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									     The Spatiotemporal
Variability of Infrasound Path
         Partitioning
     Douglas P. Drob1 and Milton Garcés2
     (1) E.O. Hulburt Center for Space Research,
        US Naval Research Laboratory
        4555 Overlook Ave, Washington, DC 20375.
     (2) HIGP, SOEST, University of Hawaii, Manoa
         73-4460 Queen Kaahumanu Hwy., #119
         Kailua-Kona, HI 96740-2632.
                   Outline
• Part One: Atmospheric Specifications for
  Infrasound Propagation Modeling
  – Objective and Background
  – NRL G2S-E/RT

• Part Two: Infrasound Path Partitioning
  – A Simple Ray Tracing Model
  – Local Propagation Characteristics
  – The Spatiotemporal Variability of Infrasound
    Propagation Characteristics
     Part One: Atmospheric Specifications for
        Infrasound Propagation Modeling
• Objective: Produce a Detailed Global Specification of the
  Atmosphere from the Ground 2 Space in Real Time (e.g. Hourly)
  or for specific Events.
• Solution: Build a semi-empirical spectral model of:
   – The atmospheric state variables [ T, P, r, u, v, F, etc.],
   – as a function of [latitude, longitude, altitude, day of year, universal time].
• Raw Materials:
   – Daily Numerical Weather Prediction (NWP) specifications such as those
     produced by NOAA, ECMWF, UKMO, and FNMOC,
   – The NRLMSISE-00 and HWM-93 empirical models,
   – And any other relevant global data sets.
• Approach: Statistical data fusion methodology using:
   – Spherical and Vector Spherical Harmonics (horizontal variations)
   – Rational B-Splines (vertical variations)
   – Standard meteorological analysis and data assimilation procedures
 Atmospheric Specification: The Problem of Combining
 Incomplete Data Sets
120
       Zonal Wind (m/s)
100    July 17, 2001, 00:06 UTC
       Longitude = -60 O W
 80
               NOAA NCEP Analysis/Forecast
 60              6-hours daily                         +                                              +
                 1x1 degree resolution
 40              < 10 mb (~35 km)

 20                                                                        HWM-93
                                                                            4D Empirical Model
  0                                                                         0-500 km
      -80       -40       0           40       80
                       Latitude                               NRL Ground to Space (G2S-E/RT)
120
      NASA Data Assimilation Office
100     6-hours daily, delayed
        1x1 degree resolution
        < 1 - .4 mb (~50 km)
80

60                                                    +...=
40

20

                                         Topography
 0
      -80      -40        0           40        80            -80    -40      0       40         80
                       Latitude                                            Latitude
Vector Spherical Harmonic   •   Various atmospheric data
                                sets are fused together in

    Data Assimilation           a self-consistent manner
                                using nonlinear least-
                                squares fitting of vector
                                spherical harmonics and
                                B-Splines.
                            •   Analysis occurs at 6-
                                hour intervals, but higher
                                resolutions are possible
                                and probably needed.
                            •   Smooth fields can be
                                constructed using the
                                estimated model
                                coefficients and basis
                                functions.
                            •   The data fields require
                                less storage space than
                                gridded data.
                            •   Spatial derivatives can
                                be directly calculated
                                from the estimated
                                coefficients.
      Preliminary
      NRL G2S-E/RT specifications
      September, 28, 2002 12:00 UTC
      Latitude = 36.7056 N
      Longitude = 115.96 W

      Data sources:
       HWM-93/MSISE-90 (> 55 km)
       NASA-DAO (25 - 55 km)
       NOAA-NCEP (0 - 35 km)




                                     Meridional Wind Velocity (m/s)
                120
                                                                                              30

                                                                                              25
                100
                                                                                              20

                                                                                              15
                80
                                                                                              10
Altitude (km)




                                                                                              5
                60
                                                                                              0

                40                                                                            -5

                                                                                              -10

                20                                                                            -15

                                                                                              -20

                           5   10        15        20           25    30   35
         Source (Bolide)            Degrees Along Great Circle Path             Receiver (IS-10)
             Additional Considerations
• Reliability and Accuracy
   – Physical Inconsistencies
        • Temporal averaging
        • Dynamic and hydrostatic balance
        • Spectral content decreases with altitude
   – Observational Biases (i.e. bad information)
        • Upper-stratospheric temperature biases (NWP)
        • MF-Radar, HRDI, TMA rocket wind measurement discrepancies
        • HRDI, MSIS, and LIDAR, Falling Sphere, temperature
          measurement discrepancies
• Technical Issues
   –   Increased information content => increased complexity
   –   Product/estimate revisions
   –   Multifunctional client software
   –   Review and selection of new data sources
   –   Routine operations and data distribution methods
    Part 2: Infrasound Propagation
             Characteristics
Objective: Investigate the spatiotemporal
 behavior of the partitioning of infrasound
 among the possible atmospheric ducts.

• Simple Propagation Model
• Modeling a Hypothetical Event
• Results from a Global Ensemble of
  Hypothetical Events
                Simple Propagation Model
• Classical Ray Theory (e.g. Groves,         dx                  dy                  dz
                                                 k xc  u,          k y c  v,         kzc
  1955) assuming a Horizontally              dt                  dt                  dt
  Stratified Plane Parallel Atmosphere
                                             dk x                dk y                dk z
• System of 6 ODE’s that can be                    nk x k z ,         nk y k z ,         n(k z2  1)
                                              dt                  dt                 dt
  numerically integrated given c(z),
                                                  dc          du      dv
  u(z), v(z) and initial ray conditions ro   n       kx         ky
  and ko.                                         dz          dz      dz
          Modeling a Hypothetical Event
• Isotropically radiating hemispheric source with a geodesic
  tessellation (2592 triangular elements).
• Use vector average of vertices of each element as the set of initial
  wave vectors {k0}.
• Integrate equations for each ray in the set until either kz < 0
  (reflections) or z > 165 km (escape).
• Four distinct groups of rays (or ducts) form.
• Group Definitions (chosen for mathematical convince)
   –   Tropospheric: zmax < 16 km
   –   Stratospheric: 16 km < zmax < 70 km
   –   Thermospheric: 70 < zmax < 165 km
   –   Escape: zmax > 165 km
• Partitioning fractions are determined by summing over the
  number of elements propagating in a given group weight by its
  fractional surface area, i.e. estimating the surface area of the
  various regions of ko space.
            Ray Turning Height, zmax (km)
                                 180

                                 160

                                 140

                                 120

                                 100

                                 80

                                 60

                                 40

                                 20
   o               o
180             90               0
Southward       Eastward
               Partitioning Fractions
• First hypothetical case:
   –   7.7 % Troposphere
   –   13.2% Stratosphere
   –   61.6% Thermosphere
   –   17.5% Escape
• Representative case studies for a global ensemble of
  events were performed:
   – February 28, 2000 (Equinox)
   – June 17, 2001 (Solstice)
• Global results (upper and lower bounds)
   –   Tropospheric ducting (0 – 15 %)
   –   Stratospheric ducting (0 – 40 %)
   –   Thermospheric ducting (40 – 85 %)
   –   Escape fractions (12 – 17 %)
Global Ducting Characteristics (February 28, 2000, 12:00 UT)
Global Ducting Characteristics (June 23, 2001, 06:00 UT)
         Tropospheric Ducting
• A small but significant amount of ducting occurs
  (0-15%).
• Fractions follow the twists and gyres of the
  tropospheric jet stream.
• Detected amplitudes should be significant due to
  below average geometric spreading and molecular
  attenuation.
• The increased number of bounces increases
  probability of diffusion by irregular surface
  reflections.
• The ducts can vanish over relatively short spatial
  scales.
        Stratospheric Ducting
• A significant fraction of stratospheric
  ducting can occur (0 – 40 %)
• Large geographic dependence
  – Common at mid- and high-latitudes (near the
    polar stratospheric vortices).
  – Rare at equatorial latitudes (winds weak,
    troposphere deep)
• Strong seasonal dependence
• Stratospheric ducting of surface sources are
  topographically dependent.
Thermospheric Ducting and Escape Fractions
• The thermospheric fractions are highly variable (40 to 85 %)
• Escape Fractions relatively constant (12-17%)
• Thermospheric ducting mirrors the stratospheric ducting fractions
• Theory and observations indicate detected signal amplitudes are
  much weaker (due to increased geometric spreading and
  gaskinetic attenuation processes)
• These fractions are functions of the phase and amplitude of the
  thermospheric solar heating driven tides.
• These fractions are also effected by cyclical Solar EUV flux
  variability (11-year, 29-day solar rotation) and Space Weather
  Events (geomagnetic storms).
• Garces M, Drob DP, Picone JM, A theoretical Study of the effects
  of geomagnetic fluctuations and solar tides on the propagation of
  infrasonic waves in the upper atmosphere, Geophys. J. Int., 148,
  77-87, 2002.
                  Conclusions
• The spatiotemporal variability of infrasound path
  partitioning is highly complex.
• This complexity arises from the natural variability
  of the atmosphere.
• The variability occurs on time scales from several
  hours to several months and over horizontal scales
  greater than 750 km.
• The majority of this variability can be accounted
  for using the NRLG2S-E/RT models.
• Observational validation of this work using
  ground truth events is need.

								
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