Transcript Hurricane Steering as a Potential Vorticity Advection Process

Hurricane Steering as a Potential
Vorticity Advection Process
Brett Hoover
21 March 2007
Copyright Brett Hoover 2007
Copyright Brett Hoover 2007
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Copyright Brett Hoover 2007
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Steering Flow – Conventional
Methodology
• Hurricane steering is composed of two parts:
1) Advection of the hurricane by
“environmental flow”
2) Self-propagation mechanisms
• Environmental advection is typically the
dominant mechanism
Copyright Brett Hoover 2007
Steering Flow – Conventional
Methodology
• Hurricane steering is composed of two parts:
1) Advection of the hurricane by
“environmental flow”
2) Self-propagation mechanisms
• Environmental advection is typically the
dominant mechanism
Copyright Brett Hoover 2007
Steering Flow – Conventional
Methodology
• Steering Column – a horizontal and vertical averaging of
the horizontal winds around the hurricane which
approximates the environmental flow near the hurricane.
-
=
Copyright Brett Hoover 2007
Steering Flow – Conventional
Methodology
• What are the characteristics of an optimal
steering column?
– Chan and Gray (1982) – 550-770 km radius averaged
over 700-500 hPa
– Simpson (1971), Dong and Neumann (1986), Pike
(1987), and Velden and Leslie (1991) – Optimal
vertical average depends on intensity of tropical
cyclone – Vortex Intensity- Vortex Depth relationship
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Vortex Intensity – Vortex Depth
Relationship
• Several studies have shown that more
intense TCs move with a deeper steering
column, while weaker TCs move with a
shallower steering column.
• Velden and Leslie (1991) proposed that
the more intense a storm becomes, the
deeper its characteristic vortex tower
builds, which is advected by environmental
flow of a greater depth.
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Vortex Intensity – Vortex Depth
Relationship
z
y
x
x
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Vortex Intensity – Vortex Depth
Relationship
z
y
x
x
Copyright Brett Hoover 2007
Vortex Intensity – Vortex Depth
Relationship
• Velden and Leslie (1991) were able to significantly
improve track forecasts by dividing TCs into intensity
‘bins’ and assigning them steering columns based on
those partitions:
Intensity
>1005
9951005
985995
975985
965975
955965
945955
935945
<935
LayerMean
850500
850500
850500
850500
850400
850400
850300
850300
850300
From Velden and Leslie (1991) Table 2 (pg. 247)
For minimized 48hr mean track forecast errors
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Hypothesis
• TC motion can be diagnosed from the
perspective of steering as a potential
vorticity (PV) advection process.
• Since the PV structure of a TC is
dependent upon the distribution of latent
heating in the cyclone, TC steering, and
ultimately TC track, is sensitive to the
choice of cumulus parameterization used
for a modeled TC.
Copyright Brett Hoover 2007
Model Setup
• NCAR/Penn State MM5 version 3 (MM5v3)
model
• Initialized with NCEP 2.5o x 2.5o data for
Hurricane Helene (2006) at 0000 UTC 14
September 2006, when Helene reached tropical
storm status
• Two simulations performed: 30km resolution, 20
sigma levels (evenly spaced), only varying in
cumulus parameterization – Grell or Betts-Miller
(BM)
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Can Cumulus Parameterization Choice
Affect TC Track?
BM
Grell
Copyright Brett Hoover 2007
Can Cumulus Parameterization Choice
Affect TC Track?
F18
BM
Grell
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Can Cumulus Parameterization Choice
Affect TC Track?
F96
BM
Grell
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Wait a Minute…
• Track split occurs during time when intensities
of simulated TCs only differ by 3 hPa:
Copyright Brett Hoover 2007
Wait a Minute…
• Track split occurs during time when intensities
of simulated TCs only differ by 3 hPa:
Copyright Brett Hoover 2007
Methodology
PV Structure of a TC
• The PV structure of a TC is typified by a cyclonic PV
“tower” beneath an elevated dynamic tropopause –
Shapiro and Franklin (1995); Wu and Emanuel (1995a,b); Shapiro (1996); Wu and
Kurihara (1996)
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Methodology
Optimal Steering Level
• We wish to analyze the steering of a simulated
TC with respect to significant regions of the PV
structure.
• It is hypothesized that the optimal steering
column will be at or near one of these regions.
Copyright Brett Hoover 2007
Methodology
Optimal Steering Level
PV Maximum (PVm)
• Maximum advection of PV by the environmetnal flow
would most likely be near the location of PVm, since the
strongest horizontal gradients in PV exist there.

 V  PV
maximized about PVm
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Methodology
Optimal Steering Level
PV “Center of Mass” (PVcom)
• Treating PV as a density function, a “center of mass”
can be calculated which may be a significant region of
advection for the volume-integrated effect of PV
advection throughout the entire PV tower.
PVcom 
east

x  west
PVx x north PVy y top PVk k
, 
,
PVtotal y  south PVtotal k bot PVtotal
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Methodology
Optimal Steering Level
•
•
•
In addition, we wish to look at two more
regions of interest:
Vorticity Maximum (VORm)
Vorticity Center of Mass (VORcom)
•
Where these are analogous to PVm and PVcom
Copyright Brett Hoover 2007
Methodology
Modeled Hurricane Motion Vector
(MHMV)
• “Observed” hurricane motion is calculated over
six hours centered on the analyzed time period.
• “Observed” steering flow is an average of the
observed motion over six hours.
Lx
t+3hrs
t0
Ly
t-3hrs
Copyright Brett Hoover 2007
Methodology
Modeled Hurricane Motion Vector
(MHMV)
• “Observed” hurricane motion is calculated over
six hours centered on the analyzed time period.
• “Observed” steering flow is an average of the
observed motion over six hours.
t+3hrs

VMHMV  um , vm 
t0
t-3hrs
Copyright Brett Hoover 2007
Lx Ly
,
6hrs 6hrs
Methodology
Steering Columns
• All possible steering
columns are
calculated at each
analyzed time –
steering columns
range in depth from 1
level to 20 levels
deep (deep layer
mean)
us, vs
Copyright Brett Hoover 2007
Methodology
Steering Columns
• All possible steering
columns are
calculated at each
analyzed time –
steering columns
range in depth from 1
level to 20 levels
deep (deep layer
mean)
us, vs
Copyright Brett Hoover 2007
Methodology
Steering Columns
• All possible steering
columns are
calculated at each
analyzed time –
steering columns
range in depth from 1
level to 20 levels
deep (deep layer
mean)
us, vs
Copyright Brett Hoover 2007
Methodology
Steering Analysis
• The accuracy of any steering column can be
described using a simple cost function, a
calculation of the length of the vector difference
between the diagnosed steering and the MHMV:
J
um  us   vm  vs 
2
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2
Analysis
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Analysis
Thin
Columns
High Error
Low Error
Deep
Columns
Top of Model
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Bottom of Model
Analysis
Full 20-level deep
column
Thin
Columns
High Error
1-level deep
column centered at
top of model
(sigma level 1)
Low Error
Deep
Columns
Top of Model
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Bottom of Model
Analysis
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Analysis
PVm
PVcom
VORm
VORcom
Error is minimized in
a thin steering
column centered
about PVm!
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Analysis: Grell Simulation
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Analysis: Grell Simulation
PVm
PVcom
At early times, the minimum in steering error is
found near the PVm and/or VORm
VORm
VORcom
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Analysis: Grell Simulation
Copyright Brett Hoover 2007
Analysis: Grell Simulation
PVm
PVcom
VORm
VORcom
At later times, a regime-change is observed when
the minimum in steering error moves to the PVcom
Copyright Brett Hoover 2007
Analysis
The evolution of steering error in both simulations
converges toward a single structure:
Error is
minimized
through two
vastly different
steering
columns:
Copyright Brett Hoover 2007
Analysis: Grell F84
The evolution of steering error in both simulations
converges toward a single structure:
1) A thin
steering
column
centered on
PVcom
2) A thick
steering
column
centered on
VORcom
Copyright Brett Hoover 2007
Analysis: BM F84
The evolution of steering error in both simulations
converges toward a single structure:
The BM
simulation
converges
toward the
same
steering
structure at
F84.
Copyright Brett Hoover 2007
Analysis: BM F84
The evolution of steering error in both simulations
converges toward a single structure:
1) A thin
steering
column
centered on
PVcom
2) A thick
steering
column
centered on
VORcom
Copyright Brett Hoover 2007
Analysis
• The relationship of PV structure to steering
column structure appears to change over the
course of the simulation: PVm  PVcom
• Is there a corresponding change in TC PV
structure?
Copyright Brett Hoover 2007
Analysis: PV Structure
• PV structure is analyzed at times before and
after the ‘regime-shift’ in steering.
• At times when steering error is minimized
around PVm, the PV structure of the TC localizes
strong advection to the location of PVm.
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Analysis: PV Structure
Grell Simulation: F18
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Analysis: PV Structure
Grell Simulation: F18
Strong PV
gradient in vicinity
of PVm
Weak PV
gradient
elsewhere
Copyright Brett Hoover 2007
Analysis: PV Structure
• At times when the steering error is minimized
around PVcom, there are significant contributions
to PV advection from regions below PVm.
• It is thought that the integrated effect of
advection throughout the depth of the PV tower
creates the minimum in steering error at PVcom.
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Analysis: PV Structure
Grell Simulation: F54
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Analysis: PV Structure
Grell Simulation: F54
Strong PV
gradient in vicinity
of PVm
Strong PV
gradient
above/below PVm
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Conclusions
• TC steering using steering columns is optimized
when the column is related to the PV structure of
the TC.
• Cumulus parameterization can change the PV
distribution in a TC, thereby significantly
changing the steering and track of a modeled
TC.
• The relationship between TC steering and TC
structure is more complicated than a simple VIVD relationship.
Copyright Brett Hoover 2007
Conclusions
Copyright Brett Hoover 2007
Conclusions
VI-VD
Relationship?
Copyright Brett Hoover 2007
Acknowledgements
This work was supported by the National
Science Foundation Grant ATM-0125169. The
first author was supported by an American
Meteorological Society 21st Century Campaign
Graduate Fellowship.
Copyright Brett Hoover 2007
References
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Chan, J. and W. Gray, 1982: Tropical cyclone movement and surrounding flow relationships. Mon. Wea. Rev.,
110, 1354-1374.
Dong, K. and C. Neumann, 1986: The relationship between tropical cyclone motion and
environmental geostrophic flows. Mon. Wea. Rev., 114, 115-122.
Pike, A. C., and C. J. Neumann, 1987: The variation of track forecast difficulty among tropical
cyclone basins. Wea. Forecasting., 2, 237-242.
Shapiro, L. J., 1996. The motion of Hurricane Gloria: A potential vorticity diagnosis. Mon. Wea.
Rev., 124, 2497-2508.
Shapiro, L. J., and J. L. Franklin, 1995. Potential vorticity in Hurricane Gloria. Mon. Wea. Rev.,
123, 1465-1475.
Simpson, R., 1971: The decision process in hurricane forecasting. NOAA Tech. Memo. NWS SR53, 30 pp. [Available from U.S. Dept. of Commerce, Washington DC, 20233.]
Velden, C., and L. Leslie, 1991: The basic relationship between tropical cyclone intensity and the
depth of the environmental steering layer in the Australian region. Wea. Forecasting, 6,
244-546.
Wu, C.-C, and K. A. Emanuel, 1995a: Potential vorticity diagnostics of hurricane movement. Part
I: A case study of Hurricane Bob (1991). Mon. Wea. Rev., 123, 69-92.
Wu, C.-C, and K. A. Emanuel, 1995b: Potential vorticity diagnostics of hurricane movement. Part
II: Tropical Storm Ana (1991) and Hurricane Andrew (1992). Mon. Wea. Rev., 123,
93-109.
Wu, C.-C, and Y. Kurihara, 1996: A numerical study of the feedback mechanisms of hurricaneenvironment interaction on hurricane movement from a potential vorticity perspective. J. ‘
Atmos. Sci., 53, 2264-2282.
Copyright Brett Hoover 2007