME: ______________________________DATE OF MODERATION: __________________

5. CONCLUSION This document provides you with a framework to develop your own research task. It also provides you with a framework of expectancy for data-handling tasks. The framework for data-handling tasks can also be used to prepare for external examinations where data-handling-type questions can be asked. A clear guideline has been developed on how to conduct research. This guideline can be applied to any topic within the CAPS in which you wish to conduct research. The marking rubric that has been included will also provide you with a clear guide on the time that should be spent on the various phases of doing research. The high standard of these tasks will provide a platform for you to develop skills such as research, interpretation of resources, integration of resources and graphs, all skills required for the final external Geography examination. These are also skills that can be put to use at a later stage in your life.

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What is the conclusion of tropical cyclone?

Table of Contents

1 What is the conclusion of tropical cyclone?
2 What is the conclusion of tropical cyclone Eloise?
3 What is the conclusion of a project?
4 What are the 3 stages of tropical cyclone development?
5 How are high resolution models used in tropical cyclones?
6 Why are cyclones so important to the world?

Cyclones are natural calamities that strike as violent storms and grievous weather conditions, caused by disturbances in the atmosphere. They lead to great devastations. The effect of a cyclone is terrible, as it destroys everything in its wake. People are left homeless and helpless.

What is the conclusion of tropical cyclone Eloise?

“Eloise poses a serious threat to the coast of Mozambique, and is dangerous cyclone,” according to RSMC La Reunion. “High winds, heavy rainfall and dangerous sea conditions are to be expected. There is a major risk of coastal flooding.”

What is the conclusion of cyclone Tauktae?

A low-pressure area over the Arabian Sea first concentrated into a depression and later intensified into a cyclonic storm named ‘Cyclone Tauktae’. The West Coast of India has been affected by the cyclone….Conclusion.

How do you respond to a cyclone?

Turn off all electricity, gas and water; unplug all appliances. Lock your doors. Make sure everyone in your household is wearing strong shoes and suitable clothing. Take your emergency survival kit; follow your evacuation plan.

What is the conclusion of a project?

A conclusion is the final piece of writing in a research paper, essay, or article that summarizes the entire work. The conclusion paragraph should restate your thesis, summarize the key supporting ideas you discussed throughout the work, and offer your final impression on the central idea.

What are the 3 stages of tropical cyclone development?

The development of cycle of tropical cyclones may be divided into three stages. a) Formation and initial development (b) Full maturity (c) Modification or decay!

What is the reason of Cyclone Tauktae?

The second depression, first cyclonic storm, first severe cyclonic storm, first very severe cyclonic storm, and first extremely severe cyclonic storm of the 2021 North Indian Ocean cyclone season, Tauktae originated from a tropical disturbance, which was first monitored by the India Meteorological Department on May 13.

What are the prevention of cyclone?

In case you need to, wear suitable footwear. Stay away from sewerage lines, gutters, drains, culverts, etc. Stay away from electric poles and fallen power lines to avoid electrocution. Eat freshly cooked or dry food.

How are high resolution models used in tropical cyclones?

Why are cyclones so important to the world.

How is LP Field calculated in tropical cyclones?

What are the effects of continental aerosol on tropical cyclones?

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Tropical cyclone
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How Cyclone forms in Tropical and Temperate areas? #UPSC #IAS #CSE #IPS
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Formulation of Hypothesis
HOW TO FORMULATE OBJECTIVES & HYPOTHESIS WITH AN EXAMPLE
6 Steps to Formulate a STRONG Hypothesis Scribbr 🎓
Probability and Statistics

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A Hypothesis for the Intensification of Tropical Cyclones under
Abstract A major open issue in tropical meteorology is how and why some tropical cyclones intensify under moderate vertical wind shear. This study tackles that issue by diagnosing physical processes of tropical cyclone intensification in a moderately sheared environment using a 20-member ensemble of idealized simulations. Consistent with previous studies, the ensemble shows that the onset of ...
Hypothesis on Tropical Cyclone Freddy in Mozambique
Guide for Generating a Hypothesis on Tropical Cyclone Freddy in Mozambique. Step 1: Understand the Problem. The first step in any scientific inquiry is to understand the problem at hand. In this case, the problem is Tropical Cyclone Freddy in Mozambique. Research about tropical cyclones, their causes, and impacts.
Tropical cyclone
A characteristic feature of tropical cyclones is the eye, a central region of clear skies, warm temperatures, and low atmospheric pressure.Typically, atmospheric pressure at the surface of Earth is about 1,000 millibars. At the centre of a tropical cyclone, however, it is typically around 960 millibars, and in a very intense "super typhoon" of the western Pacific it may be as low as 880 ...
GEOGRAPHY GRADE 12 RESEARCH TASK 2018
relation to the city that you have identified for your research task. (It. is easier to choose your local area as an area of study. The map should clearly indicate buffer zones where informal. settlements are located. The map should include areas of the city that are regarded as. crime "hotspots".
The Global Climatology of Tropical Cyclones
The interannual variability of tropical cyclones, both globally and regionally, continues to be a major area of research in the tropical cyclone community. The annual global number of tropical cyclones has been relatively steady at about 80 or so ( μ ‎ = 78.3, σ ‎ = 6.9) since the start of reliable best track records.
An analytic model of the tropical cyclone outer size
Tropical cyclone outer size can be defined by the radial extent of near-surface cyclonic circulation with a fixed wind speed 10. It was found that the outer size in the North Atlantic is ...
A hypothesis for the intensification of tropical cyclones under
This study tackles that issue by diagnosing physical processes of tropical cyclone intensification in a moderately sheared environment using a 20-member ensemble of idealized simulations. ... -surface vortex stretching, deep updrafts, and a substantial reduction of low-entropy fluxes. These results lead to the hypothesis that intensification ...
Tropical Cyclones
Following Emanuel's hypothesis about tropical cyclones, other people have investigated the impact of cyclones on OHT and the possibility of cyclones causing equable climates. The other studies have shown that tropical cyclones do increase OHT; however, there are some aspects of the system that Emanuel did not consider in his first paper ...
A hypothesis and a case-study projection of an influence of MJO
The eastward shift of the enhanced activity of tropical cyclone to the central Pacific is a robust projection result for a future warmer climate, and is shared by most of the state-of-the-art climate models. The shift has been argued to originate from the underlying El-Ñino like sea surface temperature (SST) forcing. This study explores the possibility that the change of the activity of the ...
(PDF) Tropical Cyclones in Global High-Resolution ...
tropical cyclones in numerical climate models, as detailed below. Lastly, and to some 12. extent because of the ﬁrst two reasons, no consensual theory explains the genesis and 13 ...
Lecture 6: Tropical Cyclogenesis
Lecture 6: Tropical Cyclogenesis. It is evident from the potential intensity climatology that there is no shortage of potential energy for tropical cyclones over much of the Tropics during much of the year. But tropical cyclones are rare...there are only about 80 of them every year, worldwide. The reason for this is that tropical cyclones don't ...
Tropical Cyclone Hagibis
Tropical Cyclone Hagibis, which struck Japan in October 2019, is remembered as one of the most potent and devastating cyclones to hit the region in recent decades. Rapidly intensifying to a Category 5 super typhoon, Hagibis showcased the catastrophic potential of tropical cyclones, with its development fueled by exceptionally warm ocean ...
Tropical Cyclone Nivar
Conclusion/Summary. Tropical Cyclone Nivar serves as a stark reminder of the devastating potential of tropical cyclones and the importance of preparedness, early warning systems, and effective disaster response mechanisms. The cyclone's impacts on the environment, economy, and communities highlight the multifaceted challenges posed by such ...
Remote Sensing
Typhoon Hagibis passed through Japan on October 12, 2019, bringing heavy rainfall over half of Japan. Twelve banks of seven state-managed rivers collapsed, flooding a wide area. Quick and accurate damage proximity maps are helpful for emergency responses and relief activities after such disasters. In this study, we propose a quick analysis procedure to estimate inundations due to Typhoon ...
Geography School Based Assessment Exemplars
Step 1: Formulate the hypothesis/problem statement Formulate your own hypothesis based on a problem you have identified, for example: The increasing number of informal settlements (choose localised informal settlement) in and around urban areas in South Africa has resulted in higher crime rates within the inner city due to higher unemployment.
Answers to: Formulating a hypothesis of tropical cyclone freddy
Formulating a hypothesis of tropical cyclone freddy. As an AI language model, I cannot predict weather or formulate hypotheses. However, here's an exampl...
Formulate a hypothesis for problem stated
The hypothesis for the problem stated of tropical cyclone Freddy could be "The intensity and frequency of tropical cyclones in the Northern Hemisphere will increase due to the effects of climate change, resulting in more devastating storms like Freddy."
Research TASK Grade 12 2024
OCHA Tropical Cyclone Eloise; Life Sciences P1 Feb-March 2017 Memo Eng; ... The formulation of the HYPOTHESIS will determine the nature and scope of the type of research the candidate will complete. (It is useful to dedicate more time with each candidate in the formulation of the HYPOTHESIS at the beginning so as to eliminate vagaries and poor ...
formulate the hypothesis based on the impact of tropical cyclone Freddy
Answer: Hypothesis: The impact of Tropical Cyclone Freddy resulted in significant damage and loss of life on the East Coast of Mozambique as well as in other affected countries. The cyclone's high wind speeds, heavy rainfall, and storm surges caused flooding, landslides, and infrastructure damage, leading to displacement, injury, and loss of life.
Formulate a hypothesis about the impact that tropical cyclone Freddy
Hypothesis: Tropical cyclone Freddy had a significant impact on Mozambique, leading to widespread destruction of infrastructure, loss of life, displacement of people, and economic losses in the affected areas. The impact was likely more severe in regions that were already vulnerable due to poverty and limited access to resources and basic services.
how to formulate hypothesis using climate change and tropical cyclone
Answer: The eastward shift of the enhanced activity of tropical cyclone to the central Pacific is a robust projection result for a future warmer climate, and is shared by most of the state-of-the-art climate models. The shift has been argued to originate from the underlying El-Ñino like sea surface temperature (SST) forcing.
How do u formulate a hypothesis for tropical cyclone
Explanation:You have to make a guess on whats gonna happen and explain how i sit gonna happen and what is it going to impact. Another example from tornado.sfsu.edu :Example of Hypothesis: Tropical cyclones form over the warmest postions of the oceans where ocean temperatures are so warm that much water vapor is available to condense.
What is the conclusion of tropical cyclone?
Cyclones are natural calamities that strike as violent storms and grievous weather conditions, caused by disturbances in the atmosphere. They lead to great devastations. The effect of a cyclone is terrible, as it destroys everything in its wake. People are left homeless and helpless.

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GEOGRAPHY GRADE 12 RESEARCH TASK 2018

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Tropical Cyclone Nivar – Geography Grade 12 Research Task

Why do tropical cyclones such as Nivar develop in late summer?

What is the impact of coriolis force and latent heat on the development of tropical cyclone Nivar?

Discuss the stage of development of the tropical cyclone Nivar.

Why can category 1 tropical cyclones be more destructive (damaging) than category 5 tropical cyclones?

How did this tropical cyclone impact the following?

People/Communities

What precautions can be implemented/ or has been implemented to reduce the impact of the tropical cyclone.

The local residents

Evaluate the impact of Global Warming on the frequency (regularity) of tropical cyclones such as Nivar.

Conclusion/Summary

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GEOGRAPHY SCHOOL BASED ASSESSMENT EXEMPLARS - CAPS GRADE 12 LEARNER'S GUIDE

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Second Answer

Second Answer

What is the conclusion of tropical cyclone?

What is the conclusion of tropical cyclone Eloise?

What is the conclusion of a project?

What are the 3 stages of tropical cyclone development?

How are high resolution models used in tropical cyclones?

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