## 1. Introduction

Sodars are ground-based instruments using sound to obtain wind profiles in the lowest few hundred meters of the atmosphere. They transmit a short pulse in at least three upward directions. Spectral analysis of time-gated returns from turbulent scattering gives radial velocity components, and the beam geometry allows solving for vector wind components at each range gate (Bradley 2007).

One of the challenges with these instruments is the presence of competing background acoustic noise, which includes unwanted reflections from solid objects near the sodar (ground clutter). Reflections from solid objects can be reduced by the use of acoustic shielding or baffles. While transmission through, and reflections within, these baffles are both very low, diffraction by the baffle rim remains a problem. Triangular modulations on top of the baffles, known as thnadners, are often used in an attempt to reduce diffraction (Werkhoven and Bradley 1997).

The major difficulty in the design of baffles and thnadners is in measuring and modeling the diffraction of sound over their top, because full-scale sodars are generally too large for anechoic chamber evaluation (Bradley et al. 2005). Furthermore, because of the small distance between the source and the baffle aperture in terms of wavelength, the traditional Fresnel or Fraunhofer diffraction theories cannot be used. Instead, it is necessary to use an approach such as the Kirchhoff integral theorem (Williams 1999), and some assumptions have to be made regarding the boundary conditions. It is also possible that a fraction of the central transmitted beam lobe will intersect the baffle, thereby changing the predicted shape of the beam and the volume-weighted Doppler shift. Since these instruments use the same array for both transmitting and receiving, the receiver sensitivity may also be compromised. The main effect is to potentially change the effective zenith angle of the off-vertical beams (Bradley and von Hünerbein 2013). For instance, with a tilt angle of 15°, each 1° error in beam pointing angle gives a 5% error in estimation of wind speed. Monostatic sodars are therefore *highly sensitive* to beam pointing. However, in the work described below we concentrate on the amount of energy transmitted or received laterally at low elevations, rather than on the accompanying changes in Doppler shift, which will be the subject of a later investigation.

To circumvent the difficulty of measuring beam properties on a sodar, a small-scale sodar operating at a transmitted frequency *f*_{T} = 40 kHz has been developed and is described below. The beam pattern of this device has been experimentally measured with baffles and thnadners mounted on it. This experiment was aimed at validating a numerical model computing the beam pattern of the sodar coupled with different baffle and thnadner designs. A good correlation has been found between the experimental and theoretical results, giving confidence in the validity of the model. The model is then used to optimize the baffle and thnadners design. Note that the numerical model, applied here to sodars, could be used with little adaptation to many problems facing sound diffraction where the Fresnel and Fraunhofer diffraction are not valid, such as noise barriers (Wirt 1979).

## 2. The small-scale sodar

The small-scale sodar is operating at 40 kHz. In comparison with the Metek PCS-2000/24 LP sodar (Fig. 1) operating at 1.9 kHz, there is a linear size scaling factor of 21:1. It is convenient throughout the following to use dimensionless lengths, which are the physical lengths divided by the wavelength λ. Also, for monostatic sodars the speakers are used as microphones for reception and so the terms *speaker* and *microphone* will be used interchangeably. The beam pattern created by the phased array is chiefly defined by the number of microphones *M* (24 for the full-scale sodar), their polar response *G*(Ω), and their dimensionless separation *d* (=0.75 here). The fraction of power transmitted into a solid angle range of Ω to Ω + *d*Ω is *G*(Ω)*d*Ω. The scaled sodar therefore required 24 ultrasonic transducers of diameter equal to or smaller than 6.4 mm and ideally with a beam pattern similar to the one of the Metek transducers. For the evaluation purposes in the current work, an array of microphones (not speaker/microphones) was fabricated. The WM-61A microphone manufactured by Panasonic was selected, having a diameter of 6 mm and designed for the range from 20 Hz to 20 kHz. This microphone is, however, able to record at 40 kHz (Matos et al. 2013) and has been used here at this frequency. This configuration satisfies all scaling conditions, except for the polar response of the transducers. The WM-61A microphones are more omnidirectional than the Metek sensors, so in the simulations below the problems arising from the baffles are more severe than in the Metek case, and the results presented can be considered “worst case.” While there is a small influence on the intensity of the sidelobes present in the beam pattern, their angular position is different by less than 0.3°, so evaluations of the impact of the geometry are still possible. The 24 microphones have been connected in four channels, each with six microphones, allowing applying a phase shift of π/2 between each channel and thus tilting the beam off vertical (exactly as with the full-scale Metek sodar).

The baffle and thnadners have been created with a 3D printer, allowing a very close similarity with the full-scale sodar shown in Fig. 1. The baffle geometry is characterized by two dimensions, the scaled height *H* (=6.76) and the scaled aperture edge length *D* (=9.5). The thnadners are characterized by the scaled triangle height *h* (=2.15) and the number of triangles *N*_{t} around the baffle rim (=40).

Strong reflections occurred within the scaled baffle and thnadners, requiring the use of absorbing foam, as in the full-scale sodar. This greatly reduced these reflections, but the most efficient solution was to 3D print a half baffle, so that the diffraction over one edge could be studied without contamination from reflections off the opposing baffle panel sides.

To measure the beam pattern created by the phased array, the ultrasonic sodar was mounted on a rotary table, having the microphones at the center of rotation. A transmitter (T40-16B) operating at 40 kHz was located facing the rotary table at a dimensionless distance *b*. The Fresnel number, *F* = *D*^{2}/*b* (Born and Wolf 1999), is used to describe the limit between the near field (*F* ≫ 0.5) and the far field (*F* ≪ 0.5). The rotary table was rotated from zenith angle θ = −90° to 90° with a step of 1°, and a measurement was performed at each angle simultaneously on each of the four microphone channels. To keep the similitude with the real sodars, having a pulse duration of 50 ms at 1900 Hz or 95 cycles, the pulse length of the transmitted pulse was 2.5 ms (100 cycles at 40 kHz). A Hamming window was added to give a smooth increase and decrease in power.

*b*between the array and the transmitter. The time for a pulse of duration τ to complete travel over this distance should be less than the time for the pulse to travel from transmitter to receiving array via a wall, ceiling, or floor reflection. Here the limitation is η, which is the dimensionless height of the array and transmitter above the floor. The requirement is

*b*< 174. However, the size of the laboratory room limited

*F*to 0.5, giving

*b*= 2

*D*

^{2}+

*H*= 187. However, 87% of the pulse has been received before any contamination by floor reflections, so amplitude processing is not a problem.

Measurements were performed along an axis *x*, aligned with microphone rows spaced by *d*, and along an axis *x*′ aligned with microphone diagonals spaced by

The measurement geometry with rotation of the microphone array around the *y* axis.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measurement geometry with rotation of the microphone array around the *y* axis.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measurement geometry with rotation of the microphone array around the *y* axis.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

*V*

_{i,n}of the signals from the four channels (

*i*= 1, 2, 3, 4) at Fourier frequencies

*f*

_{n}are combined to give

*t*is a beam-steering time delay and

*t*= 0 for a zenith beam, and 1/(4

*f*

_{T}) for a beam tilted off zenith in the

*x–z*plane. The normalized sound intensity (dB) for one measurement is then given by

## 3. Analytic solutions

**q**, the phase shift of the signal from speaker

*m*at position

**r**

_{m}relative to the phase of a signal from the origin is 2π

**r**

_{m}·

**q**/

*q*. For

**q**in the

*x*–

*z*plane, this is 2π

*x*

_{m }sinθ, where θ is the zenith angle. There are microphone rows at

*x*

_{m}= ±

*d*/2, ±3

*d*/2, and ±5

*d*/2, with six, four, and two microphones, respectively (Fig. 2). This leads to a relative response in that plane of

*x*–

*z*plane, allowing for a progressive phase increment of π/2 per row in the case of the tilted beam. Zeros for this function are at β = ±π/4, ±π/3, ±π/2,.. The peak sensitivity for the tilted beam is at θ = sin

^{−1}(1/[4

*d*]) = 19.5° for

*d*= 0.75. Similarly, in the

*x*′–

*z*plane, there are microphone rows at

*x*′ = 0, ±

*d*/√2, ±2

*d*/√2, and ±3

*d*/√2, with four, three, four and three microphones, respectively. This leads to a relative response in that plane of

*x*′–

*z*plane. Zeros for this function are at cos

*β*= −1,(1 ± 7

^{1/2})/6. The peak sensitivity for the tilted beam is at

*θ*= sin

^{−1}(1/[2√2

*d*]) = 28° for

*d*= 0.75.

## 4. Numerical model

The Kirchhoff integral theorem (KIT) is widely used in acoustics (Williams 1999) and has been applied to sodar baffles by Werkhoven and Bradley (1997). Figure 3 depicts the computational domain. A closed surface *S* is chosen so that no sources are enclosed, which means having the sodar and baffles outside of *S*. The KIT solves for the acoustic velocity potential at a point **q**, in terms of the potential and its derivative at a point **r** on *S*. Each speaker is treated as a point source having a polar response *G*(θ) and an electronically applied phase. The potential is then just the sum over all point sources at point **r** (Pierce 1981). The WM-61A microphone is omnidirectional according to the specifications but, since it is operated out of its specified frequency range, its polar response has been measured (Fig. 4). A first-order Legendre polynomial fit to *G*, also shown in Fig. 4, is found to be adequate for estimation of *dG*/*d*θ, which is needed to find the normal derivative of the velocity potential on *S*.

Surface and vector definition for the Kirchhoff integral theorem model.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

Surface and vector definition for the Kirchhoff integral theorem model.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

Surface and vector definition for the Kirchhoff integral theorem model.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured polar response of an individual microphone used in the scaled model (solid line) and the simple Legendre polynomial fit to this (dotted line).

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured polar response of an individual microphone used in the scaled model (solid line) and the simple Legendre polynomial fit to this (dotted line).

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured polar response of an individual microphone used in the scaled model (solid line) and the simple Legendre polynomial fit to this (dotted line).

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

If the baffle is considered completely absorbing, then the potential need only be calculated over that part of *S*, which goes across the top of the baffle and up the side of the thnadners. The approximation is not exact, since even a perfectly absorbing baffle will be slightly illuminated. This is one reason why it is important to obtain experimental validation.

## 5. Experimental and theoretical results comparison

In constructing the current model, it was found that Werkhoven and Bradley (1997) had a mistake in the computation of the surface normal for the thnadners, so direct comparison with their results is not useful. It is possible that this error has led to a less-than-optimum thnadner design for current sodars, and it is recommended that any new designs be based on the current work. Figure 5 shows measured and theoretical polar patterns for the zenith beam of the microphone array without any baffle or thnadners. The left-hand plot is in the *x*–*z* plane, which sums over six rows of sensors with *d*. The right-hand plot is in the *x*′–*z* plane, which sums over seven rows of sensors with the row spacing *d*/√2. This closer row spacing gives greater angular spacing of the diffraction lobes. It is evident in Fig. 5 that measurement signal-to-noise limitations lead to larger decibel differences between measurements and computed beam patterns for less than −20 dB. Figure 6 shows the pattern for the beam tilted in the *x*–*z* plane using a progressive phase increment between rows of π/2 as described in section 3. These figures show that measurements and theory are in good agreement down to around the −20-dB level, but for lower signal strength the signal-to-noise ratio is most likely too low and is compromising the agreement.

The measured (solid line) and computed (dashed line) polar pattern for the zenith beam of the bare phased array in (left) the *x–z* plane and (right) the *x*′*–z* plane. See Fig. 2 for the definition of the *x*, *x*′, and *z* axes.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and computed (dashed line) polar pattern for the zenith beam of the bare phased array in (left) the *x–z* plane and (right) the *x*′*–z* plane. See Fig. 2 for the definition of the *x*, *x*′, and *z* axes.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and computed (dashed line) polar pattern for the zenith beam of the bare phased array in (left) the *x–z* plane and (right) the *x*′*–z* plane. See Fig. 2 for the definition of the *x*, *x*′, and *z* axes.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and calculated (dashed line) beam pattern of the bare phased array for a beam tilted in the *x*–*z* plane. See Fig. 2 for the definition of the *x*, *x*′, and *z* axes.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and calculated (dashed line) beam pattern of the bare phased array for a beam tilted in the *x*–*z* plane. See Fig. 2 for the definition of the *x*, *x*′, and *z* axes.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and calculated (dashed line) beam pattern of the bare phased array for a beam tilted in the *x*–*z* plane. See Fig. 2 for the definition of the *x*, *x*′, and *z* axes.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

When a half baffle is added (to minimize internal reflections), the beam patterns in Figs. 7 and 8 are obtained. These figures show that high angle sidelobes can be significantly reduced along both *x* and *x*′ axes. The dominant sidelobe that was present at high angles in the tilted beam case has disappeared, confirming the validity of assuming perfectly absorbing baffles in the numerical model. The difference between measured sidelobe and calculated sidelobe intensity are summarized in Table 1. Except for measurements in the *x–z* plane with thnadners present, the KIT predictions are capable of replicating measurements from the scale model to within a few decibels, which is probably determined by the measurement errors involved. The discrepancies for the case of thnadners and transmission in the *x–z* plane are likely due to reflections from the finite-thickness edges of the thnadners, which are not covered by foam (see Fig. 1). For reception in the *x*′*–z* plane, this is not a problem, since the thnadners are more normal to the sound propagation. These discrepancies are therefore likely due to the measurement configuration, rather than to KIT model errors. This suggests that baffle and thnadner optimization can be studied using the KIT, as in the following section.

The measured (solid line) and calculated (dashed line) zenith beam pattern with a half baffle, measured in (left) the *x–z* plane and (right) the *x*′–*z* plane.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and calculated (dashed line) zenith beam pattern with a half baffle, measured in (left) the *x–z* plane and (right) the *x*′–*z* plane.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and calculated (dashed line) zenith beam pattern with a half baffle, measured in (left) the *x–z* plane and (right) the *x*′–*z* plane.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and calculated (dashed line) beam pattern of the phased array for the beam tilted in the *x*–*z* plane. A half baffle is used.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and calculated (dashed line) beam pattern of the phased array for the beam tilted in the *x*–*z* plane. A half baffle is used.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The measured (solid line) and calculated (dashed line) beam pattern of the phased array for the beam tilted in the *x*–*z* plane. A half baffle is used.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

Measured main sidelobe intensity minus modeled main sidelobe intensity.

## 6. Optimization of baffle and thnadners via modeling

The nature of the baffle design problem is illustrated in Fig. 9 for the case corresponding to the Metek baffle. The baffle intercepts a little of the energy from the first sidelobe (at around 22°) as well as the sidelobes that are at lower elevations. But this interception is accompanied by diffraction. So, while it might be thought useful to increase *H* to intercept all of the first sidelobe, this can lead to higher intensities at low elevations than were present without baffles. Similarly, thnadners centered on the original baffle height will extend both below and above that height. The extension below will potentially allow less interception, whereas the extension above will potentially produce more diffraction. The balance of these various factors requires investigating a range of baffle and thnadner geometries.

The beam pattern in the *x*′–*z* plane without baffles (solid line) and with a *D* = 9.5, *H* = 6.76 baffle (dashed line).

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The beam pattern in the *x*′–*z* plane without baffles (solid line) and with a *D* = 9.5, *H* = 6.76 baffle (dashed line).

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The beam pattern in the *x*′–*z* plane without baffles (solid line) and with a *D* = 9.5, *H* = 6.76 baffle (dashed line).

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

### a. Baffle optimization without thnadners

The *H* was varied from 5.5 to 9.5 and the aperture *D* from 8 to 12, and the far-field intensity patterns is plotted in Fig. 10. Here *F* = 0.1 so *q* = 900, where **q** = *q*(sinθ_{q} cosϕ_{q}, sinθ_{q} sinϕ_{q}, cosθ_{q}). The intensities are plotted versus normalized radial distance sinθ_{q}, and azimuth but, to improve clarity at low elevations (high θ_{q}), the radial distance is plotted on a sin^{−1} scale, so it goes from 0° to 90°. These plots have a lot of complexity, so it is useful to concentrate on low-elevation transmissions or reception, say, in the 70°–90° zenith angle range. For the vertical beam, the problem low-elevation region is along and just to either side of the *x*′ axis. For the beam tilted in the *x*–*z* plane, the problem region is around an azimuth of 40° and at right angles to that, at 130°. However, given the complexity of these patterns, it is necessary to search for the intensity maximum at all azimuth angles within the low-elevation annulus (in this case chosen to be the 70°–90° zenith angle), as shown in Fig. 11. In both the zenith and tilted cases, there is a preferred ratio of *H*/*D* that corresponds to a zenith angle from the center of the array to the rim of 33°–35°. This matches the beam pattern notch at 34° in the *x*′–*z* plane for the zenith beam. The design aim is therefore to set the angle from the center of the array to the baffle rim to match a beam pattern null, since this minimizes the energy available for diffraction over the rim edge. While this design aim is obvious for a far-field situation, it is not clear for the near-field interaction that is present here, without the modeling that has been done. There is no advantage for a particular *H* or *D* value, so a sensible design is one in which the notch condition is met as well as intercepting low-elevation sidelobes. The actual Metek design achieves this. Note that the tilted beam is much more problematic, and the gains to be made in optimizing *D*/*H* are not so large. This explains why phased array sodars remain relatively noisy in spite of their baffles.

Intensity distribution for (a) the vertical beam and (b) the tilted beam, with the *D* = 9.5, *H* = 6.76 baffle.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

Intensity distribution for (a) the vertical beam and (b) the tilted beam, with the *D* = 9.5, *H* = 6.76 baffle.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

Intensity distribution for (a) the vertical beam and (b) the tilted beam, with the *D* = 9.5, *H* = 6.76 baffle.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The maximum intensity in the zenith angle range 70°–90°, normalized to the central peak, for (top) a vertical beam and (bottom) a beam tilted in the *x*–*z* plane, as a function of baffle width and baffle height.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The maximum intensity in the zenith angle range 70°–90°, normalized to the central peak, for (top) a vertical beam and (bottom) a beam tilted in the *x*–*z* plane, as a function of baffle width and baffle height.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The maximum intensity in the zenith angle range 70°–90°, normalized to the central peak, for (top) a vertical beam and (bottom) a beam tilted in the *x*–*z* plane, as a function of baffle width and baffle height.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

### b. Triangular thnadners optimization

For all the thnadner simulations, the baffle with *D* = 9.5 is used with the thnadner centered vertically at a height of 6.76 (the thnadner extends vertically from 6.76 − *h*/2 to 6.76 + *h*/2). This is so that the extra effective baffle height is not being added by the thnadners. Figure 12a with 40 thnadners of height 2.15 shows a similar pattern to that of Fig. 10a, but with a much more fine structure. This fine structure arises because the thnadners are acting as a multislit grating and the periodicities in the intensity pattern are different from those due to the interference pattern of the microphone array (see further discussion below). In the *x*′*–z* plane, the intensity is higher than without thnadners, but it is generally lower away from this area. For a beam tilted in the *x–z* plane, Fig. 12b shows similar behavior to that in Fig. 10b, but again with much more fine structure. The −40-dB peak at around 40° azimuth has been largely removed by the thnadners.

Intensity distribution for (a) the vertical beam and (b) the tilted beam, with the *D* = 9.5, *H* = 6.76 baffle, and with 40 thnadners of height 2.15.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

Intensity distribution for (a) the vertical beam and (b) the tilted beam, with the *D* = 9.5, *H* = 6.76 baffle, and with 40 thnadners of height 2.15.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

Intensity distribution for (a) the vertical beam and (b) the tilted beam, with the *D* = 9.5, *H* = 6.76 baffle, and with 40 thnadners of height 2.15.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

In Fig. 13a optimization of thnadner width (or number of thnadners *N*_{t} around the rim of length 4*D*) and thnadner height *h* is explored. There is little variation with thnadner height, and in fact no thnadners appears better than having thnadners. There is a periodicity with thnadner numbers. This is because the dominant low-elevation sidelobes are from the *x*′ and *y*′ directions, in which the sound propagation is normal to the baffle side. Then the thnadners act as a multislit grating, and troughs in intensity will occur when there is an integer number of triangles along a side. This occurs for *N*_{t} = 24, 28, 32, 36, 40, 44, and 48 in this figure. For the tilted beam case (Fig. 13b), there is even less dependence on baffle height, and the intensity is generally higher, as expected.

The maximum intensity in the zenith angle range 70°–90°, normalized to the central peak, for (a) a vertical beam and for (b) a beam tilted in the *x*–*z* plane, as a function of thnadners numbers and height.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The maximum intensity in the zenith angle range 70°–90°, normalized to the central peak, for (a) a vertical beam and for (b) a beam tilted in the *x*–*z* plane, as a function of thnadners numbers and height.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The maximum intensity in the zenith angle range 70°–90°, normalized to the central peak, for (a) a vertical beam and for (b) a beam tilted in the *x*–*z* plane, as a function of thnadners numbers and height.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

Given the amount of fine structure in the intensity patterns with thnadners, a more meaningful measure of performance might be the average intensity within the 70°–90° annulus. This is shown in Fig. 14. Now there is a shallow minimum of −42 dB at *h* = 2.3 and *N*_{t} = 37. This compares quite closely with the Metek design of *h* = 2.15 and *N*_{t} = 40.

The mean intensity in the zenith angle range 70°–90°, normalized to the central peak, for a beam tilted in the *x*–*z* plane, as a function of thnadners numbers and height.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The mean intensity in the zenith angle range 70°–90°, normalized to the central peak, for a beam tilted in the *x*–*z* plane, as a function of thnadners numbers and height.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

The mean intensity in the zenith angle range 70°–90°, normalized to the central peak, for a beam tilted in the *x*–*z* plane, as a function of thnadners numbers and height.

Citation: Journal of Atmospheric and Oceanic Technology 32, 3; 10.1175/JTECH-D-13-00253.1

## 7. Conclusions

Investigation of the beam pattern for a full-scale sodar is difficult because the instrument does not readily fit inside conventional anechoic chambers, and measurements outdoors compete with external noise sources. Furthermore, the accuracy of models of sodar beams is uncertain because of assumptions that may be made and the near-field presence of the baffles and thnadners. The approach taken here to overcome these challenges is to design a model based on a common approach (the KIT) and then validate that with a 21:1 scale ultrasound working model of the sodar array. Measurements could be done in a small semianechoic chamber, using a precision tripod-mounted turntable.

The measurements on the scale physical model showed agreement with the numerical model to within about 2 dB, except for the case when the sound could reflect from the relatively thick edges of the thnadners. A new scale model with much thinner thnadner material could have been constructed, although possibly with some transmittance through the thnadner material, but the good agreement with all the other laboratory measurements provided a good degree of confidence in the numerical model, which was the primary aim of these measurements.

The KIT model was used to investigate optimization, first of baffle height and width, and then of thnadner dimensions. It was found that the baffle height-to-width ratio *H*/*D* was the significant parameter in defining a well-designed baffle. This ratio needs to be set so the baffle rim is at a notch in the interference pattern from the microphone/speaker array, so that diffraction by the baffle edge is minimized. In fact this has long been used as a guideline for design (Bradley 2007) but verification in the way presented here has been absent.

A number of sodar manufacturers routinely use thnadners in their sodar design. The beam patterns predicted by the KIT model for thnadners are found to be very complex. This is shown to be due to the periodicity from the multislit grating that the thnadners approximate. This periodicity is different from that due to the array itself, so the array intensity pattern is broken up by the presence of thnadners. The pattern is not sensitive to thnadner height, although all thnadner additions cause some increase in the maximum low-elevation intensities. In the case of the tilted beam, there is some improvement obtained by using optimized thnadner design, with dimensionless thnadner height being chosen around 2. Since the effect of diffraction on low-elevation sound is much stronger for the tilted beam case, this means that the addition of thnadners potentially reduces the peak low-level intensity by around 2 dB, or the annulus-averaged power by around 1 dB.

There is also some potential improvement by having an integral number of thnadners on a baffle side. In fact this is also the easiest design arrangement, and is generally used by manufacturers.

The results presented here are based on modeling a specific Metek sodar, but the above-mentioned discussion is much more general and can be applied to even parabolic dish antenna sodars. The KIT model could also be readily applied to any enclosed speaker/microphone situation.

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