**3. Hurricane Wilma in 2005 overview**

#### **3.1. Large‐scale low‐level dynamics**

University planetary boundary layer (PBL) parameterization; (v) the Monin‐Obukhov scheme for the surface layer option; (vi) the thermal diffusion scheme for the land surface physics; and (vii) Kain‐Fritsch (new Eta) scheme for the cumulus parameterization [16]. The 38 sigma (*σ*) level set of [17] was applied. The model "top" is defined at 50 hPa. The model run was set to update daily SST every 6 hours into the model integration. The daily "real‐time global" (RTG) SST data were interpolated sequentially to produce 6 hourly input data for the WRF run.

92 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

**Figure 1.** The model domain of global WRF for Hurricane Wilma in 2005. NHC best tracks were plotted with major

In the global WRF model simulation, two different runtimes were executed. The first set of simulations runs from 0000 UTC October 7 to 0000 UTC October 21, to include the anomalous circulation that Hurricane Vince introduced in the North Atlantic about 1 week prior to Wilma's TCG—a duration of 336 hours. The second set of the simulations runs from 0000 UTC October 14 to 0000 21 October UTC, which only includes the pregenesis condition, TCG, and the development of Wilma—a duration of 168 hours. Both simulations end on 0000 UTC October 21, though Wilma continued to maintain hurricane intensity until 1800 UTC October 25. The latter half of the first model simulation result is compared to the result of the second

To run the WRF model, 6 hourly NCEP Global Forecast System (GFS) final (FNL) operational global analysis data (1° × 1°) and daily RTG SST data are used for three‐dimensional input data and for SST update (available from National Weather Service at ftp://ftp.polar.ncep.noaa.gov/ pub/history/sst/), respectively. The model run is set to update SST every 6 hours into the model integration. The FNL data for this study are obtained from the Research Data Archive (RDA), which is maintained by the Computational and Information Systems Laboratory (CISL) at NCAR. The original data are available from the RDA (http://dss.ucar.edu) in dataset number

intensity changes annotated.

ds083.2.

run to evaluate the accuracy of the global WRF model.

After Tropical Storm Tammy (October 5–6, 2005) diminished over Florida, a large‐scale, low‐ level wind surge (>10 m s–1) developed off the Atlantic coast of North America (**Figure 2a**). This surge was associated with a mid‐latitude Rossby wave trough over the northern North

**Figure 2.** Wind stream analysis (850 hPa) of NCEP/NCAR reanalysis data and NOAA optimum interpolation (OI) ¼ degree daily sea surface temperature (SST) V2 data superimposed by low‐level wind surge at (a) 1200 UTC October 8, (b) 1800 UTC October 11, (c) 0600 UTC October 15, (d) 0600 UTC October 16, (e) 0600 UTC October 18, and (f) 1200 UTC October 19, 2005. Areas of low‐level wind surges exceeding 10 m s–1 are enclosed by dots within the thick solid contour lines, for which the interval is 15 m s–1. SSTs exceeding 26°C are contoured with dark shades at a 1°C interval.

Atlantic and a subtropical anticyclone to the east of North America (also known as the Bermuda‐Azores high). The mid‐latitude trough seems to have assisted the formation of the subtropical high to the east of North America and a frontal low in the eastern North Atlantic, the latter of which later became Hurricane Vince (October 8–11, 2005) off the coast of western Africa (**Figure 2a**). Interactions between the subtropical high and the frontal low (Hurricane Vince) to its east deformed the shape of the subtropical high in its southern flank in the North Atlantic.

The abnormally strong frontal low also contributed to weakening of tropical easterly winds from western Africa. Due to the weakened easterly winds over the Caribbean Sea and the Gulf of Mexico during this period, the warm SST could avoid heat loss due to advection, accumu‐ lating more thermal energy in the low‐level atmosphere and at the sea surface over the vast region. Meanwhile, vigorous southeasterly winds emanating from the South Atlantic sub‐ tropical high produced strong low‐level wind surges over a vast area northeast of Brazil (**Figure 2a**).

Regarding the development of Hurricane Wilma, low‐level westerly winds from the eastern North Pacific should not be disregarded. The evolution of synoptic‐scale low‐level vortices in the eastern North Pacific is driven by the interplay between subtropical high pressure systems in the eastern South Pacific and in the eastern North Pacific, at least in the case of Arlene four months earlier [6]. Since early in October, synoptic‐scale low‐level conditions in the Pacific had supported the development of a low‐level anticyclonic vortex in the eastern North Pacific. In particular, anomalously strong southeasterly winds from the southeastern Pacific subtropical high advected momentum effectively to the anticyclone in the eastern North Pacific, culmi‐ nating in low‐level westerly winds in the region (**Figure 2b**). Although the intensities of the low‐level wind surges changed slightly, the general setting of the large‐scale low‐level vortices distribution around Central America was maintained for an extended period of time during early October.

Particularly, the western flank of the southeastern protrusion of the elongated North Atlantic subtropical anticyclone, which was northeast of the Caribbean Sea or Puerto Rico, became a seed zone for the development of an unusually intense 850 hPa cyclonic vortex at the subsy‐ noptic scale by October 8 (**Figure 2a** and **b**). This vortex was able to develop as the easterly wind in the central tropical Atlantic weakened, allowing the cross‐equatorial southeasterly wind east of the Caribbean Sea to approach 25o N (**Figure 2a**). By October 9, the abnormally large‐scale low‐level cyclone with its center hovering over the eastern Caribbean maintained its extended shape, from the southwestern Caribbean to the northeast.

Meanwhile, the westerly winds from the eastern North Pacific were sufficiently strong to traverse the western Caribbean around October 11, and they converged with the southeasterly and easterly winds in the eastern Caribbean (**Figure 2b**). This convergence reinforced the preexisting subsynoptic‐scale low‐level cyclonic flow over the Caribbean Sea, which continued on 0000 UTC October 13 despite weakened westerly winds upon the disappearance of the eastern North Pacific low‐level circulation.

Beginning around 0000 UTC October 14, a meso‐scale high and a mid‐latitude trough were developing over Texas and inland central Canada, respectively. This anticyclone over Texas grew quickly while the subsynoptic‐scale low‐level cyclonic flow over the Caribbean Sea had split into two cyclonic circulations over the Caribbean and adjacent to the US Atlantic coast one on the northern and the other on the southern edge of the cyclonic zone (**Figure 2c**). The northern cyclonic circulation near the US Atlantic coast became an extratropical cyclone, and the southern cyclone over the Caribbean Sea strengthened near Jamaica by October 14, becoming a tropical depression by 1800 UTC October 15. Pasch et al. [8] suggested that tropical waves "traversing the Caribbean" might have been associated with the formation of the tropical depression. However, no apparent tropical wave "traversing" the Caribbean during that time might have affected the TCG. Instead, the 850 hPa streamline analysis shows clearly that the large‐scale low‐level wind was traversing the Caribbean from north to south (**Figure 2c**). By 1200 UTC October 15, the mid‐latitude trough merged with the extratropical cyclone, strengthening the extratropical cyclone further (**Figure 2d**). The enhanced extratrop‐ ical cyclone impeded low‐level easterly winds from the central tropical Atlantic from entering into the Caribbean Sea by deflecting the easterlies in the central tropical Atlantic northward to the east of the Caribbean Sea. This circulation allowed for the sustenance of the low‐level circulation in the Caribbean Sea without significant interference by the normally zonally propagating tropical waves, allowing the warm SST to accumulate more thermal energy at the sea surface and adjacent low‐level atmosphere over the Caribbean Sea (**Figure 2d**).

Atlantic and a subtropical anticyclone to the east of North America (also known as the Bermuda‐Azores high). The mid‐latitude trough seems to have assisted the formation of the subtropical high to the east of North America and a frontal low in the eastern North Atlantic, the latter of which later became Hurricane Vince (October 8–11, 2005) off the coast of western Africa (**Figure 2a**). Interactions between the subtropical high and the frontal low (Hurricane Vince) to its east deformed the shape of the subtropical high in its southern flank in the North

94 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

The abnormally strong frontal low also contributed to weakening of tropical easterly winds from western Africa. Due to the weakened easterly winds over the Caribbean Sea and the Gulf of Mexico during this period, the warm SST could avoid heat loss due to advection, accumu‐ lating more thermal energy in the low‐level atmosphere and at the sea surface over the vast region. Meanwhile, vigorous southeasterly winds emanating from the South Atlantic sub‐ tropical high produced strong low‐level wind surges over a vast area northeast of Brazil

Regarding the development of Hurricane Wilma, low‐level westerly winds from the eastern North Pacific should not be disregarded. The evolution of synoptic‐scale low‐level vortices in the eastern North Pacific is driven by the interplay between subtropical high pressure systems in the eastern South Pacific and in the eastern North Pacific, at least in the case of Arlene four months earlier [6]. Since early in October, synoptic‐scale low‐level conditions in the Pacific had supported the development of a low‐level anticyclonic vortex in the eastern North Pacific. In particular, anomalously strong southeasterly winds from the southeastern Pacific subtropical high advected momentum effectively to the anticyclone in the eastern North Pacific, culmi‐ nating in low‐level westerly winds in the region (**Figure 2b**). Although the intensities of the low‐level wind surges changed slightly, the general setting of the large‐scale low‐level vortices distribution around Central America was maintained for an extended period of time during

Particularly, the western flank of the southeastern protrusion of the elongated North Atlantic subtropical anticyclone, which was northeast of the Caribbean Sea or Puerto Rico, became a seed zone for the development of an unusually intense 850 hPa cyclonic vortex at the subsy‐ noptic scale by October 8 (**Figure 2a** and **b**). This vortex was able to develop as the easterly wind in the central tropical Atlantic weakened, allowing the cross‐equatorial southeasterly

large‐scale low‐level cyclone with its center hovering over the eastern Caribbean maintained

Meanwhile, the westerly winds from the eastern North Pacific were sufficiently strong to traverse the western Caribbean around October 11, and they converged with the southeasterly and easterly winds in the eastern Caribbean (**Figure 2b**). This convergence reinforced the preexisting subsynoptic‐scale low‐level cyclonic flow over the Caribbean Sea, which continued on 0000 UTC October 13 despite weakened westerly winds upon the disappearance of the

its extended shape, from the southwestern Caribbean to the northeast.

N (**Figure 2a**). By October 9, the abnormally

Atlantic.

(**Figure 2a**).

early October.

wind east of the Caribbean Sea to approach 25o

eastern North Pacific low‐level circulation.

Meanwhile, the tropical depression over the Caribbean Sea maintained its subsynoptic‐scale vortex between the northerly winds associated with the trough in the northeastern US and the southeasterly winds from the South Atlantic (**Figure 2d**). Neither of the two 850 hPa circula‐ tions were strong enough to support a wind surge around the intensifying tropical depression, but these two moderate drive trains caused the "weak and ill‐defined steering" [8] of the storm for the first few days of the storm that was to become Wilma. In this environment of only weak background and adjacent circulations, the depression slowly strengthened over October 16 and became a tropical storm at 0600 UTC October 17.

Over October 17–18, the North Atlantic subtropical high strengthened and began to produce more vigorous low‐level easterly winds in the central tropical Atlantic toward the Caribbean Sea (**Figure 2e**). At the same time, the mid‐latitude trough continued to advect the momentum of the low‐level atmosphere to the anticyclone centered over Texas. This anticyclone continued to produce 850 hPa northerly winds from the southeastern US toward the Yucatan peninsula, to the west of Wilma in the Caribbean Sea, thereby enhancing cyclonic vorticity of Wilma (**Figure 2e**). During that time, Wilma drifted toward the west‐northwest and strengthened into a hurricane by 1200 UTC October 18. An explosive deepening occurred during the night of the 18th/19th, and Wilma's maximum sustained wind speed had increased to near 150 kt (Category 5 on the Saffir‐Simpson Hurricane Scale) by 0600 UTC October 19 [8]. By 1200 UTC October 19, the peak sustained wind speed of 160 kt was recorded for Wilma with the estimated minimum central pressure of 882 hPa—the lowest pressure recorded for a hurricane in the Atlantic basin [8]. While Wilma underwent this unprecedented rapid intensification, low‐level wind surges associated with the North Atlantic high were active over the northeastern US and in the central tropical Atlantic (**Figure 2f**). Hurricane Wilma was located in the middle of the steering flow cornered by the terrain in Central America.

#### **3.2. Sea surface temperature conditions**

As shown in **Figure 3**, SSTs in the entire western Atlantic basin and central tropical Atlantic exceeded the 26°C climatological threshold for TC development (e.g. [18]) during the lifespan of Wilma, with western Atlantic SSTs peaking at over 30°C. In contrast, SSTs in the eastern North Pacific basin were barely over 26°C (**Figure 3**). The general SST condition over the western Atlantic was warmer than the average during 1971–2000, while the southern Carib‐ bean and central tropical Atlantic had even stronger positive anomalies during the period (**Figure 4**). It is notable that SSTs were below average over the majority of the eastern North

**Figure 3.** SSTs over the tropical and western Atlantic every 4 days during October 1–21, 2005. The thick contour lines are drawn at a 3°C interval, and SSTs exceeding 26°C are contoured with dark shades at a 1°C interval.

Pacific during the same period except for some positive anomaly hot spots along the equator (**Figure 4c**–**f**).

in the central tropical Atlantic (**Figure 2f**). Hurricane Wilma was located in the middle of the

As shown in **Figure 3**, SSTs in the entire western Atlantic basin and central tropical Atlantic exceeded the 26°C climatological threshold for TC development (e.g. [18]) during the lifespan of Wilma, with western Atlantic SSTs peaking at over 30°C. In contrast, SSTs in the eastern North Pacific basin were barely over 26°C (**Figure 3**). The general SST condition over the western Atlantic was warmer than the average during 1971–2000, while the southern Carib‐ bean and central tropical Atlantic had even stronger positive anomalies during the period (**Figure 4**). It is notable that SSTs were below average over the majority of the eastern North

**Figure 3.** SSTs over the tropical and western Atlantic every 4 days during October 1–21, 2005. The thick contour lines

are drawn at a 3°C interval, and SSTs exceeding 26°C are contoured with dark shades at a 1°C interval.

steering flow cornered by the terrain in Central America.

96 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

**3.2. Sea surface temperature conditions**

**Figure 4.** SST anomalies over the tropical and western Atlantic every 4 days during October 1–21, 2005. Contour lines are drawn at a 1°C interval. Positive anomalies are contoured with dark shades at a 1°C interval, and negative anoma‐ lies are drawn with dashed line contours.

SST changes over 3 and 6 days are depicted in **Figures 5** and **6**, respectively. Generally, SSTs over the Atlantic remained constant or increased slightly. Interestingly, 6‐day SST change maps clearly show significant SST decreases in the Atlantic during October. SST decrease during October 1–7 (**Figure 6a**) over a broad area in the northern North Atlantic seems to be related to the passage of a mid‐latitude trough that was associated with Tropical Storm Tammy (October 5–6; see **Figure 2a**). The decreasing SST in the Caribbean during October 7–13 (**Figure 6b**) represents the evaporation from the ocean, while the tropical depression (Wilma) was developing. The SST change map for October 13–19, 2005 (**Figure 6c**) suggests sea surface energy consumption by Hurricane Wilma during its early explosive intensification in the northwestern Caribbean Sea. Finally, the SST decrease in the central tropical Atlantic (**Figure 6d**) provides evidence of the vigorous low‐level southeasterly and easterly wind surges during October 19–25, 2005 (see **Figure 2f**).

**Figure 5.** SSTs change over 3‐day intervals over the tropical and western Atlantic during October 1–25, 2005. Contour lines are drawn at a 1°C interval. SST increases are contoured with dark shades at a 1°C interval, and SST decreases are drawn with dashed line contours.

Planetary‐Scale Low‐Level Circulation and the Unique Development of Hurricane Wilma in 2005 http://dx.doi.org/10.5772/64061 99

**Figure 6.** As in **Figure 5**, except for 6‐day changes.

northwestern Caribbean Sea. Finally, the SST decrease in the central tropical Atlantic (**Figure 6d**) provides evidence of the vigorous low‐level southeasterly and easterly wind surges

**Figure 5.** SSTs change over 3‐day intervals over the tropical and western Atlantic during October 1–25, 2005. Contour lines are drawn at a 1°C interval. SST increases are contoured with dark shades at a 1°C interval, and SST decreases are

during October 19–25, 2005 (see **Figure 2f**).

98 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

drawn with dashed line contours.

#### **3.3. Potential vorticity in the upper‐level atmosphere and outgoing longwave radiation**

In general, mid‐latitude troughs are associated with lower‐level instability downwind of the trough as they provide momentum from the high latitudes and incorporate moisture from the lower latitudes. In the mid‐latitudes, upper‐tropospheric troughs in the Rossby waves have positive PV by nature, and positive PV anomaly regions correspond well to the locations of the 850 hPa wind surges which seem to be associated with convection as shown by OLR anomalies (**Figures 7** and **8**). However, those relationships do not apply to the lower‐latitude region. Generally, upper‐level PV is significantly weaker in the lower latitudes than in the mid‐ latitudes. Nevertheless, strong convection can occur there even with mild wind speeds, mainly because SST conditions tend to be much more favorable for strong convection in the lower latitudes than in the mid‐latitudes (**Figure 3**). **Figure 8** clearly shows the cyclonic circulation development of Wilma with strong OLR anomalies over the Caribbean.

The mid‐latitude trough that merged with an extratropical cyclone around the TCG period of Hurricane Wilma on October 15 (**Figure 2c** and **d**) was accompanied by the anomalously latitudinally stretched Rossby waves in the Northern Hemisphere during the period. This peculiar formation of Rossby waves resulted in a rather unusual synoptic‐scale low‐level wind flow with a sharp meridional circulation pattern as well as an abnormal 200 hPa PV distribution over North America (**Figure 7**). The unusual deformation of Rossby waves is likely to have increased atmospheric momentum and turbulence in the tropical latitudes by advecting vorticity during Wilma's TCG.

**Figure 7.** Abnormal distribution of 200 hPa potential vorticity (PV, shaded, 10–6 K m2 kg–1 s–1) during the early TCG period of Wilma (October 15–16, 2005). Streamline analysis (850 hPa) is superimposed on the low‐level wind surge. Areas of 850 hPa wind surges exceeding 10 m s–1 are enclosed by dots within the thick solid contour lines, for which the interval is 15 m s–1.

During Wilma's explosive deepening (from 1200 UTC October 18 to 1200 UTC October 19), strongly positive PV and a 850 hPa trough were over the northeastern coast of the US accom‐ panied by extremely large low‐level wind surge regions from the central US to the North Atlantic (**Figure 8d** and **e**). It is interesting to note how dynamic the low‐level Northern Hemisphere atmosphere was overall, as evidenced by the low‐level wind surges during the TCG and intensification period (**Figure 8a**–**e**). Bracken and Bosart [19] suggested that vorticity advection between a subtropical anticyclone and a developing storm can play an important role in accelerating TCG. Thus, the distribution of cyclones and anticyclones affects the evolution of each circulation cell through their interplay, advecting vorticities and momentum. Therefore, the synoptic‐scale anticyclone over Texas and the subtropical high in the North Atlantic should have also assisted in the spin‐up of Wilma over the Caribbean Sea. The clockwise low‐level circulation of the Texas anticyclone to the northeast of Wilma made contact over the Gulf of Mexico, while the North Atlantic subtropical high was interacting with Wilma, mainly in the form of easterly winds. Both anticyclones seem to have contributed to Wilma's intensification at the 850 hPa level by advecting angular momentum to the outer radii of Wilma. The tropical easterly winds associated with the North Atlantic high contributed to Wilma's intensification by supplying a substantial amount of enthalpy from the central tropical Atlantic during October 19 (see **Figure 6**).

**Figure 8.** Evolution of the distribution of negative OLR anomalies (W m–2, shaded) during October 15–22, 2005. Stream‐ line analysis (850 hPa) is superimposed on the low‐level wind surge. The contour interval for OLR anomalies is 30 W m–2. Areas of 850 hPa wind surges exceeding 10 m s–1 are enclosed by dots within the thick solid contour lines, for which the interval is 15 m s–1.

**Figure 7.** Abnormal distribution of 200 hPa potential vorticity (PV, shaded, 10–6 K m2

100 Recent Developments in Tropical Cyclone Dynamics, Prediction, and Detection

the interval is 15 m s–1.

period of Wilma (October 15–16, 2005). Streamline analysis (850 hPa) is superimposed on the low‐level wind surge. Areas of 850 hPa wind surges exceeding 10 m s–1 are enclosed by dots within the thick solid contour lines, for which

During Wilma's explosive deepening (from 1200 UTC October 18 to 1200 UTC October 19), strongly positive PV and a 850 hPa trough were over the northeastern coast of the US accom‐ panied by extremely large low‐level wind surge regions from the central US to the North Atlantic (**Figure 8d** and **e**). It is interesting to note how dynamic the low‐level Northern Hemisphere atmosphere was overall, as evidenced by the low‐level wind surges during the TCG and intensification period (**Figure 8a**–**e**). Bracken and Bosart [19] suggested that vorticity advection between a subtropical anticyclone and a developing storm can play an important role in accelerating TCG. Thus, the distribution of cyclones and anticyclones affects the evolution of each circulation cell through their interplay, advecting vorticities and momentum. Therefore, the synoptic‐scale anticyclone over Texas and the subtropical high in the North Atlantic should have also assisted in the spin‐up of Wilma over the Caribbean Sea. The clockwise low‐level circulation of the Texas anticyclone to the northeast of Wilma made contact over the Gulf of Mexico, while the North Atlantic subtropical high was interacting with Wilma, mainly in the form of easterly winds. Both anticyclones seem to have contributed to Wilma's intensification at the 850 hPa level by advecting angular momentum to the outer radii of Wilma.

kg–1 s–1) during the early TCG

However, as the regional anticyclone over Texas weakened, Wilma's intensity decreased on October 20 by 30 kt (still leaving her as a Category 4 hurricane) from 160 kt at 1200 UTC October 19, although at that time the tropical easterly winds from the central tropical Atlantic strength‐ ened. These events suggest that the large‐scale circulation pattern in the immediate TC environment plays an important role in TC intensity change [20]. The multidirectional sources of angular momentum advection as described here likely provided for more efficient intensi‐ fication than if the angular momentum inflow had been from a sole source, such as low‐level easterlies. Meanwhile, the negative OLR anomaly maps after Wilma's TCG show that Hurri‐ cane Wilma's explosive deepening (from 1200 UTC October 18 to 1200 UTC October 19) was favored by the persistent low‐level inflow from the large convective region in the Caribbean Sea to the central tropical Atlantic, which is consistent with the SST change over the period (**Figures 5** and **6**).
