The Spatiotemporal Variability of Infrasound Path

PartitioningDouglas 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, , u, v, , 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

NRL Ground to Space (G2S-E/RT)

NASA Data Assimilation Office

Zonal Wind (m/s)July 17, 2001, 00:06 UTCLongitude = -60O W

Atmospheric Specification: The Problem of CombiningIncomplete Data Sets

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NOAA NCEP Analysis/Forecast

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• Various atmospheric data sets are fused together in 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 specificationsSeptember, 28, 2002 12:00 UTCLatitude = 36.7056 NLongitude = 115.96 W

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

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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

Meridional

Zonal

Sound Speed

, ,x y z

dx dy dzk c u k c v k c

dt dt dt

2, , ( 1)yx zx z y z z

dkdk dknk k nk k n k

dt dt dt

x y

dc du dvn k k

dz dz dz

• Classical Ray Theory (e.g. Groves, 1955) assuming a Horizontally Stratified Plane Parallel Atmosphere

• System of 6 ODE’s that can be numerically integrated given c(z), u(z), v(z) and initial ray conditions ro and ko.

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.

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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)

Thermosphere0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.00 0.10 0.20 0.30 0.40

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0.00 0.05 0.10 0.15

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Global Ducting Characteristics (June 23, 2001, 06:00 UT)

Thermosphere0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.00 0.10 0.20 0.30 0.40

Troposphere0.00 0.05 0.10 0.15

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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.