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					Guimond                                 Tropical Meteorology II                                           1



Midlatitude Trough Interaction with the Extratropical Transition of
                       Hurricane Michael

                                         Stephen R. Guimond

  Center for Ocean-Atmospheric Prediction Studies, The Florida State University, Tallahassee, Florida

                                              11 April 2005

                                               ABSTRACT

          The interaction of Hurricane Michael (2000) with a Midlatitude Upper Tropospheric Trough
(MUTT) as the storm was undergoing Extratropical Transition (ET) is examined. The utility of a potential
vorticity (PV) framework for diagnosing the dynamic response of a Tropical Cyclone (TC) to an influx of
high PV air in a baroclinic environment will be assessed.
    Output from the Aviation model (AVN) with a grid resolution of 1 was manipulated to calculate the
full PV on horizontal isentropic surfaces and vertical cross sections to capture both the MUTT interaction
and ET process. In addition, rain rates from the Special Sensor Microwave/Imager (SSM/I) were analyzed
to provide a quantitative evaluation of the structural changes observed during an ET event that could assist
the operational community.
    Results indicate that a trough interaction can be inferred from SSM/I data as the mean area average rain
rate centered on the storm increased with distance from the TC center, a typical signature of the asymmetric
structural change observed during trough interaction cases. PV was shown to be a rather versatile
parameter with the ability to provide a dynamically sound depiction of the kinematics involved with a
MUTT interaction and ET event that will continue to improve upon research into the complex prediction of
TC intensity change.




1. Introduction

   The impacts of Midlatitude Upper Tropospheric Troughs (MUTTs) on Tropical

Cyclones (TCs) are numerous. From a movement perspective, MUTTs can rapidly

accelerate the translational speed of TCs as well as the direction of storm motion with the

majority recurving to the north or northeast in the northern hemisphere (Jones et. al 2003;

WMO 1995). From a structural standpoint, prolonged interaction with a MUTT can

transform a TC from a warm-core symmetric vortex in a barotropic environment into a

cold-core asymmetric vortex within a baroclinic environment, a process referred to as

Extratropical Transition (ET) (Jones et. al 2003). The movement of a TC into an

environment associated with a large temperature gradient allows for complex interactions
Guimond                              Tropical Meteorology II                                  2


to take place between the transitioning storm and intense synoptic scale frontal systems.

A key component of these interactions are the frontogenetic/frontolytic processes that

occur as the front approaches and merges with the TC, a topic the author will address for

his Master’s Thesis. The greatest challenges to operational forecasters during an ET

event are the potentially massive amounts of precipitation, continuation of high winds

with an expansion of the overall wind field and the development of large ocean swells

(Abraham et. al 2004; Jones et. al 2003). The structural changes that occur with ET can

have dramatic impacts for the Canadian Maritimes and marine communities as well as

coastal locations in Western Europe (Abraham et. al 2004). Providing accurate and

timely warnings for these impacts can be difficult especially when so little is known

about the complete ET process. Finally, from an intensity/strength point of view, MUTT

interactions with TCs can cause significant pressure drops on the order of several tens of

millibars due to a secondary circulation feedback that results in a firing of eyewall

convection and amplified low-level wind speeds (Hart 2005, personal communication).

   In this study, the MUTT interaction as well as the ET of Hurricane Michael (17-19

October 2000) will be examined and shown to undergo a similar motion, structure and

intensity change to that of the generalization of such storms mentioned above (Stewart

2000). In order to describe the MUTT and ET evolution of Hurricane Michael, both

synoptic and dynamic perspectives will be considered that follow the general flow of

recent research on these subjects.

a. Distinguishing MUTT interaction from ET

   It is important for the operational and research communities to bin storms into certain

categories in order to discern a typical pattern of evolution that will assist in improving
Guimond                           Tropical Meteorology II                                   3


the track, intensity and structural changes lacking in current forecasts. The main

difference between a trough interaction and the extratropical transitioning process of a

TC is the role of the trough in the structural change process. In trough interactions, a

MUTT usually involves a rather short merging period with the TC on the order of 12-24

hours with the interaction usually resembling a smaller scale PV anomaly from the

MUTT intensifying the TC (Molinari et. al 1998; Hanley et. al 2001).      However, during

the majority of ET events, the MUTT drives the evolution of the storm and therefore

produces longer merging time periods lasting several days with the interaction depicting a

deeper, wider PV anomaly from the MUTT advecting over and wrapping around the TC

(Hart 2005, personal communication; Jones et. al 2003).

b. Framework of paper

   A large portion of the dynamic component of this study will focus on the use of

potential vorticity (PV) reasoning to explain how the approach of a MUTT can enhance

the secondary circulation of a TC. This secondary circulation is necessary to maintain

the primary circulation from the dissipative effects of angular momentum loss to the sea

surface (friction) and thermal energy loss due to radiative (evaporation) and adiabatic

(ascent) cooling (WMO 1995). It has been argued by Molinari et. al 1998, among

others, that PV provides for a more concise, beneficial dynamical skeleton of TC-trough

interactions than simply using basic variables such as vorticity, height and wind. Strong

motions through a heat source (latent heat releasing convective clouds) follow lines of

constant angular momentum and motions through a momentum source (MUTT or upper-

level jet) follow lines of constant potential temperature (WMO 1995). Thus, because of

the quasi-conservative properties of PV along surfaces of constant potential or equivalent
Guimond                            Tropical Meteorology II                                      4


temperature, one can follow the motion of air parcels along isentropic surface at higher

levels in the atmosphere where the trough and TC interact. In addition, PV links the

dynamic and thermodynamic properties of the atmosphere together into one formulation

while the traditional vorticity equation relies on implied heating from the divergence and

twisting terms allowing for a more direct interpretation of the physical processes

occurring in TC-trough interactions (Molinari et. al 1998).



2. Physical Mechanisms of PV Intensification

   PV anomalies (relative to the surrounding environmental PV) can have enhancing or

diminishing effects on the intensity of a TC that can become complex to diagnose. An

important question to consider is how the strength and duration of negative influences

from a MUTT will augment and overtake the positive influences especially at close

distances to a TC. A fine line exists between a “good” trough and a “bad” trough because

in many instances a catch exists that may render the initial intensity change useless or

reverse the process. The following sub-sections will explain these processes in detail.

a. Positive Influences

   When an approaching synoptic scale trough moves within a certain distance (see

Hanley et. al 2001) of a TC, the PV anomaly associated with the trough begins to become

somewhat spatially and temporally coincident with the TC center, a procedure referred to

as the “superposition principle”. When this happens, intensification of the TC can occur

out of a combination of two main processes. First, “constructive interference” occurs

where large eddy PV fluxes moving inward from the trough to the TC allow for enhanced

cyclonic spin-up of the initial vortex and the excitation of a conditional instability of the
Guimond                            Tropical Meteorology II                                    5


second kind (CISK) type response. Second, enhanced upward motion and an associated

evaporative-wind feedback (“WISHE”) results from several different processes that may

combine to produce the intensification. These include: (i) increasing cyclonic vorticity

advection with height associated with the approaching trough in a Q-G omega

framework, (ii) location of the TC core within the left front or right rear jet streak

quadrants and (iii) enhanced evacuation of air near the tropopause due to a jet streak

increasing the outflow anti-cyclone aloft (Hart 2005, personal communication). When (i)

is coupled with low static stability well outside the core of the TC, a surface induced

circulation can form seen through relatively lower values of vorticity. If this rotation is

within a certain distance from the TC center, the long “arms” of the TC’s vorticity will

tend to draw in sources of angular momentum and thus produce an enhancement of the

cyclonic rotation (Hart 2005, personal communication).

b. Negative Influences

   The effects of vertical wind shear on a TC are well known (WMO 1995; Molinari et.

al 1995; Molinari et. al 1998; Hanley et. al 2001). The general consensus on the effects

of vertical wind shear are to displace the heating and convection away from the center of

the storm, which does not allow for an area of focused heating to produce the pressure

falls necessary to maintain and/or strengthen a TC (Hart 2005, personal communication).

The displacement of the heating aloft acts to ventilate the upper troposphere warm

anomaly while decoupling the lower atmospheric frictional convergence and latent heat

release. This process can be seen from satellite imagery when the low-level rotational

center is displaced from the cirrus canopy and the TC begins to take on a more

asymmetric appearance (Beven seminar, 2005). Dry air intrusions act to destabilize the
Guimond                           Tropical Meteorology II                                      6


sounding away from the TC core producing unfocused convective heating ultimately

resulting in a decrease of warm-core maintenance and the typical destruction of a TC.

c. The Catch

   Generally speaking, larger troughs enable greater constructive interference effects of

upper PV anomalies from the trough and lower PV anomalies from the TC that can lead

to intensification. However, larger troughs produce substantial, long-lasting values of

vertical wind shear that will destroy convection surrounding the TC and thus, the catch.

A key aspect of the intensification from positive influences is a thinning of the

approaching positive PV anomaly that attempts to match the scale of the TC’s positive

PV anomaly. Deep convection surrounding the TC core along with the placement of an

upper-level jet to the north of the storm, which will increase the evacuation of air at high

levels, will act to lift the tropopause and build the ridge downstream. The result of this

process will enhance the outflow anticyclone and thus decrease the horizontal scale of the

trough producing the necessary thinning (Hart 2005, personal communication). The

above process allows smaller-scale PV anomalies that can have substantial magnitudes to

approach the TC core without experiencing the detrimental effects of vertical wind shear.



3. Data and analysis method

a. Data

   Twelve-hourly 1 gridded analyses are taken from the Aviation model (AVN) from 00

UTC 15 October 2000 through 00 UTC 22 October 2000 which spans the period that

Michael was a hurricane (17-19 October 2000) (Stewart 2000). In addition, the National

Hurricane Center’s (NHC) “best track” dataset from 20 November 2000 was used for the
Guimond                           Tropical Meteorology II                                      7


precise timing, positioning and intensity (based on central pressure and wind speed) of

Hurricane Michael as the storm traversed the Atlantic Ocean (Stewart 2000). Rain rates

from the Special Sensor Microwave Imager (SSM/I) on 0.25 resolution swaths taken

from Remote Sensing Systems were used to diagnose the structural changes in

precipitating convection of Michael (www.remss.com). Three different satellites (F13,

F14, F15) were used to provide the densest network of precipitation measurements

around the time of trough interaction with the storm.

b. Diagnostics

   To make use of the SSM/I data, the time each satellite passed over the TC was found

and linear interpolation between successive “best track” positions was used to find the

approximate center of the TC at the time of satellite overpass. This process produces a

TC center that is within a few tenths of a degree of the actual center due to the resolution

of the satellite. Typical TC eye diameters range from ~15-30 km and are thus on scales

smaller than the resolution of the satellites (WMO 1995). As a result, the rain rates

retrieved from the satellites at the TC “center” are most likely picking up on the intense

precipitation occurring just outside of the eye within the eyewall and beyond. To

facilitate an analysis of how the structure of precipitating convection changes upon

MUTT interaction and during the early stages of ET, 1x1, 2x2 and 3x3 area

averages positioned about the TC center were calculated and reported in Table 1.

   Many of the dynamical techniques used by previous authors to explain both MUTT

and ET processes will be incorporated in this study including vertical wind shear and the

full PV.
     Guimond                             Tropical Meteorology II                                  8


        The vertical wind shear was calculated as a simple vector difference between the 850

     and 200 mb layers given by

                                            VS  V200 V850 ,                                   (1)

     where V200 is the vector wind at 200 mb, V850 is the vector wind at 850 mb and VS is the
                                 
     shear vector within the layer.
                                                                        
        In order to plot vertical cross sections of PV in pressure coordinate form, the full PV

     equation can be expressed as

                                                ˆ V         
                                                                  
                                       
                               PV  g p  f   k     p  ,
                                                                                              (2)
                                               p     p      
                                                                   

     where  p is the vertical component of relative vorticity in pressure coordinates,  p is the
                    
     horizontal gradient operator evaluated on a pressure surface and V is the horizontal wind
                                                                         
 (Hanley et. al 2001). The full PV, which incorporates the twisting of horizontal potential

                                                            
     temperature gradients seen in the second term of (2), will be expressed in the almost

     universal potential vorticity units [PVU, where 1 PVU = 1106 m 2Ks1kg1 ; Hoskins et

     al. (1985)]. Plots of PV in the horizontal plane on a representative isentropic surface,

     which allows one to view the interaction of the 
                                                     MUTT and TC as air flows along constant

     potential temperature, will be shown at the same times as the vertical cross sections to

     enable a thorough kinematic description of the trough interaction and ET process. To

     produce isentropic surfaces, a desired potential temperature value is interpolated between

     pressure levels to produce a field of coefficients, which is then used as a weighting

     function to find the appropriate value of PV (calculations done in FERRET). This

     process pulls out high PV air from both the MUTT and TC to view their interaction at

     various levels in the atmosphere.
Guimond                           Tropical Meteorology II                                  9




4. Results

a. Remote Sensing Component

  Table 1 contains the rain rates area averaged about the TC center of Hurricane Michael

from the 18 October 2000 through the 19 October 2000. As mentioned previously, the

rain rates at the TC’s “center” are shown along with 1x1, 2x2 and 3x3 box averages

to show the structural changes occurring during a MUTT interaction and ET process. On

the 18th of October, the rain rates at the center of Michael are on average quite large (~13

mm/hr) with fluctuations (max = 21.20 mm/hr, min = 3.00 mm/hr) in the intensity due to

approximating the TC center and normal structural variability in the eyewall. On the

19th of October, rain rates are shown to increase to rather impressive levels (max = 25.00

mm/hr) early on in the day. SSM/I has an upper threshold level in rain rate returns of

25.00 mm/hr, therefore it is likely that Michael was producing more intense rainfall as

this time than the satellite can detect. The 18th and 19th of October were chosen to

exemplify the shift from a symmetric TC to a more asymmetric structure upon interaction

with a MUTT. At 1324 and 1400 UTC October 19th the rain rates changed dramatically

near the TC center to much lower intensities than previously observed. In addition, every

other time period besides the two above displayed a decrease in the rain rate averaged

over each box about the TC center, going from highest in the 1x1 box to lowest in the

3x3 box. At 1324 UTC on the 19th, the rain rate went up from 2.04 mm/hr in the 1x1

box to 4.87 mm/hr in the 3x3 box. Similar results were found at 1400 UTC on the 19th

with a rain rate of 2.36 mm/hr in the 1x1 box to 4.79 mm/hr in the 3x3 box. As a

supplement to these data, the NHC’s best track reports a 14 mb pressure drop in the six
Guimond                           Tropical Meteorology II                                   10


hour period between 1200 UTC on the 19th to 1800 UTC on the 19th, a pressure change of

more than 2.25 mb/hour (Stewart 2000). The structural and intensity changes observed

during this time period are attributed to the interaction of a MUTT with Michael as can

be seen in the Geostationary Operational Environmental Satellite (GOES) 8 water

vapory imagery at 1200 UTC 19th October in Figure 1. The MUTT displaced the core of

intense precipitation away from Michael’s center and as the TC began to rotate, the

majority of heavy rainfall was located off to the north and northwest of the eye. This

analysis indicates that structural changes in box averaged rain rates about the TC center

can be a useful tool for diagnosing a trough interaction and the early stages of ET, which

can be extended to include the complete ET process if so desired.

b. Synoptic and Dynamic Component

   A step-by-step analysis of each twelve hour period from the GFS beginning 0000

UTC 19th October 2000 and ending 1200 UTC 20th October 2000 will be examined with

heavy weight on PV-thinking to describe both the MUTT interaction and ET of

Hurricane Michael.

   Figure 2a displays the horizontal plot of PV on the 335 K isentropic surface for 0000

UTC on the 19th overlaid with horizontal wind vectors and the hurricane symbol

indicating the model’s location of the TC center at this time. From the plot, the center of

Michael can be seen by the patch of ~1 PVU air out in the Atlantic Ocean with the

strongest gradient of PV at 1.5 PVU (nominal tropopause level) and greater at ~434 km

from the TC center representing the trough. The distance inferred from Figure 2a is on

the lower end of the favorable distant interaction composite (PV maxima between 400

and 1000 km from TC center) as described by Hanley et al. 2001. The corresponding
Guimond                            Tropical Meteorology II                                  11


time of vertical cross section (sliced at 34N) in Figure 2b shows the maximum PV

anomaly associated with the TC concentrated in the lower portions of the atmosphere

between 800 and 900 mb. Contours of potential temperature clearly show the warm core

structure of the TC at this time with the tropopause (thick black line) at a fairly high,

constant height. Figure 2c shows the vertical wind shear in the 200 – 850 mb layer to be

quite low in the vicinity of the TC but with higher values associated with the trough to

the northwest and jet maximum to the north. The relative humidity at 700 mb is between

80-90 % in the region of the TC which will help to sustain the convective core, but drops

off rather quickly near the trough location depicted in Figure 2d.

   At 1200 UTC 19th October, the MLUTT has moved within ~325 km of the TC center

and is now defined as a favorable superposition composite (PV maxima within 400 km of

TC center) for TC intensification based on the criteria established by Hanley et al. 2001.

Figure 3a shows the horizontal plot of PV on the 330 K isentropic surface at the time

above with values of PV above 4 PVU at the TC center and a sharp gradient in PV

extending above 1.5 PVU close to the TC’s PV anomaly. The horizontal winds overlaid

on this plot clearly show the movement of high PV air from the base of the trough

advecting into the core of the TC producing a constructive interference effect detailed in

section 2. The vertical cross section plot (sliced at 40N) shows an arm like extension of

PV associated with the trough containing values at higher levels above 5 PVU moving

towards the center and a longer protrusion with values between 1 and 1.5 PVU located

close to the storm at around 600 mb. The TC is shown to be more intense than the

previous time period with large values of PV (between 4 and 5 PVU) at higher levels in

the atmosphere yet the entire core of the PV anomaly remains well intact and matches the
Guimond                           Tropical Meteorology II                                 12


scale of the trough. Contours of potential temperature reveal a distinct warm core

structure throughout the center of the vortex with isentropes moving apart in the lower

portions of the atmosphere within the TC’s PV anomaly. This observation indicates the

TC was experiencing an increase in relative vorticity from conservation of momentum

arguments that allowed, among other processes, for the rapid deepening (14 mb pressure

drop in six hours) of Michael during and just after the time period of analysis. Figure 3c

shows that the center of Michael is within a zone of low wind shear at this time, but is on

the cusp of an extremely large gradient in shear associated with the approach of the

trough. In addition, both the horizontal winds overlaid on the PV plot and the vertical

wind shear display stronger winds to the north and northeast of the TC indicating that the

outflow anticyclone is becoming enhanced producing trough thinning. This is a perfect

example of scale matching that enabled the trough to provide the TC with the necessary

benefits without letting the detrimental effects of wind shear overwhelm the storm.

Figure 3d explains that the TC is still within a good source region of moisture in the mid

levels to sustain convection and avoid the negative impacts of dry air intrusions.

   At 0000 UTC 20 October, the MUTT has begun to “drive” the evolution of Michael,

which leads into the progression of the ET process. Figure 4a displays the horizontal plot

of PV on the 330 K isentropic surface overlaid with the horizontal winds. The distance

of the trough’s PV anomaly from the TC center is less than 100 km, but the interaction is

difficult to discern as some of the high PV air from the trough has begun to mesh with the

PV from the TC. The maximum PV of the TC has gone down from the previous time to

roughly 3 PVU, but the anomaly has a larger diameter due to the wind field expansion in

cases of ET (Hart 2005, personal communication). A large gradient in the PV field of the
Guimond                           Tropical Meteorology II                                   13


trough exists to the southwest of the storm where high PV air has begun to wrap around

the storm a further indication of ET with maximum values at around 8 PVU (Jones et al.

2003). Figure 4b displays the vertical cross section (sliced at 48N) of PV with a rather

large region of air greater than 1.5 PVU (maximum of ~3 PVU) associated with the TC

and a sharp lobe of PV greater than 7 PVU protruding into the middle part of the

atmosphere. Potential temperature contours indicate that the vortex has begun to take on

slight cold core structure reminiscent of extra-tropical systems although the densest cold

air still remains within the narrow zone of the trough. Figure 4c shows that Michael is

experiencing larger values of vertical shear at this time around 30 m/s while Figure 4d

displays the movement of dry air associated with the trough. Strong wind magnitudes on

the horizontal PV plot across the center and to the northeast of Michael indicates ascent

along the 330 K surface and when coupled with the movement of the storm into a

baroclinic zone with increased vertical wind shear, may imply warm frontogenesis,

although further study is needed (Jones et al. 2003).

   Finally, at 1200 UTC 20 October the horizontal plot of PV along the 325 K isentropic

surface in Figure 5a displays a more pronounced wrapping of the PV anomalies with an

increased asymmetric structure. A large core of PV around 7 PVU is collocated with the

model’s location of ET Michael at this time along with the generation of a cold front

trailing down from the center of Michael indicated by the thin zone of PV around 6 PVU

to the south and southwest of the storm. The horizontal winds surrounding the storm

show an area of ascent along the 325 K surface to the northeast of Michael and descent to

the southwest of the storm, which would correspond to areas of warm and cold

frontogenesis, respectively if frontogenesis functions were analyzed in more detail.
Guimond                           Tropical Meteorology II                                   14


However, GOES infrared imagery at this time period (Figure 6) clearly shows the

development of cold and warm frontal features associated with the ET process of

Michael. The vertical cross section (sliced at 51N) of PV shows a distinctly asymmetric

cyclone with large values of PV above 5 PVU pushing down into the storm as the

tropopause descends lower in the atmosphere. Although there is a slight indication of a

warm core especially near the surface, the majority of the cyclone at this point is cold

core in nature throughout the troposphere.    Figure 5c shows that the wind shear has

begun to subside near the center of the storm although there are higher values with a large

gradient in shear off to the east. The long extension of dry air associated with the trough

shows up well in Figure 5d as this air continues to wrap around the cyclone and hinder

the growth of convection.



5. Conclusions

   The Midlatitude Upper Tropospheric Trough (MUTT) interaction with the Extra-

Tropical Transition (ET) of Hurricane Michael (17-19 October 2000) from both a

synoptic and dynamic perspective was shown to be a rather multifaceted event. The use

of full PV in the diagnoses of a MUTT interaction and ET process proved beneficial for

the analysis of storm structure in various phases. In particular, the storm composites

identified by Hanley et al. (2001) seemed to fit rather well in this study, which further

improves their utility for identification of trough interactions from both a research and

forecasting perspective. PV thinking helped to elucidate the reasoning for Michael’s 14

mb pressure drop in only six hours as a MUTT approached the TC center. PV seemed

particularly useful in explaining the ET process as high PV air wrapped around Michael
Guimond                              Tropical Meteorology II                                    15


and began to interact with the baroclinic environment. Knowledge of this process will

certainly help out the author in his work on a Master’s Thesis involving the structural

change of mid-latitude frontal systems as they merge with transitioning TCs.


Acknowledgements. I thank Dr. Robert Hart for his countless discussions and patience in a
Tropical II class that proved to strengthen my interest and knowledge in a subject I certainly hope
to be involved with in some way for my career. The author also wishes to acknowledge use of
the Ferret program for analysis and graphics in this paper. Ferret is a product of NOAA's Pacific
Marine Environmental Laboratory (Information is available at www.ferret.noaa.gov).


                                         REFERENCES

Abraham, J., J. W. Strapp, C. Fogarty, and M. Wolde, 2004: Extratropical transition of
  hurricane Michael. Bull. Amer. Meteor. Soc.,
  95, 1323-1339.

Hanley, D., J. Molinari, and D. Keyser, 2001: A composite study of the interaction
  between tropical cyclones and upper-tropospheric troughs. Mon. Wea. Rev., 129,
  2570-2584.

_____, 2002: The evolution of a hurricane-trough interaction from a satellite perspective.
Wea. Forecasting, 17, 916-926.

Jones, S.C., and co-authors, 2003: The extratropical transition of tropical cyclones:
   forecast challenges, current understanding, and future directions. Wea.
   Forecasting, 18, 1052-1092.

Molinari, J, S. Skubis, and D. Vollaro, 1995: Exernal influences on hurricane intensity.
  part III: potential vorticity structure. J. Atmos. Sci., 52, 3593-3606.

____, ____, ____, F. Alsheimer, and H.E. Willoughby, 1998: Potential vorticity analysis
  of tropical cyclone intensification. J. Atmos. Sci., 55, 2632-2644.

Stewart, S.R., 2000: Tropical cyclone report hurricane Michael 17-19 October 2000.
   NCEP Rep., 13 pp. [Available online at http://www.nhc.noaa.gov/2000michael.html.]

WMO, 1995: Global perspectives on tropical cyclones. WMO Technical Document. 693
 pp.
     Guimond                              Tropical Meteorology II                                16


                                                 TABLES

Table 1. Comparison of rain rates retrieved from SSM/I satellites during the times of
overpass of Michael's center for the area averages indicated. Also shown is the
distance of the TC center from the Potential Vorticity Anomaly (PVA = 1.5 PVU) for
each overpass.
TIME (UTC)       TC CENTER(°N,°W)*             Rain Rate (mm/hr)            DISTANCE FROM PVA (km)
18-Oct-2000                                 Center|1°x1°|2°x2°|3°x3°
    148              (30.50,71.00)             11.80|8.93|5.56|3.24                     ~705
   1100              (31.50,70.50)           21.20|15.16|11.44|7.34                     ~598
   1342              (31.75,70.25)             6.70|11.35|9.05|5.52                     ~564
   1418              (32.00,70.00)            20.50|14.15|9.38|5.33                     ~557
   2218              (33.75,68.50)            3.00|15.48|12.37|8.35                     ~456
19-Oct-2000
    106              (34.50,67.50)           10.50 |13.34|10.50|7.54                    ~424
    136              (34.75,67.25)            23.10|13.31|9.90|6.67                     ~419
   1042              (39.00,62.50)            25.00|11.83|8.62|7.12                     ~337
   1324              (40.75,60.75)             1.10|2.04|3.16|4.87                      ~299
   1400              (41.25,60.50)             1.30|2.36|3.45|4.79                      ~288
              *Closest data point to TC center from NHC since SSM/I data has 0.25° resolution.
          Guimond                                 Tropical Meteorology II                                                        17


                                                          FIGURES




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                            Figure 1. GOES 8 water vapor imagery at 12:15 UTC 19th October 2000.




Figure 2a. Horizontal plot of PV on the 335 K isentropic                             Figure 2b. Vertical cross section of PV in the x-z plane for
surface for the time period indicated in PVU with 0.5 PVU                            the time period indicated in PVU with increment of 0.5 PVU
increment. Horizontal wind vectors along the same surface are                        and 1.5 PVU (nominal tropopause) darkened. Contours of
overlaid with reference vector in m/s. Model TC center                               potential temperature are overlaid in K with increment every
indicated by the hurricane symbol.                                                   5K. Latitude of slice indicated at top of plot.
             Guimond                                   Tropical Meteorology II                                        18




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                     are needed to see this picture.




  Figure 2c. Vertical wind shear in 200 - 850 mb layer                     Figure 2d. Relative Humidity at 700 mb contoured
  overlaid with streamlines at time period indicated. Values               every 10 % for the time period indicated.
  are contoured every 5 m/s with streamline reference in m/s.




Figure 3a. Horizontal plot of PV on the 330 K isentropic surface    Figure 3b. Vertical cross section of PV in the x-z plane for the
for the time period indicated in PVU with 0.5 PVU increment.        time period indicated in PVU with increment of 0.5 PVU and
Horizontal wind vectors along the same surface are overlaid         1.5 PVU (nominal tropopause) darkened. Contours of potential
with reference vector in m/s. Model TC center indicated by the      temperature are overlaid in K with increment every 5K.
hurricane symbol.                                                   Latitude of slice indicated at top of plot.
               Guimond                                   Tropical Meteorology II                                      19




    Figure 3c. Vertical wind shear in 200 - 850 mb layer                  Figure 3d. Relative Humidity at 700 mb contoured every
    overlaid with streamlines at time period indicated. Values            10 % for the time period indicated.
    are plotted every 5 m/s with streamline reference in m/s.




Figure 4a. Horizontal plot of PV on the 330 K isentropic surface      Figure 4b. Vertical cross section of PV in the x-z plane for
for the time period indicated in PVU with 0.5 PVU increment.          the time period indicated in PVU with increment of 0.5 PVU
Horizontal wind vectors along the same surface are overlaid           and 1.5 PVU (nominal tropopause) darkened. Contours of
with reference vector in m/s. Model TC center indicated by the        potential temperature are overlaid in K with increment every
hurricane symbol.                                                     5K. Latitude of slice indicated at top of plot.
          Guimond                                  Tropical Meteorology II                                         20




    Figure 4c. Vertical wind shear in 200 - 850 mb layer              Figure 4d. Relative Humidity at 700 mb contoured
    overlaid with streamlines at time period indicated. Values        every 10 % for the time period indicated.
    are plotted every 5 m/s with streamline reference in m/s.




Figure 5a. Horizontal plot of PV on the 325 K isentropic          Figure 5b. Vertical cross section of PV in the x-z plane for the
surface for the time period indicated in PVU with 0.5 PVU         time period indicated in PVU with increment of 0.5 PVU and
increment. Horizontal wind vectors along the same surface are     1.5 PVU (nominal tropopause) darkened. Contours of
overlaid with reference vector in m/s. Model TC center            potential temperature are overlaid in K with increment every
indicated by the hurricane symbol.                                5K. Latitude of slice indicated at top of plot.
          Guimond                                  Tropical Meteorology II                                                        21




Figure 5c. Vertical wind shear in 200 - 850 mb layer                                     Figure 5d. Relative Humidity at 700 mb contoured
overlaid with streamlines at time period indicated. Values                               every 10 % for the time period indicated.
are plotted every 5 m/s with streamline reference in m/s.




                                                              QuickTime™ and a
                                                              GIF decompressor
                                                       are needed to see this picture.




                           Figure 6. GOES 8 infrared imagery at 12:15 UTC 20th October 2000.

				
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