ASTM D7145-22

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Designation: D7145 − 05 (Reapproved 2015) D7145 − 22
Standard Guide for
Measurement of Atmospheric Wind and Turbulence Profiles
by Acoustic Means
This standard is issued under the fixed designation D7145; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This guide describes the application of acoustic remote sensing for measuring atmospheric wind and turbulence profiles. It
includes a summary of the fundamentals of atmospheric sound detection and ranging (sodar), a description of the methodology and
equipment used for sodar applications, factors to consider during site selection and equipment installation, and recommended
procedures for acquiring valid and relevant data.
1.2 This guide applies principally to pulsed monostatic sodar techniques as applied to wind and turbulence measurement in the
open atmosphere, although many of the definitions and principles are also applicable to bistatic configurations. This guide is not
directly applicable to radio-acoustic sounding systems (RASS), or tomographic methods.
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this guide.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
D1356 Terminology Relating to Sampling and Analysis of Atmospheres
3. Terminology
3.1 Definitions—Refer to Terminology D1356 for general terms and their definitions.
3.2 Definitions of Terms Specific to This Standard:
Note: The definitions below are presented in simplified, common, qualitative terms. Refer to noted references for more detailed
information.
This guide is under the jurisdiction of ASTM Committee D22 on Air Quality and is the direct responsibility of Subcommittee D22.11 on Meteorology.
Current edition approved April 1, 2015March 1, 2022. Published April 2015May 2022. Originally approved in 2005. Last previous edition approved in 20102015 as
ε1
D7145 – 05 (2010)(2015). . DOI: 10.1520/D7145-05R15.10.1520/D7145-22.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D7145 − 22
3.2.1 acoustic beam, n—focused or directed acoustic pulse (compression wave) propagating in a radial direction from its point of
origin.
3.2.2 acoustic power, n—relative amplitude or intensity (dB) of an atmospheric compression wave.
3.2.3 acoustic refractive index, n—ratio of reference (at a standard temperature of 293.15 K and 1013.25 hPa pressure) speed of
sound value to its actual value.
3.2.4 acoustic scatter, n—the dispersal by reflection, refraction, or diffraction of acoustic energy in the atmosphere.
–1
3.2.5 acoustic scattering Cross-section Per Unit Volume (σ, m ), n—fraction of incident power at the transmit frequency that is
backscattered per unit distance into a unit solid angle.
3.2.6 acoustic attenuation (φ, dB/100m ), n—loss of acoustic power (acoustic wave amplitude) by beam spreading, scattering, and
absorption as the transmitted wavefront propagates through the atmosphere.
3.2.7 backscatter, n—power returned towards a receiving antenna.
3.2.8 beamwidth (degrees), n—one way angular width (half angle at –3dB) of an acoustic beam from its centerline maximum to
the point at the beam periphery where the power level is half (3 decibels below) centerline beam power.
3.2.9 bistatic, adj—sodar configuration that uses spatially separated antennas for signal transmission and reception.
3.2.10 clutter, n—undesirable returns, particularly from sidelobes, that increase background noise and obscure desired signals.
3.2.11 decibel (dB), n—logarithmic (base 10) ratio of power to a reference power, usually one-tenth bell; for power P1 and
reference power P2, the ratio is given by 10log (P1/P2).
3.2.12 directivity, n—concentration of transmitted power (dB) within a narrow beam by an antenna, measured as a ratio of power
in the main beam to power radiated in all directions.
3.2.13 Doppler frequency (f , Hz), n—shifted frequency measured at the receiver from the scattered acoustic signal.
D
3.2.14 effective antenna aperture (A , m ), n—product of antenna area with antenna efficiency.
e
3.2.15 gain (G), n—increase in power (dB) per unit area arising from the product of antenna directivity with efficiency.
n—non-dimensional effective aperture amplification factor arising from an antenna’s directivity.
3.2.16 inter pulse period (t , s), n—time between the start of successive transmitted pulses or pulse sequences.
max
3.2.16.1 Discussion—
The inter pulse period (IPP) is the inverse of the pulse repetition frequency (PRF) in Hertz (Hz).
3.2.17 monostatic, adj—sodar configuration that uses the same antenna for transmission and reception.
3.2.18 Neper, n—natural logarithm of the ratio of reflected to incident sound energy flux density at a given range.
3.2.19 pulse, n—finite burst of transmitted energy.
3.2.20 pulse length (τ, s), n—duration of a single pulse.
3.2.21 pulse sequence, n—train of pulses, often at different frequencies.
D7145 − 22
3.2.22 range (r, m), n—distance from the antenna surface to the scattering surface.
3.2.23 range aliasing, n—sampling ambiguity that arises when returns are received from a transmission that was made prior to
the latest transmitted pulse sequence, usually from a scattering surface located beyond the maximum unambiguous range.
3.2.24 range gate, n—conical section of the atmosphere containing the scattering volume from which acoustic returns can be
resolved.
3.2.25 range resolution (D , m), n—length of a segment of the scattering volume along the axis of beam propagation.
r
3.2.25.1 Discussion—
Range resolution equals half the product of speed of sound and pulse length (Δr = cτ ⁄2).
3.2.26 received power (P , W), n—electrical power received at an antenna during listening mode; the product of received acoustic
r
power with receiver conversion efficiency from acoustic to electrical power.
3.2.27 scattering volume (m ), n—volume of a conical section in the atmosphere centered on the radial along which the acoustic
beam propagates.
3.2.27.1 Discussion—
This is commonly calculated from the 3 dB beamwidth.
3.2.28 sidelobes, n—acoustic energy transmitted in a direction other than the main beam (or lobe).
3.2.28.1 Discussion—
Sidelobes vary inversely with antenna size and transmitted frequency.
3.2.29 signal-to-noise-ratio, n—ratio of the calculated received signal power to the calculated noise power, frequently abbreviated
as SNR.
3.2.30 sound detection and ranging (sodar), adj—remote sensing technique that generates acoustic pulses that propagate through
the atmosphere, and subsequently samples the scattered atmospheric returns.
n—instrument that performs these functions.
3.2.31 temperature structure parameter (C , K), n—structure constant for measurement of fast-response temperature differences
T
over small spatial separations that accounts for the effects of molecular diffusion and turbulent energy dissipation into heat.
3.2.32 transmit frequency (f, Hz), n—selected frequency or frequencies at which an acoustic transmitter’s output is achieved.
3.2.33 transmitted power (P , W), n—electrical power in watts measured at the antenna input; acoustic power radiated by an
t
antenna is the product of transmitted electrical power with the conversion efficiency from electrical to acoustic power.
3.3 Symbols:
–1
â = viscous and molecular sound absorption coefficient, Nepers per wavelength, m ,
A = effective antenna aperture, m ,
e
–1
c = speed of sound, ms ,
2 –2/3
C = temperature structure parameter, K m ,
T
ε = receiver electromechanical efficiency,
R
ε = transmitter electromechanical efficiency,
T
f = central acoustic frequency transmitted by the sodar, Hz,
f = Doppler frequency, Hz,
D
G = antenna gain,
P = received electrical power, W,
r
P = transmitted electrical power, W,
t
r = range from transmitter to a range gate, m,
r = maximum unambiguous range, m,
max
t = time between transmission of an acoustic pulse and reception of returning echoes, s,
D7145 − 22
T = temperature in Kelvins, K,
K
t = IPP, the maximum listening time between transmitted pulses or pulse sequences, s,
max
–1
V = target velocity, ms ,
t
Δr = range resolution, m,
φ = combined viscous and molecular attenuation factor,
m
φ = excess attenuation factor,
x
λ = acoustic wavelength, m,
–1
σ = acoustic scattering crossection per unit volume, m , and
τ = pulse length, s.
4. Summary of Guide
4.1 The principles of atmospheric wind and turbulence profiling using the sound direction and ranging technique are described.
4.2 Considerations for sodar equipment, site selection, and equipment installation procedures are presented.
4.3 Data acquisition and quality assurance procedures are described.
5. Significance and Use
5.1 Sodars have found wide applications for the remote measurement of wind and turbulence profiles in the atmosphere,
particularly in the gap between meteorological towers and the lower range gates of wind profiling radars. The sodar’s far field
acoustic power is also used for refractive index calculations and to estimate atmospheric stability, heat flux, and mixed layer depth
(1-5). Sodars are useful for these purposes because of strong interaction between sound waves and the atmosphere’s thermal and
velocity micro-structure that produce acoustic returns with substantial signal-to-noise ratios (SNR). The returned echoes are
Doppler-shifted in frequency. This frequency shift, proportional to the radial velocity of the scattering surface, provides the basis
for wind measurement. Advantages offered by sodar wind sounding technology include reasonably low procurement, operating,
and maintenance costs, no emissions of eye-damaging light beams or electromagnetic radiation requiring frequency clearances, and
adjustable frequencies and pulse lengths that can be used to optimize data quality at desired ranges and range resolutions. When
properly sited and used with adequate sampling methods, sodars can provide continuous wind and turbulence profile information
at height ranges from a few tens of meters to over a kilometrekilometer for typical averaging periods of 1 to 60 minutes.
6. Monostatic Sound Direction and Ranging
6.1 Sodar Design Types. Most commercially available sodars operate using a monostatic phased array antenna design composed
of a planar array of acoustic transmitters that form the emitted beam and steer it towards the desired direction. Other designs, to
include including those based on non-phased antennas for each beam and those based on bi-static configurations, are also available.
An advantage offered by bi-static sodars is that they also utilize use signals scattered from small scale velocity fluctuations that
are not available in monostatic configurations. Except for beam forming, steering, and the simplified monostatic sodar equation,
the information provided below is generally applicable to those designs as well.
6.2 Description of Operation. A phased array monostatic sodar emits acoustic pulses (adiabatic compression waves) at a transmit
frequency or frequencies. Pulses from each antenna are formed into a conical beam or wavefront with its vertex at the antenna.
Individual transducer pulse timing or phase shifting methods, indicated by Φ in Fig. 1, are used to shape the beam and steer it in
the desired direction. As it travels along a radial direction through the atmosphere at speed of sound (c), this acoustic wave
experiences attenuation by spreading, absorption, and scattering as described below. Temperature inhomogeneities and sharp
gradients encountered by the propagating beam deform and scatter the beam. Wind velocity components along the axis of
propagation also Doppler- shift the acoustic frequency of backscattered signals. A schematic drawing of acoustic wavefront
generation and backscatter from a reflecting surface is presented in Fig. 1. After its transmission of an acoustic pulse train, the sodar
switches to listening mode for backscattered acoustic signals. Returning signals are characterized by their intensity (amplitude),
spectral width, Doppler-shifted frequency, and lapsedelapsed time (t) from initial pulse transmission. Returns from lower heights
are received sooner than returns from greater heights. The relationship between lapsedelapsed time (t), speed of sound (c), and
radial range (r) to the scattering surface is given by:
r 5 ct/2 (1)
The boldface numbers in parentheses refer to the list of references at the end of this standard.
D7145 − 22
FIG. 1 Acoustic Wavefront Generation and Backscatter
D7145 − 22
where the factor of 2 accounts for travel along outward propagating and return paths. Wind profiling sodars that transmit a
minimum of three radial beams resolve horizontal and vertical wind components. Assuming homogeneity in the wind field above
the sodar, trigonometry is used to resolve distance along each radial, which is then converted to height above the sodar antenna.
The user is then presented with a vertical profile of wind, turbulence, and signal strength information. Height ranging, range
resolution, and signal quality are functions of sodar performance and its operating environment, as described below.
6.3 The Sodar Equation. The power received (P ) by a sodar’s acoustic antenna is a product of sodar performance and atmospheric
r
attenuation factors. Sodar performance factors include effective transmitted power (P ) at its transmitted frequency(ies), effective
t
antenna aperture (A ), transmitter and receiver efficiency factors (ε and ε ), and pulse length (τ). Atmospheric scattering factors
e T R
include the acoustic scattering crossection (σ) and attenuation factors φ and φ . Attenuation factor φ represents “classical”
m x m
viscous losses plus the combination of molecular rotational and vibrational absorption. The second factor (φ ) represents excess
x
attenuation due to complex interactions of the acoustic beam with larger scale atmospheric features. The sodar performance and
atmospheric factors are combined in a simplified monostatic sodar equation for received power:
P 5 sodar performance atmospheric factors 5 P A ε ε cτ/2 σφ φ (2)
$ % $ % $~ ! ~ ! ~ !% $ %
r t e T R m x
6.4 Sodar Performance. Sodar performance characteristics include the sodar transmitted acoustic power, and the efficiency with
which power is transmitted and received. P A is the power-aperture product. A = AG ⁄r is the solid angle subtended by an
t e e
antenna of aperture (A, m ) multiplied by the effective aperture factor (G, the antenna’s gain), as viewed at range (r) from the
scattering volume. Range resolution (Δr = cτ/2) is the length (m), along the radial axis of signal propagation, of the instantaneous
scattering volume and defines the volume from which a backscattered signal is resolved. Note that range resolution determines
range gate thickness. Scattering surfaces that produce useful acoustic returns often occupy only a fraction of the scattering volume
in the real atmosphere (see Fig. 1 and 6.6). The magnitude of the returned signals is directly proportional to the percentage of the
scattering volume occupied by scattering surfaces and the intensity of the turbulence (C ) producing the return.
T
6.5 Pulse Length and Inter Pulse Period (IPP). Pulse length and IPP (t ) define height and velocity limits for valid sodar signals.
max
Pulse length and system settling time (time of recovery from the state of excitation during pulse transmission) determine the
minimum height (first range gate) from which backscattered signals can be received. IPP determines the maximum range from
which unambiguous backscattered returns are received. If all measurable returns are not received prior to the initiation of the next
pulse, it is possible that returns from the earlier pulse will be received in the same time period as returns from the new pulse. This
causes an ambiguous signal known as range aliasing. Because t represents the maximum time between pulses, the maximum
max
unambiguous range is defined by:
r 5 ct /2 (3)
max max
Any returns from targets beyond r will appear as spurious signals in a range gate intended for returns from the subsequent
max
pulse. Like r , Doppler shifted velocity measurements can be unambiguously determined only within certain limits. The
max
frequency limits over which the Doppler shift can be unambiguously determined depends on t , which should be as high as
max
needed to unambiguously sample the maximum anticipated velocity. Thus, a sodar’s maximum and minimum range, range
resolution, and maximum velocity range are defined by τ and t settings and the transmitted central frequency. Some sodars are
max
designed to operate using pulse coding with multiple central frequencies. This feature helps distinguish backscattered signal from
clutter and enhances the probability of useful returns.
6.6 Attenuation by Absorption. Absorption reduces the radiated power of a propagating acoustic wave through viscous losses, and
by the excitation of rotational and vibrational modes in atmospheric gases (6). The excitation of atmospheric gases is strongly
dampened by the presence of atmospheric water vapor. Thus, sodar performance is enhanced in moist rather than dry environments.
–2âr
Combined absorption effects are represented by the viscous and molecular attenuation factor φ = e . This factor contains the
m
product of â, the molecular and viscous absorption coefficient, with range. Note that distances from the transmitter to the range
gate and from the range gate to the receiver are assumed to be the same. This is true for a monostatic sodar, but range distances
can vary for bistatic configurations.
6.7 Excess Attenuation. An additional factor known as excess attenuation φ , usually manifested as excessive beam spreading and
x
loss of returned acoustic power, is also present in the atmosphere. Excess attenuation is highly variable in magnitude and duration
due to the complex interactions between transient shear and turbulence effects with a propagating acoustic wavefront and its path
geometry (7,8). Excess attenuation increases with the wind speed, turbulence level, and acoustic frequency, but decreases with
increasing beamwidth.
6.8 Scatter. Scatter disperses propagating acoustic signal power, but also produces the sodar’s returned (backscattered) signal.
D7145 − 22
Scattering happens as acoustic wavefronts propagating through the atmosphere encounter perturbations in the acoustic refractive
index caused by turbulent patches of air containing temperature gradients. The magnitude of this turbulence is represented by the
temperature structure parameter C . Refractive index inhomogeneities most effectively scatter acoustic energy of twice their
T
wavelength. Energy propagating along one direction is scattered over many directions when it encounters a scattering surface, but
the magnitude of the off-axis power loss during a scattering event is usually much smaller than the incident power. Therefore, most
of the acoustic power continues to propagate along its original path. This Born “single scatter” approximation (6) also applies to
backscattered signals. Most back-scattered signals are expected to reach the receiver without being completely dispersed by
multiple scattering. Acoustic scattering cross-section per unit volume (σ) defines the fraction of incident power at frequency (f)
backscattered per unit distance. For a monostatic sodar, σ is represented by (9):
0.333 2 2
σ5 0.0039 2πf/c C /T (4)
~ !
T K
where T is the absolute temperature in Kelvins. Monostatic sodars rely on returns from the atmosphere’s thermal gradients,
K
while returns to bistatic sodars are enhanced by additional scatter from velocity fluctuations. Thermal gradients and turbulence is
often weak during the transition periods through sunrise and sunset, which degrades the performance of monostatic sodars during
these times.
6.9 Acoustic Wavelength and Frequency. Acoustic beams of wavelength λ and frequency (f) propagating through the atmosphere
can be characterized in terms of amplitude and phase. Amplitude is in proportion to the energy content or strength (intensity) of
an acoustic pulse, and phase refers to the position of a point along the wave relative to a chosen reference. Phase is expressed in
circular units, with a complete wave corresponding to 360° or 2π radians. Wavelength is the distance between two consecutive
points of the same phase along the wave. Frequency is the number of wavelengths that pass a measurement point per unit time,
which is usually measured in cycles per second or Hertz (Hz). The relationship between frequency, wavelength, and speed of sound
–1
(c, nominally 340 ms ) is:
fλ5 c (5)
6.10 The Doppler Effect. The Doppler effect is created by the action of reflecting surface (target) motion on a propagating acoustic
beam. Target velocity (V ) is considered positive if it is moving away fro
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