Tropical Cyclone Overview: Lesson 3 Applications 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

GOES Imager Channels : Channel 1 - Visible -.6 µm ( ) Channel 2 - Shortwave IR µm ( ) Channel 3 - Water Vapor µm ( ) Channel 4 - Longwave IR µm ( ) Channel 5 - Split Window µm ( ) SSM/I, AMSU Microwave Frequencies : Ghz ( cm) Microwave

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: km Senses below cloud-top

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

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

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

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

Properties of NOAA-15 Polar orbiting satellite 833 km above earth’s 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

AMSU Instrument Properties AMSU-A1 –13 frequencies 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: GHz –16 km maximum resolution –Water vapor soundings

AMSU-A1 Weighting Functions

AMSU-A2 Weighting Functions

AMSU-B Weighting Functions

Hurricane Mitch AVHRR Image 27 October 1998 NOAA-15 Corresponding AMSU-B 89 GHz

Typical AMSU Data Coverage

AMSU-A Moisture Algorithms Total Precipitable Water (V) –V = cos(  ) * f[T B (23.8),T B (31.4)] Cloud Liquid Water (Q) –Q = cos(  ) * g[T B (23.8),T B (31.4)] Rain Rate (R) –R = * Q 1.7 Tropical Rainfall Potential (TRaP) –TRaP = R a * D/c R a = avg. rain rate, D=storm dia., c = Storm Speed

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

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 mb RMS error K compared with rawindsondes

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

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

Hydrostatic Balance Approximation to vertical momentum equation Valid for horizontal scales > 10 km dP/dz = -gP/RT v (Height coordinates) –P=pressure, z=height, T v =virtual temperature –G=gravitational constant, R=ideal gas constant –Allows calculation of pressure as a function of height P(z), given temperature and moisture profile d  /dp = -RT v /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 (T v replaced by T)

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

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

Gradient Balance Start with horizontal momentum equations in cylindrical/pressure coordinates Assume no variation in the azimuthal direction Radial momentum equation reduces to: V 2 /r + fV = d  /dr V = tangential wind, r = radius f = Coriolis parameter  = geopotential height from hydrostatic equation

Charney Nonlinear Balance Equation NBE reduces to gradient wind in axisymmetric case NBE reduces to geostrophic wind in low- amplitude case

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

2-D AMSU Wind Retrieval: Solution of the Gradient Wind Equation Gradient Wind Equation: V 2 /r + fV =  r –Find  from V:  =  (V 2 /r + fV )dr –Find V from  : V = -fr/2 ± [(fr/2) 2 + r  r ] 1/2 Requires choice of root and [(fr/2) 2 + r  r ] > 0

2D Analyses - Hurricane Gert Temperature(r,z)Sfc Pressure (x,y)Tangential Wind(r,z) Uncorrected Hydrometeor Corrected

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 < 300 hPa Identify isolated cold anomalies related to ice scattering using threshold technique “Patch” cold regions using Laplacian filter from surrounding data

2-D AMSU Wind Retrieval Results >250 cases analyzed in Atlantic and East Pacific basins during 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

AMSU 2-D Winds For Large and Small Storms Isaac kt Joyce kt

AMSU 2-D Winds In Low-Shear and High-Shear Storm Environments. (Note the deeper cyclonic flow in the low-shear cases.) Low-Shear High-Shear

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: –r=600 to r=0 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

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

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: –R=600 to r=0 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

Predicted vs. Observed 34 kt Wind Radius (Preliminary Results with Dependent Data)

3-D AMSU Wind Retrieval: Charney Nonlinear Balance Equation Charney balance equation: –  2  = -[(u x ) 2 +2v x u y + (v y ) 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  + 1/2f 2 > 0 –Possibility of two solutions

Charney Balance Equation Iterative Solution Developed for early NWP models –Write balance equation as:  2 + f  - [(u x ) 2 + (v x ) 2 + (u y ) 2 + (v y ) 2 +  u+  2  ] = 0  2 + f  - [N ] = 0 where  =  2  u = -  y v=  x –Solve for  :  = -(f/2) ± [(f/2) 2 + N] 1/2 –N = N(  ) so iteration is necessary

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

Balance Equation Variational Solution - Hurricane Floyd AMSU 850 hPa heightFirst guess wind: (   u=0,   v=0) Nonlinear balance wind

Hurricane Floyd 850 mb Isotachs (kt)

Evaluation of AMSU Winds RECON AMSU

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