Tropical Cyclone Overview: Lesson 3 Applications of Microwave Data

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Tropical Cyclone Overview Lesson 3Applications
of Microwave Data

• Introduction
• SSM/I algorithms
• Overview of the Advanced Microwave Sounder Unit
  (AMSU)
• Review of hydrostatic and dynamical balance
  approximations
• Experimental intensity/structure estimation
  algorithm

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GOES Imager Channels Channel 1 - Visible
- .6 µm ( .52- .72) Channel 2
- Shortwave IR - 3.9 µm (3.78- 4.03)
Channel 3 - Water Vapor - 6.7 µm (6.47-7.02)
Channel 4 - Longwave IR - 10.7 µm (10.2-11.2)
Channel 5 - Split Window - 12.0 µm
(11.5-12.5) SSM/I, AMSU Microwave Frequencies
20-150 Ghz (1.5-0.2 cm)
1 2 3 4 5
Microwave
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Special Sensor Microwave Imager (SSM/I)

• Passive Microwave Imager on DMSP polar orbiting
  satellite
• Conical Scan, 1400 km swath width
• Four Frequencies, Horizontal and Vertical
  Polarization
• 19.4 GHz (H,V), 22.2 GHz (V), 37.0 GHz (H,V),
  85.5 GHz (H,V)
• Note Similar frequencies on TRMM satellite
• Horizontal Resolution 15-50 km
• Senses below cloud-top

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SSM/I Products/Applications

• Vertically integrated water vapor, liquid
• Rain rate
• Sea Ice
• Ocean Surface Wind Speed
• 85 GHz ice scattering signal useful for tropical
  cyclone analysis
• Highlights convectively active regions below
  cirrus canopy seen in IR imagery

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A
B
C
A Uses SSM/I Rain Rates B AE uses GOES Longwave
IR (Channel 4) C. GMSRA Combines all GOES channels
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Ocean Surface Winds from SSM/I

• Passive Microwave
• (SSM/I, TMI)
• 19 GHz emissivity increases as capillary waves
  and sea foam are generated by wind
• Rain, thick clouds degrade algorithm
• Combine 19V GHz, 22V GHz, 37V GHz, 37H GHz
• Winds limited to 40 kt
• Provides speed but not direction

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Hurricane Jeanne 23 Sept 98 IR
VIS 85 GHz Comp. (From NRL web-site).
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Properties of NOAA-15

• Polar orbiting satellite
• 833 km above earths surface
• 14.2 revolutions per day
• Launched May 13, 1998 (Vandenberg AFB)
• Instrumentation
• AVHRR, HIRS, AMSU, SBUV
• First in new series (NOAA-K,L,M)
• NOAA-16 Launched Fall 2000

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AMSU Instrument Properties

• AMSU-A1
• 13 frequencies 50-89 GHz
• 48 km maximum resolution
• Vertical temperature profiles 0-45 km
• AMSU-A2
• 2 frequencies 23.8, 31.4 GHz
• 48 km maximum resolution
• Precipitable water, cloud water, rain rate
• AMSU-B (interference problems)
• 5 frequencies 89-183 GHz
• 16 km maximum resolution
• Water vapor soundings

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AMSU-A1 Weighting Functions
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AMSU-A2 Weighting Functions
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AMSU-B Weighting Functions
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Hurricane Mitch AVHRR Image 27 October 1998
NOAA-15
Corresponding AMSU-B 89 GHz
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Typical AMSU Data Coverage
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AMSU-A Moisture Algorithms

• Total Precipitable Water (V)
• V cos(?) fTB(23.8),TB(31.4)
• Cloud Liquid Water (Q)
• Q cos(? ) gTB(23.8),TB(31.4)
• Rain Rate (R)
• R 0.002 Q 1.7
• Tropical Rainfall Potential (TRaP)
• TRaP Ra D/c
• Ra avg. rain rate, Dstorm dia., c Storm
  Speed

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AMSU-A Rainfall Rate for Hurricane Georges
(.01 inches/hr)
TRaP for Key West 6.7 inches
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Temperature Retrieval Algorithm

• 15 AMSU-A channels included
• Radiances adjusted for side lobes before
  conversion to brightness temperatures (BT)
• BT adjusted for view angle
• Statistical algorithm converts from BT to
  temperature profiles
• 40 vertical levels 0.1-1000 mb
• RMS error 1.0-1.5 K compared with rawindsondes

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IR Imagery March 1, 1999
AMSU Temperature Retrieval (570 mb)
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AMSU Tropical Cyclone Applications

• Input for numerical models
• Direct assimilation of AMSU radiances
• Rain rate product input to physical
  initialization procedures
• Apply hydrostatic/dynamical balance constraints
  to obtain height/wind fields
• Height/winds input for intensity/structure
  intensity estimation technique

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Hydrostatic Balance

• Approximation to vertical momentum equation
• Valid for horizontal scales gt 10 km
• dP/dz -gP/RTv (Height coordinates)
• Ppressure, zheight, Tvvirtual temperature
• Ggravitational constant, Rideal gas constant
• Allows calculation of pressure as a function of
  height P(z), given temperature and moisture
  profile
• d? /dp -RTv/P (Pressure coordinates)
• Allows calculatation of geopotential height as a
  function of pressure ?(P)
• Both forms require boundary conditions
• Integration can be upwards or downwards
• Contribution from moisture is fairly small and
  will be neglected (Tv replaced by T)

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Dynamical Balance Conditions Provides Diagnostic
Relationship Between Height and Wind

• High latitude, synoptic-scale flows
• Geostrophic balance
• Axisymmetric flows
• Gradient balance
• Higher-order approximation to the divergence
  equation
• Charney balance equation

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Geostrophic Balance(Not valid for tropical
cyclones)
U/fL
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Gradient Balance

• Start with horizontal momentum equations in
  cylindrical/pressure coordinates
• Assume no variation in the azimuthal direction
• Radial momentum equation reduces to
• V2/r fV d?/dr
• V tangential wind, r radius
• f Coriolis parameter
• ? geopotential height from hydrostatic
  equation

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Charney Nonlinear Balance Equation

• NBE reduces to gradient wind in axisymmetric case
• NBE reduces to geostrophic wind in low-amplitude
  case

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Balance Winds from AMSU Data

• Start with Advanced Microwave Sounder Unit (AMSU)
  data from NOAA-15
• Apply NESDIS statistical retrieval algorithm to
  get T from radiances
• Use hydrostatic equation to get height field
• NCEP analysis for lower boundary condition
• Apply gradient (2-D) or Charney (3-D) balance to
  get winds
• NCEP analysis for lateral boundary condition

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2-D AMSU Wind RetrievalSolution of the Gradient
Wind Equation

• Gradient Wind Equation V2/r fV ?r
• Find ? from V ? ?(V2/r fV )dr
• Find V from ? V -fr/2 (fr/2)2 r ?r1/2
• Requires choice of root and (fr/2)2 r ?r gt 0

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2D Analyses - Hurricane Gert
Temperature(r,z)
Sfc Pressure (x,y)
Tangential Wind(r,z)
Uncorrected
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Correction for Attenuation by Cloud Liquid Water
and Ice Scattering

• Use data base of 120 cases from 1999 hurricane
  season
• Derive statistical correction to temperature as a
  function of CLW for P lt 300 hPa
• Identify isolated cold anomalies related to ice
  scattering using threshold technique
• Patch cold regions using Laplacian filter from
  surrounding data

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2-D AMSU Wind Retrieval Results

• gt250 cases analyzed in Atlantic and East Pacific
  basins during 1999-2000
• Inner core winds not resolved due to limited
  AMSU-A spatial resolution
• Statistical relationship between AMSU analyses
  and intensity
• Large differences in storm sizes
• Useful for wind radii estimation
• Analyses appear to capture vertical structure
  changes
• 2-D analysis algorithm available for evaluation
  in West Pacific

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Isaac 092800 120 kt Joyce 092700 70 kt
AMSU 2-D Winds For Large and Small Storms
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Low-Shear High-Shear
AMSU 2-D Winds In Low-Shear and High-Shear
Storm Environments. (Note the deeper cyclonic
flow in the low-shear cases.)
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Statistical Intensity Estimation

• AMSU resolution prevents direct measurement of
  inner core
• Correlate parameters from AMSU analyses with
  observed storm intensity
• AMSU Predictors from 1999 storm sample
• r600 to r0 km pressure drop
• Max tangential wind at 0 and 3 km
• Max upper-level temperature anomaly
• Average cloud-liquid water
• Algorithm explains 70 of variance
• Algorithm will be tested on 2000 data

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Predicted vs. Observerd Maximum
Winds(Preliminary Results with Dependent Data)
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Statistical Size Estimation

• Correlate parameters from AMSU analyses with
  observed storm size
• Average radius of 34, 50 and 64 kt winds
• AMSU Predictors from 1999 storm sample
• R600 to r0 km pressure drop
• Max tangential wind at 0 and 3 km
• Storm latitude
• Estimated maximum wind
• Average cloud-liquid water
• Algorithm explains 80 of variance
• Algorithm will be tested on 2000 data

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Predicted vs. Observed 34 kt Wind
Radius(Preliminary Results with Dependent Data)
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3-D AMSU Wind RetrievalCharney Nonlinear
Balance Equation

• Charney balance equation
• ?2? -(ux)2 2vxuy (vy)2 f? - ?u
• For nondivergent flow u-?y, v ?x, ? ? 2?
• ? 2? -2(?xy)2 2(?xx ?yy) f ? 2? ? ?y
• Find ? from u,v Poisson equation
• Requires boundary values for ?
• Find u,v from ? Monge-Ampere Equation
• Requires boundary values for u,v (or ?)
• Ellipticity condition ? 2? 1/2f2 gt 0
• Possibility of two solutions

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Charney Balance Equation Iterative Solution

• Developed for early NWP models
• Write balance equation as
  ?2 f? - (ux)2 (vx)2 (uy)2
  (vy)2 ?u ? 2? 0 ?2 f? - N
  0
  where ? ? 2? u -?y v ?x
• Solve for ?
  ? -(f/2) (f/2)2
  N1/2
• N N(?) so iteration is necessary

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Charney Balance Equation Variational Solution

• Iterative method sometimes fails for tropical
  cyclone case
• Variational solution method
• Define cost function as square of balance
  equation integrated over domain of interest
• Add smoothness penalty term to cost function
• Find u,v to minimize cost function
• Minimization requires cost function gradient,
  determined from adjoint of balance equation
• Boundary conditions for u,v from NCEP analysis

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Balance Equation Variational Solution - Hurricane
Floyd
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Hurricane Floyd 850 mb Isotachs (kt)
-80 -60 -40 -20 0
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Evaluation of AMSU Winds
AMSU
RECON
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Summary of Lesson 3

• Passive microwave data can penetrate through
  cloud tops
• Data available from DMSP(SSM/I), NOAA-15/16
  (AMSU), and TRMM (TMI) satellites
• Algorithms available for ocean surface wind
  speed, integrated water content, rainfall rate,
  sea ice/snow cover
• Data useful for qualitative analysis of tropical
  cyclone structure (banding, eye wall, etc)
• AMSU temperature sounding can be combined with
  hydrostatic/dynamical balance constraints for
  tropical cyclone analysis